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Full text of "Scientific thought"

International Library of Psychology 
Philosophy and Scientific Method 



Scientific Thought 



Internationa] Library of Psychology 
Philosophy and Scientific Method 

General Editor: C. K. Ogden, m.a. 

{Magdalene College, Cambridge) 

VOl r w/ S Al Rl ADY ARRANGED 

PHILOSOPHICAL STUDIES .... by G. E. MOORE, Litt.D. 

THE MISl SE OF MIND by Karin Stephen 

i Note by Henri Bergson 
CONF1 ICT AND DREAM .... by W. II. R. Rivers, F.R.S. 
PSYCHOLOGY AND POLITICS . . . by W. H. R. RIVERS, F.R.S. 
PSYCHOLOGY AND ETHNOLOGY . . by W. II. R. Rivers, F.R.S. 
THE ANALYSIS OF MATTER . . by Bertrand RUSSELL, F.R.S. 

IK ACTATUS LOGICO-PHILOSOPHICUS . . .by L. Wittgenstein 

Introduction by Bertrand Russell 
MATHEMATICS FOR PHILOSOPHERS . . by G. H. Hardy, F.R.S. 
PSYCHOLOGICAL TYPES . . . . by C. G. Jung, M.D., LL.D. 
THE PSYCHOLOGY OF MYTHS . . by G. Elliot Smith, F.R.S. 
THE PHILOSOPHY' OF THE UNCONSCIOUS by E. von Hartmann 

Introduction by Professor G. Elliot Smith 
CHARACTER AND THE UNCONSCIOUS . by J. H. van der Hoop 

INDIVIDUAL PSYCHOLOGY by Alfred Adler 

SCIENTIFIC METHOD by A. V. Ritchie 

THE MEANING OF MEANING . . by C. K. Ogden and I. A. Richards 
THE THEORY OF MEDICAL DIAGNOSIS 

by F. G. Crookshank, M.D., F.R.C.P. 
THE ELEMENTS OF PSYCHOTHERAPY 6y William Brown, M.D., D.Sc. 
THE MEASUREMENT OF EMOTION . . by W. Whately Smith 
Introduction by William Brown 

EMOTION AND INSANITY by S. Thalbitzer 

Introduction by Professor H. H off ding 

THE LAWS OF FEELING by F. Paulhan 

THE PSYCHOLOGY OF MUSIC by Edward J. Dent 

COLOUR-HARMONY by James Wood 

THE DEVELOPMENT OF CHINESE THOUGHT by Liang Che-Chiao 

THE HISTORY OF MATERIALISM d; F. A. Lange 

THE PRIMITIVE MIND by P. Radin, Ph.D. 

THE PSYCHOLOGY OF PRIMITIVE PEOPLES 

by B. Malinowski, Ph.D., D.Sc. 
THE STATISTICAL METHOD IN ECONOMICS AND POLITICS 

by P. Sargant Florence 
THE PSYCHOLOGY OF REASONING . . by Eugenio Rignano 

THE PRINCIPLES OF CRITICISM . . . by I. A. Richards 

THE PHILOSOPHY OF 'AS IF' . . . . by H. Vaihinger 



Scientific Thought 



By 

C. D. pOAD 

M.A., Litt.D. 

Sometime Fellow of Trinity College, Cambridge 

Professor of Philosophy in the University of Bristol 

Author of " Perception, Physics and Reality " 




y 









uT 



NEW YORK 

HARCOURT, BRACE & COMPANY, INC. 

LONDON : KEGAN PAUL, TRENCH, TRUBNER & CO., LTD. 

I923 







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PRINTED IN GREAT BRITAIN BV 



THE EDINBURGH PRESS, Q A 



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IN PIAM MEMORIAM 

IACOBI MUDIE 

DUCIS ILLIUS DORSETIAE 

APUD CONDISCIPULOS IN UNIVERSITATE ANDREANA 

QUI A.D. MDCCCXCV TAODUNI SCOTORUM NATUS 

A.D. MDCCCCXVI IN PUGNA AD THESSALONICAM OCCUBUIT 



. . . Manibus date lilia plenis : 
Purpureos spargam flores, animamque nepotis 
His saltern accumulem donis, et fungar inani 
Munere. — Virgil, Aeneid, VI 



At ego tibi sermone isto . . . varias fabulas conseram, 
auresque tuas benevolas lepido susurro permulceam, 
modo si papyram JEgyptiam argutia Nilotici calamo 
inscriptam non spreveris inspicere . . . — Apuleius, 
The Golden Ass 



PREFACE 

The present book is ultimately based on a course of 
lectures delivered to the third year students of science 
at the University of Bristol in the session 1920-21. It 
is an admirable custom, which, like many other benefits, 
that University owes to my distinguished predecessor, 
Professor Lloyd Morgan, that all students of science 
are expected to attend such a course before completing 
their career. It seemed worth while to elaborate the 
lectures, to remove their more obvious blemishes, and 
to present them to a wider public. 

In the First Part I have started with the highly 
sophisticated concepts of the classical mathematical 
physics, have tried to express them clearly, and 
have then discussed the modifications which recent 
advances in scientific knowledge have necessitated in 
these concepts. I > have carried this account to the 
end of the Second Theory of Relativity. I have not 
penetrated into the still more revolutionary speculations 
of Weyl, because I do not feel that I yet understand 
them well enough myself to venture to explain them 
to others. A philosopher who regards ignorance of a 
scientific theory as a sufficient reason for not writing 
about it cannot be accused of complete lack of origin- 
ality, as a study of recent philosophical literature will 
amply prove. 

I begin with an Introduction, which states what I 
think Philosophy to be about, and how I think it to 



4 SCIENTIFIC THOUGHT 

be connected with the special sciences. I then try to 
explain in simple terms the nature and objects of 
Whitehead's Principle of Extensive Abstraction. This 
seems to me to be the " Prolegomena to every future 
Philosophy of Nature." It is quite possible to explain 
its motives and general character without entering 
deeply into those logico-mathematical complications 
which are inevitable when it is applied in detail. Next, 
greatly daring, I have discussed the difficult problems 
which centre upon the general notion of Time and 
Change. Here I have tried to make some answer to 
the very disturbing arguments by which Dr M'Taggart 
has claimed to disprove the reality of these apparently 
fundamental features of the Universe. After this the 
rest of the First Part should be fairly plain sailing to 
anyone of decent general education, though I do not 
pretend that it can be understood without effort by 
persons who are unfamiliar with the subjects which it 
treats. 

In some of these later chapters the reader will find 
a number of mathematical formulas. He must not be 
frightened of them, for I can assure him that they 
involve no algebraical processes more advanced than 
the simple equations which he learnt to solve at his 
mother's knee. I myself can make no claims to be 
a mathematician : the most I can say is that I can 
generally follow a mathematical argument if I take 
enough time over it. I like to believe that, in expound- 
ing the Theory of Relativity, a clumsy mathematician 
has some of the qualities of his defects. His own former 
difficulties will at least suggest to him the places where 
others are likely to have trouble. 

In Part II we start afresh at a quite different level. 
Here I try to point out the sensible and perceptible 
facts which underlie the highly abstract concepts of 



PREFACE 5 

science, and the cruder, but still highly sophisticated, 
concepts of common-sense. Beside the intrinsic interest 
and importance of this topic it has a direct bearing on 
Part I. A great deal of the difficulty which many 
people have in accepting the newer views of Space, 
Time and Motion, arises from the fact that they regard 
the traditional concepts as perfectly plain and obvious, 
whilst they feel that the later modifications are paradoxes, 
forced on them vi et armis by a few inconvenient and 
relatively trivial facts. The moment we recognise how 
extraordinarily remote the classical concepts are from 
the crude facts of sense-experience, from which they 
must have been gradually elaborated, this source of 
incredulity vanishes. The hold of the tradition is 
loosened ; and we are prepared to consider alternative, 
and possibly more satisfactory, conceptual syntheses of 
sensible facts. 

I have tried in Part II to focus before my mind what 
seems to me to be the most important work that has been 
done on these subjects since 1914, when the publication 
of my Perception, Physics and Reality unhappily pre- 
cipitated a European war. If I have learnt nothing 
else since then, I have at least come to see the extreme 
complexity of the problem of the external world and of 
our supposed knowledge of it. My obligations to 
Moore, Russell, Whitehead and Stout are continual, 
and will be perfectly obvious to anyone acquainted with 
the literature of the subject. I here make my grateful 
acknowledgments to them, once for all. To a less 
extent I have been influenced by Alexander and Dawes 
Hicks. I have merely mentioned Dawes Hicks's theory 
of appearance and then left it. This is not because I 
think it either impossible or unimportant, but because I 
am here deliberately trying to work out a different view, 
which I also think to be possible and important. 



6 SCIENTIFIC THOUGHT 

I cannot claim to have put forward any new and 
startling theory of the universe. If I have any kind of 
philosophical merit, it is neither the constructive fertility 
of an Alexander, nor the penetrating critical acumen of 
a Moore ; still less is it that extraordinary combination of 
both with technical mathematical skill which character- 
ises Whitehead and Russell. I can at most claim the 
humbler (yet useful) power of stating difficult things 
clearly and not too superficially. 

" Excudcnt alii spirantia mollius aera, 
Credo equidem ; vivos ducent de marmore vultus ; " 

but I hope that I may at least have smolten some of the 
metal and hewn some of the stone which others will 
use in their constructions. 

I must end by thanking Dr R. S. Paton of Perth 
for kindly reading the proofs and helping me with the 
index; Mr E. Harrison, of Trinity College, Cambridge, 
for his gallant efforts to involve my dedication in "the 
decent obscurity of a learned language " ; and the 
printers for the care which they have taken in printing 
what must have been a rather troublesome piece of 
work. 

C. D. BROAD. 

London, Sept. 1922. 



CONTENTS 

PAGE 

Introduction : The Subject-matter of Philosophy, 

and its relations to the Special Sciences . n 

PART I 

THE TRADITIONAL CONCEPTS OF MATHEMATICAL 

PHYSICS, AND THEIR GRADUAL MODIFICATION 

WITHIN THE REGION OF PHYSICAL SCIENCE 

CHAPTER 

I. The Traditional Conception of Space, and the 

Principle of Extensive Abstraction . . 26 

II. The General Problem of Time and Change . 53 

III. The Traditional Kinematics, and its gradual 

Modification in the Region of Physics. (1) 

The Absolute and the Relational Theories . 85 

IV. Modification of the Traditional Kinematics in 

the Region of Physics — Continued. (2) The 
Special Theory of Relativity . . .114 

V. The Traditional Kinetics, and its gradual Modifi- 
cation in the Region of Physics. (1) Newton's 
Laws of Motion and Gravitation . . . 155 

VI. Modification of the Traditional Kinetics — Con- 
tinued. (2) The General Theory of Relativity. 
Summary of Part I .... 179 



8 SCIENTIFIC THOUGHT 

PART II 

THE SENSATIONAL AND PERCEPTUAL BASIS 
OF OUR SCIENTIFIC CONCEPTS 

CHAPTER PAGE 

VII. Matter and its Appearances ; Preliminary 

Definitions 227 

VIII. The Theory of Sensa, and the Critical Scientific 

Theory 239 

IX. The Positions and Shapes of Sensa and of 

Physical Objects 284 

X. The Dates and Durations of Sensa and of 

Physical Objects and Events . . . 344 

XL Sensible and Physical Motion .... 405 

XII. Sensible and Physical Space-Time . . . 452 

XIII. The Physiological Conditions of Sensations, and 

the Ontological Status of Sensa . . . 488 

Index 549 



PART I 

THE TRADITIONAL CONCEPTS OF MATHEMATICAL 

PHYSICS, AND THEIR GRADUAL MODIFICATION 

WITHIN THE REGION OF PHYSICAL SCIENCE 



Contents of Part I 

Introduction. — The Subject-matter of Philosophy, and its 
Relations to the Special Sciences 

CHAPTER 

I. The Traditional Conception of Space, and the Principle 
of Extensive Abstraction 

II. The General Problem of Time and Change 

III. The Traditional Kinematics and its gradual Modification 

within the Region of Physics, (i) The Absolute and 
the Relational Theories 

IV. Modification of the Traditional Kinematics in the Region 

of Physics — Continued. (2) The Special Theory of 
Relativity 

V. The Traditional Kinetics and its gradual Modification in 
the Region of Physics. (1) Newton's Laws of Motion 
and of Gravitation 

VI. Modification of the Traditional Kinetics — Continued. 
(2) The General Theory of Relativity. Summary of 
Part I 



B 



SCIENTIFIC THOUGHT 



INTRODUCTION 

"Noli, Lector, expectare hoc loco, contra Philosophiam 
aut Philosophos orationem invectivam. . . . Distinguo inter 
Philosophos et non Philosophos, et inter Philosophiam 
veram, vitae humanae Magistram sapientissimam, humanae 
naturae decus singulare, et illam, quae jam diu pro Philo- 
sophia habita est, fucatam et garrulam meretriculam." 

(Hobbes, Leviathan, Part IV. cap. xlvi.) 

The Subject-matter of Philosophy, and its Relations 
to the special Sciences 

I shall devote this introductory chapter to stating what 

I think Philosophy is about, and why the other sciences 

are important to it and it is important to the other 

sciences. A very large number of scientists will begin 

such a book as this with the strong conviction that 

Philosophy is mainly moonshine, and with the gravest 

doubts as to whether it has anything of the slightest 

importance to tell them. I do not think that this view 

of Philosophy is true, or I should not waste my time 

and cheat my students by trying to teach it. But I do 

think that such a view is highly plausible, and that 

the proceedings of many philosophers have given the 

general public some excuse for its unfavourable opinion 

of Philosophy. I shall therefore begin by stating the 

case against Philosophy as strongly as I can, and shall 

then try to show that, in spite of all objections, it really 

is a definite science with a distinct subject-matter. I 

shall try to show that it really does advance and that 

it is related to the special sciences in such a way that 

ii 



12 SCIENTIFIC THOUGHT 

the co-operation of philosophers and scientists is of the 
utmost benefit to the studies of both. 

I think that an intelligent scientist would put his 
case against Philosophy somewhat as follows. He 
would say : " Philosophers discuss such subjects as 
the existence of God, the immortality of the soul, and 
the freedom of the will. They spin out of their minds 
fanciful theories, which can neither be supported nor 
refuted by experiment. No two philosophers agree, and 
no progress is made. Philosophers are still discussing 
with great heat the same questions that they discussed 
in Greece thousands of years ago. What a poor show 
does this make when compared with mathematics or any 
of the natural sciences ! Here there is continual steady 
progress ; the discoveries of one age are accepted by 
the next, and become the basis for further advances 
in knowledge. There is controversy indeed, but it is 
fruitful controversy which advances the science and 
ends in definite agreement ; it is not the aimless 
wandering in a circle to which Philosophy is condemned. 
Does this not very strongly suggest that Philosophy 
is either a mere playing with words, or that, if it has 
a genuine subject-matter, this is beyond the reach of 
human intelligence?" 

Our scientist might still further strengthen his case 
by reflecting on the past history of Philosophy and on 
the method by which it is commonly taught to students. 
He will remind us that most of the present sciences 
started by being mixed up with Philosophy, that so 
long as they kept this connexion they remained misty 
and vague, and that as soon as their fundamental 
principles began to be discovered they cut their dis- 
reputable associate, wedded the experimental method, 
and settled down to the steady production of a strapping 
family of established truths. Mechanics is a case in 
point. So long as it was mixed up with Philosophy it 
made no progress ; when the true laws of motion were 
discovered by the experiments and reasoning of Galileo 



INTRODUCTION 13 

it ceased to be part of Philosophy and began to develop 
into a separate science. Does this not suggest that the 
subject-matter of Philosophy is just that ever-diminishing 
fragment of the universe in which the scientist has not 
yet discovered laws, and where we have therefore to put 
up with guesses? Are not such guesses the best that 
Philosophy has to offer ; and will they not be swept 
aside as soon as some man of genius, like Galileo or 
Dalton or Faraday, sets the subject on the sure path of 
science? 

Should our scientist talk to students of Philosophy 
and ask what happens at their lectures, his objections 
will most likely be strengthened. The answer may take 
the classical form : " He tells us what everyone knows 
in language that no one can understand." But, even 
if the answer be not so unfavourable as this, it is not 
unlikely to take the form: "We hear about the views 
of Plato and Kant and Berkeley on such subjects as the 
reality of the external world and the immortality of the 
soul." Now the scientist will at once contrast this with 
the method of teaching in his own subject, and will be 
inclined to say, if e.g. he be a chemist: "We learn 
what are the laws of chemical combination and the 
structure of the Benzene nucleus, we do not worry our 
heads as to what exactly Dalton thought or Kekule said. 
If philosophers really know anything about the reality 
of the external world why do they not say straight- 
forwardly that it is real or unreal, and prove it? The 
fact that they apparently prefer to discuss the divergent 
views of a collection of eminent ' back-numbers ' on 
the question strongly suggests that they know that there 
is no means of answering it, and that nothing better 
than groundless personal opinions can be offered." 

I have put these objections as strongly as I can, and 
I now propose to see just how much there is in them. 
First, as to the alleged unprogressive character of 
Philosophy. This is, I think, an illusion ; but it is 
a very natural one. Let us take the question of the 



14 SCIENTIFIC THOUGHT 

reality of the external world as an example. Common- 
sense says that chairs and tables exist independently 
of whether anyone happens to perceive them or not. 
We study Berkeley and find him claiming to prove 
that such things can only exist so long as they are 
perceived by someone. Later on we read some modern 
realist, like Alexander, and we are told that Berkeley 
was wrong, and that chairs and tables can and do exist 
unperceived. We seem merely to have got back to 
where we started from, and to have wasted our time. 
But this is not really so, for two reasons, (i) What we 
believe at the end of the process and what we believed at 
the beginning are by no means the same, although we 
express the two beliefs by the same form of words. 
The original belief of common-sense was vague, crude 
and unanalysed. Berkeley's arguments have forced 
us to recognise a number of distinctions and to define 
much more clearly what we mean by the statement that 
chairs and tables exist unperceived. What we find is 
that the original crude belief of common-sense consisted 
of a number of different beliefs, mixed up with each 
other. Some of these may be true and others false. 
Berkeley's arguments really do refute or throw grave 
doubt on some of them, but they leave others standing. 
Now it may be that those which are left are enough to 
constitute a belief in the independent reality of external 
objects. If so this final belief in the reality of the 
external world is much clearer and subtler than the 
verbally similar belief with which we began. It has been 
purified of irrelevant factors, and is no longer a vague 
mass of different beliefs mixed up with each other. 

(ii) Not only will our final belief differ in content 
from our original one, it will also differ in certainty. 
Our original belief was merely instinctive, and was at 
the mercy of any sceptical critic who chose to cast 
doubts on it. Berkeley has played this part. Our final 
belief is that part or that modification of our original 
one that has managed to survive his criticisms. This 



INTRODUCTION 15 

does not of course prove that it is true ; there may be 
other objections to it. But, at any rate, a belief that 
has stood the criticisms of an acute and subtle thinker, 
like Berkeley, is much more likely to be true than a 
merely instinctive belief which has never been criticised 
by ourselves or anyone else. Thus the process which 
at first sight seemed to be merely circular has not really 
been so. And it has certainly not been useless ; for it 
has enabled us to replace a vague belief by a clear and 
analysed one, and a merely instinctive belief by one 
that has passed through the fire of criticism. 

The above example will suggest to us a part at least 
of what Philosophy is really about. Common-sense 
constantly makes use of a number of concepts, in terms 
of which it interprets its experience. It talks of things 
of various kinds ; it says that they have places and dates, 
that they change, and that changes in one cause changes 
in others, and so on. Thus it makes constant use of 
such concepts or categories as thinghood, space, time, 
change, cause, etc. Science takes over these concepts 
from common-sense with but slight modification, and 
uses them in its work. Now we can and do use 
concepts without having any very clear idea of their 
meaning or their mutual relations. I do not of course 
suggest that to the ordinary man the words substance, 
cause, change, etc., are mere meaningless noises, like 
Jabberwock or Snark. It is clear that we mean some- 
thing, and something different in each case, by such 
words. If we did not we could not use them con- 
sistently, and it is obvious that on the whole we do 
consistently apply and withhold such names. But it 
is possible to apply concepts more or less successfully 
when one has only a very confused idea as to their 
meaning. No man confuses place with date, and for 
practical purposes any two men agree as a rule in the 
places that they assign to a given object. Nevertheless, 
if you ask them what exactly they mean by place and 
date, they will be puzzled to tell you. 



16 SCIENTIFIC THOUGHT 

Now the most fundamental task of Philosophy is to 
take the concepts that we daily use in common life and 
science, to analyse them, and thus to determine their 
precise meanings and their mutual relations. Evidently 
this is an important duty. In the first place, clear and 
accurate knowledge of anything is an advance on a 
mere hazy general familiarity with it. Moreover, in 
the absence of clear knowledge of the meanings and 
relations of the concepts that we use, we are certain 
sooner or later to apply them wrongly or to meet with 
exceptional cases where we are puzzled as to how to 
apply them at all. For instance, we all agree pretty 
well as to the place of a certain pin which we are 
looking at. But suppose we go on to ask : " Where is 
the image of that pin in a certain mirror ; and is it in 
this place (whatever it may be) in precisely the sense 
in which the pin itself is in its place?" We shall find 
the question a very puzzling one, and there will be no 
hope of answering it until we have carefully analysed 
what we mean by being in a place. 

Again, this task of clearing up the meanings and 
determining the relations of fundamental concepts is 
not performed to any extent by any other science. 
Chemistry uses the notion of substance, geometry that 
of space, and mechanics that of motion. But they 
assume that you already know what is meant by 
substance and space and motion. So you do in a vague 
way ; and it is not their business to enter, more 
than is necessary for their own special purposes, into 
the meaning and relations of these concepts as such. 
Of course the special sciences do in some measure clear 
up the meanings of the concepts that they use. A 
chemist, with his distinction between elements and 
compounds and his laws of combination, has a clearer 
idea of substance than an ordinary layman. But the 
special sciences only discuss the meanings of their 
concepts so far as this is needful for their own special 
purposes. Such discussion is incidental to them, whilst 



INTRODUCTION 17 

it is of the essence of Philosophy, which deals with such 
questions for their own sake. Whenever a scientist 
begins to discuss the concepts of his science in this 
thorough and disinterested way we begin to say that he 
is studying, not so much Chemistry or Physics, as the 
Philosophy of Chemistry or Physics. It will therefore 
perhaps be agreed that, in the above sense of Philosophy, 
there is both room and need for such a study, and that 
there is no special reason to fear that it will be beyond 
the compass of human faculties. 

At this point a criticism may be made which had 
better be met at once. It may be said : " By your own 
admission the task of Philosophy is purely verbal ; it 
consists entirely of discussions about the meanings of 
words." This criticism is of course absolutely wide of 
the mark. When we say that Philosophy tries to clear 
up the meanings of concepts we do not mean that it is 
simply concerned to substitute some long phrase for 
some familiar word. Any analysis, when once it has 
been made, is naturally expressed in words ; but so too 
is any other discovery. When Cantor gave his defini- 
tion of Continuity, the final result of his work was 
expressed by saying that you can substitute for the 
word "continuous" such and such a verbal phrase. 
But the essential part of the work was to find out exactly 
what properties are present in objects when we predicate 
continuity of them, and what properties are absent 
when we refuse to predicate continuity. This was 
evidently not a question of words but of things and 
their properties. 

Philosophy has another and closely connected task. 
We not only make continual use of vague and 
unanalysed concepts. We have also a number of un- 
criticised beliefs, which we constantly assume in 
ordinary life and in the sciences. We constantly 
assume, e.g. that every event has a cause, that nature 
obeys uniform laws, that we live in a world of objects 
whose existence and behaviour are independent of our 



18 SCIENTIFIC THOUGHT 

knowledge of them, and so on. Now science takes over 
these beliefs without criticism from common-sense, and 
simply works with them. We know by experience, 
however, that beliefs which are very strongly held may 
be mere prejudices. Negroes find it very hard to 
believe that water can become solid, because they have 
always lived in a warm climate. Is it not possible that 
we believe that nature as a whole will always act 
uniformly simply because the part of nature in which 
the human race has lived has happened to act so up 
to the present? All such beliefs then, however deeply 
rooted, call for criticism. The first duty of Philosophy 
is to state them clearly ; and this can only be done 
when we have analysed and defined the concepts that 
they involve. Until you know exactly what you mean 
by change and cause you cannot know what is meant 
by the statement that every change has a cause. And 
not much weight can be attached to a person's most 
passionate beliefs if he does not know what precisely he 
is passionately believing. The next duty of Philosophy 
is to test such beliefs ; and this can only be done by 
resolutely and honestly exposing them to every objection 
that one can think of oneself or find in the writings of 
others. We ought only to go on believing a proposition 
if, at the end of this process, we still find it impossible 
to doubt it. Even then of course it may not be true, 
but we have at least done our best. 

These two branches of Philosophy — the analysis 
and definition of our fundamental concepts, and the 
clear statement and resolute criticism of our fundamental 
beliefs — I call Critical Philosophy. It is obviously a 
necessary and a possible task, and it is not performed 
by any other science. The other sciences use the 
concepts and assume the beliefs ; Critical Philosophy 
tries to analyse the former and to criticise the latter. 
Thus, so long as science and Critical Philosophy 
keep to their own spheres, there is no possibility of 
conflict between them, since their subject-matter is 



INTRODUCTION 19 

quite different. Philosophy claims to analyse the 
general concepts of substance and cause, e.g.; it does 
not claim to tell us about particular substances, like 
gold, or about particular laws of causation, as that 
aqua regia dissolves gold. Chemistry, on the other 
hand, tells us a great deal about the various kinds of 
substances in the world, and how changes in one cause 
changes in another. But it does not profess to analyse 
the general concepts of substance or causation, or to 
consider what right we have to assume that every event 
has a cause. 

It should now be clear why the method of Philosophy 
is so different from that of the natural sciences. Ex- 
periments are not made, because they would be utterly 
useless. If you want to find out how one substance 
behaves in presence of another you naturally put the 
two together, vary the conditions, and note the results. 
But no experiment will clear up your ideas as to the 
meaning of cause in general or of substance in general. 
Again, all conclusions from experiments rest on some 
of those very assumptions which it is the business of 
Philosophy to state clearly and to criticise. The experi- 
menter assumes that nature obeys uniform laws, and 
that similar results will follow always and everywhere 
from sufficiently similar conditions. This is one of the 
assumptions that Philosophy wants to consider critically. 
The method of Philosophy thus resembles that of pure 
mathematics, at least in the respect that neither has any 
use for experiment. 

There is, however, a very important difference. In 
pure mathematics we start either from axioms which no 
one questions, or from premises which are quite explicitly 
assumed merely as hypotheses ; and our main interest 
is to deduce remote consequences. Now most of the 
tacit assumptions of ordinary life and of natural science 
claim to be true and not merely to be hypotheses, and 
at the same time they are found to be neither clear 
nor self-evident when critically reflected upon. Most 



20 SCIENTIFIC THOUGHT 

mathematical axioms are very simple and clear, whilst 
most other propositions which men strongly believe are 
highly complex and confused. Philosophy is mainly 
concerned, not with remote conclusions, but with the 
analysis and appraisement of the original premises. 
For this purpose analytical power and a certain kind of 
insight are necessary, and the mathematical method is 
not of much use. 

Now there is another kind of Philosophy ; and, as 
this is more exciting, it is what laymen generally under- 
stand by the name. This is what I call Speculative 
Philosophy. It has a different object, is pursued by a 
different method, and leads to results of a different 
degree of certainty from Critical Philosophy. Its 
object is to take over the results of the various sciences, 
to add to them the results of the religious and ethical 
experiences of mankind, and then to reflect upon the 
whole. The hope is that, by this means, we may be 
able to reach some general conclusions as to the nature 
of the Universe, and as to our position and prospects 
in it. 

There are several points to be noted about Speculative 
Philosophy, (i) If it is to be of the slightest use it 
must presuppose Critical Philosophy. It is useless to 
take over masses of uncriticised detail from the sciences 
and from the ethical and religious experiences of men. 
We do not know what they mean, or what degree of 
certainty they possess till they have been clarified and 
appraised by Critical Philosophy. It is thus quite 
possible that the time for Speculative Philosophy has 
not yet come ; for Critical Philosophy may not have 
advanced far enough to supply it with a firm basis. In 
the past people have tended to rush on to Speculative 
* Philosophy, because of its greater practical interest. 
The result has been the production of elaborate systems 
which may quite fairly be described as moonshine. The 
discredit which the general public quite rightly attaches 
to these hasty attempts at Speculative Philosophy is 



INTRODUCTION 21 

reflected back on Critical Philosophy, and Philosophy 
as a whole thus falls into undeserved disrepute. 

(ii) At the best Speculative Philosophy can only 
consist of more or less happy guesses, made on a very 
slender basis. There is no hope of its reaching the 
certainty which some parts of Critical Philosophy might 
quite well attain. Now speculative philosophers as a 
class have been the most dogmatic of men. They have 
been more certain of everything than they had a right 
to be of anything. 

(iii) A man's final view of the Universe as a whole, 
and of the position and prospects of himself and his 
fellows, is peculiarly liable to be biased by his hopes 
and fears, his likes and dislikes, and his judgments of 
value. One's Speculative Philosophy tends to be in- 
fluenced to an altogether undue extent by the state of 
one's liver and the amount of one's bank-balance. No 
doubt livers and bank-balances have their place in the 
Universe, and no view of it which fails to give them 
their due weight is ultimately satisfactory. But their 
due weight is considerably less than their influence on 
Speculative Philosophy might lead one to suspect. But, 
if we bear this in mind and try our hardest to be 
"ethically neutral," we are rather liable to go to the 
other extreme and entertain a theory of the Universe 
which renders the existence of our judgments of value 
unintelligible. 

A large part of Critical Philosophy is almost exempt 
from this source of error. Our analysis of truth and 
falsehood, or of the nature of judgment, is not very 
likely to be influenced by our hopes and fears. Yet 
even here there is a slight danger of intellectual dis- 
honesty. We sometimes do our Critical Philosophy, 
with half an eye on our Speculative Philosophy, and 
accept or reject beliefs, or analyse concepts in a certain 
way, because we feel that this will fit in better than any 
alternative with the view of Reality as a whole that we 
happen to like. 



22 SCIENTIFIC THOUGHT 

(iv) Nevertheless, if Speculative Philosophy re- 
members its limitations, it is of value to scientists, in 
its methods, if not in its results. The reason is this. 
In all the sciences except Psychology we deal with 
objects and their changes, and leave out of account 
as far as possible the mind which observes them. In 
Psychology, on the other hand, we deal with minds 
and their processes, and leave out of account as far as 
possible the objects that we get to know by means of. 
them. A man who confines himself to either of these 
subjects is likely therefore to get a very one-sided view 
of the world. The pure natural scientist is liable to 
forget that minds exist, and that if it were not for 
them he could neither know nor act on physical objects. 
The pure psychologist is inclined to forget that the 
main business of minds is to know and act upon 
objects ; that they are most intimately connected 
with certain portions of matter ; and that they have 
apparently arisen gradually in a world which at one 
time contained nothing but matter. Materialism is 
the characteristic speculative philosophy of the pure 
natural scientist, and subjective idealism that of the 
pure psychologist. To the scientist subjective idealism 
seems a fairy tale, and to the psychologist materialism 
seems sheer lunacy. Both are right in their criticisms, 
but neither sees the weakness of his own position. The 
truth is that both these doctrines commit the fallacy of 
over-simplification ; and we can hardly avoid falling 
into some form of this unless at some time we make a 
resolute attempt to think synoptically of all the facts. 
Our results may be trivial ; but the process will at least 
remind us of the extreme complexity of the world, and 
teach us to reject any cheap and easy philosophical 
theory, such as popular materialism or popular theology.* 

Before ending this chapter I will say a word about 
the three sciences which are commonly thought to be 

1 Theology, whether "natural" ox "revealed," is a form of Speculative 
Philosophy, in our sense of the, word.. So, too, is Atheism. 



INTRODUCTION 23 

specially philosophical. These are Logic, Ethics, and 
Psychology. Logic simply is the most fundamental 
part of Critical Philosophy. It deals with such concepts 
as truth, implication, probability, class, etc. In fact it may 
be defined as the science which deals with propositional 
forms, their parts, their qualities, and their relations. 
Its business is to analyse and classify forms, and to 
consider the formal relations that can subsist between 
them. Now all science consists of definite propositions, 
and each of these is of one of the forms which Logic 
studies ; but it is not the business of any other science 
explicitly to discuss propositional forms. Similarly all 
science is full of inferences, good and bad, and all 
inference depends on relations that are supposed to 
subsist between premises and conclusion. But it is 
for Logic, and for it alone, to decide what relations do 
in fact justify inference, and whether these relations do 
actually subsist in a given case. Thus Logic is that 
part of Critical Philosophy which deals with the most 
general and pervasive of all concepts, and with those 
fundamental beliefs which form the "connective tissue" 
of all knowledge. 

The greater part of Ethics again is simply a branch 
of Critical Philosophy. It is a fact that we not only 
believe that such and such events happen, but that 
we also pass judgments of approval or disapproval on 
certain of them. Such judgments use peculiar con- 
cepts, like good and bad, right and wrong, duty, etc. 
A very important part of Ethics is the attempt to 
analyse and define these peculiarly obscure notions 
which we all use so gaily in everyday life. Again, 
there are a great many judgments of value which many 
people assume as certain ; e.g. Pleasure is good, It 
is wrong to tell lies, A man has a right to do what 
he likes with his own, and so on. Another important 
part of Ethics is the attempt to state such judgments 
clearly, and then to see what evidence, if any, there 
is for them. Thus, Ethics is that part of Critical 



24 SCIENTIFIC THOUGHT 

Philosophy which analyses the concepts and criticises 
the presuppositions that we use in our judgments of 
approval and disapproval. 

Psychology, as it seems to me, is not a part of 
Philosophy at all, but is simply one of the special 
sciences. This is shown by the fact that, unlike Logic 
and Ethics, it argues inductively from experiment and 
observation, though the observation takes the peculiar 
form of introspection. It is, however, a very peculiar 
kind of special science. It is obvious that Chemistry and 
Physics are much more like each other than either of 
them is like Psychology. The reason is that the two 
former sciences treat two rather different but very 
pervasive sets of material properties, whilst the latter 
deals with minds, which apparently occupy a unique 
and strangely isolated position in the Universe. Or, 
again, we may say that Psychology deals with what 
is relatively private, whilst all the other natural sciences 
deal with what is relatively public. If, now it should 
be asked why Psychology has been supposed to be 
specially connected with Philosophy, I think that the 
following answers will be fairly satisfactory. 

(i) Psychology supplies Critical Philosophy with a 
number of concepts as raw material for analysis and 
criticism. Such are the concepts of mind, self, con- 
sciousness, instinct, sensation, perception, etc. Now these 
notions we all admit to be highly confused and obscure, 
whereas we are inclined to think — until we learn better — 
that there is no particular difficulty about such concepts 
as place, date, matter, cause, etc., which we use in the 
other sciences. Thus a great part of any standard 
book on Psychology does in fact consist of attempts 
to analyse and define certain concepts, and this is of 
course Critical Philosophy. 

(ii) When we try to clear up the meanings of 
physical concepts like place, date, matter, etc., we often 
find that a reference to the processes by which they 
come to be known is essential, and that they owe part 



INTRODUCTION 25 

of their obscurity to the abstractions which science and 
common-sense have made. Thus, in doing Critical 
Philosophy, we do constantly have to appeal to facts 
which belong to Psychology, even when we are not 
primarily dealing with psychological concepts.* 

(iii) In Speculative Philosophy we ought, no doubt, 
to take into account the results of all the sciences. But, 
owing to the unique subject-matter of Psychology, we 
shall go hopelessly wrong if we omit it, whilst we shall 
not go so hopelessly wrong if we omit one of the 
sciences of matter, such as Mineralogy or Botany. 

For these reasons we may admit that Psychology 
is of peculiar importance to Philosophy, though we 
must deny that it is a part of Philosophy, like Logic 
and Ethics. 

The present book deals wholly with Critical 
Philosophy, and only with a small part of that. It is 
concerned almost entirely with an attempt to clear up 
some of the concepts used in the natural sciences. It 
does not deal even with all these, e.g. very little is said 
about causation. The reason is that I did not want to 
deal with purely logical questions ; and it is hardly 
possible to discuss causation adequately without going 
into the question of induction, in which causation is 
commonly thought to play an important part. 

Additional works that may be consulted with profit : 

F. H. BRADLEY, Appearance and Reality, Introduction. 

H. Sidgwick, Philosophy : its Scope and Relations. 

B. A. W. Russell, Our Knowledge of the External World, 

Lectures I. and II. 
J. Grote, Exploratio Philosofihica, Part I. Caps. I. and II. 
Descartes, Rules for the Direction of the Mind. 
,, Discourse on Method. 

* It is also true that we cannot give a complete treatment of Logic 
(especially the subjects of Inference and Probability) without referring to 
minds and their special limitations. 



CHAPTER I 

"When I use a word," Humpty-Dumpty said in rather 
a scornful tone, "it means just what I choose it to mean 
— neither more nor less." 

"The question is," said Alice, "whether you can make 
words mean so many different things." 

"The question is," said Humpty-Dumpty, "which is to 
be Master — that's all." 

(Lewis Carroll, Through the Looking-Glass.) 

The Traditional Conception of Space, and the Principle 
of Extensive Abstraction 

It is not ultimately possible to treat Space, Time, and 

Matter, as used in physical science, in isolation from 

each other ; for we shall see that they are closely 

bound together in their very natures. This is, however, 

a comparatively recent discovery ; and the traditional 

view, with which most of us still work in daily life, is 

that Space and Time, at any rate, can be adequately 

analysed in isolation from each other and from matter. 

As this is the familiar view, it seems best to start from it 

and gradually to point out and remove its imperfections. 

In any case we must start somewhere ; and the fact that 

the three concepts in question have so long been treated 

as separable without serious practical error shows that, 

to a great extent, they are separable. The truth is that 

what is logically most primitive in nature is not what 

is now most familiar to us, and therefore it is better for 

didactic purposes to start with the logically derivative 

but practically familiar, and work back to the logically 

primitive but practically unfamiliar. For example, the 

immediate data of sense, like coloured patches, are 

logically prior to the notion of physical objects, which 

26 



TRADITIONAL CONCEPT OF SPACE 27 

persist, and combine many qualities ; yet the latter is 
much the more familiar notion to us. I shall start then 
from the traditional conception of Space. 

Unquestionably we think of Space in ordinary life 
and in science as a single great box or container in 
which all physical objects are kept and in which all 
physical processes go on. It is true that many books 
on Mechanics do lip-service to a different view of Space, 
which makes it consist of relations between bits of matter. 
But this conception is forgotten as soon as the author 
has worked off that particular chapter, and ever after- 
wards he and his readers use the "box" theory of 
Space. We shall deal with this alternative view at a 
much later stage. Again, we shall see later that the 
notion of a single box needs overhauling, but we shall 
not be able to appreciate why this is so until we have 
considered the connexion of Space with Time. 

For the present then, we shall take the common 
practical view of Space as a single box "with no sides 
to it," in which the things and events of the physical 
world move and have their being. The first point to 
notice is that, when people talk of Space and spaces, 
they may be using these correlative terms in two 
different senses, (i) When we talk of Berkeley Square 
as one space and Grosvenor Square as a different one, 
we simply mean that they are two different regions 
which do not overlap, but which are both parts of the 
single Space of nature. We do not mean that they 
are different kinds of Space. Neither Berkeley Square 
nor Grosvenor Square is a Space — for neither is a box 
containing the whole of nature ; but each of them is a 
space, in the sense of a part of such a box. 

(ii) On the other hand, when mathematicians talk of 
Euclidean and non-Euclidean Spaces, they are discussing 
different possible kinds of Space, and not different spaces 
like the two London Squares which are parts of the 
Space of nature, of whatever kind that may be. The 
word Space is thus used (a) as a proper name, in which 



28 SCIENTIFIC THOUGHT 

case it is equivalent to the phrase " tJic Space of nature, 
of whatever kind that may be" ; and (/;) as a general 
name, in which case it connotes the property of being 
a Space, and denotes all the various wholes of that kind, 
such as Euclidean Space, Lobatchewskian Space, and 
so on. Finally, every kind of Space has parts, which 
are spaces, but not of course Spaces. 

As a matter of history the concept of Space in 
general sprang from the investigation of the Space of 
nature. Euclid certainly meant his axioms to describe 
the Space in which we live and move. But, on further 
reflection, two very important facts emerged, (i) The 
validity of Euclid's deductions does not depend in any 
way on this assumption being true, (ii) We can con- 
ceive of extended wholes which are continuous and 
have several dimensions, like the Space of nature, but 
which yet differ from the Euclidean kind of Space in 
many of their properties. We decide then to call any 
whole that sufficiently resembles the Space of nature 
a Space, but we allow that there are many possible 
wholes which agree to this extent and yet differ in 
their remaining properties. Mathematicians at first 
only made timid modifications in Euclid's axioms, but 
as boldness grew with familiarity, they gradually con- 
sidered what, from the Euclidean point of view, were 
wilder and wilder kinds of Space. 

The important thing for us to notice is that the pro- 
positions of any system of pure geometry are merely 
hypothetical. They simply state that such and such 
propositions follow from the axioms, when the terms 
employed are defined by the definitions and postulates 
of the system. We ought not to say that the angles 
of a triangle are together equal to two right angles, 
but that, if a triangle be in the Space defined by 
Euclid's axioms, this will follow. This fact is hidden 
from the beginner in mathematics, because (a) the 
Space of nature is commonly assumed to be Euclidean, 
and (6) figures are commonly used in proving pro- 



TRADITIONAL CONCEPT OF SPACE 29 

positions. But the truth is that figures in geometry 
are used only as illustrations, like statistics in the late 
Mr Chamberlain's tariff-reform speeches. They play 
no logical part in the proof, as is shown by the fact 
that a proposition about circles can be proved just as 
conclusively with a rough circle drawn in chalk on a 
blackboard as with an accurate circle drawn with a 
pair of compasses. The real premises of the proof are 
the axioms of the system, and the definitions of the 
terms which we are arguing about. 

When these facts are once grasped it is easy to 
see the connexion between the Space of physics and 
the Spaces of pure geometry. We have arrived, by 
whatever means, at the concept of one physical Space 
— the single sideless box in which all the phenomena 
of nature are kept. This has various characteristic pro- 
perties, such as continuity, three dimensions, etc. 
From this the pure mathematician generalises. He 
takes a selection of these properties as the defining 
marks of Space in general ; and then, by varying the 
remaining properties, conceives various kinds of Space 
and works out their geometry. At that stage, and not 
till then, the question can be put : " Of what kind is the 
Space of nature?" "Which of the various possible 
Spaces accords best with the Space of physics?" 

This is the question: "In what kind of a box is 
nature contained?" It turns out not to be quite so 
simple as asking whether one's clothes are in a port- 
manteau, a trunk, or a Gladstone bag. In the first 
place, the actual entanglement of physical Space with 
Time and with Matter becomes highly relevant at this 
point. For instance, our geometry and our physics 
are constructed to deal with different but intimately 
connected factors in nature, which are not met with 
in isolation. It is therefore conceivable that several 
different systems of geometry will equally fit the spatial 
side of nature provided that suitable modifications be 
made in the forms of physical laws. Apart from this, 



30 SCIENTIFIC THOUGHT 

there is the purely mathematical question as to whether 
the difference between Euclidean and certain kinds of 
non-Euclidean geometry be not merely a difference in 
the conventions for measuring a single kind of Space. 
The first kind of complication is roughly comparable 
to the possibility of a box which changes its shape 
according to the way in which we pack our clothes in 
it. If some bluff, downright person (such as an Oxford 
tutor) then asks whether your box is a trunk or a port- 
manteau, and insists on "a plain answer to a plain 
question," there is likely to be misunderstanding. It 
is not so easy to illustrate the second kind of complica- 
tion mentioned above, but perhaps the following analogy 
will be of use. The difference of temperature between 
two places might be defined either by the difference in 
length of a certain column of mercury when held at the 
two places, or by the difference in pressure of a certain 
volume of gas when it is transferred from one place to 
the other. When temperature-difference is measured 
by the first convention, two pairs of points may have 
the same temperature- difference ; when it is measured 
by the second convention the same two pairs may have 
different temperature-differences. There is no question 
of right or wrong in the matter ; we just take two 
different measures of temperature-difference, one of 
which is more convenient for one purpose and the 
second for another purpose. Substitute "distance 
between two points" for " temperature - difference 
between two places," and you have a case where two 
different systems of geometry mean, not two Spaces, 
but two alternative ways of measuring a single Space. 

So much for the distinction between the one Space 
of the natural scientist and the many Spaces of the 
mathematician. Let us now ask ourselves : What is 
the irreducible minimum of properties that the ordinary 
scientist ascribes to the Space of nature? (i) He holds 
that it is in some sense continuous, and that it has 
three dimensions. We need not go into the accurate 



TRADITIONAL CONCEPT OF SPACE 31 

mathematical definitions of continuity and dimensions. 
Roughly we mean by the former that any two spaces 
that do not overlap are at once separated and joined by 
another space, and that all these spaces are parts of the 
one big Space of nature. By saying that Space has 
three dimensions we roughly mean that three inde- 
pendent bits of information are needed to fix the position 
of a point. 

(ii) Again, the scientist and the ordinary layman 
draw a sharp distinction between Space and the things 
in Space. They hold that Space, as such, never causes 
anything. Mere position has no effect on any property 
of matter. If we move a bit of matter about, it may of 
course change in shape or size. The mercury column 
of a thermometer will do this if we move it from outside 
the window to a place near the fire. But the traditional 
view is that the mere change in position is not enough 
to account for this. The length has changed because 
the mercury has altered its position with respect to 
certain matter in Space. The complete inactivity of 
Space is, I think, for the plain man the mark that dis- 
tinguishes it from matter in Space. Whenever it seems 
to break down we feel perplexed and uncomfortable. I 
can illustrate this in two ways, (a) On the older 
theories of physics there was supposed to be a peculiar 
kind of matter, called Ether, that filled all Space. On 
these theories the Ether was supposed to produce all 
kinds of effects on ordinary matter, and it became almost 
a family pet with certain physicists. As physics has 
advanced, less and less has been found for the Ether to 
do. In proportion as this has happened physicists have 
begun to ask: "Do we mean by the Ether anything 
more than empty Space?" On Lorentz's theory of 
electro-dynamics, it is difficult to see that the Ether is 
anything but the concept of absolute Space ; and that 
eminent scientist's attitude towards it recalls Mrs 
Micawber's statement that she "will never desert 
Mr Micawber." 



32 SCIENTIFIC THOUGHT 

(/>) Conversely, many mathematicians have con- 
ceived Spaces in which difference of position does make 
a difference to the shapes and sizes of bodies, and have 
successfully explained physical phenomena thereby. 
Prof. Clifford is one example, and Einstein, in his theory 
of gravitation, is another. But we do not as yet feel 
comfortable with the theories of this type, however well 
they may explain the facts, because they seem to involve 
the action of Space on matter, and this seems to upset 
all means of distinguishing between the two. The 
average intelligent physicist will accept from the 
mathematician any kind of Space that fits the observ- 
able facts, so long as it does not act on matter. But 
the wilder kind of Spaces that the pure mathematician 
can offer him he refuses to accept as Spaces at all, 
because it is part of what he means by Space that it 
shall be indifferent to, and thus distinguishable from, 
its content. It may be that we ought not to accept 
this objection as ultimate, because the sharp separation 
between the three concepts of Space, Time, and Matter 
has all the appearance of being artificial ; but in the 
present chapter we are confining, ourselves to the tradi- 
tional view. 

Space then, at present, is to be thought of as a single 
infinite, three-dimensional receptacle, in which all the 
events of nature have their being, but which is indifferent 
to them. If we reflect, we shall see that the evidence for 
the existence of such an object is by no means obvious. 
We can neither see nor touch empty spaces ; what we 
see and touch are bits of matter. Now of course most 
things in which scientists believe cannot be perceived 
by the senses ; no one can see or touch a hydrogen 
atom or a light-wave. Such objects are inferred by the 
scientist from the perceptible effects which they are 
supposed to produce. But Space is not even in this 
position. For, as we saw, the essence of Space on the 
traditional view, is that it does not produce any effects. 
Obviously then the existence of Space cannot be inferred 



TRADITIONAL CONCEPT OF SPACE 33 

from its supposed perceptible effects, since it is not 
supposed to have any. If then Space is neither per- 
ceived nor inferred, whence do we get the concept of it? 

In dealing with both Space and Time there are two 
distinct sets of concepts used, which we might call 
distributive and collective. The collective properties of 
Space and Time are those that belong to them as 
individual wholes. Thus the questions of how we come 
to believe that there is one Space, that it is Euclidean, 
that it can be distinguished from the matter in it, and 
so on, are questions concerning collective properties of 
space. On the other hand, there are certain concepts 
that apply, not so much to Space as an individual 
whole, as to every bit of space. These are distributive 
properties, such as divisibility, order of points on lines, 
and so on. In this and the next chapter we shall 
confine ourselves to distributive properties of Space and 
Time respectively ; it is only at a much later stage that 
the question of one Space or Time, and its distinction 
from things or events in it can be faced. 

Now all the distributive properties that we ascribe 
to Space have their root in certain facts that we can 
directly observe in our fields of view, and to a less 
extent, in our fields of touch. Whenever I open my 
eyes I am aware of a variously coloured field. This is 
extended, or spread out, and this extendedness is the 
root of my notion of surfaces and volumes. Again, 
within the total field certain specially coloured patches 
will stand out against a background ; e.g. there might 
be two green patches, which are in fact the visual 
appearances of a pair of trees. Such patches have 
shapes and sizes ; and here we have the sensible basis 
of the concepts of definite figures. Then, between any 
two such outstanding patches there will always be an 
extended background with a different colour, which at 
once joins and separates the patches. If, e.g. we are 
in fact looking at two trees, standing up against a 
cloudless sky, our field of view will consist of two 



34 SCIENTIFIC THOUGHT 

characteristically shaped green patches separated and 
surrounded by a blue extension. In the visual field 
there is nothing to correspond to the notion of empty 
space, for the whole field is occupied by some colour or 
other. Still, the visual experience that we have been 
describing does suffice to give us, in a rough form, the 
distributive concepts of extension, shape, size, between- 
ness, and continuity. And it suggests, though it does 
not by itself actually give us, another concept. A field 
of view does not come sharply to an end at its edges. 
It fades gradually away, and the details become less 
and less definite the further they are from the centre. 
Thus there is nothing in the experience to suggest that 
the field of view is an independent complete whole ; it 
rather presents itself as a fragment of something bigger. 
This suggestion is strengthened by the fact that when 
we move our heads slightly the new field of view is only 
slightly different from the old one. Some details that 
were distinct have become less so, others that were 
indistinct have become clearer ; a little that was present 
has vanished and a little that was not present has been 
added at the extreme edges ; but the bulk of the field 
has scarcely altered. This confirms the feeling that 
any field of view is only a fragment of a larger whole, 
and I believe that it is one of the roots of the limitless 
character which we ascribe to Space. 

Much the same concepts are crudely presented to us 
in our tactual fields. When I grasp anything it feels 
extended, and some things feel bigger than others. 
Again, if the thing has projections, I can feel them 
as standing out from a background of " feeling" in the 
same kind of way in which the green patches stand out 
from the blue background in the visual field. But there 
are certain peculiar facts connected with touch, and 
more especially with touch in conjunction with move- 
ment, which are the germ of the distinction between 
empty and filled spaces. Had we been confined to 
sight it is difficult to see how we could have reached 



TRADITIONAL CONCEPT OF SPACE 35 

this distinction, since the visual field, as we have 
already said, is everywhere full of colour, (i) If I put 
my hand on the top of an open tin box I get a peculiar 
sensation. I feel a cold, sharp outline, and, although 
it would not be true to say that there is no felt back- 
ground within and without this, yet it is true to say that 
it is neutral and indefinite as compared with the blue 
background of the visual field in our example, (ii) 
Suppose I move my fingers along the edge of a ruler. 
I have a series of kinesthetic sensations accompanied 
by a series of tactual sensations. Suppose I continue 
the movement until my finger gets to the end of the 
ruler, and still continue it afterwards. The tactual 
sensations cease, but the kinesthetic sensations go on 
just as before. The ceasing of the tactual sensations 
is the basis of the concept of emptiness ; the persistence 
of the kinesthetic sensations is the basis of the concept 
that extension goes on in spite of the absence of extended 
matter. 

Many of these remarks, which are here just thrown 
out, will need to be more fully developed when we 
come to deal with the collective attributes of Space. In 
the meanwhile we notice that all the information gained 
in this way is extremely crude, as compared with the 
concepts that we use in •geometry and apply in physics. 
We see and feel finite surfaces and lumps of complicated 
shapes, not the unextended points and the lines without 
breadth of the geometers. And the spatial relations 
that we can immediately recognise between outstanding 
patches in our fields of view are equally crude. They 
are not relations between points and straight lines, but 
between rough surfaces and volumes. All that I am 
maintaining is that these crude objects of sense-aware- 
ness do have properties that are evidently spatial, and 
that we can see in them the germs of the refined notions 
of points, straight lines, etc. The question is : " How- 
are the refined terms and their accurately definable 
relations, which we use in our mathematics and physics, 



36 SCIENTIFIC THOUGHT 

but cannot perceive with our senses, connected with 
the crude lumps or surfaces and their rough relations, 
which we actually do sense?" 

The real problem is this. The relations of rough finite 
volumes, such as we can perceive, are of unmanageable 
complexity. Again, the continuity and boundlessness 
of Space, as suggested to us by our sense-experiences, 
are vaguely felt, not intellectually grasped. In this 
state it is impossible to lay down their laws or to reason 
about them. What we want to do is to analyse 
finite figures and their fearfully complicated perceptible 
relations into sets of terms with simpler and more manage- 
able relations. If we can do this successfully we shall 
have killed two birds with one stone. We shall have 
done full justice to the spatial properties of what we 
can perceive ; for our analysis is supposed to be 
exhaustive. And, on the other hand, we shall be able 
to grasp these properties and to reason about them 
in a way that was impossible while they remained in 
the crude unanalysed state in which we meet them 
in sense-awareness. I will give examples of what I 
mean, starting with very crude ones, and gradually 
working up to more refined cases. 

(i) If I want to measure an irregular piece of ground 
I first try to divide it up into triangles. Why? Because 
the triangle is a simple figure, and the areas of all 
triangles are connected with their linear dimensions 
by a single simple law. Moreover, I can exhaustively 
analyse any rectilinear figure into triangles. Thus, 
instead of having to apply a different principle of 
mensuration to every different rectilinear figure, I can 
treat them all by this analysis in accordance with one 
simple law. 

(ii) The notion of the distance between two finite 
bodies is clearly indefinite ; so too is that of the direction 
of the line joining them. For there is no one distance 
and no one direction in such a case. Yet evidently 
there is a certain relation between two such bodies, 



TRADITIONAL CONCEPT OF SPACE 37 

which I can perceive, and should like to be able to treat 
mathematically. Two trees are at different perceptible 
distances from a third, and one pair of them may 
define a different perceptible direction from another pair. 
Thus there are crude perceptible relations of distance 
and direction, which we should like to be able to express 
accurately and to treat scientifically. Now we notice 
that the smaller we take our patches or lumps the less 
is the inaccuracy in the notion of the distance between 
them or the direction determined by them. Still, so 
long - as they have any area or volume, the theoretical 
difficulty remains. What we should like to be able 
to do would be to cut up our finite areas and volumes 
into sets of parts of no size, as we cut up our irregular 
rectilinear figure into a set of triangles that exactly make 
it up, and to regard the crude complex relations between 
the finite wholes as compounded out of the simple and 
definite relations between these unextended parts. 

Now this second example shows us an important 
general principle and an important general difficulty, 
both of which extend beyond Space and apply equally 
to Time and Matter. We find that the relations 
between objects become simpler and more manageable 
as the objects become smaller. We therefore want to 
analyse finite objects and their relations into smaller 
and smaller parts, and their simpler and simpler 
relations. But we find that when we try to pursue 
this course to the bitter end we land in a difficulty. 
The relations do not become really definite and manage- 
able till we have come to parts with no size or events 
with no duration. And here we are faced with a dis- 
continuity. What we perceive is always objects with 
some magnitude and duration, and the relations that 
our perception tells us about are always between such 
objects. Have we any right to believe that finite 
objects consist of parts of no magnitude, or that such 
parts, if they exist at all, will have relations in the 
least like those which hold between finite areas and 



38 SCIENTIFIC THOUGHT 

volumes? A point is something different in kind from 
a volume or area, however small. We know what 
we mean when we say that a big area can be cut up 
into smaller ones ; but it is not at all clear what we 
mean when we say that it can be cut up into points. 
The one thing that is certain is that the sense in which 
points are parts of volumes must be different from the 
sense in which little volumes are parts of bigger ones. 
The latter sense of part and whole is one that we find 
exemplified among perceived objects. The former is 
not, and we are bound to define it before we can feel 
comfortable in using points and instants. 

We commonly slur over this difficulty by entertain- 
ing two incompatible notions of points, and using them 
alternately as convenience requires. This expedient 
is not unfamiliar to theologians, and to business men 
returning their incomes for purposes of taxation. When 
we want to talk of an area as analysable into points we 
think of points as little volumes. If we feel qualms 
about this we usually suppress them with the excuse 
which Midshipman Easy's nurse gave for her baby, 
that "after all, it was a very little one." When we 
want to think of points as having exactly definite 
distances we take them to have " position but no 
magnitude," as Euclid put it. Now nothing will make 
these two conceptions of points consistent with each 
other. Either points are extended or they are not. 
If they are not, how can they fit together along their 
sides and edges (which they will not possess) to make 
a finite volume or area? If they are, in what sense 
can you talk of the distance between them, or of the 
direction determined by a pair of them ? To call them 
infinitesimal volumes or areas only darkens counsel ; 
for the word infinitesimal here only serves to cover the 
attempt to combine these two incompatible qualities. 

The method by which such difficulties as these 
have been overcome is due to Whitehead, who has 
lately worked it out in full detail in his Principles of 



TRADITIONAL CONCEPT OF SPACE 39 

Natural Knozv/edge, and his Concept of Nature, two 
epoch-making works. To explain it in full would take 
us into regions of mathematical logic which I do not 
propose to penetrate in the present book. But the 
problem is so important, and the method is of such 
general application in bridging the gaps between the 
crude facts of sense and the refined concepts of mathe- 
matical physics that I shall give a sketch of it. 

The first thing to notice is that it does not in the 
least matter to science what is the inner nature of a term, 
provided it will do the work that is required of it. If 
we can give a definition of points which will make 
them fulfil a certain pair of conditions, it will not matter 
though points in themselves should turn out to be 
entities of a very different kind from what we had 
supposed them to be. The two conditions are (i) that 
points must have to each other the kind of relations 
which geometry demands ; and (ii) that points must 
have to finite areas and volumes such a relation that a 
reasonable sense can be given to the statement that 
such areas and volumes can be exhaustively analysed 
into sets of points. Any entity that answers these 
conditions will do the work of a point, and may fairly 
be called a point, no matter what its other properties 
may be. This important fact, that what really matters 
to science is not the inner nature of objects but their 
mutual relations, and that any set of terms with the 
right mutual relations will answer all scientific pur- 
poses as well as any other set with the same sort of 
relations, was first recognised in pure mathematics. 
Whitehead's great merit is to have applied it to physics. 
I will first illustrate it from pure mathematics, and 
then consider its application to our present problem. 
Consider such irrational numbers as ^2 and ^3. 
Why do we call them numbers ? Simply because they 
obey the formal laws of addition and multiplication 
which integers, like 2 and 3, obey ; i.e. because they 
have to each other relations with the same formal 



40 SCIENTIFIC THOUGHT 

properties as the relations that hold between integers. 
Now numbers like *J2 and ^3 were at first defined as 
the limits of certain series of rational numbers. Thus 
+J2 was defined as the limit of the series of rational 
fractions whose squares are less than 2. Similarly ^3 
was defined as the limit of the series of rational fractions 
whose squares are less than 3. Then you can define 
what you are going to mean by the addition and 
multiplication of such limits. These will be new 
senses of addition and multiplication. The sign + 
does not stand for the same relation when we talk of 
*Ji + ^3 as when we talk of 2 + 3. But addition and 
multiplication, in the new senses, have the same formal 
properties as they have when used in the old sense. 

Thus, e.g. s/~+ \/3 = \^3+ \/ 2 j ust as 2 + 3 = 3 + 2 - 
We have extended the meaning of addition and 
multiplication ; but, as they have precisely the same 
logical properties in both senses, no harm is done by 
using the same name for both, and talking of the 
addition and multiplication of irrationals. Consequently 
there is no harm in calling *J '2 and ^3 numbers; for 
we agreed that any set of entities were to count as 
numbers, provided they had to each other relations with 
the same logical properties as the relations between 
familiar numbers, like 2 and 3, possess. Now all 
reasoning depends entirely on the logical or formal 
properties of the objects reasoned about, and therefore 
we can henceforth reason about irrationals as if they 
were ordinary numbers. 

In exactly the same way, if we can define objects 
which have to each other relations with the same formal 
properties as the relations between geometrical points, 
these objects will do all the work of points, and can be 
called points, whatever their internal structure may be. 
Once this is grasped an initial difficulty can be re- 
moved. We are apt to think of points as internally 
simple, because they are said to have no parts and 
no magnitude. But none of the uses to which we 



TRADITIONAL CONCEPT OF SPACE 41 

put points in geometry or physics depend on this 
supposed internal simplicity. The usefulness of points 
depends entirely on the fact that any pair of them 
define a unique relation with very simple logical 
properties, viz., the straight line joining them. Now 
we see that any terms whatever that are related to 
each other by a relation with these properties will do 
this part of the work of points. Hence we must not be 
surprised if we should find that points are not really 
simple, but have a complex internal logical structure. 
This is what we shall find. But we shall also find 
that, in spite of the logical complexity of points, a 
clear sense can be given to the statement that they 
have no parts and no magnitude. 

We can now go a step further. I said that irrationals 
used to be defined as the limits of certain series of 
rationals. They are not so defined nowadays. Why 
is this? The answer is that, if we define them in this 
way, it is not certain that there is anything answering 
to the definition. ^2 is said to be the limit of the 
series of rationals whose squares are less than 2. But 
how do you know that this series has a limit at all ; i.e. 
roughly speaking, how do you know that there exists 
a number which the series continually approaches, but 
never reaches? The fact is that we do not know it and 
cannot prove it. It follows that, if we define irrationals 
in this way, it is not certain that there are any irra- 
tionals ; aJ '2 might be a symbol which stands for nothing 
at all, like the phrase "The present King of France," 
which has a meaning but no application. We want 
therefore to °ret a definition that shall amount to much 
the same thing as the definition by limits, but shall not 
leave us in any doubt as to the existence of something 
answering to it. 

Now very much the same difficulty arises over points. 
I will put it in this way. We are naturally tempted to 
define points as the limits of certain series of areas or 
volumes, just as we defined irrationals as the limits of 

D 



42 SCIENTIFIC THOUGHT 

certain series of rationals. And these attempted defini- 
tions are steps in the right direction. But they are not 
ultimately satisfactory, because they leave the existence 
of points, as of irrationals, doubtful. Let me illustrate 
this with regard to points. We saw that, as we take 
smaller and smaller areas or volumes, the spatial rela- 
tions between them become simpler and more definite. 
Now we can imagine a series of areas or volumes, one 
inside the other, like a nest of Chinese boxes. Suppose, 
e.g. that it was a set of concentric spheres. As you pass 
to smaller and smaller spheres in the series you get to 
things that have more and more approximately the 
relations which points have in geometry. You might 
therefore be tempted to define a point, such as the 
common centre of the spheres, as the limit of this series 
of spheres one inside the other. But at once the old 
difficulty would arise : "Is there any reason to suppose 
that this series has a limit?" Admittedly it has no 
last term ; you can go on finding spheres within spheres 
indefinitely. But the mere fact that it does not have a 
last term is no proof that it does have a limit. The 
limit of an endless series might be described as the first 
term that comes after all the terms of the endless series. 
But this implies that the series in question forms part 
of some bigger series ; otherwise there is no beyond. 
Now it is not at all obvious that our endless series of 
concentric spheres does form part of any bigger series, 
or that there is any term that comes after every sphere 
in it. Hence there is no certainty that points, defined 
as the limits of such series, exist. 

How is such a difficulty to be overcome? It was first 
overcome for irrational numbers, and Whitehead then 
showed that it might be dealt with in the same way for 
points. The solution will at first sight strike those who 
are unfamiliar with it as a mere tour de force ; neverthe- 
less it is perfectly valid, and really does the trick. 
Instead of defining *J2 as the limit of the series of 
rational numbers whose squares are less than 2, it is 



TRADITIONAL CONCEPT OF SPACE 43 

defined as this series itself. That is *J2 is defined as 
the series of all rational numbers whose squares are 
less than 2. There is no doubt that there is such a 
thing as ^2, so defined. For there certainly are rational 
numbers, like 1 and 1*2 and 2*5, and so on. And it 
is certain that the squares of some of them are less than 
2, that the squares of others of them are greater than 2, 
and that the squares of none of them are equal to 2. 
It is therefore certain that there is a definite class of 
rationals whose squares are less than 2, and that it 
has an infinite number of members. It is equally 
certain that the numbers in this class form a series, 
when arranged in order of magnitude. Thus there is 
no doubt of the existence of the series which is said to 
be the meaning of sj2. 

But the difficulty that will be felt at first will be a 
different one. The reader will be inclined to say: "I 
don't doubt that ^/2, as defined by you, exists ; what 
I very gravely doubt is whether, as defined by you, it 
is what I or anyone else mean by ^2, By 1J2 I under- 
stand a certain number of a peculiar kind ; I do not 
mean a series of numbers or of anything else." The 
answer to that difficulty is that series of this kind will 
serve every purpose for which irrationals, like ^2 and 
^3, are used in mathematics. You can define addition 
and multiplication for such series, and they have exactly 
the same logical properties as the addition and multipli- 
cation of integers or of rational fractions. Lastly, taking 
this definition of ^2, you can give a perfectly definite 
meaning to the statement that the length of the diagonal 
of a square, whose side is of unit length, is represented 
by *J2. The position is therefore this. The definition 
of irrationals defines something that certainly exists. 
And this something has all the formal properties and 
will do all the work of irrationals. The sole objection 
to it is that it is paradoxical, in so far as it assigns a 
complex internal structure to irrationals which we did 
not suspect them of having. But that objection is really 



44 



SCIENTIFIC THOUGHT 



unimportant, because of the general principle that in 
science it is only the logical properties of the relations 
between our terms that matter, and not their internal 
logical structure. The objection is just a prejudice to 
be got over, like our feeling that the inhabitants of 
Australia must be precariously hanging on to the earth 
by suction, like tlies on a ceiling. 

Now we deal with the difficulty about points in an 
exactly similar way. We should like to say that points 
are the limits of series of smaller and smaller volumes, 
one inside the other, like Chinese boxes. But we 
cannot feel any confidence that such series have limits 
and therefore that points, so defined, exist. Now there 
is no doubt that such series themselves exist ; ordinary 
perception makes us acquainted with their earlier and 
bigger terms, and the assumption that Space is con- 
tinuous guarantees the later ones. We see, on reflection, 
that it is of the very nature of any area or volume to 
have parts that are themselves areas or volumes. We, 
therefore, boldly define points, not as the limits of such 
series, but as such series themselves. This is exactly 
like the procedure adopted in defining irrationals. 

There are certain additional difficulties of detail in 
defining points, which do not arise in defining irrationals. 

I will just indicate them and 
refer the reader to Whitehead for 
the complete solution of them, 
(i) There may be a great many 
different series of converging 
volumes which would all com- 
monly be said to converge to the 
same point. This is illustrated 
for areas in the figure above, 
where the series of circles and the series of squares 
might equally be taken to define the point which is 
their common centre. Now, of course, the point cannot 
reasonably be identified with one of these series rather 
than with another. We, therefore, define the point, not 




TRADITIONAL CONCEPT OF SPACE 45 

as any one of these series of converging volumes, but as 
the class of all the volumes in any of the series that would 
commonly be said to converge to the point, (ii) Not 
all series of converging volumes converge to points ; 
some converge to lines, and others to areas. An ex- 
ample of a series of areas converging to a straight 
line is illustrated below. (It should be noticed that, 
although for simplicity of drawing I have always taken 
series of areas in my diagrams, the fundamental fact 
is series of volumes, and areas need definition, like points 
and lines.) 

The general principle is, however, always the same. 
Points, straight lines and areas are all defined as series 
of converging volumes. But the series that define points 



differ in certain assignable ways from those that define 
straight lines, and these in turn differ in certain assign- 
able ways from those which define areas. Ordinary 
perception gives us examples of each kind of series, 
and the only difficulty is to state in formal logical terms 
these differences which we can all vaguely see and feel. 
To do this properly is, of course, a very hard job, but it 
can be and has been done. Many of these additional 
complications arise because Space has three dimensions, 
whilst the series of real numbers has only one. Conse- 
quently, as a matter of history, moments of Time were 
defined in this way before points of Space. Time forms 
a one-dimensional series, like the real numbers, and, 
therefore presents an easier problem than Space for this 
method. 

Before going further I want to remove a legitimate 
ground of doubt which will probably be in the minds 
of most careful readers to whom the subject is new. 
Many will say: "This is no doubt highly ingenious, 



46 SCIENTIFIC THOUGHT 

but are we not merely moving - in a circle? May not 
the theory be summed up by saying that points are 
those series of volumes that converge to points? If so, 
are we not plainly using the notion of point in order to 
define it?" This would of course be a fatal objection 
if it were well founded, but it is not. The theory may 
roughly be summed up in the statement that a point 
is a series of volumes that would commonly be said to 
converge to that point. The whole question is whether 
the common phrase "converging to the point/" really 
involves a reference to points. If it does the definition 
of points is circular and useless ; if it does not there is 
no vicious circle in the theory. Now the essence of the 
theory is that it can state the meaning of such phrases 
as "converging to a point" in terms which involve 
nothing but volumes and their relations to each other. 
We see certain series of volumes which we say "con- 
verge to a point," e.g. series of concentric spheres. We 
see other series of volumes of which we do not say this. 
Here is a perceptible difference in perceptible objects. 
This difference, which can be seen and felt, must be 
expressible in terms of volumes and their relations to 
each other. It cannot really involve a relation to some- 
thing that can neither be seen nor felt, such as a point. 
Thus a series of volumes is said to converge to a point 
simply and solely because of certain relations which 
hold between the volumes of the series. Another series 
of volumes is said not to converge to a point simply and 
solely because certain other relations exist between the 
volumes of this series. These relations, as well as their 
terms, are perceptible, and this is how we come to 
distinguish two such series. It only remains to state 
the differences of relation, which can thus be seen and 
felt, in definite terms that can be grasped by the intellect. 
This the present theory does. For example, a series 
of confocal conicoids could be defined as one whose 
members cut each other at right angles ; a definition 
which makes no mention of their common focus, but 



TRADITIONAL CONCEPT OF SPACE 47 

simply mentions a relation which the members of the 
series have to each other. There is thus no circularity 
in the definition of points by this method. 

The method which we have been sketching, by which 
the accurate concepts of science are defined in terms 
of perceptible objects and their perceptible relations, is 
called by Whitehead the Principle of Extensive Abstrac- 
tion. Our next question is: Do points, lines, etc., as 
defined by Extensive Abstraction, fulfil the conditions 
that we laid down for them at the beginning? The 
first was that they must have to each other the sort 
of relations that points, etc., are said to have to each 
other in geometry. For instance, two points must 
define a unique relation with certain logical properties, 
viz., the straight line that joins them. Intersecting 
straight lines must define planes, and so on. Points, 
straight lines, and planes, defined as above, do in fact 
have relations of this kind to each other. The detailed 
proof of this must here be taken on trust, but I shall 
take one example to indicate roughly the way in which 
these results come about. Take two different series 
of concentric spheres, one in one place and the other in 
another. Choose any sphere out of one set and any 
sphere out of another. There will be a certain crude 
perceptible relation between them. For instance, as 
shown in the diagram below, there will be a volume 




which connects and contains both of them, which does 
not wholly contain any pair of larger spheres in the two 
series, but more than contains any pair of smaller spheres 
in the two series. 

Let us call this the containing volume of the selected 
pair. As we take smaller and smaller pairs of spheres 



48 SCIENTIFIC THOUGHT 

from the two series it is easy to see that the corre- 
sponding - containing volumes form a series of Chinese 
boxes of the usual kind. Now this series of containing 
volumes is obviously of the sort that defines a straight 
line. Our two series of spheres are of the sort that 
define points ; the points that they define are what we 
commonly call the centres of the two systems. And 
it is easy to see roughly that the line defined by the 
series of containing volumes is what we call the line 
joining the two centres. Of course, for accurate mathe- 
matical treatment, many more refinements are needed ; 
but I hope that the example will suffice to show in a 
rough way how points, as defined by us, determine 
straight lines, as defined by us. 

The second condition which points had to fulfil was 
that it must be possible to give a clear meaning to the 
statement that finite volumes and areas can be completely 
analysed into sets of points. Now we can see at once 
that, whatever a point may be, it is certain that it cannot 
be part of a volume in the sense in which a little volume 
can be part of a bigger one. The latter is the funda- 
mental relation ; it holds only between finite volumes, 
and it is perceptible. In this sense points, however 
defined, could not be parts of volumes. Divide a 
volume as long as you like and you will get nothing 
but smaller volumes. Put points together as much as 
you like (if this permission conveys anything to you) and 
you will not get any volume, however small. In fact the 
whole notion of ''putting together" points is absurd, 
for it tries to apply to points a relation which can only 
hold between volumes or areas. To put together means 
to place so that the edges touch ; and a point, having 
no area or volume, has no edges. We see then that, 
whatever definition we give of points, we must not 
expect them to be parts of volumes in the plain straight- 
forward sense in which the Great Court is part of the 
college buildings of Trinity. It is therefore no special 
objection to our definition of points that points, as 




TRADITIONAL CONCEPT OF SPACE 49 

defined by us, could not be parts of volumes in the 
plain straightforward sense. 

The sense in which a point p is contained in a 
volume v is roughly the following. We say that p is 
contained in v if, after a certain „---, 

volume has been reached in the 
series that defines p, all sub- 
sequent volumes in this series 
are parts, in the plain straight- --—' 

forward sense, of the volume v. The diagram illustrates 
this definition. 

The sense in which any volume can be exhaustively 
analysed into points is roughly the following : Any 
pair of volumes of which both are contained in v, but 
of which neither is wholly contained in the other, belong 
to series which define different points, both of which are 
contained in v in the sense just defined. Of course both 
these definitions need further refinements to cover all 
cases that can arise. 

Now what precisely has been accomplished by all 
this? We have shown the exact connexion between 
what we can and do perceive, but cannot deal with 
mathematically, and what we can and do deal with 
mathematically, but cannot perceive. We perceive 
volumes and surfaces, and we perceive certain relations 
between them, viz., that they intersect, or that one is 
contained in the other, or that they are separated and 
both contained in some third volume or surface. We 
do not perceive the points without volume and the lines 
without breadth, in terms of which geometry and physics 
are stated and worked out. On the one hand, we cannot 
make geometry into a deductive science at all except 
in terms of points, etc. On the other hand, we want 
to be able to apply geometry to the actual world, and 
not to treat it as a mere mathematical fairy tale. It is 
essential therefore that the connexion between what we 
perceive, but cannot directly treat mathematically, and 
what we cannot perceive, but can treat mathematically, 



50 SCIENTIFIC THOUGHT 

should be made clear. This is what we have tried to 
do, following- the method of Extensive Abstraction laid 
down and worked out by Whitehead. 

It seems to me that the more we reflect the more 
clearly we see that something like the course that we 
have followed is necessary if the application of geometry 
(and also of rational mechanics) to the real world is to 
be justified. The world of pure mathematics with its 
points, straight lines, and planes, its particles, instants, 
and momentary configurations, has an appearance of 
unnatural smoothness and tidiness, as compared with 
the rough complexity of the perceptible world. Yet 
the laws of geometry and mechanics came out of the 
study of that world, and return to it in the form of 
applied mathematics. What I have tried to do is to 
show in rough outline how the two are connected, in 
the hope that the reader may be encouraged to consult 
the original authorities to learn how the same method 
establishes the connexion in the minutest details. 

I think that possibly two difficulties may still remain 
in the reader's mind, (i) He may say : " Men used 
geometry for thousands of years, and applied it, and 
yet they knew nothing of these definitions of points, 
straight lines, and planes." I answer that this is 
perfectly true, and that it perfectly illustrates the 
difference between the special sciences and Critical 
Philosophy. Certainly people used the concepts of 
point and straight line, and used them correctly as the 
results show. But equally certainly they had the most 
confused ideas as to what they meant by points and 
straight lines, and could not have explained why a 
geometry stated in terms of these and their relations 
should apply so accurately to a world in which nothing 
of the kind was perceptible. It is the business of Critical 
Philosophy not to rest content with the successful use 
of such concepts, but to disentangle their meaning and 
thus determine the limits within which they can safely 
be employed. 



TRADITIONAL CONCEPT OF SPACE 51 

(ii) The second question that may be asked is : " Do 
points, straight lines, etc., really exist in the same sense 
as volumes, or are they merely convenient and perhaps 
indispensable fictions?" This seems to me to be 
an important point, on which even authorities like 
Mr Russell often speak with a strangely uncertain 
voice. (Probably Mr Russell calls certain things, 
which he thinks can be defined in this kind of way, 
"fictions," from the same motives as led Mr Pope, 
according to Dr Johnson, to write the lines : — 

" Let modest FOSTER, if he will, excel 
Ten metropolitans in preaching well.") 

The right answer to the question appears to me to be 
the following: Points, etc., as defined by us, are not 
fictions ; they are not made by our minds, but discovered 
by them, just as America was discovered, and not 
created, by Columbus's voyage. On the other hand, 
they do not exist in precisely the same sense in which 
finite volumes exist. They are real in their own kind, 
but it is a different kind from that of volumes. It is 
through no mere accidental limitation of our senses that 
we cannot perceive the points and straight lines of the 
geometers, whilst we can see and feel volumes. Only 
particulars can be perceived by the senses ; and points 
are not particulars. They are classes of series of 
volumes, or, to be more accurate, are the logical 
sums of such classes. The volumes and the series 
of volumes that define points exist quite literally, 
and the earlier and bigger terms of these series can be 
perceived. The points themselves are rather compli- 
cated logical functions of these. They exist in the 
sense that they are determinate functions of real series 
of actually existing particulars. 

Perhaps an illustration from another region will 
make their mode of being clearer to some people. The 
curve called a cycloid is traced out by a point on the 
circumference of a circle when the latter rolls along a 



52 SCIENTIFIC THOUGHT 

Straight line. Now the arches of Westminster Bridge 
are cycloidal, and can therefore be regarded as due to 
the rolling of a certain circle on a certain straight line. 
Now suppose we were asked whether this circle actually 
exists or is a mere fiction. In one sense I answer that 
it does not exist. So far as I know, no physical circle 
actually rolled at some date in the world's history 
on a physical straight-edge to produce the arches of 
Westminster Bridge. On the other hand, the circle is 
not a mere fiction. The cycloidal arches really do exist, 
and the circle corresponding to them is completely 
determined by the shape and size of these arches. This 
connexion is a real fact, absolutely independent of our 
minds and their operations. I therefore say that the 
circle exists, in the sense that it is a determinate function 
of the arches, which exist in the ordinary sense. Points, 
straight lines, etc., as defined by us, exist in the same 
sense as the circle determined by the arches of West- 
minster Bridge ; the particular series of volumes which 
define points exist in the same sense as the arches 
themselves. 

Additional works that may be consulted with 
profit : 

A. N. Whitehead, Principles of Natural Knowledge, Part III. 
„ Concept of Nature, Cap. IV. 



CHAPTER II 

Alice sighed wearily. " I think you might do something 
better with the time," she said, "than waste it asking riddles 
with no answers." 

" If you knew Time as well as I do," said the Hatter, " you 
wouldn't talk about wasting it." 

(Lewis Carroll, Alice in Wonderland.) 

The General Problem of Time and Change 

We have now said as much about Space as can be 
said with profit before its relations to Time and Matter 
have been dealt with. We have shown at least how 
the concepts, such as points, lines, planes, etc., which 
are needed, whatever view we finally take of Space, 
are connected with the rough, untidy facts that we 
can perceive. We have not, however, explained why 
there is supposed to be one single Space in which 
all the events of nature are located, nor how things 
have places assigned to them in it. This can only be 
done at a later stage. In the meanwhile I propose to 
treat the concepts of Time and Change, as they appear 
at the same level of thought. 

At first sight the problems of Time look very much 
like those of Space, except that the single dimension 
of Time, as compared with the three of Space, seems to 
promise greater simplicity. We shall point out these 
analogies at the beginning ; but we shall find that they 
are somewhat superficial, and that Time and Change 
are extremely difficult subjects, in which spatial analogies 
help us but little. 

The physicist conceives Time in much the same way 
as he conceives Space. lust as he distinguishes Space 

53 



54 SCIENTIFIC THOUGHT 

from the matter in it, so he distinguishes Time from 
events. Again, mere difference of position in Time is 
supposed to have no physical consequences. It is true 
that, if I go out without my overcoat at 2 a.m., I shall 
probably catch cold; whilst, if I do so at 2 p.m., I 
shall probably take no harm. But this difference is 
never ascribed to the mere difference in date, but to 
the fact that different conditions of temperature and 
dampness will be contemporary with my two expeditions. 
Again, Time, like Space, is supposed to be continuous, 
and physicists suppose (or did so until quite lately) that 
there is a single time-series in which all the events of 
nature take place. This series is of one dimension, so 
that, as far as appears at present, Time is like a very 
simple Space consisting of a single straight line. 

Just as we treat our geometry in terms of unextended 
points and their relations, so we treat our chronometry 
in terms of moments without duration and their relations. 
Duration in Time corresponds to extension in Space. 
Now, just as we never perceive points or even unex- 
tended particles, so we are never aware of moments or 
of momentary events. What we are aware of is finite 
events of various durations. By an event I am going 
to mean anything that endures at all, no matter how 
long it lasts or whether it be qualitatively alike or 
qualitatively different at adjacent stages in its history. 
This is contrary to common usage, but common usage 
has nothing to recommend it in this matter. We 
usually call a flash of lightning or a motor accident 
an event, and refuse to apply this name to the history 
of the cliffs at Dover. Now the only relevant difference 
between the flash and the cliffs is that the former lasts 
for a short time and the latter for a long time. And 
the only relevant difference between the accident and 
the cliffs is that, if successive slices, each of one second 
long, be cut in the histories of both, the contents of a 
pair of adjacent slices may be very different in the first 
case and will be very similar in the second case. Such 



TIME AND CHANGE 55 

merely quantitative differences as these give no good 
ground for calling one bit of history an event and 
refusing to call another bit of history by the same name. 
Now the temporal relations which we perceive among 
events are similar to the relations of partial or complete 
overlapping which we can perceive in the case of two 
extended objects, like a pair of sticks. The possible 
time-relations between two events can be completely 
represented by taking a single straight line, letting 
" left-to-right " on this stand for " earlier and later," 
and taking two stretches on this line to represent a 
pair of finite events. Let AB and CD be two events 
of which the latter lasts the longer ; then the possible 
temporal relations between the two are represented by 
the nine figures given below. 

y tf) 



(/) . 


C 




D 


' A B 








(2) . ? 




D 




1 ' A B 








(3) . C . 




D 




' ' A B 








(4) C , 


D 







A B 

D 



A B 

. D 



A B 

D 



■* (6) 

-> (7) 



A 8 

D 



B 



> (8) 

► (9) 



The most general kinds of relation between finite 
events are those of partial precedence and partial 
subsequence ; the rest can be defined in terms of these. 
From these crude perceptible data and their crude 
perceptible relations the concepts of momentary events 
and moments can be obtained, and their exact relations 
determined, by the Method of Extensive Abstraction. 
I believe that, as a matter of history, one of the first 
successful applications of the method was made by 
Dr Norbert Wiener to this very problem. 

The motives that lead us to apply Extensive 
Abstraction to Time are the same as those which lead 
us to apply it to Space. As scientists our main interest 
is to discover laws connecting events of one kind with 
events of other kinds at different times. Now, just 



56 SCIENTIFIC THOUGHT 

as the geometrical relations of finite volumes, as such, 
are of unmanageable complexity, so are the causal 
relations of events of finite duration. There is no 
simple relation between the contents of one hour and 
the contents of another. But the shorter we make 
our events the simpler become the relations between 
them. So, finally, we state our laws in terms of so- 
called "momentary events" and their exact relations, 
and we "analyse" finite events into sets of momentary 
ones, and explain their relations in terms of those of 
their momentary "parts." Everything that has been 
said of this procedure in geometry applies, mutatis 
mutandis ) to its use in physics. Momentary "events" 
are not really events, any more than points are little 
volumes. A momentary event is not " part of" a finite 
one in the plain straightforward sense in which the 
event of a minute is part of the event that occupies 
a certain hour. The meanings of all these concepts, 
and their relations, have to be given in terms of 
perceptible entities and their relations, by means of 
Extensive Abstraction. 

What we have been saying is most excellently 
illustrated by the science of Mechanics. What we 
want to deal with there is the movements of finite 
bodies, like wheels and planets ; and we want to treat 
their changes of position and motion over long periods 
of time. To do this we have first to analyse the finite 
bodies into unextended particles, and then to analyse 
the finite events into momentary ones. The laws of 
Mechanics are only simple when they state relations 
between momentary configurations of one set of par- 
ticles and a later or earlier configuration of the same 
or another set of particles. The gap between the 
perceptible facts, that we are trying to describe and 
predict, and the imperceptible concepts and relations, 
in terms of which we have to treat the facts, is bridged 
by Extensive Abstraction, applied both to extension 
in Space and to duration in Time. Mechanics is a 



TIME AND CHANGE 57 

kind of geometry of events, which has to take account 
of both their spatial and their temporal characteristics. 
Geometry is the kind of mechanics which results when 
we confine ourselves to a single moment, and omit the 
temporal characteristics of events. These are, of course, 
only rough general statements ; but they are perhaps 
illuminating, and they will be more fully explained 
later. 

So far, the analogy between Time and Space has 
seemed to work very well. Duration has corresponded 
to length, before and after to right and left, and 
simultaneity to complete mutual overlapping. But, if 
we reflect a little more carefully, we shall see that the 
analogy between before and after and right and left 
is not so illuminating as it seems at first sight. The 
peculiarity of a series of events in Time is that it has 
not only an intrinsic order but also an intrinsic sense. 
Three points on a straight line have an intrinsic order, 
i.e. B is between A and C, or C is between B and 
A, or A is between C and B. This order is independent 
of any tacit reference to something traversing the line 
in a certain direction. By difference of sense I mean 
the sort of difference which there is between, say, 
ABC and CBA. Now the points on a straight line 
do not have an intrinsic sense. A sense is only 
assigned to them by correlation with the left and right 
hands of an imaginary observer, or by thinking of a 
moving body traversing the line in such a way that 
its presence at A is earlier than its presence at B, 
and the latter is earlier than its presence at C. In 
fact, if we want a spatial analogy to Time, it is not 
enough to use a straight line ; we need a straight line 
with a fixed sense, i.e. the sort of thing which we 
usually represent by a line with an arrow-head on it. 
Now the points on straight lines do not have any 
intrinsic sense, and so the meaning of the arrow-head 
is only supplied by reference to something which is at 
one point before it gets to another. Thus to attempt 



58 SCIENTIFIC THOUGHT 

to understand before and after by analogy with a 
directed line is in the end circular, since the line only 
gets its sense through a tacit correlation with a series 
of events in Time. 

Now the intrinsic sense of a series of events in Time 
is essentially bound up with the distinction between 
past, present, and future. A precedes B because A is 
past when B is present. We may begin by asking 
whether there is any spatial analogy to the distinction 
of past, present, and future. We shall find that there 
is, but that once more it is not ultimately useful, because 
it involves a reference to these very temporal character- 
istics on which it is supposed to throw light. The 
obvious analogy to Now in Time is Here in Space. 

Here is primarily the name of a certain region in 
the continuum of possible positions that one's body 
can take up. When Here, is used as a predicate, as 
when I say, "So and so is here," I mean that so and 
so is within a region whose boundaries I can reach 
with little or no walking. The peculiarity of Here is 
its peculiar kind of ambiguity. Here, as used by me, 
is understood to describe a different region from that 
which is described by the same word, as used by you. 
As used by me, it means " near me" ; as used by you 
it means "near you." It is thus a word which has a 
partially different meaning as used by every different 
observer, simply because an essential part of its mean- 
ing is a relation to the particular observer who is 
using it. 

We must notice, however, that Here has a second 
ambiguity. It not only has a different meaning as 
used by you and by me at the same time, it also has 
a different meaning as used by either of us at different 
times. By Here I always mean that region which is 
near me at the time of speaking. This difference of 
meaning at two moments need not betray itself by a 
difference of application, though it often does. If I 
stand still for five minutes the region which I call 



TIME AND CHANGE 59 

Here at the end of the time will be the same as that 
which I called Here at the beginning ; but, if I have 
moved, the difference in meaning will also be accom- 
panied by a difference in application. 

We can, of course, extract a general meaning of 
" hereness " ; it means "nearness to an observer who 
uses the word Here, at the time when he uses it." But 
obviously Here is a descriptive phrase with a double 
ambiguity, since it refers both to a certain person and 
to a certain date in his history, and does not become 
definite till these two blanks have been filled in by the 
context. 

It is evident then that Here is not going to help us 
to understand Now, since it contains an essential refer- 
ence to Now. We must therefore treat past, present, 
and future on their own account, without expecting any 
help from spatial analogies. Now, the present does 
have a systematic ambiguity such as we noticed in 
Here. Whether it contains an essential reference to 
the particular observer who uses it I will not now 
discuss. The traditional view is that it is neutral as 
between various observers, but we shall later see reason 
to doubt this. However this may be, it is certainly 
ambiguous in another sense. Every place to which 
an observer's body can go is a possible Here. In the 
same way every event either is, has been or will be 
Now, on the ordinary view, provided it be short enough 
to fall into what psychologists call a Specious Present. 

We are naturally tempted to regard the history of 
the world as existing eternally in a certain order of 
events. Along this, and in a fixed direction, we imagine 
the characteristic of presentness as moving, somewhat 
like the spot of light from a policeman's bull's-eye 
traversing the fronts of the houses in a street. What 
is illuminated is the present, what has been illuminated 
is the past, and what has not yet been illuminated is 
the future. The fact that the spot is of finite area 
expresses the fact that the Specious Present is not a 



60 SCIENTIFIC THOUGHT 

mere point but is of finite, though short, duration. 
Such analogies may be useful for some purposes, but 
it is clear that they explain nothing. On this view 
the series 'of events has an intrinsic order, but no 
intrinsic sense. It gains a sense, and we become able 
to talk of one event as earlier than another, and not 
merely of one event as between two others, because the 
attribute of presentness moves along the series in a 
fixed direction. But, in the first place, the lighting of 
the characteristic of presentness now on one event 
and now on another is itself an event, and ought 
therefore to be itself a part of the series of events, and 
not simply something that happens to the latter from 
outside. Again, if events have no intrinsic sense but 
only an intrinsic order, what meaning can we give to 
the assertion that the characteristic of presentness 
traverses the series of events in a fixed direction ? All 
that we can mean is that this characteristic is present at 
B when it is past at A. Thus all the problems which 
the policeman's bull's-eye analogy was invented to 
solve are simply taken out of other events to be heaped 
on that particular series of events which is the move- 
ment of the bull's-eye. 

The difficulties that we have found in this particular 
analogy are of very wide range. For instance, it is 
extremely tempting to try to resolve the difference 
between past, present, and future into differences in 
the cognitive relations of our minds to different events 
in a series which has intrinsic order but no intrinsic 
sense. Let us confine ourselves, for the sake of sim- 
plicity, to events that fall within the knowledge of a 
certain observer O. Undoubtedly O has a different 
kind of cognitive relation to those events which he 
calls present from that which he has to those which 
he calls past and to those which he calls future. About 
future events he can only guess or make inferences by 
analogy with the past. Some present events he can 
directly perceive with his senses. Some past events 



TIME AND CHANGE 61 

he knows by direct memory, which is quite a different 
kind of experience from sense-perception. It is tempt- 
ing to suppose that these are not simply interesting 
facts about past, present, and future, but are what we 
mean by these three temporal distinctions. Can such 
a theory be made to work? 

Clearly we cannot simply define an event as present 
for O if O can perceive it or if it is contemporary with 
something that O can perceive. For we shall then 
have to define an event as past for O if O cannot per- 
ceive it but can either remember it or remember some- 
thing contemporary with it. Now, of course, every 
event that falls within O's knowledge has these two 
incompatible relations to O ; though, as we put it, it 
has them at different times. He can first perceive, 
but not remember the event, and can then remember 
but not perceive it. Hence these cognitive character- 
istics do not suffice to distinguish a past from a present 
event, since every event that O knows of has both these 
relations to him. If you add that an event always has 
the perceptual relation to O before it has the memory 
relation, you only mean that the event of remembering 
something is present when the event of perceiving it 
is past, and you have simply defined present and past 
for O's objects in terms of present and past for his 
cognitive acts. If you then try to define the latter in 
terms of different relations to O's acts of introspection, 
you simply start on an infinite regress, in which past 
and present remain obstinately undefined at any place 
where you choose to stop. 

It does not of course follow that past and present 
in external Nature may not be reducible to certain 
relations between objective events and minds which 
observe them ; but it does follow that these charac- 
teristics cannot be analysed away in this manner out 
of Reality as a whole, which of course includes observing 
minds as well as what they observe. 

The difficulty about past, present, and future in 



62 SCIENTIFIC THOUGHT 

general can be summed up in two closely connected 
paradoxes, (i) Every event has all these characteristics, 
and yet they are inconsistent with each other. And (ii) 
events change in course of time with respect to these 
characteristics. Now we believe ourselves to under- 
stand change in things, but to talk of events changing 
seems almost unintelligible. The connexion between 
the two paradoxes is, of course, that we get into the 
second directly we take the obvious step to avoid the 
first. 

We have plenty of experience of things which 
appear to have incompatible characteristics, such as 
redness and greenness, or greatness and smallness. As 
a rule we remove this apparent inconsistency by point- 
ing out that the facts have been stated elliptically, and 
that really a relation is involved. In the first example 
we say that what has been omitted is a relation to two 
different times. The full statement is that the thing 
is red at one time and green at another, and there is 
no inconsistency in this. In the second example we 
have no need even to bring in a relation to two different 
times. It is enough to point out that the predicates 
great and small themselves tacitly assume relations ; 
so that the full statement is that the thing is at once 
great as compared with one object and small as com- 
pared with another. In one of these two ways we 
always proceed when we have to deal with the apparent 
co-inherence of incompatible predicates in a single 
subject. We therefore naturally try one of these 
expedients to deal with the fact that every event is 
past, present, and future, and that these predicates are 
incompatible. 

It seems natural and childishly simple to treat the 
problem in the way in which we treated the thing that 
was both red and green. We say : " Of course the 
event E has futurity for a certain stretch of time, then 
it has presentness for a short subsequent stretch, and 
it has pastness at all other moments." Now the 



TIME AND CHANGE 63 

question at once arises: "Can we treat the change of 
an event in respect to its temporal qualities as just like 
the change of a thing with respect to qualities like red 
and green ? " 

To answer this question we must try to see what 
we mean when we say that a certain thing T changes 
from red to green. So far as I can see, our meaning 
is somewhat as follows : There is a certain long-lasting 
event in the history of the world. This stands out in 
a noticeable way from other events which overlap it 
wholly or partly. If successive short sections in time 
be taken of this long event, adjacent sections have 
spatial continuity with each other, and predominant 
qualitative resemblance to each other. On these 
grounds the whole long event is treated as the history 
of a single thing T. But, although adjacent short 
sections are predominantly alike in their qualities, there 
may be adjacent sections which differ very markedly 
in some quality, such as colour. If you can cut the 
history of the thing in a certain moment, such that a 
slice of its history before that is red and a slice after 
that is green, we say that the thing T has changed 
from red to green at that moment. To say that a thing 
changes, thus simply means that its history can be 
cut up into a series of adjacent short slices, and that 
two adjacent slices may have qualitative differences. 

Can we treat the change of an event from futurity, 
through presentness, to pastness in the way in which 
we have treated the change of a thing (say a signal 
lamp) from red to green? I think it is certain that we 
cannot ; for two closely connected reasons. In the 
first place, the attempt would be circular, because the 
change of things will be found on further analysis to 
involve the change of events in respect to their temporal 
characteristics. We have assumed that the history 
of our signal lamp can be analysed into a series of 
shorter adjacent events, and that it was true of a certain 
pair of these that the earlier was red and the later 



<> 4 SCIENTIFIC THOUGHT 

green. But to say that this series of events passes from 
earlier to later (which is necessary if we are to dis- 
tinguish between a change from red to green and a 
change from green to red) simply means that the red 
sections are past when the green ones are present and 
that the red ones are present when the green ones are 
future. Thus the notion of the history of the lamp as 
divisible into a series of sections, following each other 
in a certain direction, depends on the fact that each 
of these sections itself changes from future, through 
present, to past. It would therefore be circular to 
attempt to analyse changes in events in the way in 
which we have analysed changes in things, since the 
latter imply the former. 

Apart from this objection, we can see directly that 
the change of events cannot be treated like the changes 
of things. Let us take a short section of the history 
of the lamp, small enough to fall into a Specious 
Present, and such that the light from the lamp is red 
throughout the whole of this section. This short event 
was future, became present, and then became past. If 
we try to analyse this change in the way in which we 
analysed the change of the lamp from red to green 
we shall have to proceed as follows : We shall have 
to divide this red event into shorter successive sections, 
and say that the latest of these have futurity, the middle 
ones presentness, and the earliest ones pastness. Now 
this analysis obviously does not fit the facts. For the 
fact is that the whole event was future, became present, 
and is now past. Clearly no analysis which splits up 
the event into successive sections with different charac- 
teristics is going to account for the change in the 
temporal attributes of the event as a whole. 

We see then that the attempt to reconcile the in- 
compatible temporal qualities of the same event by 
appealing to change, in the ordinary sense of the word, 
is both circular and ineffective. The circularity becomes 
specially glaring when put in the following way : The 



TIME AND CHANGE 65 

changes of things are changes in Time ; but the change 
of events or of moments from future, through present, 
to past, is a change <?/"Time. We can hardly expect to 
reduce changes of Time to changes in Time, since Time 
would then need another Time to change in, and so on 
to infinity. 

We seem, therefore, to be forced back to the other 
type of solution, viz., that the predicates, past, present, 
and future, are of their very nature relational, like large 
and small. Unfortunately we have already had occasion 
to look at some solutions of this type — the policeman's 
bull's-eye and the different cognitive relations — and the 
omens are not very favourable. 

If we reflect, we shall notice that there are two quite 
different senses in which an entity can be said to change 
its relational properties. An example of the first is 
where Tom Smith, the son of John Smith, becomes 
taller than his father. An example of the second is 
where Tom Smith ceases to be the youngest son of 
John Smith, and becomes the last son but one. What 
is the difference between these two cases? In the first 
we have two partially overlapping life-histories, T and 
J. If we cut up both into successive short sections we 
find that the earlier sections of T have the relation of 
"shorter than" to the contemporary sections of J, 
whilst the later sections of T have the relation of 
"taller than " to the contemporary sections of J. In 
the second we have quite a different state of affairs. 
When we say that T is the youngest son of J we mean 
that there is no entity in the universe of which it is true 
to say both that it is a son of J and that it is younger 
than T. When we say that T has ceased to be the 
youngest son of J we mean that the universe does 
contain an entity of which it is true to say both that 
it is a son of J and that it is younger than T. In the 
first case then, we simply have a difference of relation 
between different corresponding sections of two existing 
long events. In the latter, the difference is that a certain 



66 SCIENTIFIC THOUGHT 

entity has changed its relational properties because a 
second entity, which did not formerly exist (and there- 
fore could stand in no relation whatever to T), has begun 
to exist, and consequently to stand in certain relations 
to T, who is a member of the same universe as it. 

Now it is obvious that the change that happens to 
an event when it ceases to be present and becomes past 
is like the change of Tom Smith when he ceases to be 
the youngest son of John Smith ; and the continuous 
retreat of an event into the more and more remote past 
is like the successive departure of Tom from being the 
"baby" of the family, as John Smith (moved by the 
earnest exhortations of the Bishop of London) produces 
more and more children. A Specious Present of mine 
is just the last thin slice that has joined up to my life- 
history. When it ceases to be present and becomes 
past this does not mean that it has changed its relations 
to anything to which it was related when it was present. 
It will simply mean that other slices have been tacked 
on to my life-history, and, with their existence, relations 
have begun to hold, which could not hold before these 
slices existed to be terms to these relations. To put 
the matter in another way : When an event, which was 
present, becomes past, it does not change or lose any 
of the relations which it had before ; it simply acquires 
in addition new relations which it could not have before, 
because the terms to which it now has these relations 
were then simply non-entities. 

It will be observed that such a theory as this accepts 
the reality of the present and the past, but holds that 
the future is simply nothing at all. Nothing has 
happened to the present by becoming past except that 
fresh slices of existence have been added to the total 
history of the world. The past is thus as real as the 
present. On the other hand, the essence of a present 
event is, not that it precedes future events, but that 
there is quite literally nothing to which it has the relation 
of precedence. The sum total of existence is always 



TIME AND CHANGE 67 

increasing, and it is this which gives the time-series a 
sense as well as an order. A moment t is later than 
a moment t' if the sum total of existence at t includes 
the sum total of existence at t' together with some- 
thing more. 

We are too liable to treat change from future to 
present as if it were analogous to change from present 
to past or from the less to the more remote past. This 
is, I believe, a profound mistake. I think that we must 
recognise that the word "change" is used in three 
distinct senses, of which the third is the most funda- 
mental. These are (i) Change in the attributes of 
things, as where the signal lamp changes from red to 
green ; (ii) Change in events with respect to pastness, 
as where a certain event ceases to be present and moves 
into the more and more remote past ; and (iii) Change 
from future to present. I have already given an analysis 
of the first two kinds of change. It is clear that they 
both depend on the third kind. We analysed the 
change in colour of the signal lamp to mean that a red 
section of its history was followed by a green section of 
its history. This is sufficient analysis for a past change 
of quality, dealt with reflectively in retrospect. But, 
when we say that the red section precedes the green 
section, we mean that there was a moment when the 
sum total of existence included the red event and did 
not include the green one, and that there was another 
moment at which the sum total of existence included all 
that was included at the first moment and also the green 
event. Thus a complete analysis of the qualitative 
changes of things is found to involve the coming into 
existence of events. 

Similarlv we have seen that the second kind of 
change involves the third. For the change of an event 
from present to past turned out to depend on the fact 
the sum total of existence increases beyond the limits 
which it had when our given event came into existence. 
Let us call the third kind of change Becoming. It 



()8 SCIENTIFIC THOUGHT 

is now quite evident that becoming cannot be analysed 
into either of the two other kinds of change, since they 
both involve it. Moreover, we can see by direct in- 
spection that becoming is of so peculiar a character 
that it is misleading to call it change. When we say 
that a thing changes in quality, or that an event changes 
in pastness, we are talking of entities that exist both 
before and after the moment at which the change takes 
place. But, when an event becomes, it comes into 
existence; and it was not anything at all until it had 
become. You cannot say that a future event is one 
that succeeds the present ; for a present event is defined 
as one that is succeeded by nothing. We can put the 
matter, at choice, in one of two ways. We can either 
say that, since future events are non-entities, they cannot 
stand in any relations to anything, and therefore cannot 
stand in the relation of succession to present events. 
Or, conversely, we can say that, if future events succeeded 
present events, they would have the contradictory pro- 
perty of succeeding something that has no successor, 
and therefore they cannot be real. 

It has long been recognised that there are two 
unique and irreducible, though intimately connected 
types of judgment. The first asserts that S is or exists ; 
and is called an existential judgment. The second 
asserts that S is so and so, or has such and such a 
characteristic. This may be called a characterising judg- 
ment. The connexion between the two is that a thing 
cannot be so and so without being, and that it cannot be 
without being so and so * Meinong, with the resources 
of the German tongue at his disposal, coins the con- 
venient words Sein and Sosein. Now it seems to me 
that we have got to recognise a third equally fundamental 
and irreducible type of judgment, viz., one of the form : 
S becomes or comes into existence. Let us call these 
genetic judgments. I think that much of the trouble 
about Time and Change comes from our obstinate 

* Uber die Stellung der Gegenstandstheorie, and elsewhere. 



TIME AND CHANGE 69 

attempts to reduce such judgments to the characterising 
form. Any judgment can be verbally reduced to this 
form. We can reduce " S is " to " S is existent." But 
the reduction is purely verbal, and those who take it 
seriously land in the sloughs of the Ontological Argu- 
ment. Similarly "S is future " is verbally a judgment 
that ascribes a characteristic to an event S. But, if we 
are right, this must be a mistake ; since to have a 
characteristic implies to exist (at any rate in the case of 
particulars, like events), and the future does not exist so 
long as it is future. 

Before passing on there is one more verbal ambiguity 
to be noted. The same word is is used absolutely in 
the existential judgment "S is," and as a connective 
tie in the characterising judgment "S is P." Much 
the same is true of the word becomes. We say "S 
becomes," and we say "S becomes P." The latter 
type of judgment expresses qualitative change, the 
former expresses coming into existence. 

The relation between existence and becoming (and 
consequently between characterisation and becoming) 
is very intimate. Whatever is has become, and the 
sum total of the existent is continually augmented by 
becoming. There is no such thing as ceasing to exist ; 
what has become exists henceforth for ever. When we 
say that something has ceased to exist we only mean 
that it has ceased to be present; and this only means 
that the sum total of existence has increased since any 
part of the history of the thing became, and that the 
later additions contain no events sufficiently alike to 
and sufficiently continuous with the history of the thing 
in question to count as a continuation of it. For com- 
plete accuracy a slight modification ought to be made 
in the statement that "whatever is has become." Long 
events do not become bodily, only events short enough 
to fall in Specious Presents become, as wholes. Thus 
the becoming of a long event is just the successive 
becoming of its shorter sections. We shall have to go 



70 SCIENTIFIC THOUGHT 

more fully into the question of Specious Presents at a 
later stage. 

We are left with two problems which we may hope 
that the previous discussions will help us to solve. 
(i) If the future, so long as it is future, be literally 
nothing at all, what are we to say of judgments which 
profess to be about the future? And (ii) What, in the 
end, is our answer to the original difficulty that every 
event is past, present, and future, and that these 
characteristics are mutually incompatible? 

(i) Undoubtedly we do constantly make judgments 
which profess to be about the future. Weather fore- 
casts, nautical almanacs, and railway time-tables, are 
full of such judgments. Admittedly no judgment 
about the future is absolutely certain (with the possible 
exception of the judgment that there will always be 
events of some kind or other) ; but this is irrelevant for 
our present purpose. No historical judgment about 
the past is absolutely certain either ; and, in any case, 
our question is not whether we can have certain 
knowledge about the future, but is the prior question : 
What are we really talking about when we profess to 
make judgments about the future, and what do we mean 
by the truth or falsity of such judgments? 

We cannot attempt to answer these questions till 
we have cleared up certain points about the nature of 
judgments in general. First, we must notice that the 
question: "What is a certain judgment about?" is 
ambiguous. It may mean: "What is the subject or 
subjects of the judgment? " or : " To what fact does the 
judgment refer?" The fact to which a judgment refers 
is the fact that renders it true or false. It is true, if it 
has the peculiar relation of concordance to the fact 
to which it refers ; and false, if it has the relation of 
discordance to this fact. Discordance, I think, is a 
positive relation which is incompatible with concord- 
ance ; it is not the mere absence of concordance. I 
see no reason to suppose that the reference of a 



TIME AND CHANGE 71 

judgment to a fact is a third independent relation over 
and above the relations of concordance and discordance. 
I take it to be just the disjunction " concordance-or- 
discordance " ; and I suppose that to say that J refers to 
F simply means that F is the fact which either makes J 
true by concording with it or false by discording 
with it. 

Now people make many judgments, which have 
nothing to do with the future, but are nevertheless 
apparently about objects which do not, in fact, exist. 
Many English peasants, in the Middle Ages, must 
have made the judgments "Puck exists" or "Puck 
has turned the milk." And the latter of these, of 
course, implies the former. I will assume (in spite 
of Sir Conan Doyle) that Puck does not in fact exist. 
What were these men referring to, in our sense of the 
word? To answer this we have simply to ask: What 
fact made their judgments false? The answer is that 
it is the negative fact that no part of the universe was 
characterised by the set of characteristics by which 
they described Puck to themselves. Their judgment 
boils down to the assertion that some part of the existent 
is characterised by this set of characteristics, and it is 
false because it discords with the negative fact that the 
set in question characterises no part of the universe. 
Naturally they did not know that this was what their 
judgment referred to, or they would not have made it. 
But, in our sense of reference, there is no reason why 
a person who makes a judgment should know what it 
refers to. 

Now it would obviously be absurd to say that what 
these men were talking about was the negative fact that 
no part of the universe has the characteristics which 
they ascribe to Puck. Hence we see the need of dis- 
tinguishing between what a judgment refers to and 
what the person who makes the judgment is talking 
about. What they were talking about was a certain 
set of characteristics, viz., those by which they described 



yi SCIENTIFIC THOUGHT 

Puck to themselves. This may be called the logical 
subject of their judgment. It is something real and 
independent of the judging mind ; having the kind of 
reality and independence which is characteristic of uni- 
versals, and not, of course, that which is characteristic 
of particular existents. Thus, although there is no 
such being as Puck, people who profess to be judging 
about him are not judging about nothing (for they are 
judging about a set of characteristics which is itself 
real, though it does not happen to characterise any 
particular existent). Nor are they referring to nothing 
(for they are referring — though they do not know it — 
to an important negative fact about the existent). 

Since the non-existence of Puck is compatible with 
the fact that the judgment "Puck exists" is an 
intelligible statement about something real, we may 
hope that the non-existence of the future may prove 
to be compatible with the existence and intelligibility 
of judgments which profess to be about the future. 
Up to a point the two kinds of judgment can be treated 
in much the same way. The judgment which is gram- 
matically about "Puck" proves to be logically about 
the set of characteristics by which the assertor describes 
Puck to himself. Similarly the judgment, "To-morrow 
will be wet," which is grammatically about "to-morrow," 
is logically about the characteristic of wetness. The 
non-existence of to-morrow is therefore consistent 
with the fact that the judgment is about something. 

Still there is one very important difference between 
the two kinds of judgment. Judgments like "Puck 
exists" are not only about something; they also refer 
to some fact which makes them true or false. This 
fact may be negative, but it is a real fact about the 
existent world. If we ask what fact judgments ostensibly 
about the future refer to, we must answer that there is 
no such fact. If I judge to-day that to-morrow will 
be wet, the only fact which this judgment can refer 
to, in our sense of the word, is the fact which renders 



TIME AND CHANGE 73 

it true or false. Now it is obvious that this fact is 
the wetness or fineness of to-morrow when to-morrow 
comes. To-day, when I make the judgment, there is 
no such fact as the wetness of to-morrow and there is 
no such fact as the fineness of to-morrow. For these 
facts can neither of them begin to be till to-morrow 
begins to be, which does not happen till to-morrow 
becomes to-day. Thus judgments which profess to be 
about the future do not refer to any fact, whether 
positive or negative, at the time when they are made. 
They are therefore at that time neither true nor false. 
They will become true or false when there is a fact 
for them to refer to ; and after this they will remain 
true or false, as the case may be, for ever and ever. 
If you choose to define the word judgment in such a 
way that nothing is to be called a judgment unless it 
be either true or false, you must not, of course, count 
"judgments" that profess to be about the future as 
judgments. If you accept the latter, you must say that 
the Law of Excluded Middle does not apply to all 
judgments. If you reject them, you may say that the Law 
of Excluded Middle applies to all genuine judgments ; 
but you must add that "judgments " which profess to be 
about the future are not genuine judgments when they 
are made, but merely enjoy a courtesy title by antici- 
pation, like the eldest sons of the higher nobility 
during the lifetime of their fathers. For convenience, 
I shall continue to speak of them as judgments. 

So far then, we have determined two facts about 
judgments which profess to be concerned with the 
future. (a) They are about something, viz., some 
characteristic or set of characteristics ; and {b) they do 
not refer to any fact at the time when they are made. 
This is clearly not a complete analysis. Two further 
points need to be cleared up. (a) If such judgments 
when made do not refer to anything, how is it that, 
if certain events become, the judgment is verified, and, 
if other events become, it is refuted? (b) If such judg- 



74 SCIENTIFIC THOUGHT 

ments are about characteristics, what precisely is it 
that they assert about these characteristics ? 

(a) Suppose I judge to-day that to-morrow will be 
wet. Nothing that may happen to-morrow will be 
relevant to this judgment except the state of the weather, 
and nothing will then make it true except the wetness 
of the weather. This is true enough, but it does not 
prove that the judgment refers to any fact, in our 
sense of reference. With any judgment we can tell 
what kind of fact will verify or refute it, as soon as 
we know what the judgment is about and what kind 
of assertion it makes. But no amount of inspection of 
a judgment itself will show us the particular fact which 
makes it true if it is true and false if it is false. There 
is therefore no inconsistency between the statement 
that we can know at once what kind of fact would 
verify a judgment about the future, and the statement 
that such judgments do not refer to any fact when made. 
(if) As regards any judgment we have to consider 
not only what it is about, but also what it asserts 
about its subject or subjects. These two questions are 
not altogether free from ambiguity, and this ambiguity 
must be cleared up before we consider the special 
question as to what judgments that profess to be about 
the future assert, (i) There is the confusion between 
what a judgment is about and what it refers to. This 
we have already dealt with. (2) There is the distinc- 
tion between what a judgment is ostensibly about and 
what it is really about. If you had asked a peasant, 
who said that Puck had turned the milk, what he was 
talking about, he would have said that he was talking 
about a certain individual fairy. This is what the 
judgment professes to be about. What it is really 
about is a certain set of characteristics. Roughly 
speaking, we may say that what a judgment professes 
to be about can be determined by a grammatical 
analysis of the sentence in which the judgment is ex- 
pressed. Although there is always a connexion between 



TIME AND CHANGE 75 

the grammatical structure of a sentence and the logical 
structure of a judgment, it is highly dangerous to sup- 
pose that what the sentence is grammatically about 
is the name of what the judgment is logically about. 
(3) When these two confusions have been set aside 
and we are quite definitely dealing with the judgment, 
and neither with the fact to which it refers nor the 
sentence which expresses it, there is still a difficulty as 
to how much is to be included under the head of what 
the judgment is about and how much is to be included 
under the head of what the judgment asserts. Take 
first a very simple characterising judgment, like " 3 
is a prime." What is this about, and what does it 
assert? We should all agree that it is at any rate 
about the number 3. But is it about the characteristic 
of primeness too? If you say Yes, what is there left 
for it to assert? If you say No, how can you face the 
obviously equivalent judgment " Primeness is a charac- 
teristic of 3 " ? Exactly the same kind of difficulty 
arises over a relational proposition, like " 3 is greater 
than 2." We should all at this time of day agree that 
it is at least about the numbers 2 and 3. But is it or 
is it not about the relation of greater? I think that we 
must say that the former judgment is about primeness 
as much as it is about the number 3, and that the 
latter is about the relation of greater as much as it is 
about the numbers 2 and 2. Really it is as misleading 
to say that the first asserts primeness as to say that it 
asserts 3. The minimum that it asserts is the prime- 
ness of 3. Similar remarks apply to the second. If 
we like to use the useful word tie, which Mr W. E. 
Johnson* has lately introduced into logic, we might say 
that the first judgment is about the number 3 and the 
characteristic of primeness, and asserts that they are 
connected by the characterising tie. The second is 
about the numbers 3 and 2 and the relation greater, 
and asserts that they are connected by the relational 

* Logic, vol. i. 



76 SCIENTIFIC THOUGHT 

tie in the order 3 to 2. But we might equally well 
distinguish different kinds of assertion, and say that 
the first is about the number 3 and the characteristic 
of primeness, and makes a characterising assertion 
about them. In the case of the second we should 
talk of a relating assertion. 

So far we have purposely chosen examples which 
are about timeless objects, like numbers. Let us now 
take the series of judgments : " It has rained," " It is 
raining," and " It will rain," which are about events, 
and contain an essential reference to time. The first 
may be analysed as follows: "There is an event which 
is characterised by raininess, and the sum total of exist- 
ence when the judgment is made includes all and more 
than all which it includes when this event becomes." The 
second may be analysed as follows : " There is an event 
which is characterised by raininess, and the sum total of 
existence is the same when this event becomes and when 
the judgment is made." Thus judgments about the past 
and the present can be analysed into judgments which 
involve the four familiar types of assertion— the exist- 
ential, the characterising, the genetic, and the relational. 
But the judgment that it will rain cannot be analysed 
in a similar way. It cannot mean anything that begins 
with the statement: "There is an event," for the only 
events that there are are the events that have become up 
to the time when the assertion is made ; the sum total 
of existence does not contain future events. We can 
only restate the judgment in the form : "The sum total 
of existence will increase beyond what it is when the 
judgment is made, and some part of what will become 
will be characterised by raininess." We cannot then 
analyse will away, as we can has been and is now. Every 
judgment that professes to be about the future would 
seem then to involve two peculiar and not further 
analysable kinds of assertion. One of these is about 
becoming ; it asserts that further events will become. 
The other is about some characteristic ; it asserts that 



TIME AND CHANGE 77 

this will characterise some of the events which will 
become. If then we ask : What are judgments which 
profess to be about future events really about? the 
answer would seem to be that they are about some 
characteristic and about becoming. And if it be asked : 
What do such judgments assert? the only answer that 
I can give is that they assert that the sum total of 
existence will increase through becoming, and that the 
characteristic in question will characterise some part of 
what will become. These answers are compatible with 
the non-existence of the future. The only "constitu- 
ents" of the judgment, when it is made, are the 
characteristic — which has the kind of reality which 
universals possess — and the concept of becoming. 
About these the judgment makes certain assertions 
of a quite peculiar and not further analysable kind. 
Something called to-morrow is not a constituent of judg- 
ments which are grammatically about " to-morrow," any 
more than an individual called Puck is a constituent of 
judgments which profess to be about " Puck." 

I have thus tried to show that there is an extreme 
difference between judgments which profess to be about 
future events and these which are about past or present 
events. The former, when made, do not refer to any- 
thing, and therefore are not literally true or false, 
though it is possible for anyone who understands their 
meaning to see what kind of fact will eventually make 
them true or false as the case may be. Again, is now 
and has been need not be taken as new and ultimate 
types of assertion, but will be apparently must be so 
taken. Nevertheless, although the future is nothing 
and although judgments which profess to be about 
future events refer to nothing, they are not about 
nothing. They are about some characteristic and 
about becoming ; and, so far as I can see, they make an 
unique and not further analysable kind of assertion 
about these terms. 

There are just two points that I want to make before 



78 SCIENTIFIC THOUGHT 

leaving this subject, (a) Of course there are plenty of 
ex post facto statements which nominally involve the 
existence of future events. We can say that the Battle 
of Hastings was future to Edward the Confessor. Such 
statements need no special analysis. We merely mean 
that the sum total of existence now includes the Battle 
of Hastings, and that when Edward the Confessor's 
death became it did not include this battle. We, who 
live after both events, are dealing with two parts of the 
existent, which can and do stand in various relations 
to each other ; and so there is no kind of difficulty in 
giving a meaning to the statement. 

(/>) It is commonly held that there can be no certain 
knowledge about the future, but that all judgments 
which profess to be about it consist of more or less 
probable conjectures made by analogy with the past. 
Now we do not always recognise how odd our certainty 
about this is on the assumption that the future really is 
something that has " future existence" as the past really 
is something that has "past existence." We have 
immediate, and not merely inferential, knowledge about 
some past events by direct memory. Hence mere 
difference in date between the act of cognition and an 
event does not necessarily prevent the event from being 
an object to the act. If the future exist, and be just 
that part of the existent which succeeds the present, it 
is difficult to see why a present act of cognition might 
not know an event which is later than itself, just as 
it can know some events which are earlier than itself. 
Why should we not have direct anticipations of some 
future events, just as we have direct memories of some 
past ones, if the future were of the same general nature as 
the past, and simply differed from it by standing in the 
converse temporal relation to the present? Still more, 
why should all claims to direct knowledge of future 
events be regarded as so wildly paradoxical? 

These facts become plausible on two theories about 
the future, one of which we have rejected, and the other 



TIME AND CHANGE 79 

of which is our own. Obviously if to be future just 
means to be incapable of being directly cognised, direct 
cognition of future events could be ruled out as a con- 
tradiction in terms. We have, however, examined and 
rejected this view of the future. But the impossibility 
of absolutely certain knowledge about the future follows 
equally from our theory. We can be absolutely certain 
that an event has the characteristic C only if we are 
directly acquainted with this event and can notice the 
characteristic in it. Now we can be directly acquainted 
only with somethings not with a mere non-entity. On 
our view we cannot stand in the relation of direct ac- 
quaintance to future events, for the same reason which 
prevents us from robbing a Highlander of his breeks. 
We can stand in this relation to present events (in sense- 
awareness) and to past events (in genuine memory), 
because such events are parts of the sum total of 
existence when the cognition in question takes place. 

(ii) The last question that we have to deal with is 
the alleged difficulty that every event is past, present, 
and future ; that these characteristics are incompatible ; 
and that there is no way of reconciling them which 
does not either involve an infinite regress, in which 
the same difficulty recurs at every stage, or a vicious 
circle. This argument has been used by Dr M 'Taggart* 
as a ground for denying the reality of Time. It is 
certainly the best of the arguments which have been 
used for this purpose ; since it really does turn on 
features which are peculiar to Time, and not, like most 
of the others, on difficulties about continuity and infinity 
which vanish with a knowledge of the relevant mathe- 
matical work on the subject. Do the results of our 
earlier discussions in this chapter help us to remove 
this supposed contradiction ? 

Let us take M'Taggart's example of the death of 
Queen Anne, as an event which is supposed to combine 
the incompatible characteristics of pastness, presentness, 

* The Unreality of Time, Mind, N.S., 1908. 



80 SCIENTIFIC THOUGHT 

and futurity. In the first place, we may say at once 
that, on our view, futurity is not and never has been 
literallv a characteristic of the event which is character- 
ised as the death of Queen Anne. Before Anne died 
there was no such event as Anne's death, and "nothing" 
can have no characteristics. After Anne died the sum 
total of existent reality does contain Anne's death, but this 
event then has the characteristic of pastness. No doubt 
I can say "Anne's death was future to William III." 
But I simply mean that, so long as William III was 
alive, there was no event characterised as the death of 
Anne ; and that afterwards, as the sum total of existence 
increased by becoming, it contained both the events 
of William's life and the event of Anne's death. Anne's 
death succeeded William's life so soon as Anne's death 
existed at all, and it succeeds it henceforth for ever ; 
but it did not succeed it while William was alive, 
because it had not become, was not anything, and 
therefore could not have any characteristics or stand 
in any relations. But it might be said that Anne 
herself or William III might have made the judgment: 
"Queen Anne's death is future"; that this is a true 
judgment on their parts; and that it cannot be explained 
in the same way as my ex post facto judgment that 
Queen Anne's death was future. To this I answer that 
the existence and the truth of William's judgment do 
not imply that there ever was an event which has the 
two characteristics of futurity and of being the death 
of Anne. When William made this judgment there 
was no event for it to refer to ; for the event which 
afterwards became, and was the death of Anne, had not 
then become and was not anything. What William 
did was to make a peculiar kind of assertion about 
becoming and about the characteristic of being the 
death of Oueen Anne. He asserted that the sum total 
of existence would increase by further becoming, and 
that some part of what would thus be added would be 
characterised as the death of his sister-in-law. He 



TIME AND CHANGE 81 

was neither talking about nor referring to that particular 
event which did in fact eventually become, and which, 
when it became, was in fact characterised as the death 
of Anne. For, when he made his judgment, there was 
no such event in the whole of reality for him to talk 
about or to refer to. Thus the first thing that we have 
to say with regard to M'Taggart's argument is that 
no event ever does have the characteristic of futurity. 
When we say that a certain event is future, the sentence 
which expresses our judgment is no doubt of the same 
form as when we say that a certain book is green. 
We are therefore tempted to treat the former judgment 
as a characterising judgment, like the latter ; and to 
suppose that the only difference between them is that 
one asserts the characteristic of "futurity" whilst the 
other asserts the characteristic of greenness. From 
what has gone before we conclude that the former 
judgment is not really a characterising judgment at 
all, and that there is no characteristic of "futurity." 
Judgments which appear to characterise events as future 
make a peculiar kind of assertion about some ordinary 
characteristic {e.g. wetness or fineness) ; they do not 
make an ordinary characterising assertion about a 
certain event and a peculiar kind of characteristic (viz. , 
"futurity"). 

Is there anything contradictory in the fact that 
Queen Anne's death has been present and is now past? 
There very well might be if we had to take the change 
of an event in respect to the characteristics of present- 
ness and pastness as analogous to the change of a 
signal lamp in respect to the characteristics of red 
and green. But we have seen that this cannot be done, 
and that the second kind of change depends on the 
first. When Queen Anne's death became, it came 
into relations with all that had already become, and 
to nothing else, because there was nothing else for it 
to be related to. All these relations it retains hence- 
forth for ever. As more events become it acquires 



82 SCIENTIFIC THOUGHT 

further relations, which it did not have, and could not 
have had while those events were non-existent. This 
is all that ever happens to the event in question. 
Suppose we now ask ourselves the question : " Does 
anything that was true of Anne's death when it first 
became get false of it afterwards, through further 
becoming? And, if so, does this raise any logical 
difficulty?" Here we must draw a distinction, (i) 
All the relations which Anne's death entered into with 
the sum total of reality, as it was when this event first 
became, persist eternally for ever afterwards, and are 
wholly unaffected by anything else that may be added 
on to this sum total by further becoming. Hence no 
true proposition about these will ever become false, 
and no false proposition about them will ever become 
true. (2) As further events become they automatically 
enter into various relations with Anne's death, which 
thus acquires additional relations and becomes a con- 
stituent in additional facts. If e.g. my Lord Bolingbroke 
swore when he heard of Anne's death, it is clear that 
something subsequently became true of the death which 
was not true of it when it first became. When Lord 
Bolingbroke had sworn it became true of Queen Anne's 
death that it caused a certain event in his lordship's 
life. And this was not true of Queen Anne's death 
before Lord Bolingbroke had heard of it, and had 
thereby been caused to swear. Thus something, which 
was not true of Queen Anne's death when it became, 
is afterwards rendered true of it by the becoming of 
Lord Bolingbroke's oath. 

Now we are inclined to think that to say that some- 
thing, which was not true of an event, subsequently 
became true of it, is equivalent to saying that something 
which was false of the event, became true of it. This 
is, I think, a mistake; for "not-true" is a wider term 
than " false." Suppose we compare the two statements : 
"It is not true that Queen Anne's death caused the 
earthquake at Lisbon," and : " It is not true that Queen 



TIME AND CHANGE 83 

Anne's death, when it happened, had caused Lord 
Bolingbroke to swear." In the former "not-true" 
is equivalent to "false." For it means that there is 
a certain negative fact (containing both the death and 
the earthquake as constituents) which discords with 
the judgment that the first caused the second. But the 
latter does not mean that at the time of Anne's death 
there was a negative fact, containing Anne's death and 
Bolingbroke's oath as constituents, and discording with 
the judgment that the death causes the oath. For, 
when Anne's death became, there was no such entity 
as Lord Bolingbroke's oath, and therefore no fact of 
which this is a constituent. What happens when Lord 
Bolingbroke swears is not that something which was 
false of Anne's death becomes true of it, but that some- 
thing becomes true of Anne's death which was before 
neither true nor false of it. 

Now I do not think that the laws of logic have 
anything to say against this kind of change ; and, if 
they have, so much the worse for the laws of logic, 
for it is certainly a fact. What the laws of identity, 
contradiction, and excluded middle, between them assert 
is that any proposition is either true or false, cannot 
be both, and cannot alter in this respect. They do not 
assert (and, if they do, they must be amended) that 
the number of propositions, is eternally fixed ; they only 
assert that it cannot be diminished. But it may be 
increased, and it is continually increased by the process 
of becoming which continually augments the sum total 
of existence and thereby the sum total of positive and 
negative facts. Or, to put it in another way, the laws 
of logic apply to a fixed universe of discourse, and we 
can at any moment get a fixed universe of discourse 
by taking the sum total of reality up to that moment. 
But the universe of actual fact is continually increasing 
through the becoming of fresh events ; and changes 
in truth, which are mere increases in the number of truths 
through this cause, are logically unobjectionable. 



84 SCIENTIFIC THOUGHT 

I can hardly hope that what I have been saying 
about Time and Change will satisfy most of my readers, 
or indeed, that it is more than a shadow of the truth, 
if that. It is admitted that this is the hardest knot 
in the whole of philosophy. The Dean of Carlisle 
judiciously remarks that "we cannot understand Time, 
but we shall not understand it better by talking nonsense 
about it." In the hope that I have not darkened counsel 
by words without understanding, I leave this most diffi- 
cult subject, to return at a later stage to the questions 
of one or many time series, the entanglement of Time 
with Space, and the placing and dating of events. 

Additional works which may be consulted with profit : 

B. A. W. Russell, Our Knowledge of the External World, 

Lecture IV. 
A. N. Whitehead, Concept 0/ 'Nature, Cap. III. 
J. M. E. M'TaGGART, The Relation of Time and Eternity 

(Mind, N.S., vol. xviii. No. 71). 
„ The Unreality of Time (MlND, N.S., xvii., 1908). 
H. Bergson, Time and Free- Will. 
„ Matter and Memory. 



CHAPTER III 

" Its eyebrows (of a vivid green) 
Have never, never yet been seen ; 
But Scientists, who ought to know, 
Assure us that it must be so. 
Oh, let us never, never doubt 
What no one can be sure about ! " 

(H. Belloc, The Microbe.) 

The Traditional Kinematics, and its Gradual Modifica- 
tion in the Region of Physics, (i) The Absolute 
and the Relational Theories 

We have now dealt with the traditional concepts of 

Space and Time, and we might turn next either to 

Matter or to Motion. I propose to treat the classical 

doctrine of Motion before touching the problem of 

Matter. As we all know, the concept of Motion has 

been the subject of constant discussion by physicists 

and mathematicians for centuries, and in recent years 

the classical kinematics has been profoundly modified, 

owing to circumstances that have arisen within the 

region of Physics itself. The older arguments between 

supporters of Absolute and Relative Motion, and the 

later ones about the Theory of Relativity, are essentially 

pieces of Critical Philosophy in our sense of the word. 

Thus we may fairly say that, as regards Motion, 

physicists have been their own philosophers, forced 

into this unwelcome position by their own domestic 

difficulties. Now this is not so in the case of Matter. 

The difficulties about Matter, which show the need 

for radical philosophic criticism of that concept, are 

not indigenous to Physics itself. They arise in the 

main when we begin to take into account the way 

85 



86 SCIENTIFIC THOUGHT 

in which we get to know matter through sensation. 
It is the apparent conflict between what our sensations 
tell us and what Physics teaches about matter, com- 
bined with the fact that our sensations are after all 
the only ultimate source of all our alleged information 
on the subject, which compels us to indulge in 
philosophical criticism. The moment we begin this 
criticism we find that it will lead us very far afield, and 
that we cannot stop till we have profoundly modified 
the traditional concepts of Space, Time, and Motion 
too. Now I hope to be able to show that these 
modifications, which are forced on us as philosophers 
when we begin to deal with the concept of Matter, are 
of somewhat the same kind as those which Physicists 
have had to make for purely domestic reasons. If this 
can be shown, even in rough outline, it will greatly 
strengthen the case for the newer views of Space, Time, 
Motion, and Matter. There is much in these views 
which is at first sight highly paradoxical and upsetting 
to common-sense, so that it is of some advantage even to 
the scientist to know that they can be justified on wider 
grounds than the special needs of his science. On the 
other hand, it is always a comfort to the philosopher 
to know that he is not simply bombinans in vacuo, but 
is working on lines which have been found to lead 
to useful results in some concrete region of science. 

This book is written primarily for scientists who 
are interested in philosophy, and secondarily for philo- 
sophers who are interested in science. It has therefore 
been my plan to diverge as gradually as possible from 
the concepts that are most familiar to scientists. Now, 
for the reasons given, the philosophic criticism of the 
concept of Motion is more familiar to most scientists 
than the criticism of the concept of Matter. It therefore 
seems right to treat the former before the latter. I 
am going, then, to deal at present with the purely 
physical arguments which have gradually undermined 
the traditional Kinematics and replaced it by that 



THE TRADITIONAL KINEMATICS 87 

of the Theory of Relativity. In spite of many excellent 
(and more, execrable) popular works which have 
appeared in the last few years, I think there is still 
room for a restatement of these arguments. To many 
scientific readers they will of course be perfectly familiar, 
but it will do no harm to the reader who is primarily a 
philosopher to put himself au courant with the present 
position in Physics before going further. At a con- 
siderably later stage, when we have seen what modifica- 
tions in the traditional concepts of Space and Time are 
forced on us by our criticisms of the traditional concept 
of Matter, we shall return to the present subject, and try 
to connect the physical with the philosophical doctrines. 
We have at least four general kinematic concepts 
to consider, viz., the Absolute Theory of Motion, the 
Relational Theory of Motion, the Special Theory of 
Relativity, and the General Theory of Relativity. This 
is approximately the historical order in which these 
concepts have arisen in Physics since the Renaissance. 
We must remember, however, that the controversy 
between the Absolute and the Relational Theories of 
Motion had a long history before ever modern Mechanics 
was founded by Galileo, Descartes, Huyghens, Newton, 
and Leibniz. This controversy was inherited by 
Mechanics, and the opposite sides were upheld by two 
such eminent contemporaries as Newton and Leibniz. 
I shall treat the concepts in their historical order, putting 
the Absolute Theory before the Relational Theory of 
Motion. But, when the various theories have been 
clearly stated and the pros and cons have been weighed, 
a further task will confront us, viz., to try to exhibit 
their logical order and interconnexions. I must confess 
that I have not seen a satisfactory account of this point 
in any work on the subject. It seems commonly to 
be assumed that the logical order has been the same 
as the historical, and that the successive kinematic 
concepts have represented a steady development of the 
doctrine that motion is purely relative. Yet some of 



88 SCIENTIFIC THOUGHT 

the chief exponents of the General Theory of Relativity, 
which is the latest phase of kinematics, use language 
which seems to imply a thoroughly Absolute Theory. 
We hear of " kinks" in Space or in Space-Time, and 
we are told that they modify the motions of matter, 
or that matter consists of such "kinks." All this is 
extremely puzzling after one has been led to believe 
by the same writers that the General Theory of 
Relativity is the final triumph of the Relational Theory 
of Motion. I think we shall find that the logical 
connexions are not so simple as we have been told ; 
and it will certainly be useful to do our best to throw 
some light on this dim spot. We cannot, however, 
profitably discuss this question until we have seen what 
precisely the various theories assert. 

The Absolute and Relational Theories of Motion. In 
the last two chapters we have been discussing the 
traditional concepts of Space and Time. Now the 
kinematic concept which strictly corresponds to these 
is that of Absolute Motion. In accordance with the 
traditional concepts of Space, Time, and Matter, the 
three are largely independent entities. The traditional 
view does not as a rule go very deeply into the question 
of their mutual relations, but I think the following 
would be a fair statement of what it tacitly assumes 
on this subject : Time could have existed without Space 
or Matter; Space could not have existed without Time, 
but it could have existed without Matter ; Matter could 
not have existed without both Space and Time. Space 
needs Time in order to endure, but the only connexion 
is that all points of Space endure unchanged for ever. 
Matter needs Time in order to endure, and it needs 
Space in order to have place and shape, which are 
essential to it. With Matter there begins the possibility 
of Motion ; Matter need not have moved, but as a fact 
it does so from time to time. 

The alternative between the Absolutist and the 
Relationist Theory of Time may be illustrated as follows : 



THE TRADITIONAL KINEMATICS 89 

We say that the Battle of Hastings precedes the Battle 
of Waterloo by a certain amount, viz., 749 years. The 
two battles are events in the world's history, and the 
Absolutist and the Relationist agree that a certain 
temporal relation subsists between them, and that it 
has a certain measure in terms of the usual units. The 
whole question between them as to Time is the follow- 
ing : Is this relation simple, direct, and unanalysable, 
connecting the two events in question and nothing else, 
or is it a complex compounded out of other relations 
which involve other terms in addition to the two events? 
The former alternative is taken by the Relationist, the 
latter by the Absolutist. On the former view there is 
not something called Time which could exist even 
though there had been no events ; Time just consists 
of the relations of before and after among events. These 
relations have various magnitudes which can be measured 
by comparison with the temporal relation between some 
standard pair of events, such as the successive occupa- 
tions of the same position on a dial by the hands of a 
suitably standardised clock. 

The Absolutist, on the other hand, holds that the 
temporal relations between events are not direct and 
unanalysable ; they are really compounded out of 
relations of two wholly different kinds. On this view 
there is something called Time which is composed of 
simple entities called moments ; and it is only moments 
which can strictly be said to be before or after each 
other. There is further a certain peculiar relation 
between events and moments which is denoted by the 
word at. At is a. many-one relation, i.e. many different 
events can be at the same moment but no momentary 
event can be at more than one moment. The Absolutist 
analyses the statement that the Battle of Hastings 
precedes the Battle of Waterloo by 749 years into 
the three following propositions: (1) The Battle of 
Hastings happened at a certain moment t v (2) The 
Battle of Waterloo happened at a certain moment t % . 

G 



90 SCIENTIFIC THOUGHT 

(3) The moment f l eternally precedes the moment t 2 
by 749 years. (I am neglecting the fact that both 
battles took up a finite time and therefore did not liter- 
ally happen at two moments. This is not important for 
the present purpose, and can quite easily be dealt with 
on either theory.) 

It is important to notice that the traditional Absolu- 
tist and the traditional Relationist agree in holding that 
there is something that can be called the dates of the 
two battles and something that can be called the time- 
lapse between them. Neither of them would admit that 
the same pair of events could stand in several different 
temporal relations ; that, for instance, they might be 
both contemporary and yet one earlier than the other, 
or again that they might precede each other by several 
different amounts. They agree that there is one and 
only one temporal relation between a given pair of 
events, and they only differ as to the right analysis of 
this relation. It is important to notice this, because it 
is here that the Theory of Relativity differs from both 
of them. For, as we shall see, this theory denies that 
there is a single relation which can be called the time- 
lapse between a given pair of events. 

Now that we have got the difference between the 
Absolute Theory of Time and the Relational Theory 
clear we can briefly consider the arguments between 
them. These fall into two classes, viz., those which 
apply directly to Time and those which apply to it only 
indirectly through the question of Motion. Absolute 
motion implies absolute Time and Space, though there 
will, of course, be relative motion even if there be 
absolute Time and Space. The Absolute Theory does 
not deny relative motion, but simply asserts that all 
relative motion is the appearance of absolute motions. 
The arguments for and against these theories, which 
depend on motion, may be reserved for the moment, 
and we will now consider those which apply directly 
to Time. 



THE TRADITIONAL KINEMATICS 91 

The main merit of the Relational Theory is that it 
is simpler and keeps closer to the observable facts. We 
can observe events, and if two events fall into the same 
specious present, or if one is sensed and the other 
remembered, we can directly observe the temporal 
relation between them. We cannot perceive moments 
of Time. Nor can we say that they are hypothetical 
entities, like atoms and electrons, which we also cannot 
perceive. We accept the latter because there are certain 
sensible facts which we can explain with them and can- 
not easily explain without them. But, whilst electrons 
are supposed to be causes with sensible effects, bare 
moments are not supposed to do anything or to produce 
any effects, sensible or otherwise. 

Undoubtedly there is something more than mere 
relations in Time. We have already seen that the Time 
series has a definite intrinsic sense, and that this arises 
because there is a continual addition to the sum total 
of existence, whilst nothing that has ever existed ceases 
to do so save in a derivative and analysable sense. 
Even though there were no "change" in the ordinary 
sense of the word, i.e. if every fresh slice of existence 
were qualitatively indistinguishable from all its pre- 
decessors, there would be this continual becoming. 
But, so long as this absolute feature in Time is recog- 
nised, there seems no objection to the Relative Theory 
as such. If it has to be rejected, it will not be in favour 
of the Absolute Theory but in favour of something still 
more relativistic than itself. 

A minor objection to the Relational Theory of Time, 
as stated in most mechanics books, is that it is incom- 
plete. Relativists, as well as other people, constantly 
talk in practice of moments and of several events 
happening at the same moment. For the Absolutist, 
of course, such statements are literal expressions of fact. 
For the Relativist they cannot be so, since he does not 
literally believe in the existence of moments. It is 
therefore his duty to give a definition of what he means 



92 SCIENTIFIC. THOUGHT 

by "moments," which shall (a) be compatible with his 
theory, and (/>) compatible with the common usage of 
this word by himself and others. This duty he invari- 
ably shirks. The problem can, however, be solved by 
the Method of Extensive Abstraction. Two applications 
of it will be needed: (i) to define momentary events 
in terms of finite events and their relations of partial 
overlapping", and (2) to define moments. A moment is 
eventually defined as a class of contemporary momentary 
events. Thus the objection under discussion is not 
intrinsic to the Relative Theory of Time, but only to 
the common presentment of it. 

Let us now consider the difference between the 
Absolute and the Relational theories of Space. This 
is much the same as the difference between the two 
theories of Time. It is, I think, harder to accept a 
purely relative theory of Space, because of certain 
additional complications which turn up here. On the 
Relational Theory spatial relations directly connect bits 
of matter, e.g. the theory says that Cambridge is 
60 miles N.N.E. of London, and takes this to be a 
direct relation between the two towns. The Absolute 
theory would analyse the fact into three propositions, 
viz. : (1) London is at a certain point p x of Absolute 
Space ; (2) Cambridge is at a certain point p., of 
Absolute Space ; and (3) p 2 is 60 miles N.N.E. of p y * 
The Absolute Theory thus assumes certain entities, 
which may be called geometrical points, in addition to 
matter ; spatial relations directly connect these. They 
only indirectly connect pieces of matter in so far as 
these are at the geometrical points in question. 

Now there is an additional complication in the case 
of Space which is not present with Time. Events 
always have the same temporal relations to each other ; 
the Battle of Hastings always precedes the Battle of 
Waterloo by 749 years when the latter Battle has once 
become. But bits of matter move about ; consequently 

* I am neglecting here the motion of the earth. 



THE TRADITIONAL KINEMATICS 93 

statements about the distance from one bit of matter 
to another or about the relative position of two bits of 
matter are ambiguous. A train travelling from London 
to Edinburgh by the East Coast Route is sometimes 
to the East of London and sometimes to the West of 
it, and is constantly at different distances from it. The 
way in which the Absolute Theory deals with these 
facts is the following : It holds that the points of 
Absolute Space have to each other purely geometrical 
relations which are wholly independent of Time. It 
puts the burden of change on the relation at, which 
connects bits of matter with points of Space. What 
it says is that at, in the present sense, is a three-term 
relation which always connects a bit of matter, a 
geometrical point, and a moment of Time. The 
simplest statement that you can make about the position 
of a bit of matter is that it is at such and such a 
point at such and such a moment. Another way of 
putting it is that the presence of a bit of matter at a 
geometrical point is an event, and that, like all events, 
this occupies a certain moment of Absolute Time. The 
relation of being at a point at a moment is held to 
have certain properties, which are just worth mention- 
ing. (1) Two bits of matter cannot be at the same 
point at the same moment. This property expresses 
the impenetrability of matter. (2) One bit of matter 
cannot be at two different points at the same moment. 
(The only alleged exception to this is the Body and Blood 
of Christ in the Celebration of the Eucharist.) (3) If one 
bit of matter is at two different points at two different 
moments it must be at a continuous series of inter- 
mediate points at the intermediate moments. This 
expresses the fact that bits of matter do not suddenly 
leave one place and afterwards turn up at another 
without following a path from the first to the second. 
(4) Every bit of matter is at some point or other at all 
moments. This expresses the indestructibility of matter. 
Now all these propositions certainly express im- 



04 SCIENTIFIC THOUGHT 

portant alleged facts which arc commonly believed to 
he true of matter, and any theory must contain them 
in some form. On the Relational Theory of Space 
it is clear that they will need a great deal of rein- 
terpretation, since that theory believes neither in 
geometrical points, nor in moments, in the literal senses 
of those words. It follows that if the Relational Theory 
of Space is to be of the slightest use, it must give 
meanings to all these statements which (a) shall not 
imply the literal existence of points or moments, and 
(/>) shall nevertheless be equivalent in practice to 
these propositions. I need scarcely say that writers of 
mechanics books, who start by telling their readers that 
Space is relative, never attempt to recast these state- 
ments in terms of their theory, and never even mention 
or apparently recognise the need of doing so. 

Now this fact, that things move about, at once 
introduces a difficulty into the notion of distance and 
relative position on the Relational Theory. We very 
often need to know the distance between one thing at 
one moment and another thing at another moment. 
When we try to measure the velocity of anything it 
is evidently necessary to know the distance between 
one piece of matter at the time of starting and another 
piece of matter at the time of arrival. Again, if we 
use a measuring rod which has to be taken up and 
laid down several times between A and B, it is clear 
that what we directly measure is neither the distance 
between A and B at t x (the moment when we begin to 
measure) nor the distance between A and B at t t (the 
moment when we cease to measure). If in certain 
cases the measured distance is held to agree with the 
momentary distance this must be a matter of inference, 
and it will be necessary for the Relational Theory to 
state and justify the assumptions made and the conven- 
tions used in drawing these inferences. 

Now the Absolute Theory can, of course, give a 
perfectly definite meaning to the distance between a 



THE TRADITIONAL KINEMATICS 95 

body at one moment and the same or a different body 
at another moment. What it says is that the distance 
required is the distance between the place where the 
one body was at the first moment and the place where 
the other body is at the second moment. In ordinary 
life we do constantly use this phraseology ; but we 
forget that, whilst it has a literal meaning on the 
Absolute Theory, it needs to be given a meaning on 
the Relative Theory. For, on that theory, the primary 
meaning of distance is distance between two bodies at 
the same moment. And, as soon as this is seen, we 
see further that the relative theory of Space cannot be 
complete without some criterion of simultaneity at 
different places. This example brings out rather well 
the characteristic merits and defects of each type of 
theory. The Absolute Theory does give a definite 
meaning to the notion of distance between two bodies 
at different moments ; but, since we certainly cannot 
perceive points of Absolute Space, it fails to explain 
how we ever know that we are measuring distance in 
the sense defined. On the other hand the Relational 
Theory gives a clear meaning only to the notion of 
distance between two bodies at the same moment ; and 
this is not enough for practical or scientific purposes. 
But it does stick to bodies, that is to things that we can 
actually perceive and deal with. 

It is pretty evident that the Relational Theory 
suffers from not being thorough enough, and not fully 
recognising its responsibilities. It ought to start with 
events, and to take the relation of distance between 
contemporary events as fundamental. The notion of 
bodies and of the distances between bodies at different 
times will have to be built on this basis ; you cannot 
take either Space or Time or Matter as something given. 
There is a common matrix out of which the concepts 
of all three are developed by experience and reflection 
thereon. The Relational Theory needs to define some 
sense of Space, which shall still be relative but shall not 



96 SCIENTIFIC THOUGHT 

be merely momentary. Science and common-sense 
require a Space which shall be timeless, in the sense 
of enduring unchanged throughout Time : a collection 
of momentary Spaces is not enough. It is one of the 
great merits of Whitehead to have grasped this point. 
The Absolute Theory does offer us a timeless Space ; 
but, as this can neither be perceived nor inferred 
causally from what is perceptible, it is rather like 
the offer of a gold brick or a Castle in Spain. The 
Relational Theory (whatever may be its pretensions) 
only offers us a collection of momentary Spaces. 
This has at least two disadvantages: (i) that strictly 
momentary relations between bodies can no more 
be directly observed than distances between points of 
Absolute Space ; and (2) that motion becomes, not 
change of position within a Space, but a movement out 
of one momentary Space into another momentary Space. 
The Relational Theory can hardly solve these unsettled 
problems without raising precisely those questions 
which lead on to the Special Theory of Relativity. 

We will now desert the subject of Absolute v. 
Relative Space, as such, for the present, and consider 
those arguments on the subject which depend on the 
question of Absolute v. Relative Motion. It is doubtful 
whether people would ever have worried their heads 
greatly about Absolute Space and Time, had it not been 
that there seemed to be very grave difficulties about 
purely relative motion. The question has really arisen 
twice in the history of modern physics, first at the 
foundation of the classical dynamics by Galileo and 
Newton, and then again in connexion with electro- 
dynamics in quite recent years. 

It is usual for scientific writers with a tincture of 
philosophy to talk as if plain common-sense unhesitat- 
ingly holds motion to be purely relative, and as if 
it were only persons debauched by metaphysics who 
believe in absolute motion. This is of course a pro- 
found mistake. It is indeed true that the plain man 



THE TRADITIONAL KINEMATICS 97 

does not mean by motion absolute motion as defined 
by Newton. But he is perhaps even more shocked by 
the theory that all motion is purely relative, when once 
the logical consequences of that theory are explained 
to him. Naturally, the scientific theories both of 
absolute and of relative motion are highly abstract 
intellectual analyses of facts which the plain man is 
content to see and feel without analysing. Still, it 
would not be going too far to say that the analysis 
offered by the absolute theory seems to common-sense 
nearer to the facts than that proposed by the Relationists. 
This is hidden by the very half-hearted and obscure 
way in which most Relationists state their views ; in 
practice it is almost as difficult to take a consistently 
relational view about motion as it is to bear constantly 
in mind the fact that men at the antipodes do not have 
the uncomfortable feeling that we should have if we 
were hanging head downwards with our feet fixed to 
the ceiling. Let us then try to state the two theories 
clearly and to draw their logical consequences. Absolute 
motion is the passing of a body from one point of 
Absolute Space to another. Absolute rest is the 
remaining of a body at a point of Absolute Space. 
Relative motion has the same meaning on both 
theories ; it is just a change in the relative positions 
of two bodies. The difference about it is that the 
Relationists say that all motion simply is a change in 
the spatial relations of one body to others, whilst the 
Absolutists say that there is absolute as well as relative 
motion and that the two must be distinguished from 
each other. On the Absolute Theory all relative motion 
implies absolute motion, and is the appearance of it to 
us, but a knowledge of relative motion does not suffice 
to determine unambiguously the absolute motions 
involved. Thus, suppose that A and B are two bodies, 
and that u is the rate at which the distance between 
them is increasing. Then u is a relative velocity. The 
Absolutist says that it must be due to absolute motions 



98 SCIENTIFIC THOUGHT 

in A or in B or in both, and that all that we can say 
about thorn is that their difference is equal to u. 

Now the point at which the purely relative theory of 
motion conflicts with common-sense is that it will never 
allow you to say of any two bodies that one is moving 
and that the other is at rest. Distance between A and 
B is a perfectly mutual relation ; if the distance between 
A and B increases at a certain rate the distance between 
B and A ipso facto increases at the same rate. If then 
motion just means rate of change of distance between 
bodies there is no sense in saying that A moves and B 
stands still. Suppose now that I am the body A and 
that B is the wall of the room. Common-sense is 
perfectly sure that I move and that the wall stands 
still. But for the consistent Relativist this is simply 
nonsense ; it is true in precisely the same sense, and 
in the only sense in which he admits motion, that the 
wall moves towards me. Thus common-sense seems 
here to be much more on the side of the Absolutist 
than on that of the Relationist. It quite admits that, 
in particular cases, it is difficult or impossible to tell in 
what proportions a particular relative motion ought to 
be divided between the two bodies, but it is quite 
convinced that in ever^ case there is a genuine meaning 
in the question : What is the real velocity of each body ? 
This question, as we have seen, has a perfectly definite 
meaning on the Absolute Theory, but its meaning is 
not obvious on the Relational Theory. 

Of course I do not regard this common-sense objec- 
tion as at all conclusive, for I think that the Relationist 
can make a fairly satisfactory answer to it. He will 
say: "You think that certain bodies are absolutely at 
rest and others in motion, not because there is really 
anything but relative motion, but because you tacitly 
assume a certain body for relating all others to." This 
body, for the ordinary man, is the earth. He says 
that the wall is at rest because it does not move relatively 
to the surface of the earth ; he says that he himself 



THE TRADITIONAL KINEMATICS 99 

moves because he does change his position with respect 
to this body of reference. It is very easy to forget 
about a relation altogether if we always tacitly relate to 
the same term in a whole series of judgments. If our 
common-sense friend replies that when he moves he 
gets tired, whilst when other things move and he 
stands still he does not get tired, the Relativist can 
easily deal with this objection. He will say: "All 
motion is relative, and all relative motions are equally 
genuine facts ; but they do not all have the same effects. 
When you and the earth move relatively to each other 
effects are produced in your body, but when you rest 
relatively to the earth and merely move with respect to 
other things which are themselves in motion with 
respect to the earth, such as tram-cars, no such effects 
are produced. This is just a law of nature which we 
have to recognise." 

So far the Relationist has a perfectly good case. 
It is when we come to deal with mechanics, and 
particularly with rotation, that his difficulties begin 
to accumulate. We will deal with rotation first, 
because it can be discussed without any knowledge of 
the laws of mechanics, and because it furnished Newton 
with one of his strongest arguments in favour of absolute 
rotation. Suppose that you take a pail of water and 
hang it up by a string, then twist the string a number 
of times and let it untwist itself. The pail will, of 
course, spin rapidly round its axis. At first the water 
will not spin, but gradually it will take up the spinning 
movement of the pail, and eventually the water and 
the pail will be spinning as one rigid body. Now stop 
the pail. The water will go on spinning for some time 
till it is gradually brought to rest by friction. Now 
what we have to notice is this : At the beginning of 
the experiment, i.e. when, in ordinary language, the 
bucket is spinning and the water is still at rest, the 
water has its maximum velocity of rotation with respect 
to the pail. And at this stage the surface of the water 



ioo SCIENTIFIC THOUGHT 

is quite flat. At the second stage of the experiment, 
when, in ordinary language, we should say that the 
water had picked up the speed of rotation of the pail, 
the water has no rate of rotation with respect to the 
pail. Yet at this stage the surface of the water is 
depressed in the middle, so that it becomes a paraboloid 
of revolution. Now we all say that this depression is 
due to the rotation of the water. But, if we confine 
ourselves to relative rotation, we see that the depression 
was nil when the relative rotation was a maximum, and 
that it was a maximum when the relative rotation is nil. 
If we now pass to the next stage of the experiment, 
where, in ordinary language, the pail has been brought 
to rest and the water is still rotating, we have again a 
maximum rate of relative rotation, but this is now 
accompanied by a maximum depression in the surface 
of the water. Thus there seems to be no regular con- 
nexion between relative rotation and depression at all ; 
for the depression can be a maximum both when there 
is no relative rotation and when the relative rotation is 
a maximum, and the depression can be nil both when 
there is maximum relative rotation — as at the beginning 
— and when there is no relative rotation — as at the 
end of the experiment. 

These are the facts which led Newton to hold that 
we must distinguish between absolute and relative 
rotation. The argument comes to this : If we take all 
rotation to be simply and solely the rotation of one body 
with respect to another we can find no general law 
connecting rotation with depression. Yet we are all 
agreed that in some sense the depression is due to 
the rotation. Newton's suggestion was that absolute 
rotation, and it alone, produces physical changes like 
the depression of the water in the pail and the flattening 
of the earth at the poles. It is true that we can observe 
only the relative rotations of bodies ; but these are 
appearances of absolute rotations, and by studying and 
measuring such physical consequences as depression 



THE TRADITIONAL KINEMATICS 101 

and flattening we can ascribe to each of the bodies its 
proper amount of absolute motion. 

Now of course the facts on which Newton based 
his argument are genuine and very important. But 
they certainly do not necessitate Newton's conclusion, 
although that is no doubt one way of explaining them. 
They can equally well be explained without recourse to 
absolute motion. If we reflect, we shall see that it is 
logically impossible that premises which are wholly 
about bodies, such as water and pails, and about their 
shapes and relative motions, could necessitate con- 
clusions about something entirely different, viz., Absolute 
Space and Absolute Time. By a logical argument you 
may learn of new relations between the terms that are 
mentioned in the premises, but you cannot possibly 
learn about the existence of other terms of a quite 
different kind from any that were mentioned in the 
premises. So we can see at once, from purely logical 
considerations, that Newton's argument cannot neces- 
sitate a belief in absolute motion. What we can 
legitimately argue is that, if there be such things as 
absolute Space, Time, and Motion, it is in rotation that 
they first disclose themselves by producing observable 
effects in matter, and that by studying these phenomena 
we may be able to detect the presence and measure the 
magnitude of the absolute motion of each body. 

But, as I have said, the Relationist can interpret the 
pail experiment in terms of his theory. If we reflect 
carefully on the results of that experiment, we see that 
all that it tells us is that one particular relative rotation 
is not connected by any simple law with the depression 
of the water in the pail. It shows that the relative 
rotation of water and bucket is irrelevant. It does not 
in the least follow that no relative rotation is relevant. 
At the beginning of the experiment the water was at 
rest relatively to the fixed stars, at the middle it was 
rotating, and at the end it was again at rest with respect 
to them. What the Relationist must say is therefore 



102 SCIENTIFIC THOUGHT 

the following: "There is nothing but relative rotation, 
and any body that you choose to mention has at one 
and the same time all sorts of different relative rotations ; 
for instance, the water at the beginning is rotating with 
respect to the pail and is at rest with respect to the fixed 
stars. Each of these states of motion is equally real 
and there is no incompatibility between them, because 
they are not properties of the water alone but are 
relations between it and other things. It is no more 
unreasonable to say that the water is at once at rest and 
in motion than it is to say that a man is at once a father 
and a son ; it only seems odd because we are haunted 
by the ghost of the Absolute Theory. But of all these 
various equally real and co-existing motions some only 
are connected by simple laws with physical changes in 
the water. Relative rotation between the water and the 
fixed stars causes depression of the surface of the latter ; 
relative rotation between the water and the walls of the 
pail causes no such depression if the water be at rest 
with respect to the fixed stars." This answer of the 
Relationist seems to me to be perfectly compatible 
with all the facts of the pail experiment and to be 
perfectly consistent with itself. 

I will now consider certain objections which have 
been brought against this interpretation of the facts. 

(i) It is sometimes said: Suppose the water stayed 
still and that the fixed stars rotated round it ; the water 
would be moving relatively to the fixed stars. On the 
above explanation the water ought to be depressed. 
Is it reasonable to suppose that the mere rotation of 
the fixed stars would have any effect on the water in 
the pail? This objection is merely silly and circular. 
It is based on an assumption which has a meaning on 
the Absolute Theory and no meaning at all on the 
Relational Theory. On the Absolute Theory there is 
a sense in distinguishing between the case where the 
water rotates and the stars keep still and the case where 
the stars rotate and the water keeps still. But the dis- 



THE TRADITIONAL KINEMATICS 103 

tinction is meaningless on the Relational Theory. The 
argument in question is therefore irrelevant as opposed 
to the Relational Theory. It is really circular, for its 
premise only has a meaning for a man who has already 
rejected the Relative Theory, and, therefore, it cannot 
consistently be used as an argument against this 
theory. 

(2) A stronger objection is the following: Even 
if the sky had always been covered with thick clouds, 
so that the fixed stars had never been observed, 
we could still have discovered that the earth rotates, 
have determined its axis, and have measured its rate 
of rotation by means of the gyrostatic compass and 
Foucault's pendulum. What is it that we discover and 
measure in such cases if it be not the absolute rotation 
of the earth ? How can it be the rotation of the earth 
relative to the fixed stars, since they do not come into 
the question at all? I think that this objection is 
fallacious, but it needs a little reflection to answer it. 
I will take the case of Foucault's pendulum ; and neglect 
the gyrostatic compass, which is harder to discuss 
without mathematics. It will suffice to say that the 
answer that I shall give about Foucault's pendulum, 
if valid at all, will apply equally to the gyrostatic 
compass. 

To simplify matters we will suppose that the compass 
is hung up at the North Pole and started swinging. 
Make a chalk mark on the ground where the plane in 
which the pendulum starts swinging cuts the earth. 
As time goes on you will find that the pendulum no 
longer swings in this plane ; if you draw another such 
chalk line it will make an angle with the first. In 
fact, the plane will slowly rotate, and the time of its 
rotation will be twenty-four hours. If this experiment 
be done anywhere else on the earth, analogous results 
will be got. The actual measurements will depend on 
the latitude, and it will be found that they are all 
connected with each other and with the latitude by a 



104 SCIENTIFIC THOUGHT 

simple law. The fact to be noticed is that what has 
been measured in all cases is a relative rotation between 
the plane of swing- of the pendulum and the earth's 
surface. Let us suppose that the sky were always 
covered with thick clouds so that the fixed stars coidd 
never be seen. What people would probably have 
said would be the following: "All pendula slowly 
rotate their planes of rotation with respect to the 
earth, and the way in which they do this at different 
places follows a simple law." 

Now, if motion be purely relative, this is precisely 
equivalent to saying that the surface of the earth rotates 
with respect to the planes of swinging pendula. It 
follows that a perfectly clear meaning could have been 
given to the rotation of the earth on the Relative 
Theory, even if no stars had ever been observed. 
Suppose some speculative scientist had said: "There 
may be other bodies beyond those thick clouds ; if so, 
does the earth rotate at the same rate with respect to 
them?" Of course, no answer could have been given. 
We who can see the fixed stars know that the planes 
in which pendula swing do not rotate with respect to 
them, and we therefore know that the rotation of the 
earth or of any other body with respect to the plane 
of swing of a pendulum is the same as its rotation 
with respect to the fixed stars. This particular fact 
of nature would, of course, have been hidden from us 
if we had never seen the stars ; but otherwise we 
should be in exactly the same position as we are in 
now. We can say: "The earth rotates at such and 
such a rate both with respect to the fixed stars and 
with respect to the planes of pendula." Men who had 
never seen the fixed stars could only make the latter 
part of this assertion. We know an extra fact which 
they do not, but what each of us knows is equally about 
relative rotation. 

(3) The third objection is one that is constantly 
mixed up with the one that has just been discussed, 



THE TRADITIONAL KINEMATICS 105 

but really is quite different from it. It is said: "If 
there were no fixed stars the earth could not be rotating 
with respect to them. Now you say that it is rotation 
with respect to the fixed stars which causes the flatten- 
ing of the earth at the poles and the depression of the 
water in a rotating pail. Can you seriously maintain 
that, if the fixed stars were annihilated, the earth would 
become perfectly spherical and the water in the pail 
perfectly flat? You certainly ought to hold this. For 
you say that the cause of the depression of the water 
is its rotation with respect to the fixed stars. If the 
fixed stars ceased to exist, this relative rotation would 
ipso facto vanish too. The alleged cause of the depres- 
sion having thus ceased to exist, we may presume that 
the depression itself would cease too." 

Before discussing this argument, I want to point 
out its precise connexion with the previous one, and 
the cause of the frequent confusion between the two. 
The present argument deals with the physical causation 
of such phenomena as the flattening of the earth at the 
poles, and the depression of the water in a spinning 
pail. It points out an implication of the Relational 
Theory which its supporters are very liable to forget. 
The theory says that the cause of such phenomena is 
the rotation of the earth or the pail with respect to 
some other body or bodies. Now, if this is to be 
literally true, it would seem that the existence of one 
at least of the assigned bodies of reference must be an 
essential part of the cause of the physical phenomena 
in question. Relationists are inclined to regard the 
fixed stars, or whatever frame of reference they may 
happen to use, as mere axes of reference, and in no 
sense causal factors. The present argument shows 
that this is inconsistent. To square the Relational 
Theory with the facts, it is necessary to hold that certain 
relative motions stand out from all others in producing 
observable physical consequences. Now these out- 
standing relative motions are those which bodies have 

H 



106 SCIENTIFIC THOUGHT 

witli respect to certain bits of matter, such as the fixed 
stars. These particular bits of matter are thus put in 
a unique position among all other bodies. Motion 
with respect to any one of this particular set of 
bodies produces physical phenomena ; otherwise similar 
motions with respect to other bodies do not produce 
similar physical consequences. Thus the existence of 
this privileged set of bodies is an essential factor in 
the production of these particular physical phenomena, 
and we have no right to suppose that these phenomena 
would continue to happen if all the bodies in this 
set were annihilated. (It is not necessary to suppose 
that the existence of any one member of the set, e.g. 
the fixed stars, is essential. What does seem to be 
essential is that there should be at least one member of 
the set, though it is immaterial which particular one 
it may be.) This is the basis of the present argument, 
and the force of it is that it is hard to believe that 
the existence of a certain privileged set of bodies is a 
necessary condition of the flattening of the earth or the 
depression of the water. 

Now the previous argument was not about physical 
causation, but was about the meaning of and the 
evidence for the statement that the earth rotates. It 
suggested that, since we could know that the earth 
rotates and measure the rate at which it does so, even 
though we had never seen the fixed stars, we cannot 
mean by the statement that the earth rotates simply 
that it does so with respect to the fixed stars. And it 
concluded from this that, when we talk of the rotation 
of the earth, we must mean absolute rotation, and that 
we must be able to detect and measure it by observations 
made on purely terrestrial bodies. As we have seen, 
the premise of this argument and the first part of its 
conclusion are true, but its final conclusion does not 
follow. What we observe in these purely terrestrial 
experiments is still relative rotation, and what men who 
could not see the fixed stars would mean when they 



THE TRADITIONAL KINEMATICS 107 

said that the earth revolved, would be that it does so 
with respect to the plane of a swinging pendulum. 
We who can observe the fixed stars have found out the 
additional fact that the rotation of the earth with respect 
to them is the same as its rotation with respect to a 
pendulum swinging at the North Pole. 

The arguments, then, are entirely different. Why 
is it that they are so often mixed up? I think the 
reason is the following : It is thought that, since you 
could find out the rotation of the earth without knowing 
anything about the fixed stars, therefore the fixed stars 
cannot be an essential part of the cause of such 
phenomena as the flattening of the earth. This is, 
however, a very bad argument. We can find out a 
good deal about the symptoms and treatment of 
influenza, though no one has ever seen an influenza 
germ. This does not prove that these symptoms do 
not depend on a germ, or that they would not cease 
altogether if the germ were exterminated. 

Having cleared up the connexions,real and imaginary, 
between these two arguments, let us consider the second 
of them. Several answers might be made to it. The 
first, which was made by Mach,* seems to me to be 
logically sound, and to contain an important truth, 
though — as I shall point out later — it does not altogether 
satisfy our physical instincts. The argument that we 
are discussing appeals to our conviction that such 
remote bodies as the fixed stars cannot really be 
essential factors in the causation of purely terrestrial 
phenomena like the flattening of the earth and the 
depression of the water in the pail. Now Mach's 
answer is to say that this conviction is a mere prejudice, 
and to point out how this prejudice arose. Mach says 
that we have really not the least idea what would 
happen if the fixed stars were annihilated, and that 
therefore we have no right to suppose that the earth 
would still be flattened and the water still depressed 

* Science of Mechanics. 



ioS SCIENTIFIC THOUGHT 

after such a cosmic upheaval. Mach's grounds for 
this assertion seem to me to be sound. They are as 
follows : The laws of motion and all other scientific 
laws have been discovered and verified in a world 
which, as a matter of fact, does contain the fixed stars. 
Our laws do not make explicit mention of these bodies, 
because they have been a constant factor, and are 
assumed to be going- to be a constant factor in all 
predictions which we make by means of these laws. 
But, though constant factors need not be mentioned, 
it does not follow that they are causally irrelevant. 
We say that gas lights when you put a match to it ; 
and we do not as a rule mention that air must be 
present, because it practically always is present when 
we strike matches and attempt to light gas. Never- 
theless this constant factor is as relevant as the matches 
and the gas, and if we argued that the absence of air 
would make no difference, we should be wrong. You 
can never safely assume that any factor which has been 
present in all cases under which a law has been verified 
is irrelevant to the truth of the law, until you have 
produced a definite negative instance in which this factor 
was absent and the law was nevertheless found still to 
hold. Now we obviously cannot remove the fixed 
stars, spin a bucket, and see whether the water is still 
depressed in the middle. Therefore we have no right 
to feel so sure that it still would be depressed in the 
middle if there were no fixed stars. 

I will now point out why this argument, though 
logically sound and based on an important general 
principle, is liable to leave us dissatisfied as physicists. 
Mach's answer accepts the view that the flattening of 
the earth and the depression of the water depend on 
motion relative to the fixed stars, and that therefore the 
existence of these bodies is an essential factor in the 
causation of such phenomena. Now we must notice 
that, if this be true, a very peculiar kind of physical 
causation is introduced. It is of such a kind that, if 



THE TRADITIONAL KINEMATICS 109 

there were much of it in the world, physics and all other 
experimental sciences would be impossible. It is a 
fundamental assumption in all our practical work that 
the more distant a body is the less difference it makes 
to the physical phenomena in a given region. The 
chemist assumes that practically everything that goes 
on outside his laboratory, and most things that go on 
outside his test-tube, are irrelevant to the phenomena 
inside his test-tube. We are, of course, prepared to 
admit that possibly everything that happens anywhere 
has some influence on everything else, and that the 
more delicate we make our experiments the less we can 
afford to treat anything as irrelevant. But, unless very 
distant things could on the whole be safely neglected, 
and neglected with greater safety the further they are 
away, all experimental research would be hopeless, 
because no phenomenon would be even approximately 
isolable from the rest of the world. If gravitational, 
electric, and magnetic forces varied directly instead of 
inversely with the square of the distance, there would 
be what Mr Mookerjee very justly termed "a rare 
hullaballoo or pretty kettle of fish. " Now Mach's answer 
does introduce a sort of physical causation which is of 
just this objectionable kind. The fixed stars are the 
most distant bodies that we know of, and yet they are 
an essential factor in causing the flattening of the earth 
and the depression of the water. This is why I said 
that the implications of Mach's answer contradicted our 
physical instincts. Of course it is quite possible that 
here our physical instincts are mere prejudices. It may 
well be that all the known laws of nature, when fully 
expressed, involve two factors, viz., those that we 
actually mention and measure on the one hand, and the 
general structure of the stellar universe on the other. 
The latter has kept fairly constant up to the present, 
and so we have come to no harm as yet by neglecting 
it and confining ourselves entirely to the first factor. 
I now turn to a second possible answer to the present 



no SCIENTIFIC THOUGHT 

objection to the Relational Theory of motion. I am 
inclined to think that Mach's answer concedes more 
than is necessary to the opponent. The opponent con- 
fines himself to the fixed stars, argues that it is only 
rotations with respect to them that produce physical 
consequences on the Relational Theory, and therefore 
confronts the Relationist with the conclusion that the 
existence of the fixed stars must be an essential factor 
in the production of these physical phenomena. Mach 
accepts this as a fair consequence of the Relational 
Theory, and simply argues that it is unobjectionable 
for the reasons given above. This seems to me too 
big a concession. I pointed out that every body has at 
one and the same time many different relative motions, 
all equally real, just as any town has at one and the 
same time any number of different " distances." There 
is no kind of contradiction or inconsistency in this unless 
we tacitly smuggle in the idea of absolute motion. 
Now, if the laws of Mechanics be true, all the motions 
of all other bodies relative to (say) the fixed stars obey 
a certain set of rules, viz., Newton's laws of motion, 
or whatever modification of them may be found to be 
necessary. Suppose that a whole set of bodies B 1? B 2 , 
. . . B a obey Newton's laws for all their motions with 
respect to the fixed stars. Let us select any body Br 
out of this set. Then the motions of any other, such 
as B : , with respect to Br, could be compounded out of 
the motions of B x and Br with respect to the fixed stars. 
But, by hypothesis, the motions of both B x and Br with 
respect to the fixed stars obey Newton's laws. Hence 
the motions of B a with respect to Br must obey laws 
which are merely mathematical transformations of 
Newton's. Precisely the same remarks apply to the 
motions of any of the other B's with respect to Br. The 
standard body Br might be as wild as we like, it might 
be a midge dancing in the sunlight ; still, if it and all 
other bodies obey a certain set of rules for all their 
movements with respect to the fixed stars, all other 



THE TRADITIONAL KINEMATICS in 

bodies will obey a set of rules for their movements with 
respect to it. No doubt these rules would be of perfectly 
awful complexity if we had chosen a midge instead of 
the fixed stars as our body of reference ; but what does 
this prove ? Only, so far as I can see, that we should 
probably never have discovered that all motions are 
subject to laws if we had not had the fixed stars avail- 
able as bodies of reference. When we say : " It is only 
motions relative to certain bodies (of which the fixed 
stars are typical) which obey the laws of Mechanics," 
this is true in one sense and false in another. It is true 
that only such motions obey even approximately the 
simple and familiar laws of motion discovered by Galileo 
and Newton. It is not true that motions with respect 
to other bodies obey no laws, or that the laws which 
they obey are incompatible with or independent of 
Newton's. The laws of such motions must be just 
mathematical transformations, often of unmanageable 
complexity, of the familiar and simple laws which 
govern motions with respect to the fixed stars. This 
seems to be a necessary consequence of the two facts 
(a) that all motions with respect to the fixed stars are 
subject to Newton's laws, and {b) that the motions of 
any body with respect to any other can be compounded 
out of the motions of both with respect to the fixed 
stars. 

If this argument be sound, we can now give an 
answer to the present objection to the Relational Theory, 
which shall accept all that is true in Mach's answer 
and shall not shock our physical instincts or prejudices. 
The objection, I may once more remind the reader, 
was this: If the earth be flattened and water in a 
spinning pail depressed only through rotation with 
respect to the fixed stars, then, if there were no fixed 
stars, the earth would not be flattened nor the water 
depressed. We can now see that this consequence 
does not really follow from the Relational Theory of 
Motion. If you twisted the pail in the absence of the 



ri2 SCIENTIFIC THOUGHT 

fixed stars there would still be relative motion between 
ii and other thing's. It is true that these other relative 
motions would not be connected with the depression 
of the water by the same simple laws which connect 
that depression with the rotation of the pail relative to 
the fixed stars. But the depression would be connected 
with these other relative motions by laws which are 
mathematical transformations of these simpler ones. In 
that sense it would be true to say that the annihila- 
tion of the fixed stars would not necessarily make any 
difference to the phenomena. On the other hand, we 
can still admit with Mach that it would not be safe 
to assume that laws which have been discovered and 
verified in the presence of the fixed stars would neces- 
sarily continue to hold when such a large and important 
part of the material universe as the fixed stars had been 
annihilated. The difference between our answer and 
Mach's comes to this : Mach accepts it as a necessary 
consequence of the Relational Theory that the exist- 
ence of the fixed stars is an essential condition of the 
phenomena under discussion ; he then devotes himself 
to showing that we ought not to be surprised at the 
disappearance of these phenomena in the absence of 
the fixed stars, and therefore that this consequence 
of the Relational Theory is no objection to it. We 
argue that this is not a necessary consequence of the 
theory, but add that we too should not be surprised 
if laws which had been ascertained in the presence of 
the fixed stars should be found to break down after so 
hug^e a change as the annihilation of those bodies. 

The upshot of the discussion seems to me to be 
that there is no conclusive objection to the view that 
all motion is relative, and that all arguments which 
have been produced to show that we must recognise, and 
can indirectly measure, absolute motion, are fallacious. 
This being so, I think there are strong reasons for 
rejecting the Absolute Theory. After all, the laws of 
motion are empirical laws, discovered by observing and 



THE TRADITIONAL KINEMATICS 113 

reflecting upon the actual movements of actual bodies. 
Now, all that we can observe in the way of motion is 
the change in position of one body with respect to 
others. It were strange indeed if such observations 
could lead to laws about something which is, from its 
very nature, unobservable, and stranger still if such 
laws enabled us to control and predict the movements 
of bodies in nature. Absolute Space, Time, and Motion 
have all the appearance of being mathematical devices, 
and not substantial constituents of nature, and a theory 
is to be preferred which reduces such mathematical 
scaffolding to a minimum, provided of course that it is 
adequate to all the facts with which it professes to deal. 
I think that mathematicians and writers on dynamics 
have been justified in rejecting the Relational Theory in 
the forms under which it has been commonly presented 
in the past ; but I think that this is because it has 
been badly and inadequately stated, and not because 
it is impossible to make it fit all the facts. 

This is about as far as we can go when we confine 
the discussion to ordinary mechanical phenomena. But 
the whole question arose again in recent years over 
electro-dynamics, and it has been found that reflection 
on the facts of this region of phenomena necessitates a 
still more radical overhauling of the traditional concepts 
of kinematics. This leads to the Theory of Relativity, 
which I shall deal with in the next chapter. 

The following additional works may be consulted 
with advantage : 

Leibniz, Correspondence with Clarke. 

E. Mach, Science of Mechanics, Chap. II., § vi., Appendix XX. 

and XXII. 
B. A. W. Russell, Principles of Mathematics, vol. i., Chap. 

LVIII. 
A. Muller, Das Problem des absoluten Raumes. (Vieweg. 

Braunschweig., 191 1.) 
P. Painleve, Les Axiomes de la Mecanique. (Gauthier- 

Villars, Paris, 1922.) 
H. Poincare, Science et Hypoth&se, Chap. VII. (Flammanon, 

Paris.) 
H. Poincare, Science et Methode, Part II., Chap. I. 



CHAPTER IV 

"Ah! that accounts for it," said the Hatter. "He won't 
stand beating. Now, if you only kept on good terms with 
Time, he'd do almost anything you liked with the clock. . . . 
You could keep it to half-past one as long as you liked." 

(Lewis Carroll, Alice's Adventures in Wonderland.) 

Modification of the Traditional Kinematics in the 
Region of Physics (continued). (2) The Special 
Theory of Relativity 

The older controversies between Absolutists and Re- 
lationists, which we have discussed in the last chapter, 
took place wholly within the region of dynamics, i.e. 
they dealt with the movements of bodies and with the 
changes of shape, such as flattening and depression, 
which some of these movements produce. It is clear, 
however, that the same kind of question could be raised 
over anything whatever that moves, and over any kind 
of effects which movement may seem to produce. Now 
there is good evidence — some of which will be men- 
tioned in a later chapter — for the view that light 
travels out from its sources with a very great but finite 
velocity ; and this velocity has been measured. Again, 
the motions of charged bodies produce magnetic effects 
which vary with the velocities of the bodies. 

Thus in theory the whole question between the 
Absolute and the Relational views of Motion might 
be argued out again in the regions of light and electro- 
magnetics. A wave of light might be expected to have 
all sorts of different relative velocities, and the question 
might be raised : Which, if any of these, is what the 

physicist means by the velocity of light? The Absolutist 

114 



FIRST THEORY OF RELATIVITY 115 

might here step in and say that by the velocity of light 
we must mean, not any of its relative velocities, but 
its absolute velocity, in the sense discussed in the last 
chapter. Similarly, we might ask : Which, if any, of 
the numerous different relative velocities of any charged 
piece of matter produces magnetic effects? And the 
Absolutist might say that no relative velocity has this 
effect, but only the absolute velocity of the charged 
body. I do not think that these additional facts really 
make any difference in principle to the conclusions 
which we reached about the Absolute and the Rela- 
tional Theories in the last chapter. I will try to justify 
this statement before going on to discuss what modifica- 
tions the new facts do make in the traditional kinematics. 
The subject is a little confused at the outset through 
the introduction of a new friend — the Luminiferous 
Ether — which did not enter into the purely dynamical 
arguments. Thus we get an apparently intermediate 
view, put forward by physicists who reject Absolute 
Space, Time, and Motion with righteous horror as 
metaphysical figments, and tell us that what is im- 
portant in light and electro-magnetics is motion, not 
with respect to this or that body, but with respect to 
the Luminiferous Ether. It seems to me that for the 
present purpose there is no important difference between 
the Ether and Absolute Space. A distinction was origin- 
ally drawn, because various physical properties, such 
as elasticity and density, used to be ascribed to the 
ether, and because it was supposed to produce various 
effects on ordinary matter. This is inconsistent with 
the traditional view that Space does nothing, has no 
physical properties, and is thus distinguished from 
Matter. But there are two circumstances which make 
the distinction between the Ether of the modern physicist 
and the Absolute Space of the older Mechanics so slight 
as not to be worth keeping. On the one hand, the 
Absolutist has really no right to say that Absolute 
Space does nothing to matter. For it is of the essence 



Il6 SCIENTIFIC THOUGHT 

of his view that absolute motion produces flattening 
and other mechanical effects on matter ; and, since 
Absolute Space is involved in Absolute Motion, it is 
clear that he ought to hold that it is an essential factor 
in the production of these effects. On the other hand, 
as we shall see, the Ether has proved to be a more and 
more retiring entity, until it is difficult to discover that 
it plays any part in physics except that which Absolute 
Space played in the older Mechanics. Thus I do not 
regard the two views that the velocity of light means 
its absolute velocity and that it means its velocity 
relative to the Ether as genuine alternatives. The 
Ether just is Absolute Space plus some hypothesis as 
to its filling, and this latter addition is irrelevant for 
our present purpose. 

Having cleared this complication out of the way, 
we can see fairly easily that the facts about light and 
electro-magnetism make no difference in principle to 
the question of Absolute versus purely Relative Motion. 
When the velocity of light was measured, and when 
the fundamental equations of the electro-magnetic field 
were laid down, writers did not as a rule state very 
clearly what frames of reference they were assuming. 
But it is certain that they were, in fact, assuming the 
familiar frame of reference with respect to which Newton's 
laws of motion hold. If this be Absolute Space, then 
they were talking about Absolute Motion, and if it be 
the fixed stars, then they were talking about motions 
with respect to the fixed stars. Every reason that there 
is for taking the latter alternative as regards ordinary 
dynamics exists for doing the same with regard to light 
and electro-magnetics. The velocity of light is some- 
thing that has been experimentally measured, and what 
has been measured must have been the time that a 
wave of light took to get from one body to another (or 
rather from one body to a second and then back again 
to the first). Clearly it was the velocity of light relative 
to these bodies that was measured, and not the time 



FIRST THEORY OF RELATIVITY 117 

that it took to get from one point of Absolute Space 
or one bit of the Ether to another. Similarly the laws 
of electro-magnetics were discovered and verified by 
experiments on bodies, and the velocities that were 
observed were the velocities of these bodies relative 
to others. Again, all the arguments that could be 
produced to show that in light and electro-dynamics 
we must be dealing with absolute motions, and that we 
have the means of indirectly measuring them, are pre- 
cisely parallel to the arguments to prove the same con- 
clusion from the phenomena of rotation. And they 
could be met in precisely the same way. Thus the 
new sciences which have developed since Newton's 
time leave the question between the Absolutists and the 
Relationists exactly where it was ; and that is, if we 
are right, they leave the Relationists in possession of 
the field, provided they state their case carefully enough. 

I do not suppose that any physicist would deny one 
side of the above statement, viz., that the facts about 
light and electro-magnetics lend no fresh support to 
the Absolute Theory. But he might be inclined to 
think that they do provide additional grounds for the 
Relational Theory. I do not think this is strictly true ; 
but it is plausible, and an explanation of why it is so 
will carry us into the heart of our present subject. 

In the purely dynamical arguments between Absol- 
utists and Relationists the Absolutist staked his case 
on absolute acceleration and absolute rotation. He did 
not profess to be able to produce any direct empirical 
evidence for absolute rectilinear velocity ; though, of 
course, if he could prove the existence of absolute 
acceleration, that of absolute velocity would be proved 
indirectly. It follows at once from the form of Newton's 
laws of motion that absolute rectilinear velocity, even 
if it exists, will not show itself by any dynamical con- 
sequences ; for it is acceleration, and not velocity in a 
straight line, which Newton's laws connect with force, 
and therefore with possible deformations of bodies. 



n8 SCIENTIFIC THOUGHT 

Now, when we come to deal with light and electro- 
magnetics, there is a real difference in this respect. If 
what is called the velocity of light be its absolute 
velocity (or its velocity with respect to the "stagnant 
ether," if you prefer that expression) we might expect 
to be able to measure the absolute velocity of a body 
like the earth by finding the velocity of light with 
respect to it and noticing how much greater or less it 
was than the velocity of light. The absolute velocity 
of the earth in its orbit would presumably be the differ- 
ence between the absolute velocity of light and the 
velocity of a wave of light as measured from the moving 
earth, given that the earth and the wave of light were 
moviner in the same direction when the measurement 
was made. Again, various observable electro-magnetic 
effects depend on the velocities of charged moving 
bodies. If it be the absolute velocity of the charged 
body that is relevant to these effects, we ought to be 
able to discover what part of the observed relative 
velocity of a moving charged body is due to its own 
absolute velocity and what part is due to the absolute 
velocity of our axes of reference, for it will be only the 
former that will be responsible for the electro-magnetic 
effects which we measure. 

Now it is a fact, and a very important one, as we 
shall see in detail in a moment, that all attempts to find 
the absolute velocities of bodies by these means have 
failed, although the experiments were quite delicate 
enough to detect the effects which were being looked for, 
if they had really happened. We can now see what 
amount of truth there is in the popular view that the 
new facts about light and electro-magnetics have pro- 
duced strong additional arguments for the Relationist 
and against the Absolutist view of Motion. It is true 
that light and electro-magnetics seemed to offer for the 
first time a means of detecting and measuring absolute 
rectilinear velocities^ and that when the experiments were 
done the results were always wholly negative. But the 



FIRST THEORY OF RELATIVITY 119 

negative results of these experiments are just as para- 
doxical on the traditional Relationist Theory as on the 
traditional Absolutist Theory. They cannot therefore 
be taken as arguing for the former and against the 
latter. It is clear that neither theory, as it stands, is 
fitted to deal with the facts. Of course, if it should 
be found that the Relationist Theory can, and the 
Absolutist Theory cannot, be so modified as to fit the 
facts of light and electro-magnetics, we may say that 
ultimately these facts furnish a conclusive argument 
against the Absolute Theory. But at present we must 
hold that their immediate consequence is simply to show 
the need of modifying both theories. To this modifica- 
tion we will now turn. 

I shall confine myself to the question of the velocity 
of light, and not touch on purely electro - magnetic 
experiments. The argument in the former case can be 
followed by any person who takes a little trouble and is 
acquainted with the first book of Euclid and with 
algebra up to simple equations ; whilst the electro- 
magnetic experiments cannot be understood without a 
fair knowledge of mathematical physics. And there is 
no loss of generality in restricting ourselves to the 
simple case of light, for light is really an electro- 
magnetic phenomenon. All that the reader needs to 
remember here is that the paradoxical result which we 
are going to explain about the velocity of light is not an 
isolated phenomenon, but is exactly paralleled by every 
electro-magnetic experiment that has ever been done 
with a view to detecting the absolute velocity of the 
earth or other bodies. 

The Michelson-Morley Experiment. I shall state the 
argument here in terms of the Absolute Theory, because, 
with our scientific traditions, this makes it more easy 
to follow. But I shall show at the end that this does 
not mean that the argument implies the truth of the 
Absolute Theory, or that it would be inconsistent to 
use the conclusion as the premise of an argument against 



IJO 



SCIENTIFIC THOUGHT 



that theory. Suppose we had a platform moving through 
the "stagnant Ether" (which, as we have seen, is 
practically the same thing as Absolute Space) in a 
certain direction with a constant velocity v. On this 
platform let there be an observer, a source of light, and 
a couple of plane mirrors. Draw a straight line on the 
platform through the source of light and parallel to the 
direction of motion of the platform. Draw another 
straight line on the platform through the source and at 
right angles to the first line. Measure off equal distances 
from the source along the two lines. At the points thus 
obtained place the two mirrors, each one normally to its 
line. The illustration below will show the arrangement. 




At a certain moment let the source S give out a 
flash of light and let part of this go to the mirror M 1 , 
and another part to the mirror M 2 . Let us first consider 
the part that travels to M r This will have to travel 
further through the ether than the marked distance / 
between S and M 1} for M x will have travelled a certain 
distance through the ether while the light is moving 
towards it, and therefore the light will have to overtake 
it. Now let the light be reflected back along its old 
path to the source. It will now have to travel less than 
the marked distance through the ether, because the 
source is moving towards it. Suppose the light left S 
at time O, reached M x at t v was reflected instantaneously, 
and got back to S at t % . Let c be the absolute velocity 
of light, i.e. its velocity through the " stagnant ether." 
It is then clear that 



and 






FIRST THEORY OF RELATIVITY 



121 



M 



/ 



M ^T 



f 






\ 



whence it follows that t. z = 2lc\(c l — v % ). This then is 
the total time that elapses between the emission of this 
part of the light and its return to the source after its 
double journey. 

Let us now deal with the light which travels to the 
other mirror M., and is reflected back from it to the 
source. This light must not travel out in the direction 
SM 2 , as marked on the platform, 
or it will never reach M 2 . For M 2 
will have moved to the right by 
the time such light had got to 
where it was when the light started. 
We have therefore to consider light 
which strikes the mirror at a point 
in the ether equidistant between 
the point where the source was when the light left it 
and the point where the source will be when the light 
returns to it. The diagram above will make this 
quite clear. 

The actual course of the light in the ether is the line 
SWgS 2 . If T 2 be the time when this light gets back to 
S it is easy to see that 

*"P 2 T * 7 

£2±2_ = /2 + t ,2i2 



5° 



S' 



>V 



whence 



TV 



2/ 



*Jc 2 -v 2 



Thus the two parts of the original beam of light do not 
get back to the source at the same time ; or, to put 
it in a different but equivalent way, light which gets 
back to the source at the same time from the two mirrors 
must have started from the source at different times. 
Now, under these conditions, there ought to be a 
shifting of the position of the interference bands which 
always arise when the two beams of light which have 
travelled by different paths from the same source meet 
again. And from the shift of the bands it would be 
possible to find the difference between t t and T 2 . From 



122 SCIENTIFIC THOUGHT 

this we could calculate v, the absolute velocity of the 
platform, in terms of c f the absolute velocity of light, by 
using the two formula? just proved. 

An experiment of this kind was done with great 
care by Michelson and Morley. Their moving platform 
was the earth. The velocity v was the tangential 
velocity of the earth in its yearly motion round the 
sun. Their apparatus was quite delicate enough to 
detect smaller shifts in the interference bands than those 
which were expected. Yet not the slightest trace of 
any shifting at all was detected. A great many other 
experiments have been tried in which electro-magnetic 
effects were looked for as a result of the earth's motion 
through the ether ; in every case the results have been 
nil. This negative fact, that no effect due to the 
uniform rectilinear motion of a body through the ether 
has ever been detected, although it had been predicted, 
and although the apparatus used was quite delicate 
enough to detect and measure it if it were present, is 
the basis of the first Theory of Relativity. 

Before going any further I want to impress on the 
reader the extremely paradoxical nature of this fact, 
and to point out that it is as embarrassing to the 
traditional Relational Theory of Motion as to the 
additional Absolute Theory. If I travel in a slow local 
train, and an express passes me going in the same 
direction on the main line, I expect to find and I do 
find that the express moves more slowly relative to me 
than it would if I were standing on the platform of a 
station. It is obvious that the express takes longer 
to pass me under the former circumstances than under 
the latter. Now we should certainly expect this to 
happen for all kinds of motion, and this is common 
ground to the traditional Absolutist and the traditional 
Relationist. Yet the negative result of the Michelson- 
Morley and the electro-magnetic experiments might 
quite fairly be summed up as follows : The velocity 
of light with respect to various bodies is the same, even 



FIRST THEORY OF RELATIVITY 123 

though these bodies be moving with various velocities 
in the same direction as the light or in the opposite 
direction to it. In the Michelson-Morley experiment 
the earth in its orbit corresponds to a slow local train, 
and the light which goes from S to M x corresponds to 
a very fast express moving in the same direction on a 
parallel line. The result is as if an express train should 
appear to be going just as fast to observers in the local 
train as to observers standing on a station platform. 
The paradox can be stated just as well in terms of the 
Absolute and in terms of the Relational Theory. In 
terms of the Absolute Theory we can say that, although 
the earth is moving with an absolute velocity through 
the ether in the same direction as the light, this does 
not diminish the velocity of the light with respect to 
the earth ; everything goes on as if the earth were 
absolutely at rest in the ether. In terms of the Rela- 
tional Theory we can say that the relative velocities of 
a wave of light, with respect to a number of bodies 
which are moving relatively to each other in the same 
direction as the light, are nevertheless all the same. 

Naturally the first thing to do is to see whether any 
physical explanation can be given for this paradox, 
without modifying the traditional views of Space and 
Time which are common to the older Absolute and 
Relational Theories. What physical assumptions were 
made in the argument which led to the formulas of the 
Michelson-Morley experiment? We assumed (a) that 
the ether is not dragged along by the moving platform, 
as water would be by a stick that was trailed through 
it ; (b) that the absolute velocity of light in the 
" stagnant ether" is the same in all directions ; (c) that 
the reflection at the mirrors takes place practically 
instantaneously ; and (d) that the fact that a source, 
which emits light, is itself in motion through the ether 
makes no difference to the velocity of the emitted light. 
Would it be reasonable to account for the negative 
result of the Michelson-Morley experiment by rejecting 



124 SCIENTIFIC THOUGHT 

or modifying any of these physical assumptions? As 
regards (a) any modification will bring us into imme- 
diate conflict with another set of well-established 
experimental facts, viz., the aberration of light from 
distant stars, due to the yearly movement of the earth 
in its orbit. We shall have occasion to refer again to 
this phenomenon in a later chapter. For the present 
we may say that the amount of aberration will vary 
according to the extent to which the earth drags the 
ether along with it. The actually observed aberration 
corresponds to the hypothesis that there is no dragging 
at all, which is what we assumed in our argument. 

The assumption (/;) seems to be the only reasonable 
one to make on the subject. Nor would it help us to 
reject it. For the earth is moving in its orbit in 
different directions at different times of year. It follows 
that the assumption that the velocity of light in the 
ether is different in different absolute directions, even 
if it be intelligible, could only account for the negative 
result of the Michelson-Morley experiment at one time 
of year. At other seasons the discrepancy between 
prediction and observation would be worse than before. 

The assumption (<r) is needlessly sweeping ; all that 
we need to assume is that, whatever time the reflection 
may take, it is the same for both mirrors. It were 
surely absolutely arbitrary to suppose that reflection at 
M always takes up a different amount of time from 
reflection at M x , and that this difference is always exactly 
such as to neutralise the expected difference in the times 
of arrival of the two beams of light at the source. 

{d) On the wave theory of light there is no reason 
why the velocity of a source at the moment of emission 
should have any effect on the velocity with which the 
emitted disturbance afterwards travels through the ether. 
If we held the corpuscular theory of light, matters would 
be different ; for a corpuscle shot out of a moving source 
would presumably have a velocity compounded of that 
of the source and that due to the emitting impulse. 



FIRST THEORY OF RELATIVITY 125 

But the cumulative evidence for the wave theory and 
against the corpuscular theory is so strong that it 
seems idle to try to explain the negative result of the 
experiment by a hypothesis which is only plausible 
on the latter view. 

Interpretation of the Michelson-Morley Result in terms 
of the Absolute Theory. It is clear then that no ordinary 
modification in our physical assumptions will explain 
the negative result of the Michelson-Morley experiment 
without bringing us into still worse collision with well- 
established facts. We are therefore forced to consider 
the assumptions that were tacitly made in our measuring 
of distances and time-lapses. This brings us, as regards 
Space, to the Lorentz - Fitzgerald Contraction, and, as 
regards Time, to the notion of Local Time. 

I shall still confine myself in my exposition to the 
terminology of the Absolute Theory, and we shall 
now be seeing what assumptions as to our measure- 
ments of distance and time-lapse have to be made in 
order to square the results with that theory. It will 
be remembered that we measured off on our platform 
two lines at right angles to each other, each of which 
had the measured length /. This means that our 
measuring rod had to be laid down exactly / times 
(if it was of unit length) before we made our mark 
on each line. Now, on the assumption that identity 
of measure means identity of physical distance, we saw 
that the times taken by the two beams to get back 
to the source were t v for the one that travelled parallel 
to the direction of motion of the platform, and T 2 
for the other. The physical distances travelled by 
the two, on the present assumption, will, of course, 
be ct., and cT. 2 respectively. The first of these is 

and the second is 



c 1 T ? 



Now actually the two get back at the same time 
instead of the two different times /., and T.,. It therefore 



m 



[2 6 SCIENTIFIC THOUGHT 

is necessary to suppose that really they travelled the 
same physical distance through the ether. We can 
only explain this on the assumption that, although our 
measurements in the two mutually normal directions 
on the platform were the same, the physical distances 
measured were not the same. This is equivalent to 
assuming that our measuring rod does not remain of 
the same physical length when it is turned in different 
directions on the moving platform. If we suppose 
that the physical distance at right angles to the direction 
of motion really is /, whilst that in the direction of the 

otion is only /./ I — -^ , we can account for the negative 

result of the experiment. For, in that case, both beams 
will have traversed the same physical distance through 

2/ 

the ether, viz. : . ; and, as they travel with the 

J v L 

same velocity c, they will get back at exactly the 
same time. What we have to assume then is that a 
measuring rod, which is of unit physical length when 
held broadways on to the direction of motion of the 
platform through the ether, shrinks to a physical 

/ V- 

length v i — — when laid down on the platform in the 

direction of its motion. This is what is called the 
Lorentz - Fitzgerald Contraction. It is not, of course, 
supposed to be confined to one particular rod, but is 
common to the platform and everything on it. The 
result is that it cannot be detected by the use of another 
measuring rod, because that will contract in precisely 
the same way as the first when you lay it alongside 
the first. 

We can now deal with the question of Local Time. 
We have supposed that the velocity of light in the 
stagnant ether is c units of length per second. Now, 
assuming the Lorentz-Fitzgerald Contraction, we have 
seen that the distance travelled in the ether by either 



FIRST THEORY OF RELATIVITY 127 

beam of light from source to mirror and back again to 
2/ 



2/ 
source is , units of length. It is clear then that 



c 2 



a clock at the source, which marked zero when the 
flash started ought to mark . . ^-c seconds when the 

flash returns to the source, if it is set in such a way 
that it accurately measures seconds of physical time- 
lapse. Now the distance travelled by the light relatively 
to the platform is 2/ units of length. Therefore the 
measured velocity of the light relatively to the platform 

will be 2l^r ,= =* or , 9 units of length per 

<? e* 

second, assuming that the clock at the source is going 
at such a rate that a second, as measured by it, really 
does represent a physical time-lapse of one second. 
The relative velocity of light would therefore vary with 
the velocity of the platform. But this is exactly what 
we do not find, although we might have expected to 
do so. We actually find that the measured velocity 
of the light does not depend on the velocity of the 
source, the observer, or his instruments. It is therefore 
evident that some further explanation beside the Lorentz- 
Fitzgerald Contraction is needed to account for the facts. 
It is evident that this further assumption must be con- 
cerned with our clocks, since we have already dealt with 
our measuring rods. Suppose that, when one second 
of physical time has elapsed, the clock at the source only 

indicates * \ — — seconds, i.e. that it is a little slow. 
c z 

2/ 
Then when . seconds have really elapsed the 

2/ 
clock at the source will only indicate . 2 x / j 

CsJ ^ V T _ V _J 

9 9 



128 SCIENTIFIC THOUGHT 

i.e. 2/ r seconds. The measured distance travelled by 
the light relatively to the platform is, as before, 2/. 
Thus the measured relative velocity of the light will 
now be c y and will thus be independent of the motion 
of the platform. This, as we saw, is the result which 
is actually found by experiment. We must therefore 
accept it as a fact that the clock at the source on the 
moving platform goes more slowly than it would do if 

the platform were at rest in the ratio of v 1— 2 to 1. 

This assumption is of course additional to the Lorentz- 
Fitzgerald Contraction, and makes no difference to it. 

But we are not yet out of our difficulties about the 
measurement of time. So far we have dealt only with 
the case of a single clock in a single place on the 
platform ; for the light came back in the end to the 
place whence it started, and the time-lapse was measured 
wholly by the clock there. This of course does corre- 
spond to the way in which the velocity of light is 
measured in purely terrestrial experiments, such as 
that of Fizeau and Foucault. Still, it is clear that we 
often want to compare the time at which one event 
happens in one place with the time at which another 
event happens in some other place. In order to do 
this we must have some reason to believe that the clocks 
in the two places are, not merely going at the same 
rate, but also that they agree in their zeros. Now the 
mere fact that they agreed in these respects when they 
were together is no guarantee that they will continue 
to do so when one has been taken away to a distance. 
In the case of a pair of ordinary clocks, for instance, 
the shaking that one of them gets on its journey, the 
possibly different average temperature of the region to 
which it has been moved, the different gravitational 
attraction at different parts of the earth, and many other 
factors, combine to make it most unsafe to argue that, 
because the two agreed when they were together, they will 
continue to do so now that they have been separated. 



FIRST THEORY OF RELATIVITY 129 

It is thus absolutely necessary to have some criterion 
of sameness of rate and sameness of zero which can be 
applied to widely separated clocks whilst they remain 
in situ. The only method that seems possible is that 
of signals which travel from one to the other. Let a 
signal be sent out from clock A when this marks t A and 
received at clock B when this marks t B . Let another 
be sent out when the first clock marks t' A and received 
when the second marks f B . If it is found that t' A —t A = 
t\—t m we say that the two clocks are going at the same 
rate. Again, if a signal leaves A at /.,, reaches B when 
the clock there marks t n , is immediately reflected back 
to A, and reaches there when the local clock marks 
t' A , it seems reasonable to conclude that the zeros of 
the two clocks agree, provided that t B = \(t A + t' A ). This 
would obviously be the right criterion to adopt on the 
Absolute Theory, provided the platform were at rest 
in the ether. But, we have seen, whether the platform 
be at rest in the ether or not, there is no observable 
phenomenon by which the observers on it can detect 
its absolute motion or rest. Hence, in any case, they 
are forced to use this criterion faute de mieux. More- 
over, with this criterion and with it alone, the observers 
on the platform will find the same value for the velocity 
of light relative to the platform whether they measure 
it by observations all made with a single clock in one 
place, or by observations made with two different clocks 
in two different places. We can easily show this, as 
follows : We have seen that the velocity of light, as 
determined by observations with a single clock, is found 
to have the same value c, no matter what may be the 
velocity of the platform through the ether. Now let 
the clock B be put where the mirror M x was in the 
Michelson-Morley experiment. Let a flash leave the 
source (where the clock A is) when this clock marks O, 
reach the clock B when this marks t B , be immediately 
reflected back, and reach A again when this marks t' A . 
Then, if the two clocks have been set by our criterion, 



130 SCIENTIFIC THOUGHT 

t H = i(0 + /'.,)--= A /'.i- Now we know that the velocity of 
light relative to the platform, as measured entirely by 
observations made at A with the clock there, is c. And 
the measured distance that this light has travelled 
relatively to the platform is 2/, i.e. the measured dis- 
tance on the platform backwards and forwards between 
A and B (or S and M 1 in the diagram to illustrate 
the Michelson-Morley experiment). Hence t' A = 2l\c. 
Hence t in which is It' n is l\c. That is, a beam of light 
which left A when A's clock marked O and travelled 
the distance / relative to the platform to the point B, 
will reach B when the clock there marks l\c. Thus the 
observers at A and B on comparing notes will again 
conclude that the velocity of light with respect to the 
platform is c, which is exactly the same conclusion as 
experimenters who had confined themselves to making 
observations at A with A's clock had already reached. 
So that the conventions just laid down for standardising 
distant clocks are not only those which are practically 
forced on the observers by their inability to detect the 
movement of their platform through the ether, they 
are also the only conventions which will lead to the 
same measure for the velocity of light relative to the 
platform, when two different but equally reasonable 
methods of measurement are adopted. (It ought to be 
remarked that the last point is of merely theoretical 
interest, since the only practical method of measuring 
the velocity of light by terrestrial experiments is by 
observations made in a single place.) 

Now these conventions, reasonable and inevitable as 
they seem, lead to the result that on a moving platform 
clocks which are set by them do not " really" agree in 
their zeros. This means, in terms of the Absolute 
Theory, that identity of clock-readings in different 
places does not imply identity of physical date, if the 
clocks have been standardised by these conventions and 
are dotted about a platform which is in absolute motion 
through the ether. This we will now show. We have 



FIRST THEORY OF RELATIVITY 131 

just seen that, with these conventions, if a flash leaves 
A when the clock there reads O, it will get to B when 
the clock there reads l\c. If there were nothing wrong 
with the clocks except the systematic slowness which 
we have already had to assume, this clock-reading would 

mean a physical time-lapse of amount -. Now 

actually the light which left A and went to B has 

I ~v % 
travelled (a) a distance /./ 1 — -^(allowing for the Lorentz- 

Fitzgerald Contraction of the platform and the rod with 
which it is measured), and (b) has had further to catch 
up B, which is itself travelling through the ether in the 
same direction with a velocity v. A very simple 
calculation of exactly the same kind as that given on 
p. 120 will show that the actual amount of time that has 

elapsed between leaving A and reaching B is ' 

Now we have seen that, if we only allow for the 
systematic slowness of all the clocks on the moving 

platform, the physical time-lapse would be ,- — 

r J sj v* 1 c 



l ~~ 2 
c z 



These two quantities are not equal, and the one that we 
have just obtained by direct calculation is the right one. 
Hence the clock at B is not merely going somewhat too 
slowly, like the clock at A ; it is also not really in 
agreement with A as to its zero, i.e. identity of readings 
between the two clocks do not represent identity of 
physical dates. When the clock at B reads l\c the true 

physical time-lapse is This equals 



c—v 



■I v_t 



1 — .2\ C — V / 



l ~T* 



C32 SCIENTIFIC THOUGHT 

In general, if the clock at B marks /„, and the measured 
distance of B from the source in the direction of motion 
of the platform be denoted by x m the physical time-lapse 
corresponding to the reading t B is given by the equation 



sM*+?) <■> 



i — 

c~ 

We see then, that if clocks be dotted about a platform 

which is moving through the ether with uniform velocity 

in a straight line, and if these clocks be standardised by 

means of light signals, and we want to pass from the 

readings of any clock to the corresponding physical 

time-lapse, we must not merely divide the reading by 

s/ v* 

i — — . Before doing this we must add to the reading 

a quantity —^, where x H is the measured distance from 

the standard clock to the given clock, in the direction of 
motion of the platform. Not only are all the clocks 
slow, in the sense that they all take more than an hour 
of physical time to make a complete rotation ; in addi- 
tion to this the hands of the various clocks are pushed 
back from the very start by amounts which increase the 
further they are away from the standard clock in the 
direction of motion of the platform. Clock-readings, 
like t Bi are called Local Times, because they vary with 
the position of the clocks on the platform, even when 
the absolute time is the same. 

It is usual, for convenience, to denote the fraction 

i 



I — ~2 by k. We can then say that the Lorentz- 

Fitzgerald Contraction means that a measured length 
x in the direction of motion of the platform represents a 
physical length of only x\k. And the equation just 
reached tells us that the absolute time is connected with 
the local time of a clock on a moving platform by the 

formula t=k(t a + vxj^ (l) 



FIRST THEORY OF RELATIVITY 133 

assuming- that the clocks have been set by light signals 
according to the conventions laid down on p. 129. We 
want one more equation before we can get any further. 
Suppose that when the standard clock on the platform 
marked O it was opposite to a point a in Absolute Space. 
When the clock B marks t B let that clock be opposite to 
a point (3 of Absolute Space. The co-ordinate of /3, in 
the direction of motion of the platform and relative to 
the platform, will of course simply be x„ the distance as 
measured along the platform in 

this direction from the standard a. — 5ji ,s 

clock to the clock B. How | x B \ 

will this be related to X/3, the ! ' " — 1 — * /i = 

physical distance in Absolute A g— ^-* f B = f B 

Space between the point /Sand 

the point a, which the standard clock was opposite to 
at the beginning? The diagram above will illustrate 
the problem. 

We have two factors to consider. (1) Owing to the 
Lorentz-Fitzgerald Contraction the measured length x B 
only represents a physical length x B /k. (2) The plat- 
form has moved through the ether for the physical 
time-lapse that corresponds to the local time t B . If this 
lapse be / the platform has moved a physical distance vt. 

(VX \ 
t R -\ — 2" B J. Hence 

= k\X B \ , 2 



1 v\ \ 

= k{x B + vt B ). (2) 



This is the other fundamental equation of the subject, 
for it connects the physical distance of two points in 
Absolute Space with the measured magnitude of their 
co-ordinates relative to a moving platform. The k factor 



134 SCIENTIFIC THOUGHT 

enters through the Contraction and the Local Time, the 
v factor through the ordinary rules of relative motion. 

We can now sum up the results of the Michelson- 
Morley experiment in terms of the Absolute Theory. 
To explain the negative results of that experiment, 
whilst preserving the Absolute Theory, we have had 
to make three assumptions. Two of these involve 
action between Space and Matter ; the third is merely 
the explicit recognition of a convention, (i) We have 
had to assume that Absolute Motion of a body produces 
a contraction in the direction of motion. (2) We have 
had to assume that all clocks on a platform, which moves 
through the ether, are thereby made to go more slowly. 
These are both definite assertions as to the action of 
Absolute Space (or ether) on matter. (3) We saw that 
the conventions which we use to judge of identity of 
zero in scattered clocks are not justified if the clocks 
be in motion through the ether. This is not a new 
physical assumption, but is in accordance with common- 
sense. What is new is that we must still go on using 
this convention, because we can never tell whether we 
are in motion or not through the ether. It will be seen 
then that the results of the Michelson-Morley Experi- 
ment can be dealt with in terms of the Absolute Theory, 
provided we are prepared to make suitable physical 
assumptions as to the effect of absolute motion on clocks 
and measuring rods. Thus, it cannot be said that the 
newer facts definitely settle the old question betweerf 
Absolutists and Relationists in favour of the latter. 
Nevertheless, I think that reflection on the newer facts 
does strengthen the case of the Relationists by making 
the Absolute Theory seem more and more arbitrary and 
improbable. Before going further I will point out why 
I think this. (1) In order to explain the fact that 
motion through the stagnant ether does not produce 
the observable effects which one might reasonably 
expect it to do, the Absolutist has to assume that it 
does produce two different effects on matter, and that 



FIRST THEORY OF RELATIVITY 135 

the combination of these exactly neutralises the ex- 
pected phenomena. If a student, when taxed with not 
showing up an essay, were to reply that he had written 
it and then upset the ink over it, we should perhaps 
feel a little doubtful, and ask him to let us see the paper. 
If he then said that, by a strange coincidence, as the 
ink dried it faded, so that it was now impossible to 
see anything on the paper, even the Charity which 
"believeth all things" would be severely strained. 
Yet this is about the position in which the Absolute 
Theory finds itself when dealing with the Michelson- 
Morley experiment. (2) The alleged physical effects of 
motion through the ether are of the most extraordinary 
kind. For instance, the Lorentz-Fitzgerald Contraction, 
if taken as a physical fact, affects all kinds of matter 
equally. A rod of steel contracts as much as a bit of 
india-rubber. We might at least expect that such a 
contraction would be accompanied by strains, and that 
these would show themselves in the usual way by lead- 
ing to phenomena, such as double refraction, in other- 
wise isotropic transparent materials like glass. Such 
effects have been carefully looked for* and have never 
been found. Similar remarks apply to the systematic 
slowing of the clocks. In fact we may fairly say that 
the assumptions which the Absolute Theory has to 
make to square itself with the results of the Michelson- 
Morley experiment are so " fishy " as to cast additional 
^grave doubt on that theory. Let us then try to interpret 
the Michelson-Morley result in terms of the Relational 
Theory. 

Interpretation of the Michelson-Morley Result in terms 
of the Relational Theory. The two transformation equa- 
tions which we reached in the last section contain 
unobservable factors which we must now try to eliminate. 
On their left-hand sides they contain absolute time- 
lapses and absolute distances. On their right-hand 
sides they contain v, the supposed absolute velocity 

* In particular, by Rayleigh and Brace. 



136 SCIENTIFIC THOUGHT 

of the platform through the ether, which it is admitted 
we cannot detect. This occurs both explicitly, and also 
implicitly in the term /'. We want to get equations 
which will contain nothing but relative velocities, 
actual clock-readings, and measured distances. This 
is not difficult to do. First of all we must take 
two platforms, p x and p v Let us still talk in terms 
of the Absolute Theory, and suppose that p 1 has an 
absolute velocity v x and p., an absolute velocity v 2 in the 
same direction. Let this common direction, as before, 
be taken as the ,i-axis. The first thing that we must find 
is the measured relative velocity z/ a which the platform /> 2 
has with respect to observers on/j, who measure it with 
their own clocks and rods. Let a certain point on the 
platform p % be opposite to the standard clock of p x when 
this reads O. Let the same point of p 2 be opposite to B 
in p x when the clock there reads t B . The velocity of p 2 
relative to p x as measured by the observers on p x will 
then obviously be x B \t B . This is v,, x . Now from equations 
(i) and (2) we can easily derive the equations 

t r =k(t-v x Xp/c 2 ) (1) 

and x = k(Xp —v x t). (2) 

Xp-vJ 
Hence v 9 , = ^ 

21 f ^t 

1 c 2 
Now — ' s = z/ 2 , the absolute velocity of/ 2 . 

.•., dividing through by i, we get 

21 !_?!&_. (3) 

This formula is both intrinsically interesting, and 
essential for the next stage of our work. Let us put 

h= , l 2 , h= /==, and K= /=^= 2 . 

c 2 c 2 c 2 



FIRST THEORY OF RELATIVITY 137 

We have t = k x {t x + *f) = k % (t % + V -f) 

and x = k 1 (x l + v 1 t 1 ) = k 2 (x 2 + v 2 t 2 ), 

where x x and t x are the measured co-ordinate and the 
clock-reading on p x which correspond to physical 
distance x and absolute time-lapse t respectively, 
whilst x 2 and t 2 are the measured co-ordinate and clock- 
reading that correspond on p 2 to the same physical 
quantities. From these equations we can at once 
show that 



fj — ^i^2\ I 



V l V 3\ ( t > + *2 V 2- V l 



= ^ 2 (i-^ 2 )(^^ 2 ) by (3). 

i — -V 2 ) ; whence 

'1 = ^2 + ^)' (4) 

In the same way we can prove that 

x \ = ^21(^2 + v ziQ' (5) 

These equations are absolutely symmetrical as between 
t x and t 2 , x l and x 2 . For it follows from them that 

t -k (t - v *&\ 

and x 2 = k 2l {x x — v 2l t^) . 

But k 2X = k 12 and v 2l = — v 12 , whence 

' 2 = M/i + ^) (4 1 ) 

and x 2 = k 12 (x\ + v^tj (5 1 ) 

which are of precisely the same form as (4) and (5) 
respectively. 

We have thus eliminated almost the last trace of 
anything " absolute " and unobservable. Our equations 

K 



138 SCIENTIFIC" THOUGHT 

now contain only clock-readings ; measured distances ; 
relative velocities of one platform to another ; and 
the velocity of light with respect to the two platforms, 
which the Michelson-Morley experiment shows to have 
the same value for all platforms, even though they be 
in motion relatively to each other, provided the motion 
be rectilinear and uniform. The equations now tell 
us what co-ordinates and dates observers on one plat- 
form will ascribe to an event, provided we know what 
co-ordinates and dates the observers on any other 
platform ascribe to the same event, and also know the 
measured velocity of the one platform with respect to 
the other. The only trace of "absoluteness" that is 
left is the proviso that the platforms must be moving 
in straight lines, and with uniform velocities in the ether. 
This must be left till we come to the General Theory 
of Relativity in Chapter VI. 

In the meanwhile the reader may be inclined to raise 
a purely logical question, which ought to be settled 
before we go anv further. He may say : "You have 
just been deducing certain transformation equations 
from the assumption of absolute motion through the 
stagnant ether, and in this connexion you have 
assumed a real physical contraction in moving bodies 
and a real physical slowing down of moving clocks. 
It is true that you have at last deduced a set of equations 
which are entirely in terms of measured distances, 
clock-readings, and measured relative velocities. But 
even these were deduced from the assumption of two 
platforms moving with different absolute velocities 
through the stagnant ether. Would it not be a gross 
inconsistency if you were finally to make these equations 
the basis of a purely Relational Theory of Space, Time, 
and Motion? Would you not obviously be using your 
conclusions to prove something which directly con- 
tradicts the premises from which you derived those 
conclusions? And is this not plainly inconsistent?" 

This objection is invalid, as I shall now show. To 



FIRST THEORY OF RELATIVITY 139 

some people this fact may be obvious, and they may 
think the whole objection far fetched. I can assure 
them, however, that it is fetched from no farther than 
the University of Oxford ; and respect for the difficulties 
felt by that learned body induces me to make the logical 
position perfectly clear. To say that p is the premise 
from which we deduce q means more than to say that 
p implies q, though of course it involves this. It means 
in addition that our belief in p is our only ground for 
believing in q. When p and q are related in this way 
we cease to have any ground for believing in q so soon 
as we cease to believe in p. But/ may imply q, though 
/ is false and q is true. And, provided that we have 
other grounds for believing q, there is not the least 
logical objection to our first getting to know q as an 
implication of p and then using our belief in q as an 
argument against p. A foreigner might come to believe 
the true proposition that the Prime Minister of Great 
Britain in 192 1 was a Welshman because he mistakenly 
believed that Mr Asquith was Prime Minister at that 
date and that Mr Asquith was a Welshman. He might 
then find other grounds for believing that the Prime 
Minister was a Welshman ; he might, e.g., read in the 
papers that the Prime Minister had delivered a moving 
address in Welsh to the Free Calvinistic Anabaptists of 
Llanfairpwllgwyn. ... On subsequently comparing 
the Welsh national characteristics with what he could 
learn about those of Mr Asquith he might begin to 
feel a legitimate doubt as to his original belief that 
Mr Asquith was Welsh. Yet he would commit no 
inconsistency if he continued to believe that the Prime 
Minister in 192 1 was Welsh. He would have been 
inconsistent if he had never had any other reason for 
thinking that the Prime Minister was Welsh except 
the belief that Mr Asquith was Welsh and was Prime 
Minister ; but we are assuming that this was only his 
original ground for his conclusion, and that he subse- 
quently found other reasons to support it. 



i 4 o SCIENTIFIC THOUGHT 

Now this is precisely the position about the trans- 
formation equations. They do not begin to be directly 
verifiable till they are got in the purely relational 
forms (4) and (5). Once they are in these forms they 
contain nothing but what is observable, and the 
evidence for them is that they, and they alone, fit all 
the known facts. They do indeed follow from the 
Absolute Theory, together with the physical assumptions 
about contractions and clocks. This is not surprising, 
since those assumptions were made precisely in order 
to square the Absolute Theory with such facts as the 
negative result of the Michelson-Morley experiment. 
But, once they have been reached, by whatever means, 
the evidence for or against them is direct and inductive. 
The Absolute Theory is not the premise of them, and 
there is thus no inconsistency in using them to cast 
doubt on the Absolute Theory. We do this just 
because the Absolute Theory only leads to them when 
supplemented by certain physical assumptions which 
are intrinsically very improbable. If q be known to 
be true, and p only leads to q when supplemented by 
the very improbable premise p', the truth of q reflects 
the improbability of p' back on to p. This I think 
settles the purely logical question. In future the trans- 
formation equations in the relational forms (4) and (5) 
are to be accepted on their own merits, and without 
regard to the particular way in which it happens to be 
convenient to introduce them to the notice of readers 
brought up (as most of us are) on Absolutist traditions. 

There is, however, a real logical incoherence in a 
good many expositions of the Theory of Relativity. The 
Lorentz-Fitzgerald Contraction and the slowing of the 
clocks on a moving platform are first introduced as 
physical changes due to absolute motion. Later on 
the Absolute Theory is rejected. But the Lorentz- 
Fitzgerald Contraction is still recognised as a fact, and 
the same is true of the slowing down of the clocks. 
There is an apparent inconsistency here which is very 







FIRST THEORY OF RELATIVITY 141 

puzzling to the student of the subject. It is clear that, 
if the Contraction and the slowing of the clocks are 
still to be recognised, they must be reinterpreted, and 
this is what is actually intended but not always clearly 
brought out. Let us then reinterpret them in purely 
Relational terms. 

We have two platforms, p x and p. 2 , of which the 
second moves in a straight line along the Jt-axis of the 
first with a uniform measured relative velocity of v. 21 . 
A rod is lying on p 2 along the A'-axis. The people on 
p. 2 measure it and find that their unit measure goes into 
it / 2 times. What measure will the people on/j ascribe 
to this rod? They cannot, of course, measure it directly 
so long as it remains on p 2 , so they will have to adopt the 
following expedient. Suppose that one end of the rod is 
opposite to a point B of p x when the clock there marks t iB . 
Suppose that the other end is opposite to a point C of P 1 
when the clock there marks he. Let ti B — t v: . Then the 
people on p i will say that the distance BC on their plat- 
form, as measured by themselves, is the length of the 
rod which is fixed in p. 2 . For it is the distance between 
the points in p i which were opposite the two ends of 
the rod at the same moment, as judged by the clocks 
on p Y . The length, as measured by them, will therefore 
be Xic — x-iB' Now, by equation (5), 

x iC = k 2 i{x 2c + v 2i t 2c ) 

and x 1B = ti 21 [x 2ll + ^21*2^) 

X lc Xi B = K 21 \{X 2c . X 2ls ) +^2i('2c Izb))' 

By equation (4), 

+ h ( / _1_ V ^ X '' 



and tu, = k 2l (t 2C + V ^) 
Now / 1B = t lc , by hypothesis, 

• • t 2c t 2B = ZzK^-ZC X 2b ). 



142 SCIENTIFIC THOUGHT 

Hence x x — x 1B = k n {x t0 — x iB )[i - ^ 

= T (.X Zr -Vj/.j 
A 21 



i.e. / ' h^i-Hh (6). 

Thus we see that a rod whose length is /.,, as measured 
by observers who are at rest relatively to it, has a 
shorter length as measured by observers relatively to 
whom it moves with a uniform rectilinear velocity. If 
the two sets of observers can communicate with each 
other, those on p x will say that moving bodies are 
shortened in the direction in which they are moving, 
and the amount of shortening is that given by the 
Lorentz-Fitzgerald formula. Suppose now that the rod 
were transferred from p., to pi, and the observers on 
p t now measured it directly, whilst those on p., now 
measured it in the same indirect way which the p x 
observers had to use before. The observers on p x 
would now find that the rod had the measured length / 2 , 
whilst those on p. 2 would ascribe to it the measured 

length j^, which is the same as 2 - since k vz = k 21 . 

The observers on p 2 would put the case to themselves 
as follows : They would say that the rod, which was 
formerly at rest, has now acquired the velocity v l2 
(which is equal to — v 21 ), and that this makes it con- 
tract in the proportion given by the Lorentz-Fitzgerald 
formula. Thus both parties would agree that motion 
causes contraction, and both would agree in the formula 
which connects contraction with velocity. Both get 
the same measure when the rod is at rest on their plat- 
forms and they can measure it directly. This measure 
is l % . Both get the same measure when the rod is 
moving relatively to their platform and they can only 

measure it indirectly. This measure is ~, or, what is 



FIRST THEORY OF RELATIVITY 143 

the same, ~ • The contraction is thus no longer a 

^2t 

physical change caused by absolute motion through the 
stagnant ether ; it is simply a change in the measure 
of length of the same body, according as it is at rest 
relatively to the observers and can be measured directly, 
or is in uniform motion with respect to the observers 
and can only be measured indirectly. The measure- 
ments of the two sets of observers are perfectly con- 
cordant with each other, whenever the conditions under 
which they are made are precisely similar. And there 
is nothing particularly shocking in the fact that the 
measurements by two different sets of observers of the 
same body are not concordant when the conditions under 
which they measure it are not precisely similar. It is 
not even inconvenient, since the transformation equa- 
tions tell us how to pass from the one measure to the 
other. 

We can now deal with the interpretation of the 
facts about the clocks in terms of the Relational Theory. 
Let the clock at the point B on p 2 first read t 2B and 
later on let it read T 2 «. The time-lapse as measured 
by observers on p 2 will, of course, be T 2S — t 2B . Let 
the clock which is opposite to B in p 1 on the first 
occasion read t 1B , and the clock which is opposite 
to B in p i on the second occasion read T lB . Then 
we have 



^21-^2 B 
IB" ~ 72" 



A « B /Soil 1 OB ~T 



"^21^ZB 



and *i* = &2i(*m+ — 

Whence T lB —t 1B = k 21 (T 2B —t 2B ) = 2 (T 2fl — t 2B ) (7). 

V I ~ U 21 



c 2 



Thus the time-lapse, as measured indirectly from p v 
is greater than the time-lapse as measured directly on 
p 2 . The people on p x , on communicating with those 
on p 2 , will therefore say that the clocks on p 2 are 



i 4 4 SCIENTIFIC THOUGHT 

rendered slow by the motion of f> 2 . If, however, a 
clock from /> 2 were transferred to p x and the time-lapse 
were measured with it directly by people on p t and 
indirectly by people on p. 2 , the latter would say that 
their old clock was now going more slowly, and would 
ascribe this to its transference to the moving body p x . 
Thus both parties would agree that rectilinear motion 
slows clocks, and both would agree as to the connexion 
between this slowing and the relative velocity. But, 
once again, the slowing is not now a physical effect, 
due to absolute motion through the ether. It is simply 
a change in the measure of time-lapse, according as it 
is measured by the readings of a single clock which 
is fixed in the place where the time-lapse is measured, 
or by the readings of two different clocks which 
successively face this place in the course of their 
motion with respect to it. The measurements of the 
two sets of observers are again quite concordant, 
whenever they are carried out under precisely similar 
conditions; and when the conditions of the two observa- 
tions differ in the way described above, we can always 
pass from the one measured time-lapse to the other 
by using the equations. 

We might sum up these results as follows: (i) 
There is a direct and an indirect way of measuring 
length. The former can only be applied to bodies that 
are at rest relatively to the person who is making the 
measurement, and consists of the familiar process of 
applying a measuring rod and seeing how many times 
it has to be laid down before it reaches the other end 
of the body. When the body to be measured is moving 
relatively to the observer this method cannot be applied. 
What has to be done then is for two observers on the 
same platform to note what points on the platform the 
two ends of the moving body face at the same moment 
as judged by the clocks on their platform. They then 
measure this distance directly, and take it as the 
measure of the length of the moving body. These 



FIRST THEORY OF RELATIVITY 145 

two methods lead to the same measure for the same 
body (assuming that clocks have been standardised on 
the two platforms by the principles laid down earlier 
in the chapter) if and only if the two platforms be at 
rest relatively to each other. If the two platforms be 
in uniform rectilinear relative motion, the two methods 
do not lead to the same measure for the same body. 
The two measures are then connected with each other 
and with the measured relative velocity by the Lorentz- 
Fitzgerald formula. It will be noticed — and this is 
very important — that the indirect method of measuring 
length necessarily involves a reference to time, since we 
measure the distance between those two points which 
the two ends of the moving body are judged to face 
simultaneously. Whether the direct method of measure- 
ment also implicitly involves a reference to time we 
will not discuss at present, though we shall have to 
do so later. 

(2) There is a direct and an indirect way of 
measuring the time that elapses between two successive 
events which happen at the same point on a platform. 
The former can only be applied by observers who are 
and remain at this place on the platform, and it con- 
sists of the familiar process of noting how far the 
hands of the clock there have turned between the two 
events. When the two events happen on a body which 
is moving relatively to the observer this method cannot 
be used. What has to be done then is for two observers 
to note the readings of their clocks when the first event 
happens opposite to one and the second event happens 
opposite to the other. The difference between the 
readings of these two separated clocks is then taken 
as the measure of the time-lapse between the two events 
on the moving body. These two methods lead to the 
same measure for the time-lapse between the same pair 
of events (assuming that both sets of clocks have been 
standardised by the principles already laid down) if 
and only if the two platforms be at rest relatively 



i 4 <) SCIENTIFIC THOUGHT 

to each other. If the two platforms be in uniform 
rectilinear relative motion, the two methods do not 
lead to the same measure of the time-lapse between 
the same pair of events. The two measures are then 
connected with each other and with the measured 
relative velocity by the formula (7). It is important 
to notice that the indirect measure of time-lapse is 
essentially bound up with distance. For the two events 
which happen in the same place with respect to the 
one platform happen in different places with respect 
to the other. The greater the relative velocity of 
the two platforms the greater the spatial separation 
of the two events will be, and the greater will be 
the discrepancy between the two measures of the time- 
lapse. 

This connexion between the spatial and temporal 
separations of a pair of events comes out still more 
clearly when we consider a more general case, which 
must anyhow be treated for the sake of completeness. 
We have assumed so far that the two events whose 
temporal separation was to be measured happened at 
the same point on one of the platforms. Let us now 
suppose that a certain event happens at B on p 2 when 
the clock there reads i iB . Let a second event happen 
at C on p 2 when the clock there marks t 2C . 

Then the time-lapse as measured on p 2 ist iC .— t 2B . But 



1 7 / 21 2.C \ 

and t 1 c = Ki[t2o+— -J-)- 

Whence t lc -t Vl = k 21 {(t 2C -t 2lj ) + -f(x 2c -x 2H )}. (8). 

Now x 2 B = k 12 {x 1H + v lZ t 1B ) 

X 2 c = A\ 2 [X 1 +"V 12 t xc ). 

Whence x 2C -x 2R = k 12 {(x lc -x lls ) + v 12 (t lc -t 1B )} 

— K n {\x\ c —x lB ) — v 2k (t lC —t lB )}. 



FIRST THEORY OF RELATIVITY 147 

Whence t lc -t x = £ 21 {(7 2 - t 2B ) + -^r{x 10 -x 1B ) 

,-2 Vl l \n)) 



k 2 V 

Whence k^{t x - t llt ) = k 21 (t 2 -t 2R )+^ L ^{x lc -x\ B ), 



V 2X t 



° r *X -tlB=T-{t 2 C-t 2 B) + -2{X 10 -X 1B ). (9) 



k 21 



Thus the time-lapse between two remote events has 
a different measure according to whether it is deter- 
mined by clocks which are at rest relatively to the 
events, or by clocks which are in uniform rectilinear 
motion relatively to ^em. The discrepancy between 
the two measures depends on the spatial separation 
between the two events, in the direction of relative 
motion of the two platforms. Equation (8) expresses the 
relation in terms of the spatial separation, as measured 
by observers who are at rest relatively to the two events ; 
equation (9) expresses it in terms of the spatial separa- 
tion as measured by observers who are in uniform 
rectilinear motion relatively to the two events. In par- 
ticular, let us suppose that the two events are contem- 
porary as judged by the clocks of their own platform. 
This means that t ilB = t. 1 . Then they will not be contem- 
porary as judged by the clocks on the other platform, 

for t xc — t XB will be equal to z( x \c~ x \b)- Thus the tem- 
poral separation with respect to p will increase with 
the spatial separation. 

The upshot of the whole matter is to show how 
inextricably our measurements of distance and of time- 
lapse are bound up with each other. It is now quite 
evident that any attempt to measure lengths of bodies 
which are moving relatively to us involves judgments 
of simultaneity. On the other hand, a pair of events 
which are simultaneous with respect to a certain plat- 
form, and are separated in space with respect to that 



148 SCIENTIFIC THOUGHT 

platform, will be successive with respect to any platform 
that moves relatively to the first; and the time-lapse 
between them with respect to the second platform will 
depend on the spatial separation of the two events. It 
is only pairs of events that happen both at the same 
place and at the same date with respect to some platform 
which will happen at the same place and date with 
respect to rf// platforms that move with uniform rectilinear 
velocities relative to the first. A pair of contemporary 
events, which occupy different places with respect to the 
platform in which they are contemporary, will be succes- 
sive in all other platforms that move relatively to the 
first. A pair of successive events, which occupy the 
same place with respect to a certain platform, will occupy 
different places with respect to all other platforms which 
move relatively to the first. The latter fact was familiar 
enough before the Theory of Relativity was developed. 
If I travel to Scotland and eat my lunch in the dining- 
car, the two events of eating my soup and drinking my 
coffee are successive ; and they happen in the same 
place relatively to the train, viz., at my seat in the 
dining-car. But, with respect to the earth, they happen 
at different places, e.g., at Grantham and at York. The 
fact which has only lately been recognised is that the 
same applies to the dates of events which happen in 
different places. If the watches of the travellers and the 
officials on the train had been set, by the same principles 
as clocks are set on the earth, while the train was in 
motion, we should have the following result : My 
neighbour and I might each take a mouthful of soup at 
the same time, as judged by our watches ; but, as judged 
by the clocks on the earth, his mouthful would happen 
a little later than mine, if I were facing the engine and 
he had his back to it. And the difference in date would 
be proportional to the width of the table at which we were 
both sitting. The reason why this point has long been 
obvious about Space but has needed very delicate experi- 
ments to force it on our attention as regards Time is 



FIRST THEORY OF RELATIVITY 149 

the following : The separation between Grantham and 
York is gross and unmistakable. But the separation 
in time between my mouthful and my neighbour's, as 
judged by clocks on the earth, is proportional to the 
ratio of the velocity of the train to the square of the 
velocity of light (see equations S and 9). Now the 
velocity of light is enormous as compared with that of 
the trains on even so efficient a railway as the Great 
Northern, and so the temporal separation is negligible 
and can only be detected indirectly through the negative 
results of such delicate experiments as the Michelson- 
Morley. 

We see then that, in the long run, the Theory of 
Relativity is more whole-heartedly relational than the 
traditional Relational Theory of Motion which we 
discussed in the last chapter. For, according to it, 
not only is the spatial separation of successive events 
relative to the system of co-ordinates chosen, but also 
the temporal separation of two events in different places 
is relative to the system of co-ordinates and the clocks 
associated with them. 

The Restricted Physical Principle of Relativity. I will 
end this chapter by trying to state this physical principle 
clearly, and then to explain it. It may be stated as 
follows : The laws of any physical phenomenon have 
the same mathematical form, whether they have been 
discovered and verified by observers who were at rest 
relatively to this phenomenon or by observers who 
were moving relatively to it with a uniform rectilinear 
velocity. Let us now try to see exactly what this means. 
The law of any phenomenon, when expressed in 
mathematical form, is a differential equation connecting 
some measured quantity which is observed in a certain 
place at a certain time with some other measured 
quantity which is observed in some other (or it may be 
the same) place at some other (or it may be the same) 
time. The law will also involve the distance between 
the two places and the time-lapse between the two 



150 SCIENTIFIC THOUGHT 

dates. Maxwell's equations are a perfect example 
of a physical law. Now it is clear that such laws 
are, in the end, verifiable only in so far as they 
express relations between actually measured magnitudes, 
such as clock-readings, deflexions of galvanometers 
or magnetometers, number of weights put into a balance, 
number of times that a certain rod has to be laid down 
to get from one place to another, and so on. We may 
take these measures to represent so much time-lapse, so 
great a current or magnetic force, such and such a 
gravitational attraction, so much length, etc. ; and 
we may, if we like (and if we can make clear what 
we mean), raise the question whether these actual 
measures which we read off our instruments "truly" 
represent the "real" physical magnitudes in question. 
But, so far as our laws and their verification are con- 
cerned, the measured magnitudes are the important 
things, and the question of what they stand for in 
the physical world is a secondary matter of theoretical 
interpretation. E.g., Maxwell's equations, so far as 
they can be verified, state relations between the readings 
of electrometers, magnetometers and galvanometers in 
various places ; the readings of clocks in these places ; 
and the number of times rods have to be laid down to 
get from one place to another. 

Now it is not true, and the Physical Principle of 
Relativity does not assert, that if one observer is at rest 
with his instruments relatively to a certain phenomenon, 
and a second observer is in uniform motion with his 
instruments relatively to the first, the corresponding 
instruments of the two observers will give the same 
readings. We already know in fact that they will 
ascribe different time-lapses and different spatial separa- 
tions to the phenomena under observation. And the 
same is true in general of their other measurements. 
Suppose, e.g., that one observer with a magnetometer 
and a quadrant electrometer is at rest with respect 
to a charged particle, and the other observer, provided 



FIRST THEORY OF RELATIVITY 151 

with similar instruments, is in uniform rectilinear 
motion with respect to the first. The first observer's 
magnetometer will give a zero reading, whilst the second 
observer's will give a finite reading. What the Physical 
Principle of Relativity does assert, and what is true, so 
far as we know, is the following proposition : The 
equations which interconnect the readings of one 
observer's instruments with each other and with his 
measured distances and time-lapses are of precisely 
the same form as those which interconnect the read- 
ing's of the other observer's instruments with each 
other, and with his measured distances and time- 
lapses. 

To put the principle formally, let us suppose that 
the observers on p x are at rest with respect to the 
phenomenon in question. Let the relevant readings 
of their measuring instruments be P x , Q x , R r . . . Let 
the relevant distances and time-lapses, as measured by 
them, be d t and t x respectively. The velocity of the 
phenomenon with respect to them is o. Suppose they 
find that these various readings are connected with each 
other and with the measured distances, time-lapses, 
and velocity, by the equation or set of equations — 

<£i ( p i> Qi> R r • • • ; d x ; t x \ 0)= o. 

Let the corresponding readings of the observers on p 2 
who watch the same phenomenon be P 2 , Q 2 , R 2 . . . . 
Let their measured distances and time-lapses be d 2 
and t 2 respectively. With respect to them of course 
the phenomenon under observation has the measured 
velocity v 12 . Then their readings will be connected 
with each other by the equation or set of equations — 

& ( p 2 > Q 2 > R 2 . . . • ; 4 ; 4 ; ^12) = 0. 

Now what the physical principle states is that <£ 2 is the 
same as <\> x . This may be briefly summed up in the 
statement that, according to the Restricted Physical 
Principle of Relativity, the laws of nature are co-variant 



152 SCIENTIFIC THOUGHT 

with respect to the space-time transformations of the 
Special or Restricted Theory of Relativity. 

It is important to be quite clear as to the connexion 
between this principle and the invariance of the 
measured velocity of Light with respect to all observers 
who move relatively to each other in straight lines with 
uniform velocities. This latter fact neither implies nor 
is implied by the physical principle, though it is of 
course compatible with it. It is obvious that a fact 
about light could not by itself logically imply a principle 
about all natural phenomena whatever. Conversely, 
the physical principle only implies that the measured 
velocities of light with respect to all observers will be 
the same function of their respective measurements of 
distance and time-lapse. It does not imply that all 
these measured relative velocities will have the same 
numerical value. That they do in fact have the same 
numerical value is an uncovenanted mercy, revealed to 
us by the Michelson-Morley and other experiments. 
This fact is of immense practical importance, because 
it enables us to bring the Physical Principle down from 
the clouds and apply it to get concrete results. For 
the invariance of the measured velocity of light enables 
us, in the way that we have described, to reach the 
transformations for space and time, i.e., to express d 2 
and t 2 in terms of d x and t x . Having done this, we 
can see how P 2 , Q 2 , R 2 . . . . must be related to P x , Q x , 
R r ... in order that the form of the laws of any 
phenomenon may be the same for the observers on p x 
as for those on p % . The result is that, if we once know 
the readings on the instruments of an observer who is 
at rest with respect to a phenomenon, we can calculate 
the corresponding readings of the instruments of an 
observer who is moving with uniform rectilinear velocity 
relatively to the phenomenon. This is of course an 
immensely important power to possess. 

If we accept the Physical Principle we shall have 
to investigate all alleged laws of nature to see whether 



FIRST THEORY OF RELATIVITY 153 

they agree with it, i.e., whether they be co-variant with 
respect to the transformations of the Special Theory 
of Relativity. Some alleged laws of nature, we find, 
are already in the right form ; Maxwell's equations are 
a case in point. Others are not, e.g., the Conservation 
of Momentum, on the traditional view that mass is 
independent of velocity. Such examples might, at first 
sight, be taken as casting doubts on the principle. 
Here, however, there are two points to notice: (1) If 
the principle be true and the laws wrongly stated, it 
is not surprising nevertheless that the laws have seemed 
to be constantly verified. For the divergence would 
only begin to show itself when we deal with velocities 
which are comparable with that of light. Now of 
course the velocities of ordinary bits of matter are quite 
negligible in comparison with that of light. (2) As 
soon as people did come to deal with matter moving 
with very high velocities, as in the case of particles 
shot out from radio-active bodies or from the poles of 
vacuum tubes, it was found that the traditional laws 
had to be modified, and that the modification was in 
the same direction and of the same order as that de- 
manded by the Physical Principle. The strong point 
about the principle in such cases is this : If you keep 
the traditional form of the laws and try to reconcile 
them with the facts about particles that move with 
velocities comparable to that of light, you have to 
make special physical hypotheses as to the nature 
and minute structure of matter. The other plan, of 
modifying the laws till they accord with the Physical 
Principle, has the advantage that it accounts for 
the experimental results, and requires no special 
physical hypotheses as to the nature and structure of 
matter. 

With the further development of the Theory of 
Relativity, and the further modification of traditional 
physical concepts which this entails, I will deal in the 
next chapter but one. 



154 SCIENTIFIC THOUGHT 

The following works may be consulted with 
advantage : — 

L. Silbkrstein, Theory of Relativity. 

M. SCHLICK, Space and Time in Contemporary Physics. 

E. Cunningham, Relativity, Electron Theory, and Gravitation. 

[The reader may here be warned that most popular 
expositions of the Theory are either definitely wrong, 
or so loosely expressed as to be dangerously misleading; 
and that all pamphlets against it — even when issued by 
eminent Oxford tutors — are based on elementary mis- 
understandings.] 



CHAPTER V 

" Die Entscheidung dieser Fragen kann nur gefunden werden, 
indem man von der bisherigen durch die Erfahrung bewahrten 
Auffassung der Erscheinungen, wozu Newton den Grund gelegt, 
ausgeht und diese durch Tatsachen, die sich aus ihr nicht 
erklaren lassen, getrieben allmahlich umarbeitet ; solche Unter- 
suchungen, welche .... von allgemeinen Begriffen ausgehen, 
konnen nur dazu dienen, dass diese Arbeit nicht durch die 
Beschranktheit der Begriffe gehindert und der Fortschritt im 
Erkennen des Zusammenhangs der Dinge nicht durch iiber- 
lieferte Vorurteile gehemmt wird." 

(Riemann, Uber die Hypothesen welche 
der Geometrie zu Grunde liegen.) 

The Traditional Kinetics, and its Gradual Modification 
in the Region of Physics, (i) Newton's Laws of 
Motion and Gravitation 

I do not propose to pass directly from the Special 
Theory of Relativity, explained in the last chapter, 
to the General Theory of Relativity. The latter is 
largely concerned with the laws of motion and the law 
of gravitation, and so it will be more profitable to begin 
by discussing the traditional form of these. Thus this 
chapter will be more closely connected with Chapter III, 
and the next with Chapter IV. 

Newton's first law of motion states that, under the 
action of no forces, a body continues at rest or in 
uniform rectilinear motion. This statement, as it stands, 
is meaningless, if we do not assume the Absolute Theory, 
and is a mere pious opinion incapable of verification or 
refutation if we do assume that theory. If we assume 
the Relational Theory, it is an incomplete statement. 
If all motion be change of position of one body with 
respect to others it is useless to talk of rest or of motion 

155 



156 SCIENTIFIC THOUGHT 

in a straight line until we have specified what set of 
bodies we are using as our axes of reference. I am at 
rest with respect to my room and in motion with respect 
to the sun. The planet Mars is describing an ellipse 
with respect to the sun and a very complicated curve 
with respect to the earth. No doubt the law, as origin- 
ally stated, professed to apply to motions in Absolute 
Space. But, as these, even if they exist, are unobserv- 
able, the law with this interpretation is as idle as the 
statements in the Athanasian Creed on the internal 
structure of the Blessed Trinity. The first thing needed 
then, is to assign our axes of reference. I assume these 
to be the fixed stars primarily. But it follows from the 
form of the first two laws that any set of axes which 
is in uniform rectilinear motion with respect to the 
fixed stars will do equally well, provided we take tradi- 
tional views about the measurement of Space and Time, 
and do not at present introduce the complications which 
emerged in the last chapter. 

Even when the spatial axes have been fixed there 
remained two unexplained terms, viz., uniformity and 
force. Let us begin with uniformity. Uniformity of 
motion is meaningless unless it refers to absolute 
motion or states clearly what it takes as its standard 
measurer of time. A uniform motion means one which 
covers equal distances in equal lapses of time. If we 
take the Relational View of Time a lapse of time is a 
relation between two events ; and, even if in theory 
we take the Absolute View, it is only lapses between 
events that can actually be observed and measured. 
It is therefore assumed that we have some process 
which recognisably repeats itself, and that the time- 
lapse between corresponding stages in each repetition 
is the same. A uniform motion is one that covers 
equal distances during the same number of repetitions 
of some standard process which is itself isochronous. 

The question at once arises : How are you to tell 
that your standard process is isochronous, i.e., that the 



TRADITIONAL KINETICS 157 

time-lapse between corresponding stages in it is always 
the same ? If you determine this indirectly by mechanical 
arguments the first law of motion becomes a tautology, 
for you will first use arguments based on the law to 
prove that such and such a process is isochronous and 
will then use this process to give a meaning to the 
uniformity of motion, which the first law is about. 
This fallacy is not, of course, commonly committed in 
so glaring a form. But, in a rather subtler form, some- 
thing very like it is committed. Our common standard 
of isochrony is the successive swings of a pendulum. 
Suppose then we define uniform motion with respect 
to a certain set of axes, as motion that covers equal 
distances with respect to these axes during successive 
swings of a pendulum. So far no fallacy has been 
committed. But if we verify the first law experiment- 
ally on this definition of uniformity, and then later on 
use the first law as the basis of an argument to explain 
that the pendulum does not take quite equal times for 
successive swings, and to correct its errors, we do 
commit a fallacy. If uniformity of motion in the first 
law just means uniformity as compared with a pendulum, 
anyone who afterwards says that pendula do not move 
quite isochronously cannot continue to use "uniformity" 
in the original sense in which it was used in formulat- 
ing the first law. And then two difficulties will arise. 

(1) We must ask him what process he is now taking 
as his standard, since it is admitted that uniformity, if 
it is to be observable and measurable, must involve 
a comparison with some standard physical process. 

(2) We may remind him that, if the first law has been 
verified when uniformity is interpreted by reference to 
a pendulum, no argument resting on the law can fairly 
be used to prove that pendulums do not in that sense 
move isochronously. Whilst (3), if the law be not 
accurately true, when uniformity is defined in this way, 
it ought not to be used to prove anything until either 
(a) it has been modified so as to be accurately true on 



158 SCIENTIFIC THOUGHT 

the old definition of uniformity, or (/<>) a new meaning 
of uniformity has been given in which it is accurately 
true in its original form. 

There are in fact only two alternatives open to us. 
Either the first law is simply a definition of uniformity, 
in which case it reduces to the statement that a uniform 
motion means one that takes place under the action of 
no forces. Or it is a substantial statement, in which 
case some standard process or set of processes must be 
judged immediately to be isochronous and used after- 
wards as the criterion of uniformity. I think it is quite 
certain that the first alternative is not the right one. It 
seems quite clear that the meaning of uniformity or of 
isochronism has nothing to do with the laws of motion. 
People judged certain processes, such as the swings 
of pendula, the burning of candles in the absence of 
draughts, the descent of sand in hour-glasses, etc., as 
isochronous long before they had thought of the 
question whether forces were present or absent. 

We must therefore take the second alternative. This 
implies that, under favourable circumstances, we can 
directly judge equality of time-lapses, just as we can 
judge equality of lengths. This seems to be true. It 
does not of course imply that such judgments are 
infallible. And the question arises : Can we ever con- 
sistently correct our standard process by means of laws 
which are in terms originally defined by it? I think 
that we can and do, and that the logic of such a pro- 
cedure is well worth considering. 

I take it that our immediate judgment that the time- 
lapses between successive swings of an ordinary 
pendulum are equal is very approximately true, if we 
be at rest with respect to it. Suppose we take this as 
our original standard of isochrony and define uniformity 
by means of it, and that we find that, with this defini- 
tion, the first law is verified over a wide range. This 
verification again will only be within the limits of 
experimental error. Now, suppose we apply the first 



TRADITIONAL KINETICS 159 

law, thus stated and thus approximately verified, to a 
very large number of phenomena. We may find, as we 
extend our observations and make our measurements 
more accurate, that a great number of phenomena are 
very approximately, but not exactly, in accordance with 
the first law. There are, we will suppose, small residual 
effects left unexplained in a number of cases. At this 
stage two alternatives are open to us : (1) We may keep 
the first law, as originally stated, and hold that small 
disturbing causes are operating in all the exceptional 
cases. We may then put forward physical hypotheses 
to account for these. Or (2) we may say that the first 
law, as originally stated, is not accurately true. Sup- 
pose we find that a single slight modification in it will 
account for all the slight inaccuracies in the predictions 
based upon it. Obviously it is more reasonable to 
make this one modification than to put forward different 
supplementary physical hypotheses in each case which 
the original law fails accurately to account for. Now, 
this modification of the first law might itself take place 
in two alternative ways, (a) We might say: "The 
pendulum is accurately isochronous, and under the 
action of no forces, bodies move with very nearly, but 
not quite, uniform rectilinear motions with respect to the 
fixed stars. " Or we might say (b): " The swinging of a 
pendulum is an approximately, but not exactly iso- 
chronous process, and therefore a body that moves 
'uniformly,' as judged by a pendulum, is not really 
moving uniformly." If we assume that the times taken 
by successive swings differ by a certain very small 
amount, we may be able to keep the form of the first 
law unmodified, and yet accurately explain all the facts. 
So, in a sense, you may say that the first law was 
formulated in terms of uniformity, as defined by a 
pendulum, and was then used to show that such 
"uniformity" is not quite uniform. Is there any 
logical objection to such a process? 

Not if we clearly understand what we are doing. 



160 SCIENTIFIC THOUGHT 

We did not start by defining equality of time-lapses to 
mean the relation between the successive swings of a 
pendulum. We simply said that these two durations 
could be immediately perceived to be in fact very nearly 
equal. We admitted that this judgment might quite 
well ignore differences too small to be immediately per- 
ceived. Again, we find that, with the sense of uniformity 
which is based on the assumption that pendula are 
accurately isochronous, the first law is true within the 
limits of unaided observation. More extended and more 
delicate observations forced us either to modify the law 
itself, or to make a large number of supplementary 
physical hypotheses, or to reject the view that pendula 
are exactly isochronous. We preferred to take the last 
of these alternatives. The result is that both the law 
and the standard of uniformity contain a small leaven 
of convention and a large mass of substantial experi- 
mental fact. Uniformity is tested by a standard physical 
process, known to be nearly isochronous, but slightly 
"cooked," so as to keep the form of the first law fixed. 
The first law is known to be very nearly true, even when 
uniformity is tested by the uncorrected process ; but the 
test for uniformity is slightly changed, so as to make the 
law, in its original verbal form, quite true and yet 
compatible with all the facts. 

This mixture of convention and observation is a very 
common feature in scientific laws, and is unobjection- 
able on three conditions: (i) That, even without it, 
the law is verified very approximately over a very wide 
range; (2) that the amount of " cooking " needed is 
below the limits of possible direct observation ; and 
(3) that, with it, the law keeps its original simple form, 
and yet now accounts accurately for all the facts without 
supplementary hypotheses. 

The remaining ambiguous term in the first law 
is Force. Granted that the first law is not a definition 
of uniformity, it might still be held to be a definition 
of the absence of forces. If it is not to be this, but is to 



TRADITIONAL KINETICS 161 

be a substantial statement, the following conditions 
must be fulfilled. We must, in certain cases at least, 
be able to know whether a body is or is not acted on 
by forces, independently of knowing whether that body 
is in fact moving uniformly in a straight line in the 
sense defined above. For the first law says that, under 
the action of no forces, bodies rest or move uniformly 
in straight lines. If this be an experimental fact about 
nature it must be based on observing bodies which were 
known to be under the action of no forces, and finding 
that they always rested or moved in straight lines with 
respect to the fixed stars with a velocity which is uniform, 
as judged by some standard process, corrected, if 
necessary, in the way discussed above. We must 
therefore ask : What do we mean by force, and can 
we ever tell, apart from the laws of motion, whether 
forces are acting on a body or not? 

To answer this question we shall need to take account 
of the second law of motion as well as the first. Many 
eminent men have held that the notion of force is need- 
less and useless in Mechanics. Their view is that the 
so-called second law of motion is not the expression 
of an experimental fact, but is simply a definition of 
force; so that, wherever the latter word occurs in 
Mechanics, we can substitute for it the definition given 
in the second law. Now, the second law may be put 
in the form that the rate of change of momentum of 
a particle at any moment in a given direction is equal 
to the force which is acting on the particle at that 
moment in that direction. "Direction" of course 
involves a tacit reference to some set of axes, and 
" rate of change " involves a reference to some standard 
process for time measurement. These may be taken to 
be the same as those which have already been fixed 
upon in discussing the first law. Now, we might regard 
the second law in two different ways : (i) We might 
suppose that we already know what we mean by force, 
and already have a method of measuring its magnitude 



162 SCIENTIFIC THOUGHT 

and direction. On that view the second law is a sub- 
stantial statement expressing the observed connexion 
in magnitude and direction between a force and the 
rate of change of momentum of a particle. (2) The 
other view is that the second law simply gives a meaning 
to the word " force," and defines the phrase "a force of 
such and such a magnitude acting in such and such a 
direction." The latter interpretation is, for some reason 
or other, considered to be tremendously hard-headed and 
"scientific," the former to savour of metaphysics. We 
shall see that, although there is a certain amount of truth 
underlying the second view, it is greatly exaggerated 
and has nothing to do with any antithesis between 
" science " and " metaphysics." 

It seems clear to me that no one ever does mean or 
ever has meant by " force " rate of change of momentum. 
It is certain that the second law, as originally stated, 
was not intended for a definition of force but for a 
substantial statement about it. Unquestionably the 
sensational basis of the scientific concept of force is 
the feelings of strain that we experience when we drag 
a heavy body along, or throw a stone, or bend a bow. I 
do not understand that this historical fact is denied by 
the upholders of the "descriptive" (or better, "defini- 
tional ") theory. What they would probably say is 
that, in this sense, force is purely human and has no 
relevance to the laws of Mechanics. We cannot 
seriously suppose, e.g., that the sun feels a strain in 
keeping the earth in its orbit, as we do when we whirl 
a weight on a string. Hence it is argued that what we 
mean, when we say that the sun exerts a force on the 
earth, cannot be derived from the experiences of strain 
which we feel. I think there are two answers to this : 
(1) We must distinguish between our feeling of strain 
and the strains that we feel, just as we must distinguish 
between our feeling of movement and the movement 
which we feel ourselves to be making-. Force is not 
supposed to be our feelings of strain ; it is simply 



TRADITIONAL KINETICS 163 

supposed that the strains which we feel are forces, or 
are indications of forces. It is of course absurd to 
suppose that the sun feels a strain when it pulls the 
earth ; but this is absurd, not because the sun could not 
be subject to a strain, but because — having no mind — it 
cannot yW a strain or anything else. It is thus perfectly 
consistent for a man to describe forces as the sort of 
factors in nature which reveal themselves to us directly 
in our feelings of strain, and to add that inanimate 
bodies, like the sun, are subject to forces. (2) The 
argument under discussion, if pressed, would make it 
as unreasonable to say that an inanimate body like the 
earth is round or rotates as to say that it is acted on by 
forces. For there is no kind of doubt that our concepts 
of roundness and rotation are founded upon sensations 
of sight and touch. If I had not had sensations of 
round or approximately round objects, I should no 
more know what roundness means than a colour-blind 
man knows what red means. The person who uses the 
argument about the sun not feeling strains, as an 
objection to the view that the feeling of strain is the 
sensational experience which gives a meaning to the 
concept of force, may be invited to consider the follow- 
ing parallel argument : " How can the concept of 
roundness be based on our sensations of sight and 
touch when the earth, which can neither see nor feel, 
is admitted to be round?" The answer of course is 
that the earth has the sort of properties which we have 
become acquainted with by seeing and feeling, and that 
it does not need to see or feel in order to have them. 
Similarly, there seems to be no reason why the earth 
should not be subject to forces which it does not 
feel, whilst forces are the sort of natural facts which 
we become acquainted with through our feelings of 
strain. 

I think then that we may quite reasonably hold 
that the strains that we feel are the original sensational 
data on which we have based the concept of physical 



i64 SCIENTIFIC THOUGHT 

force, just as coloured and shaped patches sensed by 
us are the original sensational data on which we have 
based the concepts of physical shapes and colours. The 
descriptive theory simply puts our sensations of sight 
and touch into a quite irrationally privileged position 
as compared with our sensations of strain. We shall 
see later on, what amount of practical justification there 
is for this procedure. 

t Now, even if we confine ourselves to the crude data 
of muscular sensation, we can distinguish the factors of 
direction and magnitude. We have to exert ourselves 
more to throw a heavy hammer than to throw a small 
stone with the same velocity. And to make a thing 
move in a given direction we have got to adjust our 
bodies so as to push, pull, or throw it in that direction. 
Thus force, as actually sensed in our feelings of strain, 
is obviously in rough general agreement with the second 
law, when the surface of the earth is taken as our spatial 
axes and any common rate measurer as our standard 
of time. The trouble, of course, is that felt strains are, 
and remain, vague both in magnitude and direction. 
Moreover, most of the forces with which we have to 
deal in science are not felt by us as strains. We cannot, 
then, base a satisfactory scientific measure of force on 
felt strains. But this is not a peculiarity of strains. 
It is equally true of felt temperatures. The meaning of 
temperature and of force is derived from felt hotness 
and felt strain respectively. A person who had no 
such sensations would not understand these terms at all. 
Again, both these felt characteristics have a perfectly 
noticeable though vaguely discriminated intensive mag- 
nitude. We want to define methods of measurement 
in each case, which shall agree in the main with our 
rough immediate judgments, but shall be capable of 
much greater accuracy, and of application to cases 
where the sensations cannot be got at all. This is what 
a thermometer does for us, in the instance of tempera- 
ture; but no one " except a fool or'an advanced thinker" 



TRADITIONAL KINETICS 165 

(to quote Mr Bradley) imagines that what we mean by 
temperature is the height of a column of mercury, 
v In any case, then, the second law is not a statement 
of what is meant by force. But it might still be merely 
a statement of how force is to be measured for scientific 
purposes. -' It will be so if the one and only way of 
measuring force is by measuring rate of change of 
momentum. If, however, there be any independent 
way of accurately determining the direction and magni- 
tude of a force, the second law will be neither a defini- 
tion of force nor a mere statement as to how it is to be 
scientifically measured. It will be a substantial state- 
ment about force. Now I think it is quite evident 
that, in favourable cases, we can measure force without 
reference to rate of change of momentum. Suppose a 
number of strings are attached to a body ; that they 
then pass over pulleys ; and have weights attached to 
them. Then the momentary directions of the strings 
give a clear and measurable meaning to the directions 
of the forces, and the weights give a clear measure of 
their magnitudes. And these magnitudes and direc- 
tions are: (1) in fair agreement with what our sensations 
of strain tell us in all cases where a comparison can 
be made ; (2) are far more accurate and definite, and 
can be determined in cases where we cannot get sen- 
sations of strain ; and (3) are quite independent of all 
reference to rate of change of momentum. The second 
law is, therefore, neither a definition nor a statement 
as to how force is to be measured ; but is a substantial 
proposition, asserting a connexion between two inde- 
pendently measurable sets of facts in nature. ' Of course, 
once this connexion between the magnitude and direc- 
tion of a force on the one hand and the rate of change of 
momentum of a body on the other has been established 
from a study of those favourable cases where force can 
be measured independently, we can use the law to 
measure indirectly the forces which are acting in un- 
favourable cases, where direct measurement is impossible, 



i66 SCIENTIFIC THOUGHT 

If I want to find the pull on a string which is whirling 
a weight, my best plan now is to find the angular 
velocity of the weight and its mass; to determine from 
these data its rate of change of momentum ; and to 
equate the magnitude of the pull to this. But I now 
use this method, not because I mean rate of change 
of momentum by " force" ; nor because this is the only 
possible way of measuring force accurately ; but because, 
in the past and in more favourable cases, I have been 
able to measure force independently, and have found it 
to be proportional to rate of change of momentum. 

So far then we have not seen anything in favour of 
the " descriptive " theory of force. Yet I believe that an 
important truth underlies it, and that it has been obscured 
by carelessness of statement. The typical descriptionist 
generally combines the two views that force just means 
rate of change of momentum and that force is not 
ultimately a very important conception in Mechanics. 
He often gives the former as a reason for the latter 
proposition. We have seen that the former is false. 
And in any case it is inconsistent to combine it with 
the latter. For, if force just means rate of change of 
momentum, and if force be unimportant in Mechanics, 
it follows inevitably that rate of change of momentum 
is unimportant in Mechanics. And no one in his senses 
would maintain this proposition. I believe the truth to 
be that force is not ultimately a very important concep- 
tion in Mechanics ; although this is not implied by the 
view that force means rate of change of momentum, 
and although that view about the meaning of force is 
mistaken. 

I will now try to explain why I hold this. To know 
what forces are acting on a body you need to know 
what other bodies, near and far, are made of, what 
physical and chemical states they are in, and so on. 
For instance, when magnetic forces are under discussion, 
it is vital to know whether the moving body and those 
in its neighbourhood are made of iron or of wood, and 



TRADITIONAL KINETICS 167 

so on. Again, when motion is produced by impact or 
impeded by friction, it is vital to know the elasticities 
of the bodies and the state of their surfaces. Now, 
when we reflect on the special laws of nature which 
involve these special properties that vary from one bit 
of matter to another, we notice that force simply acts 
as a kind of middle term between the special laws of 
nature and the general laws of motion ; and that, except 
for convenience of expression, it might be dropped. 
You may regard the laws of motion as being expressed 
by equations, with force on one side and rate of change 
of momentum on the other. You may regard the special 
laws of nature as being expressed by equations, with 
forces on one side and the special configurations, electric 
charges, magnetic properties, etc., of the bodies that you 
are dealing with, on the other. Thus you might just 
as well express the facts by a single set of equations, 
directly connecting the configurations, charges, etc., 
with the rate of change of momentum, and drop the 
mention of force altogether. In practice this is what we 
generally do when we get the final equations for solving 
any particular problem. To take a very simple case, 
the final set of differential equations for the motion of 
a particle in a central orbit contains nothing that stands 
for force. They connect the rate of change of momentum 
of the particle directly with the mass and distance of 
the attracting central body, and with the gravitational 
constant. 

Why then do we trouble to keep the concept of force, 
and why were the laws of Mechanics stated in terms of 
it? The main advantage of keeping it is when we want 
to make general statements. We want to be able to 
state and discuss the general laws of motion, without 
reference to any particular cause which produces or 
modifies motion. It is then convenient to lump to- 
gether every such cause under the common name of 
force. Again, we want to be able to state the special 
laws of nature (e.g., those of electricity or magnetism), 



168 SCIENTIFIC THOUGHT 

without referring to the particular motion of some definite 
body in some definite system of other bodies. It is 
then convenient to use the term force for the effect of 
any such system on a hypothetical particle of unit mass. 
When we pass from general statements to some definite 
problem the notion of force becomes useless and drops 
out. Now many, though by no means all, material 
systems which affect the motions of a body also cause 
feelings of strain in our own bodies. That is why force 
does not appear to us as a mere mathematical parameter, 
although this is the position that it actually comes to 
occupy in the treatment of concrete problems. Lastly, 
material systems which affect the motions of bodies do 
also produce other measurable effects, such as balancing 
weights on strings over pulleys, or stretching spring- 
balances. The first and second laws are really state- 
ments about the observed relations between these latter 
effects of material systems and their effects in modifying 
the motions of bodies. 

We have now cleared up the notion of force, so far 
as it is common to the first and second of the traditional 
laws of motion. But the second law involves another 
concept, viz., that of mass, and this we must now discuss. 
The momentum of a body is defined as the product of 
its velocity by its mass. All that we need say at present 
about its velocity is that its magnitude and direction 
must be determined with reference to a suitable set of 
material axes, such as those given by the fixed stars, 
and a suitable physical time-measurer, such as an 
ordinary pendulum. 

The factor of mass actually enters into the traditional 
Mechanics in two quite different ways ; and it is simply 
a stransre coincidence that the two kinds of mass are 
proportional to each other, so that, by a suitable choice 
of units, the two masses of a body have the same 
measure. We may call the two kinds of mass gravita- 
tional and inertial respectively. The first is the mass 
that is mentioned in the law of gravitation, the second 



TRADITIONAL KINETICS 169 

is the mass which is involved in the second law of 
motion. At present we shall deal with inertial mass, 
a factor which occurs equally in every kind of motion, 
whether produced by impact, gravitation, electric or 
magnetic attraction, or any other cause. We will start, 
as we did in treating force, with the crude data of 
sensation, and consider what feature it is in these which 
forms the basis of the scientific concept of inertial mass. 
If we take two bodies which are geometrically exactly 
alike, say a sphere of wood and an equal sphere of 
platinum, we may find that we have to exert ourselves 
to a markedly different extent to make them move with 
the same velocity relative to the same axes and the 
same time-measurer. We have already seen that, with 
a single body, e.g., the wooden sphere, we have to exert 
ourselves more the faster we wish to make it move. We 
see then that the effort that we feel ourselves exerting 
when we try to make a body move depends on two 
factors. One of these is the velocity which we give to 
the body. The other is a factor which apparently depends 
simply on the material of the body itself. It is the latter 
which gives us the primary meaning of inertial mass. 
As usual, the crude data of sense only allow of a very 
crude measure of magnitude. We therefore need some 
method of measuring mass which shall agree pro tanto in 
its results with the rough judgments based on our ex- 
periences of effort, but shall be capable of much greater 
accuracy. 

Experiments on the impact of bodies give us a means 
of accurately measuring inertial mass in favourable 
cases. When two bodies B x and B 2 hit each other, it 
is found that we can ascribe a numerical coefficient m vl 
to B x and a coefficient m 21 to B 2 , such that, if u x and u 2 
be their respective velocities before and v A and v 2 their 
respective velocities after the collision 

m 12 u 1 + m 21 u 2 = ?n 12 v 1 + in 2X v 2 . 

What we have learnt at this stage is that (1) the two 

M 



170 SCIENTIFIC THOUGHT 

coefficients are independent of the velocities u x and 
u. y And (2) that, for any pair of bodies, such a pair of 
coefficients can be found. But, suppose that we first 
try the experiments with a pair of bodies Bj and B 2 , 
and then with B., and a third body B 8 . It is ante- 
cedently possible that m nt the coefficient which has 
to be ascribed to B. 2 in its transactions with B p might 
differ from ;;/., 3 , the coefficient which has to be ascribed 
to B 2 in its transactions with B.,. Further experiments 
prove that this is not so, i.e. that the coefficient of any 
given body is independent, not only of its velocity, but 
also of the other bodies with which it is interacting. 
We can thus in future drop doubly-suffixed coefficients, 
like w. (1 , and write simply m lf m v etc. We find then 
that to any body there can be ascribed a certain co- 
efficient, which is independent of its velocity, and 
which it carries with it into all its mechanical trans- 
actions with other bodies. This coefficient is the 
scientific measure and meaning of inertial mass. It 
obviously accords in rough outline with the notion of 
mass which we get from our sensations of effort, but 
it is capable of accurate measurement. Having defined 
and measured the inertial mass of a body in this way, 
we find two further important facts about it by experi- 
ment. (1) It belongs to a body, not only in the case 
of motions caused by impact, but in all its motions 
however produced or modified. (2) Such coefficients 
are additive scalar magnitudes. If you do experiments 
with a compound body, made up of two smaller ones, 
to which you have already ascribed the masses m x and 
m 2 , you will find that you have to ascribe to this 
compound body the mass m 1 + m. 2 . 

We can now deal with gravitational mass. All 
bodies, no matter what their inertial mass may be, 
fall to the ground with the same acceleration in vacuo 
in the same region of the earth. Now the rate of 
change of momentum of a body of constant mass is 
equal to the product of its mass by its acceleration. 



TRADITIONAL KINETICS 171 

Since bodies of different inertial mass all fall with the 
same acceleration, it follows from the second law that 
they must be acted on by unequal forces, and that 
these forces must be proportional to the inertial masses 
of the bodies. Again, if we do experiments with a 
delicate torsion balance, we find that the attraction of 
a body A on a body B is proportional to the inertial 
mass of A. Combining these two facts we see that 
the gravitational attraction between any two bodies is 
proportional to the product of their inertial masses. 
It is evident then that, even if we had never done 
experiments with moving bodies at all, but had con- 
fined ourselves to statical experiments with balances, 
torsion apparatus, etc., we should have come to ascribe 
certain coefficients to every body. We should also 
have found that these coefficients were independent of 
the velocity, chemical or physical state, etc., of the 
body to which they were ascribed, and were more- 
over independent of the other bodies with which it was 
interacting. And these coefficients would have been 
additive. They would, in fact, be proportional to the 
inertial masses ; and therefore, with a suitable choice 
of units, identical with the latter. Now, the coefficients 
required by the gravitational facts are what we mean 
by gravitational masses ; and, on the traditional theory, 
it is just a strange coincidence that the two masses of 
a body are proportional to each other. The theory of 
gravitation which is bound up with the General Theory 
of Relativity suggests a reason for this identity of 
inertial and gravitational mass. 

We must next consider the third law of motion, 
which says that action and reaction are equal and 
opposite. It involves no new concepts, but it makes 
a most important additional statement about force. 
It says, in fact, that the force on one particle is only 
one side of a transaction which, taken as a whole, is 
a stress between two particles. It is in virtue of this 
principle that we are able to deal with the motions 



172 SCIENTIFIC THOUGHT 

of finite rigid bodies, which rotate as well as change 
their places, and therefore cannot be treated as particles. 
The law, as stated, is indefinite both as to direction 
and as to time. The action and reaction between two 
particles might be equal and opposite, but might make 
any angle with the line joining them. It seems to be 
sometimes assumed that the law requires the direction 
of the two forces to be the line joining the particles. 
This is not so, and the law would be false if it were. 
Two moving electrons exert equal and opposite forces 
on each other, but these are not in the line joining 
the two electrons. In fact the question of the direction 
of the two opposite and equal forces belongs to the 
special laws of nature, such as gravitation, electricity, 
magnetism, etc., and not to the general laws of motion. 
Again, I think it is often assumed that action and 
reaction are always contemporary. If the law be 
understood to assert this, it is certainly false, unless 
we supplement it by assuming particles of ether and 
a mechanical theory about stresses among them. 
When a beam of light from the sun strikes upon any 
surface on the earth it produces a pressure on that 
surface. If there be any reaction from the earth it 
will be exerted primarily on the surface of the ether 
next to the earth, and will not be conveyed back to 
the sun in less time than light takes to travel between 
the two. Thus, if you confine yourself to the earth 
and the sun, action and reaction are not contemporary 
as regards light-pressure. 

The first "two laws of motion have been stated with 
respect to motions relative to the fixed stars and to a 
standard time-measurer, such as an ordinary pendulum. 
Now, it is very important to notice that, apart from the 
third law, this restriction to a particular set of axes 
and a particular physical time-measure could be removed, 
provided that we introduced suitable new forces with 
each new frame of reference. I will illustrate what I 
mean by two examples : (i) Suppose that a particle is 



TRADITIONAL KINETICS 173 

at rest on a plane with respect to a Newtonian frame 
of reference, i.e., with respect to such axes and such a 
time-measurer as we have hitherto been assuming. 
Suppose that in this plane there lies a wheel, and that 
we take two mutually normal spokes of this wheel as 
our X and Y axes respectively. So long as the wheel 
is at rest, these two spokes and the line through the 
centre of the wheel perpendicular to the plane in which 
it lies, constitute a Newtonian set of axes ; and the 
particle is at rest with respect to them. It is therefore 
under the action of no Newtonian forces. Now suppose 
that the wheel is spun with a uniform angular velocity 
co in its own plane. Let us continue to take the two 
spokes as our axes, and the old clock as our time- 
measurer. The resulting frame is, of course, non- 
Newtonian, for it is neither at rest nor in uniform 
rectilinear motion with respect to the fixed stars. 
Relatively to this new frame the particle describes a 
circle in the X-Y plane with uniform angular velocity <o. 
It therefore has a relative acceleration of amount m? 
towards the origin. But this can be made compatible 
with the first and second laws if we assume a force of 
this intensity per unit mass attracting the particle to 
the origin. The particle is acted on by no forces with 
respect to the Newtonian frame ; it is acted upon by 
an attraction of amount mroo 2 towards the origin with 
respect to the new non-Newtonian frame. Thus the 
first and second laws have been rendered independent 
of special reference to Newtonian frames by the assump- 
tion that force (like position, velocity, etc.) is relative 
to the spatio-temporal frame of reference which is 
used for placing and dating the phenomena under 
consideration. 

(2) Let us now take a slightly more complex case. 
Let us suppose that the particle in question is a friction- 
less ring which can slide along the particular spoke 
of the wheel that is chosen as the X-axis, and that the 
wheel rotates as before. Relative to Newtonian axes 



174 SCIENTIFIC THOUGHT 

the ring has no acceleration along the instantaneous 
direction of this spoke. Along the instantaneous 
direction of the normal to it, it has an acceleration 
2.1V0. It is therefore acted upon by a Newtonian force 
(viz., the pressure of the spoke pushing it from behind) 
of amount P = 2mxa>. How will this appear to people 
who rotate with the wheel? Relatively to their axes, 
the particle will move along the X-axis with an accelera- 
tion .r, whilst it will have no velocity or acceleration 
along the Y-axis. They will therefore have to say (if 
they want to keep the form of the first two laws of 
motion) that the ring is repelled from the origin with a 
force mx. And it is easy to show that the intensity 
of this must be ;/mo 2 , i.e., it will be a force varying 
directly with the distance of the particle from the origin. 
On the other hand, they will have to say that there is 
no resultant force acting on the ring in the direction 
of their Y-axis. For the ring keeps all the time to the 
X-axis. But, if they measured, they might be expected 
actually to find the pressure P acting from the spoke 
to the ring. How would they get over this? They 
would say : "The spoke attracts the ring with a force 
equal to P, and this just balances the pressure of the 
spoke on the ring." Thus by assuming a repulsive 
force from the origin, varying directly with the distance, 
and an attractive force between the ring and the spoke, 
varying directly with the velocity along the spoke, they 
could reconcile the form of the first two laws with their 
non-Newtonian frame of reference. This latter force 
would indeed be of a curious kind, for particles would 
be attracted by the side of the spoke that faced the 
direction of rotation and repelled by the other face, but 
they could deal with this by something like a "two- 
fluid theory." 

In these two examples we have only partially departed 
from a Newtonian frame of reference. We have taken 
non-Newtonian axes but have kept to a Newtonian clock. 
It is obvious that, if we kept Newtonian axes but took a 



TRADITIONAL KINETICS 175 

non-Newtonian clock, we could equally preserve the 
form of the first two laws by introducing suitable non- 
Newtonian forces. Suppose a particle were moving 
with a uniform rectilinear velocity with respect to a 
Newtonian frame. Suppose that we then substituted 
for a pendulum clock a water-tank with a hole in it as 
our time-measurer, and judged equal times as those in 
which equal masses of water flowed from the tank. Let 
us keep the Newtonian spatial axes this time. As the 
head of water in the tank decreases the water flows out 
more slowly, as judged by a Newtonian clock. It follows 
that, at the latter part of the experiment, the particle will 
move further while a pound of water flows out of the 
tank than it did at the beginning. Hence, with respect 
to our new non-Newtonian clock, the particle will be 
moving with an accelerated rectilinear motion. If we 
want to keep the form of the first two laws we shall 
therefore have to introduce a non-Newtonian force, acting 
in the direction of motion of the particle. 

It should now be evident that, so far as concerns the 
first two laws of motion, their form can be kept, irre- 
spective of the frame of reference chosen, provided we 
admit the (at any rate partial) relativity of forces to 
frames of reference. It remains to consider more care- 
fully the nature of the non-Newtonian forces that would 
have to be introduced with non-Newtonian frames of 
reference. In particular we want to know whether the 
third law can be kept too when we give up the restriction 
to Newtonian frames. One thing we notice at once. 
That is that the non-Newtonian attractionsand repulsions, 
which were introduced by the adoption of non-Newtonian 
frames of reference, are all proportional to the inertial 
masses of the particles on which they act. Again, they 
act on every particle under consideration, regardless of 
its physical or chemical peculiarities, of the medium in 
which it may happen to be, and so on. Now this reminds 
us irresistibly of gravitational attractions ; and suggests, 
as it did to Einstein, that the law of gravitation may 



176 SCIENTIFIC THOUGHT 

have some connexion with these non-Newtonian forces 
which are bound up with non-Newtonian frames of 
reference. Compare e.g., the two cases of a heavy body 
resting on a weighing machine, and the ring in the 
second example. The heavy body rests in a Newtonian 
frame, and yet the spring of the machine is compressed, 
thus indicating that an upward thrust is being exerted 
by the spring on the heavy body. We say that this 
thrust must be balanced by a pull downwards on the 
body, and we ascribe this pull to the gravitational 
attraction of the earth. In exactly the same way we 
found that the observers who used the rotating wheel 
as their spatial axes would have to assume an attraction 
between the ring and one side of the spoke, to account 
for the fact that the ring did not move at right angles to 
the spoke in spite of the observable pressure of the latter 
on the former. Lastly, consider the repulsive force 
from the origin which the observers on the moving 
wheel would have to suppose to be acting on the ring. 
The peculiarity of this is that to all appearance it does 
not obey the third law. There is a field of force, to 
which every particle is subjected when referred to the 
axes in question ; but it cannot be said that the force 
on one particle is balanced by an equal and opposite 
force on another particle. Some non-Newtonian forces 
then, it would seem, do not obey the third law. Thus 
it seems that the first two laws are more general than 
the third, since they can be reconciled with any frame 
of reference by the introduction of suitable forces, whilst 
it is only for Newtonian forces that the third law holds 
universally. This conclusion could however, in theory, 
be avoided by the introduction of hypothetical concealed 
masses ; so that the non-Newtonian forces on observable 
masses might be regarded, as the third law requires, 
as one side of stresses between these observable masses 
and the hypothetical concealed ones. Thus all the laws 
of motion can be formally preserved relative to any 
frame of reference, provided it is assumed that new 



TRADITIONAL KINETICS 177 

frames imply new forces, and provided that we are 
allowed to assume such concealed masses as we need. 

I will end this chapter by trying to make clear the 
difference between the laws of motion and the special 
laws of nature, such as those of electricity or magnetism 
or heat. We shall then see that, on the traditional 
view, the law of gravitation occupies a curious position, 
intermediate between the two sets of laws. 

The laws of motion do not profess to tell us in detail 
how motions are caused or modified. What they do is 
to tell us the general conditions which all motions, how- 
ever produced, must conform to. They take no account 
of the kind of matter which is moved, or of its physical 
or chemical state at the time ; the one property of 
matter, other than purely geometrical properties, which 
appears in the laws of motion is inertial mass. The 
special laws of nature, on the other hand, tell us about 
the various causes of motion. They have to take into 
account all sorts of properties of bodies beside their 
inertial masses. They have to consider whether they 
be electrically charged or not, whether they be hot 
or cold, magnetised or unmagnetised, and what sort 
of medium surrounds them. Now, the law of gravi- 
tation, on the traditional view, is in one way like a 
special law of nature, and, in another way, more like 
the general laws of motion. It professes to tell us one 
of the causes which start and modify motions. So far 
it resembles a special law of nature. But the only 
property of matter that it has to consider is common 
to all matter, viz. gravitational mass. And this proves 
to be identical with the one property which is considered 
in the laws of motion, viz. inertial mass. Thus there 
seems to be a very much closer connexion between the 
laws of motion and the law of gravitation than between 
any of the special laws of nature and the laws of motion. 
Again, if we are in earnest with the Relational Theory 
of Motion, we must suppose that all the motions with 
which Mechanics deals take place with respect to 



i 7 8 SCIENTIFIC THOUGHT 

material axes. And, since all matter attracts all other 
matter gravitationally, on the traditional view, all bodies 
will be attracted more or less by the axes to which their 
motions are referred. It thus seems not unlikely ante- 
cedently that there should be a very close connexion 
between the laws of motion and the law of gravitation, 
and that a completely Relational system of Mechanics 
should contain a theory of gravitation. The details of 
this are reserved for the next chapter, but it is hoped 
that the foregoing discussion of the traditional laws of 
motion and gravitation may have brought the reader 
into a proper frame of mind for understanding and 
criticising the General Theory of Relativity. 

The following additional works may be consulted 
with advantage : 

B. A. W. Russell, Principles of Mathematics, vol. i, Part VII. 

E. Mach, Scie?ice of Mechanics. 

H. Poincare, La Science et VHypothese. 

„ Scie?ice et Methode. 

,, Le Vaieur de la Science. 

P. Painleve, Les Axiomes de la Mecaniq ue. (Paris. Gauthier- 
Villars.) 



CHAPTER VI 

"What's the use of Mercator's North Poles and Equators, 
Tropics, Zones, and Meridian Lines ?" 
So the Bellman would cry ; and the crew would reply ; 
" They are merely conventional signs ! " 

" Other maps are such shapes, with their islands and capes ! 
But we've got our brave Captain to thank," 
(So the crew would protest), " that he's bought us the best — 
A perfect and absolute blank ! " 

(Lewis Carroll, The Hunting of the Snark.) 

Modification of the Traditional Kinetics (continued). 
(2) The General Theory of Relativity. Summary 
of Part I 

In the last chapter we treated the traditional laws of 
motion without reference to the kinematic results of the 
Special Theory of Relativity, outlined in Chapter IV. 
That is to say, we combined the traditional Kinetics 
with the traditional Kinematics. We must now take 
a step forward, and show that the traditional laws of 
motion are not compatible with the modified kinematics 
of even the Special Theory of Relativity. We shall 
then be able to advance to the General Theory. 

There is no need for me to treat the kinetics of 
the Special Theory in any detail, because it is only a 
half-way house to the General Theory. I will therefore 
content myself with a single example to show that 
the traditional laws of motion cannot be reconciled, 
without modification, with the kinematics of the Special 
Theory and with the Restricted Physical Principle of 
Relativity. 

Let us suppose that two sets of observers were doing 

179 



i8o SCIENTIFIC THOUGHT 

experiments to determine inertial mass by the impact 
of bodies, as described in the last chapter. One shall 
be on the platform/, and the other on the platform /> 2 of 
Chapter IV. These platforms are in uniform rectilinear 
relative motion in a Newtonian frame. The velocity 
of the first with respect to the second, as measured by 
observers on the second, is v 12 . Let two bodies be 
moving along />, in the direction in which p x is itself 
moving relatively to p 2 . Let their velocities relative 
to />,, as measured by observers on it, be Uj and u t 
respectively, before they hit each other. After they 
have hit, let their velocities with respect to p x be W, 
and w 1 respectively. Let the observers on p x ascribe 
to these bodies the inertial masses M 1 and m x respec- 
tively. As we saw in the last chapter, 

M 1 U l + m 1 u 1 =M 1 W 1 + m l w 1 . (i) 

Each body has its own coefficient, which it keeps when 
its velocity is altered by the collision, and which is 
independent of its initial velocity. There is no doubt 
that this is very approximately true under ordinary 
conditions of experiment ; the question is whether it 
can be exactly true, consistently with the Physical 
Principle of Relativity and the kinematics of the 
Special Theory. 

Let the whole experiment be also watched by the 
observers on p 2 . Let the velocities which they ascribe 
to the bodies relatively to p 2 be U 2 , u 2 , W 2 and w 2 
respectively. The Physical Principle of Relativity tells 
us that if equation (i) expresses a genuine law of nature 
in terms of the observations of people on/j, the people 
on p 2 must be able to find an equation of precisely the 
same form in terms of their observations on the same 
phenomena. That is, they ought to find that their 
observed relative velocities are connected by an equation 

M 2 U 2 + m 2 u 2 =M 2 W 2 + m 2 w 2 . (2) 

In this equation M 2 and m 2 will have to be independent 
of the velocities of the bodies ; for it is obvious that 



GENERAL THEORY OF RELATIVITY 181 

the form of the law would not be the same for both sets 
of observers, if, in the one case, the coefficients were 
constants, and, in the other, were functions of the 
velocity of the body. 

Now it is easy to see that anything of the kind is 
inconsistent with the kinematics of the Special Theory 
of Relativity. If the reader will look back to equa- 
tion (3) in Chapter IV he will see that 



U.= 






2 — TT „. : 

I — ■ 



C 8 

with similar equations, mutatis mutandis, for u 2 , W, and 
zv 2 . It is quite obvious that, if these values be substi- 
tuted in equation (2), we shall reach a result which is 
inconsistent with equation (1), on the assumption that 
the masses are independent of the velocities. It follows 
that the traditional view that mass is independent of 
velocity cannot be reconciled with the Physical Principle 
that genuine laws of nature have the same form for 
all observers who are in uniform rectilinear relative 
motion, and with the kinematics of the Special Theory 
of Relativity. It is not difficult to see what modification 
is needed. Let us denote by M liTJ the mass which has 
to be assigned to a body moving with a measured 
velocity \J 1 relatively to the Newtonian frame p x . Let 
us put 

M M 

M — Q— — K M M — ° — K M • 

m l. u— -. FT~2 — l- u 01 m i,w— ,— tTt~2 — i- w o> 






l —* l 



and 



m o _u _ m m o 



J III \ / ,_ z ^l 



c* 



where M and m are independent of the velocity. Let 
us then see whether the equation 



M 1 , u U 1 + *« 1 , 1( K 1 =M 1 , w W 1 + 7// 1 , w ze/ 1 (4 



182 SCIENTIFIC THOUGHT 

expresses a possible law of nature, consistent with the 
Physical Principle of Relativity and the kinematics of 
the Special Theory. If it does, we ought to find that 
the measured velocities U 2 , etc., which the observers on 
/\, ascribe to the bodies under experiment, are inter- 
connected by the equation 

M vv U % +m v jt a = M 2 , w W z +m 2 ,„w 2 . (5) 

By using the transformation equation for relative 
velocities, and doing a little tedious but quite straight- 
forward algebra, the reader will be able to see for him- 
self that this is so, on one condition. The condition is 
that the total mass of the system in the direction of 
motion is unaltered by the collision, i.e. , that 

M 1 , u + w 1 „ / =M 1 , w + /« 1 ,,„. (6) 

On the traditional view this is of course a merely 
analytical proposition, since it is part of that view that 
the mass of each body is an absolute constant. On the 
present view of mass, it is an additional assumption. 
The law, obtained by combining (4) and (6) with the 
definitions embodied in (3), is then a permissible law 
of nature, whilst the traditional law embodied in (1) is 
not. The assumption (6) is, to a very high degree of 
approximation, equivalent to the assumption that the 
total kinetic energy of the system is unaltered by the 
collision. For 

M 
1 M U 2 

M 1 , u = N / I _Ui 2 =M + 2 -^ very nearly. 

c 2 
Whence (6) practically reduces to 

1 MoU, 2 + Imp* = iMoW, 2 + l-m^w*. (7) 

2 22 2 

Thus the attempt to express the laws of Mechanics in 
a form which is consistent with the kinematics of the 
Special Theory of Relativity leads to a connexion 
between the three principles of the Conservation of 



GENERAL THEORY OF RELATIVITY 183 

Momentum, of Mass, and of Energy, which was not 
obvious on the traditional view. 

The modified conception of mass, which the Special 
Theory of Relativity requires, differs so little in 
magnitude from that of the traditional view, for all 
ordinary velocities, that it is reasonable to suppose 
that the modified laws are not merely admissible in 
form but also true in substance. Moreover, the modified 
laws agree with observations on the motions of electrons, 
shot out with enormous velocities in vacuum tubes ; 
whereas the traditional form of the law cannot be 
brought into accordance with these results, except by 
the help of supplementary physical hypotheses about 
the charges, shapes, etc., of the particles. 

The General Theory of Relativity. Enough has now 
been said to show that the traditional kinetics needs 
modification as soon as the traditional kinematics is 
dropped and that of the Special Theory of Relativity 
is substituted for it. And, as I have tried to show in 
Chapter IV, the negative results of the Michelson- 
Morley and other experiments leave us no option about 
making at least this substitution. The question now is, 
not whether we shall go so far, but whether we ought 
not to go further still. Let us open the subject by 
asking : In what way is the Special Theory of 
Relativity special? 

The answer to this question is obvious. In discuss- 
ing the Special Theory of Relativity we explicitly 
confined ourselves to Newtonian frames. In the first 
place, our kinematic transformations assumed that the 
two platforms p x a.ndp 2 were in uniform rectilinear relative 
motion. We did not deal at all with the case of p t 
rotating with respect to p t or moving with a rectilinear 
but accelerated motion with respect to p x . But this is 
not all. If one frame be Newtonian and another moves 
with a uniform rectilinear motion relatively to it, the 
second is also Newtonian. But the converse of this is 
not true. Two platforms might be in uniform rectilinear 



184 SCIENTIFIC THOUGHT 

relative motion, but neither of them need, for that reason, 
be Newtonian. E.g., if their clocks were non-Newtonian 
(e.g., were water-tanks, as in a previous example) both 
these platforms would have accelerated rectilinear 
motions in a Newtonian frame, and therefore neither 
of them would be a Newtonian set of axes. Again, 
suppose that p x and p a were attached at different 
distances from the centre to the same spoke of a wheel 
which rotated uniformly in a Newtonian frame. There 
would be no relative motion between them, but neither 
of them would be Newtonian axes. So the "speciality" 
of the Special Theory is that it is wholly concerned 
with Newtonian frames ; and this not only restricts 
the transformations to uniform rectilinear relative 
motion, but imposes a further condition, in virtue 
of which one at least of the set is known to be 
Newtonian. 

How does this limitation show itself? The funda- 
mental fact on which the kinematic transformations 
of the Special Theory was based was that light was 
found to travel with the same velocity, and in a 
straight line, relative to all the observers, although 
they were in motion relatively to each other. It is 
quite obvious that, if observers had chosen the spokes 
of a rotating wheel as their axes, they would not have 
found that light travelled in straight, lines with respect 
to them. And, if they had taken as their time-measurer 
some process which was not isochronous as compared 
with a Newtonian clock, they would not have found 
the velocity of light to be uniform, even though they/ 
had used the fixed stars as their axes. A Newtonian 
frame may then be defined in one of two alternative 
ways : (i) It is a set of axes and a physical time- 
measurer with respect to which light in a homogeneous 
medium travels with a uniform rectilinear velocity. 
Or (2) it is a set of axes and a time-measurer with 
respect to which a particle, under the action of no 
resultant force, rests or moves uniformly in a straight 



GENERAL THEORY OF RELATIVITY 185 

line. Owing to the universality of gravitation the 
second criterion cannot literally be applied. We shall 
also see, later on, that the same reason renders the 
first criterion not strictly true of any natural frame. 
Thus a Newtonian frame is an ideal limit rather than 
an actual fact. Still, the frame in which the fixed stars 
form the axes and a properly constructed and regulated 
clock forms the time-measurer is very nearly Newtonian 
for all experiments that we can do. The transformation 
equations of the Special Theory enable us to pass from 
the place and date of any event in any one such frame 
to its place and date in any other such frame. But 
they tell us nothing about its place or date in any 
frame which is not Newtonian ; and no frame is 
Newtonian unless its axes either rest or move with 
a uniform rectilinear velocity, as judged by a New- 
tonian clock, relatively to Newtonian axes. Again, the 
Restricted Physical Principle of Relativity only says 
that observers on different Newtonian frames will all 
find laws of identical form for the same natural 
phenomena. It does not assert that an observer on 
a non-Newtonian frame will find no difference in the 
form of the laws which interconnect the magnitudes 
that he measures, when watching a certain natural 
phenomenon. 

The question is whether, and to what extent, this 
restriction to a certain set of frames of reference can 
be removed. It is easy to state in general terms the 
kind of problem with which we are faced. On the 
one hand, we can get at the laws of nature only by 
measuring various observable magnitudes and finding 
out the functional correlations that hold between them. 
And we can do this only by referring all events 
in nature to a spatio-temporal frame of reference of 
some kind, in which each event has a certain place 
and date. Innumerable different frames of reference 
could be taken for dating and placing the events of 
nature. On the other hand, presumably there are laws 

N 



i86 SCIENTIFIC THOUGHT 

of nature which are absolute, and independent of any- 
particular frame of reference. The laws discovered by 
observers who use a certain frame of reference w r ill 
be transcriptions of these absolute relations, in terms 
of that particular frame. Thus, we may suppose that 
they will depend partly on the absolute relations of 
events in nature and partly on the particular frame 
used by these observers. It would thus be reasonable 
to suppose that, on comparing the laws discovered by 
observers who observe the same phenomenon and use 
all kinds of different frames of reference, we might be 
able to extract a kind of "kernel," which should be 
neutral as between them all. This kernel would be the 
absolute law of the phenomenon in question, and it 
is this which the General Theory of Relativity seeks 
to extract. 

It may be worth while to give a few illustrations 
from other regions, in order to make the idea familiar 
to the reader. (i) Suppose the League of Nations 
were to lay down certain general rules about naviga- 
tion, which were binding on all members of the 
League. They would have to be translated into 
English, French, Italian (and soon, one hopes, German 
and Russian). These various translations would look 
extremely different. And it would be impossible to 
express the rules without some symbolism or other 
until telepathy becomes commoner than it now is. 
Yet there would be something, viz., the content of the 
rules, which would be independent of any particular 
language or other system of symbols in which they 
happened to be expressed. 

(2) Another example may be helpful to persons with 
an elementary knowledge of mathematics. It is a very 
simple intrinsic property of the triangle that the bisectors 
of its three angles all meet at one point. If you try 
to prove this by analytical geometry you will have to 
choose some set of co-ordinates ; they may be rect- 
angular Cartesians, or oblique Cartesians, or polars. 



GENERAL THEORY OF RELATIVITY 187 

In any case you will get very complicated equations 
in terms of the co-ordinates which you assign to the 
three corners of the triangle. And these equations 
will be very different according to the system of co- 
ordinates that you have chosen for reference. Yet they 
all express the same simple fact, which is intrinsic to 
the triangle as such, and quite independent of any set 
of co-ordinates. 

Now, on the traditional view, the distance between 
two events and the time-lapse between them are two 
distinct facts. It is true that, on the traditional view, 
the measured distances between non-contemporary events 
will be different for observers who are in uniform recti- 
linear motion with respect to each other. But it is 
supposed that their dates will be the same for all 
Newtonian frames, and that it will be independent of 
the distance between the events. Now, the Special 
Theory shows that this is not true even when we 
confine ourselves to Newtonian frames. We saw that 
observers on platforms which are in relative recti- 
linear uniform motion will not ascribe the same time- 
lapse to the same pair of events ; and that, if these 
events be separated in space, the amount of time-lapse 
ascribed to them by observers who move relatively 
to them will depend on their distance apart. Thus, 
measured distance between events and measured time- 
lapse between events are mixed up with each other, 
and are partly dependent on the frame of reference, 
even when we confine ourselves to Newtonian frames. 
Is there anything connected with spatial and temporal 
separation which has the same measure for all Newtonian 
frames? There is, as can easily be seen. Suppose that 
two adjacent events have respectively the co-ordinates 
and dates x ly y x , z 1} /,, andx x + dx x , y x + dy x , s x + dz x , and 
t l J r dt 1 with respect to the Newtonian frame p x . Let 
them have the corresponding letters, with 2 suffixed 
instead of 1, with respect to the frame p^, which moves 
relatively to p x in the ^-direction with the uniform 



iSS SCIENTIFIC THOUGHT 

velocity v 21 . It follows immediately from the transfor- 
mation equations of Chapter IV that 

dx 2 = k n (dx 1 — v^dtj) 
a n d dt t = kAd^ — " dx x ) • 

Whence 

since k ol --= —==. by definition. 

c 2 

Now d^ 2 = d[y 2 2 and dz* = ^ 2 a , since there is no relative 
motion in these directions. Therefore finally, 

dx 2 + dy 2 + dz 2 — c 2 dt 2 = dx 2 + dy 2 + dz 2 — c 2 dt 2 . (8) 

Here then we have a magnitude, connected with a 
pair of events, which has the same numerical measure 
with respect to all Newtonian frames. We will take 
this magnitude with its sign reversed, for reasons which 
will appear later. We will call it the square of the 
Spatio-Temporal Separation of the two events, and will 
denote it by dcr. The square of the spatial separation 
is, of course, dx^ + dy^ + dz^ in the one system and 
dx£-\-dy£-\-dz£ in the other. The temporal separation 
is dt x in one system and dt 2 in the other. It is clear 
that the spatio-temporal separation has a claim to 
represent something intrinsic to the pair of events, 
and neutral as between different frames of reference, 
which claim cannot be made for either the spatial or 
the temporal separation. It is, at any rate, invariant 
and neutral as between all Newtonian frames, whilst 
the other two are not invariant or neutral, even with 
this restriction. 

It will be noticed that, if the two events be the 
successive occupations of two adjacent places by some- 
thing that travels with velocity u x with respect to one 



GENERAL THEORY OF RELATIVITY 189 

frame and u 2 with respect to the other, the spatio- 
temporal separation takes the form 

do* = {<*- u*)dt* = (c- 2 - tt*)dt 2 \ 

If what is travelling be light, or any other electro- 
magnetic disturbance, ?/ x = u 2 — c. Whence da* = o. 
That is, the spatio-temporal separation between two 
events which are the successive arrivals of a wave of 
light at two adjacent positions is o, although of course 
both the spatial and the temporal separations of the 
two events are finite. This explains why we took the 
expression with its sign reversed. We want the square 
of the separation to be always positive for the successive 
events that constitute any real motion. With the present 
choice of sign this will be so, unless the moving thing 
travels faster than light. With the other choice of 
sign the square of the separation would always be 
negative for anything that travelled more slowly than 
light. Now we know nothing that travels faster and 
innumerable things that travel more slowly than light. 
Hence our convention as to sign is justified. 

This concept of spatio-temporal separation is funda- 
mental to the General Theory of Relativity. We take 
it as a hypothesis that this separation is an intrinsic 
relation between a pair of events, which has nothing to 
do with frames of reference, though, of course, we shall 
always meet with it and measure it in terms of the 
particular frame that we happen to use in order to place 
and date the events of nature. If it be asked what 
ground there is for this hypothesis, I think we must 
begin by distinguishing between what suggests it and 
what justifies it. What suggests it is the in variance of 
this measured magnitude as between all Newtonian 
frames. But, if it is to be justified, this must be done 
in the usual way by working out the consequences of 
the hypothesis and seeing whether they accord with 
experimental facts. 

We have seen what form the spatio-temporal separa- 



190 SCIENTIFIC THOUGHT 

tion takes when expressed in terms of Newtonian co- 
ordinates and clock- readings. It will be worth while, 
however, explicitly to mention the important character- 
istics of this expression before going further, (i) It 
is homogeneous and of the second degree in the four 
variables which it involves. (2) The coefficients of the 
variables are all constants. In fact, by a suitable choice 
of units, they could all be reduced to unity. When 
distance is measured in centimetres and time-lapse in 
seconds, light has the velocity c, and the time-factor 
has to be multiplied by this constant. But, if the unit 

of time were taken to be, not the second, but - of a 

c 

second, the velocity of light would be unity. We chose 
our units of space and our units of time quite inde- 
pendently, when it was not suspected that there was a 
fundamental connexion between these two factors in 
nature. It so happens that we have chosen a very 
large unit of time as compared with the unit of space ; 
and that is the only reason why the large constant c 
appears in the expression for the spatio-temporal separa- 
tion. (3) The last important point to notice in this 
connexion is that the coefficient of the time-variable is 
of opposite sign to that of the space-variables in the 
expression for the spatio-temporal separation. This 
betrays the fact that there is ultimately a radical dis- 
tinction between the space factor and the time factor 
in nature, in spite of their intimate interconnexion, and 
in spite of the fact that the two are, within certain limits, 
interchangeable. 

Now we can quite well understand that the expres- 
sion for the spatio-temporal separation, in terms of the 
co-ordinates and time - readings of a non-Newtonian 
frame, may be very different from the expression for the 
same fundamental fact in terms of a Newtonian frame. 
Let us first illustrate this by a very simple example 
from ordinary geometry. If we take the traditional 
view of Space and Time the distance between two points 



GENERAL THEORY OF RELATIVITY 191 

is an intrinsic relation between them, and is wholly 
independent of the system of co-ordinates to which we 
refer the points. Let us first suppose that they are 
referred to a set of rectangular Cartesian co-ordinates 
C x . Let their ;r-co-ordi nates in this system be x\ and 
.r 1 + dx\ respectively, with similar expressions for their 
y- and ^-co-ordinates. Then the expression for the 
square of their distance apart is 

dx\ 2 4- dyf + dz*. 
Now refer them to another set of rectangular Cartesians 
C 2 . This might consist of the original ones twisted as 
a rigid body about their origin. The three edges of a 
biscuit box with one corner fixed would be an example. 
Let the co-ordinates of the points with respect to this 
system be x\ and x 2 + dx' 2 , etc., respectively. The ex- 
pression for the square of the distance apart of the two 
points in the new co-ordinates is 

dx 2 2 + dy 2 2 + dz?. 
It is of the same form and the same magnitude as 
before. This is exactly analogous to the invariance of 
the expression for the spatio-temporal separation of two 
events with respect to two Newtonian frames. 

Suppose now that, instead of referring the two points 
to Cartesian co-ordinates, we were to refer them to polars. 
Call this system P 3 . Let the co-ordinates of the two 
points be respectively r 3 ,# 3 ,c£ 3 and r 3 + dr 3 ,9 3 + d6 3 ,<f> 3 + d<i> 3 , 
in this system. The distance apart will now be ex- 
pressed by the formula 

dr./ + r 3 2 d0 3 2 + r 3 2 sin%d<f> 3 *. 

It will be noticed that this expression has one important 
analogy to, and one important difference from, the ex- 
pression in terms of Cartesians. It resembles the latter 
in that it is still a homogeneous function of the second 
degree in terms of the three differentials. It differs in 
that these differentials no longer all have constant co- 
efficients. Their coefficients now contain functions 
of the co-ordinates themselves. 



K)j SCIENTIFIC THOUGHT 

Now, just as the passage from Cartesian to Polar 
co-ordinates makes this difference in the expression for 
the distance between two points on the ordinary geo- 
metrical view, so we may expect that the passage from 
a Newtonian to a non-Newtonian frame of reference 
will make a similar difference to the expression for the 
spatio-temporal separation between two events. We 
may expect that the expression will still be homo- 
geneous and of the second degree in terms of the 
differentials of the non-Newtonian co-ordinates and 
dates, but that these differentials will no longer have 
constant coefficients. 

In order to make the next step, let us again revert 
to a simple example in ordinary geometry. Let us 
confine ourselves to points on a surface, and let us 
suppose, to begin with, that this surface is a sphere. 
We will suppose that persons confined to the surface 
of the sphere are trying to find an expression for the 
distance apart of two adjacent points, as measured on 
the surface of the sphere. This will of course be that 
part of the great circle passing through the two 
points, which is included between them. Now the 
surface of the sphere could be mapped out into a 
network of co-ordinates in innumerable different ways. 
We might fix the position of a point by parallels 
of latitude and meridians of longitude, as ordinary 
Atlases do. Or we might fix it by taking an origin 
on the equator and drawing a great circle from here to 
the point in question, and noticing the length of this 
arc and the angle that it makes with the equator. 
Again we might take the equator and some meridian 
of longitude as a pair of mutually normal axes and 
define the position of a point by the arcs of the two 
great circles which pass through it and are normal to 
the equator and the meridian respectively. The last- 
mentioned set of co-ordinates would be analogous to 
Cartesians in a plane, and the set mentioned before 
would be analogous to plane Polars. We should find 



GENERAL THEORY OF RELATIVITY 193 

that two independent variables were always necessary 
to fix the position of a point. And we should find that 
the distance between any pair of adjacent points on the 
sphere, as measured along the sphere's surface, was 
always a homogeneous quadratic function of the small 
differences between their corresponding co-ordinates in 
any system. So far there is complete analogy with a 
plane. But we should find the following very important 
difference. In the plane, or in ordinary three dimen- 
sional Space, as we saw, we always can find a system 
of co-ordinates, viz., Cartesians, in terms of which the 
expression for the distance involves no coefficients 
other than constants (which can of course always be 
reduced to unity by a suitable choice of our units). 
On the sphere we should find that it was impossible to 
choose any set of co-ordinates for the whole surface, in 
terms of which the expression for the distance between 
two points involves nothing but constant coefficients. 
Always we shall find that one or both of the differentials 
is multiplied by a function of the co-ordinates. 

This then is an intrinsic difference between spheres 
and planes. It is connected with the fact that a sphere 
cannot be unfolded into a plane without stretching, as, for 
instance, a cone can. We see then that there are at least 
two intrinsically different kinds of surface. With both 
of them the expression for the distance of two points 
measured along the surface will involve non-constant 
coefficients, when expressed in terms of some set of co- 
ordinates upon the surface. But with the one kind of 
surface this will be so, not merely for some, but for all 
possible sets of co-ordinates upon the surface. And, 
with the other kind, it will be possible to find a set of 
co-ordinates on the surface, in terms of which the ex- 
pression for the distance of two adjacent points involves 
no coefficients but constants. 

Let us now leave the points and surfaces of pure 
geometry, and apply our results to the events of nature 
and their spatio-temporal separations. Just as surfaces 



194 SCIENTIFIC THOUGHT 

mav be of two intrinsically different kinds, so nature, 
as a sum total of events, might theoretically be of one 
kind or another. It might have such an intrinsic 
structure that it was always possible to find a frame, 
viz., a Newtonian one, with respect to which the spatio- 
temporal separation of any pair of events takes the form 

<*d?-cb?-df-d&. 

On the other hand nature might, like the sphere 
in geometry, have such an intrinsic structure that no 
possible frame could be found with respect to which 
the spatio-temporal separation involved only constant co- 
efficients. Now the most general homogeneous quadratic 
expression for the spatio-temporal separation of a pair 
of adjacent events in terms of any frame is obviously of 
the form 

+ g u dOidt + g 2Z dd 2 d6 3 + g ti de 2 dt + g Zi dO z dt, (9) 

where 6 V 2 , and $ 3 are the spatial parameters, and t is 
the temporal parameter, which one of the events has in 
respect to the spatial axes and the clocks of this frame. 
The g's are any functions whatever of these four 
variables. Now, if it is to be possible to find a frame 
with respect to which the spatio-temporal separation 
takes the Newtonian form, these g's cannot be just any 
functions. The reducibility to the Newtonian form 
imposes certain very general conditions on the g's. 
It can be shown that it is possible to find a frame, 
with respect to which the spatio-temporal separation 
assumes the form with constant coefficients, if and only 
if the g's are of such a kind that a certain very com- 
plicated function of them, called the Riemann-Christoffel 
Tensor', vanishes. To say that the Riemann-Christoffel 
Tensor vanishes would therefore be equivalent to saying 
that nature, as a system of interconnected events, has 
a certain kind of intrinsic structure, which is formally 
analogous to that of the plane in Euclidean space and 



GENERAL THEORY OF RELATIVITY 195 

formally unlike that of the surface of a sphere in 
Euclidean space. 

The next thing that we have to consider is the 
dynamical meanings of the various conceptions which 
we have been introducing and discussing. There are 
now two problems to be considered. The first is 
independent of the view that we take as to the two 
alternative possible intrinsic structures of nature. This 
leads to a generalisation of the first law of motion, so 
that it becomes independent of any particular frame of 
reference. The second depends on which alternative 
the facts force us to choose as to the intrinsic structure 
of nature. This leads to a generalisation of the law of 
gravitation. We will now consider them in order. 

(1) According to Newton's first law of motion a 
particle which is under the action of no resultant force 
in a Newtonian frame either rests or moves with uniform 
rectilinear velocity in that frame. Consider two events 
in the history of this particle as it moves. One is 
its presence at the point x M jr,, z A in the axes of the 
frame at the date t A as measured by the A-clock of 
the frame. The other is its presence at the point x B , y Ey 
z B , in the same axes when the B-clock reads t a . Since 
the particle is under the action of no Newtonian forces 
it will have moved in a straight line between these 
two points with a uniform velocity. Let us consider 
the total spatio-temporal separation between these two 
events. By this we are going to mean the sum of 
all the infinitesimal spatio-temporal separations between 
successive closely adjacent events in the history of the 
particle, which are intermediate between the first and the 
last event under consideration. It is easy to show that, 
when the particle moves uniformly in a straight line, 
this total separation has a stationary value. This 
means that it would either be greater for all alternative 
ways of moving from the one place to the other in 
the given time, or that it would be less for all alternative 
ways. As a matter of fact the actual path is that which 



196 SCIENTIFIC THOUGHT 

makes the total spatio-temporal separation a maximum. 
If the particle moved in any other course, or with a 
non-uniform velocity, the total spatio-temporal separa- 
tion would be less than it is when it moves uniformly 
in a straight line. 

Now the fact that the total separation between remote 
events in the history of this particle is a maximum is 
an intrinsic fact about the history of the particle. It 
depends in no way on the frame of reference which is 
chosen for placing and dating the events. We have 
thus got to something about the motion of the particle 
which is independent of frames of reference. Now 
refer the particle to any other frame you like. The 
characteristics of the new frame are completely summed 
up in the ten g's which appear in the expression for 
the spatio-temporal separation of two adjacent events 
in terms of the spatial and temporal parameters of this 
frame. We have therefore simply to express the fact 
that the integral of the expression (9) has a stationary 
value for the course which the particle actually takes 
with respect to this frame. This can easily be done 
by the Calculus of Variations. As a result a set of 
four second-order differential equations emerges. These 
are the equations of motion in any frame whatever for 
a particle which is under the action of no forces in a 
Newtonian frame. 

Now, as we saw in last chapter, the change from a 
Newtonian to a non-Newtonian frame of reference in- 
volves the introduction of non-Newtonian forces. These 
forces are completely determined by the nature of the 
non-Newtonian frame chosen. Again, as we have seen, 
the nature of the frame is completely determined by 
the ten gs which appear in the expression for the 
spatio-temporal separation in terms of the parameters 
of the frame. Thus there is complete correlation between 
the g's which characterise the frame, and the non- 
Newtonian forces which people who used this frame 
would observe to act on particles. Thus, if all forces 



GENERAL THEORY OF RELATIVITY 197 

be of this type, the four differential equations which 
express the fact that the total spatio-temporal separation 
for the actual course of the particle is to be stationary 
will be the laws of motion. For they will sum up the 
relations between the motion of any particle with respect 
to any frame and the observable forces which people 
who use that frame find to be acting on the particle. 
To observers on a Newtonian frame it will appear that 
the other observers are using very foolish axes and 
very wild clocks {e.g., a rotating wheel and a water- 
tank). For the Newtonian observers then, theg's will not 
seem to have anything to do with forces, but only to 
characterise the particular kind of axes and clocks which 
the other observers are using. But, for the observers 
who use the frame characterised by the gs, these g's 
will appear as the potentials of forces which are functions 
of position and time with respect to their frame. (I 
say as potentials of forces, and not as forces, because the 
g's do not appear as such in the equations of motion, 
but appear in the form of first-order differential co- 
efficients with respect to the co-ordinates and dates 
which events have in the frame.) The four differential 
equations of motion, thus deduced for any frame what- 
ever, degenerate, in the special case of a Newtonian 
frame, to the three ordinary equations which express 
the fact that the acceleration of the particle vanishes 
in three mutually rectangular directions, and to the 
platitude = 0. 

I will illustrate the connexion between the g's and 
the potentials of the non-Newtonian forces which are 
introduced along with a non-Newtonian frame, by 
working out a little further a simple example which 
was used in the last chapter. It will be remembered 
that we there took a particle at rest on a plane in a 
Newtonian frame and referred it to a non-Newtonian 
frame, consisting of the same clock as before for the 
time-measurer and two mutually rectangular spokes 
of a rotating wheel, that lay in this plane, as the spatial 



igS SCIENTIFIC THOUGHT 

axes. We saw that the observers who use this frame 
will ascribe a non-Newtonian attraction from the particle 
to the origin of amount mrao 2 . The non-Newtonian 
potential required to produce this force is £////"V, since 

F r = — -3— by definition, and F,. = — mrw in this case. 

Ov 

Now let us consider what will be the expression for 
the separation of two adjacent events in terms of the 
new frame. In terms of the original Newtonian frame 
it is, of course, c*dt z — dx 2 — dy 2 . It is easy to show that 
it will be {c"-i^)df-de-dif+2^rid^dt-2i,4d n dt in 
terms of the new frame. Thus the new frame is 
characterised by the following values for the six g's 
which are needed when we confine ourselves to a two 
dimensional space, as we are doing in this example : — 

g tt = <*- o)V ; g^ = g vv = - 1 ; g$= 2a)>7 ; g ¥ 2< ; 

gt„ = o. If we ascribe to the non-Newtonian force a 
potential — hng tt ^ we shall account for the observable 

facts, since — ^-( — \mg )= — ?WV, and the observed 

dr tt 

non-Newtonian force is —mw 2 r. Thus we see that g to 
which, from the point of view of observers on the 
Newtonian frame, is merely one of the coefficients 
that characterise the special non-Newtonian frame used 
by the other observers, is, from the point of view of 
the non-Newtonian observers themselves, the potential 
of a force which acts on all particles with respect to their 
frame. 

So far we have confined ourselves to the case of a 
particle which is under the action of no Newtonian 
force, and we have derived the equations of motion for 
such a particle under the action of the non-Newtonian 
forces to which it will be subjected when referred to a 
non-Newtonian frame. But of course most particles, 
if not all, are, at some time at least in their history, 
under the action of Newtonian forces, and do not move 
uniformly or in straight lines with respect to Newtonian 



GENERAL THEORY OF RELATIVITY 199 

frames. What are we to say of the equations of motion 
of such particles? 

We have said that a particle under the action of no 
Newtonian force moves in such a way that the total 
separation between two remote events in its history is 
greater than it would be for any other possible way of 
moving. We also said that this property of the actual 
history of the moving particle is independent of the 
particular frame of reference to which it may be referred. 
Before we can get any further we must clear up these 
two statements a little further. We will begin with a 
geometrical analogy. 

Suppose there were two remote points and we were 
told to find the shortest possible path from one to the 
other. The problem would not yet be perfectly deter- 
minate. Possibility is always relative to a set of 
conditions implied or asserted. What would be the 
shortest possible path, relative to one set of conditions, 
would not be so, relative to another set. If we were 
allowed to move from one point to the other on the 
Euclidean plane on which they both lie, the shortest 
possible path would of course be the Euclidean straight 
line joining them. But if we were told that we must 
keep to the surface of a certain sphere on which both 
points are situated, the shortest possible path would be 
along the great circle on this sphere which joins them. 
And a great circle is an intrinsically different kind of 
curve from a Euclidean straight line. Thus the curve 
which is the shortest path between two points depends on 
the intrinsic structure of the region in which the points 
are situated, and to which all paths between them are to 
be confined. Once this intrinsic structure is given, the 
property of being the shortest path between the two 
points is independent of all possible sets of axes which 
might be used for mapping out the region. But, of 
course, the intrinsic character of the region will impose 
certain restrictions on the kind of axes that are possible 
for mapping it out. Similarly, the nature of the move- 



200 SCIENTIFIC THOUGHT 

ment which gives the maximum possible spatio-temporal 
separation for two remote events in the history of a 
moving particle will depend on the structure of that 
part of the history of Nature in which the events happen, 
and within which all courses from one to the other are 
to be confined. Given the structure of this part of the 
history of Nature, the course with the maximum possible 
total spatio-temporal separation is independent of all 
frames of reference which can be used for placing and 
dating events within this region. But the intrinsic 
structure of this part of the history of Nature will 
impose certain restrictions on the kind of frames that 
are possible for mapping it out. 

We can now deal with the case of a particle subject 
to Newtonian forces. We assume (a) that it is a general 
fact about all moving particles (and not merely about 
those which are under the action of non-Newtonian 
forces) that they move in such a way that the total 
spatio-temporal separation for two remote events in 
their history is greater than it would be for any other 
way of moving which the intrinsic structure of the 
part of the history of Nature in which the two events 
fall would allow, {b) That, in those parts of the history 
of Nature in which Newtonian forces show themselves, 
the intrinsic structure is not such that the expression 
for the spatio-temporal separation for two adjacent 
events can be reduced to the form with constant 
coefficients. This is equivalent to assuming that 
Newtonian frames are strictly applicable only to those 
parts of the history of Nature (if such there be) in which 
no Newtonian forces are acting. 

On these assumptions the general equations of 
motion, which have just been deduced for ?ton- 
Newtonian forces, will hold for all forces. These 
four equations are simply the analytical conditions 
which must be fulfilled if the actual course of a particle 
is to be such that the total spatio-temporal separation 
between two remote events in its history shall be a 



GENERAL THEORY OF RELATIVITY 201 

maximum or minimum. And they were deduced from 
the most general expression possible for the spatio- 
temporal separation of a pair of adjacent events. For, 
although we were in fact dealing with cases where the 
expression for the separation can be reduced to the 
Newtonian form with constant coefficients, no use was 
made of this special assumption in deducing the con- 
ditions that the total separation for the actual course 
shall be stationary. We may say then that, if the 
above assumptions be true, we have got the general 
equations of motion in a form which is (a) independent 
of any special frame of reference, and (b) applies equally 
to Newtonian and non-Newtonian forces. If the forces 
be all non-Newtonian there will in addition be a set of 
equations between the g's of all possible frames, ex- 
pressing the fact that the structure of the region under 
discussion is such that the separation can be reduced 
to the form with constant coefficients. If some of the 
forces be Newtonian this extra set of conditions will 
not of course hold, though it will still be possible that 
the g's of all possible frames are subject to some less 
rigid set of conditions. 

On this view the one fundamental mechanical fact, 
which is absolute and independent of all frames of 
reference, is the stationary character of the actual history 
of a moving particle, i.e., the fact that it moves with 
such a velocity and in such a path that the total 
separation between remote events in its history is a 
maximum or minimum. This is independent of whether 
it be under the action of Newtonian forces or not. But 
the course which in fact has the greatest or least possible 
separation will differ intrinsically, according to the 
intrinsic structure of the history of Nature in the spatio- 
temporal region under discussion. If this region be 
such that the separation between two adjacent events 
in it can be expressed in the form with constant co- 
efficients, the course which has the stationary property 
is a Euclidean straight line traversed with a uniform 

o 



202 SCIENTIFIC THOUGHT 

velocity as judged by a Newtonian clock. If the region 
be such that the separation cannot, by any choice of 
frame, be reduced to this specially simple form, the 
stationary course will be some intrinsically different 
kind of curve traversed with a non-uniform velocity. 
It is assumed that the presence of Newtonian forces in 
a region of the history of Nature is a sign that the 
intrinsic structure of that region is such that no frame 
can be found, with respect to which the separation of 
two adjacent events takes the form with constant 
coefficients. 

How are we to verify or refute these assumptions? 
Obviously the only way is to see whether (a) they 
agree with known facts as well as the traditional 
theory, and (b) account for and predict facts which were 
not predicted or accounted for by the traditional theory. 
We have seen that, when the forces are purely non- 
Newtonian, the g's of any frame of reference appear 
to the observers who use that frame as the potentials 
of the non-Newtonian forces. Reversing this analogy, 
it is reasonable to suppose that the potentials of 
the Newtonian forces that are observed with respect 
to any frame will be the g's which characterise the 
spatio-temporal separation of two adjacent events in 
that part of the history of Nature in which these 
Newtonian forces act. In dealing with any particular 
field of Newtonian force we must therefore find a set 
of g 1 s which (a) satisfy the general equations of motion, 
and {b) differ numerically from the potentials which 
the traditional theory would ascribe to this field by 
amounts which fall below the limits of experimental 
error in the experiments that have already been done 
with such fields. If this can be done, the resulting 
equations will have at least as good a claim to represent 
the facts of motion in this field as the traditional 
equations. And if, in addition, they enable us to 
predict small residual effects, which are not accountable 
for on the traditional theory but can be observed when 



GENERAL THEORY OF RELATIVITY 203 

looked for, they will have better claims to truth than 
the traditional equations. It must be admitted, how- 
ever, that this would not amount to a knock-down 
proof of the truth of the assumptions, since the 
modified equations could no doubt be deduced on 
traditional views of space and time, provided suitable 
modifications were made in the expressions for the 
potentials. 

Evidently then we can only hope to find evidence 
for or against the present theory by considering definite 
fields of force and the observable phenomena that 
happen in them. And, even so, as it seems to me, 
no absolutely conclusive proof of the theory will ever 
be found, since alternative explanations which involve 
the traditional views of space, time, and force could 
always be constructed to fit the facts. If, however, 
these should prove to be very complicated and artificial, 
as compared with the explanation offered by the new 
theory, we shall have the same sort of grounds for 
preferring the latter as we had for preferring the 
Relational Theory of Motion, in spite of the fact that 
no downright refutation of the Absolute Theory is 
possible. 

(2) We have now to raise the question whether 
Nature, as a sum total of events, has any one type of 
intrinsic structure always and everywhere, and, if so, 
of what type the intrinsic structure is. It is admitted 
that not all forces are. non-Newtonian, i.e., that, if we 
insist on trying to refer all the events in Nature to 
a Newtonian frame, many particles will at some time 
in their history be subject to observable forces with 
respect to it. And there is no frame that we can take 
which will transform away all forces always and every- 
where, though it is always possible to find a sufficiently 
wild frame which will transform away Newtonian forces 
over a small enough region of space for a short enough 
lapse of time. Now we might deal with this fact in one 
of two alternative ways : (a) We might hold that the 



204 



SCIENTIFIC THOUGHT 



intrinsic structure of Nature is such that the spatio- 
temporal separation of a pair of adjacent events can 
take the Newtonian form always and everywhere. We 
shall then have to hold that this fact is disguised from 
us by the presence of forces in Nature, which appear 
in every frame we choose. This is a little like Swift's 
view that the English Government always chose admir- 
able bishops for Ireland, but unfortunately they were 
always stopped on Hounslow Heath by highwaymen, 
who exchanged clothes with them and travelled on in 
their coaches. Or (b) we might hold that Nature is so 
constituted that no frame can be found with respect 
to which the separation takes this simple form. We 
might then try to explain the forces, which are found 
in all frames, by reference to the intrinsic peculiarity 
of structure in Nature, which prevents the separation 
from being expressed in this simple way. 

Before attempting to decide between these two 
alternatives for the dynamical case, I will, as usual, 

illustrate their precise meaning by 
a geometrical example. Suppose 
people were confined to the sur- 
face of a sphere, and that they 
took as axes a pair of mutually 
normal great circles. The co- 
ordinates of any point P on the 
sphere are to be the arcs of the 
two great c.ircles through it which 
are normal to these two axes respectively. The figure 
above will illustrate the arrangement. 

If they measured the arcs OP, P;« and Pn, and 
found their lengths to be r, x and y respectively they 
would find that r 2 is not equal to x*+y*, as it would be 
if the square of the spatial separation for adjacent points 
on a sphere were of the form dxt + dy*. But, if they were 
specially wedded to the view that the spatial separation 
must take this form, they could get over the difficulty 
by assuming that there are forces of suitable magni- 




GENERAL THEORY OF RELATIVITY 205 

tudes and directions at different points on the sphere 
which distort their measuring rods. Conversely, they 
might just recognise that they were "up against" an 
intrinsic peculiarity of spherical surfaces, and avoid the 
supposition of distorting forces. Similarly, when you 
find that there are untransformable forces with respect 
to Newtonian frames, you can either leave it at that, 
or take up the suggestion that Nature has such an 
intrinsic structure that the spatio-temporal separation 
of two adjacent events is not accurately expressible in 
the Newtonian form. 

The actual relation between r, the total separation, 
and x and y, the co-ordinates in this system is 

• 2 r • 2 x , • 2 y 
sin 2 T = sin 2 -7 +sin ^ 

where k is the radius of the sphere. If the observers 
confined themselves to a very small region, the sines 
could be replaced by the angles themselves, and the 
relation 

r 2 = x 2 +y\ 

which is characteristic of the Euclidean plane, would 
approximately hold. This is analogous to the fact, 
already mentioned, that it is always possible to find 
a frame, in terms of which particles move with uniform 
rectilinear velocities for a sufficiently small region of 
Space and for a sufficiently small lapse of time, though 
not for all places and all time. 

We can now return from the geometrical analogy 
to the dynamical problem. If we consider the various 
kinds of Newtonian forces we find that they divide 
sharply into two classes, viz., gravitational attractions 
and the rest. We have already pointed out the 
peculiarities of gravitation. It acts always and every- 
where, it is independent of all properties of matter 
except its inertial mass, it is indifferent to the sur- 
rounding medium, and so on. We saw that these 
peculiarities make gravitation closely analogous to the 



206 SCIENTIFIC THOUGHT 

non-Newtonian forces to which a particle, at rest or in 
uniform motion in a Newtonian frame, is subjected 
when referred to a non-Newtonian frame. Again, we 
saw that, in no frame composed of material axes and 
clocks, could a particle literally be under the action of 
no forces, since there would always be gravitational 
attractions between it and the axes themselves, though 
these might be negligible if it were a solitary particle 
referred to the fixed stars as axes. For these reasons 
it seems plausible to suppose that gravitation, at least, 
is something connected with the intrinsic structure of 
Nature as a sum total of events. This structure is such 
that no frame, in which the spatio-temporal separation 
takes the simple form with constant coefficients, accu- 
rately fits the whole of Nature ; and the gravitational 
forces, which we find when we use a Newtonian frame, 
are an expression of the "misfit" of that frame to the 
structure of Nature. This is exactly analogous to the 
fact that the contracting and expanding forces, which 
observers on the sphere would have to assume to be 
acting on their measuring rods in the last example, 
would simply be an expression of the " misfit" between 
the intrinsic character of the surface of a sphere and 
the plane system of co-ordinates which they insisted 
on applying to it. 

As regards other kinds of Newtonian forces, which 
depend on the special properties of bodies and of the 
medium, and do not show themselves always and 
everywhere, as gravitation does, we can hardly expect 
a similar explanation to work. We may illustrate this 
difference again from the example of people living on 
the surface of a sphere and trying to measure it, on 
the assumption that the expression for the square of the 
spatial separation of two adjacent points must be reduc- 
ible to the simple form dx 2 ' + dy 2 '. Let us suppose that 
there were big fires burning at some parts of the surface 
of the sphere. The measurements of the observers 
would then be inconsistent with their fundamental 



GENERAL THEORY OF RELATIVITY 207 

assumption and would have to be " cooked" in two 
different ways : (a) They would be systematically 
wrong - on account of the fact that no system of co- 
ordinates on the surface of a sphere can really give 
an expression for the separation, which shall involve 
only constant coefficients. This systematic error they 
will have to correct by ascribing contracting and ex- 
panding forces on their rods to the sphere itself, (fr) 
Apart from these systematic errors, there will be special 
discrepancies when they measure near one of the fires, 
owing to the physical expansion of their rods in such 
a neighbourhood. Now we should say that it was 
not unreasonable of the observers to ascribe the special 
discrepancies in their measurements near the fires to 
forces acting there on their rods, for there is something 
visible and tangible there (viz., the fire) to account for 
these assumed forces. But we should think it very 
foolish of them to ascribe the systematic discrepancy 
between measurement and theory, which they find 
everywhere on the sphere, to forces bound up with 
the sphere and varying in a systematic way from place 
to place on its surface. We should advise them, 
instead of sticking obstinately to their view that the 
separation of adjacent points on the sphere must take 
the form with constant coefficients, and then invoking 1 
forces to account for the discrepancies between this fact 
and their observations, to see whether they could not 
account much more simply for the facts by supposing 
that the surface on which they live is intrinsically of 
such a character that no set of axes, in which the ex- 
pression for the separation of two adjacent points takes 
this specially simple form, can exist upon it. In the 
same way, when you find that there is a certain kind 
of force, viz., gravitation, which acts always and every- 
where on all particles, when referred to Newtonian 
frames, it becomes reasonable to suppose that this 
"force" is merely an expression of the inappropriate- 
ness of a Newtonian frame to the intrinsic structure 



208 SCIENTIFIC THOUGHT 

of Nature, as a sum total of events. Other Newtonian 
forces, which act in one place and not in others, or 
at one time and not at another, or on one kind of 
matter and not on another, are in a different situation, 
and may be compared to the fires at various places 
on the sphere in our geometrical example. 

We are going to see then, whether we can account 
for the gravitational forces, which are present in all 
Newtonian frames, by the assumption that the events 
of Nature form an interconnected manifold of such an 
intrinsic structure that no frame of reference can be 
found, in respect to which the expression for the spatio- 
temporal separation of two adjacent events accurately 
takes the form (8) with constant coefficients. 

Now we have so far distinguished two kinds of 
surfaces in ordinary space. With one of them (such 
as the plane ; the cone, the cylinder, etc.) it was 
possible to find a system of co-ordinates on the surface, 
in terms of which the expression for the spatial separa- 
tion of two adjacent points, as measured along the 
surface, contains only constant coefficients. The sign 
of this was the vanishing of the Riemann-Christoffel 
Tensor. The more familiar criterion is that such 
surfaces are either planes or can be unfolded without 
distortion or stretching into planes. In the other kind 
of surface this condition is not fulfilled. We gave 
the sphere as an example. We agree then that the 
universality and other peculiarities of gravitation suggest 
that the structure of Nature, as a sum total of events, 
is not formally analogous to that of surfaces of the 
first kind, i.e., we shall henceforth [reject the view that 
the intrinsic structure of Nature is such that the 
Riemann-Christoffel Tensor vanishes for all frames of 
reference within Nature. Does Nature then impose 
no general condition on possible frames of reference 
except this negative one? 

If we return once more to elementary geometry we 
shall see that the surfaces for which the expression for 



GENERAL THEORY OF RELATIVITY 209 

the spatial separation cannot take the form with constant 
coefficients can be further subdivided. We took the 
sphere as an example of such a surface. The outside 
of an egg would be another example. Now these two 
surfaces have an important intrinsic difference. A 
sphere is a much more special type of surface than 
an egg-shell, just as a plane or a cone is of a much 
more special type than a sphere. The sphere agrees 
with the plane and differs from the egg-shell in the 
following respect : A triangle bounded by arcs of 
great circles on the sphere could be slid about all 
over the surface, remaining everywhere in complete 
contact with it, and needing no stretching or distortion. 
In fact any figure that fits on to the sphere in one part 
will do so in all parts. The same is obviously true 
of figures in a plane. It is not true of figures on 
the surface of an egg-shell. A cap, which fitted the 
blunt end of the egg-shell, could not be made to fit 
exactly on to the sharp end without stretching some 
parts of it and folding others. Thus, granted that 
the Riemann-Christoffel Tensor does not vanish for 
Nature, and that the intrinsic interconnexions of events 
in Nature are therefore not formally analogous to those 
of points on a plane, the question can still be raised : 
Are the intrinsic relations of events in Nature formally 
analogous to those of points on a sphere or to those of 
points on an egg-shell? If the former alternative be 
fulfilled a function of the g's, derived from the Riemann- 
Christoffel Tensor, and called the Modified Riemann- 
Christoffel Tensor, will have to vanish. This imposes 
a limitation upon possible gs, and therefore upon 
possible natural frames of reference, but the restriction 
is less rigid than it would be if the unmodified Tensor 
were to vanish. 

If then gravitation be the way in which a certain 
intrinsic peculiarity in the structure of Nature exhibits 
itself, we might suppose that the equating of the 
Modified Tensor to O would be the generalised expres- 



210 SCIENTIFIC THOUGHT 

sion for the law of gravitation, with respect to any 
admissible frame of reference. So far, however, this is 
merely a conjecture. It might be that gravitation is 
not the expression of a general intrinsic peculiarity in 
the structure of Nature, as a sum total of interconnected 
events. And it might be that, even if this were true, 
the structure is not of the particular kind which is 
expressed by the vanishing of the Modified Tensor. 
Here, as elsewhere, we must carefully distinguish 
between what suggests the theory and what verifies it. 
What suggests that gravitation is an expression of the 
general intrinsic structure of Nature is its universality 
and its peculiarities as compared with other forces. 
What suggests taking the vanishing of the Modified 
Tensor as the expression of this structure is that it is 
the next simplest assumption to make, after the facts 
have proved to be inconsistent with the still more 
special structure which would be indicated by the 
vanishing of the unmodified Tensor. We have now 
to see what verifies the theory thus suggested. 

We know the traditional form of the law of gravita- 
tion, with respect to the nearest approach that we can 
get to Newtonian frames. For a region free from 
matter (approximately for the inside of an exhausted 
bulb) it takes the form of Laplace's Equation 

9 2 V 9 2 V 9 2 V_ 

dx* dy 2 dz 2 ~ °' 

where V stands for the gravitational potential at a point 
in the region, and x, j>, and z are the Cartesian co- 
ordinates of this point with respect to a Newtonian 
frame. There is no doubt that this equation is true 
to a very high degree of approximation. It follows 
that any candidate for the position of the true law of 
gravitation must reduce to something which differs 
very slightly indeed from Laplace's equation, when 
expressed in terms of the nearest approach to a 
Newtonian frame that we can get. 



GENERAL THEORY OF RELATIVITY 211 

Now the Modified Riemann-Christoffel Tensor is 
an expression involving second order differential co- 
efficients of the g's for a frame, with respect to the co- 
ordinates and dates of an event as referred to this frame. 
So far there is a formal analogy between it and the 
left-hand side of Laplace's Equation, if the g's be re- 
garded as analogous to Laplace's V. The right-hand 
side is o in both cases. Now Laplace's V is a potential, 
and we have already seen the close analogy between 
the g's of a frame and the potentials of the forces which 
act on particles when referred to that frame. The 
only question that remains then, is the following: Can 
we find a set of ten functions g^v of the Newtonian 
co-ordinates and clock-readings, which (a) when sub- 
stituted in the expression for the Modified Tensor 
make it equal to o, and {b) differ so little from the 
gravitational potentials of the ordinary Newtonian 
theory that the difference could only have been detected 
by very special methods, and when there was a very 
special reason for looking for it? If so, we may 
reasonably suppose that gravitation is an expression 
of the fact that Nature has a kind of intrinsic structure 
formally analogous to that of the sphere, and that 
the formula obtained by equating the Modified Tensor 
to o is the true form of the law of gravitation. The 
answer to this question is in the affirmative ; and so 
we may take it that the vanishing of the Modified 
Tensor is the true form of the law of gravitation for 
a region empty of matter. 

There is one point which must be mentioned here. 
We are accustomed to think of the traditional law of 
gravitation in the form that two particles attract each 
other with a force proportional to their masses and 
inversely proportional to the square of the distance 
between them. And we are wont to regard Laplace's 
differential equation as a rather recondite mathematical 
deduction from this. In the Relativity theory of gravi- 
tation the order is reversed. The law obtained by 



212 SCIENTIFIC THOUGHT 

equating the Modified Tensor to o is directly analogous 
to Laplace's Equation. The notion of remote particles 
attracting each other is here a rather recondite mathe- 
matical deduction from the differential equations. In 
fact, material particles turn up now only as points of 
singularity in a gravitational field ; the field itself is 
the fundamental thing. And, when you do make this 
deduction, it is found that the force between two 
particles is not wholly in the line joining them, if I 
may put it rather crudely. The remaining term, 
which the new form of the law involves, accounts for 
the slow rotation of the orbits of the planets as wholes 
in their own planes. This had been noticed for the 
planet Mercury, and was unintelligible on the tradi- 
tional law of gravitation. It is accounted for both 
qualitatively and quantitatively by the Relativity 
theory. 

The last point to be noticed is that, on the present 
theory, gravitation modifies the movements, not merely 
of ordinary material particles, as on the traditional view, 
but also of any form of energy, such as light, radiant 
heat, etc., which travels through space. We must 
now see how this comes about. In the first place some 
such consequence is suggested at once by the modifica- 
tions which the Special Theory of Relativity entails in 
the traditional conception of mass. We saw at the 
beginning of this chapter that, if a body moves with 
velocity v in a straight line with respect to a Newtonian 

.. M . 

frame, it is necessary to ascribe to it a mass 8 in 

l - V -2. 

r 
order to get the Principle of the Conservation of 
Momentum into a form consistent with the Restricted 
Physical Principle of Relativity. We also saw that 

this is approximately equal to M + | — |— . Now the 

second term in this is the kinetic energy of the particle 
divided by the square of the velocity of light. It is 



GENERAL THEORY OF RELATIVITY 213 

thus certain that the kinetic energy of a particle of 
matter appears as an increase in its inertial mass. It 
is therefore plausible to suppose that any region filled 
with any form of energy, such as light or radiant heat, 
would thereby acquire an inertial mass equal to the 
total energy contained in it divided by the square of 
the velocity of light. It by no means follows, on the 
traditional theory of gravitation, that such a region 
would contain any gravitational mass. It is true that 
for any particle of matter the gravitational and the 
inertial masses are proportional, to an extremely high 
degree of approximation. Still, this would be com- 
patible with the view that the gravitational effect 
depends wholly on the factor M ; seeing that the 
second factor in the inertial mass contains the square 
of the velocity of light in its denominator, and is there- 
fore excessively small unless the energy of the body be 
excessively great. On this view we should not expect 
a beam of light to have gravitational mass, in spite of 
its having inertial mass. On the other hand, it is of 
course possible that the gravitational and the inertial 
masses are always exactly, and not merely approxi- 
mately, proportional. In that case we should expect 
the course of a beam of light to be modified when it 
passes through a gravitational field, just as the path 
of a material particle is known to be modified under 
like conditions. Now experiments with pendulums 
had already suggested very strongly that the gravita- 
tional mass of a piece of matter is accurately, and not 
merely approximately, proportional to its whole inertial 
mass, and not only to the first factor in this. Thus, 
the Special Theory of Relativity had already made it 
extremely likely that the course of a beam of light or 
any other kind of radiant energy would be modified 
when it passed through a gravitational field. 

Now what is thus merely a plausible suggestion on 
the traditional theory of gravitation, combined with the 
modified dynamics of the Special Theory of Relativity, 



214 SCIENTIFIC THOUGHT 

is a necessary consequence of the General Theory of 
Relativity. We know that light would not travel 
uniformly or in a straight line with respect to non- 
Newtonian frames. The people, e.g., who used the 
spokes of the rotating wheel as their axes would not 
find that light travelled in a straight line with respect 
to their axes, or with a uniform velocity with respect 
to their clocks. And the actual course that a beam of 
light would follow in their system would be determined 
by the^-V which characterise that system. Now it is a 
fundamental assumption of the General Theory that 
the analogy between the g's of a non-Newtonian frame 
and the potentials of the non-Newtonian forces which 
act on particles with respect to that frame is to be 
extended to the potentials of Newtonian forces. 

Suppose then that we have found the equations for 
the path of a beam of light with respect to any frame, 
in terms of the gs of that frame, on the assumption 
that it would move accurately in a straight line with a 
uniform velocity relative to a Newtonian frame in the 
absence of gravitation. To find its actual path with 
respect to a Newtonian frame in a gravitational field we 
must just substitute in these equations those values of 
the g's which (a) satisfy the condition that they make 
the Modified Riemann-Christoffel Tensor vanish, and 
{b) account for the observed strength and distribution 
of the field. These equations will not in general 
represent a motion with a uniform velocity in a 
straight line with respect to the axes defined by the 
fixed stars. The divergence, which is excessively small 
even in the intense gravitational field which surrounds 
a huge body like the sun, can be calculated and has 
been experimentally detected. 

I have now sketched to the best of my ability the 
gradual modifications which experimental facts and 
reflection upon them have forced upon physicists. 
There are two dangers to be avoided here by plain 
men. One is to think that the Theory of Relativity is 



GENERAL THEORY OF RELATIVITY 215 

essentially unintelligible to all but profound mathe- 
maticians, and that therefore it is useless to try to 
understand it. The other, and much more serious 
danger, is to suppose that it can be made intelligible 
in popular expositions of a few pages to men who have 
never had occasion to consider the subjects with which 
it deals. Like every other conceptual scheme it grew 
up, by a kind of inner necessity, against a whole 
background, of interconnected concepts, principles, and 
experimental facts. Presented in the absence of this 
background it is and must be as unintelligible as the 
orthodox doctrine of the Trinity is to persons who know 
nothing of the theological controversies which preceded 
the formulation of the Athanasian Creed. In the course 
of my exposition I have constantly enlivened the dis- 
cussion by geometrical anecdotes about men living on 
spheres, and dynamical parables about persons with an 
unintelligible fondness for rotating wheels as axes of 
reference. I think this course was inevitable, in order 
to illustrate the conceptions which I was expounding. 
But it has the grave disadvantage of breaking the train 
of argument and obscuring that distinction between 
inference and illustration which it is so important to 
keep clear. I shall therefore end by summarising the 
whole matter in a connected form. 

Summary of Arguments and Conclusions of Part I. 
(1) Nature is a sum total of interconnected events; 
and every actual event lasts for some time, has some 
extension, and is in spatio-temporal relations to the 
other events in Nature. (2) But the extensions, 
durations, and spatio-temporal relations of events are 
of such a kind that we can apply the Principle of 
Extensive Abstraction to them, and thus define 
"instantaneous point-events" and their exact spatio- 
temporal relations. We can then give a clear meaning 
to the statement that the actual extended and enduring 
events of Nature are "composed of" instantaneous 
point-events, and that the crude relations of such actual 



216 SCIENTIFIC THOUGHT 

events are " compounded out of " the exact relations of 
the instantaneous point-events which compose them. 
(3) This being so, we can henceforth safely state our 
theory in terms of instantaneous point-events and their 
exact relations, which are notiora nobis, though not 
notiora Natunc. For we know how to translate pro- 
positions about instantaneous point-events and their 
merely conceivable relations into propositions about 
actual extended and enduring events and their per- 
ceptible relations. 

(4) It is impossible to state general laws about the 
events in Nature till we have fixed on some way of 
assigning a date and a position to every instantaneous 
point-event in Nature. For the laws of Nature express 
universal types of connexion between events of one 
kind happening in one place at one date and events 
of the same (or some other) kind happening at the 
same (or some other) place at the same (or some other) 
date. If the places and dates be different, the laws of 
Nature will in general involve the difference between 
the spatial co-ordinates and the difference between the 
dates of the events. (5) There are infinitely many 
different ways of assigning places and dates to all the 
instantaneous point-events in Nature ; but each will 
involve the choice of certain observable events and 
processes in Nature as spatial axes and time-measurer. 
All other events will be placed and dated by their 
spatio-temporal relations to these chosen ones. Any 
such chosen set of events may be called a Frame of 
Reference. (6) It is reasonable to suppose that the 
expression for the laws of Nature in terms of any 
frame will depend partly on the particular frame chosen 
for placing and dating the events of Nature and partly 
on the intrinsic structure of Nature. The aim of science 
should be to find general formulas for the laws of 
Nature, which will immediately give the special ex- 
pression of the law in terms of any particular frame, as 
soon as the defining characteristics of the frame are 



GENERAL THEORY OF RELATIVITY 217 

known. This is as near as anyone but God can get 
to the absolute laws of Nature. (7) There are two 
intrinsic peculiarities of Nature which reveal them- 
selves at once, (a) No matter what frame we choose, 
we shall need four independent pieces of information 
to place and date any instantaneous point-event. This 
fact is expressed by saying that Nature is a four- 
dimensional manifold ; and nothing further is expressed 
thereby, (h) In whatever frame we choose we shall 
find that our four pieces of information divide into 
two groups ; three of them are spatial and one is tem- 
poral. Thus we must be careful not to talk, or listen 
to, nonsense about "Time being a fourth dimension 
of Space." 

(8) There is one frame which has been tacitly used 
in the past for placing and dating the events of Nature 
for scientific purposes, and therefore the laws of Nature 
have been expressed in terms of this frame. The axes 
of it are defined by the fixed stars, the dating is done 
by pendulum clocks set in agreement with each other 
by means of light signals. (9) The choice of this frame 
is not altogether arbitrary. With it, the supposed laws 
of Nature can be expressed in a comparatively simple 
form, and yet are verified to a high degree of approxi- 
mation. With it, again, distances and time -lapses 
which we should immediately judge to be unequal, 
. when we are favourably situated for making such 
comparisons, are unequal, whilst those that we should 
immediately judge to be equal, under similar condi- 
tions, are either exactly or approximately so. In many 
frames this approximate agreement with our immediate 
judgments of equality and inequality would not hold. 
(10) With respect to such a frame, light in vacuo 
travels, to an extremely high degree of approximation, 
in straight lines and with a constant velocity ; and the 
laws of motion, in the traditional Newtonian form, are 
very approximately true. Until quite recent years there 
was no motive for adding these qualifying phrases. 

p 



218 SCIENTIFIC THOUGHT 

(i i) Suppose now that we take a set of frames, whose 
clocks are set in the same way as those of the funda- 
mental frame just described, and which only differ from 
it and from each other in that they move with various 
uniform velocities in the same straight line with respect 
to the fundamental frame. On traditional views about 
the measurement of space and time the measured time- 
lapse between any pair of events should be the same 
with respect to all these frames, and should be inde- 
pendent of their spatial separation and of the relative 
velocities of the two frames. The spatial separations 
should have different measured values in terms of any 
two frames of the set, and they should depend on the 
time-lapse and the relative velocities ; but they should 
depend on nothing else, and the connexion between 
them should be of a very simple form. If this be 
so, the measured velocity of anything that moves with 
respect to the various frames should be different for 
each frame. (12) But very accurate experiments, which 
would be quite capable of detecting these expected 
differences in the measured velocity of light with 
respect to a pair of such frames, fail to show any 
sign of difference. Hence the traditional views about 
the measurement of time and space must be revised, 
or some purely physical explanation must be found 
for this discrepancy between theory and observation. 
(13) No plausible physical explanation can be found, , 
which does not conflict with other well-established 
physical results. Hence the traditional views about the 
measurement of space and time must be revised. (14) 
The transformation equations of the Special Theory 
of Relativity express the relations which must hold 
between the measured distances and the measured time- 
lapses of a pair of events with respect to any two frames 
of this set, if the measured velocity of light with respect 
to all these frames is to be the same. They must 
therefore be accepted. (15) According to these trans- 
formation equations the measured time-lapses between 



GENERAL THEORY OF RELATIVITY 219 

the same pair of events will not be the same with 
respect to all frames of the set. They will depend on 
the measured distances of the events and on the relative 
velocities of the frames. And the measured distances 
will not be connected with the measured time-lapses 
in the simple way in which they are connected on 
the traditional theory. The differences between the 
traditional transformation equations and those of the 
Special Theory of Relativity are, however, so extremely 
small, when the relative velocities of the frames are 
small as compared with that of light, that it is not 
surprising that the defects of the traditional view should 
have remained unnoticed until recent years. (16) It 
follows that, although (as stated in (7)) the distinction 
between time and space will appear in every frame, time- 
separation and space-separation are not independent facts 
in Nature. Events that are separated in time but co- 
incident in space for one of these frames will always 
be separated in space for another of them. And events 
which are separated in space but coincident in time for 
one frame will be separated in time for another. But, if 
a pair of events be coincident both in time and in space 
for one frame, they will be so for all. 

(17) Newton's laws of motion are in such a form that 
they are co-variant with respect to this set of frames for 
the traditional transformation-equations, but are not 
co-variant for the transformations of the Special Theory 
of Relativity. On the other hand, Maxwell's equations 
for the electro-magnetic field are co-variant for the latter 
and not for the former. This means that Maxwell's 
equations are already in a form which remains un- 
changed with change of frame, so long as we confine 
ourselves to the particular group of frames at present 
under discussion and use the transformation equations 
which the facts about light have shown to be necessary. 
Since this is not true for Newton's laws, unless we use 
a set of transformation equations which the facts about 
light have proved to be slightly inaccurate (viz., 



220 SCIENTIFIC THOUGHT 

those of the traditional kinematics), we must con- 
clude that Maxwell's equations are a nearer approach 
to "absolute" laws of Nature than the laws of motion 
in their traditional form. (18) It is, however, easy to 
make quantitatively small modifications in the traditional 
laws of motion, which will render them co-variant for all 
frames of the present set when the true transformation 
equations are used. The modified laws will then be 
as near an approximation to absolute laws of Nature 
as Maxwell's equations. (19) The necessary modifica- 
tions require us to drop the notion that inertial mass is 
an absolute constant. The measured inertial mass of 
a particle with respect to a frame of the set depends 
on its velocity in that frame, and very approximately 
splits up into two factors, one of which is a constant 
and the other is its traditional kinetic energy divided 
by the square of the velocity of light. (20) Delicate 
experiments with pendula strongly suggest that the 
gravitational mass of a body is accurately proportional 
to its total inertial mass, and not merely to the part of 
this which is independent of the energy. (21) The 
frame whose axes are determined by the fixed stars 
and whose clocks are regulated by light-signals, and 
all other frames whose clocks are regulated in the 
same way and whose axes move with a uniform recti- 
linear velocity with respect to the former, together 
make up the set of empirically Newtonian frames. With 
respect to all frames of this set it is certain that light 
travels very approximately in straight lines with the 
same constant velocity, and it is certain that Newton's 
laws of motion — as modified by the Special Theory of 
Relativity — very approximately hold. So close is the 
approximation in both cases that nothing but theo- 
retical considerations would induce us to look for any 
exception to it. We have now to remove our previous 
restriction to Newtonian frames, and to try to generalise 
the laws of Nature for frames that are not Newtonian. 
(22) It is possible to keep the form of Newton's first 



GENERAL THEORY OF RELATIVITY 221 

two laws of motion for non-Newtonian frames, provided 
we will introduce appropriate non-Newtonian forces 
with each non-Newtonian frame. These forces will be 
peculiar in that (a) they act on all particles referred to 
the frame, and are in general functions of the position 
and date of an event in the frame ; (If) they depend on 
no property of the particle except its inertial mass ; and 
(c) they do not in general obey Newton's third law, 
unless concealed particles be assumed ad hoc to carry 
the reaction. In the first two of these respects they 
resemble the Newtonian force of gravitation. (23) 
According to Newton's first law a particle under the 
action of no force rests or moves uniformly in a 
straight line with respect to a Newtonian frame. This 
is equivalent to saying that the total spatio-temporal 
separation between any two remote events in its history 
is either greater or less than it would be for all other 
possible ways in which the history of the particle might 
unfold itself between these two events. (24) The spatio- 
temporal separation between two adjacent events (unlike 
the spatial and the temporal separations) is independent 
of the frame of reference, though it depends on the 
intrinsic structure of the region in which the events 
happen, and this in turn determines the set of frames 
which can be used for mapping out this part of the 
history of Nature. Its particular expression, in terms of 
co-ordinates and dates, of course varies with the particular 
member of the whole set of admissible frames which 
is used. Thus, the fact that the total spatio-temporal 
separation between a pair of remote events is a maxi- 
mum or minimum is independent of frames, though the 
particular course for which the total separation is in fact 
stationary differs according to the intrinsic structure of 
the region in which the events are contained. (25) The 
particular conditions which must hold if the total spatio- 
temporal separation is to be a maximum or minimum 
can be stated in a form which applies equally to all struc- 
tures and all frames. The four equations which sum 



222 SCIENTIFIC THOUGHT 

up these conditions constitute the equations of motion of 
a particle, at least under the action of non-Newtonian 
forces. On comparing them with the traditional 
Newtonian equations, we see that the g*s which 
characterise any non - Newtonian frame are of the 
nature of potentials of the non-Newtonian forces intro- 
duced by that frame. (26) We now make two assump- 
tions, which are only justified in so far as they work. 
(«) We assume that it is a universal law of Nature 
that a particle moves in such a way that the total 
separation of remote events in its history is stationary, 
as compared with that of all other possible ways of 
moving. This is to hold equally whether it be subject 
only to non-Newtonian or also to Newtonian forces. 
In that case the equations deduced for the non- 
Newtonian case become the equations of motion, (b) 
We assume that in those regions of Nature, regarded 
as a sum total of events, in which Newtonian forces 
show themselves, the structure of Nature is not such 
that the separation can be reduced to the form with 
constant coefficients. If that be so, the course with 
the maximum total spatio-temporal separation is not 
a Euclidean straight line traversed with a constant 
velocity, as judged by a Newtonian clock. We treat 
the traditional potentials of the Newtonian forces in 
any field as first approximations to a set of g's, which 
satisfy the general equations of motion thus deduced. 
And we treat the result as the true law of the field. 

(27) Continuous manifolds of several dimensions, 
such as Nature has proved itself to be, can be of various 
intrinsically different kinds. As we might put it, they 
can be "plane-like," "sphere-like," "egg-like," and 
so on. Whatever intrinsic spatio-temporal structure 
Nature may have, there will be an infinite number of 
different possible frames to be found for placing and 
dating the events of Nature. Nevertheless, the intrinsic 
structure of Nature will impose certain conditions on 
all possible natural frames of reference. These re- 



GENERAL THEORY OF RELATIVITY 223 

strictions will take the form of certain very general 
equations connecting the g's of any possible natural 
frame. If the structure of Nature be plane-like, the 
condition is that the unmodified Riemann-Christoffel 
Tensor shall vanish for the g's of all possible natural 
frames. If its structure be sphere-like, the condition 
is that the Modified Riemann-Christoffel Tensor 
shall vanish for the gs of all possible frames. The 
latter is a less rigid condition than the former. (28) 
If the intrinsic structure of Nature be plane-like, an 
accurately Newtonian frame will be fitted for dating 
and placing all the events of Nature ; otherwise it 
will not. (29) If we try to map out a manifold by a 
frame which is unsuited to its intrinsic structure, we 
shall only be able to square our measurements with 
our theory by the assumption of forces which distort 
our measuring instruments and upset their readings. 

(30) We cannot find any frame that will transform 
away gravitational forces always and everywhere, 
though we can find non-Newtonian frames which will 
transform them away over sufficiently small regions 
of space and time. With respect to Newtonian frames 
all particles are always acted on by gravitational forces, 
though these may sometimes be negligibly small for 
practical purposes. It is therefore plausible to suppose 
that the universality of gravitation with respect to 
Newtonian frames is a mark of the misfit between this 
type of frame and the intrinsic structure of Nature. 
(31) On the other hand (a) gravitation has many 
analogies to non-Newtonian forces ; (b) the traditional 
law of gravitation, which is certainly very nearly true, 
can be expressed as a differential equation of the 
second order, involving the gravitational potential at 
a place and the co-ordinates of the place with respect 
to Newtonian axes ; and (c) we have already assumed 
that potentials and the g's of frames are mutually 
equivalent. (32) The facts mentioned in (31) strongly 
suggest that the law of gravitation must be some 



224 SCIENTIFIC THOUGHT 

general condition imposed on the g's of all possible 
natural frames, and expressed as a differential equation 
of the second order involving these g's. The facts 
mentioned in (30) suggest that this condition is not 
that the unmodified Tensor vanishes. For, if this 
were so, the intrinsic structure of Nature would be 
such that a Newtonian frame is suited to it, and the 
necessity of assuming gravitational forces always and 
everywhere with Newtonian frames strongly suggests 
that this is not so. (33) It is obvious that the 
next suggestion to try is to suppose that the law of 
gravitation is expressed by the vanishing of the 
Modified Tensor, i.e., that gravitation is the sign of 
an intrinsically sphere-like structure in Nature. (34) 
It is found that, if this be the true law of gravitation, 
the observable effects will in most cases differ so little 
from those predicted by the traditional law that the 
difference could not be detected. Hence the very full 
verification which the traditional law has received is 
no obstacle to accepting the amended law. (35) On 
the other hand, there are certain very special cases 
in which a small observable effect might be expected 
on the new form of the law and not on the old. In 
such cases (notably the movement of the perihelion of 
Mercury and the bending of a ray of light in passing 
near a very massive body like the sun) the predicted 
effects have been verified both qualitatively and 
quantitatively. 

The following additional works may be consulted 
with advantage : 

A. S. Eddington, Report on the Relativity Theory of 

Gravitation. 
„ ,, Space, Time, and Gravitation. 

E. Cunningham, Relativity, Electron Theory, and Gravitation. 

B. Riemann, Uber die Hypothese?i welche der Geometrie zu 

Grunde liegen . (Julius Springer. Berlin.) 
H. Weyl, Space, Time, and Matter. 



PART II 

THE SENSATIONAL AND PERCEPTUAL BASIS 
OF OUR SCIENTIFIC CONCEPTS 



Contents of Part II 

CHAPTER 

VII. Matter and its Appearances ; Preliminary Definitions 

VIII. The Theory of Sensa, and the Critical Scientific Theory 

IX. The Positions and Shapes of Sensa and of Physical Objects 

X. The Dates and Durations of Sensa and of Physical Objects 
and Events 

XL Sensible and Physical Motion 

XII. Sensible and Physical Space-Time 

XIII. The Physiological Conditions of Sensations, and the Onto- 
logical Status of Sensa 



CHAPTER VII 

" Fallunt nos oculi, vagique sensus 
Oppressa ratione mentiuntur. 
Nam turris, prope quae quadrata surgit, 
Detritis procul angulis rotatur." 

(Petronius Arbiter.) 

Matter and its Appearances ; Preliminary Definitions 

In the First Part we have been dealing with the 
gradual development and modification of the traditional 
scientific concepts of Space, Time, and Motion, within 
the region of Physics. These concepts were taken over 
by science from educated common-sense, and we have 
been tracing the process of clarification and definition 
which they have undergone at the hands of scientists 
in pursuit of their own business. At two places only 
have we deliberately gone outside the range of ordinary 
scientific reflection. The first was where we explained 
the Principle of Extensive Abstraction, and tried to 
justify by its means what mathematical physicists take 
for granted, viz., the application of geometry and 
mechanics, stated in terms of points, instants, and 
particles, to a world of extended objects and non-instan- 
taneous events. The second was where we dealt with 
the general problem of Time and Change, and tried 
to defend their reality against the very plausible ob- 
jections which have been made to them by certain 
philosophers. 

Now the careful reader will have been struck by 
two points in Part I. (i) He will have noticed that the 
" raw material," which science took over from common- 
sense and elaborated, was really anything but "raw." 

227 



>2$ SCIENTIFIC THOUGHT 

It was already highly complex and sophisticated. The 
common-sense notions of a single Space, a single Time, 
and persistent bits of Matter which exist, move, and 
change within them, are by no means primitive. They 
must be the results of a long and complex process of 
reflection and synthesis, carried out by countless genera- 
tions of men on the crude deliveries of their senses, 
embodied in everyday speech, and thus handed down 
from father to son for further elaboration. The main 
outlines of this conceptual scheme have been accepted 
without question by scientists, and we have so far 
merely been tracing those modifications of detail within 
the scheme, which a more accurate knowledge of the facts 
of nature has shown to be necessary. In Part II, I 
want to dig below the foundations of Part I, and to 
try to connect the concepts of science and common- 
sense with their roots in crude sensation and perception. 
If we should find, as I think we shall, that recent 
modifications in the traditional concepts, which have 
been made on purely scientific grounds, bring the 
general scheme into closer connexion with its sensible 
and perceptual basis, this will be an additional argument 
in favour of such modifications, and should tend to 
neutralise the impression of paradox which these later 
developments produce on men who have been brought 
up on the traditional scheme. 

(2) The second point which will have struck the 
reader is that practically nothing has been said so far 
about the concept of Matter. This is true. There is 
a much wider divergence between the common-sense 
and the scientific concepts of Matter than between the 
two concepts of Space or of Time. The scientific con- 
cepts of Space and Time are fairly straightforward de- 
velopments and clarifications of the concepts of common- 
sense. But common-sense thinks of Matter as having 
many intrinsic qualities, such as colour, temperature, 
etc., besides its merely spatio-temporal characteristics. 
Science, on the other hand, tends to think of Matter 



MATTER AND ITS APPEARANCES 229 

as being simply "the movable in space," and to ascribe 
to it no intrinsic non-spatio-temporal qualities except 
mass. Now the treatment of Matter and our knowledge 
of it will bring us in the most direct way to the heart 
of the problem of Part II. Matter is admitted to be, 
or to be specially closely connected with, what we 
perceive with our senses. And again, it would be 
admitted by most people that we should never have 
known of spatial attributes, like shape, size, and posi- 
tion, if we had not perceived bits of matter of various 
shapes and sizes in various places. Lastly, we learn 
about Motion by watching bits of Matter moving about, 
and by moving about ourselves. Thus, in trying to 
clear up the relations between Matter, as conceived by 
science, and what we perceive with our senses, we 
shall at the same time be dealing with the sensible and 
perceptual bases of the concepts of Space, Time, and 
Motion. So, in one sense, this Part will be wholly 
about the concept of Matter. But this will involve a 
reconsideration of the concepts of Space, Time, and 
Motion. I shall begin by stating the problem in its 
most general form, and shall gradually go into greater 
detail. 

The Traditional Notion of a bit of Matter. — When we 
ask what is meant by a bit of Matter the question is 
itself ambiguous. In one sense a complete answer to 
it would be a complete theory of Matter, and this 
could only be made, if at all, at the very end of our 
discussion. This, however, is not the sense in which 
I am asking the question here. All that I am asking 
is: "What is the irreducible minimum of properties 
which practically everybody would agree that an object 
must possess if it is to be called a bit of Matter?" I 
think that science and common-sense would agree that 
at least the following conditions must be fulfilled : 
(i) Its existence and properties must be independent 
of the minds that happen to observe it, and it must 
be capable of being observed by many minds. This 



230 SCIENTIFIC THOUGHT 

characteristic may be summed up by saying that Matter 
is neutral as between various observers, or is "public" 
— to use a convenient word of Mr Russell's. This dis- 
tinguishes Matter sharply from any ordinary conscious 
state of mind. The latter is in a unique way private 
to the person whose state it is. My belief that 2 + 2 =4 
is different from yours, though the two beliefs refer to 
the same fact. My belief cannot literally wander out 
of my mind and turn up in yours. It is true that I 
may convert you from your erroneous belief that 
2 + 2 = 5, an d replace it by my true belief that 2 + 2=4. 
This does not, however, mean that my belief has 
become yours, in the sense that it has left my mind 
and taken up its abode in yours. Were this so, I 
could never persuade you of anything without losing 
my own belief in it, and schoolmasters would pre- 
sumably be distinguished from other men by an ultra- 
Humian scepticism as to all the subjects that they 
teach. This is not, in fact, found to be the case. All 
that really happens when A converts B to his own 
belief is that A's arguments, or the amount of A's 
bank balance, produce in B's mind a state of belief 
which refers to the same fact as B's belief, and has 
the same relation of concordance or discordance to this 
fact. My belief and yours are only called the same 
belief in the derivative sense that they are two different 
acts of believing which are related in the same way 
to the same fact. 

Exactly the same is true of desires. We do some- 
times say that you and I have the same desire ; but 
what we mean is that your desire and mine, though 
two states of mind, have a single object. Now, if 
there be such things as bits of Matter at all, they are 
not private in this way to each mind, but are common 
to all the minds that observe them. We talk of my 
beliefs and your wishes ; we do not talk of my hydrogen 
atom or of your electron. We just speak of the or this 
atom or electron. It is, of course, true that a hat or 



MATTER AND ITS APPEARANCES 231 

an umbrella is regarded as a bit of Matter, and that 
we do talk of my hat and of your umbrella. But this, 
which at first sight seems an objection, is seen on 
further reflection to support what we have been saying. 
The sense in which my umbrella is mine is different 
from that in which my beliefs are mine. My umbrella 
is mine only in the sense that it is legally my property ; 
my beliefs are mine in the sense that they could not 
exist out of my mind or pass into yours. You cannot 
take my beliefs ; it is only too fatally easy for you to 
take my umbrella. So that even those bits of Matter 
to which we apply possessive adjectives are public in 
a way in which no state of mind is public. 

(ii) A bit of Matter is supposed to be neutral, not 
only between different observers, but also to be in a 
certain way neutral as between several senses of the 
same observer. We are said to see, hear, and feel a 
bell. This sort of neutrality is not supposed to be 
complete. The shape and size of the bell are indeed 
supposed to be in some way common to sight and 
touch. As regards its sensible qualities the view of 
common-sense is that any bit of Matter combines a 
number of these, and that different senses are needed 
to reveal different sensible qualities. Thus sight, and 
it alone, makes us aware of the colours of bodies ; 
touch, and it alone, makes us aware of their temper- 
atures ; and so on. But it is part of the ordinary view 
of a piece of Matter that all these various sensible 
qualities co-exist in it, whether the requisite senses 
be in action to reveal them all or not. If we first 
only look at a body, and then shut our eyes and go 
up to it and feel it, it is not supposed that it had no 
temperature on the first occasion and no colour on 
the second. 

(iii) These two properties of publicity, as between 
different observers, and neutrality, as between the 
various senses of a single observer, are closely con- 
nected with a third feature which is held to be 



232 SCIENTIFIC THOUGHT 

characteristic of Matter. Bits of Matter are supposed 
to persist with very little change, whether anyone 
happens to observe them or not, and to pursue their 
own affairs and interact with each other, regardless of 
our presence and absence. 

(iv) This brings us to the fourth characteristic of 
Matter. It is commonly held to be part of what we 
mean by a bit of Matter that it shall have a more or 
less permanent shape and size, and that it shall have 
a position in Space, and be capable of moving from 
one position to another. It is admitted that bits of 
Matter are constantly changing their shapes, sizes, 
and positions ; but it is held that they do this through 
their interactions with each other and not through any 
change in our acts of observation, and that in all their 
changes they continue to have some shape, size and 
position. If it could be shown that nothing in the 
world actually has such properties as these, it would 
commonly be held that the existence of Matter had 
been disproved, even though there were public, inde- 
pendent, and persistent objects. 

Berkeley, e.g., is commonly held to have denied 
the existence of Matter, and he certainly thought 
himself that he had done so. Yet Berkeley's theory 
undoubtedly involves the existence of certain entities, 
viz., the volitions (and perhaps the sensations) of God, 
which are independent of the mind of any finite observer 
and are neutral as between my mind and yours. The 
reason why we say that, if Berkeley be right, there is 
no Matter, is because the volitions of God, though 
neutral and independent of us observers, have nothing 
corresponding to shape, size, and position ; whilst the 
only entities which Berkeley allows to have these 
attributes, viz., our sensations, are private to each of 
us, and exist only so long as we have them. Very 
few philosophers have denied that there are entities 
answering to the first three conditions, but a great 
many have denied that there are any answering both 



MATTER AND ITS APPEARANCES 233 

to these and to the fourth condition. Such philosophers 
are held by themselves and by common-sense to have 
denied the existence of Matter. Now we shall have 
plenty of opportunity for seeing that there is a real 
difficulty in holding that the entities which have shapes, 
sizes, and positions are neutral and independent, and 
that those which are neutral and independent have 
shapes, sizes, and positions. 

Before we consider these points in detail at all we 
must mention an additional complication which, though 
partly verbal, is sure to puzzle us if we do not resolutely 
drag it into the light. No doubt it is part of what we 
mean by a bit of Matter that it shall, in some sense, have 
shape, size, and position. But in how literal a sense 
must this be true? We have already seen that, in some 
sense, an extension or a duration is composed of points 
or of instants respectively. But this sense is highly 
complicated and sophisticated, or, to use a happy 
phrase of Dr G. E. Moore's, "Pickwickian." Now 
we shall doubtless be able to find Pickwickian senses 
in which there are entities that are at once public and 
extended. The question is : How Pickwickian may 
the terms in our statement become before it ceases to 
be useful, and becomes merely misleading, to say that 
we accept the existence of matter? Our theological 
friends have much the same difficulties in their inter- 
pretations of the terms that are used in the Creeds. It 
could obviously only be true in a highly Pickwickian 
sense that the Second Person of the Trinity is the son 
of the First. No one supposes it to be true in the 
literal sense in which George V is the son of Edward 
VII ; and the only substantial point at issue is whether 
the sense in which it might be true (assuming, for the 
sake of argument, that the Persons exist) is not so 
extremely Pickwickian that the statement is more likely 
to mislead than to enlighten. Fortunately for us the 
terminology of our problem is not surrounded with the 
same emotional fringe as surrounds the terms used in 

Q 



234 SCIENTIFIC THOUGHT 

Theology. It is no part of our duty to pay compliments 
to Matter, and so long as we state clearly what we do 
mean, it is of little importance whether our terms be 
used in a literal or in a highly Pickwickian sense. It 
will be a question of taste whether it shall be said that 
the theory that we finally adopt amounts to the accept- 
ance or the denial of Matter. If we should be accused 
of saying that " Matter is not Matter," we shall at least 
be better off than *Dr F. R. Tennant, who labours under 
the dreadful imputation of teaching that "Sin is not 
Sin." 

The Notion of Sensible Appearance. — I have now tried to 
point out what is the irreducible minimum of properties 
which ordinary people consider must be possessed by 
anything if it is to count as a piece of Matter. I have 
also pointed out, by anticipation, that the history of 
philosophy shows there to be a great difficulty in 
holding that there are any entities which fulfil all these 
conditions in a literal sense. Lastly, we have noticed 
that the question of the reality or unreality of Matter, 
thus defined, is not perfectly clear-cut, because of the 
practical certainty that many of our terms will have to be 
interpreted in a more or less Pickwickian manner, and 
the doubt whether it is worth while to go on using 
familiar phrases after their literal meaning has been 
departed from beyond a certain point. We must now 
consider what facts make it hard to believe that anything 
obeys all four conditions in at all a literal sense. 

The difficulty arises because of the group of facts 
which we sum up by saying that it is necessary to 
distinguish between things as they are and things as 
they seem to us, or between physical reality and sensible 
appearance. Difficulties always arise when two sets of 
properties apparently belong to the same object, and 
yet are apparently incompatible with each other. Now 
the difficulty here is to reconcile the supposed neutrality, 
persistence, and independence of a physical object with 

* See his Origin of Sin. 



MATTER AND ITS APPEARANCES 235 

the obvious differences between its various sensible 
appearances to different observers at the same moment, 
and to the same observer at different moments between 
which it is held not to have undergone any physical 
change. We know, e.g., that when we lay a penny 
down on a table and view it from different positions it 
generally looks more or less elliptical in shape. The 
eccentricity of these various appearances varies as we 
move about, and so does the direction of their major 
axes. Now we hold that the penny, at which we say 
that we were looking all the time, has not changed ; 
and that it is round, and not elliptical, in shape. This 
is, of course, only one example out of millions. It would 
be easy to offer much wilder ones ; but it is simple and 
obvious, and involves no complications about a trans- 
mitting medium ; so we will start with it as a typical 
case to discuss. 

Now there is nothing in the mere ellipticity or the 
mere variation, taken by itself, to worry us. The 
difficulty arises because of the incompatibility between 
the apparent shapes and the supposed real shape, and 
between the change in the appearances and the supposed 
constancy of the physical object. We need not at 
present ask why we believe that there is a single 
physical object with these characteristics, which appears 
to us in all these different ways. It is a fact that 
we do believe it. It is an equally certain fact that 
the penny does look different as we move about. 
The difficulty is to reconcile the different appearances 
with the supposed constancy of the penny, and the 
ellipticity of most of the appearances with the supposed 
roundness of the penny. It is probable that at first 
sight the reader will not see much difficulty in this. 
He will be inclined to say that we can explain these 
various visual appearances by the laws of perspective, 
and so on. This is not a relevant answer. It is quite 
true that we can predict what particular appearance an 
object will present to an observer, when we know the 



236 SCIENTIFIC THOUGHT 

shape of the object and its position with respect to 
the observer. But this is not the question that is 
troubling' us at present. Our question is as to the 
compatibility of these changing elliptical appearances, 
however they may be correlated with other facts in 
the world, with the supposed constancy and roundness 
of the physical object. 

Now what I call Sensible Appearance is just a general 
name for such facts as I have been describing. It is 
important, here as always, to state the facts in a form 
to which everyone will agree, before attempting any 
particular analysis of them, with which it is certain 
that many people will violently disagree. The funda- 
mental fact is that we constantly make such judgments 
as: " This seems to me elliptical, or red, or hot," as the 
case may be, and that about the truth of these judgments 
we do not feel the least doubt. We may, however, at 
the same time doubt or positively disbelieve that this 
is elliptical, or red, or hot. I may be perfectly certain 
at one and the same time that I have the peculiar 
experience expressed by the judgment: "This looks 
elliptical to me," and that in fact the object is not 
elliptical but is round. 

I do not suppose that anyone, on reflection, will 
quarrel with this statement of fact. The next question 
is as to the right way to analyse such facts ; and it is 
most important not to confuse the facts themselves 
with any particular theory as to how they ought to 
be analysed. We may start with a negative remark, 
which seems to me to be true, and is certainly of the 
utmost importance if it be true. Appearance is not 
merely mistaken judgment about physical objects. When 
I judge that a penny looks elliptical I am not mistakenly 
ascribing elliptical shape to what is in fact round. 
Sensible appearances may lead me to make a mistaken 
judgment about physical objects, but they need not, and, 
so far as we know, commonly do not. My certainty 
that the penny looks elliptical exists comfortably along- 



MATTER AND ITS APPEARANCES 237 

side of my conviction that it is round. But a mistaken 
judgment that the penny is elliptical would not continue 
to exist after I knew that the penny was really round. 
The plain fact is then that "looking elliptical to me" 
stands for a peculiar expedience, which, whatever the -* 
right analysis of it may be, is not just a mistaken 
judgment about the shape of the penny. 

Appearance then cannot be described as mistaken 
judgment about the properties of some physical object. 
How are we to describe it, and can we analyse it? Two 
different types of theory seem to be possible, which I 
will call respectively the Multiple Relation Theory, and 
the Object Theory of sensible appearance. The Multiple 
Relation Theory takes the view that " appearing to be 
so and so" is a unique kind of relation between an 
object, a mind, and a characteristic. (This is a rough 
statement, but it will suffice for the present.) On this 
type of theory to say that the penny looks elliptical to 
me is to say that a unique and not further analysable 
relation of "appearing" holds between the penny, my 
mind, and the general characteristic of ellipticity. The 
essential point for us to notice at present about theories 
of this kind is that they do not imply that we are aware 
of anything that really is elliptical when we have the 
experience which we express by saying that the penny 
looks elliptical to us. Theories of this type have been 
suggested lately by Professor Dawes Hicks and by 
Dr G. E. Moore. So far, they have not been worked 
out in any great detail, but they undoubtedly deserve 
careful attention. 

Theories of the Object type are quite different. 
They do not involve a unique and unanalysable 
multiple relation of " appean;/^"," but a peculiar kind 
of object — an "appear«/z^." Such objects, it is held, 
actually do have the characteristics which the physical 
object seems to have. Thus the Object Theory analyses 
the statement that the penny looks to me elliptical into 
a statement which involves the actual existence of an 



238 SCIENTIFIC THOUGHT 

elliptical object, which stands in a certain cognitive 
relation to me on the one hand, and in another relation, 
yet to be determined, to the round penny. This type 
of theory, though it has been much mixed up with 
irrelevant matter, and has never been clearly stated and 
worked out till our own day, is of respectable antiquity. 
The doctrine of "representative ideas" is the tradi- 
tional and highly muddled form of it. It lies at the 
basis of such works as Russell's Lowell Lectures on the 
External World. In this book I shall deliberately con- 
fine myself to this type of theory, and shall try to state 
it clearly, and work it out in detail. 

The following" additional works may be consulted 
with advantage : 

G. E. Moork, Philosophical Studies, V. and VII. 
G. D. HlCKS, Proceedings of the Aristotelian Society, 1913, 1916. 
G. F. Stout, Manual of Psychology, Bk. III., Part II. Cap. I. 
,, „ Proceedings of the Aristotelian Society, 19 13. 



CHAPTER VIII 

" Jack. — That, my dear Algy, is the whole truth, pure and 
simple. 

" Algernon. — The truth is rarely pure and never simple. 
Modern life would be very tedious if it were either, and modern 
literature a complete impossibility." 

(Wilde, Importance of being Earnest.) 

The Theory of Sensa, and the Critical 
Scientific Theory 

I propose now to state more fully the theory that 
appearances are a peculiar kind of objects, and to con- 
sider what sort of objects they must be. The reader 
will bear in mind throughout the whole of the long 
story which follows that there is a totally different view 
of sensible appearance, viz., the Multiple Relation 
Theory, and that this may quite possibly be true. 
In this book I shall leave it wholly aside. On the 
theory that we are now going to discuss, whenever 
a penny looks to me elliptical, what really happens 
is that I am aware of an object which is, in fact 
elliptical. This object is connected in some specially 
intimate way with the round physical penny, and for 
this reason is called an appearance of the penny. It 
really is elliptical, and for this reason the penny is said 
to look elliptical. We may generalise this theory of 
sensible appearance as follows : Whenever I truly 
judge that x appears to me to have the sensible quality 
q, what happens is that I am directly aware of a certain 
object y, which (a) really does have the quality q, and 
(a) stands in some peculiarly intimate relation, yet to 
be determined, to x. (At the present stage, for all that 
we know, y might sometimes be identical with x, or 

239 



240 SCIENTIFIC THOUGHT 

might be literally a part of x.) Such objects as y I 
am going to call Sensa. Thus, when I look at a penny 
from the side, what happens, on the present theory, 
is at least this : I have a sensation, whose object is an 
elliptical, brown sensum ; and this sensum is related 
in some specially intimate way to a certain round 
physical object, viz., the penny. 

Now 1 think it must at least be admitted that the 
sensum theory is highly plausible. When I look at a 
penny from the side I am certainly aware of something ; 
and it is certainly plausible to hold that this something 
is elliptical in the same plain sense in which a suitably 
bent piece of wire, looked_at from straight above, is 
elliptical. If, in fact, nothing elliptical is before my 
mind, it is very hard to understand why the penny 
should seem elliptical rather than of any other shape. 
I do not now regard this argument as absolutely con- 
clusive, because I am inclined to think that the Multiple 
Relation theory can explain these facts also. But it is 
at least a good enough argument to make the sensum 
theory well worth further consideration. 

Assuming that when I look at a penny from the side I 
am directly aware of something which is in fact elliptical, 
it is clear that this something cannot be identified with 
the penny, if the latter really has the characteristics that 
it is commonly supposed to have. The penny is sup- 
posed to be round, whilst the sensum is elliptical. Again, 
the penny is supposed to keep the same shape and size 
as we move about, whilst the sensa alter in shape and 
size. Now one and the same thing cannot, at the same 
time and in the same sense, be round and elliptical. Nor 
can one and the same thing at once change its shape 
and keep its shape unaltered, if "shape" be used in the 
same sense in both statements. Thus it is certain that, 
if there be sensa, they cannot in general be identified 
with the physical objects of which they are the appear- 
ances, if these literally have the properties commonly 
assigned to them. On the other hand, all that I ever 



THEORY OF SENSA 241 

come to know about physical objects and their qualities 
seems to be based upon the qualities of the sensa that 
I become aware of in sense-perception. If the visual 
sensa were not elliptical and did not vary in certain 
ways as I move about, I should not judge that I was 
seeing a round penny. t 

The distinction between sensum and physical object 
can perhaps be made still clearer by taking some wilder 
examples. Consider, e.g., the case of looking at a stick 
which is half in water and half in air. We say that it 
looks bent. And we certainly do not mean by this that 
we mistakenly judge it to be bent; we generally make 
no such mistake. We are aware of an object which is 
very much like what we should be aware of if we were 
looking at a stick with a physical kink in it, immersed 
wholly in air. The most obvious analysis of the facts 
is that, when we judge that a straight stick looks bent, 
we are aware of an object which really is bent, and 
which is related in a peculiarly intimate way to the 
physically straight stick. The relation cannot be that 
of identity ; since the same thing cannot at once be bent 
and straight, in the same sense of these words. If there 
be nothing with a kink in it before our minds at the 
moment, why should we think then of kinks at all, as 
we do when we say that the stick looks bent? No doubt 
we can quite well mistakenly believe a property to be 
present which is really absent, when we are dealing 
with something that is only known to us indirectly, like 
Julius Cagsar or the North Pole. But in our example 
we are dealing with a concrete visible object, which is 
bodily present to our senses ; and it is very hard to 
understand how we could seem to ourselves to see the 
property of bentness exhibited in a concrete instance, 
if in fact nothing was present to our minds that possessed 
that property. 

As I want to make the grounds for the sensum theory 
as clear as possible, I will take one more example. 
Scientists often assert that physical objects are not 



242 SCIENTIFIC THOUGHT 

" reallv " red or hot. We are not at present concerned 
with the truth or falsehood of this strange opinion, but 
only with its application to our present problem. Let 
us suppose then, for the sake of argument, that it is 
true. When a scientist looks at a penny stamp or 
burns his mouth with a potato he has exactly the same 
sort of experience as men of baser clay, who know 
nothing of the scientific theories of light and heat. 
The visual experience seems to be adequately described 
by saying that each of them is aware of a red patch 
of approximately square shape. If such patches be 
not in fact red, and if people be not in fact aware of 
such patches, where could the notion of red or of any 
other colour have come from ? The scientific theory 
of colour would have nothing to explain, unless people 
really are aware of patches under various circumstances 
which really do have different colours. The scientists 
would be in the position of Mr Munro's duchess, who 
congratulated herself that unbelief had become impos- 
sible, as the Liberal Theologians had left us nothing 
to disbelieve in. Thus we seem forced to the view 
that there are at least hot and coloured sensa ; and, if 
we accept the scientific view that physical objects are 
neither hot nor coloured, it will follow that sensa cannot 
be identified with physical objects. 

The reader may be inclined to say, " After all, these 
sensa are not real ; they are mere appearances, so why 
trouble about them ? " The answer is that you do not 
get rid of anything by labelling it "appearance." 
Appearances are as real in their, own way as anything 
else. If an appearance were nothing at all, nothing 
would appear, and if nothing appeared, there would be 
nothing for scientific theories to account for. To put 
the matter in another way: Words like real and reality 
are ambiguous. A round penny and an elliptical visual 
sensum are not real in precisely the same sense. But 
both are real in the most general sense that a complete 
inventory of the universe must mention the one as 



THEORY OF SENSA 243 

much as the other. No doubt the kind of reality which 
is to be ascribed to appearances will vary with the 
particular type of theory as to the nature of sensible 
appearance that we adopt. On the present theory an 
appearance is a sensum, and a sensum is a particular 
existent, though it may be a short-lived one. On the 
Multiple Relation theory appearances have a very 
different type of reality. But all possible theories have 
to admit the reality, in some sense, of appearances ; and 
therefore it is no objection to any particular theory 
that it ascribes a sort of reality to appearances. 

I hope that I have now made fairly clear the grounds 
on which the sensum theory of sensible appearance 
has been put forward. Closely connected with it is a 
theory about the perception of physical objects, and 
we may sum up the whole view under discussion as 
follows : Under certain conditions I have states of 
mind called sensations. These sensations have objects, 
which are always concrete particular existents, like 
coloured or hot patches, noises, smells, etc. Such 
objects are called sensa. Sensa have properties, such 
as shape, size, hardness, colour, loudness, coldness, 
and so on. The existence of such sensa, and their 
presence to our minds in sensation, lead us to judge 
that a physical object exists and is present to our 
senses. To this physical object we ascribe various 
properties. These properties are not in general identical 
with those of the sensum which is before our minds 
at the moment. For instance, the elliptical sensum 
makes us believe in the existence of a round physical 
penny. Nevertheless, all the properties that we do 
ascribe to physical objects are based upon and correlated 
with the properties that actually characterise our sensa. 
The sensa that are connected with a physical object 
1 in a certain specially intimate way are called the 
appearances of that object to those observers who sense 
these sensa. The properties which x is said to appear 
to have are the properties which those sensa that are 



244 SCIENTIFIC THOUGHT 

.vs appearances really do have. Of course, the two 
properties may happen to be the same, e.g., when I look 
straight down on a penny, both the physical object and 
the visual appearance are round. Generally, however, 
there is only a correlation between the two. 

It follows from this theory that sensa cannot appear 
to have properties which they do not really have, though 
there is no reason why they should not have more 
properties than we do or can notice in them. This point 
perhaps needs a little more elaboration, since a good 
deal of nonsense has been talked by opponents of the 
sensum theory in this connexion. We must distinguish 
between failing to notice what is present in an object 
and " noticing " what is not present in an object. The 
former presents no special difficulty. There may well 
be in any object much which is too minute and obscure 
for us to recognise distinctly. Again, it is obvious 
that we may sense an object without necessarily being 
aware of all its relations even to another object that 
we sense at the same time. Still more certain is it 
that we may sense an object without being aware of 
all its relations to some other object which we are not 
sensing at the time. Consequently, there is no difficulty 
whatever in supposing that sensa may be much more 
differentiated than we think them to be, and that two 
sensa may really differ in quality when we think that 
they are exactly alike. Arguments such as Stumpfs 
render it practically certain that the latter possibility 
is in fact realised. 

The real difficulty is when we seem to be directly 
aware of some property in an object, and this property 
is not really present and is perhaps incompatible with 
others which are present. This is the kind of difficulty 
that the sensum theory is put forward to meet. We 
seem to recognise elliptical shape in the penny, when 
the penny really has the incompatible quality of round- 
ness. The solution which the sensum theory offers is to 
" change the subject." Something, it admits, is elliptical, 



THEORY OF SENSA 245 

and something is round ; but they are not the same 
something. What is round is the penny, what is ellip- 
tical is the sensum. Now clearly, this would be no 
solution, if the same sort of difficulty were to break 
out in sensa themselves. In that case we should need 
to postulate appearances of appearances, and so on 
indefinitely. 

We must hold, as regards positive sensible qualities 
which characterise a sensum as a whole and do not 
involve relations to other sensa, that a sensum is at 
least all that it appears to be. Now, so far as I know, 
there is no evidence to the contrary. Some people have 
thought that arguments like Stumpf's raised this diffi- 
culty ; but that is simply a mistake. Stumpf's argu- 
ment deals merely with the relation of qualitative 
likeness and difference between different sensa, and 
shows that we may think that two of them are exactly 
alike when there is really a slight qualitative or quanti- 
tative difference between them. This has no tendency to 
prove that we ever find a positive non-relational quality 
in a sensum, which is not really there. 

Next, we must remember that attributes which in- 
volve a negative factor often have positive names. A 
man might quite well think, on inspecting one of his 
sensa, that it was exactly round and uniformly red. 
And he might well be mistaken. But then, "exactly 
round" means "with no variation of curvature," and 
"uniformly red" means "with no variation of shade 
from one part to another." Now universal negative 
judgments like these can never be guaranteed by mere- 
inspection ; and so, in such cases, the man is not "see- 
ing properties that are not there " in the sense in which 
he would be doing so if a round sensum appeared to 
him to be elliptical. To sum up, it is no objection to 
the sensum theory that a sensum may seem to be less 
differentiated than it is ; it would be a fatal objection 
if a sensum ever seemed more differentiated than it is ; 
but we have no evidence that the latter ever happens. 



246 SCIENTIFIC THOUGHT 

Before going further we must remove a baseless 
prejudice which is sometimes felt against the sensum 
theory. It is often objected that we are not aware of 
sensa and their properties, as a rule, unless we specially 
look for them. It is a fact that it often needs a good 
deal of persuasion to make a man believe that, when 
he looks at a penny from the side, it seems elliptical 
to him. And I am afraid that very often, when he is 
persuaded, it is not by his own direct inspection (which 
is the only relevant evidence in such a matter), but by 
some absurd and irrelevant argument that the area of 
his retina affected by the light from the penny, is an 
oblique projection of a circle, and is therefore an ellipse. 
Accordingly, it is argued that we have no right to 
believe that such a man is directly sensing an object 
which is, in fact, elliptical. To this objection a partial 
answer has already been given, by implication. It is 
only when we are looking at a penny almost normally 
that any doubt is felt of the ellipticity of the sensum ; 
and, in that case, the sensum is, in fact, very nearly 
round. Now we have seen that it is no objection to 
our theory that a sensum which is not quite round 
should be thought to be exactly round, though it would 
be an objection if an exactly round sensum seemed to 
be elliptical. The reason, of course, is that an ellipse, 
with its variable curvature, is a more differentiated figure 
than a circle, with its uniform curvature. There is no 
difficulty in the fact that we overlook minute differentia- 
tions that are really present in our sensa ; difficulties 
would only arise if we seemed to notice distinctions that 
are not really present. 

Apart, however, from this special answer, a more 
general reply can be made to the type of objection under 
discussion. The whole argument rests on a misunder- 
standing of the view about perception which the sensum 
theory holds. If the theory were that, in perceiving a 
penny, a man first becomes aware of a sensum, then 
notices that it is elliptical, and then infers from this 



THEORY OF SENSA 247 

fact and the laws of perspective that he is looking at 
a round physical object, the argument would be fatal 
to the theory. But this is quite obviously not what 
happens. Perceptual judgments are indeed based upon 
sensa and their properties to this extent, that if we were 
not aware of a sensum we should not now judge that 
any physical object is present to our senses, and that 
if this sensum had different properties we should ascribe 
different properties to the physical object. But the 
relation between the sensum and its properties, on the 
one hand, and the perceptual judgment about the physical 
object, on the other, is not that of inference. The best 
analogy that we can offer to the relation between our 
sensing of a sensum and our perceiving a physical 
object, is to be found in the case of reading a book in 
a familiar language. What interests us as a rule is the 
meaning of the printed words, and not the peculiarities 
of the print. We do not explicitly notice the latter, 
unless there be something markedly wrong with it, 
such as a letter upside down. Nevertheless, if there 
were no print we should cognise no meaning, and if the 
print were different in certain specific ways we should 
cognise a different meaning. We can attend to the 
print itself if we choose, as in proof-reading. In exactly 
the same way, we are not as a rule interested in sensa, 
as such, but only in what we think they can tell us 
about physical objects, which alone can help or hurt 
us. Sensa themselves "cut no ice." We therefore 
pass automatically from the sensum and its properties 
to judgments about the physical object and its properties. 
If it should happen that the sensum is queer, as when 
we see double, we notice the sensum, as we notice an 
inverted letter. And, even in normal cases, we generally 
can detect the properties of sensa, and contrast them 
with those which they are leading us to ascribe to the 
physical object, provided that we make a special effort 
of attention. 

From what has just been said, it will not appear 



248 SCIENTIFIC THOUGHT 

strange that, even though there be sensa, they should 
have been overlooked by most plain men and by many 
philosophers. Of course, everyone is constantly sensing 
them, and, in specially abnormal cases, has noted the 
difference between them and physical objects. But 
sensa have never been objects of special interest, and 
therefore have never been given a name in common 
speech. A result of this is that all words like "seeing," 
" hearing," etc., are ambiguous. They stand sometimes 
for acts of sensing, whose objects are of course sensa, 
and sometimes for acts of perceiving, whose objects are 
supposed to be bits of matter and their sensible qualities. 
This is especially clear about hearing. We talk of 
"hearing a noise" and of "hearing a bell." In the 
first case we mean that we are sensing an auditory 
sensum, with certain attributes of pitch, loudness, 
quality, etc. In the second case we mean that, in 
consequence of sensing such a sensum, we judge that 
a certain physical object exists and is present to our 
senses. Here the word "hearing" stands for an act 
of perceiving. Exactly the same remarks apply to 
sight. In one sense we see a penny ; in a somewhat 
stricter sense we see only one side of the penny ; in 
another sense we see only a brown elliptical sensum. 
The first two uses refer to acts of perceiving, the last 
to an act of sensing. It is best on the whole to confine 
words like "seeing" and "hearing" to acts of per- 
ceiving. This is, of course, their ordinary use. I shall 
therefore talk of seeing a penny, but not of seeing a 
brown elliptical sensum. I shall speak of the latter 
kind of cognition as "visually sensing," or merely as 
"sensing," when no misunderstanding is to be feared 
by dropping the adjective. This distinction will be 
found important when we come to deal with illusory 
perceptions. 

I have now tried to clear up certain ambiguities in 
the sensum theory, and to remove certain mistaken 
objections which many folk feel against it. If it be 



THEORY OF SENSA 249 

admitted that there may be such things as sensa, and 
that the sensum theory at least provides a possible and 
even plausible way of analysing sensible appearance, 
we can pass to the question of the nature of sensa and 
their status in the universe. This splits into two 
questions, viz., (i) the relation of sensa to minds ; and 
(ii) their relation to physical objects. Neither of these 
can be completely answered at the present stage, but 
we can say a good deal here that is relevant, and will be 
useful, about them. 

(i) Are Sensa in any way Mental ? — Sensa have been 
supposed by many philosophers to be in some way 
mental. This opinion is based partly on sheer verbal 
confusions, and partly on genuine facts. The verbal 
confusion is that the word "sensation" has often been 
used ambiguously, and that, in one of its meanings, it 
does undoubtedly stand for something that is mental. 
When a man talks of a "sensation of red," he is some- 
times referring to a red patch which he senses, some- 
times to his act of sensing the patch, and sometimes to 
the whole complex state of affairs which, on the sensum 
theory, is analysable into (act of sensing) — directed on 
to — (red patch). In the second meaning, "sensation" 
is obviously mental ; in the third it is undoubtedly a 
complex whole which involves a mental factor. In the 
first meaning it is by no means obvious or even plausible 
to say that a sensation is mental. I shall always use 
"sensation" in the third meaning. Now, as the same 
name is thus often used, both for the patch and for 
something which undoubtedly is mental, or is a complex, 
involving a mental factor, it is not surprising that some 
people should have been inclined to think that the red 
patch is itself mental. For is it not a "sensation"? 
And is not a sensation a mental state? This is, of 
course, mere verbal confusion, and need not trouble 
us further. But philosophers who have not fallen into 
this confusion between sensum, sensation, and act of 

R 



250 SCIENTIFIC THOUGHT 

sensing, have yet held that sensa are mental. The most 
important living holder of this view is Professor Stout 
(at any rate he held it at the time when he wrote the 
last edition of his Manual of Psychology. 

Before we can profitably carry the discussion of this 
point further, we must clear up the various meanings 
which can be attached to the statement " x is mental." 
(i) The first distinction that we must draw is between 
being " a state of mind " and being " mind-dependent." 
It is commonly held (and I do not here propose to 
question it) that whatever is a state of mind is mind- 
dependent, i.e., that it could not exist except as a con- 
stituent of a mind, and, in fact, that it could only exist 
as a constituent of that particular mind, whose state it 
is said to be. An example would be my belief that 
2 + 2 = 4 or mv desire for my tea. But it seems perfectly 
possible that a term might be mind-dependent without 
being a state of anyone's mind. What would this 
mean? I think it would mean that such a term can 
only exist as a constituent of a state of mind, but that 
it is not itself a constituent of a mind. Take some 
admitted state of mind, such as my perception of my 
table. There is clearly an important sense which we 
can all recognise, even though none of us can define it, 
in which it is true to say that this perception is a 
constituent of my mind, whilst the table is not. I 
should say that there was also an important (though 
<very different) sense in which it is true to say that the 
table is a constituent of my perception of it, so long as 
that perception lasts. It is thus quite common for a 
term to be a constituent of one of my states of mind 
without being a constituent (and therefore without being 
a state) of my mind. Now, if chairs are anything like 
what they are commonly supposed to be, they do not 
only exist as constituents of states of mind, since it is 
commonly believed that such things go on existing 
with little or no change of quality when we cease to 
perceive them. But, just as states of mind can only 



THEORY OF SENSA 251 

exist as constituents of minds, so there might be terms 
which can only exist as constituents of states of mind. 
Such terms would be mind-dependent without being 
states of mind. If Berkeley's famous saying that "the 
essence of a sensible object is to be perceived " be taken 
quite literally, it implies that such objects are mind- 
dependent, whilst it does not imply (though it is, of 
course, consistent with) the view that they are states 
of mind. 

(2) Even when this distinction has been drawn, there 
is a possibility of confusion. We must distinguish a 
more and a less radical sense of "mind-dependence." 
The sense just discussed is the more radical, and may 
be termed "existential mind-dependence." A term that 
is existentially mind-dependent, though not a state of 
mind, can only exist as a constituent of a certain state 
of mind. But a term which was not existentially mind- 
dependent, might be to a certain extent "qualitatively 
mind-dependent." By this I mean that, although it 
can exist and have qualities when it is not a constituent 
of any state of mind, it might acquire some new qualities 
or alter some of its old qualities on becoming a con- 
stituent of a state of mind. It is certain that everything 
that at some period in its history becomes a constituent 
of any state of mind thereby acquires at least one new 
quality, viz., that it is now cognised, or desired, or 
shunned, or so on, by that mind. And I do not see 
any reason in principle why these changes of relation 
should not produce changes in the non-relational 
qualities of the object. If wax melts when brought 
into the relation of proximity to a fire, I know no reason 
why some qualities of an object should not be added 
or modified when it comes into the relation of being 
sensed by a mind. 

(3) Some psychologists, of whom Stout is one, draw 
a fundamental distinction between two sorts of states of 
mind. They divide them into acts and non-acts. And a 
state of mind which is not an act they call a presentation. 



252 SCIENTIFIC THOUGHT 

1 propose to state this distinction in a different way, 
for reasons which I will now explain. A little while 
ago I took my perception of my table as an undoubted 
example of a state of mind. And I said that there was 
no doubt that the table is a constituent of it. That is, 
I took the whole complex situation (my perceiving) — of 
—(table) as a state of mind. What Stout calls an 
"act" is " my perceiving." He calls this a "state of 
mind," 1 call it a "constituent of a state of mind." 
The table is not a constituent of the state of mind, in 
Stout's sense of the word, whilst it is a constituent 
of the state of mind, in my sense of the word. In 
my terminology the act may be described as the non- 
objective constituent in a state of mind whose other 
constituent is its object. An act is something which 
cannot exist by itself, but can only exist as a constituent 
in a complex, whose other constituent is its object. 
And it is, of course, the characteristically mental factor 
in such a complex, since the other constituent may 
(though it need not) be non-mental. My reason for 
calling the whole complex fact, and not the act itself, 
a state of mind, is the following : Practically everyone 
agrees that there are such things as states of mind. 
And practically everyone agrees that the phrase "my 
perception of the table " describes something real. 
But people differ greatly as to the right analysis of 
this fact, and the notion of "act" is connected with 
one special mode of analysis which would not be 
accepted by everyone. It therefore seems better to give 
the name "state of mind" to the fact which everyone 
admits to exist, and not to a supposed constituent, 
which some people deny to be present in it. 

It is quite easy to restate the distinction which Stout 
has in mind in terms of my phraseology. Some mental 
states can be analysed into an act directed on an object. 
These are non-presentational states of mind. Others 
cannot be analysed into act and object. These are pre- 
sentations. A non-presentational state may contain a 



THEORY OF SENSA 253 

presentation as object. For instance, a feeling of tooth- 
ache would be a presentation on Stout's view. For, 
according to him, it is mental and is not analysable into 
an act of sensing and a " toothachy " object ; it is just 
a "toothachy" state of mind. Now, if I were to intro- 
spect my toothache, in order to describe it to my 
dentist, my introspection would be a non-presentational 
mental state whose object is a presentation ; for it is a 
complex containing an act of introspecting directed on 
to a toothachy feeling. The perception of a chair would 
be an example of a non-presentational mental state, 
whose object is not a presentation, because not mental. 

We are now in a better position to deal with the 
question: " Are sensa mental? " This might mean (1) 
Are they acts? (2) Are they states of mind analysable 
into act and object? (3) Are they presentations? (4) Are 
they existentially mind-dependent, though not states of 
mind? (5) Are they to some extent qualitatively mind- 
dependent, though not existentially mind-dependent? 

No one has ever suggested that sensa are acts or 
that they are states of mind analysable into act and 
object. A red patch sensed by me when I look at a 
pillar-box is an example of a sensum. It is plausible 
to hold that the whole fact known as " mv sensation of 
the red patch " is a state of mind, analysable into act of 
sensing and red patch sensed. But there would be no 
plausibility in holding that the red patch itself was an 
act, or that it was itself divisible into act and object. 
Thus, if sensa be states of mind at all, they must be 
presentations. Now, there are two very different views 
included under the statement that sensa are presenta- 
tions. The first would deny the analysis of " my 
sensation of red patch " into act of sensing and red 
sensum. It would treat the whole thing- as an un- 
analysable state of mind, and therefore as a presentation. 
This view would hold that there is no real distinction 
between sensa and sensations. It would say that 
"sensation of red patch " = " red patch sensed," and 



254 SCIENTIFIC THOUGHT 

is a presentation.* The second view would admit that 
in mv sensation of red we can distinguish my act of 
sensing and the red patch sensed ; but it would hold 
that the red patch is itself a state of mind, and, being 
indivisible into act and object, .is a presentation. I do 
not think that most philosophers have very clearly 
distinguished these two varieties of the presentational 
theory of sensa. Moreover, those philosophers who 
have accepted the analysis of sensations into acts of 
sensing and sensa, and have asserted that sensa are 
mental, have seldom clearly distinguished the alterna- 
tives that sensa are presentations and that sensa are 
mind-dependent without being states of mind. And 
lastly, the distinction between existential and qualitative 
mind-dependence has not always been clearly seen. So ,\ 
that there is a very pretty mess for us to wipe up as 
well as we can. • 

(i) Are Sensations analy sable into Act of Sensing and 
Sensum ? The most plausible argument against this 
analysis would seem 'to be the following: If we 
consider the various experiences called "sensations," 
we seem to be able to arrange them in an order, 
starting with those of sight, passing through those of 
taste and smell, and ending with bodily sensations, like 
headache. Now, as regards the top members of the 
series, the analysis into act of sensing and object sensed 
seems pretty clear. A sensation of red seems clearly to 
mean a state of mind with a red object, and not to mean 
a red state of mind. 

If we now pass to the other end of the series the 
opposite seems to be true. It is by no means obvious 
that a sensation of headache involves an act of sensing 
and a "headachy" object; on the contrary, it seems 
on the whole more plausible to describe the whole 
experience as a "headachy" state of mind. In fact 
the distinction of act and object seems here to have 

* This seems to be Stout's view in the Manual of Psychology, but I may 
be misinterpreting him. 



THEORY OF SENSA 255 

vanished ; and, as there is clearly something mental in 
feeling a headache, just as there is in sensing" a red 
patch, it seems plausible to hold that a sensation of 
headache is an unanalysable mental fact, within which 
no distinction of act and object can be found. 

Now this contrast between the top and the bottom 
members of the series would not greatly matter, were 
it not for the fact that the two kinds of sensation seem 
to melt insensibly into each other at the middle of the 
series. It is about equally plausible to analyse a 
sensation of a sweet taste into an act of sensing and a 
sweet sensum, or to treat it as an unanalysable mental 
fact, having no object, but possessing the property of 
sweetness. Common speech recognises these distinc- 
tions. We talk of a sensation of red, but never of a 
feeling of red or of a red feeling. On the other hand, 
we talk indifferently of a sensation'of headache, a feeling 
of headache, a headachy sensation, and a headachy 
feeling. The English talk of a sensation of smell, 
whereas the Scots more usually speak of "feeling" a 
smell. Now sensations of smell are just on the border- 
line between the two kinds of sensation. The rule is 
that, when a sensuous experience seems clearly to 
involve act and object, it is called a sensation and never 
a feeling ; when it is doubtful whether any such analysis 
can be applied, it is called indifferently a feeling or a 
sensation. 

Now the fact that all these experiences are classed 
together as sensations, and that the two kinds melt into 
each other at the middle of the series, naturally tempts 
men to treat them all alike. If we do this, we must 
hold either (a) that it is a mistake to think that a 
sensation of red can be analysed into an act of sensing 
and a red sensum ; or (f3) that it is a mistake to think 
that a sensation of headache cannot be analysed into an 
act of sensing and a headachy sensum. The former 
alternative makes sensation and sensum fall together 
into a single peculiar state, even in the case of sight ; 



256 SCIENTIFIC THOUGHT 

and, since the experience as a whole certainly is mental, 
we have to say that a sensation of red = a red sensum = 
a feeling or presentation which is red. The second 
alternative is that which is taken by Realists, like 
Professors Laird and Alexander. 

Now it is evident that, if you insist on treating all 
experiences which are called "sensations" in the same 
way, it is antecedently as reasonable to take the Laird- 
Alexander alternative as the Presentationist alternative. 
You might argue : " It is obvious that a sensation of 
red involves an act of sensing and a red sensum, so a 
sensation of headache must involve an act of sensing 
and a headachy sensum." Thus the mere fact that 
sensations can be arranged in a series, such as I have 
described, does not specially favour the presentationist 
view ; since exactly the same type of argument, starting 
from the other end of the series, would lead to exactly 
the opposite conclusion. There are just two remarks that 
seem to me worth making at this point. 

(a) I do not find either the realist or the presentationist 
view very satisfactory as a complete account of all the 
experiences which are called "sensations." But, if I 
were forced to take one alternative or the other, I should 
prefer the former. It seems to me much more certain 
that, in a sensation of red, I can distinguish the red 
patch and the act of sensing it, than that, in a sensation 
of headache, I cannot distinguish a headachy object and 
an act of sensing it. {b) I think, however, that there is 
no need to insist on the realist analysis of bodily feelings 
in order to deal with the question whether sensations 
be analysable into act of sensing and sensum. It seems 
to me that the simplest and least doubtful way of treating 
the whole question raised by the series of sensations is 
the following: The word "sensation," as commonly 
used, is defined, not by direct inspection, but by causa- 
tion. We say that we are having a sensation, if our 
state of mind is the immediate response to the stimula- 
tion of a nerve. Now, since sensations are not defined 



THEORY OF SENSA 257 

psychologically through their intrinsic properties, but 
physiologically through their bodily antecedents, it is 
surely very likely that they may include two very 
different kinds of experience, one of which can and the 
other cannot be analysed into act of sensing and sensum. 
These might be called respectively "true sensations" 
and "bodily feelings." The mere fact that both are 
often called "sensations" is surely a very poor reason 
for insisting that thes tructure o f both must be the same.^j, 
It is true indeed that there are marginal cases of which 
it is very difficult to say into which class they fall. But 
this ought not to make us slur over the plain intro- 
spective difference between the top and the bottom 
members of the series. The top ones at least do seem 
quite clearly to involve acts of sensing and sensa on 
which these acts are directed. It does seem clear that, 
when I have a sensation of a red triangular patch, some 
things are true of the patch itself {e.g., that it is red and 
triangular) which it is very difficult to believe to be true 
of my sensation of the red patch. If so, it seems neces- 
sary to hold that the sensation and the sensum are not 
identical ; that the sensum is an objective constituent 
of the sensation ; and that there is another constituent 
which is not objective and may be called "the act of 
sensing." Into the question whether this latter factor 
is capable of further analysis, and, if so, what the right 
analysis of it may be, it is fortunately not necessary to 
go for our present purposes. 

I conclude, then, that some sensations at least are 
analysable into act of sensing and sensum, and there- 
fore that we cannot argue that sensum = sensation = 
a presentation. 

(2) Are Sensa, though distinct from Sensations, them- 
selves Presentations ? Though sensations are not pre- 
sentations but contain objects, which are sensa, it is 
perfectly possible that these objects might themselves 
be presentations. To prove that sensa are presentations, 
it would be necessary to prove that they are states of 



258 SCIENTIFIC THOUGHT 

mind. And this involves proving (a) that they are 
existentially mind-dependent, and (/>) that they are 
constituents of minds and not merely of certain states 
of mind. Obviously it might be possible to prove the 
first, even if it were not possible to prove the second, of 
these propositions. I do not know of any reasonably 
plausible argument to prove that sensa are not merely 
mind-dependent, but are also states of mind, once you 
accept the view that sensa must be distinguished from 
sensations. Indeed, the assertion would be open to 
the same kind of objection which we made to the view 
that sensa and sensations can be identified. On either 
view something is said to be a state of mind, though it 
possesses properties which it is very difficult to ascribe 
to states of mind. If a sensum be a state of mind, then 
there are states of mind which are literally red or round 
or hot or loud or triangular, and so on. I have no 
difficulty in believing that many states of mind contain 
such terms as objects, but I do find it very difficult to 
believe that any state of mind actually is a term of this 
sort. Yet the latter is implied by the statement that 
sensa are presentations, just as much as by the state- 
ment that sensations are presentations. In fact, the 
reasons which forced us to distinguish sensations from 
sensa, and to regard the latter as objects contained in 
the former, equally forbid us to treat sensa themselves 
as states of mind. This objection may, of course, be a 
mere prejudice ; but it is worth while to point out that 
the view that sensa are presentations does logically 
imply the very paradoxical propositions that some states 
of mind are literally hot or red or round, for most 
philosophers who have held the view under discussion 
have successfully concealed this consequence from them- 
selves and their readers. I shall therefore reject the 
view that sensa are states of mind, until someone pro- 
duces much better reasons than anyone has yet done 
for believing such an extremely par^oxical proposition. 
There are, however, quite plausible arguments to 



THEORY OF SENSA 259 

prove that sensa are existentially mind-dependent, though 
not states of mind. That is to say, that, although sensa- 
tions are analysable into act and sensum, and the sensum 
must therefore be distinguished both from the sensation 
and from the act of sensing, which is the other factor in 
the sensation, yet these two factors are not capable of 
existing separately from each other. No act of sensing 
without some sensum on which it is directed, and no 
sensum without an act of sensing directed upon it. The 
arguments for this view are three : (a) The privacy and 
variability of sensa ; {b) the analogy between sensa and 
bodily feelings ; and (c) the analogy between sensa and 
so-called "mental images." 

(a) We notice at once that sensa have some of the 
characteristics of physical objects and some of those of 
mental states. On the one hand, they are extended, and 
have shapes, sizes, colours, temperatures, etc. On the 
other hand, they do seem to be private to each observer ; 
and this, it will be remembered, is one of the chief marks 
of the mental as distinct from the physical. It is at 
least doubtful whether two people, who say that they are 
perceiving the same object, are ever sensing the same 
sensum or even two precisely similar sensa. This does 
suggest that sensa are mental — at any rate in the sense 
of being mind-dependent. 

If, however, we look more closely, we see that this 
conclusion does not necessarily follow. The facts are 
on the whole much better explained by supposing that 
the sensa which a man senses are partly dependent on 
the position, internal states, and structure of his body. 
Since no two men's bodies can be in precisely the same 
place at precisely the same time, it is not surprising that 
the sensa of the two men should differ. And, since the 
internal states and the minute structure of no two living 
bodies are exactly alike, it is still less surprising. Now 
this explanation not only accounts as well for most of 
the facts as the view that sensa are mind-dependent ; it 
accounts a great deal better for some of the most striking 



260 SCIENTIFIC THOUGHT 

of the facts. The orderly variation in the shapes of 
visual sensa, as we move about, is intelligible if we 
suppose that the sensa which we sense are partly con- 
ditioned by the positions of our bodies. The assumption 
that they depend on our minds gives no explanation 
whatever of such facts. 

There is, however, a better form of this argument, 
which has, I think, been somewhat neglected by people 
who want to hold that sensa are never mind-dependent 
to any degree. It does seem to me undeniable that in 
certain cases, and to a certain extent, our past experi- 
ences and our present expectations affect the actual 
properties of the sensa that we sense, and do not merely 
affect the judgments about physical objects which we 
base upon sensa. We shall go into this point in some 
detail in a later chapter; at present I will just illustrate 
my meaning by two examples. 

When I look at the "staircase figure," which is 
given in most psychology text-books as an instance of 
ambiguous figures, it seems to me that it actually looks 
sensibly different from time to time. Its sensible 
appearance changes " with a click," as I look at it, from 
that of a staircase to that of an overhanging cornice. 
This change tends to take place as I concentrate my mind 
on the idea of the one or on that of the other. Now, 
on the present analysis of sensible appearance, such 
a change as this involves an actual qualitative change 
in the sensum. So far is it from being a mere change 
in the judgments which I happen to base on one and 
the same sensum, that the direction of my thoughts 
changes first and is the condition of the change in the 
sensible appearance. 

Again, when I turn my head, the visual sensa are not 
as a rule affected with any sensible movement. If, 
however, I put my glasses a little out of focus or look- 
through a window made of irregularly thick glass, 
and then turn my head, the sensa do sensibly move. 
Whether they move or keep still seems to depend on 



THEORY OF SENSA 261 

my past experiences and my present expectations about 
physical objects. The whole psychology of vision is 
full of such cases, some of them of a highly complex 
kind. 

Now, of course, these examples do not suggest for a 
moment that sensa are existentially mind - dependent, 
but they do strongly suggest that they are to some 
extent qualitatively mind-dependent. And it cannot be 
said here, as in the previous examples, that reference 
to the mind gives no help in explaining the facts. Here 
the boot is rather on the other foot. No doubt the facts 
just mentioned could in theory be accounted for by 
referring to the past history of the body, in addition 
to its present state and position. I.e., we could talk 
learnedly about the traces left on our brains and nervous 
systems by the past experiences, and could say that 
they are among the conditions of our sensa. But this 
would not help us to explain any concrete characteristic 
of our sensa in any particular case. For the plain fact 
is, that we do often know what relevant experiences we 
or others have had, whilst we know nothing whatever 
in detail about traces in the brain and nervous system. 
So here a reference to mental conditions really does 
explain concrete facts, whilst a reference to bodily con- 
ditions does not. We shall have to return to this point 
at a much later stage. 

(b) We have already noticed the arrangement of 
"sensations" in a scale from sensations of colour and 
sound to bodily feelings. We saw that this might be 
used as an argument to prove that even sensations of 
colour and sound are presentations, or equally as an 
argument to prove that even sensations of headache 
are divisible into act and object. Suppose we take the 
latter alternative, which, as I have .said, seems to me 
to be the more plausible of the two, though I do not 
think that the facts compel us to adopt either. It is 
then possible to produce a fairly plausible argument for 
the view that sensa are existentially mind-dependent. 



262 SCIENTIFIC THOUGHT 

The arerument would run as follows: "Granted that 
a sensation of headache can be analysed into act of 
sensing and headachy sensum, it is surely obvious that 
the latter, from its very nature, could not exist without 
the former. An unfelt headache is surely a mere Uniting. 
Now, if this be true of headachy sensa, does not the 
very continuity of the series of sensations on which you 
have been insisting make it likely to be true of red 
sensa, and indeed of all sensa? If so, sensa will be 
from their very nature existentially mind -dependent 
and incapable of existing save as objective constituents 
of sensations." 

1 think that this is quite a plausible argument, but 
I do not think it conclusive. Two questions could be 
asked about it. (a) Supposing it to be true that an 
unfelt headache is inconceivable, does the continuity of 
the series of experiences called " sensations," justify us 
in extending this conclusion to all sensa, and, in par- 
ticular, to those of sight and hearing? Secondly (/3), 
is it really true that an unfelt headache is inconceivable? 
(a) To the first question I answer that, as a matter of 
fact, I do not find the slightest intrinsic difficulty in 
conceiving the existence of unsensed red patches or 
unsensed noises, whilst I do find a considerable difficulty 
in conceiving the existence of unfelt headaches. I do 
not think that it is safe to reject this plain difference on 
the grounds of a mere argument from continuity. 

(/3) Moreover, I think I can see why it seems so 
difficult to conceive of the existence of unfelt headaches, 
and can see that this difficulty is not really conclusive. 
Our main interest in bodily feelings is that they are 
pleasant or painful ; sensations of sight are, as a rule, 
intrinsically neutral, or nearly so. Now I am quite 
prepared to believe that an object has to be cognised 
by us in order to be pleasant or painful to us. For it 
seems to me that the pleasantness or painfulness of 
anything is (or, at any rate, depends upon) my recog- 
nising it and taking up a certain attitude of liking or 



THEORY OF SENSA 263 

disliking to it. It might, therefore, be perfectly true 
that an unfelt headache would not be a pain, just as an 
unmarried woman is not a wife. Since we are mainly 
interested in headaches as pains, we are inclined to 
think that an unfelt headache would be nothing, when 
the truth merely is that it would not be a. pain. This 
would be comparable to the mistake which a fanatical 
admirer of matrimony would make if he ignored the 
existence of all spinsters because they were not wives. 
I, therefore, am not convinced that, if a feeling of head- 
ache be a genuine sensation and not a mere presentation, 
the headachy sensum which it contains could not exist 
unsensed. Still less could I extend this view to sight 
and sound sensa. 

(c) The third argument for thinking that sensa are 
incapable of existing unsensed is founded on their 
resemblance to "mental images," whose very name 
implies that they are commonly supposed to be existen- 
tially mind-dependent, if not actually states of mind. 
The resemblances must be admitted, though in favourable 
cases there seems to be some intrinsic difference which 
it is easy to recognise but hard to describe. But it 
seems to me doubtful whether images are existentially 
mind-dependent. I do not see any very obvious reason 
why there should not be " unimaged " images. It is, 
of course, perfectly true that images are to a much 
greater extent qualitatively mind-dependent than are 
sensa. Most, if not all, of them depend on our past 
experiences ; and many of them depend in part on our 
present volitions. Voluntary images do, no doubt, 
depend on our minds, in the sense that they would not 
be imaged here and now, if we did not will them. But 
exactly the same is true of many things, which no one 
would think of calling existentially mind-dependent. 
Most chemical reactions that take place in a laboratory 
would never have happened if someone had not deliber- 
ately mixed the reagents in a flask and heated the 
latter over a flame. No one supposes that this renders 



264 SCIENTIFIC THOUGHT 

such reactions in any important sense mind-dependent. 
Thus the fact that some images are voluntary seems 
irrelevant to the present subject. 

The other point, that all images that we can now 
image are in part determined in their characteristics by 
our past experiences, is more important. It must be 
counted along with the fact, already admitted, that many 
sensa are to some extent qualitatively mind-dependent. 
Here, as before, we can, if we like, substitute a reference 
to traces in our brains and nervous systems. But here, 
too, the doubt remains whether this kind of explanation 
is ultimately of much philosophic importance, in view 
of the fact that we often know directly what our relevant 
past experiences are, whilst the traces, etc., of the 
physiologist are purely hypothetical bodily correlates 
of these. Further treatment of this subject must be 
deferred till we face the problem of the part played 
by our own bodies in sensation and imagination. 

I will now try to sum up the results of this rather 
long and complex discussion on the relation of sensa 
to minds and their states. The sensum theory is 
bound up with a special view as to the right analysis 
of the kind of fact which is described by such phrases 
as u my sensation of .r." It holds that this is complex, 
and that within it there can be distinguished two factors 
— x itself, which is the sensum and is an object, and 
a subjective factor, which is called the "act of sensing." 
The latter may, of course, be capable of further analysis, 
such, e.g., as Russell attempts in his Analysis of Mind ; 
or it may be (or contain) a peculiar unanalysable 
relation. Now, there is also a theory which refuses to 
analyse "my sensation of x" in this way. It holds 
that the whole thing is unanalysable into act and object. 
On such a view the distinction between sensum and 
sensation vanishes ; and the experience, which may be 
called indifferently by either name, is a mental state of 
the kind called presentations. This view is supported 
by reference to bodily feelings, and by an argument 



THEORY OF SENSA 265 

from the continuity between them and the higher 
sensations. As against this we pointed out (a) that 
there is just as good reason to use the argument from 
continuity in the opposite direction ; and (b) that very 
possibly, in spite of the continuity, there is a real 
difference in nature between genuine sensations and 
bodily feelings. In favour of the view that genuine 
sensations are analysable into act and object, we pointed 
out that there seems to be a plain difference between a 
red patch sensed by me and the total fact described as 
" my sensation of a red patch." And we suggested that 
those who refuse to make this analysis are forced to 
the very paradoxical conclusion that there are states of 
mind which are literally red, round, hot, loud, etc. 

The next point was this. Assuming that sensations 
are analysable into act of sensing and sensum, we 
raised the question whether sensa are states of mind, 
or, if not, whether they are existentially mind-dependent. 
We agreed that, if they are states of mind at all, they 
must be presentations. But we found no positive reason 
for thinking that they are states of mind, and much the 
same reasons against that view as led us to hold that 
sensations are analysable into act and sensum. 

We then discussed three more or less plausible 
arguments to show that sensa are existentially mind- 
dependent, i.e., that they cannot exist except as objective 
constituents of sensations. We saw no intrinsic reason 
why coloured patches or noises should not be capable 
of existing unsensed. And we refused to be moved 
from this view by an argument from continuity with 
bodily feelings. For we were far from sure whether 
bodily feelings really are analysable into act of sensing 
and sensum ; and we suggested that, even if they be, 
it is by no means certain that their sensa could not 
exist unsensed. We tried to show why this was thought 
to be obvious, and to show that it is not really so. 

The two remaining arguments seemed to us to show 
that sensa are partly dependent on the position, etc., 

s 



266 SCIENTIFIC THOUGHT 

of the />0(/v, but they did not have any tendency to show 
that they are existentialist dependent on the wind. Still, 
some of the facts adduced did rather strongly suggest 
that sensa and, a fortiori, images, are to some extent 
qualitatively mind-dependent. We thought that this 
reference to the mind might be removed by extending 
the bodily conditions, so as to include physiological 
traces and dispositions. But, in view of the wholly 
hypothetical character of these, we were not prepared 
at this stage to deny that sensa and images might be 
to some extent qualitatively mind-dependent. And 
there we leave the matter, till we deal more fully with 
the part played by the human body in sense-perception. 
We have seen that the whole question is highly 
complex, and that the arguments for the view that sensa 
are mental are by no means lacking in plausibility. We 
shall not therefore be tempted to think that everyone 
who has been persuaded by them must be either a 
knave or a fool. Some of those who call themselves 
New Realists have been too much inclined to take this 
attitude ; and, on one reader at least, they have produced 
the impression of being rather offensively "at ease in 
Zion." 

(ii) How are Sensa related to Physical Objects ? — 
We can now turn to the second question which we 
raised about sensa. The plain man does not clearly 
distinguish between physical objects and sensa, and 
therefore feels no particular difficulty about their mutual 
relations. We first come to recognise sensa as distinct 
from physical objects by reflecting on the fact of 
sensible appearance, and the contrast between it and 
the supposed properties of physical reality. But once 
the existence of sensa has been clearly recognised, the 
problem of their relation to the physical world becomes 
pressing. We all believe in a world of physical objects, 
and profess to have a great deal of detailed knowledge 
about it. Now this world of physical objects makes 



THEORY OF SENSA 267 

its existence and its detailed nature known to us by 
the sensible appearances which it presents to us. And, 
on the sensum theory, these appearances are sensa. 
Sensa are therefore in some way the ratio cognoscendi 
of the physical world, whilst the physical world is in 
some way the ratio essendi of sensa. Our problem 
therefore divides into an epistemological and an onto- 
logical one. The two problems are not ultimately 
independent, but it is useful to state them separately. 

(1) How far is it true that our beliefs about the 
physical world depend on our sensa? Before we can 
answer this, we must draw some distinctions among 
our beliefs. First, there is our belief that there is a 
physical world of some kind. This, as we have seen, 
involves at least the belief that there are things which 
are relatively permanent, which combine many qualities, 
and which persist and interact at times when they are 
not appearing to our senses. These we may call 
constitutive properties of the physical world, since they 
are part of what we mean by "physical." Then there 
is the belief that these objects have spatial or quasi- 
spatial characteristics. This may almost be called 
constitutive, but it is a shade less fundamental than 
the first set of properties. Lastly, there are what might 
be called empirical beliefs about the physical world. 
These are beliefs about points of detail, e.g., that some 
things are red, and that there is now a red fluted lamp- 
shade in my rooms. 

Now I have already asserted that it is false psycho- 
logically to say that we, in fact, reach our perceptual 
judgments about the existence and properties of physical 
objects by a process of inference from our sensa and 
their properties. Further, it is false logically to suppose 
that the existence of a physical world in general could 
be inferred from the existence of our sensa, or from 
anything that we know about their intrinsic properties 
or their mutual relations. I suppose that the existence 
of sensa is a necessary condition, but it is certainly not 



4 

268 SCIENTIFIC THOUGHT 

a sufficient condition, of my belief in the existence of 
the physical world. If there were no sensible appear- 
ances to me, I suppose that I should not judge there to 
be any physical reality. But, on the other hand, there 
is nothing in my sensa to force me logically to the 
conclusion that there must be something beyond them, 
having the constitutive properties of physical objects. 
The belief that our sensa are appearances of something 
more permanent and complex than themselves seems 
to be primitive, and to arise inevitably in us with the 
sensing of the sensa. It is not reached by inference, 
and could not logically be justified by inference. On 
the other hand, there is no possibility of either refuting 
it logically, or of getting rid of it, or — so far as I can 
see — of co-ordinating the facts without it. 

There are groupings among my own sensa and 
correlations between my sensa and those of others 
which fit in extremely well with the belief in a physical 
world of which all the sensa are so many appearances. 
It might be held that this at least forms the basis of 
a logical argument in inverse probability, to show that 
the belief in the physical world is highly probable. 
But the snag here is that all such arguments only 
serve to multiply the antecedent probability of a pro- 
position, and, unless we have reason to suppose that 
this probability starts with a finite magnitude, they lead 
us nowhere. Now, although I do not know of any 
reason antecedently against the existence of a physical 
world, I also know of no antecedent reason for it. So 
its antecedent probability seems quite indeterminate, 
unless we are prepared to hold that the fact that 
everybody does in practice believe it, is a ground for 
ascribing a finite antecedent probability to it. It seems 
to me that the belief that there is a physical world is 
logically in much the same position as those assump- 
tions about the constitution of the existent on which all 
inductive proofs of special laws of nature rest. If these 
assumptions start with a finite antecedent probability, 



THEORY OF SENSA 269 

their success justifies us in ascribing a high final prob- 
ability to them. But do they have a finite antecedent 
probability? We can say of them, as of the belief in a 
physical world, that we all do believe them in practice, 
that there is no positive reason against them, and that 
we cannot get on without assuming them. But, having 
said so much, we shall do wisely to change the subject 
and talk about the weather. 

We shall not then attempt to prove the existence of 
a world of entities having the constitutive properties of 
physical objects ; for, if this can be done, I at any rate 
do not know how to do it. But we shall point out those 
facts about our sensa and their groupings which specially 
fit in with the view that sensa are various partial and 
fleeting appearances of relatively permanent and inde- 
pendent things. That is, we shall try to indicate those 
facts about our sensa which would give a high final 
probability to the belief in a physical world, provided it 
had a finite antecedent probability. This will be our 
main task in the next two chapters, which deal with 
the spatial and temporal characteristics of sensa and of 
physical objects and events. The first of these chapters 
will be concerned with the facts about our sensa which 
fit in with the view that they are appearances of objects 
which combine many properties, and which can be per- 
ceived by many different observers at the same time. 
The second will be concerned with the facts about our 
sensa which fit in with the view that they are relatively 
fleeting appearances of more permanent things and 
processes. 

Now, assuming that there is a world of enduring 
and independent things, there is still room for wide 
differences of opinion as to the kind of whole that it 
forms, the way in which it is divided into parts, and the 
various empirical qualities which these parts possess. 
Common-sense and science are agreed that it is in some 
sense a spatial whole, whose parts have various shapes, 
sizes and positions, and are capable of moving about 



270 SCIENTIFIC THOUGHT 

within the whole. This alleged spatial character of the 
physical world may be called "semi-constitutive"; for, 
as 1 have said, we hardly admit that a world of non- 
spatial entities would deserve to be called "physical," 
even though it were persistent, independent of us, and 
many-qualitied. Now, it is clear that all the spatial 
characteristics which we ascribe to the physical world 
are based, both in general outline and in detail, on the 
spatial characteristics of our sensa. Moreover, I think 
it can be rendered highly probable that, if there be a 
physical world at all, and our sensa be appearances of it, 
then that world is quasi-spatial. The importance and 
complexity of this subject seem to justify the length 
of the next chapter, in which I have treated it to the 
best of my ability. 

When we come to the purely empirical qualities of 
the physical world there is a sharp difference of opinion 
between science and common-sense. The latter ascribes 
qualities, like colour, temperature, etc., to physical 
objects, whilst the former refuses to do so. In dis- 
cussing this matter the partial dependence of sensa on 
what goes on inside the body of the observer becomes 
of great importance, and the concluding chapter has 
been devoted to this problem. 

(2) This last question leads in the most natural way 
to the ontological problem as to the status of sensa in 
the existent world. There is a world of physical objects 
and a world of sensa. In some way the latter seems to 
be dependent on the former. But both are parts of the 
whole of existent reality. How are the two related? 
This is a problem which common-sense ignores, because 
it does not definitely distinguish between sensa and 
physical objects. Science also ignores it, because, 
although in theory it makes an equivalent distinction, 
it uses it simply as an excuse for ignoring sensa and 
concentrating on physical objects and processes. This 
is a perfectly legitimate procedure for the special 
purpose which natural science has in view, but it is not 



THEORY OF SENSA 271 

permissible to the philosopher. His whole business is 
to drag such skeletons from the cupboards in which it 
has been found convenient to shelve them, and to give 
them their right place in the whole scheme of things. 

Now the epistemological and the ontological problems 
about sensa and their relations to physical objects are 
connected in the following way. Our primitive belief 
in the existence of a world of relatively permanent, 
independent things is extremely vague. It is little 
more than a general scheme, in terms of which the actual 
groupings which we find among our sensa are stated. 
Even when we go a step further, and say that the spatial 
character and the special groupings of sensa practically 
force us to think of the physical world as a quasi-spatial 
whole, containing parts with fairly definite shapes, sizes, 
and positions, we still have only a very general, though 
much more definite scheme. Within this general quasi- 
spatial scheme all kinds of alternative specifications are 
possible. We are not tied down to any special view 
as to the number of its dimensions. Again, we are not 
tied down to any special view as to the " geometry" of 
it, when the number of its dimensions is settled. Lastly, 
we might put forward dozens of different theories as to 
the nature of physical objects, all compatible with the 
general scheme and with the special facts about our 
sensa and their groupings. It is this extreme variety 
of alternative theories, left open to us by the general 
concept of a physical world and the special facts about 
our sensa, which gives a legitimate hope for indefinite 
progress with the problem under discussion, provided 
the scientists and the patriots between them do not 
destroy civilisation, and with it all disinterested thinking. 
With traditional views about the nature of Space, Time, 
and Matter, it is extremely difficult to fit the world of 
sensa and the world of physical objects together into 
a coherent whole. But, once the immense number of 
possible alternatives within the scheme is grasped, the 
devising of theories of the physical object which shall 



272 SCIENTIFIC THOUGHT 

give sensa a locus standi in the physical world will be a 
winter evening's pastime for symbolic logicians. This 
task we shall leave to those better fitted than ourselves 
to accomplish it ; we shall be concerned rather with 
those facts about our sensa with which any theory of 
physical objects must deal. 

The Critical Scientific Theory. — 1 propose now to 
try to state clearly, in terms of the Sensum theory, 
what appears to be involved in the common scientific 
view of physical objects and their sensible appearances. 
As scientists never state their own position on this 
point clearly, it is necessary for us to do so for them. 
We can then see how far the view can be accepted, 
and how far its plausibility has depended on its modest 
obscurity. 

Let us take the old example of a boy looking at a 
penny. He believes that it is quite literally round and 
just as literally brown. He believes that the brown 
(and, as he thinks, round) patch which he is sensing 
is quite literally a part (viz., the upper side) of the 
penny. And he believes that this, which he now sees, 
is the same as what he can feel if he puts out his 
hand. As he grows up he is probably told, on the 
authority of "science," that the penny is not "really" 
brown, though it is "really" round. The sort of 
reason which he is given for this startling statement 
is (so far as I can remember) that things appear to 
have different colours in different lights. If he should 
study heat and light, he will be told that the colour 
which he sees depends on vibrations which strike his 
eye, and that the temperature that he feels depends on 
molecular movements which are going on in the penny. 
He still thinks of the penny as literally round, and 
thinks now of all sorts of movements going on within 
its contour, and sending disturbances to his eye and 
his hand. But he no longer thinks of the penny as 
literally brown or cold. The brownness and coldness 



THEORY OF SENSA 273 

are thought to be effects which the processes in the 
penny produce by transmission. The round shape is 
"in" the penny; the brownness and coldness are not. 
They are effects which the penny produces "in" his 
eye or his hand or his brain or his mind. He still 
thinks that he literally senses the same round upper 
side of the penny, both with his eyes and with his 
hand, but he no longer thinks that there is a brown 
colour or a cold temperature literally spread over this 
round surface. 

This, I think, is a fair account of what the average 
person with a scientific training believes on these 
matters ; so far as anything so incoherent can be said 
to be believed by anyone. It is perfectly obvious 
that such a view as this cannot stand criticism. It is 
an inconsistent mixture of two utterly different theories 
of perception. As regards spatial attributes, it keeps 
to the naively realistic view of unsophisticated common- 
sense. According to it, the seen and felt shape is not 
an effect produced in us by something else. It is out 
there, whether we see it or feel it or not. Processes in 
it simply make us see it or feel it under suitable cir- 
cumstances. But, as regards colour and temperature, 
the scientific theory takes quite a different view. It is 
a causal theory. The processes in the penny do not 
make us see a colour or feel a temperature which is 
already there to be seen or felt. They produce the 
colour or temperature " in us," to use a discretely 
vague phrase, which may cover our minds, our brains, 
and our special sense-organs. 

Now this muddled mixture of theories is not con- 
sistent with itself or with the facts. It is inconsistent 
with itself for the following reason. When I look at 
a penny, the brown colour that I see is seen spread out 
over the round contour. Similarly with the cold tem- 
perature that I feel. We are asked to believe that 
there is brownness without shape "in me," and round 
shape without colour out there where the penny is. 



274 SCIENTIFIC THOUGHT 

and yet that in some mysterious way, the shapeless 
brownness "in me" is projected into the round con- 
tour of the penny "out there." If this be not nonsense 
I do not know what nonsense is. We can all sav this 
kind of thing, but can we attach any clear meaning 
to what we are saying? 

Moreover, as Berkeley long ago pointed out, the 
theory only takes account of half the facts. Certainly 
colours vary with the illumination, the state of our 
eyes, and so on. But it only needs a little careful in- 
spection to see that visible shapes also vary with changes 
in the medium, and with the position of the observer. 
If the former fact proves that colours and temperatures 
are not "in the object" but "in us," the latter should 
t prove the same thing for visible shapes. It is impos- 
sible to reconcile the view that the penny is round, in 
the literal straightforward sense, with the view that, 
when we look at it, we literally sense visually the upper 
surface of it. For we sense all sorts of elliptical patches 
from various positions. It is clear that none of these 
can be identical with the round upper surface of the 
penny, and it is equally clear that they are not parts 
of it in the literal sense in which the King's head is a 
part of it. 

If we want to be consistent then, we must treat visual 
shape in the same way as colour and temperature. 
What we sense visually is a sensum, and the shape 
and the brownness both belong to it. If anything be 
produced "in us" by an external object when we look 
at it, it is not just the colour, but is the whole patch 
with its colour and its shape. And, as we have seen, 
this patch cannot be regarded as being the upper 
surface of the external object, or as being literally a 
part of that surface. Nor can we any longer hold that 
what we sense by touch is literally identical with what 
we sense by sight, and that sight and touch merely 
reveal two different qualities of this one object. For 
what we sense tactually is round and of constant size. 



THEORY OF SENSA 275 

What we sense visually is not round, except when we 
are in that very special set of positions from which 
we are said to be "looking straight down on" the 
penny. And, even if we confine ourselves to this series 
of positions, the sizes of the various round patches 
which we sense are not the same for different positions 
in the series. It is therefore clear that the scientific 
view needs to be completely restated in terms of the 
sensum theory. And this is not easy, because the 
scientific theory assumed that we really were sensing the 
contour of the actual physical object out in space, and 
that our sensations were due to what was going on 
within that contour. 

As we move about and continue, as we say, to " look 
at the same object," we are aware of a series of sensa, 
each having shape and colour, and all very much alike 
in these respects. But there are certain variations 
which we commonly overlook. These strike us in 
exaggerated cases, and can be noticed by careful 
inspection in all cases. Moreover, they are as a rule 
reversed when we retrace our steps. If we are going 
to attempt a causal theory of perception we must try 
to explain this conjunction of predominant agreement 
throughout the series with slight, regular, and reversible 
variations between its different members. The explana- 
tion that naturally strikes us is that the series of sensa 
depends on two sets of conditions. One of these is 
relatively permanent, and accounts for the predominant 
agreement of the members of the series. The other is 
variable, and accounts for their minor variations. 

Again, if we feel an object, such as a penny, and 
meanwhile look at it from various points of view, the 
series of predominantly similar, but slightly variant, 
visual sensa is correlated with an invariant tactual sensum. 
The shape of the latter is very much, but not exactly, 
like those of most of the former. It is exactly like that 
of the visual sensa which are sensed from a certain 
series of positions. As regards other qualities, there 



276 SCIENTIFIC THOUGHT 

is complete difference between the visual and the tactual 
sensa. The former have colour, but no temperature or 
hardness ; the latter have coldness and hardness, but no 
colour. Now we have to explain this predominant 
agreement, combined with minor differences, between 
the shapes of the many visual sensa and the shape of 
the one tactual sensum. And we have to remember 
that, as regards other sensible qualities, the difference is 
complete. Here, again, it seems natural to suppose that 
there is something common and relatively permanent, 
which accounts for the predominant agreement in shape 
between the visual and the tactual sensa, and something 
variable that accounts for their minor differences in 
shape. This other factor seems clearly to be connected 
with the position of the sense-organ. As the eye moves 
about, the shape of the visual sensa varies. The shape 
of the tactual sensum does not change : but then we 
cannot move the hand to a distance and continue to sense 
the tactual sensum at all, as we can change the place 
of the eye and still continue to see. We may further 
suppose that different factors are needed to determine 
such very different sensible qualities as colour and tem- 
perature ; but it is reasonable to suppose that, whatever 
these factors may be, they are subject to some common 
condition which determines the very similar shape of 
both visual and tactual sensa. 

Lastly, when we compare notes with other people who 
say that they are looking at the same thing as we are, 
we find again a predominant agreement between their 
sensa and ours, combined with minor variations. It seems 
reasonable to suppose that there is a set of conditions, 
common to their sensa and ours, which accounts for the 
predominant agreement between the two. In addition, 
there must be variable factors, one specially connected 
with one observer and another with another observer. 
These are responsible for the minor variations. It 
seems, then, that we have good grounds for supposing 
that there are physical objects in the sense of conditions 



THEORY OF SENSA 277 

which (a) are common to us and to others ; (#) are 
relatively permanent, and, at any rate, do not ipso facto 
change when we move about ; and (c) determine in 
some way the attributes of our sensa, in conjunction 
with other conditions which do vary from person to 
person at the same time and for the same person at 
different times. 

It might be asked at this point by a sceptical reader, 
"Why go outside the series of correlated sensa at all? 
Why not be content to take them as a fact? Why 
make them all depend on conditions outside the series 
of sensa itself?" As I have said, this is a step which 
everyone does take, but which no one can be logically 
compelled to take. At present we may say that what 
induces us to do this is the fact that we have reason 
to think that physical objects change and act on each 
other when we do not happen to be sensing any sensa 
from them. We can drop such series of sensa as I 
have been describing (e.g., by turning our heads or 
going out of the room), and then by making suitable 
movements we can pick it up again either where we left 
it, or in a form that is obviously a later development of a 
course of change whose earlier stages we noticed before 
we turned away. It is facts of this kind which (rightly 
or wrongly) make us look beyond such series of correlated 
sensa to relatively permanent conditions, which lie out- 
side the series and can develop on their own account 
when the series is interrupted. 

Now these common and relatively permanent con- 
ditions might, for all that we have seen up to the 
present, be so utterly unlike the sensa that they 
condition that it would be misleading to call them 
physical objects. The question therefore at once arises : 
"Can we determine anything further about their 
properties, either with certainty or with reasonably 
high probability?" I do not think that we could 
determine anything further with certainty, but I do 
think that we might determine something further with 



278 SCIENTIFIC THOUGHT 

high probability. It is, of course, perfectly true that a 
set of conditions — and, moreover, a set which is only 
one part of the total conditions — of a sensum, must not 
be assumed to resemble in its properties the sensum 
which it partially determines. On the other hand, it 
were equally unreasonable to assume that the two cannot 
resemble each other. There can be no inner contra- 
diction in the qualities of shape and size, since sensa, 
at least, certainly have shape and size and certainly 
exist. If such qualities involved any kind of internal 
contradiction, no existent whatever could possess them. 
Hence it is perfectly legitimate to postulate hypothetic- 
ally any amount of resemblance that we choose between 
sensa and the permanent part of their total conditions. 
If now we find that, by postulating certain qualities in 
these permanent conditions, we can account for the 
most striking facts about our sensa, and that without 
making this hypothesis we cannot do so, the hypo- 
thesis in question may reach a very high degree of 
probability. 

Now we find that the visual sensa of a group which 
we ascribe to a single physical object are related pro- 
jectively to each other and to the tactual sensum which 
we ascribe to the same object. If we regard their 
common permanent condition as having something 
analogous to shape, we can explain the shapes of the 
various sensa in the group as projections of the shape 
of their common permanent condition. If we refuse 
to attribute anything like shape to the permanent 
conditions, we cannot explain the variations in shape 
of the visual sensa as the observer moves into different 
positions. This does not, of course, prove that the 
common and relatively permanent conditions of a 
group of sensa do have shape, but it does render the 
hypothesis highly plausible. We have already seen 
that it is a legitimate one, that there is no reason why 
these common conditions should not have shape ; we 
now see that it is also a plausible one, since with it we 



THEORY OF SENSA 279 

can, and without it we cannot, account for the variations 
in the shapes of the sensa of the group. 

What about the so-called "secondary qualities," 
like colour and temperature? We know that Descartes, 
Locke, and the orthodox natural scientists, hold that we 
have no right to ascribe them literally to physical 
objects, whilst Berkeley and many other philosophers 
have argued that primaries and secondaries must stand 
or fall (and that they, in fact, fall) together. What is 
the truth about this matter? The first need is to state 
the doctrine of primary and secondary qualities in a 
clear and intelligible form. Unquestionably, colour 
and temperature belong to our sensa, at any rate, in 
the same literal way in which shape and size belong 
to them. What I am immediately aware of when I 
look at a penny stamp is as indubitably red as it is 
indubitably more or less square. Similarly, when I 
hold a round piece of ice in my hand, what I am aware 
of is as certainly cold as it is certainly round. Thus, 
to say that colours and temperatures are "unreal," or 
"do not really exist," is patently false, if this means 
that there is nothing in the Universe of which it is true 
to say: "This is literally red," or "This is literally 
cold." Such statements are true of many sensa, at 
any rate, and sensa are parts of the existing Universe. -"' 

The only substantial question is : " Do colours and 
temperatures ever literally belong to physical objects, 
or do they belong literally only to sensa?" What the 
scientist is trying in an extremely muddled way to 
do is to assert the physical reality of shapes and sizes, 
and to deny the physical reality of colours, temperatures, 
noises, etc. Now this view, when clearly stated, comes 
to the following : " Shapes and sizes belong to physical 
objects in the same literal way in which they belong 
to sensa, and from the shapes and sizes of sensa we can 
generally infer with reasonable certainty those of that 
physical object of which these sensa are appearances. 
Colours, temperatures, etc., belong literally to sensa, 



y 



28o SCIENTIFIC THOUGHT 

but they belong to physical objects only in a derivative 
and Pickwickian sense. There must, of course, be some- 
thing in the permanent conditions of a group of sensa 
which wholly or partly determines the colour or tem- 
perature of the latter. But this something is not colour 
or temperature." We have seen what sort of ground 
there is for the positive part of this view : is there any 
good reason to believe the negative part of it? 

It is sometimes thought that the physical theories 
of light and heat positively disprove the common-sense 
view that physical objects are literally coloured or hot. 
This is a sheer logical blunder. The physical theory 
of light, e.g., asserts that, whenever we sense a red 
sensum, vibrations of a certain period are striking our 
retina. This does not prove that bodies which emit 
vibrations of that period are not literally red, for it 
might well be that only bodies which are literally red 
can emit just these vibrations. The vibrations might 
simply be the means of stimulating us to sense the 
red colour, which is literally in the body, whether we 
happen to sense it or not. (I am quite certain that 
this simple-minded theory cannot be made to fit the 
extremely complicated facts ; but it is compatible with 
the fact that we only become aware of colours when 
vibrations of a certain kind affect our eyes ; and there- 
fore this fact does not, as is often supposed, refute the 
common-sense view that bodies are literally coloured 
and that we actually sense the colours which are on 
their surfaces.) 

I think that the negative part of the scientific view 
does express an important fact, but that it needs to be 
stated in a much more guarded way. (i) It is certain 
that, if physical objects possess shape and size at all, 
they must have some other quality, related to shape and 
size in the same general kind of way in which colour 
and temperature are related to the shape and size of 
sensa. You cannot have extension et praterea nihil ; 
you must have something that can be spread out and 



THEORY OF SENSA 281 

cover an area or fill a volume. (2) There is no reason 
why these "extensible" qualities, which must be 
present in physical objects, if they be extended at all, 
should not actually be colour and temperature. Since 
sensa certainly exist, and are certainly coloured, there 
can be no internal contradiction in the notion of an 
existent colour. (3) On the other hand, of course, the 
extensible qualities of physical objects need not be 
colour or temperature. So long as they are qualities 
that can cover areas and fill volumes, as colour and 
temperature do, they might differ from any quality 
that is ever present in our sensa. (4) Whilst we found 
that the assumption that the permanent conditions of 
groups of sensa have shape, and that they and our 
bodies have position, does help us to predict the shapes 
of various sensa in the group, we do not find that the 
ascription of colours or temperatures to these permanent 
conditions helps us to predict the colours or tempera- 
tures of the sensa in the group. It is found more 
profitable to correlate the colours and temperatures of 
sensa with the hypothetical movements of hypothetical 
parts of their permanent conditions. This does not 
prove, as has often been thought, that physical objects 
cannot literally have colours or temperatures. Of course, 
if the sensa that we sense cannot literally be parts of 
the surfaces of physical objects, it follows that the 
colours and temperatures of these sensa cannot literally 
be identical with the colours and temperatures of 
physical objects, even if the latter have such qualities. 
The facts under discussion do show that the hypothesis 
that physical objects literally have colours and tempera- 
tures, though legitimate enough, is not capable of 
empirical verification, and therefore cannot be asserted 
with any high probability. 

The view which I have been trying to state may 
be called the Critical Scientific Theory. It is simply an 
attempt to formulate clearly, in terms of the Sensum 
Theory of sensible appearance, the view about the ex- 

T 



282 SCIENTIFIC THOUGHT 

ternal world which has been at the back of the scientific 
mind since the time of Descartes and Locke. In its 
original form this view was a mass of inconsistencies, since 
it was naively realistic for our perception of shape, size, 
and position, and held a causal theory for our perception 
of colour, temperature, etc. This combination of theories 
proved to be inconsistent with the inextricable entangle- 
ment of the two kinds of qualities, which we actually find. 
Moreover, the naively realistic part of it proved unten- 
able in face of the variations of visual shape and size, 
which are obvious when we view what is regarded as a 
single unchanged physical object from various positions. 

Thus the only hope for the scientific view was to 
restate it in a completely causal form. A serious diffi- 
culty at once arose. The causal part of the old view 
presupposed the naively realistic part. When we were 
told that motions within a circular contour at a certain 
place in space caused sensations of colour and tempera- 
ture "in us," we understood this, because we thought 
that we literally saw and felt this contour in this place. 
But, as soon as the theory is made completely causal, 
both spatial and non-spatial attributes belong primarily 
to the effect produced "in us" by something else. It 
then becomes difficult to see that we have any better 
right to regard this cause as literally endowed with 
shape, size, and position, than as literally endowed with 
colour and temperature. Yet the scientific theories 
about the causation of our sensations of colour, tem- 
perature, etc., are stated in terms which seem to lose all 
meaning unless the causes of these sensations literally 
have shapes, sizes, and positions. The Critical Scientific 
Theory, as stated by us, has been an attempt to meet 
these difficulties, to reformulate the distinction between 
primary and secondary qualities, and to estimate the 
amount of value which this distinction can justly claim. 

I think that the Critical Scientific Theory is internally 
consistent, so far as it goes ; but I certainly do not 
believe that it is ultimately satisfactory. In the first 



THEORY OF SENSA 283 

place, it continues to use a number of phrases whose 
meanings are no longer obvious when we have given 
up the notion that we literally sense parts of the surfaces 
of physical objects. It still talks of pennies being 
" round," of a number of different people at " the same 
time" and the same person at "different times" all 
perceiving " the same penny " from "different places." 
We must reinterpret all these phrases in terms of our 
sensa and their relations before we can hope to get a 
consistent theory. I shall try my hand at this very 
difficult job in the next three chapters. 

Secondly, our theory uses the phrase that processes 
in external physical objects and our bodies "jointly 
produce in us" the sensa by which we become aware 
of them. The phrase in inverted commas covers a 
multitude of problems. Do physical processes create 
sensa out of nothing? Or do they just cause us to sense 
now one and now another selection out of a mass of 
already existing sensa? And, on either alternative, 
what is the status of sensa once they have come into 
existence? Do they just exist alongside of physical 
objects? Do they ever interact with each other or pro- 
duce effects on the physical world ? Or are they, in some 
Pickwickian sense, parts of physical objects? With some 
of these problems I shall try to deal in my last chapter. 

The following additional works may be consulted 
with advantage : 

B. A. \V. Russell, Lectures on the External World, Lects. 

III. and IV. 
M ,, A nalysis of Mind, Lects. V. and VII. 

G. F. Stout, Manual of Psychology, Bk. III. Part II. Cap. 

I., and Bk. II. Cap. I. 
,, ,, Proceedings of the Aristotelian Society, 191 3. 

J. Laird, Problems of the Self,. Cap. III. 
S. Alexander, Space, Time, and Deity, Vol. II. p. 124, 

et seq. ; p. 170, et seq. 
G. E. Moore, Philosophical Studies. 
Berkeley, Principles of Human Knowledge. 
Descartes, Meditations. 



r 



CHAPTER IX 

" Nam si colorcs et soni in ipso Objecto csscnt, separari ab 
illis non posscnt. Separantur autcm, ut manifestum in reflexioni- 
bus visibilium per specula, et audibilium per loca montana. 
Scimus autem corpus quod videmus in uno tantum loco esse, 
sed apparentias in plurimis." 

(Hobbes, Leviathan, Part I. Cap. I.) 

The Positions and Shapes of Sensa and of 
Physical Objects 

We have now to dig beneath the assumptions that are 
tacitly made by the Critical Scientific Theory, and to 
discover their precise meaning and value. In expound- 
ing it we talked of a number of people all " looking at 
the same penny." We assumed that there is a certain 
place "seen" by all the observers, and that in this 
place there is a round physical object. We have now 
to ask what is meant by a common place ; what is 
meant by a physical object occupying that place ; and 
what is meant by calling that object round. We shall 
find that all these questions, which seem so childishly 
simple, present great difficulties, and can only be 
answered in highly Pickwickian senses. They seem 
easy, because we habitually confine ourselves to cases, 
which are indeed of frequent occurrence, and are of 
practical interest, but which really owe their simplicity 
to the existence of specially simple conditions. These 
conditions are not always fulfilled, and then difficulties 
arise. This happens, for instance, with mirror images 
which turn up in places where nothing relevant is 
going on. As a rule, we simply ignore these "wild" 
isensa ; but we shall find that the only way to deal fairly 
Nwjth all the facts is to base our theory on them, and to 

284 



POSITIONS AND SHAPES OF SENSA 285 

regard "tame" sensa as owing their tameness to the 
fulfilment of certain special simplifying conditions. 

In dealing with our present problem we shall not 
only be learning something more about the concept of 
Matter and its appearances ; we shall also be carrying 
the theory of Space a step further. In Chapter I we 
simply took the common-sense notion of a single all- 
containing Space for granted ; we have now to consider 
the exact cash value of that conception. 

If we want to discover the meaning of the statement 
that we all see a certain physical object in a certain 
place, we must start from the spatial characteristics of 
our visual sensa. Unfortunately, there is a good deal 
of disagreement as to what these actually are. Thus 
we are often told that we do not "see" distance or 
solidity ; and this is undoubtedly meant to mean that 
distance and solidity are not characteristics of visual 
sensa, as shape and size are. This seems to me to be 
a mistake, and the whole matter has become so much 
confused that our first duty is to try to clear it up. 
This will be rather a long process. 

Spatial Characteristics of the Visual Field. — When- 
ever I open my eyes I am aware of a coloured field of 
view, which I will call a "visual field." It is admitted 
that this is spread out and internally differentiated into 
patches of various shapes and colours. These are at 
once joined and separated by a background, which also 
has colour. The middle part of this field is the most 
distinct. If I turn my head a little, the field changes 
slightly. What is now in the middle and most distinct 
differs from what was in the middle of my former field. 
But it is extremely like something that was slightly to 
one side of the former field and was slightly indistinct. 
Conversely, what is slightly to one side of the present 
field is very much like what was in the middle of the 
former field and had there maximum distinctness. The 
process of turning one's head is, of course, associated 



jS() scientific thought 

with certain kinesthetic sensations, which last longer 
and ijTow more intense the more the head is turned. 

(d) Usual Motion. — So much, I suppose, is admitted 
by everyone. I now want to call attention to certain 
facts that have an important bearing on our present 
problem, and are not so commonly noticed. As a rule, 
we see objects through a practically homogeneous 
medium, viz., air, in which they and we are immersed. 
Under these conditions the slight turning of the head 
only produces those changes in centrality and distinct- 
ness that we have noticed, combined, of course, with the 
loss of certain features which were on the extreme edge 
of the first field and the gain of others on the opposite 
extreme edge of the second. So long as the medium 
is homogeneous, the turning of the head does not affect 
the visual sensa with sensible movement. If, on the 
other hand, we are looking through a bad bit of window 
glass, or through any optical instrument imperfectly 
focused, the sensa in the field do visibly move as we 
turn our heads. What I call "sensible movement" is 
as distinct and irreducible a character of certain sensa 
at certain times as colour or shape. We notice then 
that, under normal conditions of sight, the sensa in our 
visual field may be unaffected with sensible movement, 
though we turn our heads ; but, as soon as the condi- 
tions become unusual, a turn of the head affects all the 
sensa of the field with sensible movement. 

Again, some of the sensa in a field may be affected 
with sensible movement though I keep my head still. 
As I write, I am sitting at an open window in Trinity, 
and looking out at the opposite side of Nevile's Court. 
All the points that I have mentioned are illustrated in 
my present visual field. I can turn my head without 
the visual appearances of the opposite windows being 
affected with sensible movement. If I look through the 
shut window, which is at the side of my open one, and 
is made of rather irregular glass, I find that I cannot 
turn my head without the visual appearance of the 



POSITIONS AND SHAPES OF SENSA 287 

opposite side of the Court jumping about. Lastly, there 
are certain features in the field, viz. , the visual appearances 
of bedmakers and washerwomen — for it is a Saturday — 
which sensibly move, even though I keep my head still. 
To these cases we must add one more, which is the 
least common in ordinary experience. Sometimes we 
find the whole field affected with sensible movement, 
though we keep our heads still. This happens if my 
open window swings to in the breeze. 

The position, then, is this: There is no doubt that 
sensible motion and rest are genuine unanalysable 
properties of visual sensa. I am aware of them as 



v- 



directly as I am aware of the redness of a red patch, 
and I could no more describe them to anyone who had 
never sensed them than I could describe the colour of 
a pillar-box to a man born blind. Now, there are three 
entirely distinct, but constantly confused, questions that 
can be asked about a quality of a sensum. (1) Do sensa 
really have this quality? (2) What conditions must be 
fulfilled in order that sensa with this quality may occur? 
and (3) What right have I to base on this quality of 
my sensa those judgments about physical objects and 
their properties which I do in fact base on it? The first 
question is absolutely independent of the other two. 
The only way to find out whether a sensum does or 
does not have a certain quality is to inspect the sensum 
itself as carefully as possible. The second question 
belongs partly to physics, partly to physiology, and 
partly perhaps to psychology (if sensa be to any extent 
mind-dependent). The third is a question for Critical 
Philosophy. Naturally, the answer to it will determine 
the interpretation which we put on the answers given 
by scientists to (2). Conversely, the answer to (3) will 
have to be such as to allow for any well-established facts 
that the scientists have discovered in answering (2). 

Now it is a very common mistake to suppose that if 
(2) has to be answered in a certain way it follows that 
sensa cannot have the quality in question. This fallacy 



288 SCIENTIFIC THOUGHT 

seems to me to have been committed by those persons 
who deny that visual sensa have sensible solidity and 
position. They argue that those qualities could only 
have been acquired through certain past experiences, 
and conclude from this that the qualities in question 
cannot now belong to visual sensa. This is, of course, 
a sheer fallacy ; but before discussing it in detail for 
position and solidity, I propose to deal with the case of 
sensible motion. For exactly similar arguments could 
be used to prove that visual sensa do not have sensible 
motion ; and it must surely be obvious, even to the most 
advanced thinker, that some visual sensa do have this 
quality. 

When I look through a homogeneous medium and 
turn my head, the stimulus of light from various objects 
moves over my retina ; nevertheless, my sensa are not 
affected with sensible motion. When I look through 
a non-homogeneous medium, and turn my head, the 
stimulus moves across my retina ; and this time my 
sensa are affected with sensible motion. Thus the 
movement of the stimulus over the retina may be a 
necessary, but is certainly not a sufficient, condition 
of the sensible movement of my visual sensa. When 
I believe that the object that I am looking at is the sort 
of object that will not move {e.g., the opposite side of 
the Court), and when I am seeing it under normal 
conditions {i.e., through a homogeneous medium) the 
sensa keep still, in spite of the movement of the stimulus, 
provided this movement is caused by the voluntary 
turning of my head. Thus it seems to me to be clear 
that one condition which partly determines the present 
motion or rest of my visual sensa is my beliefs as to the 
motion and rest of the objects of which these sensa are 
appearances. These beliefs must be due to past experi- 
ences, not wholly visual, in connexion with similar 
sensa. They are presumably present in the - form 
of traces. Under normal circumstances these traces 
neutralise the sensible movement which the motion of 



POSITIONS AND SHAPES OF SENSA 289 

the stimulus over the retina would itself produce. But, 
as soon as the conditions become abnormal, this neutral- 
isation (which is merely associative and instinctive, not 
deliberate and rational) fails to fit the unusual conditions, 
and the sensa visibly move. 

If the above theory be true, the present motion or 
rest of a sensum is not entirely determined by anything 
in the nature of the present stimulus. The traces left 
by past experiences, some of which were not wholly 
visual, also co-operate ; and we have what Mr Russell 
calls a case of " mnemic causation." Yet it is clear 
that this makes no difference to the fact that here and 
now visual motion and rest are properties of visual sensa, 
which are "seen," as truly as shapes and colours, and 
which would be inexpl icable to a blind man. 

These facts are typical of visual perception, and 
render the situation with which we have to deal highly 
complex and confusing. On the one hand, we now 
pass from the visible motion or rest of our sensa to 
perceptual judgments about the behaviour of our bodies, 
of the medium, and of the object at which we say 
that we are looking. We could not get so much out 
of so little if it were not that many past experiences 
of ourselves and others co-operate with the present 
visual sensum to form the basis of our perceptual judg- 
ments. But they do not only co-operate to form judg- 
ments. The actual present qualities and movements of . / 
ourfsensalare modified by the traces left by these past [ji.»s 
experiences. We have thus to deal with a double 
process. The experiences of many people (conveyed 
to us from our earliest years by speech and corporate 
action) and many past experiences of our own, have 
helped to produce our present beliefs in the places, 
shapes, movements, etc., of physical objects, and have 
helped to produce our present classification of these 
into medium, observer's body, object looked at, etc. 
Pari passu with this, the traces left by these past experi- 
ences (which express themselves in consciousness, if 



2Q0 SCIENTIFIC THOUGHT 

they do so at all, as expectations and beliefs about 
physical objects) co-operate with present stimuli, and 
modify the qualities of our sensa. And our present 
judgments about physical objects are, of course, based 
on our sensa as thus modified. 

(/>) Visual Solidity. — Let us now apply these general 
principles to the debated case of visual solidity and 
distance ; and let us begin with solidity. It seems to 
me perfectly clear that, whatever may have been true 
of my infancy or of my remote ancestors, solidity is now 
as genuine a quality of some of my visual sensa as flat 
shape or red colour. A sphere does look different 
from a circle, just as a circle looks different from an 
ellipse. That this is due to past experiences of touch 
and past kinesthetic sensations may very well be 
true in one sense, though I think that it is certainly 
false in another. We must distinguish between a 
general quality, capable of various specific modifications, 
and the particular form of it possessed by a certain 
particular sensum. Thus visual solidity, on my view, 
is a general quality of visual sensa, whilst sphericity is 
a particular form of it, which belongs to some sensa and 
not to others. Now I can quite well believe that the 
particular form of solidity possessed by a certain sensum 
may be in part due to traces of past experiences of 
touch and movement. I can believe, for instance, that 
the particular distribution of light and shade over my 
present sensum resembles that of a past sensum which 
was associated with the experience of passing my hand 
over a spherical surface. And I can believe that the 
resemblance of the stimulus excites the traces left by 
that experience,, and that these co-operate with the 
present stimulus on my retina to produce a sensum 
which is visibly spherical. But I find it very hard to 
believe that experiences of touch or movement could 
create a third dimension in visual sensa which originally 
had only two. 

Now it does seem to me clear that visual solidity is in 



POSITIONS AND SHAPES OF SENSA 291 

itself as purely visual as visual shape and size. It does 
not consist of visual flatness, together with judgments 
about past or future tactual sensations. Nor does it 
consist of visual flatness, together with associated 
images of past or future tactual sensa. It is a matter 
of plain inspection that the experience of visual solidity 
is as unitary an experience as that of visual shape in 
two dimensions, and that it is impossible to distinguish 
it into a visual and a tactual part. We are therefore 
forced to suppose, either that the experiences of one 
sense can create an additional dimension in the sensa 
of another sense, or that visual sensa are of their own 
nature three dimensional. I should not be prepared 
to accept the former alternative unless very strong 
arguments could be produced against the second. We 
shall see in a moment that the arguments are feeble 
in the extreme. I shall therefore suppose that visual 
solidity is a primitive characteristic of visual sensa, and 
that the traces left by past visual and tactual experiences 
merely help to determine what particular form of visual 
solidity a particular sensum shall have. 

If this be the genuine result of careful inspection, 
no argument from the physical and physiological con- 
ditions of visual sensation can possibly have anything 
to say against it. On the contrary, it will be one of 
the facts with which any theory as to the conditions of 
visual sensation will have to reckon. All arguments 
which attempt to prove that solidity is not a primitive 
property of visual sensa are of the following type. 
Whenever we see an object, a certain area of the retina 
is stimulated by the light from this object. This area 
is a projection of the object on to the surface of the 
retina, and such an area could equally well be the 
projection of a solid or of a plane figure of suitable 
shape. Consequently, it is argued, there is nothing 
in the retinal stimulus to distinguish between light from 
a solid and light from a plane figure of suitable contour. 
Therefore sight cannot give us an awareness of solidity. 



292 SCIENTIFIC THOUGHT 

This may be illustrated in the following way : Take 
a sphere, and suppose that we are looking at it with 
one eye. The light from it affects a circle on the retina, 
of diameter, era'. 



If we were to cut away all the sphere in front of SS' and 
all the sphere behind it, leaving merely the circular 
disc of diameter SS', the area of the retina affected by 
the light from this disc would be exactly the same as 
that affected by the light from the whole sphere, viz., 
the circular area of diameter ar<r' . Hence, it is argued, 
the visual sensum must be the same in both cases. No 
doubt there will be a difference in light and shade in 
the sensum connected with the sphere, but this is the 
only difference. And this effect could be reproduced 
by using a suitably shaded fiat disc instead of an 
uniformly illuminated one, as is in fact done when 
painters want to represent spheres on flat canvases. 
Conversely, arrangements of lines which are really in 
one plane may "look solid." It is concluded (a) that 
solidity is not a primitive property of visual sensa ; 
and (d) that, even now, "to look solid," means simply 
to evoke certain images, memories, or expectations of 
tactual and kinesthetic experiences. 

This argument, which must be mistaken if it is a 
fact that visual solidity is a unitary and unanalysable 
property of sensa, does rest on tacit assumptions ; and, 
when these are laid bare, it loses its plausibility. It 
assumes (a) that, because the retinal stimulus for visual 
sensation is two-dimensional, therefore, the corre- 
sponding visual sensum cannot have more than two 
dimensions. It is this assumption that makes it so 
plausible to hold that the visual sensum must itself be 
a mere surface, and therefore that visual solidity needs 



POSITIONS AND SHAPES OF SENSA 293 

to be explained. But there is not the least reason to 
accept the assumption. There is no reason, whatever, 
why a sensum should not have a greater number of 
dimensions than the physiological stimulus on which 
it depends. Hence, even if it be true that the necessary 
and sufficient condition of a visual sensation is an 
excited area on the retina, this is no reason why some* 
or all visual sensa should not be voluminous, {b) The 
argument in question does make the further assumption 
that the complete conditions of a visual sensum must 
be present in the retinal stimulus with which it is 
connected. If anything else, such as the trace of a 
past tactual or kinesthetic experience, co-operates, it 
is assumed that it can only produce associated tactual 
images and not modifications of visual sensa. This 
again is a sheer assumption, and one that is not even 
antecedently probable. In any case, the visual sensation 
does not arise till the stimulus has passed from the 
retina, through the optic nerve, to the brain. It is the 
wildest dogmatism to assert that what happens in the 
brain corresponds point for point to what happened 
on the retina, and that no additional factors come into 
operation there, which may be constant when the 
retinal stimuli vary, or variable when the retinal stimuli 
are the same. Now if every visual sensation is partly 
dependent on what happens in the brain as well as on 
what has happened on the retina, it is surely mere 
pedantry to assert that the solid shape of a certain visual 
sensum cannot be a genuine property of it, because one 
of its conditions was a trace left on the brain by a past 
tactual experience. We must judge sensa, like O.B.E.'s, 
by their present properties and not by their ancestry. 

The truth seems to me to be as follows : (1) Visual 
sensa, as such, are capable of being solid. There is 
such a quality as visual solidity, and it belongs to some 
sensa as much as the shape of a flat sensum belongs to 
it. (2) The complete conditions of any visual sensum 
include (a) a stimulated area of the retina (or what 



204 SCIENTIFIC THOUGHT 

corresponds point to point with this in the brain by 
transmission through the optic nerve); and (/>) certain 
conditions in the brain which are independent of the 
present stimulus on the retina. (3) Among these 
independent conditions are traces left on the brain by 
past experiences of sight, touch, and movement. These 
do not generally show themselves in consciousness at 
all. If they happen to do so, they express themselves 
as memories and expectations about physical objects. 
(4) Generally these traces merely co-operate with the 
brain states which are due to the retinal stimulus, to 
produce a visual sensation whose sensum is of such and 
such a kind. It is, therefore, reasonable to expect that 
the visual solidity of two sensa may be different, though 
the stimulated retinal area is the same. Let us illustrate 
this by the case of the disc and the sphere. In both 
cases the same circular area of the retina is stimulated 
and the disturbance is transmitted from it to a correlated 
part of the brain. In neither case is this sufficient to 
determine completely the nature of the visual sensum 
which shall be sensed at the moment. The other 
necessary conditions include factors in the brain which 
are independent of the present stimulus and existed 
before it took place. Among these are traces left by 
past experiences. Now the distribution of the light in 
the case of the sphere excites certain traces, t s , whilst 
the different distribution of the light in the case of the 
uniformly illuminated disc excites certain other traces, t d . 
Calling <r a and a- d the visual appearances of sphere and 
disc respectively, and r the common area of the retina 
stimulated, we have 

<r, = 4>(r,t,) and o-a=<f>(r,t d ); 

and the sensible shape of the two sensa takes different 
forms, viz., the solid spherical form and the flat round 
form. Conversely, suppose we are looking at a per- 
spective drawing of a cube on a flat bit of paper. If 
we happen to be thinking mainly of solids, as we 



POSITIONS AND SHAPES OF SENSA 295 

generally are, a trace, 4, left by past experiences of 
touching cubes, will tend to be excited ; if we are think- 
ing mainly of the flat bit of paper a different trace, 
t p will tend to be excited. The two visual sensa, 

Sc = <t>{r,t c ) and s = <f>(r,t / ), 

will then differ in the specific form that their sensible 
shape takes. 

(c) Visual Distance. — We can now pass to the question 
of visual distance, which is more important for our 
present purpose, and about which almost exactly the 
same controversy has arisen. We have been told 
ad nauseam since the days of Berkeley that we do not 
see objects at a distance from ourselves, but that the 
perception of distance by sight is simply associated 
images of tactual and kinesthetic sensations. I take 
this to mean that distance is not an intrinsic property 
of our visual fields, as colour, size, and shape are. 
Now it is perfectly obvious to me that I do sense 
different patches of colour at different visual distances. 
When it is said that we do not see distances out from 
the body, the only sense in which it is true is that, in 
monocular vision, there is nothing in the retinal stimulus 
which is uniquely correlated with the distance of the 
source of light from my eye. In binocular vision 
there is, I suppose, parallax between the two retinal 
impressions. To make the case that I am arguing 
against as strong as possible, I will confine myself to 
monocular vision. 

It is true that, if I fix a stick 6 inches long at 6 feet 
from my eye, its projection on my retina is the same 
as that of a stick 1 foot long held at 12 feet from my 
eye and parallel to the first. The one factor of length 
in the retinal impression has to represent the two factors 
of length and distance in the physical object. This is, 
of course, still clearer if we keep one end of the stick 
fixed and move the other end about in various directions 
in Space. The various projections on the retina are 



296 scientific thought 

of many different lengths ; but all these various pro- 
jections could equally have been produced by sticks of 
suitable lengths, with their directions all confined to 
the plane parallel to the observer's body. Hence there 
is nothing in the retinal impression to distinguish 
between a number of sticks of various lengths put in 
various directions in a plane parallel to the body, and 
a single stick with one end at a fixed distance and the 
other turned in various directions in Space. The con- 
clusion drawn is that distance out from the body is 
not an attribute of visual sensa as such, like length 
and breadth; the distance that is apparently "seen" 
consists of associated images of kinesthetic and tactual 
experiences that have been enjoyed in the past. 

We must make much the same criticisms on this 
argument as we have already made on the argument 
to prove that there is no such quality as visual solidity, 
(i) Whatever may be the history of the process, it is 
now a fact that one visual sensum is visibly remoter 
than another, and that a stick 6 inches long and 6 feet 
away looks different from a parallel stick i foot long 
and 12 feet away. (2) This sensible distance is not 
now analysable into a sensum of a certain size and 
no distance, together with revived images of past kin- 
esthetic and tactual sensations. Visual distance is as 
simple and unitary a quality in itself (whatever may 
be true of its conditions) as visual length or breadth. 

(3) It is extremely difficult to believe that visual sensa 
started with no such quality as distance, and then 
acquired an extra quality, perfectly interchangeable 
with their former qualities of length and breadth, 
through association with experiences of another sense. 

(4) The fact that there is nothing in the retinal stimulus 
which is uniquely correlated with distance in no way 
proves that visual sensa do not, from the very first, 
have some form of visual distance. It is equally true 
that there is nothing in the retinal stimulus that 
uniquely corresponds to the length or breadth of the 



POSITIONS AND SHAPES OF SENSA 297 

object at which we are looking ; yet the present theory 
does not hesitate to hold that length and breadth are 
genuine qualities of visual sensa. In fact, nothing 
but prejudice can make us suppose that, because a 
physiological stimulus has only n dimensions, the 
sensum which is correlated with it cannot have more 
than n dimensions. It is, therefore, perfectly open to 
us to hold that all visual sensa have, of their very 
nature, some visual distance or other. The only problem 
is to account for the fact that here and now one visual 
sensum has one sensible distance and another visual 
sensum has another. (5) To account for this we have 
to remember that, on any view, it is not the retinal 
stimulus itself, but a process in the brain, which is the 
last link in the train of events which ends with a visual 
sensation. This being so, it is not unreasonable to 
suppose that the total physiological conditions of any 
visual sensation include (a) a set of brain-states which 
correspond by transmission to the events in an excited 
area of the retina; and (b) certain brain-states which are 
independent of the present retinal stimulus. Among the 
latter are traces left by past experiences of sight, touch, 
movement, etc. ; and these play an important part in 
determining the particular visual distance that a given 
visual sensum shall have. It is thus perfectly intelligible 
that the sensible length and distance of two sensa should 
differ when the retinal stimulus is of the same size 
and shape, and conversely. This is simply another 
instance of the same general principle which we have 
already seen at work in the case of sensible motion and 
rest and in that of visual solidity. 

A special difficulty with which we must now deal, 
has been felt about ascribing distance to visual sensa. 
It is argued that distance is essentially a relation between 
two terms, and that a relation cannot literally be sensed 
unless both its terms are also sensed. Thus we do not 
visually sense a given line, unless we visually sense 
both ends of it. Now we certainly do not visually sense 

u 



298 SCIENTIFIC THOUGHT 

our own retina, and therefore it is impossible that we 
should visually sense the distance of visual sensa from 
them. This is a perfectly sound argument, and to meet 
it we must draw certain distinctions. 

(i) The first thing to recognise is that the awareness 
of visual distance is primarily an awareness of the 
distance between two visual sensa, and is not an aware- 
ness of the distance of either of them from our retina. 
It is perfectly true that the distance of sensa from our 
retina is not sensed by sight. Indeed, it is only possible 
to srive a meaning to the notion of distance between a 
visual sensum and something, like the retina, which is 
not a sensum at all, in a highly Pickwickian sense. All 
I am asserting is that, when I open my eyes, I am aware 
of a visual field in which different parts have different 
depths. What I sense as visual distance is the difference 
of depth between two sensa in this field. 

(2) We must therefore distinguish between visual 
depth and visual distance. Depth is a sensible quality, 
not a sensible relation. Visual distance is a sensible 
relation between two visual sensa, founded upon the 
difference of their respective visual depths. When we 
sense two sensa with different visual depths we ipso 
facto sense the relation of visual distance between them. 

If we only sense a single visual sensum (say a luminous 
flash on a perfectly dark night) we do not sense distance, 
but we do sense depth. It is, of course, quite true that 
it is extremely difficult to estimate depth accurately 
apart from distance. But there is nothing odd in this. 
It is extremely difficult to estimate length accurately 
except by comparing an object with some other. Never- 
theless, objects do have lengths of their own, and the 
relations between them which we notice when we com- 
pare and measure, are founded on the lengths of each 
of them. 

(3) Sensa are at no distance from our retina, not in 
the sense that they are at zero distance from it, as the 
points of contact of two billiard balls are from each other 



POSITIONS AND SHAPES OF SENSA 299 

when they hit, but in the sense that the concept of 
visual distance does not apply at all to anything but 
pairs of visual sensa. They are at no distance apart 
in the kind of way in which it is true that my belief 
that 2x2 = 4 is at no distance from my desire for my 
tea. A Pickwickian sense of distance can be defined 
in which it is true generally to say that visual sensa of 
less depth are nearer to my eye than visual sensa of 
greater depth. But this Pickwickian sense involves a 
reference to movement and other things which we have 
yet to consider. The interpretation of the depth of a 
single visual sensum in terms of distance between it 
and the eye is, of course, greatly helped by the fact that, 
when two sensa of different depth are both sensed, the 
correlated relation of visual distance between them is 
also immediately cognised. 

I have spoken at some length about visual motion 
and rest, solidity, and distance, for three reasons : (i) 
They illustrate the extreme complexity of the relations 
between sensa (if there be such things, as we are assuming 
throughout this book) and physical objects and processes, 
and show that the past history and present expectations 
of the percipient must be supposed to be partial con- 
ditions of some of the qualities and relations of sensa. 
This cuts out at once any of those cheap and easy forms' 
of naive realism which are produced in mass and ex- • 
ported in bulk from the other side of the Atlantic, (ii) 
The problem of the perception of distance and solidity 
by sight is an intrinsically interesting and very complex 
one, and we have at least shown that many venerable 
arguments on these subjects rest on assumptions which 
are not convincing when clearly stated, (iii) The con- 
clusions which we have reached about visual distance 
and solidity are of the utmost importance for our 
immediate purpose, viz., a discussion of the concepts of 
position and shape, as applied to sensa on the one hand 
and to physical objects on the other. 

My view is that nearly all the general concepts that we 



300 SCIENTIFIC THOUGHT 

use in dealing with Space, e.g., distance, direction, place, 
shape, etc., come from sight, whilst the notion of one 
Space and the particular quantitative values which these 
general concepts assume in special cases are due mainly 
to touch and to movement. Series of kinesthetic sensa- 
tions are not, as such, experiences of distance, direction, 
etc.; and I do not see how they could ever be interpreted 
in such terms unless the necessary concepts had already 
been supplied by sight. Before going further, I will 
sum up our conclusions and sketch the general outline 
of the view that I take. 

(a) The physical world is conceived as comprising 
at any moment a number of co-existing objects of 
various shapes and sizes in various spatial relations to 
each other, (b) The concepts, in terms of which this 
view is stated, come mainly from sight, and could 
hardly have arisen apart from it. Sight supplies each 
of us at each moment with an extended visual field in 
which there are outstanding coloured patches of various 
shapes and sizes. These co-exist ; are in many cases 
sensibly solid ; and have various spatial relations to 
each other in three dimensions, which relations are 
directly sensed, (e) These visual experiences, however, 
need much supplementation before they can give rise 
to the traditional concept of physical Space. In the 
first place, visual shape, size, distance, etc., are not 
quantitatively very definite. Again, Space is not 
thought of as either momentary or private. It, and 
the objects in it, are thought of as public property 
which all observers can perceive. And it is thought 
of as the permanent container in which physical objects 
exist, persist, change, and move. Thus it is necessary 
to connect up with each other (i) the successive visual 
fields of the same observer, and (ii) the contemporary 
visual fields of different observers. This fact may well 
make us anticipate that the traditional separation of 
Space and Time is not an ultimate fact, but is a con- 
venient fiction, which works as well as it does because 



POSITIONS AND SHAPES OF SENSA 301 

of certain simplifying conditions which are generally 
fulfilled in everyday life. (d) The connecting link 
between various visual fields I believe to be mainly 
experiences of bodily movement and of touch. These 
also enable us to give quantitative definiteness to the 
mainly qualitative concepts which we derive from sight. 
(e) These series of movement-sensations are not them- 
selves sensations of spatial relations. They are series 
in Time, whereas spatial relations are conceived to 
link contemporary terms. They are interpreted spatially, 
in terms of the concepts which sight alone can supply, 
through their association with visual experience. (/) 
The accurate quantitative detail, and the unity of 
physical Space, as conceived by us, are thus due to 
the intimate association of sight with touch and move- 
ment-sensations. But the traces of the latter do not 
work simply by calling up judgments or images of 
past or possible movements and touch experiences. 
They also continually modify the actual properties of 
our visual sensa ; so that the sensa connected with a 
given retinal disturbance may come to acquire different 
visual shape, size, and depth, from that which they 
at first had. {g) I do not, of course, mean that the 
spatial attributes of visual sensa can be indefinitely 
modified by association with other experiences, or that 
such association does not often express itself by mere 
judgment, without modification of the qualities of the 
sensa. For instance, it is true that if I look at what 
I believe to be a round object in a considerably oblique 
direction, the visual sensum is not rendered round by 
the traces of past experiences, but remains visibly ellip- 
tical. What the traces do here is not to modify the 
sensum, but merely to produce the judgment that I 
am in fact dealing with a round physical object. The 
meaning of roundness is mainly based on visual ex- 
periences ; the fact that I apply the concept of roundness 
and not that of ellipticity to the perceived object is 
mainly due to the associated traces of past tactual and 



302 SCIENTIFIC THOUGHT 

motor experiences ; but the latter only modify my judg- 
ment about a physical object in this case, and do not 
actually render the visual sensum round. This may 
be contrasted with the case of looking through a 
homogeneous medium at an object which is believed to 
be still, and turning my head. Here the traces left by 
tactual and kinesthetic experiences, which I have had 
in the past in connexion with similar retinal stimuli, 
do prevent the sensum from having any sensible move- 
ment. If the medium be not in fact homogeneous, 
these traces will automatically supply an "over-correc- 
tion," and the sensa will visibly move. (//) On the 
whole, we may say that traces of past experiences do 
tend to modify the qualities of visual sensa in such a 
direction that they approximate more closely to those 
which we believe the object at which we are looking 
possesses. Often the approximation is very imperfect; 
but, as a rule, this makes little difference to the judg- 
ments that we make about physical objects on the basis 
of our sensa. (/) In any case, the spatial attributes 
that we ascribe to a physical object, on the basis of a 
present stimulus and the traces of past experiences, 
gain their whole meaning from sensa and their proper- 
ties, and in the main from the properties of visual sensa. 
I may judge that I am looking at a round penny 
because I am sensing an elliptical sensum ; but what 
I mean by calling it "round," is that it has the same 
sort of shape as certain visual sensa that I have sensed 
in the past {e.g. when I look straight down on pennies). 
U) We must further remember that, in ninety-nine cases 
out of a hundred, the result of association, whether 
it modifies the present sensum or not, is not to produce 
an explicit judgment about a physical object and its 
properties, but to guide us to appropriate actions. 
When we say that an elliptical sensum, together with 
traces of past experiences, leads us to judge that we 
are looking at a round physical object, this is generally 
an over-intellectual statement of the facts. The peculiar 



POSITIONS AND SHAPES OF SENSA 303 

experience of judging or believing may not arise in our 
minds at all, and probably will not, if we are at the 
time more interested in action than in reflection — as the 
present state of the world proves most people to be 
at most times. What really happens is that we act as 
we might reasonably have been expected to act if we 
had made such and such a judgment. 

The Concept of Place : (a) Sensible Place. — Let us now 
deal in detail with the concept of place, as applied to 
sensa and to physical objects. We will start with 
visual sensa. The fundamental meaning of "place 
for visual sensa is their place in the visual field of the 
observer who senses them. This I shall call Sensible 
Visual Place. We shall also find it convenient to say 
that such and such a coloured patch is sensibly present at 
a certain place in a visual field. Sensible presence is 
(a) directly experienced by sight ; (b) is literal and un- 
analysable, not Pickwickian ; and (c) is private to a 
single observer, in the sense that it only applies to the 
sensa of his field. It is a relation between a sensum, 
which is part of a field, and the rest of the field. Two 
different men have different visual fields, and the s ame 
man has different fields at different times. A given 
field may be said to last as long as the specious present 
of the observer whose field it is. We shall have to go 
fully into this matter when we deal with the concepts 
of date and duration, as applied to sensa and to physical 
objects. In the present chapter I shall make the 
simplifying assumption that our successive fields are 
literally momentary. This is certainly not true, for a 
momentary field is something that can only be defined 
by Extensive Abstraction ; but it is best to deal with 
one difficulty at a time. 

I have already said that it seems to me that the 
visual field, with its various coloured patches standing 
out at different depths and in different directions against 
a more neutral background, is the sensible basis which 




4 



. 



304 SCIENTIFIC THOUGHT 

alone gives meaning to the concept of Space. The 
concept of Space is that of a perfectly unique kind of 
whole of co-existing parts, and, if we had never been 
sensibly acquainted with a concrete individual instance 
of such a whole, we could never have formed the con- 
cept. The visual field seems to me to be an instance, 
and the only instance, of a space-like whole with which 
we are directly acquainted. Now, of course, once a 
concept has been acquired through sensible acquaintance 
with a particular instance of it, it can be applied by 
thought to wholes which are never sensed as such, 
but are only conceived by reflection on experiences 
which come to us piecemeal. In order to apply the 
concept to such wholes, many modifications in detail 
may be necessary, and these will be suggested by the 
characteristics of the various experiences which we are 
synthesising under the concept of a quasi-spatial whole. 
For example, if you ask a scientist what he under- 
stands by the statement that an atom consists of a number 
of electrons arranged in a characteristic pattern in 
Space, he will not be able to answer you by defining 
his meaning in terms of other concepts. But he will be 
able to answer you by exemplifying what he means. He 
can ask you to look up at the sky on a clear night. He 
can then say that he thinks of the electrons as analogous 
to the little twinkling dots in your visual field, and that 
he thinks of them as forming a pattern in Space, in the 
sense in which those little dots form a pattern in your 
visual field. In fact, a bit of matter is to physical Space 
as a visual sensum is to a visual field. This is the 
fundamental, non-Pickwickian sense in which things are 
conceived to occupy places in Space. What we have 
now to consider is the facts about our sensa and the other 
experiences which encourage us to extend the applica- 
tion of this concept beyond the visual field and its 
sensa. *\ 

(b) Compresence\of Visual Sensa from different Fields. — 
If I look at a penny, and either stand still or walk 



POSITIONS AND SHAPES OF SENSA 305 

about, I sense a successive series of visual fields. In 
each of these there is a sensum which is an appearance 
of the penny. Again, if a number of observers look 
at the penny together, there are as many different visual 
fields at any moment as there are observers. Each 
contains a sensum which is an appearance of the penny. 
We say that the appearances in the successive fields of 
each observer, and the appearances in the contemporary 
fields of the various observers, are in a certain sense all 
"in the same place," and we say that this is the 
"place where the penny is." It is evident that facts 
such as I have just been describing are the sensible 
basis of such statements as that I " go on seeing the 
same penny," and that other people and myself " see the 
same penny together." If there were no such correla- 
tions between the successive fields of myself and between 
the contemporary fields of several observers, there would 
be no ground for making assertions of this kind. 

Now it is quite clear that when I say that a number 
of sensa from different fields are in the same place, I 
cannot be talking of "sensible place," as described 
above, for that concept refers essentially to the relation 
between a sensum and its own field. We must, there- 
fore, try to find the exact cash-value, in terms of sensible 
experience, of the statements {a) that the various visual 
sensa are in the same place ; and {b) that this is the place 
where the physical penny is. By considering abnormal 
cases, like mirror images, we shall see that sometimes 
the first is true when the second is false. But we will 
begin with more ordinary cases. 

Very often the successive visual fields of an observer 
are largely similar. In particular, there may be a series of 

sensa s 1 s n in his successive fields/^ f m 

which are very much alike. Let us take the case of a 
man who would be said to be looking directly at some rest- 
ing luminous object through a homogeneous medium. 
What sort of visual sensa will he sense? To start with, 
a certain sensum s in the field f may attract his atten- 



306 SCIENTIFIC THOUGHT 

tion. This may be somewhere to the side of the field. 
Suppose he turns his head so that, as we say, he is now 
looking at the object of which this sensum is an appear- 
ance. What happens is that he turns his head until he 
is aware of a field/ 1? in the middle of which is a sensum 
s v which in colour, shape, etc., very much resembles 
the sensum s , which originally attracted his attention. 
This will have a certain sensible depth. Suppose that 
he now begins to walk, " following his nose." He will 
sense a series of visual fields, of which the following 
propositions will generally be true, (i) In any one of 
these f r there will be a sensum s r in the middle, closely 
resembling s 1 in shape and colour, (ii) The sensible 

depths of the successive sensa ^ s n will steadily 

diminish, whilst their brightness, distinctness, and size 
will increase, (iii) This increase in distinctness and size 
will go on up to a maximum, say in the sensum s n of 
the field f n . (iv) If he now goes further, various new 
and startling things will begin to happen. He will 
often find that, if he stretches out his hand in front of 
him, he will sense tactual sensa, correlated in shape 
with the visual sensum. He may also burn his fingers 
badly. He will generally find that his path is blocked. 
(v) If he manages to get past the obstacle he will find 
that his field f a+x contains no sensum s n+v like those of 

the series s x s n . (vi) Very often he will be able 

to sense a field _/"', l+1 , which does contain a sensum s' n+1 of 
the right kind, provided that he turns right round. The 
essence of the process, then, is a succession of visual 
fields, each containing at its centre one of a series of 
qualitatively similar sensa of steadily diminishing depth 
and increasing brightness and clearness, followed by a 
great discontinuity and the beginning of new, though 
often correlated, sensations. 

Next, let us suppose that on another occasion the 
man does not try to turn his head so as to sense a visual 
field with a sensum like s in the middle of it. Let him, 
instead, walk in some other direction, and let him stop 



POSITIONS AND SHAPES OF SENSA 307 

at some point in this course. Call his visual field at 
that time <£„. 4> n may or may not contain a sensum like 
s . If it does, the sensum will certainly not be in the 
middle of the field, and will probably be a very distorted 
projection of s . But, on either alternative, he will 
generally be able, by suitably turning his head, to sense 
a field f' v in the middle of which there is a sensum s' v 
which is a good deal like s , though not as a rule so 

much like it as the sensa of the series j^ s n are 

like each other. (As we say, he is seeing a different 
side of the object.) If he now follows his nose, he will 

in general sense a series of visual fields f\ f'„, 

in the middle of each of which is a sensum of a series 

s\ /„. This series will have the same sort 

of internal relations as the series s x s„, and 

will end up in the same catastrophic way. Now our 
solitary observer will often find that, wherever he 
starts, he can, by suitable head-turning, sense such 
a series of sensa. He thus comes to recognise a central 
region of discontinuity, to which he can walk from any 
position, and to which he passes through series of 
similar visual sensa of decreasing depth and increasing 
brightness. 

Now he will find this notion of a central volume rein- 
forced by some of his other senses. The two other 
senses that act at a distance are hearing and the feeling 
of radiant heat. They have interesting differences from 
each other and from sight, which will be worth mention- 
ing. Let us begin with sound. There is an auditory 
continuum from which particular noises stand out, as 
particular coloured patches stand out from the sight 
continuum. But, whilst patches of colour have definite 
shapes and sizes, noises do not. It is extremely hard 
to state the vague spatial characteristics of a field of 
sound. Differences of direction in it can certainly be 
sensed, but each sound seems to fill the whole sound- 
field, though one is more intensely present in one part 
of it and another in another part. Coloured patches 



3 o8 SCIENTIFIC THOUGHT 

in the same visual field do not interpenetrate. Two 
different colours cannot be sensibly present in the same 
place in the same visual field. A colour is either 
sensibly present in a place or it is not. There is no 
question of degree. But each sound seems to be present 
everywhere in the auditory field, though it is "more" 
present in some parts than in others. This difference 
between the sensible presence of sounds and of colours 
leads to a difference in the way in which common-sense 
supposes them to be present in physical Space. 
Common-sense says that the colours that it sees are 
spread out over the surfaces which it can touch. It 
refuses to say that they are present in the medium 
between this and the observer's body. But common- 
sense does not hold that the noise of a bell is spread out 
over the surface of the bell, or even that it is confined 
to the volume of the bell. I think it would prefer to 
say that the noise is present throughout the whole 
surrounding air, and that there is merely " more of it 
per unit volume " as we approach the bell. 

Apart from this very important difference, to which 
we shall have to return, there are striking likenesses 
between sight and hearing. If we sense a sound s {e.g. 
the auditory appearance of a tolling bell) we can turn 
our heads in such a way that a similar sensum s 1 
" occupies the middle of the auditory field." If we then 
follow our noses we shall, as a rule, sense a succession 

of auditory fields f x f n , each of which contains 

at its centre one member of a series of auditory sensa 
s t s„. These are qualitatively alike and of in- 
creasing loudness, though I do not think we can say 
that there is anything corresponding to the continual 
decrease in sensible depth which we should find in a 
series of visual sensa. After you have reached a certain 
stage in this series you will generally find that, on 
stretching out your hands in front of you, you get 
tactual sensa, and that, as you do so, the sound ceases 
or is modified. Exactly parallel results to those 



POSITIONS AND SHAPES OF SENSA 309 

described in the case of sight are found, when we 
approach from different starting-points, or pass the 
obstacle in which such series generally end. Thus 
auditory sensa equally lead us to the notion of "centres." 
Now in very many cases, whether you move under the 
guidance of your visual sensa or under that of your 
auditory sensa, you will end up with similar tactual 
sensations after a similar series of kinesthetic sensations. 
This happens, e.g. if we first look at a sounding bell 
with our ears stopped, and then unstop our ears and 
shut our eyes. Thus we come to think of centres of 
discontinuity which can be approached from all sides, 
and which are not merely centres for colour or for 
sound, but are centres for both. 

If we now ask ourselves why colours are held to be 
on the bounding surfaces of such central volumes, and 
not anywhere else, whilst sounds are held to be both 
in and all round the sounding centre, the answer is 
plain. Visual sensa have sensible depth ; this steadily 
diminishes in the successive sensa that we sense as we 
approach a centre, but never vanishes altogether till we 
are too near the centre to sense any sensum of the series 
at all. On the other hand, noises have no fixed 
boundaries ; they do not exclude each other from the 
same sensible place ; and they do not, I think, have 
sensible "depth." We have thus no ground for saying 
that we approach the sound when we approach the sound- 
ing centre. A part of the sound is held to be wherever 
we are when we hear it ; it merely is present in greater 
density at places nearer the sounding centre. 

Let us next say a word or two about our sensation 
of radiant heat. We have here series of sensa of the 
same kind as we have with sound. They lead us again 
to the notion of centres of discontinuity, and in general 
to centres which are common to radiant heat, sound, 
and sight. But there is one interesting and important 
peculiarity in the case of heat. If we start at a distance 
from a centre we feel a heat sensum ; and, as we 



310 SCIENTIFIC THOUGHT 

approach, our successive heat sensa are more and more 
intense, in the usual way. Now, as usual, when we 
get to a certain point in the series we can sense tactual 
sensa, if we stretch out our hands in front of us. These 
sensa will usually be intensely and painfully hot. The 
interesting point is that, in this case, heat is felt both in 
the surrounding space and on the surface of the central 
volume. There is no sensible depth in the field of heat 
sensa, so that, as with sound, we do not localise the 
successive sensa on the central volume. On the other 
hand, when we do feel the central volume, the tactual 
sensa are themselves hot. So the heat is regarded as 
both filling the surrounding space and residing in or on 
the central volume. Now common-sense regards what 
can be felt as the physical object par excellence, and the 
place to which one has to move in order to sense the 
tactual sensa as the place of the object. Owing to the 
fact of visual depth, and its gradual decrease as such 
central volumes are approached, common-sense regards 
all the successive visual sensa as localised on this 
volume. It therefore says that the central volume is 
coloured, not that it causes colour. In the case of the bell 
it does not say that this is endowed with sound, but that 
it is the cause of the surrounding space being filled with 
sound. In the case of heat it thinks of the central 
volume as both being hot and causing the surrounding 
space to be filled with heat. The discrete side of the 
common-sense view of the physical world is based on 
the peculiarities of the visual field, and on the fact that 
long intervals of free movement often come between 
tactual sensations. The continuous side of the common- 
sense view of the physical world is based on the 
peculiarities of the fields of radiant heat and sound. 
Heat sensations in some way form a connecting link 
between the two aspects of nature, since they are felt 
both on and between the centres of discontinuity. 

It is obvious that these two sides of the common-sense 
view correspond to real facts in nature. But we may 



POSITIONS AND SHAPES OF SENSA 311 

reasonably suspect that the separation between them 
has been made too sharp, as all separations that are 
made primarily in the interests of practice tend to 
be. As a matter of fact, the common-sense view has 
been based mainly on experiences of touch, sight, and 
movement. Pervasive media, like air and ether, have 
only been recognised in historical times. Thus the 
continuous and transmissive side of nature has had to 
be fitted into a prehistoric metaphysic of the external 
world, made up mainly to deal with our experiences of 
visible and tangible volumes with sharp outlines. 
Atomic theories are so much more comfortable to most 
of us than hydrodynamic theories, because they fit in 
so much better with the scheme that we have inherited 
from the practical philosophers of the Stone Age. We 
learn, as time goes on, that light itself travels through 
a medium with a velocity, that colours seen depend on 
events in central volumes, just as do sounds heard, and 
that these colours may turn up in places where no 
correlated tactual sensa can be felt. All this will have 
to be dealt with later, more especially when we come 
to treat of date and duration. But, in the meanwhile, 
we may offer the suggestion that a good deal of our 
difficulty with the philosophy of the external world is 
due to the fact that we are trying to fit new data into a 
scheme based on experiences which did not include 
them, and which ignored or minimised the sensible 
facts, such as images, shadows, echoes, etc., to deal 
with which new concepts are needed. In just the same 
way we insist on forcing the facts of modern society into 
the ethical and political framework of a simpler age, 
without even the excuse that this "works well in 
practice." 

So far, we have confined ourselves to the case of a 
solitary observer, immersed in a homogeneous medium, 
such as air, and dealing with resting objects. These 
are, of course, very common and practically important 
conditions, and the corresponding experiences are there- 



312 SCIENTIFIC THOUGHT 

fore common, and have left their traces deeply on every- 
one. I have tried to show that such an observer will 
soon reach the notion of "centres of discontinuity," 
dotted about in various places which he can reach by 
movement ; and that his successive visual sensa fall 
into series which we will localise on the surfaces of these 
central volumes. Further, we have seen that the senses 
of hearing and of feeling heat will reinforce this notion, 
and will lead him to recognise these centres as common 
to the sensa of different senses. In particular, heat and 
sound will combine to give him the notion of centres 
surrounded with "physical fields." Sight, for reasons 
mentioned above, does not give to unsophisticated people 
the notion of a physical field ; and when the advance of 
science makes it necessary to introduce this, consider- 
able difficulties are felt in reconciling the omnipresence 
and the finite velocity of the light field with the strict 
localisation of colours on central volumes remote from 
the observer. We may say, if we like, that colour 
belongs physically to the continuous side of nature, but 
that it has so far belonged epistemologically to the discrete 
side of nature. 

We can now pass to the case of a number of observers ; 
and thence to the more complex cases of non-homo- 
geneous media, which considerably "stain the white 
radiance " of our original view about sight and the 
localisation of its objects. Even with the solitary 
observer in the homogeneous medium we have passed 
to a new meaning of "place" for visual sensa. The 
first and most primitive meaning was the place of a single 
visual sensum in its own visual field. We have passed 
beyond this to a group of visual sensa, each selected 
out of different sensible fields of the same observer. 
The members of such a group are said to be in the 
same place, through their correlation with each other 
and with the movements of the observer. The "place" 
referred to here is clearly not a place in any visual field, 
but is a place in the continuum of possible positions of 



POSITIONS AND SHAPES OF SENSA 313 

the observer's body. And the presence of a visual 
sensum at such a place is not an ultimate unanalysable 
relation, like its sensible presence at a place in its own 
visual field. On the contrary, we have just been 
analysing the meaning of the statement that a visual 
sensum is present at a certain place in the movement 
continuum, and have found that it means that the 
sensum in question is one of a set of sensa belonging 
to successive visual fields and connected with each 
other and with the observer's movements in the ways 
indicated above. 

When a set of visual sensa from successive fields of a 
single observer have the sort of relations that we have 
been describing, we will say that they are optically 
compresent with respect to that observer. Each member 
of the set may be said to be optically present at the 
place in the continuum of possible positions of the 
observer's body which he reaches when the character 
of the set begins to change abruptly. Looking at the 
matter from the point of view of this place in the move- 
ment-continuum, we may say that it is optically occupied 
by sensa of such and such a kind from such and such 
a direction. When we have a number of such sets, 
which all converge on a central volume wherever the 
observer may start, we will say that this place is 
" optically fillecV with sensa of a certain kind. We shall 
see later that a place may be optically occupied without 
being optically filled. We have seen that, as a rule, 
when a place in the movement-continuum is optically 
filled, correlated tactual sensa are present at that place. 
(We have not as yet considered what is meant by 
saying that tactual sensa are present at a place in the 
movement-continuum, but we will for the moment take 
this notion for granted. We have also not as yet ade- 
quately discussed the notion of place in the movement- 
continuum. To these points we shall return later.) 

Now, under normal conditions, we can not only 
find groups of optically compresent sensa in the sue- 



314 SCIENTIFIC THOUGHT 

cessive visual fields of a single observer. We can also 
find something of the same kind in the fields of different 
observers. Let us consider what is meant by saying 
that the sensa s A and s,., belonging to visual fields /ii and 
f n of the observers A and B respectively, are in the same 
place. We will suppose that A and B have turned their 
heads in such directions that s t is in the middle of/, and 
s B in the middle o(f n . If they change places and repeat 
the process, A's new sensum will, as a rule, resemble 
B's old one in shape, and conversely. Suppose that, 
when they have both turned their heads so as to sense 
fields with these correlated sensa at their respective 
centres, they start to walk, following their noses. Let 
A do this till he senses the sensum .?,", which is the 
most distinct of the series. Let him then stop, and let 
B now start to follow his nose. B's body will, in general, 
get nearer and nearer to A's, and by the time that B 
senses his most distinct sensum s ;;, they will be nearly 
in contact. If they now follow up their respective 
courses they will certainly run into each other. If they 
both stretch out their hands they will, in general, both 
sense tactual sensa correlated in shape with their visual 
sensa. Thus the notion of a common centre in the 
movement-continuum, at which a number of visual 
sensa are optically compresent, is extended to include 
series of optically compresent sensa belonging to the 
fields of different observers as well as to those of a 
single observer. 

Now it will be noticed that the place which a group 
of optically compresent sensa are said to occupy is 
defined by bodily movement. I have called the con- 
tinuum of possible positions of an observer's body "the 
movement-continuum." I think that "place," in the 
physical sense, refers primarily to places in this con- 
tinuum. Before we can deal with the more complicated 
cases of visual sensa sensed by an observer who is not 
surrounded by a homogeneous medium, we must get 
clearer about the notion of place in the movement- 



POSITIONS AND SHAPES OF SENSA 315 

continuum. The experiences of turning one's head so 
much and then walking so far in a straight line are not 
in themselves spatial experiences. They are simply 
series of kinesthetic and muscular sensations, different 
stages of which fall into different specious presents. 
They last for sensibly different times, and tire us to 
sensibly different degrees. How do they come to lead 
to the notion of a continuum of physical places, which 
are common property to all the observers and are co- 
existent? We cannot fully deal with this question till 
we have dealt with the dates and durations of sensa 
and of physical objects ; but we can at least say this 
much : These series of successive kinesthetic sensa- 
tions would not lead to the notion of a continuum of 
contemporary places if it were not for their correlation 
with experiences of sight. All the fundamental con- 
cepts needed for dealing with Space have their origin, 
and their only literal exemplification, in the visual field. 
Space is thought of as a whole of contemporary parts, 
spread out at various distances and in various directions. 
A whole of this kind is sensed, if I am right, at each 
moment by sight, and in no other way. Turnings of 
the head are interpreted in terms of direction because 
(a) different sensa do have different visible directions 
in the same visual field ; and (b) because with every 
turn of the head is correlated a change in the sensible 
position of some sensum within the field of view. Or, 
to put it more accurately, when we turn our heads a 
field y^, with a sensum s x at a certain sensible place in it, 
can be replaced by a field f 2 , with a similar sensum s 2 
in a different place in it, e.g. in the middle. Again, 
a series of kinesthetic sensations is interpreted as the 
traversing of a physical line of a certain length by the 
observer, because the sensible depths of the similar 

sensa s x s n in the middle of the successive 

fields f\ f n continually diminish as the series 

lasts longer. Sight and movement are thus under 
reciprocal obligations. Were it not for sight, with its 



J 



16 SCIENTIFIC THOUGHT 



extended fields of contemporary parts with different 
sensible depths and in different sensible directions, we 
should lack the very concepts needed for interpreting 
the movement-continuum spatially. On the other hand, 
were it not for the existence of groups of visual sensa, 
correlated with each other and with movements, in the 
way described, we should never have reached the notion 
of the optical compresence in the same place of visual 
sensa from different fields. 

But, although the facts about visual sensa which 
lead to the recognition of "centres" in which groups 
of visual sensa are optically compresent, are necessary 
in order that the movement-continuum may be inter- 
preted spatially, we must not suppose that all places 
in the movement-continuum are optically full or even 
optically occupied at all. The vast majority of them 
are not. Moreover, some which are optically occupied 
from several directions are yet not centres at which 
correlated tactual sensa are present. Let me illustrate 
the first point. If I direct my movements by a certain 
series of optically compresent sensa in the way described, 
but stop before I reach the end of the series, I have 
reached a place in the movement-continuum. But I 
have not arrived at the place in which the sensa of 
this series are optically compresent, and when I stretch 
out my hands I may feel nothing at all. And the place 
in the movement-continuum at which I have stopped 
may quite well not be occupied by any visual sensa 
of any series. What do we say under such circum- 
stances? We say that we have indeed reached a 
physical place, for we have walked so far, and in such 
and such a direction. But we add that this place is 
neither optically nor tactually occupied. If no places 
had been optically or tactually occupied, we should 
almost certainly not have interpreted the movement- 
continuum spatially, or have arrived at anything like 
our present conception of the external world. As it is, 
a large number, though a minority, of places in the 



POSITIONS AND SHAPES OF SENSA 317 

movement-continuum are optically occupied ; many are 
optically filled ; and most of these are also centres for 
sound and heat, and are also tactually occupied. This 
fact gives us the contrast between the filled and the 
empty parts of the movement-continuum, and helps us 
to conceive it as a Space dotted about with physical 
objects in definite places and with definite boundaries. 
We are now in a position to deal with the less 
usual forms of optical presence. These arise when, as 
the physicist would say, we are surrounded by a non- 
homogeneous medium. Our present task, however, is 
to describe as accurately as possible the actual facts 
about our visual sensa, and not to offer causal explana- 
tions of them in terms of their correlations with physical 
events. To begin with a very simple case, let us 
suppose that I am looking at the image of a luminous 
point in a plane mirror. I can, as before, turn my 
head in such a way that I sense a visual field f x with 
a sensum s x in the middle of it, similar to the sensum 
s that originally attracted my attention. Having done 
this, I can, as before, follow my nose. Up to a point 
my experiences will be exactly like those which we 
have already described. There will be the same kind 

of series of sensa s x s n , qualitatively much alike, 

each in the middle of its field, of steadily decreasing 
visual depth, and so on. But at a certain stage in the 
series I shall suddenly sense certain tactual sensa, quite 
uncorrelated with the visual sensa of the series {i.e. I 
shall "bump into the mirror"). This is illustrated by 
the figure below : 



If I, or anyone else, were to start from B instead 
of from A, the same sort of experiences would be 



318 SCIENTIFIC THOUGHT 

enjoyed. Tliis, however, is by no means all. A and 
B might both have experiences of this kind if they 
were both looking directly at some source of light 
through a thin sheet of transparent glass. The differ- 
ence is the following: In the former case, if A or B 
break through or get round the mirror and try to 
continue their course, there will be nothing in their 
visual fields corresponding to the visual sensa that led 
them up to the mirror. (That is to say, their visual 
experiences, as they move along the dotted part of the 
line AI or BI, are quite different from those which they 
had when they traversed the undotted parts of these 
lines.) If there were merely a thin sheet of transparent 
glass at M, and A and B were viewing through it a 
source of light at I, the series of visual sensa would 
go on steadily after they had broken through or got 
round the obstacle. 

The next point to notice is that the courses of A, 
B, C, etc., who start from the same side of the mirror, 
really do converge on a common place in the movement- 
continuum. If they pursued them through the mirror 
or the glass they really would meet at I. The difference 
in the two cases would be this : If they were looking 
at something directly through a thin piece of glass, the 
series of visual sensa of each of them would end at about 
the time when their bodies came in contact with each 
other, and correlated tactual sensa could be sensed by 
each if he stretched his hand forward. If they are look- 
ing at a mirror-image the series of visual sensa which 
leads them up to the mirror not only ceases abruptly as 
soon as they get through or past it ; they also find 
that, when they meet, they either sense no tactual sensa 
at all, or, if they sense any, these are quite uncorrelated 
with the visual sensa that originally guided them on 
their respective ways. If they want to sense correlated 
tactual sensa, they will have to go to quite a different 
place in the movement-continuum, and one that is not 
on their course of movement at all, viz., the place O 



POSITIONS AND SHAPES OF SENSA 319 

in the figure. Now this place O, which is on A's and 
B's side of the mirror, is also a place in which visual 
sensa, much like those that guided A and B up to the 
mirror, are optically compresent. But, as we have 
remarked, it is in quite a different direction from those 
followed by A and B ; and people who walked up to 
it would sense tactual sensa correlated with the visual 
sensa that led them to it, and therefore also correlated 
with the visual sensa that led A and B away from it 
towards I. 

There is one further point to notice about I as 
compared with O. Not only are there no tactual 
sensa at I correlated with the visual sensa that guide 
observers from the other side of the mirror on their 
paths towards I ; there is also a purely optical 
peculiarity about I. The place O is optically filled 
with visual sensa of the kind in question. That is, 
any observer, no matter in what direction he may 
approach O, will sooner or later begin to sense a series 
of visual sensa of this kind, which are optically com- 
present at O. This is far from being true of I. I is 
not a centre which is occupied by visual sensa of the 
kind in question for all observers, or even for the latter 
parts of the course of any observer. People at the back 
of the mirror, who look directly at the place I, either 
see nothing there or else they sense sensa which have no 
resemblance to those which A and B sense on the earlier 
part of their courses. Again, A and B, during the latter 
part of their courses, sense no such sensa as they did 
when they were on the reflecting side of the mirror. We 
must say, then, that I is occupied by the sort of sensa that 
constitute the mirror-image, from certain places, but 
by no means from all ; whilst it may be filled with 
visual sensa of quite a different kind. On the other 
hand, O is not merely occupied, but is filled, with such 
visual sensa as constitute the mirror-image. (For the 
moment I neglect the inversion of the image, which of 
course makes a characteristic difference between the 



320 SCIENTIFIC THOUGHT 

sensa that till O and the otherwise similar sensa that 
optically occupy 1 from places on the reflecting side of 
the mirror.) 

We may sum up the peculiarities of mirror-images 
with respect to place, as follows: (i) The usual correla- 
tion between visual and tactual sensa breaks down. 
Usually, when visual sensa are optically com present 
at a certain place, correlated tactual sensa can be sensed 
by an observer who walks up to that place. If, however, 
you want to sense tactual sensa correlated with the 
visual sensa that constitute a mirror-image, you must 
go to quite a different place from that at which these 
visual sensa are optically compresent. This is, of course, 
puzzling, because unusual ; but there is no theoretical 
difficulty in the fact that two sorts of sensa, which are 
generally compresent, should sometimes not be so. 
People whom we meet are generally compresent with 
their trousers, but this rule is liable to break down in 
swimming-baths. (ii) The optical places of mirror- 
images are never optically filled with the sensa that 
constitute the image, but are only occupied by such 
sensa from certain directions and from the remoter 
places on these directions. On the other hand, they 
may be at the same time optically filled with visual 
sensa that are not in the least like the mirror-image, 
but are correlated with tactual sensa which can be 
sensed by people who walk to these places. 

We can now ask : What is it precisely that the 
laws of geometrical optics tell us about mirror-images? 
The answer is simple. They tell us where sources 
would have to be placed, and what tangible shapes 
they would need to have, in order that an observer 
who stands in a given position shall continue to sense 
the same visual sensum when the heterogeneous medium, 
with which he is in fact surrounded, is replaced by air. 
If we like to use the convenient language of the general 
Theory of Relativity, we can say that the introduction 
of suitable sources in suitable places in a homo- 



POSITIONS AND SHAPES OF SENSA 321 

geneous medium will always "transform away" {i.e. 
be equivalent to) the effects of any heterogeneous 
medium for any one visual sensum of any one observer 
in any one position. In favourable cases the trans- 
formation may apply to many sensa of many observers 
in many positions. But no arrangement of sources in 
a homogeneous medium will be equivalent to the 
effects of a heterogeneous medium for all observers 
in all positions. For instance, if we remove the mirror 
M and put a luminous point of the right colour at I, 
A's and B's visual sensa will be unchanged ; but very 
different sensa will now be introduced into the fields 
of observers at the back of the mirror. The laws of 
geometrical optics are then simply the rules according 
to which we can calculate the tactual shapes and the 
positions of such hypothetical sources as would trans- 
form away the effects of a heterogeneous medium for 
a given sensum of a given observer in a given place 
in the movement-continuum. 

(c) The Relation of Optical Occupation. — I think that 
we are now in a position to go a step further in our 
analysis of the optical places of visual sensa. We 
notice that three types of case can arise, ranging from 
the completely normal, through the mildly abnormal, 
to the wildly abnormal, (i) There is the case of seeing 
things by direct vision in a homogeneous medium. 
Here all observers in all directions (provided they be 
not too far off) can sense very similar sensa, and can 
bring them into the middles of their respective fields 
of view ; and the paths of all these observers converge 
to a common place in the movement-continuum, at which 
all the sensa of all these series are optically compresent. 
The proviso that the observers are not to be too far off 
is added in order to allow for the possible interposition 
of opaque obstacles between the place where the observer 
is and the centre of optical compresence. If a luminous 
point be inside a room, it is true that the place where it 
is said to be is optically occupied by sensa of similar 



3 22 SCIENTIFIC THOUGHT 

quality from all directions; it is not true, however, that 
it is occupied by such sensa from all places on any one 
of these directions. It is not so occupied from places 
that are outside the room. What we can say is that 
there is some finite distance r, such that the place in 
question is optically occupied by such sensa from all 
places within a sphere of radius r drawn with this place 
as centre. The figure below illustrates this restriction. 

The dotted parts of the lines are 
the positions from which P is not 
----* optically occupied by sensa of the 
sort with which it is optically filled, 
(ii) In the case of seeing a 
* mirror-image there is a certain 

place behind the mirror which (a) is occupied by 
similar visual sensa from many, but not from all, 
directions which converge on the point, (b) It is only 
occupied by visual sensa of this kind from certain places 
on any one of these directions, and no series of such 
places extends up to the place where the image is said 
to be. On the contrary, these series always end abruptly 
at a finite distance from the place, (c) The place of the 
mirror-image may, though it need not, be also a place 
of complete optical compresence from all directions. 
But, if so, the sensa with which it is optically filled 
will be quite unlike those which optically occupy it 
from places on the reflecting side of the mirror. In 
the figure below, M is a mirror, N an opaque obstacle, 
and I the place of a mirror-image. The full thick part 
of a line represents the places on it from which I is 
optically occupied by the sensa which constitute the 
mirror-image. The full thin part represents the places 
from which it is optically occupied by sensa of the sort 
with which it is optically filled. The dotted parts 
represent places from which it is occupied by neither 
kind of sensa. 

(iii) Lastly, with distorted mirrors or other kinds of 
more heterogeneous media, any observer may find that 



POSITIONS AND SHAPES OF SENSA 323 

he has continually to turn his head at each step, if he 
wants to sense a series of visual fields with at all similar 
sensa at their centres. In such cases the observers will 




also generally find that their sensa are affected with 
sensible movement as they turn their heads. 

We thus have a series of cases, ranging from the 
complete tameness of (i) to the extreme wildness of (iii). 
Now it seems to me that the psychological and the 
logical order are here opposite to each other. Psycho- 
logically our concept of Space, and of the places of 
things in it, is built on (i), i.e., on the commonest and 
most practically important cases. If these had been less 
common and less practically important, it is doubtful 
whether we should have reached anything like our 
present view of the external world. But, logically 
considered, it is the wild cases, of type (iii), that are of 
fundamental importance. It seems pretty clear that the 
normal cases can only arise when certain special simpli- 
fying conditions are fulfilled, viz., those which we sum 
up by saying that the medium is homogeneous. These 
special conditions mask the real complexity of the 
relations involved ; whereas the wilder cases exhibit 
these relations in their most general form. There is 
some hope that, if we treat the wild cases as funda- 



324 SCIENTIFIC THOUGHT 

mental, we may be able to deal with the normal ones 
as specially simplified instances of a more general 
relation ; as, e.g, y a circle may be regarded as a specially 
simplified case of an ellipse. But there is very little 
hope that, if we take the relations involved in the normal 
cases as fundamental, we shall be able to interpret the 
abnormal cases in terms of them. And, as Critical 
Philosophers, it is our business to try to deal with all 
the facts, and not to hush up the existence of abnormal 
sensa, as though they were the peccadillos of a Cabinet 
Minister. 

We can now say something about the logical 
characteristics of the relation of optical occupation, (i) 
It is a relation between a visual sensum on the one 
hand and a place in the movement-continuum on the 
other. (2) It is a many-one relation. This means that 
a given sensum s can only occupy optically one place 
in the movement-continuum, but one place in the 
movement -continuum can be optically occupied at 
the same time by many sensa. (3) I think we must 
also hold that the relation of optical occupation is 
irreducibly triadic. This means that any complete 
statement, which asserts this relation to hold, involves 
three terms, viz., the sensum, the place that it optically 
occupies, and a third term. My reason for saying this 
is the following: The statement that the place p is 
optically occupied by the sensum s seems to be incom- 
plete ; the full statement would seem to be that p is 
optically occupied by s from q, where q is the place in 
the movement-continuum occupied by the observer's 
body. We see this more clearly if we state exactly 
what we mean when we say that s optically occupies p. 
s will be a sensum which is sensibly present in a certain 
observer's visual field at the time. This observer will, 
in fact, be in a certain place q. To define the direction 
of p, the place optically occupied by s, we have to 
suppose that the observer turns till he senses a visual 
field with a sensum s', similar to s, in its centre. The 



POSITIONS AND SHAPES OF SENSA 325 

direction of p is then the direction in which he would 
start to walk if he followed his nose. The distance of p 
is determined by the sensible depth of/ in the observer's 
visual field. It is the distance that he would have to 
walk to reach a source if, in fact, the medium were homo- 
geneous and s' were due to the transmission of light 
directly from this source to his eye. It seems therefore 
that the full meaning of the statement that s is optically 
present atp cannot be understood without a reference to 
the place q occupied by the observer in whose visual field 
s is sensibly present. If so, the relation of optical occupa- 
tion is triadic, and the minimum complete statement is 
that s occupies/ from q. 

Of course, in a great many cases, if the observer 
were to walk to a place />, thus determined, he would 
not find any centre of discontinuity there which could 
be taken as the source of his original sensum s. And, in 
many cases, he would not find that a series of sensa like 
s were sensibly present in the middle of his successive 
visual fields as he moved in the line from q to /. This, 
however, does not prove that our definition of optical 
occupation is wrong. It merely shows that the fact that 
a sensum s occupies/ optically from q is no guarantee that 
p is physically occupied by anything closely connected 
with s. This we already knew from our experiences 
with mirrors and other types of non-homogeneous 
medium. 

We must not be frightened of triadic relations, for 
there are plenty of other examples of them in daily life. 
The relation of giving is an example, since it essentially 
involves a giver, a gift, and a recipient. The minimum 
intelligible statement which asserts the relation of giving 
is of the form " x gives y to z." It is true that we some- 
times use apparently simpler phrases, like " Smith gives 
to the Additional Curates' Fund " ; but these are clearly 
elliptical, and, when fully stated, appear in the form 
"Smith gives something to the Additional Curates' 
Fund." Of course, whenever x, y, and z stand in a 



326 SCIENTIFIC THOUGHT 

» 

triadic relation, this involves certain dyadic relations 
between them by pairs; but the assertion of the triadic 
relation is not analysable into the conjoint assertion of 
these dyadic relations. The latter are derived from the 
former, and the former is not built up out of the latter. 
Contrast the relation of " uncle " with that of " giving." 
Both involve three terms. For to say that x is uncle of 
.; means that x is brother of some third person j, who is 
a parent of s. This does not make the avuncular 
relation triadic ; for it is completely analysable into the 
conjoint assertion of these two dyadic relations, and 
they are not merely derived from it. 

Now we are very liable to ignore the fact that a 
relation is polyadic and to treat it as dyadic. This 
happens if two of the terms mainly interest us and the 
rest are uninteresting or generally constant. When 
this condition ceases to be fulfilled we are liable to find 
apparent contradictions, which can only be avoided by 
recognising the polyadicity of the relation. When we 
say that A is to the right of B, we often ignore the fact 
that we are really asserting a triadic relation between 
A, B, and our own hands. Eventually we meet some- 
one as sane as ourselves, who insists that A is to the 
left of B. This is a contradiction, until we take into 
account the neglected third term, which is different in 
the two cases, and see that both parties may be right 
when their full meanings are made explicit. 

If we accept the view that the relation of optical 
occupation between visual sensa and places in the move- 
ment-continuum is triadic, there is no difficulty in the 
fact that a place may be at once optically filled with 
sensa of a certain kind and optically occupied from 
many places with sensa of quite a different kind, which 
have no connexion with the physical filling of this place. 
P is optically filled with sensa of the kind k if there is a 
closed surface in the movement-continuum such that it 
contains P, and such that P is optically occupied by 
sensa of the kind k from all places between the outside 



POSITIONS AND SHAPES OF SENSA 327 

of P and the inside of this surface. This is quite com- 
patible with the fact that there are other places in the 
movement-continuum from which P is not occupied by 
sensa at all. It is also quite compatible with P being 
optically occupied from many other places with sensa 
of a different kind k '. This is what happens in the case 
of mirror-images. With a plane mirror the situation is 
as follows : There is a set of places from each of which 
a sensum of the kind k' is optically present at P. 
These places are on lines of approach which converge 
on P. But (a) all the lines on which such places are 
situated are confined within a certain solid angle with P 
as vertex ; and (/;) even for lines within this region the 
series of places from which sensa of the kind k' are 
optically present at P does not reach P, but stops short 
at a finite distance from it. 

The question might now perhaps be raised: " Is it 
enough to suppose that the relation between a visual 
sensum and a place which it occupies in the movement- 
continuum is triadic?" Ought we not, in the case of 
the mirror-image, for instance, to bring in the positions 
of the source and the mirror as well as that of the 
observer, and thus make the relation at least pentadic? 
This is a plausible question, but I think that it rests on 
a confusion. Undoubtedly, if we want to predict in what 
place a sensum of a certain kind will be optically present 
from the place of a certain observer we need to know 
the positions of the source and the mirror. But these 
are not involved in the meaning of the statement that 
such and such a sensum is optically present in such and 
such a place. We saw that a reference to the place 
of the observer is an essential part of the meaning 
of this statement. But the parts played by the source 
and the mirror are merely causal and not constitutive. 
This is clear from the fact that we have been able to 
give a satisfactory definition of optical occupation with- 
out mentioning the positions of the source or the mirror. 
The way in which these do become relevant is the 



328 SCIENTIFIC THOUGHT 

following : The positions of the source and of the mirror 
do determine causally, according to the physical laws 
of light, the sensible place of the sensum s in o's visual 
field. And the place p in the movement-continuum, 
which is optically occupied by s from where the observer 
is, depends (by definition) on the sensible place of s in o's 
visual field. But it is one thing to say that the positions 
of the source and the mirror are factors which causally 
determine the nature of the sensum which optically 
occupies a particular place / from another place q, and 
quite another thing to say that the positions of source 
and mirror have to be stated before the proposition that 
s optically occupies/ from q can be understood. If the 
latter were true, the relation between a sensum and its 
optical place would be at least pentadic, for the minimum 
intelligible statement about optical occupation would be 
of the form " s optically occupies / from q with respect 
to the medium m and the source o-." But this does not 
seem to be true, and therefore I see no reason at present 
to hold that the relation of optical occupation is more 
than triadic. 

(d) Physical Place. — Having dealt with the puzzling, 
but most illuminating, case of abnormal optical occupa- 
tion, we can now treat the places of physical objects. 
Before the notion of physical place can be profitably 
discussed, we must form a clearer idea of what we mean 
by a physical object. For a physical place is the sort 
of place that can be occupied by a physical object. So 
far we have simply contrasted physical objects with the 
sensa which are their appearances. But it may well be 
that " physical object," in this sense, is a somewhat loose 
term, and covers several different kinds of entity. We 
must even be prepared for the possibility that what 
common-sense calls a physical object may be really a 
number of correlated objects of fundamentally different 
kinds. 

That this is so will be plain, I think, if we compare 
the following four entities : a particular visual appear- 



POSITIONS AND SHAPES OF SENSA 329 

ance of a certain penny ; an image of the penny in a 
plane mirror ; what common-sense understands by the 
penny; and the atoms, electrons, etc., which science 
asserts to be the ultimate physical constituents of the 
penny. The first, no one would think of calling a 
physical object. The second would not indeed be 
called a physical object ; but it is much more than a 
mere sensum. It can be "seen" by a number of 
different observers from different places in exactly the 
same sense in which the penny itself can be seen. And 
it has a certain persistence and independence. It is, in 
fact, a group of closely correlated visual sensa, and a 
certain place in the movement-continuum is optically 
occupied by members of this group from a great many 
places, although it is not filled by them. We refuse to 
call it a physical object, because of the lack of complete 
optical filling, and because of the absence of correlated 
tactual sensa when we come to the place which is opti- 
cally occupied by sensa of such a group. I will call 
such a thing as a mirror-image a Partial Optical Object: — 
optical, because it consists wholly of visual sensa; 
partial, because it does not optically fill the place which 
it optically occupies. 

Now what common-sense understands by a physical 
object, such as a penny, is something more than this 
in two ways at least. (1) It involves a Complete Optical 
Object, for the place where the penny is said to be is 
optically filled with correlated brown elliptical and round 
sensa. (2) It involves something more, which is not 
optical at all. The place in the movement-continuum 
which is marked out for us by being filled with the 
complete optical object very often resists our efforts to 
move into it. It is often a centre for sound and radiant- 
heat sensa. And, as a rule, we sense tactual sensa of 
characteristic shape and of some temperature or other 
when we come to this place. It is very exceptional for 
condition (1) to be fulfilled without condition (2); though 
I suppose we may say that condition (2) is evanescent 

Y 



SCIENTIFIC THOUGHT 

in the case of clouds and wisps of coloured vapour. 
Lei us call the penny, as common-sense understands 
it, a Perceptual Object. Now the important thing to 
notice is that a perceptual object is really not one single 
homogeneous object, present in a place in the movement- 
continuum in one single sense of "presence." It is 
a number of interconnected objects of different types, 
and the different kinds of object included in it are present 
in different senses in the place where the perceptual 
object is said to be. I will call the various correlated 
objects which together constitute a perceptual object 
constituents of the perceptual object. It would be mis- 
leading to call them parts of it, because this would 
suggest that they literally fit together to fill up the 
place in which the perceptual object is said to be. This 
could not be true, because they are of radically different 
kinds, and are in this place in radically different senses. 
Take, for example, the perceptual object which is what 
common-sense means by a penny. One constituent of 
this is a complete optical object. This consists of visual 
sensa. Each of these is literally present only at a place 
in its own visual field. The optical object is only 
present at the place in the movement-continuum in the 
sense that this place is optically filled by the visual 
sensa which together make up the complete optical 
object. Another constituent of the perceptual penny 
is a group of tactual sensa. Each of these is literally 
present only in its own tactual sense-field. The whole 
group is present at the place where the penny is said 
to be, in some Pickwickian sense which we have not 
yet defined, but which, from the nature of the case, 
cannot be identified either with sensible presence or 
with optical presence. It is because the perceptual 
object is not one homogeneous thing, but a complex 
of correlated constituent objects of various types, that 
science finds it necessary to pass beyond the perceptual 
objects of common-sense. This does not mean, as we are 
liable to think, that the latter are "unreal." It only means 



POSITIONS AND SHAPES OF SENSA 331 

that they are unsuitable units for scientific purposes, 
though admirably convenient units for the purposes of 
everyday life. This leads us to the last meaning of 
"physical object," viz., what Whitehead calls Scientific 
Objects. (Though I use this convenient expression of 
Whitehead's, and mean it to apply to much the same 
things as he applies it to, it does not necessarily follow 
that he would agree with the account that I am going 
to give of the concept of such objects.) 

Science tells us that a penny "consists of" large 
numbers of colourless particles, moving about with great 
velocities in characteristic ways. This is understood 
both by science and common-sense to mean that the 
colourless particles are parts of the perceptible brown 
penny in the same literal sense in which a visual 
appearance of the King's head is a part of the visual 
appearance of the penny. It would be difficult to 
accept this interpretation, even on a naively realistic 
view of pennies and our perception of them. It is not 
easy to believe that the brown continuous surface of the 
penny, which, on that view, we sense, can literally be 
composed of colourless particles. Anyhow, this simple- 
minded interpretation of the scientific statement becomes 
impossible when we remember that the perceptual 
penny is not one homogeneous object, but is a complex 
of connected constituent objects of different types, 
which all occupy a place in the movement-continuum in 
different Pickwickian senses. It is clear that nothing 
could be a part of all the constituents of a perceptual 
object in any one sense of the word "part," whether 
literal or Pickwickian. If it be literally part of one of 
the constituents, it can only be a part of the others in as 
many different Pickwickian senses as there are different 
types of constituent. Moreover, some at least of the 
constituents are such that nothing could literally be a 
part of them. One constituent, e.g., of a perceptual 
object is a complete optical object. Nothing could 
claim to be a literal part of this except one of the visual 



332 SCIENTIFIC THOUGHT 

appearances of the perceptual object. And even these 
are not literally parts of the complete optical object. A 
visual appearance of a penny is a "part" of the complete 
optical object only in the sense that the latter is a group 
of optically compresent sensa of which this appearance 
is one member. But the various members do not literally 
fit together to make up a surface, and therefore they 
are not literally parts of the complete optical object. 

We can now return to the statement that perceptual 
objects, like pennies, are "composed of" scientific 
objects, like electrons. From what we have just said, 
this cannot mean more than that the scientific objects are 
literally parts of one of the constituents of a perceptual 
object. It is further quite clear that they are not literally 
parts, or even members, of the optical constituent of the 
perceptual object. This, I take it, is why there is no 
objection to the view that a brown penny is composed 
of colourless electrons. The brownness belongs to the 
optical constituent ; and the electrons are not literally 
parts of this, but at most of some other constituent of 
the perceptual object. 

Now I think that by a scientific object we mean 
something that literally occupies a place in the move- 
ment-continuum. And by this I mean that it occupies 
it in the same indefinable way in which a sensum 
occupies its sensible place in its own field. If this be 
right, the relation between the place of the perceptual 
object and its component scientific objects may be stated 
as follows : The perceptual object marks out a certain 
region in the movement-continuum by the presence in 
this region of its various constituents. These con- 
stituents are all present in this place in different ways, 
and these ways are all definable and Pickwickian. We 
have attempted to define the way in which the optical 
constituent is present, because this is the most difficult 
and important case. Science conceives that the regions 
in the movement-continuum, thus marked out, are liter- 
ally occupied by certain objects which have an important 



POSITIONS AND SHAPES OF SENSA 333 

causal bearing on the nature of the sensa which occupy 
such regions in their various Pickwickian ways. These 
supposed objects, defined as the literal occupants of 
places in the movement-continuum, are what we mean 
by scientific objects. And a perceptual object is com- 
posed of certain scientific objects, in the sense that the 
latter literally occupy that region of the movement- 
continuum which the constituents of the former occupy 
in Pickwickian senses. 

(e) Summary of Conclusions about Place. — There is one 
and only one literal sense of " being in a place." This 
is not definable, but it is exemplified in our sense- 
experience most clearly in the presence of a visual 
sensum at a certain sensible place in its visual field. 
The concept of being in a place is based on our sensible 
acquaintance with such instances as this. It can then 
be applied in thought to types of object and of con- 
tinuum which we cannot sense as simultaneous wholes. 
Again, there is one and only one kind of place which 
we deal with when once we leave individual sensa and 
their fields and pass to physical objects in the widest 
sense of the term. This is a place in the continuum 
of possible positions of our bodies as we move. This 
continuum is not sensed as a simultaneous whole ; but 
our successive experiences of motion are synthesised 
under the concept of a spatial whole, through analogy 
with visual fields which we can sense simultaneously. 
Now, although there is only one literal sense of being 
in a place ; and although by " place " we always mean 
"place in the movement- continuum, spatially con- 
ceived," so soon as we leave the individual sense-field ; 
still there are many derivative, definable, and Pick- 
wickian senses of " being in a place." Whenever we 
talk of any sensum occupying a place in the movement- 
continuum, we are using terms in a Pickwickian manner, 
and are bound to define them. And for different kinds 
of sensa different Pickwickian kinds of occupation will 
have to be defined. 



334 SCIENTIFIC THOUGHT 

Now there are certain correlations between the sensa 
of successive fields sensed by the same observer, between 
contemporary sensa of different observers, and between 
sensa of different kinds, which constantly occur in real 
life, and make these definitions possible and useful. 
But we are liable to overlook cases where these correla- 
tions break down in whole or in part, and thus to 
produce an illusory simplification. This mistake is 
avoided by considering - such facts as mirror-images. 
We found that the perceptual objects of everyday life 
are not homogeneous, but are really composed of a 
number of correlated constituent objects, all occupying, 
in various Pickwickian senses, the same region of the 
movement-continuum. A mirror-image bears a close 
resemblance to the complete optical object which is one 
of the constituents of an ordinary perceptual object. It 
differs from a perceptual object in three ways: (i) It 
is not a complete optical object, but only a partial one. 

(2) The place which it optically occupies is not also 
occupied by correlated tactual and other types of object. 

(3) There is good reason to think that the place of a 
perceptual object is literally occupied by certain scientific 
objects, which are intimately connected causally with the 
sensa which occupy this place in Pickwickian ways. In 
the case of a mirror-image, the place which is optically 
occupied by the sensa which make up the image may 
or may not also be literally occupied by scientific objects. 
But, on either alternative, the nature of the sensa is not 
causally determined by the scientific objects which occupy 
this place, and is causally determined by the scientific 
objects which occupy certain other places, viz., the places 
where the source and the mirror are perceptually present. 
Finally, just as a place in the movement-continuum may 
be optically occupied without containing any relevant 
scientific objects, so there may be many places in the 
movement-continuum which contain important scientific 
objects without beingeitheropticallyortactually occupied. 
If there had been no perceptual objects, or if the relevant 



POSITIONS AND SHAPES OF SENSA 335 

scientific objects had not as a rule occupied the region 
marked out for us by the perceptual objects to which 
they are most relevant, we should hardly have reached 
the notion of scientific objects at all. But, once having 
reached this notion from reflecting on perceptual objects, 
there is no reason why we should not apply it to regions 
which are not occupied by perceptual objects at all. 
Nevertheless, this is a late development of human 
thought, which has happened well within historical 
times, whereas the recognition of perceptual objects is, 
of course, prehistoric and almost certainly pre-human. 

The Concept of Shape.— It remains to consider what 
is meant by " shape," and what is the exact cash value 
of common statements about shape, such as "This 
penny is round." The notion of shape is one of the 
many points where the traditional separation between 
Space and Time wears very thin. This is readily seen 
if we ask: " What is the shape of a cloud of coloured 
vapour?" As the outlines of a cloud are continually 
shifting, there is nothing that can strictly be called the 
shape of it. We can, however, divide up the history 
of the cloud into shorter and shorter successive sections, 
and talk of the shape of each of these. Shape only 
becomes a perfectly definite concept when it refers to 
a momentary extended object ; it can therefore only be 
defined strictly by the use of Extensive Abstraction. 
It is true, however, that there are many objects, 
such as pennies, for which the shapes of successive 
momentary sections are practically identical over a 
long slice of history. In such cases we can talk of 
the shape of the object. We can say that a penny has 
a definite shape, and that this is circular. We have 
now to consider the precise meaning of such statements. 

(a) Sensible Shape. — Just as there is one and only 
one non-Pickwickian sense of being in a place, so there 
is only one literal sense of having a shape. We cannot 
define "shape" in its literal sense, any more than we 



336 SCIENTIFIC THOUGHT 

can define "being in a place " in its literal sense. 
But we can and do become acquainted with concrete 
instances of shape in our sense-fields. The literal 
meaning of shape is best illustrated by a visual sensum 
which persists unchanged throughout the whole of 
the short duration of a single sense-field. It will be 
remembered that, in the present chapter, we are making 
the simplifying assumption that sense-fields and the 
sensa which they contain are literally momentary. 
This assumption will be corrected in the next chapter. 
But in the meanwhile we may say that Sensible Shape 
is the sort of shape possessed by visual and other 
sensa, and that this is the fundamental meaning of 
shape. 

{U) Optical Shape. — We talk of a number of different 
observers "seeing the same object from different places." 
We have already discussed the cash value of this state- 
ment with sufficient accuracy for the purpose of defining 
optical occupation. For the present purpose we must 
go a little further and draw a distinction which we 
have hitherto ignored for the sake of simplicity. When 
several people are said to "see the same object," this 
sometimes means that they all "see the same part of 
the object," and it sometimes means that they "see 
different parts of the same object." Moreover, when 
they are seeing different parts of the same object, it 
would be held that sometimes the parts which they 
see are entirely separate, and that sometimes they 
partially overlap each other. The following examples 
will illustrate these distinctions: (i) If a penny be 
laid on the table and a number of people stand round 
and look at it, we should say that they all "see the 
whole of the upper surface of the penny." (2) If I 
am in my rooms with the door shut, and I look at 
the door from inside the room whilst you look at it 
from outside in the passage, we should be said to be 
"seeing wholly separate parts of the same object." 
(3) If a cricket-ball be put on the table and a number 



POSITIONS AND SHAPES OF SENSA 337 

of people stand round and look at it, we should say 
that they all "see partially different parts of it, but 
that the parts seen by adjacent observers partially over- 
lap." It is quite evident that these three different 
types of statement express three genuinely different 
situations, all of which often arise in real life. On the 
naive view, that we literally sense parts of the surfaces 
of physical objects when we look at them, the meanings 
of such statements are tolerably obvious. But we have 
long ago deserted that view ; and indeed one of the 
reasons which made us do so was the differences in 
sensible shape of the sensa of various observers who 
were all "seeing the whole of the upper surface of a 
penny." It is therefore necessary for us to define Pick- 
wickian senses in which such statements are true. 

A and B may be said to see the same part of a 
perceptual object when the visual sensa s A and s B , which 
are the appearances of this object to A and B respectively, 
are optically present in precisely the same region of the 
movement-continuum. It might be said: "How is 
this possible, when s A may be circular and s B elliptical ; 
or, again, both may be circular, but s A much bigger 
than j^?" This objection rests on a confusion between 
optical and literal occupation. There is nothing in the 
definition of optical occupation to prevent precisely the 
same region of the movement-continuum being optically 
occupied from different places with sensa of various 
sensible shapes and sizes. What would be impossible 
is that either (a) the same place in a sense-field should 
be sensibly occupied by two sensa of different shape or 
size ; or (d) that the same region of the movement-con- 
tinuum should be physically occupied by scientific 
objects of different shape or size. It is now easy to deal 
with the other two cases. We see wholly different parts 
of a perceptual object if the visual sensa, which are the 
appearances of this object to us, are optically present in 
wholly separate regions of the movement-continuum. 
Lastly, A and B see partially overlapping parts of a 



338 SCIENTIFIC THOUGHT 

perceptual object if (n) the sensa .v., and s„ are optically 
present in different regions of the movement-continuum ; 
(/>) these regions partly overlap ; and (c) the overlapping 
part is optically occupied by a part of s A and by a 
part of .<• . What we must clearly understand is that 
literally it is nonsense to suggest that the various 
sensa which constitute a complete optical object them- 
selves overlap and together make up a single surface. 

It is hardly worth while to take great trouble to 
define the optical shape of a perceptual object. This 
would involve defining some Pickwickian sense in which 
we could talk of the shape of the complete optical object 
which is a constituent of the given perceptual object. 
Now common-sense would admit that no one can literally 
see the whole of any perceptual object from any one 
position. And it would admit that the visual shape and 
size of any part depend on the position of the observer. 
In fact we only use visual shape and size as indications 
(trustworthy enough under normal conditions, if suit- 
ably corrected) of the shape of the perceptual object. 
And by the shape of the perceptual object common- 
sense understands its felt shape. It is possible, and 
perhaps useful, to define the optical shape and size of a 
part of a perceptual object from a given direction. This 
might be done as follows : If we look at the place where 
a perceptual object is, bring the visual appearance of 
the object into the middle of our visual field, and then 
follow our noses, we do sense a series of visual fields, each 
containing an appearance of the object. These sensa, 
as we have already seen, do increase to a maximum 
of size and brightness as we approach the place which 
they optically occupy. We might, perhaps, take the 
size and shape of the largest and clearest sensum of 
such a series as what is meant by the optical size and 
shape from a given direction of a certain part of the 
perceptual object. But I do not think that it would be 
possible to generalise this definition, so as to give a mean- 
ing to the size and shape of a complete optical object. 



POSITIONS AND SHAPES OF SENSA 339 

(c) Physical Shape. — We have said that common- 
sense identifies the " real " shape of a perceptual object 
with its felt shape. This statement requires a good 
deal of analysis. The first thing to notice is that we 
are much more inclined to believe that we feel literal 
parts of the surfaces of physical objects than that we 
see them. Mirror-images, and the variations of visual 
shape and size with the position of the observer, make 
it fairly evident, even to common-sense, that visual sensa 
are not literally parts of the surfaces of perceptual 
objects, though, of course, common-sense does not under- 
stand what radical changes a consistent application of 
this conclusion involves. But we are convinced that 
what we touch is literally a part of the surface of a 
physical object. I believe that, with suitable explana- 
tions and qualifications, some such view can be held ; 
but we must gradually work up to it, and make the 
necessary distinctions as we go along. 

(1) There are tactual fields, just as there are visual 
fields. And within them there are sometimes out- 
standing tactual sensa, with recognisable sensible shape 
and position within the field. Tactual sensa stand out 
from the rest of the tactual field, if they be markedly 
different in temperature or in "feel" from the rest. 
These remarks would be illustrated by laying one's 
hand on a table with a small bit of ice lying on it or 
with a nail sticking up from it. In each case we should 
sense a tactual field with a certain outstanding tactual 
sensum at a certain sensible place within it. In the 
first case the sensum would stand out by its coldness 
from the background, and it would have a sensible 
shape. In the second a sensum would stand out from 
the background by its peculiar "prickly feel." But, in 
the ordinary man, the tactual field is much less clearly 
differentiated than the visual field, and sensible tactual 
position and shape are far vaguer than the sensible 
shapes and positions of visual sensa. Very possibly 
this is not true of blind men. The tactual field, such 



340 SCIENTIFIC THOUGHT 

as we have just been describing, is connected with what 
psychologists call " passive touch " ; audit is generally 
admitted that passive touch by itself gives very vague 
information about shape and size. 

(2) Just as visual sensa are literally present only in 
their own fields, so tactual sensa are literally present 
only in tactual fields. When we say that there is a cold 
round tactual sensum at a certain place in the movement- 
continuum, we are necessarily speaking in a Pickwickian 
sense, as much as when we say that there is an elliptical 
brown visual sensum there. This Pickwickian sense 
is fairly obvious. A certain tactual sensum may be said 
to occupy that place in the movement-continuum to 
which I have to move my hand before I can sense 
this sensum. The total region in which a certain 
perceptual object is present may, in this sense, be 
occupied in different parts by a great number of different 
tactual sensa from contemporary fields of different 
observers and from successive fields of a single observer. 
The whole of such a group of tactual sensa would be 
the Tangible Constituent, which, along with the complete 
optical object and perhaps other constituents, makes up 
the perceptual object. 

(3) It would generally be admitted that it is by 
" active touch," i.e., by passing our fingers over surfaces 
that we learn about the "real shapes" of objects like 
pennies. Now active touch is partly a movement- 
experience and partly a tactual experience. The purely 
tactual side of it is illustrated in isolation in passive 
touch, and we have seen how very little it has to tell 
the normal man about shape and size. But active 
touch is movement of very much the same kind as we 
experience when we walk about, accompanied by sensa- 
tions of temperature, pressure, "sharpness," " blunt- 
ness," etc. We find that there are certain regions of 
the movement-continuum into which we cannot enter or 
push our hands. Our previously free course is stopped. 
This stoppage is accompanied and emphasised by 



POSITIONS AND SHAPES OF SENSA 341 

tactual sensations of various kinds. It is always 
accompanied by pressure-sensations, which grow in 
intensity the more we try to penetrate the region in 
question. When we actively feel a body we are trying 
to penetrate a certain region of the movement-continuum 
from various directions, and are failing to do so. And 
our failure is marked bv characteristic tactual sensations. 
The points on its surface are the points at which 
attempted courses of further movement are stopped. 
Thus, it seems to me that what we feel when we are said 
to be actively exploring a certain perceptual object is 
a closed surface in the movement-continuum. The felt 
boundaries are the boundaries of a volume which is in 
the movement-continuum in the same literal sense in 
which a tactual sensum is in its tactual field or a visual 
sensum in its visual field. The optical constituent and 
the tangible constituent of the perceptual object are on 
the surface of this felt region in their respective Pick- 
wickian ways, whilst relevant scientific objects are 
within this region in a perfectly literal sense. 

There is one important point to remember here. 
The experience of being stopped when we try to pene- 
trate a certain region of the movement-continuum from 
various directions is not one simultaneous experience, 
but is a series of successive attempts and failures, accom- 
panied by characteristic tactual sensations. On the 
other hand, the region which we are said to feel is con- 
ceived as a network of contemporary points. If we had 
not got the concepts of shape and volume from our 
visual, and in a much smaller degree, our tactual fields, 
we should never have been able to interpret these 
successive stoppages as a network of contemporary 
points in a kind of space. This is simply a further 
illustration of the general fact, already noted, that apart 
from the characteristic peculiarities of visual fields 
and their correlations with our bodily movements we 
should never have interpreted the movement-continuum 
spatially at all. 



342 SCIENTIFIC THOUGHT 

(//) Summary of Conclusions about Shape. — Shape 
has a perfectly definite meaning only as applied to 
extensive wholes of co-existent parts. It is therefore 
impossible to deal with it adequately apart from time. 
Strictly speaking, only momentary extended events 
have shape, and we can only talk of the shape of a 
persistent object on the assumption that successive 
momentary sections of its history are extended events 
with the same shape. Leaving these temporal compli- 
cations aside till the next chapter, we may say that we 
reach the concept of shape by acquaintance with 
particular instances of it in the form of visual and (to 
a much less degree) tactual sensa. Having reached 
the concept in this way, we can, as usual, proceed to 
apply it to other cases which we cannot sense. 

The notion of the shape of a perceptual object has 
the same kind of confusion as the perceptual object 
itself. For the latter is a compositum of constituent 
objects of various types. Each of these constituent 
objects will have a shape only in a Pickwickian sense, 
if at all. And the Pickwickian sense will be different 
for each different type of constituent object. It proved 
to be unprofitable, and perhaps impossible, to define 
a meaning for the shape of the optical constituent or 
the tangible constituent. In fact, what is meant by the 
shape of a perceptual object seems not to be the shape 
of any of its constituent objects. It is rather the shape 
of a certain region of discontinuity within the move- 
ment-continuum. This is the region on whose surface 
the optical and tangible components of the perceptual 
object are present in the Pickwickian senses of 
"presence" appropriate to each. And within this 
volume are supposed to reside those scientific objects 
which are mainly relevant in determining the optical 
and tangible filling of the region. 

The boundaries of such regions of the movement- 
continuum are learnt by active exploration. Attempts 
at further movement are here stopped, and the stoppage 



POSITIONS AND SHAPES OF SENSA 343 

is emphasised by the accompanying tactual sensations. 
The interpretation of these successive stoppages as a 
network of contemporary points within the movement- 
continuum involves the application of concepts derived 
mainly from the visual field, and the same is true of 
the spatial interpretation of the movement-continuum 
itself. The shapes of visual sensa are taken as indica- 
tions of the shape of this region in the movement- 
continuum, but are admitted by common-sense to need 
correction, a correction which we apply automatically 
and properly in familiar cases. 

This is as far as we can profitably go without con- 
sidering the temporal characteristics of sensa, physical 
objects, and physical events. With these we shall deal 
in the next chapter. 

The following additional works may be consulted 
with advantage : 

G. F. STOUT, Manual of Psychology, Book III. Part II., Caps. 

III. and IV. 
W. James, Principles of Psychology, Chapter on Space. 
Berkeley, Theory of Vision. 



CHAPTER X 

" She is settling fast," said the First Lieutenant as he returned 
from shaving. 

" Fast, Mr Spoker ? " asked the Captain. " The expression 

is a strange one, for Time (if you will think of it) is only 

relative." 

(R. L. Stevenson, The Sinking Ship.) 

The Dates and Durations of Sensa and of 
Physical Objects and Events 

We have now to raise the same kind of questions about 
date and duration as we have just been raising about 
place and shape. As in the last chapter we were 
learning something fresh, not only about Matter, but 
also about Space, so here we are going to dig beneath 
the traditional concepts of Time and Change which 
were treated in Chapter II. We shall also be correcting 
certain simplifying assumptions which were made in 
the last chapter, such, e.g., as the assumption that our 
successive sensible fields are literally momentary. 

Comparison of Spatial and Temporal Characteristics 
of Sensa. — Let us begin with the temporal characteristics 
which belong to sensa in the same direct and literal 
way in which sensible place in their own fields belongs 
to them. There are three ways in which temporal 
characteristics are more pervasive than spatial ones, 
(i) Only objects have places and shapes in a literal or 
even a Pickwickian sense. Mental acts, like believing, 
wishing, etc., neither have sensible places, such as 
sensa have in their own fields, nor are they commonly 
held to be in physical Space, even in a Pickwickian 
sense. This is denied by Alexander, but I am quite 

344 



DATE AND DURATION 345 

unconvinced by his arguments. It is no doubt possible 
to give a Pickwickian meaning to the statement that our 
mental acts are in our heads, but we make so little 
scientific use of such statements that it is hardly worth 
troubling to do so. On the other hand, it seems to me 
that mental acts have dates in the same literal sense as 
sensa and other objects, which are not acts. When I 
say that I began to think of my dinner at the moment 
when I heard a noise, I am asserting that a certain act 
of thought and a certain sensation of sound were con- 
temporary ; and this is an expression of an immediate 
experience, and has nothing Pickwickian about it. 
(ii) The spatial characteristics of the sensa of one sense 
do not literally extend to those of another sense, even 
in the case of a single observer. My visual sensa have 
places in my visual field, and my tactual sensa have 
places in my tactual field ; there is no place in which 
both are literally present. We do, indeed, come to say 
that certain visual sensa are compresent with certain 
tactual ones ; but, as we have seen, this only means 
that both are present, in different Pickwickian senses, in 
a region of the movement-continuum. This is not the 
kind of fact that can be directly sensed. On the other 
hand, it does seem to me that temporal relations do 
literally connect sensa belonging to different senses of 
the same observer. I can often judge quite immediately 
that a certain noise that I sense is contemporary with 
a certain flash that I sense, and is later than a certain 
twinge of toothache which I remember. Here I seem 
to be using the names of these temporal relations quite 
literally, and in no Pickwickian sense. On the other 
hand, temporal relations do not literally stretch across 
from one observer to another. You and I may judge 
that two visual sensa, one of which was sensed by you 
and the other by me, were contemporary ; and you may 
judge that your visual sensum was contemporary with 
a twinge of toothache that you felt. But my flash and 
yours are not contemporary, in the same literal sense 



346 SCIENTIFIC THOUGHT 

in which your flash and your toothache are con- 
temporary. Temporal relations between the sensa 
or the mental acts of two different observers have to 
be defined in terms of a good manv other facts beside 
the two which they are said to relate, just as we found 
with spatial relations between the sensa of different 
observers, (iii) Spatial relations do not literally extend 
from the sensa of one field of a certain observer to the 
sensa of a later field of the same sense of the same 
observer. It is only in a Pickwickian sense that we 
can say that a certain visual sensum of mine is corn- 
present with another visual sensum of mine, which 
belongs to a later field. On the other hand, direct 
memory seems often to bridge the gap between two 
of our sensa of different dates, and to enable us to 
judge directly that one is literally later than the other. 

Sensible Duration : (a) Sensa and Sense-objects. — We 
assumed temporarily, and for the sake of simplicity, 
in the last chapter that our successive sensible fields 
are literally momentary, and that a sensum in one field 
is ipso facto different from any sensum in another held. 
We must now get behind these simplifying assumptions. 
The second of them is partly a matter of definition. 
It is obvious that what is now past cannot be precisely 
and numerically the same as what is now present, even 
though the sensible qualities and shapes of both should 
be exactly the same, and though they should occupy 
precisely similar sensible places in their respective 
sensible fields. I am therefore justified in using the 
term "sensum " in such a way that they shall be called 
different sensa. This is, of course, without prejudice 
to the fact that the resemblances and the continuity 
between the members of a series of different sensa in 
successive fields may be such that it is possible and 
useful to speak of a single persistent sense-object, of 
whose history the sensa of the series are different and 
successive slices. When there is a series of sensa 



DATE AND DURATION 347 

s r s„ in a set of successive fields of an observer 

O, and when there is enough qualitative likeness between 
adjacent sensa of the series, we can say that a sense- 
object S exists and persists, and that these sensa are 
successive parts of its history. If all the sensa of the 
series be indistinguishable in their qualities, we can 
say that the sense-object S has persisted unchanged 
throughout a certain duration. If the successive sensa 
have different places in their respective fields, and if 
certain further conditions be fulfilled, we can say that 
the sense-object S has moved. The sort of continuity 

that is required of the sensa s 1 s„ in order that 

they shall all count as parts of the history of a single 
sense-object S, is that the nearer together two sensa 
are in the series the more alike are their sensible places 
in their respective fields. If this condition be fulfilled, 
we say that there is a single sense-object, and if the 
successive sensible places are different, we say that it 
has moved. We can, of course, remember the place of 
a sensum s r in its field f r , and compare it with that of 
s r+1 in its field f r+1 . This is not generally an act of 
deliberate memory and comparison, but we automatically 
notice if s r+1 's position in/,. +1 is greatly different from s^s 
position in f r . If the fields which come after a certain 
field/,, do not contain sensa with the right sort of resem- 
blance and continuity with the previous s's, we say that 
the sense-object S has ceased to exist. As we have 
already explained, nothing that has ever existed really 
ceases to exist. The parts of its history that have be- 
come, merely recede into the more and more distant 
past ; and nothing that henceforward becomes, is of 
such a nature that it adds on to these past events to 
make a continuation of that particular sense-object. It 
were therefore less misleading to say that the sense- 
object in question ceases to persist. The past, like 
the unhappy Theseus, " Sedet, ceternumque sedebit" 

(/>) Duration of Sense-fields and of Sensa. — On the 
assumption that sensible: fields are literally momentary, 



348 SCIENTIFIC THOUGHT 

it follows that sensa are also literally momentary. But 
this assumption must now be dropped, and we must 
come closer to the actual facts of sensible experience. 
A sensible event has a finite duration, which may 
roughly be defined as the time during which it is sensed, 
as distinct from being remembered. The two kinds 
of act are markedly different when a long gap of time 
separates the act of remembering from the object re- 
membered. As the time-lapse between act and object 
decreases, the distinction between sensing and remember- 
ing grows fainter, and no absolutely sharp line can be 
drawn where one ends and the other begins. Still, 
it is certain that what can be sensed at any moment 
stretches a little way back behind that moment. This 
is the phenomenon to which we have already referred 
as the Specious Present. I do not find the accounts 
of the Specious Present given by psychologists very 
clear, and I shall therefore try to illustrate the matter 
in my own way, which will lead us to definitions of 
momentary fields and momentary acts of sensing. It 
is obvious that, if we are to hold that all object-events 
are really of finite duration, and that momentary objects 
are to be defined by Extensive Abstraction, we ought 
to take up the same attitude towards acts. I shall 
begin by assuming literally momentary acts of sensing, 
and shall then correct this abstraction. 

Let us represent the history of O's acts by a directed 
line OO. Let us represent the history of his sensible 
fields by a parallel line ce. Let O x , on the upper line, 
represent a momentary act of sensing done by O at 
a moment t\. I take it to be a fact that this act grasps 
an event of finite duration which stretches back from 
the moment t\ to a moment t lf which is earlier by an 
amount t. This duration t is the length of O's Specious 
Present. I call this event e x e' v and I represent the act 
of sensing which grasps it as a whole by the right- 
angled triangle ^O^, with e x e\ as base and 1 as 
vertex. 



DATE AND DURATION 



349 




Let us now suppose that, at a slightly later date 
(separated by less than the length of the Specious 
Present), O performs another act of sensing. We will 
represent this by the dotted triangle e 2 0./. 2 , which is 
similar to e x O x e\. This grasps an 
event of duration t, stretching 
back from the moment when the 
act happens. The event is repre- 
sented by e 2 e 2 . Now it is evident 
that there is a part e 2 e\, which is 
common to the two events e 1 e' 1 
and e 2 e 2 . This part is sensed 
by both the acts O x and 0. 2 . On 

the other hand, there is a part e x e 2 of the first event 
which is not sensed by the second act, and a part 
e\e' 2 of the second event which is not sensed by the 
first act. It will be noticed that the duration of e 2 e\, 
the event which is sensed by both O x and 2 , is such 
that, when added to the time that elapses between the 
two acts, it makes up the duration of O's Specious 
Present. If we finally take an act O n , separated from 
O x by the length of the Specious Present, the event e n e' n 
which it grasps has nothing in common with e x e\, except 
the single point which is labelled both e\ and e H . Thus, 
if two acts of sensing by O be separated by the length 
of O's Specious Present, the only " event " that is sensed 
in both of them is a " momentary event." In general, 
we notice that the shorter the time-lapse between two 
of O's acts of sensing, the longer is the event which is 
sensed in both of them ; and that, as the lapse tends 
to nothing, the duration of the event tends to t. 

(c) Momentary Fields and Momentary Acts of Sensing. — 
We are now able to remove the supposition of literally 
momentary acts, and to define by Extensive Abstraction 
both momentary acts and momentary fields. If the 
reader will look back at the diagram he will see that 
the event e 2 e' v which is common to the two acts of 
sensing O x and 2 , is a fortiori common to O x and any 



350 SCIENTIFIC THOUGHT 

act that happens between Oj and 0. 2 . For it will be a 
proper part of the longer event which is common to 
this pair of more closely adjacent acts. If we imagine 
a continuous series of momentary acts between O a and 
(X we can regard them as momentary sections of an 
act or process of finite duration, and can say that the 
finite event e i e\ is present throughout the whole of this 
process of sensing. The parts e x e 2 and c\e\ form a kind of 
penumbra ; the latter was not present at the beginning, 
and the former is not present at the end, of this finite 
process of sensing ; but the part c./\ is present all 
through. A momentary sensible field may thus be 
roughly defined as the limit which the event that is 
present throughout the whole of a process of sensing 
approaches, as the duration of the process of sensing 
approaches to the length of the observer's Specious 
Present. The reference to limits can then be got rid 
of in the usual way by Extensive Abstraction. The 
momentary field e\ might finally be defined as follows : 
It is a class of events such that each member of it is 
present throughout the whole of some process of sensing 
which begins at t\ and does not last longer than O's 
Specious Present. 

In the same kind of way we can define a momentary 
act of sensing. The longer an event the shorter is the 
process of sensing throughout the whole of which it is 
present. As the length of the sensed event approaches 
that of the Specious Present, the duration of the process 
of sensing throughout the whole of which the event is 
present approaches to nothing. We could, therefore, 
roughly define a momentary act of sensing as the limit 
which a process of sensing approaches as the duration 
of the event which is present throughout the whole of 
this process approaches to that of the observer's Specious 
Present. The reference to limits can then be got rid of 
in the usual way. The momentary act O x might ulti- 
mately be defined as follows : It is a class of acts such 
that throughout each member of it there is present some 



DATE AND DURATION 351 

event which ends at t\ and does not last longer than the 
duration of O's Specious Present. 

In real life we may assume that our acts of sensing 
are not momentary, but are processes that last for a 
finite time. What we choose to count as one process 
of sensing, of course, depends on many factors, of which 
the most important is probably unity of interest. If our 
account of the Specious Present be right, the funda- 
mental fact is that a process of sensing which lasts for 
a finite time (provided it be shorter than the duration 
of the Specious Present) will actually sense a certain 
event of finite duration throughout the whole time that 
the process lasts. Since, however, we have succeeded 
in defining momentary acts and momentary sensible 
fields in terms of processes of sensing and sensible 
fields of finite duration, we are henceforth at liberty 
to use the momentary conceptions whenever we find it 
convenient to do so. 

(d) Sensible Change. — We are now in a position to deal 
with sensible change and movement. We have already 
defined what is meant by the statement that a sense- 
object has changed or moved. We saw that it depended 
on a comparison between the sensible positions and 
other qualities of sensa in successive fields. But it is 
a notorious fact that we do not merely notice that some- 
thing has moved or otherwise changed ; we also often 
see something moving or changing. This happens if we 
look at the second-hand of a watch or look at a flickering 
flame. These are experiences of a quite unique kind ; 
we could no more describe what we sense in them to a 
man who had never had such experiences than we could 
describe a red colour to a man born blind. It is also 
clear that to see a second-hand moving is a quite different 
thing from "seeing" that an hour-hand has moved. 
In the one case we are concerned with something that 
happens within a single sensible field ; in the other we 
are concerned with a comparison between the contents 
of two different sensible fields. Now we have just seen 



352 SCIENTIFIC THOUGHT 

that, in the total event which is sensed by a process 
that lasts for less time than the duration of the Specious 
Present, there is a finite part which is sensibly present 
throughout the whole process of sensing - . Even if a 
certain process of sensing goes on for longer than a 
Specious Present, there will be parts of it that are 
shorter than the duration of a Specious Present, and 
some event of finite duration will be sensed throughout 
any one of these shorter parts of the total process. Let 
us consider any such finite event, which is sensed 
throughout the whole of a finite process of sensing. 
It will constitute a sensible field, and it lasts for a 
finite time. It can therefore be divided into successive 
fields of shorter duration, which together make it up. 
If anything in one of its earlier sections be qualitatively 
different from anything in any of its later sections there 
will be change within the original finite field. But the 
whole of this field is sensed throughout a finite process 
of sensing. Thus the qualitative differences between 
its earlier and its later sections will be sensed together ; 
i.e. the observer will actually sense the changing and 
will not merely notice that something has changed. 
We can now easily see why a change must surpass a 
certain minimum speed if it is to be sensed as such. 
If a change takes place slowly, this means that closely 
adjacent events are qualitatively very little different 
from each other. It may therefore happen that two 
events are not qualitatively distinguishable by us unless 
they are separated by more than the duration of a 
Specious Present. If this be so, these two qualitatively 
distinguishable sections of a single long event are too 
far separated to be sensed together even by a momentary 
act. A fortiori they could not be sensed throughout the 
whole of any process of sensing which lasts for a finite 
time, as all real acts of sensing do. Thus we may be 
able in such a case to judge by memory and comparison 
that something has changed, but we shall not be able 
to sense its changing. 



DATE AND DURATION 353 

The fact that, in favourable cases, changes can 
actually be sensed, is of great importance in developing 
the concept of change in general. A sufficiently short 
act of sensing senses a field of finite duration. This 
field is divisible into earlier and later parts, which to- 
gether make it up. Now, since I sense this finite field 
as a whole, I actually sense the way in which its earlier 
half joins up with its later half to make up the whole. 
By analogy with this, I am able to conceive how two 
successive adjacent fields, which no act, however short, 
can sense together, are joined up with each other in 
nature to form a single long event. I thus interpret 
those qualitative differences, which I can notice only 
between successively sensed fields, in terms of the 
changes which I can actually sense within a field that 
is short enough to be sensed as a whole by an act of 
finite duration. If there were no sensible change, it 
would still be true that a sufficiently short act of sensing 
senses a field of finite duration ; but it would be ex- 
tremely difficult for us to recognise that this was divisible 
into successive shorter sections which join up with each 
other to make the finite field. For there would be no 
recognisable qualitative difference between the earlier 
and the later sections. In this case, it would be ex- 
tremely difficult for us to conceive the way in which a 
finite field, which is now sensed, joins on to an earlier 
finite field, which is now only remembered. It would 
be proportionately difficult for us to interpret any 
qualitative differences that we might find between two 
such fields in terms of slow continuous change. 

(e) Conclusions about Sensible Duration. — We have now, 
I think, got all the facts that are needed to deal with 
the concept of the duration of sensa. A sensible field 
is the total event that is sensed throughout the whole 
of any process of sensing. No process which lasts for 
longer than the duration of a Specious Present senses 
a single sensible field, and no sensible field can last 
longer than the duration of a Specious Present. But, 



354 SCIENTIFIC THOUGHT 

on the other hand, every process of sensing that lasts 
for a shorter time than a Specious Present senses 
throughout the whole of it a sensible field of finite 
duration. Since we can always divide up a process 
of sensing into successive bits, each of which is shorter 
than a Specious Present, we can always divide up the 
total event that an observer has sensed in the course of 
a long process of sensing into successive sensible fields, 
each of a finite duration less than that of the Specious 
Present. There is thus a maximum possible duration 
for a sensible field, but any sensible field is divisible 
into shorter fields which join together at their ends to 
make up the whole. This divisibility is made obvious 
to us by the fact of sensible change, and the mode of 
junction of successive adjacent fields is conceived to be 
analogous to that which is actually sensed in the case 
of the earlier and the later half of a single sensible field. 
Now we have already seen that even a momentary 
sensible field (especially, for example, a visual one) is 
spatially extended. We have now seen that any real 
sensible field has a certain duration, which cannot 
exceed that of the observer's Specious Present. It is 
thus also temporally "extended." It may thus be 
regarded as a four-dimensional spatio-temporal whole. 
I define a sensum as a part of a sensible field. Now, 
if we consider an ordinary three-dimensional volume, 
like a cube, and neglect the question of duration 
altogether, w r e see that anything that is literally a part 
of it must be a three-dimensional volume too. For it 
is only such things that could literally fit together to 
make up the cube. Plane sections of the cube are not 
parts of it in this literal sense, though it is perfectly 
easy to define by Extensive Abstraction Pickwickian 
senses in which planes, lines, and points can be truly 
and usefully said to be "parts" of volumes. In the 
same way, it is clear that the only sort of thing that 
can literally be a part of a spatio-temporal whole, like 
a sensible field, must be something that is extended in 



DATE AND DURATION 355 

time as well as in space. Any actual sensum is there- 
fore extended both spatially and temporally. Granted 
that no sensum is to be held to last longer than the 
sensible field of which it is a part, we have still to ask 
what is meant by the statement that one sensum persists 
through the whole of a certain sensible field and that 
another sensum does not. The following cases can 
arise: (i) A certain place in a sensible field may be 
occupied by a sense-quality {e.g., a colour of a certain 
definite shade, brightness, and saturation) throughout 
the whole duration of the sensible field. We should 
then say that a sensum of this colour has persisted and 
rested in one sensible place throughout the whole 
duration of the field. Of such a sensum we can only 
say that it cannot last longer than the sensible field of 
which it is a part (and therefore not longer than the dura- 
tion of a Specious Present), though, of course, it may 
be continued by qualitatively indistinguishable sensa, 
occupying similar sensible places in successive sensible 
fields, (ii) A certain place might be sensibly occupied 
by a continuously changing sense-quality throughout 
the whole duration of the sensible field. This means 
roughly that, if we divide up the history of this place 
throughout the duration of the field into successive 
thinner sections, any two sections will be occupied by 
a different sense-quality, but the thinner we make the 
sections the more nearly alike will be the sense-qualities 
that occupy this place throughout adjacent sections. 
In this case we should actually "sense the change of 
quality." The sensible identity of place, and the 
continuity of the sense-quality, would generally be 
regarded as sufficient to justify us in saying that a 
single sensum has persiste d throughout the sensib le 
field and has rested in one sensible place, but that it 
sensibly and continuously changes in quality v (iii) 
It might be possible to divide the history of a certain 
sensible place in a sensible field into three successive 
sections, of which the first is occupied by a quality q v 



356 SCIENTIFIC THOUGHT 

the second by a markedly different quality q.,, and the 
third by a markedly different quality q :i . We should 
then say that there were three successive sensa, each of 
which persisted for so long, and then was succeeded by 
another. If the middle one of these sections should 
be excessively short, we could say that we had sensed 
a " sense-flash of quality q., at this sensible place." (iv) 
It might happen that, as we divide up the sensible field 
into successive thinner sections, we find that in each 
section there is a sensible place occupied by the same 
sense-quality. Moreover, the shapes of these sensible 
places might be indistinguishable. But the sensible 
places occupied by this quality in successive sections 
of the sensible field might differ. And it might be 
found that the thinner we made the sections the more 
nearly alike were the sensible places occupied by 
this quality in adjacent sections. On the grounds of 
this continuity of place and identity of shape and 
sensible quality, we should be justified in saying that 
we were dealing with a single sensum, which persists 
throughout the whole of the sensible field. But we 
should actually sense its movement ; and should there- 
fore say that a moving sensum of such and such shape 
and sensible quality persisted throughout the whole of 
this sensible field. In real life it is unlikely that the 
shapes of the successive places would be exactly alike, 
or that precisely the same sense-quality would occupy 
each of them. But, provided that the change of shape 
and of sense-quality was continuous in the sense defined 
above, we should still say that we were dealing with a 
single sensum ; but should add that it changes sensibly 
in shape and quality as it sensibly moves. Of course 
a moving or qualitatively changing sensum need not 
persist throughout the whole of a sensible field, any 
more than a resting or qualitatively fixed one need do 
so. The change may begin after the beginning and 
end before the end of the sensible field in question. 

I think that we have now said all that is necessary 



DATE AND DURATION 357 

about the duration of sensa. As in all questions of 
duration, the answer depends in part on mere matters of 
definition. When we ask how long so and so lasts, we 
have first to lay down our criterion of identity for so 
and so. If anything lasts at all, the successive parts 
of its history are necessarily numerically different, or 
they could not be successive. Our criterion of identity 
must, therefore, depend on identity of quality, in a wide 
sense of that word, which includes shape and place. 
Thus the question is: "How much qualitative differ- 
ence can we allow between successive slices of a long 
event before it ceases to be appropriate to call the whole 
event the history of so and so?" Obviously, this is a 
question which admits of various answers; but no one 
holds that complete qualitative identity of successive 
events is necessary if they are all to be regarded as 
parts of the history of one persistent object. I have 
defined the word sensum in such a way that nothing 
which cannot be sensed throughout the whole of some 
process of sensing is to be called one sensum, no matter 
how great the qualitative resemblance and the con- 
tinuity between successive slices of this long event may 
be. Such a long event may count as the history of a 
single sense-object ; because the kind of identity needed 
for the persistence of a sense-object, as defined by me, 
is different from that required for the persistence of a 
sensum. Within these limits, however, I have not 
considered that complete identity of place, shape, or 
sense-quality is essential to the identity of a sensum. 
I therefore recognise the existence of sensibly moving 
and sensibly changing sensa. Since the experiences 
of sensible change and movement are peculiar and 
important, and since they occur within fields that are 
sensed as wholes by processes of sensing of finite 
duration, this seems to be the most reasonable course 
to take. Anyone who disapproves of it has merely to 
make appropriate modifications in his definition of the 
word sensum ; he will still have to recognise and deal as 



358 SCIENTIFIC THOUGHT 

best he ran with all the facts which we have been 
passing under review. 

Dating of Sensa. — We can now turn to the subject 
of date. The notion of date only becomes perfectly- 
definite when we deal with momentary events ; and no 
actual events are momentary. It therefore has to be 
defined by Extensive Abstraction. We will first con- 
sider the dating of sensa which are sensed by a single 
observer, and we will then pass to the concept of 
temporal relations between sensa of different observers. 
When a meaning can be assigned to the statement that 
a sensum s v which is sensed by 1} is contemporary 
with s v which is sensed by O,, and later than s 3 , which 
was sensed by 3 , it will be possible to see what is 
meant by the notion of a date which is neutral as 
between various observers. But I must just say a 
word about the dates of acts of sensing. 

(a) Temporal Relation between Act of Sensing and 
Sensum. — If the reader will refer back to the diagram, 
by w r hich we illustrated the facts of the Specious Present, 
he will see that we there tacitly assumed that a 
momentary act of sensing would be contemporary with 
the end-point of the finite event which it senses. This 
is implied by making lines, like 1 c\ in the diagram, 
normal to the line of objects sensed. I suppose that it 
is possible that an act of sensing might be later by a 
finite amount than the whole of the event that it senses. 
It could not, of course, on our view of the future, be 
earlier than any part of what it senses. For, when the 
act is present, there is nothing later than it ; and to 
sense what has not yet become, would be literally to 
sense nothing. Our assumption seems to be the most 
reasonable one to make. On the one hand, there is, 
so far as I know, nothing conclusive against it. On 
the other hand, the distinguishing mark of an act of 
memory is that it is separated by a finite time-lapse from 
the latest part of the event which it remembers. Hence, 



DATE AND DURATION 359 

any other assumption than that which we made, would 
render it difficult to distinguish, even in theory, between 
an act of sensing and an act of remembering. The 
practical difficulty which there sometimes is in drawing 
this distinction can easily be accounted for on our view. 
We can well suppose that, as the gap between an act 
of remembering and the end of the event remembered 
gets shorter and shorter, it will be more and more 
difficult to distinguish the act of remembering from an 
act of sensing, in which, if we are right, the gap 
vanishes altogether. I shall therefore take it that the 
assumption tacitly made in the diagram is justified. In 
general, then, we may say that the beginning of a pro- 
cess of sensing, throughout the whole of which an 
event of finite duration is sensed, is contemporary with 
the end of the event in question. Thus, in the diagram, 
O x , the beginning of the act C^O.,, is contemporary 
with e' v the end of the event e.-,e' v which is sensed 
throughout the whole of this process. This will suffice 
as to the connexion between the dates of an act of 
sensing and of an event sensed by it ; a question to 
which nothing comparable arises when we deal with 
Space, since mental acts do not have places, as they 
have dates. 

(d) Temporal Relations within a Sense-field. — Having 
cleared this point out of the way, let us consider 
the dating of sensa that are sensed during the life- 
history of a single observer. This inquiry falls into 
two parts. We have first to consider the dating of 
sensa that fall within a single sensible field of the 
observer, and then to consider the extension of this to 
sensa that do not fall into the same sensible field but into 
successive ones. I must first clear up a slight ambiguity 
in the term sensible field. In the last chapter we counted 
the fields of two different senses, e.g., an auditory and a 
visual field of the same observer, as different sensible 
fields which do not form parts of a single larger whole. 
This is true as regards spatial characteristics, which we 



3 6o SCIENTIFIC THOUGHT 

were then considering- ; since sensible spatial relations 
do not connect the sensa of one sense with those of 
another. But, as regards temporal characteristics, the 
distinction between the sensible fields of different senses 
ceases to be of importance. A noise that I sense 
auditorily may be sensibly and literally contemporary 
with a flash of colour that I sense visually. We can 
therefore say that the special sensible fields of the various 
senses form parts of a single general sensible field, so far 
as temporal characteristics are concerned. When I 
speak of a sensible field in the sequel, I shall mean a 
o-eneral sensible field, unless the context makes it plain 
that I am referring to some special one, such as that of 
sight or that of hearing-. 

Let us then take a certain sensible field of a certain 
observer. As we have explained, this is of finite 
duration and its parts of finite duration are sensa. Some 
of these endure throughout the whole of it, others do 
not. Of two sensa, neither of which endures through- 
out the whole of this field, one may be completely 
separated from the other, i.e., one may cease and some 
third sensum may intervene before the other begins. 
On the other hand, the end of one may exactly coincide 
with the beginning of the other. Or, finally, the two 
may partially or totally overlap. These various temporal 
relations between sensa of finite duration that fall into 
the same sensible field can be and are directly sensed, 
just as the spatial relations between two coloured patches 
in the same visual field can be. Two sensa would be 
said to be sensibly simultaneous if each completely overlaps 
the other. If one sensum only partially overlaps another, 
there is a shorter part of one which completely over- 
laps and is completely overlapped by a certain shorter 
part of the other. Thus these two parts will be sensibly 
simultaneous, though the wholes are not. It will be 
seen that sensa which are sensibly simultaneous both 
persist through the same slice of the sensible field. As 
this slice is made thinner and thinner, the sensa that 



DATE AND DURATION 361 

persist through it are made shorter and shorter. Pro- 
ceeding to the limit, we get the notion of exact simul- 
taneity between momentary events. The reference to 
limits can then be removed by Extensive Abstraction. 
The details of the process will be found in Whitehead. 

{b) Temporal Relations within a Sense-history. — We 
can see roughly how, in this way, the sensa that fall 
within a single sensible field can be arranged in a 
temporal order and dated. We have now merely to 
extend this to successive fields of the same observer. 
Any sensum in a later field is later than any sensum 
in an earlier field. A field is later than another if it 
was sensed when the other could only be remembered. 
(This is not the meaning of being later, as we have 
seen, but it is a criterion of it that we can and do use 
in practice.) Now we have seen that earlier and later 
sections of any one sensible field can be distinguished 
and dated. Successive fields of the same observer are 
conceived as joining on to each other in the same way 
in which successive sections of the same field are actually 
sensed to join up with each other and to constitute that 
field. Thus we conceive of the total event, that is 
gradually and piecemeal sensed by an observer in the 
course of his life, as being completely analogous in its 
temporal characteristics to those short sections of it 
which can be sensed as wholes throughout the whole of 
a single process of sensing. 

The particular duration of an observer's Specious 
Present may fairly be regarded as a peculiarity of 
himself or of his species. It is known that this duration 
is much the same for all men under normal conditions. 
It is known that it is short as compared with the dura- 
tion of most events that are practically interesting to us, 
but long as compared with that of many events — such as 
a single vibration of an electron — which are of great 
scientific importance. (These statements can, of course, 
only receive a perfectly definite meaning at a later stage, 

when the temporal characteristics of physical objects and 

2 A 



362 SCIENTIFIC THOUGHT 

events have been discussed.) In the meanwhile it is a 
fact that we can easily conceive of Specious Presents 
which are longer than our own. In particular, we can 
imagine ourselves replaced by an observer who differs 
in no respect from us except that his Specious Present 
covers the whole of his history. Such a man would still 
distinguish the present from the past and the future, 
and the less from the more remote past. But, whilst the 
distinction between present or past and future would be 
as important for him as for us, since it is the distinction 
between something and nothing, the difference between 
present and past would be much less important for him 
than for us. With us the sinking of an event into the 
past is accompanied by a change in our mode of 
cognising it. We have to cognise it by memory or 
inference, if at all ; and the further it sinks into the past 
the vaguer is our knowledge of it likely to become. 
But the hypothetical observer would sense the whole of 
his past history at every moment, and therefore would 
have the same full knowledge of its earliest parts as of 
those that have only just become. This conception of 
an observer with an indefinitely long Specious Present 
is useful, because we conceive the whole content of our 
history to be such as this observer would sense it to be. 

(c) Neutral Temporal Relations. — We have now to 
deal with the temporal relations between sensa of 
different observers. Let us call the whole series of 
sensible fields which an observer O senses in the course 
of his life, O's sense-history. We have seen that, within 
any sense-history, momentary sections can be defined 
and dated by Extensive Abstraction. We have now 
to take into account the existence of a number of ob- 
servers, each with his own sense-history. Our task is 
to treat the temporal relations between a certain event 
in one sense-history and a certain event in another. 
Let us start with the fundamental relation of simul- 
taneity. This is illustrated in its most literal sense by 
sensa in the same field ; the question is, how far it can 



DATE AND DURATION 363 

be extended to a pair of sensa, one from the field of 
one observer and the other from the field of another 
observer. 

We will begin by pointing out a complication which 
did not arise over spatial relations. When we dis- 
cussed in the last chapter the meaning of the statement 
that visual sensa from several different fields are "in 
the same place," it was clear that we were giving a 
definition and not a mere test. This is perfectly evident 
from the following consideration : Two different visual 
appearances of a penny are at once sensibly present 
in different places and optically present in the same 
place. This would be a sheer contradiction if optical 
and sensible presence had the same meaning. Thus, 
when we say that, under such and such conditions, 
two visual sensa are optically compresent, the con- 
ditions are part of the definition of what is meant by 
"optical compresence." It is impossible to hold that 
optical presence really means the same thing as sensible 
presence, and that the conditions mentioned are simply 
tests, by which we can establish that this relation holds 
in cases where the evidence of direct sense-awareness 
fails us. 

Now, when we deal with temporal relations, and try 
to state the conditions under which two sensa in different 
sense-histories are said to be contemporary, it is by 
no means obvious whether we are defining a new sense 
of simultaneity, or merely giving a test by which the fact 
of simultaneity, in the old sense of the word, can be estab- 
lished in cases where it cannot be directly sensed. I 
think that failure to distinguish clearly these two possi- 
bilities has caused much confusion in the writers and 
readers of books on the Theory of Relativity. It is 
very much more plausible to hold that "simultaneity" 
always means the same in all its applications, than to 
hold that "compresence" means the same always and 
everywhere. For it is admitted that sensa belonging 
to different senses of the same observer can be con- 



364 SCIENTIFIC THOUGHT 

temporary with each other, in precisely the same way 
in which two visual or two tactual sensa of the same 
observer can be contemporary. It is therefore not 
glaringly absurd to suggest that sensa belonging to 
different sense-histories may be contemporary in the 
same way in which sensa in the same sense-history can 
be so. In that case the conditions under which two 
sensa belonging to different sense-histories are said 
to be simultaneous do not define a new meaning of 
u simultaneity," but merely give a test for simultaneity, 
in the old meaning of the word, which we use in those 
unfavourable cases where the relation cannot be directly 
sensed. 

The only way of deciding between the two alter- 
natives would be the following : The relation of sensible 
simultaneity has certain logical characteristics. For 
instance, it is transitive, i.e., if A has it to B, and B has 
it to C, then A necessarily has it to C. If we found that 
" simultaneity," as tested by the conditions commonly 
laid down, did not have all these logical characteristics, 
we could conclude that we were dealing with a new 
meaning of " simultaneity." This would not, of course, 
preclude the possibility that sensa from different sense- 
histories have also in fact the relation of simultaneity, in 
the original sense. But it would show that the conditions 
laid down were not a test for that relation. And it 
might turn out that no conditions that we could think 
of would be a test for that relation between sensa belong- 
ing to different histories. In that case, it would be a 
mere personal idiosyncrasy to hold that simultaneity, in 
the original sense, ever holds between sensa in different 
histories ; and it would be better to regard the conditions 
laid down as defining a new sense of " simultaneity." 
For the present we must confine ourselves to the question 
of fact: "Under what conditions do people hold that 
sensa from different sense-histories are contemporary?" 
We may later on raise the question whether these condi- 
tions are simply a test for simultaneity, in the original 



DATE AND DURATION 365 

sense of the word, or whether they define a new meaning 
of " simultaneity." I will use the vague word determine, 
to cover both " being a test for " and " being a condition 
of" so and so. 

Under what conditions do two observers in fact 
judge that they sense two contemporary sensa? Often 
two men assert that they both "see the same flash" or 
" hear the same noise." If this means literally that the 
two men sense precisely and numerically the same visual 
or auditory sensum, and if their statement be true when 
so interpreted, it is easy to lay down the conditions 
under which sensa from their respective sense-histories 
would be said to be simultaneous. If A's twinge of 
toothache be sensibly contemporary with this common 
sensum, and B's twinge of stomach-ache be also sensibly 
contemporary with it, we might say that A's toothache 
and B's stomach-ache are neutrally contemporary with 
each other. 

Now there is no doubt at all that it is under condi- 
tions of this kind that sensa belonging to different sense- 
histories are said to be "simultaneous." But it will 
take us some time to find the exact meaning of these 
conditions, and to make sure what are the properties of 
"simultaneity" thus established. Evidently the first 
question that arises is : What is meant by the common 
statement that two observers " hear the same noise" or 
" see the same flash "? Do they mean that they sense 
a single sensum which is common to the sense-histories 
of both of them ? And, whether they mean it or not, 
is it ever true? As ordinary people do not explicitly 
draw a distinction between sensa and physical objects, 
it is difficult to say whether they mean that they sense 
a common visual sensum when they assert that they see 
the same flash. But, as it is quite certain that by words 
like " seeing " and "hearing," people commonly mean 
to refer to acts of perceiving and not to acts of sensing, 
it is probable that by "the same flash" or "the same 
noise" they intend to refer to a common physical eve?it 



366 SCIENTIFIC THOUGHT 

and not necessarily to a common sensum. In that case 
no such simple interpretation of the statement that A's 
toothache and B's stomach-ache are contemporary, as was 
offered above, can be accepted. For we should need to 
know how to determine whether two sensa are con- 
temporary with the same physical event before we could 
determine whether they are contemporary with each 
other. Now, at present, all that we know is what is 
meant by one sensum of an observer being simultaneous 
with another sensum of //W observer. Hence to determine 
neutral simultaneity between two sensa in terms of the 
simultaneity of each with a common physical event tells 
us nothing, since it involves simultaneity in a sense 
which has not yet been determined. 

Let us then ask ourselves what is the exact cash 
value of the statement that A and B hear the same noise. 
I would like to point out at the beginning that nothing 
that has been said so far about sensa and sensible fields 
precludes the possibility that one and the same sensum 
should be in several sensible fields of different observers. 
A sensum is defined as a part of some sensible field ; 
this clearly leaves open the possibility that two or more 
sensible fields, sensed by different observers, might have 
a part in common. If so, there are sensa common to 
several fields of several different observers. Whether 
this is an actual fact remains to be seen. 

It is fairly easy to show, subject to certain subtle 
qualifications, that when a number of observers say that 
they hear the same noise and that they see the same 
flash, this cannot mean both that they all sense the same 
auditory sensum and that they all sense the same visual 
sensum. For, as we shall see in a moment, it is very 
difficult to reconcile this view with all the facts. Let us 
suppose that I fire a pistol, and that there is a number 
of other observers dotted about at different places. All 
the observers, including myself, will sense a short 
auditory sensum and a short visual sensum. These 
will be sensibly contemporary for me ; for an observer 



DATE AND DURATION 367 

at some distance from me they will only partially over- 
lap, the visual sensum beginning before the auditory 
one does so. For an observer still further off, the visual 
sensum will totally precede the auditory one, though 
both may be in the same sensible field. Finally, for a 
very distant observer the visual sensum may fall into a 
different (and earlier) field from that into which the 
auditory sensum falls. Nevertheless, all the observers, 
on comparing notes, will say that they heard the same 
noise and saw the same flash. Now, if this literally 
means that there is one single visual sensum which 
they all sense, and one single auditory sensum which 
they all sense, we shall have to hold that the same pair 
of sensa can be both sensibly simultaneous, partially 
overlapping, and completely separated in time. Now 
these relations seem to be incompatible with each other, 
and therefore we seem forced to conclude that, when 
several observers say that they see the same flash and 
hear the same noise, this cannot mean both that they all 
sense one and the same visual sensum, and that they all 
sense one and the same auditory sensum. Theoretically, 
it would be possible to interpret one of these statements 
{e.g., that they all saw the same flash) in this literal way, 
provided we did not interpret the other (viz., that they 
all heard the same noise) literally. But, even apart 
from the additional facts which have led physicists to 
ascribe a finite velocity to light as well as to sound, 
such a course would hardly be reasonable. If at least 
otie of the statements, that we all hear the same noise 
and that we all see the same flash, must be interpreted 
in some Pickwickian manner, it is hardly reasonable to 
suppose that the other can be interpreted literally. 

Is there any way out of the conclusion that to hear 
the same sound and to see the same flash cannot mean 
that a number of observers literally sense a single visual 
and a single auditory sensum ? So far as I can see, there 
are at least two alternative wavs in which this conclusion 
could be avoided. One would be to hold that sensa can 



;..S SCIENTIFIC THOUGHT 

be sensed at various times after they have ceased to 
persist, and that the further a man is from a source of 
sound, the greater is the gap between his act of sensing 
and the end of the auditory sensum which it senses. I 
do not think that this is a satisfactory alternative, for 
reasons which I have given earlier in this chapter, when 
I tried to justify the view that the beginning of a process 
of sensing, throughout which a finite event is sensed, 
is contemporary with the end of that event. 

The second alternative is a much more important 
one. It is to adopt the usual expedient, which has 
already been mentioned as useful when two entities seem 
to have incompatible relations to each other. This 
expedient is to assume that what has been taken to be 
a dyadic relation between these two entities is really 
irreducibly polyadic, and involves some other term or 
terms beside the two entities in question. It is un- 
doubtedly true that the same pair of sensa cannot be 
simultaneous, and partially overlapping, and wholly 
separated, -with respect to the sense-history of a single 
observer. But suppose that this pair of sensa belongs 
to the sense-histories of several observers, and that the 
temporal relations in question are really irreducibly 
triadic. Suppose that the minimum intelligible state- 
ment that can be made about the temporal relations of 
two sensa in a sense-history is of the form " s x is con- 
temporary with s 2 (or partially overlaps it, or wholly 
succeeds it, as the case may be) with respect to the 
sense-history //." In that case there need be no incon- 
sistency in the same pair of sensa being contemporary 
with respect to one sense-history, partially overlapping 
with respect to another, and completely separated with 
respect to a third sense-history. We see then that our 
argument from the facts of sound does not conclusively 
prove that, when a number of observers say that they 
all hear the same sound and see the same flash, they 
cannot all be sensing precisely the same auditory 
sensum and precisely the same visual sensum. It does, 



DATE AND DURATION 369 

however, tie us down to one of two alternatives. Either 
this conclusion must be accepted, or we must give up the 
common-sense notion that the temporal relations between 
the sensa in the same sense-history are dyadic, and must 
substitute for it the view that they are at least triadic, 
and that the third term which is always involved is some 
sense-history in which both the sensa are contained. 

Is there any way of deciding between these two 
alternatives? I think that we can at least show that 
the second alternative could not stand by itself, but 
would need to form part of a general Multiple Relation 
theory of sensible appearances. The various observers 
in my example do not really all sense auditory sensa 
which are exactly alike in quality. Both the auditory 
and the visual sensa which are sensed by very distant 
observers are much fainter than those which are sensed 
by me and by observers near me. Now, on the sensum v 

theory, sensa have all the qualities that they appear to \^/ 
have. What really differs in quality c annot be numeri- \^ 
cally identical ; hence a faint sensum cannot be the same . ^^"^) 
sensum as a loud one, however much alike they may 
be in other respects. This argument would not be 5 
conclusive on a Multiple Relation theory of sensible 
appearance ; because, on such a theory, sensa need 
not have the qualities that they seem to have. But I 
am deliberately ignoring Multiple Relation theories 
of sensible appearance in this book, in order to test 
Sensum theories, as Cardinal Newman tested the 
Thirty-nine Articles to see how much Catholic Truth 
they could be made to contain. I am as indifferent as 
he was to the possibility of the subject of my experi- 
ment blowing up at the end of the process ; for negative 
results are often as valuable as positive ones. Accord- 
ingly, I think I may conclude that, on the Sensum 
theory of sensible appearance, it cannot be true that 
when a number of observers say that they see the 
same flash or hear the same noise they literally sense a 
single visual or auditory sensum common to all of them. 



370 SCIENTIFIC THOUGHT 

On either alternative the determination of neutral 
simultaneity between A's toothache and B's stomach- 
ache is going to be a much harder job than it would be 
if the facts about sound (and as we shall see later, about 
light) were different. If what we call the same noise be 
really a group of auditory sensa, the simultaneity of A's 
toothache and of B's stomach-ache with this noise only 
means that the former is sensibly contemporary with a 
certain auditory sensum sensed by A, and that the latter 
is sensibly contemporary with a different auditory sensum 
sensed by B. It is true that these two auditory sensa 
are both members of a group of sensa which are so con- 
nected with each other that the whole is called one noise. 
But it is by no means obvious that this rather indirect 
relation between A's toothache and B's stomach-ache will 
have the kind of properties that we demand of simul- 
taneity. The same difficulty arises if we suppose that 
there is literally only one auditory sensum, which is 
sensed by both A and B, and that the relation of 
sensible simultaneity is triadic. The fact that A's 
toothache is contemporary with a certain auditory 
sensum with respect to A's sense-history, and that 
B's stomach-ache is contemporary with the same 
auditory sensum with respect to B's sense-history, does 
indeed constitute a relation between the toothache and 
the stomach-ache. But there seems no particular reason 
to expect that this relation will have the kind of pro- 
perties that we demand of simultaneity. 

Let us begin by imagining a set of observers who 
tried to determine neutral simultaneity entirely by 
sound. We need, not suppose them to be blind, but 
we will suppose that they have no means of producing 
flashes of light either by igniting combustible things 
or by opening and shutting opaque shutters. A 
number of them hear what they call the same noise. 
They all sense short, outstanding auditory sensa. 
These are very similar in quality and are connected 
with a common centre in the way described in the last 



DATE AND DURATION 371 

chapter. They agree that any pair of sensa belonging 
to the sense-histories of different observers shall count 
as neutrally simultaneous provided that one is sensibly 
contemporary with one member of such a group of 
auditory sensa and that the other is sensibly con- 
temporary with one member of the same group of 
auditory sensa. What properties will neutral simul- 
taneity, so determined, possess? 

In the first place, it will be necessary slightly to 
extend this way of determining neutral simultaneity, 
so as to deal with the various auditory sensa that 
constitute a single noise. If we are going to allow 
them to have any neutral temporal relations to each 
other, we must suppose that they are all neutrally con- 
temporary, or we shall get into difficulties. For suppose 
that any two sensa, s\ and j 2 , belonging to different 
sense-histories, were neutrally contemporary, as deter- 
mined by the present method. This will mean that s t 
is sensibly contemporary with one auditory sensum and 
that s. 2 is sensibly contemporary with another auditory 
sensum, and that these two auditory sensa belong to 
a single noise. Now, unless we hold that the two 
auditory sensa in question are neutrally contemporary 
with each other, we shall have to admit that two 
neutrally contemporary sensa can be respectively 
sensibly simultaneous with two auditory sensa which 
are neutrally successive to each other. This does not 
accord with the view of neutral temporal relations as 
a consistent extension of the sensible temporal relations 
that hold between sensa in the same sense-history. We 
must therefore determine neutral simultaneity, on the 
present method, as follows: Two sensa in different 
sense-histories are neutrally contemporary if (a) they 
are two auditory sensa belonging to the same noise ; 
or (b) they are respectively sensibly simultaneous with 
two auditory sensa which belong to the same noise. 
Would such a mode of determination be satisfactory? 

Let A and B be two observers at a considerable 



372 SCIENTIFIC THOUGHT 

distance apart, and let there be a bell near A and 
another bell near B. Let the strokes of both bells be 
audible to both observers. We will call them " A's 
bell "and " B's bell" respectively. Suppose that A's 
bell ring's and that B hears the noise. It may happen 
that B's bell rings at such a date that he hears its stroke 
at the same time as he hears the stroke of A's bell. If 
so, A will hear this stroke of B's bell sensibly later than 
the stroke of his own bell. Call A's sensum of the 
stroke of A's bell a A) A's sensum of the stroke of B's 
bell a in B's sensum of the stroke of A's bell b A , and 
B's sensum of the stroke of B's bell b B . Then by 
definition we have : 

(i) a A is neutrally contemporary with b A ; 

(2) a,, is neutrally contemporary with b„ ; 
and, by the terms of the experiment, we have 

(3) b n is sensibly contemporary with b A . 
Under these circumstances we should find that 

(4) a B is sensibly later than a A . 

Now, if neutral simultaneity be just an extended 
application of sensible simultaneity, we should expect 
that (2) and (3) would together imply that a B is neutrally 
contemporary with b A . Combining this with (1), we 
should expect to find that a A and a B were sensibly 
simultaneous. But this contradicts the fact stated in 
(4). In fact, if we determine neutral simultaneity in 
this way, we shall find that two sensa in the same 
sense-history can be neutrally simultaneous respectively 
with two sensa in another sense-history, which are 
sensibly simultaneous with each other ; and yet the 
first pair of sensa are not sensibly simultaneous with 
each other, but are sensibly successive. Thus neutral 
simultaneity, determined by this method, cannot be a 
mere extension of sensible simultaneity. This can 
only be got over if we admit that, when two people 
" hear the same noise," the auditory sensum of the one 
who is nearer the source is neutrally earlier than that 



DATE AND DURATION 373 

of the one who is further away from it. But, as soon 
as we admit this, the purely auditory determination of 
neutral simultaneity has been given up ; for we cannot 
determine in purely auditory terms the neutral temporal 
relations between auditory sensa which belong to "the 
same noise." We have to introduce spatial measure- 
ment, and the notion of influences travelling out from 
sources with a finite velocity. The intimate linkage of 
Space and Time becomes evident here, as in so many 
places. 

So far then we see that, if observers tried to determine 
neutral temporal relations by sound alone, they would 
be forced to the view that what they call the same noise 
is a set of auditory sensa of different neutral dates ; 
these dates depending on the distance between the 
observer who senses a sensum of the group and the 
source of the noise. This fact was early recognised 
about sound for several reasons, (i) Sound travels so 
slowly that the difficulties pointed out above are quite 
obvious to ordinary observers at reasonable distances 
apart, and provided with no delicate apparatus, (ii) 
Sounds, as we have seen, are not thought of as confined 
to a central volume, but as being in all the space that 
surrounds their source. Each observer is thought of 
as sensing the particular part of this physical field of 
sound which is "where he is at the moment." It is 
thus natural enough to think of this physical field as 
travelling out from the centre and reaching different 
observers at different times. (iii) Again, the phen- 
omenon of echoes makes the notion of the velocity of 
sound pretty obvious to anyone. An echo is quali- 
tatively very much like the original sound with which 
it is obviously connected. But it is separated from it, 
as a rule, by a distinct sensible interval. This naturally 
suggests something travelling from the observer to a 
wall (for instance), and then travelling back to him. 
(iv) Lastly, we are not like the observers in our example. 
We can produce flashes of light by various means at 



374 SCIENTIFIC THOUGHT 

will. Now, if a number of observers count two sensa 
as neutrally contemporary with each other, when each 
is sensibly contemporary with the same flash of light 
that they all see, they will not, in ordinary life, get into 
difficulties which arise for observers who try to define 
neutral simultaneity by means of sound. But, of course, 
if they do this, they will be obliged to recognise that«the 
various auditory sensa which they sense when they say 
that they all hear the same noise are not neutrally con- 
temporary. It is, in fact, by a combination of ight- 
signals and sound-signals that the velocity of sound is 
generally measured. 

The next step that naturally suggests itself is to 
determine the neutral simultaneity between two sensa 
in different sense-histories, as the relation which holds 
between the two when each is sensibly contemporary 
with some sensum of the group which constitutes a 
single flash of light. If we adopt this method, we shall 
have to begin by extending it slightly in the same 
direction, and for the same reasons as we extended the 
auditory method of determining neutral simultaneity. 
That is, we shall have to assume that two visual sensa 
belonging to the same flash are neutrally contemporary, 
or we shall get into difficulties. We may therefore give 
the following as the visual definition of neutral simul- 
taneity : Two sensa, belonging to different sense- 
histories, are neutrally contemporary, if (i) they are two 
visual sensa of a group which constitutes a single flash ; 
or (ii) are respectively sensibly simultaneous with two 
visual sensa which belong to such a group. 

There is, I think, no doubt that this is the way of 
determining neutral simultaneity, with which we all 
work in practice, except in extremely delicate scientific 
investigations or in cases where distances of astronomical 
order of magnitude are under discussion. Nevertheless, 
we all know that no scientist would accept it as ultimately 
satisfactory. He would point to the facts which are 
alleged to prove that light travels with a finite velocity 



DATE AND DURATION 375 

as a conclusive objection to the definition. The asser- 
tion that light travels with a finite velocity implies, 
inter alia, that there is an extremely important sense in 
which the various sensa of observers in different places 
who see the same flash are not simultaneous but succes- 
sive. The above definition of neutral simultaneity is 
therefore unsatisfactory, because it leads us to call sensa 
simultaneous, which are in some very important, but as 
yet undefined sense, successive. 

Let us then consider this definition and the facts that 
are held to render it inappropriate. In the first place, 
there are two things to be said in its favour: It is not 
circular, and it does not directly conflict with our 
judgments about sensible temporal relations, as the 
attempted auditory definition did. It would, of course, 
be circular if we could not define what we mean by " the 
same flash " without introducing temporal relations 
between sensa in different sense-histories. But we can 
define "the same flash" without this. A number of 
observers may be said to see the same flash when the 
following conditions are fulfilled : (i) Each is aware of 
a single outstanding visual sensum of very short dura- 
tion, (ii) These sensa are all qualitatively very much 
alike, (iii) They are all optically compresent at a 
common centre, in the sense defined in the last chapter. 
(The first condition seems to be enough to secure that 
we are all dealing with a single flash, and that different 
observers are not seeing similar but successive flashes. 
For, if successive flashes were being sent out, some at 
least of the observers would sense two or more qualita- 
tively similar sensa which were sensibly successive.) 

Again, there is nothing in our light-experiences to 
correspond to the case that we adduced of two distant 
observers hearing two bells, and one of them finding 
his auditory sensa sensibly contemporary, and the other 
finding the auditory sensa belonging to the two noises 
sensibly successive. We can only deal with pairs of 
observers separated by distances of a few miles ; and 



3/0 SCIENTIFIC THOUGHT 

for such distances there is no conflict between sensible 
temporal relations and neutral temporal relations as 
determined by light-signals. 

It is therefore possible to determine neutral simul- 
taneity visually without committing a circle and without 
conflict with any judgments of sensible simultaneity 
that we can make. The conflict is with the facts that 
prove that light has a finite velocity. What are these 
facts and what do they prove? When people say that 
light travels with a finite velocity they mean that some 
change moves from a distant centre to the observer and 
that his visual sensum begins as soon as this change 
reaches him and goes on till it ceases to reach him. 
By a single flash they think of a single event at the 
source (e.g., the opening of a shutter) and the change 
that travels out from this. Let us consider the facts 
and arguments which are supposed to prove this. We 
may take three typical examples. These are Fizeau's 
experiment, with a rotating cogwheel and a mirror ; 
Romer's argument from the times that apparently 
elapse between successive eclipses of a satellite of 
Jupiter ; and Bradley's argument from the shift in the 
apparent positions of the fixed stars. These three 
arguments are placed in order of simplicity. The first 
keeps the source and the observer relatively at rest for 
the whole time, and literally consists in producing 
" light-echoes," and showing that there is a time-lapse 
between them and the flash of which they are the 
"echoes." The second depends on the fact that an 
observer and a certain source are at different distances 
apart at different times of year. The last depends 
on the relative velocity of source and observer, and 
belongs rather to the subject of the next chapter than 
to the limits within which we are at present confining 
ourselves. I must state as shortly as possible the facts 
on which these arguments are based, so that we may 
be able to see what exactly they assume in order to 
reach their conclusion. 



DATE AND DURATION 377 

(i) Fizeaiis Experiment. — Light is sent through a hole, 
in front of which is a cogwheel. When one of the teeth 
of the wheel is in front of the gap, light cannot pass ; 
otherwise it can. The light travels some considerable 
distance, and is then reflected back along its old course, 
and the image is viewed from behind the cogwheel. If 
the passage of the light between the source and the 
mirror and back again be instantaneous, the image will 
be visible, no matter how fast the cogwheel revolves ; 
for if no time has elapsed, the cogwheel cannot have 
moved any distance since the flash left it and before the 
light returned to it. The gap cannot, therefore, have 
become shut, in the meanwhile, by the rotation of the 
cogwheel. But if any finite time elapses between the 
departure and the return of the light, it must be possible 
to cause the original gap to be replaced by the next 
tooth by the time that the light returns, provided that 
the cogwheel has moved fast enough. In that case no 
image will be seen. If the speed of the wheel be now 
increased enough, the image ought again to be seen, 
since the wheel will have turned so far in the time taken 
by the passage of the light that the next gap will be in 
position to admit the reflected beam when it returns. It 
is found that the image can be made to disappear by 
rotating the wheel fast enough, that it can be made to 
reappear by rotating the wheel faster, and that the 
wheel needs to be rotated faster and faster the nearer 
the mirror is to the source, in order to make the image 
disappear. All these facts are what we should expect if 
the reflected sensum depends on the passage of some- 
thing with finite velocity from source to mirror, and from 
mirror to observer, and begins when this something 
reaches the observer's eye, and does not end till it ceases 
to reach his eye. 

It is clear that the result of the experiment does not 
bear directly on the question of the neutral temporal 
relations between two sensa of observers who see the 
same flash. For we are actually dealing with a single 

2 B 



;-s SCIENTIFIC THOUGHT 

sensum (the reflected image) of a single observer. The 
connexion, however, is this: It is argued that the result 
of the experiment shows that any visual sensum begins 
when something that has started from a source reaches 
the observer, and that this something takes a finite 
time to travel. The various visual sensa that together 
constitute a single flash are simply those sensa which 
begin to be sensed by various observers when something 
that left a source at a certain moment reaches them. If 
the observers are at different distances from the source, 
their various sensa will be correlated with different stages 
in this process of transmission. Hence, there is an im- 
portant sense in which what is called one flash is a 
group of successive sensa. It would, therefore, be incon- 
venient to determine neutral simultaneity in such a way 
that all the sensa in a single flash would count as 
neutrally simultaneous. 

Thus a single flash of light comes to be treated as 
a set of successive sensa, because different sensa in the 
set are held to be correlated with different stages in a 
certain process of transmission from the source through 
the surrounding Space. 

(ii) Router's Argument. — The earth and the planet 
Jupiter revolve about the sun in approximately the 
same plane and approximately in circles. Jupiter has 
a much larger orbit than the earth, and takes much 
longer to complete it. Thus, at certain times, the two 
are in the position shown below, 

S/ E/ J/ 



and at other times they are in the position shown below. 
The first is called a conjunction and the second an 
opposition. 

Eg S2 J e 

Jupiter has satellites which revolve round it as the 
moon does round the earth. When a satellite moves 



DATE AND DURATION 379 

into the shadow on the far side of Jupiter from the sun, 
it is eclipsed, and becomes invisible to us. Now it 
is found that the number of eclipses that take place 
between a conjunction and the next opposition is the 
same as the number that take place between an 
opposition and the next conjunction. But there is 
quite a marked difference (about 33 minutes) between 
the total times that elapse from the first to the last of 
these eclipses in the two cases. 

Now the eclipse of a satellite is comparable to the 
shutting of a shutter. The movement of the earth 
ensures that the observer on it is at different distances 
from this shutter at different times of year. He is 
nearer to it at the time of conjunction than he is at the 
time of opposition by the whole diameter of the earth's 
orbit. If we suppose that the visual sensum ceases to 
persist as soon as the shutter is closed, we can only 
explain the facts by supposing a periodic change in the 
time of revolution of the satellite. This would be 
extremely difficult to fit in with the facts that we believe 
about the laws of mechanics and the forces acting on 
the satellites. If, however, we assume that the visual 
sense-object persists after the shutter is closed, for a 
time which increases with the distance between the 
observer and the shutter, we can fully account for the 
divergence of 33 minutes, without needing to suppose 
that the periodic time of the satellite changes as Jupiter 
progresses in its orbit. The time-lapse between an 
eclipse and the cessation of the corresponding visual 
sense-object, which is necessary to account for the 
33 minutes' discrepancy, can easily be calculated ; 
and, if the radius of the earth's orbit be known, the 
velocity of light can be determined. It is found to be 
approximately the same as that deduced from Fizeau's 
experiment. Here there is no complication about 
mirror-images ; we simply have a source and an 
observer which are at different distances apart at 
different times of year. 



3 8o SCIENTIFIC THOUGHT 

Once again the result of the argument does not bear 
directly on the question whether it is appropriate to 
determine neutral simultaneity in such a way that the 
various sensa which constitute a single flash of light 
shall be all neutrally contemporary. We are not deal- 
ing with two observers seeing a single flash ; on the 
contrary, we are dealing with a single observer who sees 
three different flashes (if an eclipse may by courtesy be 
called a flash) at widely different dates in his history. 
There is, however, an indirect connexion. The 
argument is, that you must either abandon certain very 
well-established laws of motion, or assume that the 
occurrence of visual sensa depends on the motion of 
something from the source to the observer. The visual 
sense-object lasts so long as any of this something 
meets the eye, no matter what may have happened 
to the source in the meanwhile. On this assumption, 
you can account for the facts without abandoning the 
familiar laws of motion. But, as before, if you make 
this assumption, you must suppose that what we 
call a single flash is a group of sensa correlated with 
various stages in the process of transmission of this 
something. And, on that supposition, it is unsatis- 
factory to determine neutral simultaneity by a method 
which presupposes that the various sensa which belong 
to a single flash are neutrally simultaneous. 

(iii) The Aberration Argument. — It is found that, if 
the fixed stars be observed night after night, their 
apparent positions undergo a periodic change. Each 
describes a closed curve in the course of a year. Now 
the apparent position of a star is, of course, the optical 
place of the visual sensum which is an appearance to 
us of the star. The direction of this place will be 
determined by the direction in which we have to point 
our telescope in order to bring this visual sensum into 
the middle of our visual field. Now, of course, we might 
suppose that all the fixed stars are describing closed 
curves in the time which it takes the earth to move 



DATE AND DURATION 



381 



round the sun. But this would be a most extraordinary 
state of affairs, and it is not one that we readily accept. 
Now it happens that the facts can be quite easily ex- 
plained on the same assumption as before about light. 

Let S be a star, and let the line OO represent the 
course of a moving- observer with a telescope. In the 
first figure we will suppose that he is pointing his 
telescope at the physical place of the star. At a certain 
moment let his position be O, and let light from the 
star have reached l v a point in the middle of the far 
end of his telescope. At a slightly later moment let 
his position be 2 . The light will then have got to / 2 



*s 



//„ 



°, °e 



ftp/ 




O, q, 3 o 4 



/%& 



in its original straight line, and will no longer be passing 
down his telescope at all. It is clear then that v if the 
moving observer points his telescope at the physical 
place of the star, he will see no star at all. Suppose 
now that he tilts his telescope forward by an appropriate 
amount in the direction of his movement. Let O v 2 , 
3 , 4 represent four successive positions of the tele- 
scope, and / 1} /.,, / 3 , / 4 , the four corresponding positions 
in the course of the light which is travelling from the 
star. It is clear from the figure that the light will pass 
down the telescope and meet his eye, provided that he 
slopes the telescope forward at an angle to his course, 
whose tangent is cjv, where c is the velocity of light 
and v is that of the observer. Now an observer on the 
earth is moving with it in the course of a year round 
a closed curve — the earth's orbit — with considerable 



382 SCIENTIFIC THOUGHT 

velocity. It is thus easy to understand that, although 
the physical place of a star remains constant, the optical 
places of the sensa by which the star appears to us will 
vary in the course of the year, and will repeat their 
variations over and over again in that period. From 
the speed of the earth in its orbit and the amount of the 
aberration of a star, it is easy to calculate the velocity 
of light. It is once more found to be the same, within 
the limits of experimental error, as that found by Romer's 
argument and by Fizeau's method. 

This argument is of particular interest to us, not 
merely in connexion with the question of neutral dating, 
but also as reinforcing the distinction that has already 
been drawn on other grounds between physically and 
optically occupied places. We introduced that dis- 
tinction originally because of facts which are found 
to arise when the medium surrounding an observer is 
non-homogeneous. We now see that the optical place 
of a visual appearance and the physical place of its 
source may be different, even when the medium is 
homogeneous, if the source and the observer be in 
relative motion. 

Let us now consider what these arguments have to 
teach us. (i) We see that three extremely different 
lines of argument tend to the conclusion that visual 
sensa are connected with something that is transmitted 
from a source to an observer with a finite velocity. 
And they all lead to approximately the same numerical 
value for this velocity. Now, in each separate case, 
there is no doubt that the facts could be explained 
without taking this particular view about light, provided 
we made some other assumption. But, in the first place, 
each of these assumptions would conflict with some law 
of Nature which has been well established in other cases. 
And, in the second place, these assumptions would be 
quite disconnected with each other ; each would be an 
independent piece of "cooking." On the other hand, 
a single assumption as to the nature of light explains 



DATE AND DURATION 383 

all these very different facts, and reconciles them with 
the established natural laws with which they would 
otherwise conflict. Thus the hypothesis in question is 
established about as solidly as any scientific hypothesis 
can be. The simple-minded scientist may think that I 
have needlessly laboured this point ; but I have deliber- 
ately insisted on it, because I know that some eminent 
"realist" philosophers, finding- that the finite velocity 
of lierht "stains the white radiance" of their theories of 
perception, are inclined in private to deny it, or at least 
to "damn with faint praise, assent with civil leer." 

(ii) We notice that the finite velocity of light is 
never proved directly ; but always by the argument that, 
unless it be true, certain observable facts will not be 
reconcilable with well verified laws about the motion of 
matter. The only direct way to verify the proposition 
would be for two observers to stand at a distance apart, 
see the same flash of light, and find that their respective 
visual sensa were not contemporary. Now there is both 
a practical and a theoretical difficulty about any such 
experiment. The theoretical difficulty is this. The 
two observers would need to be provided with some 
means of marking, and thus comparing, the dates of 
their respective sensa. Suppose that the means adopted 
were two stop-watches. This would be useless, unless 
they had reason to suppose that the two watches agreed 
in their zero points and were going at the same rate. 
They might, of course, set the watches in synchronism 
when they are both together ; but what guarantee have 
they that they will remain in synchronism when one 
has been carried a long distance away? To assume 
that they do, is to make an assumption which is con- 
tradicted by quite gross experiences. To test their 
synchronism after they have been separated, can only 
be done by means of light or electrical signals ; and 
there is obviously a circle in setting two watches by light- 
signals and then using them to test whether two visual 
sensa belonging to the same flash are contemporary or 



;S., SCIENTIFIC THOUGHT 

successive. The only way out of this difficulty would be 
if both observers could observe a certain pair of flashes, 
and if one of them should find that his two visual sensa 
were sensibly simultaneous, and the other should And 
that his two visual sensa were sensibly successive. But, 
in practice, this cannot be done, because of the great 
velocity of light and the fact that the only observers 
who can compare notes with each other are confined to 
the earth's surface. Thus it seems clear to me that the 
neutral simultaneity of visual sensa belonging to the 
same flash is denied wholly and solely because it con- 
flicts with another system of dating which depends on 
certain alleged laws of motion. 

(iii) It is evident that if we accept the view that the 
various sensa belongingto the same flash are not neutrally 
simultaneous, we shall have to admit either that two 
sensa which seem simultaneous may not really be so, or 
that two sensa which are neutrally successive may be 
sensibly simultaneous. The latter alternative would 
prevent neutral temporal relations from being consistent 
extensions of sensible temporal relations, and we shall 
therefore not take it, unless we are forced to do so. Now 
there is nothing in the Sensum theory of sensible appear- 
ance to force us to the second alternative. A sensum 
belonging to a certain flash and a sensum belonging 
to its reflected flash, seem to us to be sensibly simul- 
taneous. If the physical theory of light be accepted, the 
latter is neutrally a little later than the former. But the 
sensible simultaneity of two sensa only means that each 
exactly overlaps the other in their common sensible 
field. Now the notion of exactness ahvays involves a 
negative factor ; it means that no part of the one sensum 
sticks out beyond the end of the other. And we saw, 
when dealing with the general theory of sensa, that 
there is no reason why negative judgments about sensa 
should be infallible. Thus, two sensa may often seem 
to be sensibly quite simultaneous, when really one begins 
a little later and ends a little later than the other. 



DATE AND DURATION 385 

We see then that the question of a neutral dating of 
events in different sense-histories leads inevitably to the 
question of motion, whether it be the transmission of 
those changes which are connected with sound and light, 
or the motion of ordinary physical bodies through Space. 
Thus the separation of Space and Time, with which we 
started, which has been wearing thinner and thinner as 
the argument has advanced, has now broken down 
altogether. This does not mean that there is no differ- 
ence between temporal and spatial relations ; but it does 
mean that it is impossible to apply the concept of a 
single Space to Nature without referring through Motion 
to Time, and that it is equally impossible to date the 
events of Nature in a single Time without referring 
through Motion to Space. And this, it will be noted, 
is one of the characteristic features of the Theory of 
Relativity. 

To sum up : If I want to determine neutral temporal 
relations between an event which is in my sense-history 
but not in yours, and an event which is in your sense- 
history but not in mine, the only possible way seems to 
be to find something which is common to the sense- 
histories of both of us, and to determine the neutral 
temporal relations between the two "private'" events 
by means of their respective sensible relations to this 
"public" event. At first sight this seems perfectly 
plain sailing, since there are events, like noises and 
flashes, which are admittedly "public" in a way in 
which headaches and toothaches are not. If it were 
really true that, when we say that we "hear the same 
noise " or " see the same flash," there is a single auditory 
or visual sensum in all our sense-histories, it would be 
easy to determine neutral simultaneity in this way. 
And, since it would have the same logical properties 
as sensible simultaneity, it would be reasonable to hold 
that it is really the same relation, and that the pro- 
posed method of determination is simply a test and not 
a definition of a new kind of relation. But, although it 



;>N<> SCIENTIFIC THOUGHT 

is not logically impossible that a single sensum might be 
in a number of different sense-histories, eloser observa- 
tion of the facts makes it almost impossible to believe that 
a noise or a Hash really is a single sensum. Moreover, 
it seems impossible to hold that it is even a group of 
contemporary sensa. Thus, such methods of determina- 
tion, though practically useful for most purposes, owing 
to the considerable velocity of sounds and the very great 
velocity of light, are not theoretically satisfactory. 

Temporal Characteristics of Physical Events. — The 
further development of this subject must be left to the 
next two chapters, but it is possible in the meanwhile to 
say something about the durations and dates of physical 
objects and events. A single flash of light or a single 
noise may be called a. perceptible physical event. When a 
man says that he sees a flash of light, he does not mean 
either {a) merely that he senses a certain visual sensum, 
or (/;) that he sees the movement, e.g., of an electron at 
the source which is responsible for the flash. For (a) 
he admits that other people can see the same flash, 
whereas we have found reason to think that two people 
who see the same flash do not sense the same visual 
sensum. And (d), so far from admitting that he saw 
the movement of the electron, he would say that this 
is invisible, and that he only believes it to have taken 
place on the authority of a scientific theory which he 
does not himself understand. Thus, to see a flash means 
something more than to sense a visual sensum, and 
something, partly more and partly less, than to perceive 
the motion of an electron. An angel might perceive the 
motion of the electron and see no flash, whilst a man 
sees the flash and does not perceive the motion of the 
electron. Seeing the flash involves sensing the sensum 
and also something more. It involves the excitement 
of traces connected with similar experiences in the past. 
These may or may not actually produce the explicit 
perceptual judgment that other observers are sensing 



DATE AND DURATION 387 

similar sensa which are optically in the same place, 
and that some movement has happened in that place. 
But, whether these judgments actually arise or not, the 
observer will tend to behave in a way in which it would 
be reasonable to behave if he had explicitly made these 
judgments. If such judgments be not true in a particular 
case, we say that the observer is mistaken in his belief 
that he has seen a flash of light, even though he has 
sensed a short, bright visual sensum. Thus a man 
who "sees stars," because he has hit his head against 
a post, senses a bright visual sensum, but would be 
deceiving himself and others if he said that he had seen 
a flash of light. 

A perceptible physical event, like a flash or a noise, 
may therefore be defined as a certain group of sensa 
having certain similarities to each other and certain 
neutral spatial relations. Nearly always they will be, 
in some sense, compresent at a certain place in Space. 
We have seen that, as a rule, they will not all be 
neutrally simultaneous, but that their neutral dates will 
depend upon the positions of the various observers who 
sense them. To perceive such a perceptible event 
means (a) to sense a sensum belonging to such a group ; 
and (b), in consequence of the traces left by similar 
experiences in the past, either explicitly to judge that it 
is a member of such a group, or to act as it would 
be appropriate to act if one had explicitly made this 
judgment. 

(a) Dates of Perceptible Physical Events. — Now, since 
a perceptible physical event consists of a number of 
sensa of different neutral dates, it is obvious that the 
question: "What is the date of a certain perceptible 
physical event?" can only be answered in a more or 
less Pickwickian manner. To give any answer to it 
we must notice the two following facts : The neutral 
dates of the sensa in such a group are none of them 
earlier than the date of a certain physical movement, 
such as the opening of a shutter. If we include in the 



,ss SCIENTIFIC THOUGHT 

flash not only actual sensa but the sensa of possible 
observers, the dates of the various sensa would approach 
the date of this movement at the source as their lower 
limit. This date might, therefore, be defined as "the 
date at which the perceptible physical event begins.''' 
The second point to notice is that, where a group of 
sensa have later and later neutral dates as the observer 
is further and further from the source, the sensa in 
question are fainter and fainter. Thus the dates of the 
sensa which constitute a single noise approach a limit 
where we are dealing with an observer so remote that 
he can only just sense a sensum of the group. This 
does not give an absolutely sharp date which may be 
taken as "the date at which the perceptible physical 
event ends" because the question of the different acute- 
ness of different observers comes in. Still it is clear 
that in this way we could define approximately the 
date at which such an event ends. The duration of a 
perceptible physical event may then be defined as the 
time that elapses between its beginning and its end. 

(if) Relative Dates of Act of Perceiving and Event 
Perceived. — Next we see that, although the beginning 
of an act of sensing may be regarded as contemporary 
with the end of the sensible field that is sensed through- 
out the whole of it, there is not the same simple relation 
between the date of an act of perceiving and the date of 
the physical event perceived by it. This is obvious, 
since there is nothing that can appropriately be called 
the date of a perceptible physical event. We may 
reasonably identify the date of an act of perceiving 
with that of the act of sensing on which it is based. 
So that, in general, all we can say is that an act of 
perceiving is later than the beginning and earlier 
than the end of the physical event that it perceives. 
It is very common to suppose that an act of perceiving 
must be contemporary with the event perceived. This 
is, of course, a mere mistake, due to a confusion 
between an act of sensing, whose object is a sensum, 



DATE AND DURATION 389 

and an act of perceiving, whose object is a physical 
event. 

There is one more confusion to be pointed out 
before we leave this subject. It might be said : " Does 
not a physical event, such as a flash of light, persist 
for ever once it has started?" I answer that the move- 
ment that is transmitted from the source and is corre- 
lated with the various visual sensa of the group, may 
very well go on for ever. But this movement, of what- 
ever nature it may be, is not the flash of light. A flash 
of light is a perceptible object ; the movement in the 
ether is not perceptible — by us at any rate. It is merely 
silly to say that a certain perceptible event lasts for ever, 
because a certain imperceptible event, with which it is 
closely connected, does so. 

(c) Scientific Events. — This naturally brings us to 
the question of the dates and durations of imperceptible 
physical events. We know that perceptible physical 
events, such as flashes of light, are supposed to be 
intimately connected with movements of electrons and 
changes in the ether which we cannot perceive. These 
are much more important theoretically to the scientist 
than perceptible events. The epistemological relation 
between the two is the following: It is by observing 
and noting the relations between perceptible events 
that we infer the existence of these imperceptible events, 
which, following Whitehead, I will call scientific events. 
Instead of stating the laws of Nature as direct relations 
between perceptible events, we analyse these relations 
into the relative product of two different kinds of rela- 
tions, viz., (a) those of scientific events to each other, and 
(b) those of scientific events to perceptible events. This 
process seems to be indispensable, if we are to deal 
satisfactorily with Nature at all. The relations between 
perceptible events are very complex, and few simple 
and invariable laws can be stated about them. On the 
other hand, the relations of imperceptible events to each 
other and to perc'eptible events are reasonably simple, 



390 SCIENTIFIC THOUGHT 

and laws of very wide range can be stated about them. 
We can then use these hypothetical laws to predict 
what perceptible events will be perceived under assigned 
perceptible conditions. In so far as the predicted 
events actually take place, our hypothesis about imper- 
ceptible events and their laws is strengthened. It is 
very easy for a scientist, who constantly deals with 
scientific events and sees their great practical and 
theoretical importance, to fall into the mistake of 
supposing that they alone are " real." This is a great 
error. The actual position is this : The existence of 
sensa is absolutely certain, and those positive sensible 
properties which they seem to have they certainly do 
have, if the Sensum theory be accepted at all. The 
existence of some perceptible physical events is prac- 
tically certain, if we are prepared to accept the existence 
of other observers and to believe what they tell us 
about their sensa. But, in any particular case, an 
observer who thinks that he perceives a certain physical 
event may be mistaken. For he may sense a sensum 
of a certain kind and mistakenly suppose that it is one 
of a group of connected sensa, when really it is "wild" 
and isolated. Lastly, since imperceptible physical 
events are only assumed in order to fill the gaps 
between the various sensa of single perceptible events 
and to connect different perceptible events with each 
other, it is clear that our certainty that there are such 
and such imperceptible events cannot logically exceed 
our certainty that there are such and such percep- 
tible ones. 

There is a connecting link between purely percep- 
tible events, like flashes of light, and purely scientific 
events, like the movements of electrons and ether-waves. 
This link is the unperceived parts of perceptible events. 
We defined a flash as a certain group of visual sensa, 
and we said that its duration was the time that elapses 
between the earliest and the latest of these sensa. But, 
it must be admitted that the really important point about 



DATE AND DURATION 391 

perceptible events is not the actual sensa in the group, 
but the possible sensa. Actually only a few of the 
sensa in such groups are sensed by anyone, and it may 
quite well happen that only one of them is sensed. The 
perceptual judgment does not assert that other sensa of 
the group are sensed, but only that they would be by 
any observer sufficiently like ourselves placed in any 
suitable position. Thus the cash value of the statement 
that perceptible events persist, even when no one happens 
to sense any sensum of the group, is that whenever a 
suitable observer is present at any position in a certain 
spatio-temporal region, he will sense a member of the 
group. We are not content with this merely hypo- 
thetical assertion. We assume that if any observer at 
any position of a certain spatio-temporal region will 
sense a sensum of a certain group, this must be because 
something independent of all observers is going on at 
all positions in this region. This assumption rests 
partly on our passion for spatio-temporal continuity. 
When there is a close connexion between events in 
different places and of different dates, we feel that the 
gaps between them must be filled in somehow. And 
this conviction is strongly reinforced if we find that 
any observer who takes up his position at random 
within the spatio-temporal region in question equally 
senses a member of the group. 

We must notice, moreover, that the presence of an 
observer is found to be irrelevant to most chains of 
physical causation. If I put a kettle on the fire and 
watch both, the perceptible event of the fire burning 
is followed after a certain time by the perceptible event 
of the kettle boiling. If I and all other observers go 
away for a time and then return, we find that the kettle 
has boiled after the same lapse of time. These and 
millions of other experiences show that the gaps 
between the sensa belonging to a perceptible event 
are filled by something that produces just the same 
effects as if we were present. Thus, even at the level 



392 SCIENTIFIC THOUGHT 

of common-sense, a perceptible physical event is thought 
of as a group of sensa connected by events that go on 
in the absence of observers. Common-sense is very 
vague as to the nature of these unperceived parts of 
perceptible events. I think that it generally supposes 
in a rather half-hearted way that they are of the same 
nature as the parts that are actually sensed. How far 
such a view can be maintained cannot be decided until 
we have dealt with the physiological conditions of sensa. 
But, at any rate, we can say that it seems essential to 
suppose that something bridges these gaps ; and science 
professes to determine more and more accurately the 
nature of this something. Whether it has the properties 
of sensa or not, it certainly has the properties of scientific 
events, subject of course to the possibility of scientific 
theories being wrong on points of detail. 

In the last chapter I said that scientific objects are 
conceived to have shapes and to occupy places in the 
movement-continuum in the same literal way in which 
visual sensa are immediately sensed to have shapes and 
to occupy sensible places in their fields. In fact, the 
concepts of what I will now call Scientific Space and 
scientific physical objects are constructed together in 
an inseparable union. They are constructed on the 
analogy of sensa and their fields out of data derived 
from the sense-experiences of many observers through 
various senses and at various times. Exactly similar 
remarks apply, mutatis mutandis, to the concepts of 
what I will call Scientific Time and scientific events. 
Scientific Time is conceived by analogy with a sense- 
history ; scientific events are conceived to have dates in 
Scientific Time as sensa have dates in the sense-history 
of the observer who senses them ; scientific objects are 
conceived to have duration in Scientific Time as sense- 
objects have duration in a sense-history. There is one 
difference, however. For reasons already stated, it is 
impossible that sensa should literally occupy places in 
scientific space, though it may not, of course, be im- 



DATE AND DURATION 393 

possible to construct a space-like whole of more than 
three dimensions, in which sensa of all kinds, and 
scientific objects, literally have places. If so, I suppose 
that Scientific Space would be one kind of section of 
such a quasi-space, and e.g., a visual field would be 
another kind of section of the same quasi-space. But, 
if such a construction can be made at all, I, at any rate, 
am not capable of doing the trick. On the other hand, 
it is not obviously impossible that sensa should literally 
have dates and durations in the same Scientific Time as 
scientific events ; for, as we have seen, temporal relations 
are much more pervasive than spatial relations. The 
scientific dates of sensa would seem to be the dates at 
which certain scientific events happen in the brain of 
the observer who senses these sensa. Unless there be 
some positive inconsistency between the temporal rela- 
tions of such scientific events and the sensible temporal 
relations of the corresponding sensa, there seems no 
reason to reject the naive view that the temporal re- 
lations between sensa in our own sense-history, with 
which we become acquainted through sensation and 
memory, are literally the same as the temporal relations 
between the corresponding scientific events in our brains. 
Whether this view can be held, is a question which must 
be reserved for a later chapter. 

Duration of Physical Objects. — We have now said 
all that can be said with profit about the dates and 
durations of physical events before dealing with motion 
and the union of Space with Time. It remains to say 
something about the durations of physical objects or 
" things." A thing, as we have seen, is simply a long 
event, throughout the course of which there is either 
qualitative similarity or continuous qualitative change, 
together with a characteristic spatio-temporal unity. 
A sense-object, as defined earlier in the chapter, is an 
example of such a long event ; though, for reasons which 
will appear in a moment, it would hardly be called a 

2 c 



394 SCIENTIFIC THOUGHT 

" thing," und it is certainly not " physical." Thus the 
dividing line between events and thing's cannot be 
very sharply drawn in theory. Nevertheless, we can 
draw a rough practical distinction, and it is useful to 
do so, in order not to depart too far from common 
speech. 

(a) Perceptual Objects. — A flash of light would be 
called a perceptual event, but not a perceptual thing or 
object. This is because each person who sees the flash 
senses a single short sensum, and not a series of sensa 
in successive fields which join up with each other to 
form a sense-object of decent duration. This is true, 
although, as we have seen, the flash itself as a per- 
ceptible event has considerable duration, which may 
extend to thousands of years. Thus one point about a 
perceptible object is that it must be capable of being 
perceived for a long time by the same observer. And 
this means that its appearance to him must be not 
merely a sensum but a sense-object. Again, a perceptible 
thing is always understood to combine a number of 
connected qualities which can only be perceived by 
different senses. An observer might see a mirror- 
image for an hour at a time, but he would never say 
that he was seeing a physical object, so long as he knew 
that it was a mirror-image. For he would know that, 
if he went to the place where it is optically present, he 
would sense no correlated tactual sensa, and that there 
would be no relevant scientific objects there. 

Of course, as I have already hinted, these criteria 
are not theoretically satisfactory. What we count as 
a perceptible object may be moving so fast that we 
sense only one short sensum in connexion with it. 
Conversely, an observer who moved in the right direction 
with the velocity of light would continually sense sensa 
connected with a single flash, so that he would be 
aware of a sense-object of considerable duration, and 
might therefore be inclined to say that he was seeing a 
perceptible thing and not merely a perceptible event. 



DATE AND DURATION 395 

Still, the criteria that we have just laid down work in a 
great many cases and will do for our present purpose. 

We can now improve the definition of a perceptual 
object which we gave in the last chapter, where we 
deliberately overlooked for the moment complications 
due to time. We still cannot give a perfectly satis- 
factory definition, because we have not yet dealt 
properly with the movement of physical objects and 
observers and the consequent displacement of visual 
sensa in the movement-continuum. We will assume 
for the present that we are confining ourselves to a 
resting object and resting observers, and we shall not 
attempt to remove this restriction until the next chapter. 
Suppose that a scientific event of the kind which is 
connected with a single flash of light were to happen 
at a certain moment at a certain place in scientific 
space. Suppose that observers were dotted about in all 
directions and at all distances around this place. Then 
it is true that the place in question would be optically 
occupied by visual sensa from all directions for a very 
long time. But it would be optically occupied only 
for a moment by visual sensa from a given distance. 
At any given moment the sensa which occupied the 
place would occupy it from places on a certain sphere 
surrounding it, and at a later moment it would be 
occupied only by sensa from places on a larger sphere. 
It would never be occupied at once by sensa from places 
on two such spheres. If there were a persistent optical 
object, instead of a mere flash, at the place, this place 
would be optically occupied at a given moment from 
many different distances as well as from all directions. 
We might regard a persistent optical object as a con- 
tinuous series of successive flashes. Each flash is 
itself a series of successive sensa belonging to different 
fields, and the later a sensum is in its flash the further 
off is the place from which it is present at the luminous 
centre. Thus there are two temporal series to be con- 
sidered : (1) The series of flashes which together make 



396 SCIENTIFIC THOUGHT 

up the history of the persistent optical object ; and (2) 
the series of successive sensa which together make up 
a single flash. It is obvious that an early sensum 
belonging to a later flash and a late sensum belonging 
to an earlier flash may be simultaneous with each other. 
The former will be optically present at the centre from 
a near place, and the latter will be optically present at 
the centre from a more remote place. Thus the centre 
is optically occupied by sensa from different distances at 
the same moment. Imagine for simplicity a visible 
object of very small spatial dimensions, which we can 
treat as a point. Suppose it lasted for a time T, and 
that a time / has now elapsed since it began to exist. 
Then the places from which sensa are 
present at this point at the moment / are 
all the points contained in the volume 
between a pair of spheres with the 
point as centre and ct and c (7 + T) as 
radii. (Here c is the velocity of light.) 
The diagram will make this plain. 

At this moment sensa from the first flash in the 
history of the object will be present at P from places on 
the outer sphere, and sensa from the last flash in its 
history will be present at P from places on the inner 
sphere. Sensa of intermediate flashes will be present 
at P from places in the volume contained between the 
two spherical surfaces. Thus the thickness of this solid 
shell of places, from which sensa are contemporaneously 
present at P, is characteristic of the duration of the 
optical object. From places within the smaller sphere 
there are no longer any sensa present at P, and from 
places outside the larger sphere there are not yet any 
sensa present at P. The " shell " will continually 
spread out from the centre, but it will always remain of 
the same "thickness," and this thickness is character- 
istic of the duration of the optical object. 

So far, we have confined our attention to the places 
from which sensa are present at a given place at a given 




DATE AND DURATION 397 

moment. But we can equally well regard the whole 
situation from another point of view. We can consider 
the moments at which sensa are present at a given place 
from a. given place. In the case of a flash each observer 
senses just one sensum, which is optically present at 
the place where the flash is said to be. In the case of 
a persistent optical object all the observers will be aware 
in course of time, not merely of a single sensum, but 
of a sense-object. And the duration of this sense-object 
would commonly be identified with that of the optical 
object. The sense-object in this case is a group of 
successive visual sensa in a single sense-history, one 
of which belongs to each of the successive flashes into 
which the history of the persistent optical object can be 
analysed by Extensive Abstraction. It is clear that we 
must distinguish between (1) the duration of an optical 
object from a place, and (2) the total duration of an optical 
object. The former is simply the duration of the sensible 
object which is the appearance of the optical object 
to an observer at that place. But an optical object, 
however short its duration from any one place, has an 
enormously great duration, when you take into account 
all the sensa which belong to it from all places. Its 
total duration is the time that elapses between the earliest 
and the latest visual sensum which belongs to it. And 
this, even in the case of a momentary flash, may amount 
to millions of years. A flash, in the limit, has only 
duration of the second kind ; a persistent optical object 
has both kinds of duration. 

We can now define a persistent complete optical object, 
subject to the limitations about motion which we have 
already indicated. Such an object is a group of visual 
sensa of various dates, correlated with each other, and 
having the following properties: (1) There is a certain 
closed contour in Scientific Space (the " place occupied 
by the optical object"), such that every member of this 
group of sensa is optically present at some part of its 
surface from somewhere. (2) Every part of this contour 



398 SCIENTIFIC THOUGHT 

is optically occupied from somewhere by some member 
(or members) of the group. (3) At any moment after 
the optical object has started to exist, any part of this 
central contour is occupied by sensa of the group from 
all the places within a certain volume. This volume is 
bounded by two closed surfaces, both of which contain 
the place occupied by the optical object. After the 
optical object has completed its history, the thickness of 
this volume is a measure of the duration of the object 
from any point. (4) From any point a certain part of 
the central contour is occupied by a series of successive 
sensa, forming a sense-object in the sense-history of an 
observer who stays at this point. The duration of this 
sense-object is the duration of the optical object from 
this place. 

To define a non-persistent complete optical object, i.e. 
a complete optical event, or "flash," we leave clauses 
(1) and (2) standing, and modify clauses (3) and (4) as 
follows: In (3) substitute "on a certain surface" for 
"within a certain volume." In (4) substitute "a single 
sensum " for "a series of successive sensa," and omit 
the rest of the clause. Finally, a mirror-image of a 
chair or a pin would be a persistent incomplete optical 
object, whilst a mirror-image of a flash would be a non- 
persistent incomplete optical object. 

We said in the last chapter that an ordinary per- 
ceptual object, like a penny, as understood by common- 
sense, is really a composition consisting of a number of 
correlated constituent objects of various kinds, all 
occupying a place in the movement-continuum in their 
various appropriate Pickwickian ways. This place, 
moreover, is conceived to be literally occupied by cor- 
related scientific objects ; and the difference between 
science and common-sense is largely a difference in 
the amount of knowledge which the two claim to have 
about these scientific objects. It is obvious that some 
of the constituents of a perceptual object may cease 
to persist while others remain. Again, a place where 



DATE AND DURATION 399 

a perceptual object has once been, may continue to be 
haunted from certain places by its ghost, in the form 
of its optical constituent. The compositeness of a 
perceptual object infects the notion of "its" duration 
with an incurable vagueness. We can make accurate 
statements about the durations of its constituents, and 
we can make accurate statements about the durations 
of the correlated scientific objects, but the perceptual 
object of common-sense is too much a mixture of non- 
homogeneous constituents to be worth treating very 
seriously as a whole. 

We saw that an observer can very well be mistaken 
in thinking that he perceives a physical event of a 
certain kind, because this implies a reference beyond 
the sensum which he senses to other sensa, actual and 
possible, of other observers. A fortiori, we can be mis- 
taken in supposing that we perceive a certain physical 
thing ; and this can happen even when we are quite 
right in thinking that we perceive a physical event or 
a series of them. Such mistakes take various forms, 
and contain various amounts of error, (i) We may 
mistake a partial for a complete optical object, i.e., we 
may think that a certain place is optically occupied from 
all directions when really it is occupied only from one 
or from a restricted range of directions. This happens 
in optical illusions which really deceive us. (ii) If we 
make this mistake we shall almost certainly make the 
further mistake of supposing that the place in question 
is also occupied by correlated tactual and other con- 
stituents, that it is a centre for sound and radiant heat, 
and that it is occupied literally by scientific objects 
specially correlated with our visual sensa. Actually 
the most relevant scientific objects will be at some 
remote place, (iii) We may make very grave mistakes 
about time. We practically always think that physical 
things have endued and remained in the same place 
longer than our visual perceptions really justify us in 
believing. If an ordinary man sees a star in a certain 



400 SCIENTIFIC THOUGHT 

optical place, he assumes that it must have been there 
at least up to the time when he ceases to see it. This 
is of course unjustified. My visual sensa are indeed 
optically present at this place at the time when I sense 
them, and for as long as I go on sensing them. But, 
in saying that the star is there at that time, I am assert- 
ing much more than this. I am asserting that other 
types of constituent object are also there, and that the 
place is now occupied by correlated scientific objects 
and events. This may happen to be true, but it is not 
justified by my visual perception alone. The star may 
have blown up or moved elsewhere since the light left 
it. The first statement implies that there is now no 
centre occupied by scientific objects correlated with my 
present visual sensa. The second implies that there is 
still a centre occupied by events of this kind, but that 
it is no longer at the place where the optical object is 
present. The facts of aberration show that such diver- 
gences between the place of a perceptual event and 
that of the thing with which it is connected, may arise 
through mere movement of the observer. 

{b) Scientific Objects. — It is admitted that ordinary 
perceptual objects, like pennies and chairs, begin to 
exist, last for so long, and then come to an end. In 
the chapter on Time and Change in Part I, I tried to 
explain what exactly is meant by saying of any object 
that it began to exist, lasted so long, and came to an 
end. Now perceptual objects are supposed to be con- 
nected with scientific objects in the way described 
earlier in the present chapter. And the total scientific 
object specially connected with any perceptual object 
is believed to be a very complex whole of related 
parts. Such structures have more or less stability, 
once they are formed ; but they do begin to exist and 
come to an end under suitable conditions. We shall 
have to distinguish between scientific objects of various 
orders. The sort of scientific object which is specially 
connected with a perceptual object, like a chair, may be 



DATE AND DURATION 401 

called a first order object. It is supposed, as we know, 
to consist of a great many molecules arranged in 
a pattern in space. These may be called second order 
objects. Each molecule is supposed to consist of a 
number of atoms, characteristically arranged in space 
and moving in characteristic ways in time. These 
atoms are third order objects. Finally, each atom is 
supposed to be an arrangement of positive and negative 
electrons, with characteristic types of motion. These 
are fourth order objects ; and it is of course possible that 
they are themselves complicated structures composed 
of fifth order objects. 

Such a hierarchy represents real facts about Nature. 
The simplest way to look at it is the following : Many 
agents, such as the presence of a sufficiently prosperous 
profiteer on the seat, will break up a chair without 
affecting the molecules of cellulose of which it is com- 
posed. Other agents, such as heat, will break up the 
cellulose molecules, but leave the atoms of carbon, 
hydrogen, and oxygen of which they are made, un- 
altered. A very few agents will, with great difficulty, 
break up the atoms themselves into their constituent 
electrons. So far as I know, no agent yet employed 
will break up an electron, though it is possible by 
heroic methods to knock pieces off the nucleus of an 
atom. Thus the orders in the hierarchy of scientific 
objects are the stages where certain disintegrating 
agents, which have previously been effective, cease to 
be so. Chairs really are permanent under a great 
variety of conditions, cellulose molecules under a greater 
variety, carbon atoms under a still greater range, and 
electrons under all variations that have been tried. 

Now, for our present purpose, the important thing 
to notice is that scientific objects of different orders need 
different minimal spaces and durations to live in. This 
is generally recognised in regard to space, though it is 
stated in a rather misleading way, e.g., that " molecules 
are divisible and electrons are not." It is equally true 



402 SCIENTIFIC THOUGHT 

of time, and it is one of Whitehead's great merits to 
have pointed this out clearly. I will first explain what 
is meant by this statement as regards space. If you 
divide up the space which is occupied by a chair into 
two parts, neither of these parts will be occupied by a 
chair, though one may be occupied by a leg and another 
by a seat. Again, you could divide up the space occupied 
by a chair into partitions, each of which was occupied by 
a cellulose molecule. If you further subdivided one of 
these divisions you would find that some of your sub- 
divisions were occupied by a hydrogen atom, some by 
a carbon atom, some by an oxygen atom, and some by 
nothing at all. When a person says that a molecule is 
divisible in space, whilst an electron is not, what he 
means, over and above the fact that one has been experi- 
mentally split up and that the other has not, is roughly 
the following: If you take a space containing one and only 
one molecule and nothing else, you can divide it into a 
set of exhaustive and mutually exclusive partitions, such 
that there is a positive difference of quality between the 
contents of some of these partitions and the contents 
of others. [E-g-, the contents of one may have the 
"hydrogen quality," that of another the "oxygen 
quality," and so on. Of course, some of your partitions 
may have no contents at all.) If you take a space 
containing one electron and nothing else, then either 
(i) all sets of exhaustive and mutually exclusive par- 
titions into which you can divide the space are occupied 
by contents of the same quality, or (2) you can divide 
the space into two mutually exclusive and exhaustive 
partitions, one of which is empty whilst the other has 
the property (1). What is called "indivisibility" is 
really rather homogeneity of quality for all spatial sub- 
divisions below a certain maximum. Whether in fact 
an electron answers to this definition is, of course, a 
matter for empirical investigation. 

Now, as Whitehead has pointed out, we have the 
same distinction among objects as regards division of 



DATE AND DURATION 403 

their history into successive slices. There are many 
types of object whose characteristic qualities need a 
certain minimum of duration to inhere in. E.g., memory 
is one of the outstanding features of the sort of thing 
that we call a "mind." It is, therefore, clear that the 
very notion of a " momentary mind " is nonsense. Now 
the same is true of any scientific object which is partly 
characterised by some special type of motion. Suppose 
that a certain kind of atom consisted of a nucleus and 
an electron rotating about it at a certain characteristic 
rate. Such an atom would need at least the duration 
of one complete rotation to display its characteristic 
properties. The history of such an atom is a " pattern " 
in time, just as the momentary arrangement of electrons 
and nucleus is a pattern in space. If the duration of 
one complete rotation be sliced up into adjacent successive 
parts, the contents of the parts will differ in quality from 
the contents of the whole. 

On the other hand, there may well be objects which 
are temporally homogeneous. This would mean that, 
however you choose to divide up their history, the 
contents of all the slices are the same as each other and 
as the whole in quality. Many types of scientific object 
then have a characteristic minimum duration as well 
as a characteristic minimum extension. 

Now science regards the ultimate scientific objects 
as being spatio-temporally homogeneous. And it 
assumes that these ultimate scientific objects never 
begin or end. Thus the ultimate scientific objects are 
regarded as eternal in the sense of existing throughout 
all time. The only ultimate scientific changes are the 
groupings and regroupings of such objects according 
to a single set of fundamental laws. Whether this 
assumption be true, and whether it be self-evident, I do 
not profess to know. But I believe we may assert (as 
I have pointed out elsewhere, and as Mr Keynes has 
independently and much more clearly shown in his 
Treatise on Probability) that, without some such assump- 



4 04 SCIENTIFIC THOUGHT 

tion, it is impossible to justify the confidence which 
we feel in the results of " well-established " inductions. 
I do not propose to pursue this subject further here. 

In the next chapter I shall say what I can about 
Motion, and, in the next but one, I shall discuss the 
concept of Space-Time, from which Scientific Space 
and Scientific Time are two abstractions of different 
types. 

The following additional works may be consulted 
with advantage : 

B. A. W. Russell, Lectures on the External World, Lectures 

III. and IV. 
A. N. Whitehead, Principles of Natural Knowledge, Part IV. 
S. Alexander, Space, Time and Deity, Book I. 
A. A. ROBB, Absolute Relations of Time and Space. 



CHAPTER XI 

" Oh, how glorious and resplendent, 
Fragile Body, shalt thou be ! " 

(Hymns Ancient and Modern.) 

Sensible and Physical Motion 

In the last chapter I touched incidentally on the 
sensible motion of sensa within their own fields. Both 
in it and in the chapter before I talked of the motion of 
our bodies, and said that the concept of physical Space 
is based on such motions, interpreted spatially by 
analogy with our visual fields. I propose now to go 
considerably more into detail about these matters ; to 
consider exactly how the concepts of physical Space 
and Motion are connected, on the one hand with our 
bodily movements, and on the other with the positions 
and movements of our sensa in their fields ; and finally 
to work up to the concept of physical Space-Time. 
We shall find that the consideration of our own bodies 
and of the bodies of other observers who can communi- 
cate with us about their experiences fills a gap in our 
concept of physical objects, and is an essential factor 
in the development of the concept of physical Space. 

General Remarks about Change and Motion. — 

When we say that something changes, or, more 
particularly, that it moves, we imply a certain identity 
and a certain difference. There must be enough 
identity for us to be able to say that we are dealing 
with the same object, in spite of the movement or other 
change. And there must be some difference between 
one part of the history of the object and others, or we 



4 o6 SCIENTIFIC THOUGHT 

should not say that it had changed or moved. Change 
is a more general concept than movement, since move- 
ment is simply change of position in space. We will, 
therefore, begin with change in general. 

In ordinary life we distinguish between an object 
and its history, and we are inclined to think that the 
former is logically prior to the latter. We say, e.g., 
that there is a certain object, such as a penny, and that 
it may either rest or move, keep bright or tarnish, 
and so on. These events, we say, "happen to" the 
object, and its history is just all the events that happen 
to it. You might, we think, have an object without a 
history, but you could not have a history without an 
object. I believe this to be a profound mistake, which 
arises from taking "history" in too narrow a sense. 
An object, separated from its history, is clearly not the 
kind of thing that could possibly exist. Every object 
that is not merely momentary has a history of some 
kind, and no merely momentary object could really 
exist. " Object," apart from "history," is therefore as 
much an abstraction as " history," apart from " object." 
Of course some histories are very tame, e.g., that of a 
penny which keeps in one place and never varies in its 
other qualities. Others are more exciting, e.g., that of 
a penny which moves about, gets bent and defaced, 
and is finally dropped into the collection-plate. Now 
we are inclined to identify history with exciting, i.e., 
variable, history. We then identify the object with 
the tame tracts of its history ; and forget that these are 
history at all, because they are so uniform. But really 
all that literally exists is strands of history, some tamer 
and some more exciting. 

Now it is conceivable that there might have been 
succession but no history. If so, there would have 
been neither an object nor a plurality of objects. Let 
us consider a fragment of the whole course of Nature, 
lasting for an hour. Let us imagine it cut up into 
successive slices, each lasting for a second. Theoreti- 



SENSIBLE AND PHYSICAL MOTION 407 

cally there are three possibilities, (i) We might find 
that the contents of any adjacent pair of seconds had no 
particular resemblance either in whole or in part. And 
we might still find the same result if we took shorter 
and shorter divisions. In that case we could hardly 
talk of history at all ; there would merely be a perfectly 
chaotic hail of events, (ii) We might find that there 
was considerable qualitative resemblance between the 
whole contents of any adjacent pair of seconds, and that 
this resemblance increased as we took shorter and 
shorter sub-divisions. But we might have to compare 
the contents of each second en bloc. We mio-ht not be 
able to divide it into clearly distinguishable co-existing 
parts. In that case we should say that there is a history 
(of the world as a whole), but that there is not a 
number of distinct strands of history. We could then 
talk of an object, which endures and perhaps changes, 
viz., the universe; but not of a number of distinct 
objects, (iii) We might find, as we actually do, that 
the content of each second is distinguishable into 
different co-existing parts, and that a certain part of 
the content of one is hooked on to a certain part of the 
content of the next by close qualitative resemblance. 
Under this head I include resemblance of shape and 
position, as well as resemblance of colour, temperature, 
etc. We should then say, not only that there is a 
history of the world as a whole, but also that there are 
various distinct strands of history. Each strand would 
be called the history of such and such an object, but 
this does not mean that there is another existent, viz., 
"the object," beside the strand itself. It is only 
because there are such strands that we can talk of a 
plurality of objects. The world as a whole would have 
a history, partly because it is composed of such strands 
of history. But its history is more than the sum total 
of a number of distinct strands lying side by side. If 
there be causal and other regularities which hold 
throughout the whole period under discussion, there 



408 SCIENTIFIC THOUGHT 

will be characteristic relations between the strands, 
and the history of the world as a whole would have 
more unity and complexity than is implied by the 
simple statement that it is composed of such and such 
parallel strands. 

Whenever we talk then of "objects," the funda- 
mental fact is the existence of distinct strands of history. 
A given object is a certain strand, pervaded by a certain 
special unity and continuity, which characterise it and 
mark it out from strands of other kinds. To say that a 
certain object has not changed in any respect is to say 
that all the successive slices of a certain strand are 
qualitatively indistinguishable from each other. An 
unchanging object is thus a completely uniform strand of 
history. To say that a certain object has moved, but 
has not otherwise changed, is to say that the positional 
qualities of successive slices of a certain strand are 
progressively different. A moving object is therefore a 
positionally non-uniform strand. 

Now it happens, of course, that there are many distinct 
strands which are so much alike in the characters of 
their slices, and in the type of unity that pervades them, 
that they are called histories of objects of the same kind. 
Yet some of these strands may be positionally uniform, 
whilst others are positionally non-uniform. An example 
would be given by a resting and a moving penny. 
Again, a strand which has enough unity and continuity 
throughout to count as the history of a single object 
may yet for some part of its length be positionally 
uniform and for others be positionally non-uniform. 
An example would be a penny which sometimes keeps 
still and sometimes moves. I think that it is partly in 
consequence of such facts that we tend to separate 
objects from their histories, and to treat their histories 
as something more or less external, which may or may 
not "happen to" them. A given penny really is a 
certain definite strand of history, positionally uniform 
if it be a resting penny, positionally non-uniform if it 



SENSIBLE AND PHYSICAL MOTION 409 

be a moving penny, and so on. But you can always 
find plenty of other strands of history sufficiently like 
this one in their non-positional qualities to be called 
histories of pennies, and yet uniform where this history 
is positionally non-uniform. You tend to identify the 
first penny with a uniform history, such as the second 
penny, and to regard the non-uniform part of the first 
pennyas something that "happened to" it, but was not 
a part of it. The real fact, however, is that the first 
penny is the first strand and nothing else, and the 
second penny is the second strand and nothing else. 
Of course the general characteristic of " being a penny " 
is common to both, since it is the general type of 
qualitative character which pervades all such strands ; 
but this is a universal, not a particular existent ; and 
when people talk of "objects," and say that they rest 
or move, they are certainly not primarily talking about 
universal characteristics but about particular existents. 

It is evident then that every object has a time- 
dimension as well as any space-dimensions that it 
may have. There is nothing mysterious about this ; it 
means no more than that every existing object, whether 
at rest or in motion, is a strand of history with some 
duration. The question whether it is a changing or 
an unchanging object is simply the question whether 
successive slices of the strand, normal to the time- 
dimension, are exactly alike or progressively different 
in quality. The notion of an object with nothing but 
spatial dimensions is an abstraction. You can divide 
up the object into thinner and thinner slices normal to 
its time-dimension, and these slices will approximate, 
as you make them thinner and thinner, to purely spatial 
figures. In the limit each will be a purely spatial 
figure, in general of three dimensions. But these are 
not the object, nor are they literally even parts of it. 
The object is the whole four-dimensional strand of 
history. And these momentary spatial figures are 

"parts" of the object only in the Pickwickian sense in 

2 D 



4 io SCIENTIFIC THOUGHT 

which plane sections of an ordinary solid are "parts" 
of the solid. A person who refuses to identify an object 
with its whole history must either identify it with a 
momentary section of that history or with a uniform slice 
of it. If he does the former, the object is a mere abstrac- 
tion, incapable of existence. If he does the latter, his 
restriction to the uniform part of the whole strand of 
history is clearly arbitrary. 

If it should happen that all the successive momentary 
sections of an object have the same shape, you can call 
this the shape of the object. But, if they have different 
shapes, there is nothing that can be called the shape of 
the object. A penny and a mist are both objects ; but, 
whilst you can talk of the shape of the former, you 
cannot talk of the shape of the latter. 

Motion and Rest in Visual Fields and Sense-histories. 
— After these general remarks about the nature of objects 
and their motion or rest, we can consider the various 
types of motion and rest which happen within our visual 
fields and sense-histories. 

(a) Motion and Rest of Visual Sensa. — A single sense- 
field lasts for a finite, though short, time. Spatially it 
is of three dimensions. It is therefore a four-dimensional 
spatio-temporal whole. In sensing it, we thus sense 
directly a four-dimensional whole with three spatial 
dimensions and one temporal. A sensum is an outstand- 
ing part of the total content of a sense-field. It has some 
duration, which cannot be greater than that of the sense- 
field, and it has spatial extension. It is therefore in 
general a four-dimensional object. Now, as we have 
seen, a visual sensum may shift its position in its own 
field or not. If it does, it is affected with sensible motion, 
otherwise it is sensibly at rest. Thus all visual sensa 
are four-dimensional objects, and those that are affected 
with sensible motion are positionally non-uniform objects. 
Just as we cannot see at once an object of more than a 
certain size, so we cannot sense by one act an object 



SENSIBLE AND PHYSICAL MOTION 411 

that exceeds the duration of a Specious Present, whether 
it be uniform or non-uniform. In sensing a resting 
sensum we are aware in one act of a positionally uniform 
four-dimensional object of short duration ; in sensing a 
moving sensum we are aware in one act of a positionally 
non-uniform four-dimensional object of short duration. 
Thus, sensible motion is the way in which the positional 
non-uniformity of a four-dimensional object presents 
itself to us when this non-uniformity is "sharp" enough 
to be noticeable within the duration of a single sense- 
field. 

(b) Motion and Rest of Visual Sense-objects. — Our 
successive visual fields join up with each other to 
form a single sense-history, as already described. This 
is simply a four-dimensional whole, of the same general 
nature as a single visual field, but of greater duration. 
It cannot, of course, be sensed as a whole, though some 
of its earlier slices may be remembered while its latest 
slice is being sensed. Now, when a certain resting 
sensum has occupied a certain position throughout the 
whole of one field, similar sensa may occupy exactly 
similar positions in a series of successive fields. Just 
as the fields join up to give one sense-history, of which 
they are successive slices, so these resting sensa join 
up to give a single sense-object, of which they are 
successive slices. This will be a positionally uniform 
sense-object, and may be described as a sense-object 
which rests in the space of the observer s sense- history. 

Now it may happen that there is a series of more 
or less similar sensa in a series of successive fields, but 
that they occupy progressively dissimilar positions in 
their respective fields. And it may be that the thinner 
two fields are and the nearer they are together, the less 
is the dissimilarity between the positions of the sensa 
of this set which belong to these fields. On these con- 
ditions the sensa of the set still join up to form a sense- 
object of which they are successive slices. But this 
sense-object is positionally non-uniform, and may be 



412 SCIENTIFIC THOUGHT 

described as a sense-object which moves in the space of the 
observers sense-history. Often there is no sensible non- 
uniformity in the individual sensa of such a group, 
although they join up to form a positionally non-uniform 
sense-object. On the other hand, it often happens that 
each of the component sensa of a moving sense-object 
is itself affected with sensible motion in its own field. 
It is reasonable to suppose that, even in the former case, 
the component sensa are really not quite positionally 
uniform objects, but that their departure from uniformity 
is not "sharp" enough to be sensed as movement within 
the sense-field. 

Now, it is very important to notice that the move- 
ment of sensa in their fields and of sense-objects in the 
spaces of their sense-histories is the ultimate empirical 
basis of the concept of absolute motion. The sensible 
motion of a sensum in its field really is something 
absolute ; it does not simply consist in the fact that 
this sensum alters its spatial relations to other sensa 
in the field, though, of course, it involves this as a 
necessary consequence. This is quite clear, from the 
following example: Suppose I am looking at the sky, 
and a shooting star darts across. I am aware of a 
field ; and within this are sensa which are the appear- 
ances of the other stars, and a sensum which is the 
appearance of the shooting star. The latter is affected 
with sensible motion, whilst the former are not. Now, 
if the sensible motion simply consisted in a change of 
relative position within the field, it would be perfectly 
symmetrical, and it would be impossible to say that 
the shooting star sensum sensibly moves and that the 
other sensa do not. But it is quite clear that in fact 
we do sense an intrinsic peculiarity of the shooting 
star sensum which is not present in the others. Thus, 
sensible motion and rest are something absolute and 
intrinsic, not merely relational ; and I take it that this 
fact is at the basis of the concepts of absolute motion 
and rest. It does not, of course, follow that the 



SENSIBLE AND PHYSICAL MOTION 413 

concept thus formed really is applicable beyond sense- 
fields and sense-histories. It may well be that the 
absolute motion or rest of a sense-object in the space 
of my sense-history is connected with merely relative 
motion between my body and other physical objects. 
This does not alter the fact that the motion of the 
sense-object in the space of my sense-history is itself 
absolute, and not a mere change of relation to other 
contents of the history. We shall consider this question 
at a later stage in the chapter. 

Correlations between the Motions of Visual Objects 
and the Kinesthetic Sensations of an Observer. — The 
best way to approach this complicated subject seems 
to be by taking special cases as illustrations. Taking 
a single observer and a single physical object, we 
can begin by distinguishing four cases which con- 
stantly happen : (A) The observer stands still, and 
(i) watches a resting physical object, or (ii) watches 
a moving physical object. (B) The observer moves 
bodily, and (i) watches a resting physical object, or 
(ii) watches a moving physical object. These four 
cases must be distinguished from each other by certain 
differences in our sensible experiences, and I shall begin 
by pointing out the peculiarities of each in turn. 

(A) There are two kinds of kinesthetic sensation, 
one connected with walking, and the other with turning 
the head. I will call them respectively translational and 
rotational kinassthetic sensations. The A-cases are all 
alike in the fact that the observer feels no translational 
kinesthetic sensations. 

(i) When a resting observer watches a resting 
physical object he finds that, once having turned his 
head so as to sense a field with a visual appearance of 
this object in the middle of it, he must henceforth keep 
his head still if he wants to go on sensing fields with 
similar sensa at their centres. That is, in order that 
the physical object may appear in his sense-history as a 



414 SCIENTIFIC THOUGHT 

resting sense-object, he must henceforth keep free from 
rotational kinesthetic sensations. If at any moment 
he chooses to start turning his head, the physical object 
will still continue for a time to appear in his visual 
sense-history. But the visual sensa by which it appears 
will occupy progressively dissimilar places in his suc- 
cessive fields. Moreover, they may be affected with 
sensible motion within their fields. Thus, in this case, 
the physical object still appears, for a time at least, as 
a visual sense-object in the observer's sense-history. 
But its appearance is now a positionally non-uniform, 
i.e.., a moving, sense-object. 

There are also certain points to be noticed about the 
shapes, etc., of the successive sensa in this sense-object. 
While the observer keeps his head still, the successive 
sensa will be indistinguishable in shape, unless, of 
course, physical changes are going on in the object. 
But when he moves his head, the successive appear- 
ances will differ in shape ; they will be more and more 
distorted as he turns his head more, and as they occupy 
more eccentric positions in his successive fields. Thus, 
when he turns his head, the sense-object by which the 
physical object appears in his sense-history is not only 
positionally non-uniform ; it is also non-uniform as 
regards shape. There is another difference between the 
successive sensa, which I will just mention here and deal 
with more fully later. They do not differ merely in 
the fact that each is a distortion of the original central 
sensum. Very often there is something in the later 
sensa to which nothing corresponded in the earlier 
ones, and conversely. This is the sensible basis of 
the fact which we express by saying that, as we turn 
our heads, "fresh parts of the object come into view, 
whilst others which were formerly visible cease to 
be so." 

A final and very important point to notice is that, 
in the present case, by exactly reversing the series of 
rotational kinesthetic sensations I exactly reverse the 



SENSIBLE AND PHYSICAL MOTION 415 

series of sensa, and end up with a field like that from 
which I started, with a sensum like the original one 
in its centre. I can do this as often as I like, and 
always with the same result. Again, I can move my 
head from its initial position in a great variety of 
ways, which are distinguished for me by characteristic 
differences in my rotational kinesthetic sensations. 
Each such way will involve a non-uniform sense-object 
of the kind described ; and each, on reversal, will 
bring: me back to a field like that with which I started. 
But there are characteristic differences of detail between 
the various non-uniform sense-objects which correspond 
to the various series of rotational kinesthetic sensations, 
(ii) When I stand still and watch a moving physical 
object, I find that I must keep turning my head if I want 
to keep the successive appearances of the physical 
object in the centres of my successive fields. And I 
must do this in a perfectly definite way. Moreover, 
there is a difference between the sense-object which I 
sense in this case and in the last. In the last case, if 
I keep my head still, I sense a completely uniform sense- 
object. In the present, the sense-object never is com- 
pletely uniform ; it is not even completely uniform in 
position. What we should find would be this : There 
would be a steady increase, a steady decrease, or the 
one followed by the other, in the sizes and depths of 
the sensa. There will be distortion in their shapes. 
There will be variations in brightness. And, finally, 
the later sensa will have parts to which nothing corre- 
sponds in the earlier, and conversely. 

Suppose now that, at a certain moment, I stop 
moving my head. From that moment the successive 
appearances of the physical object will begin to occupy 
dissimilar positions in my successive fields. Very 
probably each will have sensible motion in its own 
field. And the distortion of later sensa, and the 
addition of new and dropping of old features, will be 
greatly accelerated. In fact, the physical object will 



416 SCIENTIFIC THOUGHT 

henceforth appear as an extremely non-uniform sense- 
object, both positionally and in other respects. Very 
soon it will cease to appear at all in my sense-history, 
i.e., the later parts of the sense-history will be fields 
containing no sensa connected with this physical object. 
When this is so, I could, as a rule, start again at will 
to sense a field with an appearance of this physical 
object at its centre. In order to do this, I shall have 
to turn my head to a definite extent, independent of 
my choice. And, when I do at length sense another 
field with a sensum of the required kind in the middle 
of it, I shall find that this sensum differs in shape, 
brightness, depth, etc., from the one that was in the 
middle of the last field which I sensed before I stopped 
turning my head. 

(B) The B-cases resemble each other, and differ 
from the A-cases, in that the observer experiences 
translatory as well as rotational kinesthetic sensations, 
(i) If a man walks, and wants to keep his eye on a 
resting physical object, he will find that he must 
continually turn his head as he walks. And the amount 
of rotational kinesthetic sensation needed is correlated 
with the amount of translational kinesthetic sensation 
experienced. Provided he turns his head properly, the 
physical object will appear in his sense-history as a 
partly, but only partly, uniform sense-object. It will 
not be uniform in depth or brightness. There will 
also be distortion and revelation of new parts. But 
the sensa will be at the centres of his successive fields. 
If he walks, and keeps his head and eyes fixed, the 
physical object will appear in his sense-history as a 
moving sense-object, and possibly the constituent sensa 
may have sensible motion in their respective fields. 
The non-uniformity in respect of shape will be very 
much greater than when he keeps his eye on the 
physical object, and soon this will cease to appear at 
all in his sense-history. After it has disappeared he 
can again sense a field with a sensum of the group 



SENSIBLE AND PHYSICAL MOTION 417 

at its centre, provided he turns his head properly. The 
amount of rotational kinesthetic sensation needed for 
this purpose will be completely determined by the 
nature and amount of translational kinesthetic sensation 
which he has experienced since he ceased turning his 
head. Lastly, the sensum which will occupy the middle 
of his present field will never be exactly like that which 
occupied the middle of the field which he was sensing 
when he stopped turning his head. There will be 
differences in shape, depth, brightness, etc. ; and there 
will be parts to which nothing corresponded in the 
last sensum, and conversely. 

It is obvious that, on the visual side, there is a 
close analogy between B (i) and A (ii), i.e., between 
the visual experiences of a moving observer watching 
a resting object and those of a resting observer watching 
a moving object. There is also a partial resemblance 
between the rotational kinesthetic sensations, since both 
of them are obliged to keep moving their heads in a 
certain way in order to keep the appearances of the 
physical object in the centres of their successive fields. 
The difference is that in A (ii) the rotational kin- 
esthetic sensation needed is absolutely independent of 
the observer's volition, whilst in B (i) it is indirectly 
dependent on his volition. It is primarily dependent 
only on the amount and kind of his translational kin- 
esthetic sensations ; but these in turn are dependent on 
his will, since he can walk as he chooses. This gap, 
however, is bridged by the case of observers whose 
bodies are carried about in trains, motor cars, etc. 
Their movements do not involve translational kinesthetic 
sensations, and here the analogy between B (i) and A 
(ii) becomes practically complete. Such facts as this 
analogy lie at the basis of the concept of the relativity 
of physical motion. 

(ii) When an observer moves about and keeps his 
eye on a moving physical object he will find that the 
nature and amount of kinesthetic sensation needed are 



418 SCIENTIFIC THOUGHT 

determined partly, but only partly, by his translational 
kinesthetic sensations. He will sometimes have to turn 
his head more quickly, and sometimes less quickly than 
if he were walking in the same way and keeping his eye 
on a resting physical object. If he were to retrace his 
steps, and then walk over his old course again, it would 
be useless to repeat the same head-movements which he 
made on the previous occasion. If he did this, it is very 
likely that the physical object would no longer appear 
in his sense-history at all ; and, even if it did so, it 
would certainly not appear in the form of a sense-object 
whose successive sensa occupied the centres of his 
successive fields. 

There is a very important point to notice about these 
B-cases. In them the observer has both translational 
and rotational kinesthetic sensations. Now these fall 
into pairs of correlated series in the following way : The 
successive appearances of a physical object can be kept 
at the centres of one's successive fields in an infinite 
variety of different ways, all of which involve different 
combinations of translational and rotational kinesthetic 
sensations. Take first a resting physical object, (a) 
Its successive visual appearances can be kept in the 
centres of one's successive visual fields by suitably 
turning the head and henceforth moving neither the 
head nor the body. (/3) A similar result (though not an 
identical one) can be produced by walking in innumer- 
able different ways, and at the same time continually 
turning the head in correlated ways. Lastly, (y) there 
is one and only one way of walking without turning the 
head which will produce similar results, though, of course, 
this one way may be pursued at different rates. This is 
what we call "walking straight up to the object." (a) 
and (y) are two extreme cases of the huge group included 
under (/3). It must be noticed that the various combina- 
tions of correlated rotational and translational kinesthetic 
sensations are not absolutely equivalent in their results 
on the sense -object by which the physical object 



SENSIBLE AND PHYSICAL MOTION 419 

appears in the observer's sense-history. The (a)-method 
gives a completely uniform sense-object. Each of the 
(/3)-methods gives a somewhat different sense - object. 
All these sense-objects are non-uniform in shape and 
depth ; for different component sensa will have different 
depths in their respective fields. Moreover, there is 
always that difference between successive sensa which 
we describe by saying that we " see fresh parts and lose 
sight of some which we saw before." Lastly, the 
(y)-method gives a sense-object which is uniform, in the 
sense that there is no distortion between the successive 
sensa which constitute it. But each of these sensa has 
a larger size and a smaller depth than the one before, 
whilst there will be a progressive increase in brightness. 
In spite of this, there may be the difference which we 
should express by saying that the earlier sensa " reveal 
parts of the physical object which cease to be revealed 
by the later ones." 

Somewhat similar remarks apply to the correlation 
between rotational and translational kinesthetic sensa- 
tions in watching a moving physical object. But there 
are certain differences, (a) Its successive appearances 
cannot be kept in the centres of our successive fields if 
we neither walk nor turn our heads. (/3) If we choose 
to do both, there are innumerable combinations of the 
two which will produce the required kind of sense- 
object. But the rotational kinesthetic sensations which 
have to be combined with a given set of translational 
sensations for this purpose are not the same as they 
would be if we were looking at a resting object. In fact, 
no general rule of correlation can be laid down without 
bringing in an additional factor, viz., the motion of the 
physical object itself, (y) There is one and only one 
way of keeping the successive appearances of a moving 
physical object in the centres of our successive fields with- 
out continually turning our heads, and that is, of course, 
by walking parallel to its line of motion at a suitable 
pace. The particular series of kinesthetic sensations 



4 20 SCIENTIFIC THOUGHT 

needed for this purpose varies, of course, with the motion 
of the particular physical object which is being watched. 
By the (y)-method, and by it alone, does a moving 
physical object appear to us as a completely uniform 
sense-object. 

There is thus a close resemblance between the cases 
A (i) and B (ii) (y). So far as the visual object is con- 
cerned, they are precisely alike. The difference is that in 
A (i) a completely uniform sense-object requires complete 
absence of both kinds of kinesthetic sensation, whilst 
in B (ii) (y) it requires a characteristic series of trans- 
lational kinesthetic sensations. The gap here is to 
some extent bridged, as in the analogy between A (ii) 
and B (i), by the fact that an observer's body may be 
carried parallel to another physical object without effort 
of his own. This happens, e.g., when an observer in 
a moving train keeps his eye on a certain window of a 
carriage, moving at the same rate and in the same 
direction on a parallel line. Here we have another 
sensible fact which lies at the basis of the concept of 
the relativity of physical motion. 

(b) Summary of Facts elicited in the last Sub-section. 
We have been discussing the sensible experiences, 
both visual and kinesthetic, which make an observer 
say sometimes that he stands still and watches a resting 
body, sometimes that he stands still and watches a 
moving body, sometimes that he moves and watches a 
resting body, and sometimes that he moves and watches 
a moving body. The most important general conclusion 
that emerges is that there is a mixture of arbitrariness 
and compulsion in all such cases, and that it is the 
particular character of the mixture which causes us 
to make now one and now another of these four types 
of statement. 

(i) I can always, if I choose, sense a series of visual 
fields, each of which contains an appearance of an 
assigned physical object at its centre, (ii) I can always, 
if I choose, sense a series of fields in which successive 



SENSIBLE AND PHYSICAL MOTION 421 

appearances of the assigned physical object occupy 
progressively more dissimilar sensible positions. But 
(iii), once I have decided which kind of sense-object I 
want to sense, conditions are imposed on my kinesthetic 
sensations, which I must simply accept. And these 
imposed conditions vary from case to case. Sometimes 
I must keep my head and body still if I want to sense 
a completely uniform sense-object ; sometimes I must 
move bodily to secure this result. If the latter, I 
cannot move just as I like ; only one way of moving 
will secure the result in a given case, and the right way 
will vary from occasion to occasion. Then (iv) there 
are various mixtures of rotational and translational 
kinesthetic sensations which will cause the physical 
object to appear as a. partially uniform sense-object with 
its successive sensa at the centres of my successive 
fields. But (v) the sense-object will not be uniform 
in depth, shape, brightness, etc. And (vi) not every 
mixture of translational and rotational kinassthetic sensa- 
tions will secure even this result. If I arbitrarily choose 
to experience a certain series of translational kinesthetic 
sensations, the amount and speed of the rotational 
kinesthetic sensations needed will always be partly 
and sometimes wholly determined by the former series. 
Similar remarks apply, mutatis mutandis if we arbitrarily 
choose a certain series of rotational kinesthetic sensa- 
tions, (vii) Sometimes when we deliberately confine 
ourselves to rotational kinesthetic sensations, i.e., when 
we deliberately stand still and merely turn our heads, 
we find that as often as we completely reverse the series 
a qualitatively unchanged appearance of the given 
physical object occupies the centre of our final visual 
field. On other occasions we find that, if we have once 
turned our heads and thus ceased to sense an appearance 
of a certain physical object at the centre of our field, 
mere reversal of the original series of rotational kin- 
esthetic sensations will not suffice to restore a similar 
field. In such cases the amount and kind of rotational 



422 SCIENTIFIC THOUGHT 

kinesthetic sensation needed for the purpose are 
independent of our choice, and vary from one object 
to another, (viii) When, in spite of our best endeavours, 
the physical object fails to appear in our visual sense- 
history as a completely uniform sense-object, the kind 
of non-uniformity in depth, shape, brightness, etc., 
which it displays is independent of our choice. It is 
determined partly by the particular mixture of trans- 
lational and kinesthetic sensations which we have 
chosen out of the whole set which will keep the 
successive appearances in the centres of the successive 
fields. As a rule, it is not wholly determined by this, 
but is partly determined by another factor which is 
quite independent of us. This other factor is what 
we come to know as "the physical motion of the body 
at which we are looking." 

It is this mixture of arbitrary choice and subsequent 
external compulsion which is at the basis of our dis- 
tinction between "objective physical motion and rest," 
and "subjective sensible motion and rest." I shall 
now go into this important matter a little more fully, 
taking some important special cases which we have 
so far touched on only incidentally. 

(c) Successive Sensible Appearances of Co-existing Physical 
Objects. — We have already seen that, when a physical 
object moves away from us while we stand still and 
keep our eyes on it, it never appears in our sense- 
history as a completely uniform sense-object, although 
its successive appearances are in the centres of our 
successive fields. I am not at present concerned with 
the non- uniformity of the sense -object in respect to 
depth or brightness. Nor am I now concerned with that 
kind of non-uniformity which may be described as "dis- 
tortion" of the successive appearances as compared with 
the appearance in some standard field of the sense- 
history, i.e., with the kind of variation which takes place 
in the successive appearances of the upper surface of 
a penny as it moves away from us while we keep our 



SENSIBLE AND PHYSICAL MOTION 423 

eyes on it. What I want to discuss is that kind of 
change which we describe by saying that, as time goes 
on, we see parts of the object which we could not see 
before, and cease to be able to see parts of it which 
we could see before. 

As far as our visual sensa are concerned, there is 
no particular difficulty in describing such experiences. 
We sense a series of sensa which have enough con- 
tinuity with each other to count as successive slices of 
a single sense-object. But, although closely adjacent 
sensa of the series are barely distinguishable in quality, 
those at some distance apart differ in the following 
way : The earlier has some parts to which nothing 
corresponds in the later, and the later has some parts 
to which nothing corresponds in the earlier. The real 
problem is this: These sensa are successive; when the 
last is present the first is past. But we suppose that 
the part of the first to which nothing corresponds in 
the second, and the part of the second to which nothing 
corresponds in the first, are appearances of co-existing 
parts of the physical object. Why do we assert physical 
co-existence on a basis of sensible succession? Since 
the spatial parts of physical objects are themselves 
physical objects, and the spatial parts of sensa are 
themselves sensa, we may generalise the problem as 
follows : Under what conditions do two successive sensa 
justify us in asserting the existence of two contemporary 
physical objects? 

This question is, of course, roughly equivalent to 
a very famous one discussed by Kant in the Analytic 
of Principles of his Critique of Pure Reason. I think 
that Kant hit on one very important part of the answer, 
but that other important factors are involved beside the 
one which he stresses. Moreover, the Sage of Konigs- 
berg did not number clearness of exposition among his 
many merits, so that it will be well worth while to 
discuss the whole question afresh. Let us take a very 
simple concrete example. From where I am sitting, 



424 SCIENTIFIC THOUGHT 

if I look straight in front of me, the middle of my 
visual field is occupied by an appearance of a certain 
picture. The rest of the field consists almost wholly 
of a cream-coloured background, which is an appear- 
ance of the wall. In this field there is nowhere an 
appearance of a door. If I turn my head enough to 
the left I sense a field whose general background is 
much as before. But, in the middle of it, is an appear- 
ance of a door, and nowhere in it is there an appearance 
of the picture. From where I sit it is impossible for 
these two physical objects to be represented by simul- 
taneous visual appearances in a single field. Neverthe- 
less, I judge them to co-exist, although their appearances 
are always successive. 

Now, first of all, what does my judgment of co- 
existence really profess to assert? It does not, I think, 
mean that the part of the history of the picture which 
appears to me when I look in one direction, and the 
part of the history of the door which appears to me 
when I look in the other direction, are contemporary. 
If physical objects exist and endure, they must be strands 
of history, just as sense-objects are, i.e., they must be 
extended in time. And a sensum is presumably an 
appearance of a short slice of the history of a physical 
object. Now, apart from complications about the velocity 
of light, it is reasonable to suppose that successive sensa 
are appearances of successive slices of physical history ; 
and I think we always do assume this in the absence 
of special reasons to the contrary. Thus the judgment 
that the picture and the door co-exist, although their 
appearances are successive, does not mean that the 
successive appearances reveal contemporary slices of 
their histories. What it means is this : The history 
of the picture has gone on while I turned to the door ; 
and, when the door appears to me, there is a slice 
of picture-history contemporary with the slice of door- 
history which now appears to me, and practically indis- 
tinguishable in quality from the slice of picture-history 



SENSIBLE AND PHYSICAL MOTION 425 

which appeared to me when I last looked toward the 
picture. Conversely, the door-history extends back- 
wards from the slice which is now appearing to me ; 
and there is a slice of it which is contemporary with 
the slice of picture-history which appeared to me when 
I formerly looked at the picture. So what we are really 
asserting is that the picture-history extends forward for 
some time with practically no qualitative variation after 
the last slice that has appeared to me, and that the 
door-history extends backwards for some time with prac- 
tically no qualitative variation before the first slice that 
appeared to me. 

Now, I have already said that I do not profess to be 
able to prove that such assumptions are ever true. If 
anyone says that the existence of long strands of physical 
history of almost uniform character does not follow logic- 
ally from the mere existence at certain times of picture- 
sensa and at other times of door-sensa, I heartily agree. 
I can only answer that we all do, in fact, assume that 
sensa are appearances of short slices of things which 
last longer than themselves, and that we can neither 
refute this assumption, get rid of it in practice, nor 
stir a step without it. What we can do, however, is to 
state the special conditions under which we hold that 
successive sensa are appearances of co-existing physical 
objects (in the sense defined above), and show that, 
subject to the general assumption just mentioned, these 
conditions are reasonable. 

I find that over a long period of time I sense a practi- 
cally uniform picture-sense-object, whenever I look in 
a certain direction. Moreover, I can look away and then 
look back again after all kinds of different intervals, and 
I still find a similar sense-object. Exactly similar remarks 
apply, mutatis mutandis, to the sense-object by which the 
door appears to me. Now, theoretically, there are four 
possibilities : (i) My looking in a certain direction is a 
sufficient as well as a necessary condition for producing 

a field with a picture-sensum in the middle of it. (ii) 

2 E 



426 SCIENTIFIC THOUGHT 

The occurrence, at a certain moment, of a field with a 
picture-sensum at the middle of it, is a necessary and 
sufficient condition of my turning my head at that 
moment in a certain direction, (iii) There is a certain 
event which (a) causes me to turn in the given direction 
whenever it occurs, and (/3) produces the picture-sensum 
at the same time, (iv) The head-turning, and the pro- 
duction of the sensum when I have turned, are the 
results of two causally independent series. 

We will first give familiar examples of these various 
possibilities. Suppose that on a certain day I pass a 
certain building several times at various intervals, and 
that on each occasion a brick falls on my head as I pass. 
It might be (i) that my passing shakes down a loose 
brick, which would not otherwise have fallen. Or (ii) 
that whenever I see that a brick is about to fall, I am 
so much interested that I rush to the spot, and that 
nothing else ever takes me there. Or (iii) that I go to 
the place when and only when a workman who is working 
there calls me, and that he throws down a brick when 
and only when I get there, because he is a "class- 
conscious proletarian " and regards me as a " lackey of 
the bourgeoisie." Or (iv) it might be that my journeys 
to the place and the falling of the bricks belong to 
causally independent series. Now I might be able to 
cut out the first three alternatives by reflecting on the 
facts. I might know that I am not heavy enough to 
shake bricks down by passing underneath. I might 
know that I had not gone to the place because I saw 
that a brick was going to fall, and I might know that 
no workman had called me or thrown the bricks at me. 
I might be able to explain why I had passed there on 
each occasion without needing to refer to anything going 
on at the place whatever. 

Supposing that this is so, only one explanation of 
the facts would be reasonable, viz., that a fairly steady 
stream of bricks has probably been falling for most of 
the day. It is almost incredible that each of my visits 



SENSIBLE AND PHYSICAL MOTION 427 

to the place should happen to coincide with the fall of 
a brick, granted that the causes of the visits and of the 
falls are quite independent, unless many more bricks 
fall than the few that I happen to "stop." Now let us 
apply this argument to the sensible appearance of the 
picture and of the door. It is certain that merely to 
look in a given direction is not sufficient to produce one 
particular sensum in the middle of my visual field ; for 
at other times I can look in the same direction and sense 
no such sensum (e.g., if someone has moved the picture). 
It is also certain that the occurrence of the sensum does 
not make me turn my head in that direction ; on the 
contrary, I often turn my head simply in order to see 
whether I shall again sense the same kind of sensum 
as before. And, in general, I know why I turn my 
head on each occasion, and can see that my act is com- 
pletely determined by causes which have no discover- 
able connexion with the causes which produce the 
sensum in the middle of my field when I do turn. I am 
therefore forced to conclude, either that there is a pretty 
continuous strand of very similar picture-sensa, of which 
I sense the particular one which happens to be occur- 
ring when I turn my head, or at least that there must 
be a pretty steady stream of similar physical events, 
each of which is sufficient to produce a sensum of the 
required kind whenever my eye is turned in the right 
direction. Which of these two alternatives is to be 
accepted does not much matter for the present purpose, 
and the question must be left to the next chapter. On 
either alternative we are justified in concluding that 
there is a persistent and practically uniform "picture- 
object," slices of which fill up the gaps between my 
successive picture sensa. On the same grounds I am 
justified in supposing that there is a persistent and 
practically uniform "door-object," slices of which fill 
up the gaps between my successive door-sensa. 

Now let us suppose that I start by looking at the 
picture, and then turn my eyes several times between 



428 SCIENTIFIC THOUGHT 

the picture and the door, ending up finally with the 
picture. We will suppose that I do this at different 
rates on different occasions, also that I sometimes dwell 
for a time on one of the objects without moving". Let 
us represent picture-sensa by little crosses, door-sensa 
by little circles, and the lapse of time by a direction from 
left to right. Then my sensible experience may be re- 
presented by the diagram below. 

X a X 

Now let us represent the physical events which appear 
as picture-sensa by dots, and those which appear as 
door-sensa by little lines. Then the argument from 
causal independence, applied to both objects, justifies 
me in filling out my sensible experience as indicated 
below. 

o o o o _>o cr 

A slightly more dangerous argument would justify me 
in extrapolating to some extent, i.e., in assuming that 
the history of the door and that of the picture extend 
backwards for some distance before my earliest door- 
and picture-sensa. It would also justify me in supposing 
that the history of the door extends forward for some 
distance after my last door-sensum. For, unless there 
be sorne special reason to think otherwise, it is highly 
improbable that I should happen to have looked first 
in the door- or the picture-direction just when there first 
began to be door or picture events. And it is highly 
improbable that door events ceased to happen just when 
I happened to turn my head in the picture-direction for 
the last time. Like all extrapolations, this argument 
is weaker than an intrapolation, and its probability is 
quickly diminished as it is extended further before the 
first sensum of one series or after the last sensum of 
the other series. 



SENSIBLE AND PHYSICAL MOTION 429 

The argument for co-existence is now quite straight, 
forward. There is a slice of picture-history between 
my first and last picture-sensum. And there is a slice 
of door-history between my first and last door-sensum. 
But my first door-sensum is after my first picture-sensum 
and my last door-sensum is before my last picture- 
sensum. Hence the interpolated picture-history com- 
pletely overlaps the interpolated door-history, as the 
second diagram shows. I believe this to be the truth 
underlying Kant's rather confused argument in the 
Analytic of Principles ; but that is a purely historical 
question in which I take no particular interest. 

There are, however, at least two other criteria of 
physical co-existence in face of sensible succession. 
One of these can be dealt with only when we have 
considered our knowledge of our own bodies. The 
other may be mentioned at once. I am not obliged to 
stay in one place. While I sit in my chair at the table 
it is true that the picture and the door can only appear 
successively in my sense-history. But, if I move back- 
wards to the other side of the room, I can sense a single 
field with a picture-sensum at the middle, and a door- 
sensum to the left. These sensa co-exist, and they are 
extremely like the corresponding sensa in my successive 
fields when I was nearer the wall. They are smaller, 
and have greater depth ; otherwise there is very little 
difference. As I approach the wall on which the picture 
is hanging, keeping my eye on it, I first sense a series 
of fields with both the door and the picture-sensa in each 
of them. As I go on, the door-sensum is more and 
more to the extreme left of its field, and more and more 
distorted. At last there comes a point where the field 
does not contain any appearance of the door. The two 
kinds of sensa can now only be sensed successively. 
Now the co-existent sensa were presumably appearances 
of contemporary slices of two overlapping strands of 
physical history. And the subsequent successive sensa 
are so much like the former simultaneous ones, that it 



430 SCIENTIFIC THOUGHT 

is reasonable to suppose that the same pair of strands 
of physical history continue, and continue to overlap in 
time, although contemporary slices can no longer appear 
in my sense-history. 

Similar remarks apply to looking at a physical object 
and gradually feeling its surface. It is true that the 
tactual sensa are successive, and yet that I take them as 
informing me about the shape of the physical object at 
some one moment. But we find that we can make the 
tactual sensa follow each other in various series at will, 
provided we initiate suitable series of kinesthetic sensa- 
tions. And we can repeat any of these series as often 
as we like. Meanwhile, the visual appearances keep 
constant, and we sense a completely uniform visual 
sense-object. In whatever order we sense our tactual 
sensa, they are connected with a part of the visual 
appearance at the time. It is difficult to resist the con- 
viction that we are dealing with a uniform strand of 
physical history, and that each of our tactual sensa 
reveals a bit of some slice of it. True, the slices revealed 
by successive tactual sensa are presumably successive ; 
but then the uniformity of the visual sensa-object 
suggests that they are all alike in their spatial character- 
istics. Hence, what we learn by touch about different 
parts of successive slices may be put together to tell us 
about the whole of any one slice. Here, again, there are 
certain facts about our experiences of our own bodies 
which reinforce this interpretation. 

(d) Single Observer Watching two Physical Objects in 
Relative Motion. — In the last sub-section we were really 
dealing with the case of one observer who watches two 
physical objects which are at rest relatively to each 
other and to his body, but which cannot both be seen 
at once. Let us now consider the case of an observer 
who watches two physical objects, which are in motion 
relatively to each other. As we have already seen, 
the observer will always be able to make one of these 
physical objects appear as a uniform sense-object, 



SENSIBLE AND PHYSICAL MOTION 431 

whose successive sensa are at the centres of his successive 
fields, provided he moves suitably. We can therefore 
simplify matters by supposing that one of the bodies 
appears in the observer's sense-history as a completely 
uniform sense-object. Let this body be A. It may be 
that at first he will sense a series of fields in which 
both A and the other body B appear as sense-objects. 
If so, he will notice that B does not appear in the form 
of a uniform sense-object. Each sensum of the sense- 
object by which B appears, will very likely have sensible 
motion in its own field. Again, successive B-sensa will 
occupy more and more eccentric positions in their 
respective fields and will be more and more distorted. 
Thus A and B appear at first as two sense-objects which 
overlap in time, i.e., as two overlapping strands in the 
observer's sense-history. But, if we take successive 
pairs of contemporary slices of the two strands, we shall 
find a progressive variation in their respective sensible 
distances apart. Sensum a,, and sensum b r in the field f r 
have a certain sensible distance d r . This is slightly greater 
than d r _ x , the sensible distance between a r _ x and b r __ x in 
the field f r _ x . And it is slightly less than d r+l , the 
sensible distance between a r+1 and b r+l in the field f r+l . 
In fact, if you take the two sense-objects together as 
forming a kind of composite sense-object of a higher 
order in the observer's sense-history, it has the peculiar 
kind of non-uniformity which I have just been describing. 
And this kind of non-uniformity is characteristic of the 
relative motion of sense-objects. 

Now as time goes on the sensa of the B-sense-object 
will occupy more and more eccentric positions in their 
respective fields, till at length no more sensa of the 
B-kind appear in the observer's sense-history. After this, 
he will still be able to sense appearances of A and of B, 
provided he turns his head ; but he will no longer be 
able to sense them in a single field : they must be sensed 
successively or not at all. Let us now compare and 
contrast this with the cases discussed in the last sub- 



432 SCIENTIFIC THOUGHT 

section, (i) Obviously the later stages of this case bear 
a certain resemblance to the last; t'.e., in both, the 
observer can only sense appearances of the two physical 
objects successively. One important difference is that 
this situation has developed out of one in which he could 
sense appearances of both objects together. And it has 
developed independently of the observer ; it is not due to 
any changes of bodily position that he has made. In 
the previous case, if he started by being able to sense 
appearances of the two objects in the same field, he went 
on being able to do so, unless he deliberately moved 
nearer to the two objects. (2) It is true that, in the 
present case, if the observer chooses to walk backwards 
quickly enough, he can again sense fields in which both 
A and B appear. But, whereas in the former case he 
could continue to sense the two appearances together by 
merely walking a certain distance backwards and stopping 
there, he will now find that he must keep on walking 
backwards if he wants to keep on sensing fields in which 
both the objects appear. It is thus clear that in this 
case there is a lack of reversibility, due to the operation 
of some external condition, which is not present in 
the former cases. The externally imposed condition is 
evidently something of the nature of a continuous process, 
with a rate and direction of its own, which, if it is to be 
compensated for at all, must be compensated for by 
another appropriate continuous process in the observer's 
body. The interpretation of this process as movement is 
rendered almost inevitable by the fact that, so long as A 
and B are appearing under the form of two sense-objects 
with contemporary slices in each of the successive fields 
of a sense-history, there is sensible relative motion 
between these sense-objects, as described above. (3) 
Finally, the irreversibility of the present, as compared 
with the reversibility of the last case, shows itself in 
another way. When I dealt with two resting physical 
objects which I could see only successively, I could 
always pass from the field containing an appearance of 



SENSIBLE AND PHYSICAL MOTION 433 

A at its centre to the field containing an appearance of B 
at its centre, and back again, by a mere reversal of my 
rotational kinesthetic sensations. And the amount of 
turning needed was quite independent of the rate at 
which I turned, or the time for which I dwelt on one 
of them before turning to the other. With the relatively 
moving physical objects this complete reversibility breaks 
down. The position here is as follows : If I turn from 
A to B on one occasion, a reversal of the process will 
indeed bring me back to A. But, if I now repeat the 
process, the amount of turning will always be greater 
than before, and it will be greater the longer I have 
dwelt on A. Again : If I turn too slowly, I shall not be 
able to pick up an appearance of B at all ; and, if I turn 
quickly enough to do this, then the quicker I turn 
the less amount of turning will be needed. Lastly, the 
minimum quickness needed will be correlated with the 
swiftness of the relative motion between the sense-objects 
of A and B, when both these co-exist in my sense- 
history. 

(e) Rotation. — For the sake of completeness I must 
say something about rotation, and for the sake of brevity 
I shall say but little. It will be fairly easy for the 
reader to work out the details for himself by analogy 
with what has already been said. I have so far assumed 
that we were looking at objects which either rested 
altogether or moved with a purely translatory motion in 
space. Let us now consider the experiences of an 
observer who stands still and watches a rotating physical 
object which is translationally at rest. He will be able 
to keep its successive appearances in the centres of his 
successive fields without needing to have either transla- 
tional or rotational kinesthetic sensations. But the 
sense-object, which is the appearance of the rotating 
physical object in his sense-history, will be far from 
uniform. In the first place, each of the sensa may have 
sensible rotation (a quite peculiar and characteristic 
sense-quality) in its own field. Then, although closely 



434 SCIENTIFIC THOUGHT 

successive appearances will be very much alike, there 
will always be a part of the later to which nothing 
corresponds in the earlier, and conversely. In this 
respect the sense-object which is the appearance of a 
rotating body bears some resemblance to the sense- 
object by which a moving, but non-rotating, body 
appears in the sense-history of an observer who follows 
the body with his eye by turning his head. 

There is, however, an important difference. After 
a time the series of sensa will begin to repeat itself in 
the same order, and it will do this again and again. 
We may say, then, that a rotating body, which keeps in 
the same place and is looked at by a resting observer, 
appears in his sense-history as a positionally uniform, 
hut periodic, sense-object. Now it is possible for a non- 
rotating body to appear as a periodic sense-object, and 
for a rotating body to appear as a non-periodic sense- 
object. But in each case the observer will have to 
"walk round" the body; and, as he does so, suitably 
turn his head at each moment. "Walking round" a 
body appears in the sense-experience of the observer as 
a peculiar series of kinsesthetic sensations. If he wants 
a rotating physical object to appear in the form of a 
completely uniform sense-object, he must walk round at 
a perfectly definite rate, which depends on circumstances 
over which he has no control. Thus, again, we are 
forced to the conclusion that there are external pro- 
cesses of change, connected with changes in our visual 
sense-histories ; and that certain definite series of kin- 
aesthetic sensations are the signs of processes of change 
in our own bodies which are "equivalent to" these, in 
the sense that they compensate for them and give a 
uniform sense-object. 

(/) Summary of Results of the present Section. — The 
upshot of our discussion on the correlations between 
visual motion and rest and the kinesthetic sensations 
of a single observer seems to be as follows: (i) In 
dealing with a single physical object we can generally 



SENSIBLE AND PHYSICAL MOTION 435 

arrange at will whether it shall appear in the form of 
a positionally uniform or a positionally non-uniform 
(i.e., moving) sense-object. But (2) in order to do this, 
we must sometimes initiate series of kinaesthetic sensa- 
tions, and must sometimes refrain from doing so. 
Sometimes a physical object will appear in my sense- 
history as a uniform sense-object, if and only if I 
refrain from starting a series of kinesthetic sensations. 
If so, it will appear as a non-uniform sense-object when 
I do initiate any such series. And the nature of the 
non-uniformity will depend wholly on the nature of the 
series which I choose to carry on. (3) Sometimes a 
physical object will appear in my sense-history as a 
uniform sense-object if and only if I initiate a certain 
series of kinesthetic sensations. If so, the appropriate 
series is fixed for me. If I do not carry out one of the 
group of appropriate series, the physical object will 
appear as a non-uniform sense-object, whose particular 
non-uniformity depends partly, and only partly, on me 
and my kinesthetic sensations. Having made up my 
mind whether I want a physical object to appear as 
a uniform or a non-uniform sense-object, I have to 
conform to conditions which are imposed on me. And 
these conditions vary from one case to another. (4) Now 
a series of kinesthetic sensations in me is presumably 
an appearance of a certain process of change in my 
body. I know that this process is one condition which 
produces non-uniformity of sense-objects in my sense- 
history ; for in many cases I do sense a uniform 
sense -object so long as I refrain from having kin- 
esthetic sensations, and it becomes non-uniform so soon 
as I start to have such sensations. Conversely, I know 
that in many other cases sense-objects have the same 
kind of non-uniformity when I have no kinesthetic sensa- 
tions, and that this non-uniformity can be eliminated 
if I start a suitable series of kinesthetic sensations. It 
therefore seems reasonable to suppose that the other 
set of conditions, to which I have to conform, is another 



436 SCIENTIFIC THOUGHT 

process of the same general character as that in my 
own body which is revealed to me by my kinesthetic 
sensations. In fact, it seems probable that the positional 
uniformity or non -uniformity of the sense-object by 
which a certain physical object appears to me, depends 
in general on the co-operation of two sets of physical 
processes, one in my body and the other in the physical 
object ; and that the latter process is of the same general 
character as the former, which is revealed to me by 
my kinesthetic sensations. (5) Of course it remains a 
question whether these processes should be regarded as 
mot ions, and, if so, in what Space and what Time they 
happen. For the present all that we can do is to 
make the following tentative suggestion : Two different 
physical objects often appear as two temporally over- 
lapping sense-objects throughout a long tract of my 
sense-history. One may be positionally uniforrh and 
the other not ; if so, one of the sense-objects will be 
in sensible relative motion to the other. Let A be the 
physical object which appears as a uniform sense- 
object a ; and let B, the other physical object, appear 
in my sense-history as the non-uniform sense-object /3. 
From what has gone before, I conclude that the uni- 
formity of a depends on certain processes (or, in the 
limiting case, on the absence of such processes) in my 
body and in A. Similarly, the positional non-uniformity 
of /3 depends jointly on certain processes in my own 
body and B. Since the process in my body is common 
to both, it seems certain that there must be a difference 
between the A-process and the B-process ; for otherwise 
there is no apparent reason why a should be uniform 
and /3 non-uniform. Thus a difference between the 
processes in A and B is correlated with sensible relative 
motion between a and /?, the two sense-objects by which 
A and B appear in this tract of my sense -history. 
Conversely, if A and B had both appeared as uniform 
sense-objects, a similar argument would show that there 
is no reason to assume that there is any difference 



SENSIBLE AND PHYSICAL MOTION 437 

between the relevant physical processes in A and B. 
Thus sensible relative rest between a and ,8, the sense- 
objects by which A and B appear in this tract of my 
sense-history, is correlated with identity of the processes 
in A and B. 

This, I think, is about as far as we can go without 
entering into further detail about the human body as 
a physical object, and our knowledge about it. When 
we have done this, we shall find that the general con- 
clusion (4), and the more special conclusion that the 
physical processes on which the uniformity or non-uni- 
formity of visual sense-objects depends are of the nature 
of motions, are greatly strengthened. We will, there- 
fore, make this the subject of our next section. 

The Human Body as a Physical Object. — Human 
bodies may be, as we are told that they are, "temples 
of the Holy Ghost" ; in which case it must be admitted 
that the Third Person in the Trinity sometimes displays 
a strange taste in temples. But, whatever else they 
may be, they certainly are physical objects as much as 
chairs or tables. Nevertheless, they do occupy a peculiar 
position among physical objects. In the first place, 
each is connected in a perfectly unique way with an 
observing mind, which looks out at the rest of the world 
from its body. Secondly, each of these minds has a 
peculiar knowledge of its own body, which it does not 
have of any other body in the universe. A given mind 
perceives every other body except its own in exactly the 
same way as it perceives a chair or a potato. It per- 
ceives its own body, partly in this way, and partly in a 
quite different way, viz., by organic sensations. Lastly, 
the minds connected with various human bodies can 
and do constantly communicate with each other, so that 
observer A learns that observer B perceives B's body in 
the same way in which A perceives his own body. A 
also learns that B can no more perceive A's body in 
this way than he himself can perceive B's body in this 



438 SCIENTIFIC THOUGHT 

way. 1 believe that these peculiarities of human bodies 
and of our knowledge about them are essential factors 
in founding- the common-sense and scientific notions of 
physical objects, and in developing the concepts of 
physical Space, Time, and Motion. 

(<i) A Solitary Observer s Perception of his ow)i Body. — (i) 
I do not know very much about my own body directly 
by sight, but I do know something. I cannot see my 
own head at all, though by means of a mirror I can see 
an incomplete optical object in a different place, and I 
now conclude on various grounds that it is very much 
like the optical constituent of my head. I can see the 
front of my trunk from a little below the chin ; can see 
my hands and feet often quite distinctly ; and can see 
less distinctly the upper parts of my arms. The greater 
part of the visual appearance of that fraction of my body 
which does appear in the visual field is very vague and 
distorted. 

There are two important points to notice about the 
visual appearances of my trunk, (i) Although they are 
so fragmentary, they are almost invariably present in 
my visual sense-history. To sense a visual field with 
no such sensa in it, I have to follow the advice given to 
the " happy band of pilgrims," and " look upward to the 
skies," in a most unnatural and uncomfortable way. In 
fact, my own trunk appears to me as a highly uniform 
and highly persistent visual sense-object. Whenever I 
carry on a series of translatory kinesthetic sensations the 
greater part of the contents of my later fields bears no 
resemblance to that of my earlier fields. But the visual 
appearances of my body are present with little variation 
throughout. (ii) The other peculiarity is that all the 
visual appearances of my trunk have a very small visual 
depth in all the fields. They are at the extreme " front " 
of each field, and the visual appearances of all other 
physical objects are "behind" them at various greater 
depths in the field. 

Now, with other objects that appear in my visual 



SENSIBLE AND PHYSICAL MOTION 439 

sense-history, I have to initiate a certain series of trans- 
latory kinesthetic sensations before I can sense any corre- 
lated tactual sensa. As this series goes on, the visual 
depths of the successive sensa, which together make up 
the sense-object, steadily decrease in each successive 
field. But, as I have said, the visual appearances of 
my own body have a practically constant minimal depth 
in all my successive visual fields. Thus, when I walk 
up to a resting physical object, there are two sense- 
objects which co-exist throughout this tract of my sense- 
history. One is the sense-object by which the distant 
physical object, to which I am walking, appears. This 
is positionally non-uniform, in so far as the successive 
sensa that belong to it have progressively diminishing 
depths in their respective fields. There are also corre- 
lated variations in size, brightness, etc. The other is 
the sense-object by which my own body appears in my 
sense-history. This is practically uniform, since all its 
successive sensa have minimal visual depth. Thus, 
successive pairs of contemporary sensa, one from one 
sense-object and the other from the other, have progres- 
sively smaller visual distances apart. So the series of 
translatory kinesthetic sensations, experienced in walk- 
ing up to an external physical object, is associated with 
sensible relative motion between the sense-object which 
represents the external body and the sense-object which 
is the appearance of my own body in my visual sense- 
history. 

(2) My tactual sensations of my own body are 
peculiar, (i) As I have said, most physical objects 
which appear in my visual sense-history can only be 
touched after an appropriate series of translatory kin- 
aesthetic sensations. If this series be reversed, we soon 
cease to be able to sense any tactual sensa correlated 
with our visual sensa. But we do not need to walk in 
order to touch our own bodies ; and, having once 
touched them, we do not cease to be able to do so by 
walking away. In fact, all other tactual sense-objects 



440 SCIENTIFIC THOUGHT 

are rigidly bound up with series of translatory kin- 
a\sthetic sensations; but the tactual sense-object which 
represents my body is indifferent to all such series. 
This must be correlated with the fact that translatory 
kinesthetic sensations make no difference to the depths 
of successive visual appearances of our own bodies, 
whereas they do make a difference to the depths of the 
successive visual appearances of nearly all other physical 
objects. My trunk is the only physical object which 
appears throughout the whole of my visual sense-history 
as a positionally uniform sense-object ; and it is the 
only physical object which I can touch whenever I like, 
i.e., which I need not walk up to and cannot walk 
away from. 

(ii) The tactual sensa which I sense when I touch 
my own body are characteristically different from those 
which I sense when I touch any foreign body. Suppose 
that in each of two successive visual fields of my history 
there is an appearance of my hand. In the first, let this 
be in visual contact with an appearance of my table, 
and in the second let it be in visual contact with an 
appearance of my leg. Apart from minor qualitative 
differences there will be the fundamental difference that, 
in the second case, I "feel my leg being touched" as 
well as "feel my leg with my finger." This peculiar 
experience of " double contact," as it is called, helps me 
to distinguish the surface of my own body from those of 
all other physical objects. It also helps the solitary 
observer to fill out the very fragmentary knowledge of 
his own body which he would have if he were confined 
to visual appearances alone. He can feel a closed 
surface, marked out by the characteristic of double 
contact ; and can gradually explore its contours. Only 
a very small part of these tactual sensa will be correlated 
with his visual sensa. But I can start with a visual 
appearance of my hand visibly in contact with a visual 
appearance of some part of my trunk, and can gradually 
move my hand so that its successive appearances in 



SENSIBLE AND PHYSICAL MOTION 441 

successive fields are nearer and nearer to the extreme 
edge of the appearance of my trunk. At length I shall 
no longer be able to see my hand ; but the character- 
istic tactual sensa will still be sensed, and they will be 
continuous with those earlier ones which were correlated 
with the visual appearance of my hand visibly in contact 
with the visual appearance of part of my trunk. 
Finally, as I go on moving my hand, it may become 
visible again ; and its visual appearance will again be 
in visible contact with the extreme edge of a visual 
appearance of part of my trunk. My own body is thus 
known to me by tactual exploration as a closed surface 
which resists my efforts to penetrate it, like any other 
physical object. But it is marked out from the other 
closed surfaces that I feel by the qualitative peculiarity 
of the tactual sensa, and by the fact that I do not have 
to walk up to it and cannot walk away from it. 

(3) We come finally to a most important peculiarity 
of our sense-experience of our own bodies. I am 
constantly getting mild tactual sensations from the 
whole surface of my body without actively exploring it 
with my hand. These come from the contact of my 
clothes, from air-currents, and so on. In each Specious 
Present they form a mass which is the largest part of 
what I will call the somatic field. These somatic fields 
are, in the main, extremely alike over long periods of 
time ; they thus join up with each other to form an 
extremely uniform somatic sense-object. Within each 
somatic field certain characteristic sensa stand out ; e.g., 
at one time I may itch in one place, and at another time 
I may feel a burn at another place, and so on. Now 
literally " inside " the somatic fields there are from time 
to time outstanding bodily feelings, like headaches and 
toothaches and stomach-aches, which enliven my somatic 
history and prevent it from being perfectly tame and 
uniform. Again, my kinesthetic sensations are sensible 
events with places in my somatic fields. Thus a 

peculiarity of my body is that I have sense-perception 

2 F 



442 SCIENTIFIC THOUGHT 

of events which happen in its inside, as well as of events 
on its outside. Of course, events in the inside of my 
body appear to me in a very peculiar way, viz., by kin- 
aesthetic sensations, bodily pains, etc. But the insides 
of other bodies do not appear to me in sense-perception 
in any way whatever, unless, of course, I cut them open 
or "turn them inside out." And if I do this, I am not 
perceiving their insides while they are inside, but am 
only perceiving new outsides, which for various reasons 
I take to be exactly similar to former insides. 

(/;) Several Intercommunicating Observers watching each 
other s Bodies. — If I were and had always been a com- 
pletely solitary observer, these facts about my body 
would not help me very much to form the concept of 
physical objects, having insides as well as outsides, 
occupying positions in physical Space, and moving 
about in it as physical Time elapses. I should rather 
be inclined to stress the differences between my own 
body and all other objects that appear to me, and leave 
the matter there. But I am not in this solitary situation. 
The important fact is that there are other people like 
myself, whose bodies I can see and touch, and with 
whom I can exchange notes by verbal communication 
and gestures. I am convinced that this fact plays a 
vitally important part both in the development of the 
general concept of physical objects, and in the develop- 
ment of the connected concepts of physical Space, Time, 
and Motion. 

Any other human body is perceived by me in exactly 
the same way as I perceive a stone or a chair. If I look 
at it, it appears as a characteristic visual sensum in the 
middle of my visual field. I can then approach it and 
sense correlated tactual sensa. And there is no essential 
difference in the experiences which I have in this case 
and in that of an ordinary inorganic object. Similarly, 
I perceive the motion or rest of another human body 
in precisely the same way as I perceive those of any 
other external object. But I recognise that other human 



SENSIBLE AND PHYSICAL MOTION 443 

bodies are connected with minds like my own ; and, 
although I can only know their bodies from the outside, 
they tell me that they know them from the inside, and 
that they know mine only from the outside. I under- 
stand what they mean, because of my own experiences, 
described in the last sub-section. I thus come to 
recognise that there are plenty of other bodies beside 
my own, having internal processes ; although I cannot 
perceive these processes in any body except my own. 
So the fact that I cannot perceive such processes else- 
where ceases to be any reason for supposing that they 
do not exist elsewhere. I know that they happen in my 
body, although other people tell me that they cannot 
perceive them ; and I am therefore ready to believe that 
they happen in other mens bodies, though / cannot 
perceive them ; since they tell me that they can 
do so. 

The logical position is therefore as follows : (i) I 
know what is meant by internal processes from my own 
sense-experiences of pleasures, pains, kinesthetic sensa- 
tions, etc. (ii) I believe that there are other instances 
of bodies with such internal processes, from communica- 
tion with other minds ; though I cannot myself perceive 
these processes in the other instances. (iii) I then 
extend this conception that bodies have "insides," in 
which all kinds of interesting events happen, from 
human bodies to others, which, so far as I know, are 
not connected with minds, (iv) This is reasonable, 
because they appear to me in exactly the same way as 
do all human bodies except my own ; and I already 
know, from the instances of other human bodies, that 
the non-appearance of internal processes to my senses 
is quite compatible with the fact that such processes are 
going on. I thus conceive that all my sense-objects are 
appearances of physical objects, which have an inner 
history of their own, and are seats of internal processes 
in the way in which human bodies are the seats of those 
processes which appear to the minds connected with 



444 SCIENTIFIC THOUGHT 

them as headaches, toothaches, (anaesthetic sensations, 
etc. How far in detail the analogy is to be pressed is 
of course another question, which can only be gradually 
answered by empirical investigation. I propose now 
to apply these general considerations, first to the general 
concept of physical objects, and then to the more special 
concept of physical motion and rest. 

(c) The Human Body as the typical Physical Object. — 
Intercommunication with other human minds, and 
observation of the appearances of their bodies, fill out 
the general concept of physical objects in the following 
ways : 

(i) Any of the sense-objects by which other physical 
objects appear to us is liable to sudden interruptions. 
The visual sense-object comes to an end in darkness, 
or when we shut our eyes or turn our heads away. 
And the tactual sense-object exists only when we are 
at or near a certain place. But, in spite of these 
interruptions in the sensible appearances of other men's 
bodies in my sense-history, the minds connected with 
these bodies tell me that their somatic history has gone 
on all the time with very little change. Thus, in the 
case of human bodies, I have reason to believe that 
their inner history is much more permanent and 
continuous than their appearances in my sense-history. 
I extend this conclusion by analogy to non-human 
bodies, which appear in the same kind of way in my 
sense-history. This argument is strengthened by the 
fact that I know that my own somatic history is going 
on steadily at times when other men tell me that my 
body has ceased to appear in their sense-histories. 

(2) I know that I can initiate noises, bodily move- 
ments, etc., and that when I do so they are preceded 
by special series of events in my somatic sense-history. 
Other people tell me that they hear noises, see move- 
ments, and so on, at the centre which is the optical 
place of the visual appearances of my body. Similarly, 
when I hear noises or see movements connected with. 



SENSIBLE AND PHYSICAL MOTION 445 

the place occupied by the optical constituent of another 
man's body, he will tell me. that he has been " making" 
the noises or movements. This means that he produced 
them by initiating an appropriate series of sensible 
events in his somatic history. Thus we arrive at the 
general conclusion that many changes in the visual 
appearances of A's body in B's visual sense-history are 
connected with changes in A's somatic sense-history. 
Now the latter are appearances to A of physical events 
within his own body. Thus, in the case of a human 
body, we reach the notion that the place which is optically 
occupied by its optical constituent is physically occupied 
by certain events which produce changes in this optical 
object, or at any rate in parts of it. This is the crude 
beginning of the notion of scientific events and their 
connexion with sensible appearances. We extend this 
result in the usual way to those places which are 
optically occupied by complete optical objects which 
are constituents of non-human bodies. That is, we 
conclude that these places are physically occupied by 
certain events which are responsible for the changes 
that take place from time to time in the complete 
optical object. 

(3) The comparative constancy of my somatic sense- 
history, combined with the fact that no one can "see" 
the whole surface of my body at once, supports the 
view that successive visual sensa often justify a belief 
in co-existing- physical objects, or parts of one physical 
object. No one can see my face and the back of my 
head at the same time, though there may be an appear- 
ance of each of these in successive visual fields of the 
same observer. But I know that my somatic history 
includes "face-feelings" and "head-feelings" in each 
of its successive fields. Thus, although the observer's 
visual sensa were successive, and presumably revealed 
non-contemporary slices of my body-history, yet there 
is reason to suppose that each of these slices (and all 
that came between them) included a part corresponding 



446 SCIENTIFIC THOUGHT 

to the appearance of a head, and a part corresponding 
to the appearance of a face. 

These seem to be the main factors which our per- 
ception of our own bodies and our intercommunication 
with other observers supply to the concept of physical 
objects in general. The human body is the physical 
object par excellence ; with an "inside" which is con- 
tinually, if inadequately, perceived by its own mind 
through bodily feelings ; with an outside which is 
perceived on and off by other observers through their 
visual and tactual sensations ; and with internal pro- 
cesses, which reveal themselves to its own mind as 
kinesthetic and other bodily feelings, and reveal them- 
selves to other minds as movements and other changes in 
its visual and other appearances. Each observer reaches 
the notion of human bodies as complete physical objects 
by combining his own experiences of the inside of his 
body with what other observers tell him about their 
experiences of the outside of his body. He then extends 
the general conception, thus formed, to non-human 
physical objects, which cannot tell him about their own 
insides. 

(d) The Human Body and the Concept of Physical 
Motion. — In the section on the correlations between 
kinesthetic sensations of a single observer and the 
motion or rest of visual sense-objects in his sense- 
history, we made no special assumption as to the nature 
of the physical objects which he was watching. They 
might be other human bodies, or they might be 
inorganic bodies, like pennies or chairs. Even so, we 
reached the following results, of which I will remind 
the reader : (i) That this observer might reasonably 
conclude that the positional uniformity or non-uniformity 
of the visual sense-object, by which a certain physical 
object appears in his sense-history, depends in general 
on the co-operation of two processes, one in his own 
body and the other in the physical object which he is 
watching. The one in his own body appears to him 



SENSIBLE AND PHYSICAL MOTION 447 

in the form of a series of kinesthetic sensations in his 
somatic sense-history. And it is reasonable to think 
that the other is of the same general nature, (ii) That 
this observer might reasonably hold that a certain 
identity between such processes in two physical objects 
A and B involves relative rest between them, and that 
differences between the two processes involve relative 
motion between A and B. 

Now these conclusions, which are rendered highly 
plausible by the mere correlations between a solitary 
observer's kinesthetic sensations and the motion or 
rest of his sense-objects, are greatly strengthened when 
the physical objects which he watches are the bodies 
of other observers who can communicate with him. 

(1) Suppose that observer a watches B, the body of 
observer ft, and that at the same time observer ft 
watches A, the body of observer a. The correlations 
between the kinesthetic sensations and the visual sense- 
objects of each observer are of exactly the same kind 
as if he were watching an inorganic body. But, in 
the present case, the observer and the observed can 
compare notes about their kinesthetic sensations and 
their visual sense-objects. Let us first suppose that a 
does not have to keep turning his head in order to keep 
his eye on B, and that B appears to him as a completely 
uniform visual sense-object. Then ft will tell a that 
he, too, does not need to keep turning his head in order 
to keep his eye on A, and that A appears in his sense- 
history as a completely uniform visual sense-object. If 
they now compare their translatory kinesthetic sensa- 
tions, they will find either that they are absent in both, 
or, if present, are of precisely the same character. 

Let us next suppose that a finds that he has to keep 
turning his head in order to keep his eye on B. B will 
then appear in a's sense-history as a partly, but only 
partly, uniform sense-object. The nature of its non- 
uniformity has already been fully described. Now ft 
will also find, and will tell a that he finds, that he must 



448 SCIENTIFIC THOUGHT 

keep turning his head in order to keep his eye on A, 
and thai A appears in his sensedustory as a partly, but 
only partly, uniform sense-object of the kind already 
described. In this case o and (3 will find, on comparing 
notes, that they both experience a series of rotational 
kinesthetic sensations, and that there is an analogy 
between them. But, on the other hand, they will 
always find that there is a difference between their trans- 
lators kinesthetic sensations. This will sometimes take 
the form that one and only one of them has such 
sensations at all (I am leaving out of account for the 
sake of simplicity observers who are carried about 
without effort in trains or motor-cars). There is one 
other important point which they will discover on 
comparing their experiences. The appearance of a's 
head in /3's sense-history will be a rotating visual sense- 
object, and so will be the appearance of /3's head in a's 
sense-history. Thus each will discover that, of his two 
kinds of kinesthetic sensation, one is correlated with a 
rotationally non-uniform sense-object by which his head 
appears in the sense-history of the other observer, and 
the other kind is correlated with a positionally non- 
uniform sense-object, by which his body appears in the 
sense-history of the other observer. 

(2) So far, we have confined ourselves to two observers 
a and /3 respectively watching B and A, the bodies of 
the other. Let us now take an observer y, who watches 
the bodies A and B of the two observers a and ft, who 
can communicate with him and with each other. As we 
have said before, if y keeps up a suitable series of 
kinesthetic sensations, he can always make A appear in 
his sense-history as a completely uniform sense-object, 
each of whose successive constituent sensa is at the 
middle of its field. We will suppose that y does this. 
He may then find either (i) that B appears as a com- 
pletely uniform sense-object, or (ii) that B appears as 
a positionally non-uniform sense-object. Each of the 
component sensa in this may have sensible movement 



SENSIBLE AND PHYSICAL MOTION 449 

in their fields. And, even if they do not, successive 
pairs of contemporary A- and B-sensa will have pro- 
gressively different sensible distances in their respective 
common fields in y's visual sense-history. 

Now, in case (i), a and /3 will tell y that, on 
comparing notes with each other, they find no difference 
in their translational kinesthetic sensations, which may, 
of course, in the limiting case both be non-existent. In 
case (ii), a and [3 will tell y that, on comparing notes, 
they do find a difference in their translational kinesthetic 
sensations. If one of them has no such sensations the 
other will have them. Moreover, each of them will tell 
y that the body of the other appears to himself as a non- 
uniform sense-object. And y's body C will appear in 
/3's, though not in a's, sense-history as a non-uniform 
sense-object. 

Now these communicated experiences (1) and (2) 
leave no doubt at all that the positional uniformity or 
non-uniformity of the sense-object, by which one human 
body appears in the sense-history of another observer, 
depends jointly on those physical processes in the two 
bodies which are revealed to their respective minds in 
the form of kinesthetic sensations. Moreover, they 
show clearly that uniformity in the sense-object depends 
on a certain identity of quality and quantity in the two 
processes, whilst positional non-nniformity in the sense- 
object depends on certain qualitative and quantitative 
differences between the two processes. Lastly (2) shows 
that relative motion of the sense-objects by which two 
human bodies appear in the sense-history of a third 
observer depends on a difference between these two 
processes in the two human bodies, whilst relative rest 
of two such sense-objects depends on an identity of 
character between the two processes. 

We now extend this conclusion in the usual way to 
physical objects which are not connected with minds 
that can communicate with us. We assume that, in all 
cases, the uniformity of a sense-object in the sense- 



450 SCIENTIFIC THOUGHT 

history o\ an observer depends upon a certain identity 
between that physical process in his own body which 
appears to him as a series of kinesthetic sensations, and 
another physical process of the same general type, 
which happens in the physical object of which this 
uniform sense-object is the visual appearance in the 
observer's sense-history. And we assume that, in all 
cases, the positional non-uniformity of a sense-object in 
the sense-history of an observer depends on differences 
between the physical process in his body which appears 
to him as a series of kinesthetic sensations, and another 
physical process of the same general type, which happens 
in the physical object of which this non-uniform sense- 
object is the visual appearance in this observer's sense- 
history. 

(e) Several Intercommunicating Observers watching the 
same Physical Object. — One more very important fact 
remains to be described. Suppose that two observers, 
a and /?, are watching a certain physical object O, and 
that a third observer y is watching their bodies, A and 
B. It may happen that O appears in a's sense-history 
as an uniform sense-object, and that it appears in /3's 
sense-history as a positionally non-uniform sense-object. 
If this be so, the observer y will always notice that the 
sense-objects by which A and B appear in his sense- 
history are in relative motion to each other. And, as 
usual under these conditions, there will be a difference 
in the translational kinassthetic sensations of a and /3. 
If we generalise this from human bodies to all physical 
objects we reach the following conclusion : It is possible 
for any physical object to appear at once as a uniform 
sense-object in the sense-history of one observer and as 
a non-uniform sense-object in that of another observer. 
But, if it does so, it will always be found that there is 
some difference between those physical processes in the 
bodies of the two observers which appear to them as 
series of their kinesthetic sensations. 

This result, which can actually be observed, might 



SENSIBLE AND PHYSICAL MOTION 451 

also have been deduced from what has gone before. If 
the physical object O appears as a resting sense-object 
in a's visual sense-history, this implies a certain identity 
of character between the relevant physical processes in 
A and in O, according to the argument of the last sub- 
section. If O appears as a moving sense-object in /3's 
sense-history, this implies a difference between the 
relevant physical processes in B and in O, on the same 
principles. It follows at once that, under these circum- 
stances, there must be a difference between the relevant 
physical processes in A and in B. And this should appear 
to a and to j8 as a difference between their kinesthetic 
sensations. That such a difference is actually found 
supports the conclusions of the last sub-section, since 
they are here used as hypothetical premises from which 
it follows that such a difference ought to be found. 

In the next chapter I propose to apply the results of 
this one to the notions of sensible and physical Space- 
Time, and so to end my treatment of the spatio-temporal 
aspects of Nature and their sensible and perceptual basis. 

The following additional works may be consulted 
with advantage : 

G. F. Stout, Manual of Psychology, Bk. III. Part II. 
W. James, Principles of Psychology. 
Kant, Critique of Pare Reason {Analytic of Principles). 
Schopenhauer, World as Will and Idea, Vol. I. Bk. II. 



CHAPTER XII 

" And nu bit and for Godcs naman halsath selcne thara the 
tlias boc raedan lyste thaet he for nine gebidde, and him ne wite 
gif he hit rihtlicor ongite thonne he mihte. Forthsemthe selc 
mou sccal be his ondgites masthe and be his a^mettan sprecan 
thaet he sprecth and don thset thaet he deth." — King Alfred, 
Preface to his Translation of Basthius. 

Sensible and Physical Space-Time 

We have at length reached a position where it becomes 
possible to deal with the concept of physical Space-Time, 
from which, as we shall see, the concepts of physical 
Space and of physical Time are abstractions of two 
different kinds. We shall thus finally work back, from 
a wholly different starting-point, to the position which 
we reached at the end of Part I. 

Let us first take a backward glance over the country 
that we have crossed, and see how the universe looks 
from our present standpoint. We shall then be able to 
see what part of our journey from crude sensation to the 
refined concepts of mathematical physics remains to 
be completed ; and, having done so, we can try to 
complete it. 

(a) Statement of the Present Position. — The situation, 
so far as it has now developed, is roughly as follows : 
There is a world of physical objects, some of which, 
like my own body, are connected with observing minds 
which can communicate with each other. Others, so 
far as we know, are not connected with minds ; but in 
their general character they are very much like those 
which are. Correlated with each human body there is 
a general sense-history, which is split up into several 
special sense-histories, visual, tactual, auditory, somatic, 

452 



SPACE-TIME 453 

and so on. We can sense temporal relations between 
sensa in our different special sense-histories, just as we 
can sense temporal relations between different sensa in 
the same special sense-history. But we cannot sense 
spatial relations between contemporary sensa in our 
different special sense-histories, though we can sense 
such relations between contemporary sensa of the same 
special history. These spatial characteristics are much 
more marked in the visual sense-history than in any of 
the others. 

My somatic sense-history contains sensa which are 
appearances of internal states and processes of my own 
body. In my other special sense-histories are various 
sense-objects, some uniform for a time, others non- 
uniform. There are correlations between certain sense- 
objects in my different special histories which lead me 
to regard them as different kinds of appearances of the 
same external physical object. All these remarks about 
me and my sense-histories apply equally, mutatis mutandis, 
to other observers and their sense-histories ; as I learn 
by intercommunication. 

Between sensa in the histories of different observers 
neither spatial nor temporal relations can be sensed by 
either of the observers or by any third observer known 
to us. But there are correlations between certain sense- 
objects of different observers which lead us to say that 
the same physical object is appearing to all of them. 
When this is so, there is generally a certain external 
place which all these sensa maybe said to "occupy" 
in some Pickwickian and definable sense, such as optical 
occupation. Again, there are certain methods, discussed 
in the last chapter but one, by which some sensa of 
different histories are grouped together as "neutrally 
simultaneous," and others are grouped apart as 
" neutrally successive." 

Then there are the very elaborate correlations between 
the uniformity or non-uniformity of sense-objects in 
the visual histories of observers, and certain events 



454 SCIENTIFIC THOUGHT 

in their somatic histories called " kinesthetic sensa- 
tions." We have been studying these in the last 
chapter. We came to the conclusion that the positional 
uniformity or non-uniformity of the sense-object by 
which a certain physical object appears to an observer, 
depends upon certain physical processes in the external 
object and the observer's body ; and that these pro- 
cesses in one's own body appear to oneself as kines- 
thetic sensations. A more careful study of these corre- 
lations revealed two further closely connected points. 
One is that the positional uniformity of a sense-object 
depends on an identity of character between these two 
physical processes, and that positional non-uniformity 
is correlated with certain differences between them. 
The other is that relative rest between two sense-objects 
in a sense-history depends on a similar kind of identity 
between two such physical processes in the bodies which 
appear as these two sense-objects, whilst relative motion 
between two sense-objects is correlated with similar 
kinds of difference between two such physical processes 
in the bodies which appear as these two sense-objects. 
Sensible motion and rest are absolute, but they seem to 
depend on relations of identity and difference respectively 
between physical processes in the body which appears 
and the body of the observer to whom it appears. 

(b) Statement of the Remaining Problem. — These, then, 
are some of the facts which have so far been elicited, 
and some of the highly probable inferences which have 
been made from them. The next thing is to state 
clearly the problem which still remains. The rest of 
the problem is to make, if possible, a further synthesis 
by analogy with what we already know. Can we treat 
the world of physical objects and events as forming a 
whole which is analogous to a single sense-history ? 
That is : Can we regard scientific objects as analogous 
to sense-objects ; can we suppose that they have spatial 
relations to each other, such as we can sense only between 
sensa in a single sense-field ; and can we suppose that 



SPACE-TIME 455 

they endure, and have temporal relations to each other, 
such as we can sense only between sensa within a single 
general sense-history? Lastly, can we suppose that 
physical objects rest and move in this spatio-temporal 
physical whole, as sensa do in their fields, and as sense- 
objects do in our sense-histories? This, I think, is the 
real problem about physical Space, Time, and Motion. 
It is the problem of constructing a single, neutral, 
public Space-Time of physical objects and events, on 
the analogy of the many personal private space-times 
of the various observers' sense-histories. 

Now it is not, of course, a question of just making 
such suppositions in the abstract. Our only possible 
justification for supposing anything of the kind is that 
it provides a scheme which summarises all the known 
correlations between sensa, and is, at the same time, 
familiar to us because of its analogy to our own sense- 
histories with which we are directly acquainted. It is 
theoretically possible that no such supposition would do 
justice to the actual correlations among sensa. It is 
still more likely that no supposition which made the 
structure of physical Space-Time exactly analogous to 
that of an individual sense-history would account for 
the known facts. Again, if the physical world can be 
consistently regarded as a spatio-temporal whole with 
considerable, though not complete, analogy of structure 
to an individual sense-history, it is probable that this 
can be done in a number of alternative ways, all of 
which will synthesise the known facts equally well. 
Even if up to a certain date human beings had only 
happened to think of one view of the structure of physical 
Space-Time, there is no reason to doubt that, if they 
thought more carefully and paid less attention to certain 
traditional points of view, they would be able to devise 
dozens of alternative structures for physical Space-Time 
equally capable of doing justice to all the known corre- 
lations among sensa. No doubt the physical world has 
a certain absolute intrinsic structure ; and this structure 



456 SCIENTIFIC THOUGHT 

exhibits itself, in part at least, in the correlations between 
sensa of the same and of different observers. But we 
have to treat this structure piecemeal in the sciences 
of geometry, ehronometry, kinematics, dynamics, and 
electro-magnetics, and by making suitably correlated 
modifications in the axioms of these various partial 
sciences we can express the same absolute structure in 
innumerable different and equally satisfactory ways. If, 
so far, very few alternative schemes have been proposed, 
this is due to nothing more recondite than lack of 
scientific imagination and the imperfection of our techni- 
cal mathematical and logical apparatus. 

It is, nevertheless, an interesting and important inquiry 
to see how far we can do justice to the known facts by 
supposing that the structure of the physical world is 
analogous to that of our sense-histories, and to see what 
is the minimum difference of structure between the two 
which we must postulate. For, after all, our physical 
concepts have their roots in our sense-histories. 

It is evident that it might be possible to regard the 
physical world as forming a spatio-temporal whole 
analogous in general outline to a single sense-history, 
and yet that we might have to postulate differences of 
detail. I do not mean by this simply that the contents 
of the two might be different. It is perfectly certain 
that they will be. The ultimate contents of a sense- 
history are the sensa of the observer whose sense-history 
it is. The ultimate contents of physical Space-Time 
are scientific events. Even if it should be possible to 
regard scientific events as composed of sensa (which is 
far from certain), each scientific event will be composed 
of sensa from the histories of many different observers, 
and also presumably of many more sensa which do not 
belong to the history of any observer. Thus, even on 
this hypothesis, the ultimate contents of physical Space- 
Time will be groups of correlated sensa. But, beside this 
difference which there certainly must be between physical 
Space-Time and any sense-history, there may well be 



SPACE-TIME 457 

a difference of structure between the two, e.g., the kind 
of difference which there is between a Euclidean and 
a hyperbolic space. A sense-history and the physical 
world are both four-dimensional spatio-temporal wholes, 
and we must therefore talk of their geo-chronometry rather 
than their geometry. What I am saying then is that, 
although a sense-history and the physical world may be 
so far analogous in structure that we can say that both 
have a geo-chronometry of some kind, yet the geo- 
chronometries of the two may differ in detail. 

The reader must beware of supposing that a Space- 
Time is an entity which exists in its own right, side by 
side with its contents. It is often convenient to talk as 
if this were so, and it does no harm, provided we 
recognise that it is always an abbreviated expression, 
and understand clearly what it is an abbreviation for. 
Having got rid of the absolute theories of Space and of 
Time, we must not introduce them again for Space- 
Time. Many really eminent writers on the Theory 
of Relativity have expressed themselves in a most 
unfortunate way, which suggests to innocent readers 
that they think of Space-Time as a particular existent, 
with properties of its own, which acts on matter like 
a cue acts on a billiard-ball. When we talk of the 
properties of physical Space-Time we are simply 
enumerating certain very general structural character- 
istics of that spatio-temporal whole which is the physical 
world. The only existent under discussion is this 
whole, which is composed of scientific events bound 
together in a characteristic unity by spatio-temporal 
relations. 

An analogy will perhaps make this clearer than 
much discussion will do. The French and British 
armies are two elaborately organised hierarchies. Their 
contents are different ; since the former is composed of 
Frenchmen, and the latter of Englishmen and Scotsmen 
and a few items from the Celtic Fringe. There is a 
great analogy between the organisations of the two, 

2 G 



45^ SCIENTIFIC THOUGHT 

which renders it reasonable to call them both armies. 
But there are also considerable differences in detail. 
If a military writer set (Hit to describe in general terms 
the structure of the French army and that of the British 
army, he would be studying something akin to two 
systems of geo-chronometry. He could do this without 
referring to particular French and English soldiers, 
such as Jacques Bonhomme and Tommy Atkins. He 
could even talk intelligibly of the "effects" which these 
two types of organisation "produce" on French and 
English soldiers of various temperaments. But, if this 
led him to suppose that the organisations whose 
structure he is describing were substances that existed 
side by side with the soldiers, he would be talking 
nonsense ; and it would be the same kind of nonsense 
as is talked by people who imagine Space-Time to be 
an existent substance which pushes and pulls bits of 
matter about. It must, therefore, be clearly understood 
that, when we talk of the geo-chronometry of Space- 
Time, we are simply describing certain very general 
and abstract structural features of that whole which is 
the physical world. 

Since the geo-chronometry which is to be ascribed 
to physical Space-Time depends entirely on the cor- 
relations between our sensa, we must not be surprised 
if opinions about it alter with the growth of scientific 
knowledge. For one view might fit all the facts that 
were known up to a certain date, and a different view 
might be needed to fit both them and certain new facts 
which were discovered later. This is exactly what has 
happened in the change from Newtonian to Relativistic 
dynamics and kinematics. 

(e) The Concept of an Idealised Sense-history. — If we 
want to see how closely the geo-chronometry of the 
physical world can be approximated to that of a single 
sense-history, we must begin by considering what is 
the geo-chronometry of a sense-history. But, before 
doing this, it will be well to remove in thought certain 



SPACE-TIME 459 

limitations, which are, in fact, present in all our sense- 
histories, but which seem rather to depend on de facto 
limitations of our powers of sensing and remembering 
than on anything characteristic of the structure of sense- 
histories as such, (i) We can think of a sense-history 
as stretching back indefinitely into the past, although 
in fact we can only remember a certain distance back, 
and although presumably the history does not extend 
backwards beyond our birth. (2) We can remove in 
thought the limitation of a finite Specious Present. We 
can regard the fact that only a very thin slab can ever 
be sensed at once, and that the whole history is a series 
of such slabs, as contingent. That is, we can regard 
the whole history as a continuous four-dimensional 
strand. (3) We can remove in thought those limita- 
tions which our finite powers of seeing, hearing, etc., 
impose on the extension of each of our actual sense- 
fields. We can, e.g., imagine the spatial limits of our 
visual fields indefinitely extended ; as they would be 
if we could see everything, however distant from our 
bodies. (4) We can also remove the limitation which 
is imposed by the fact that we cannot see all round us at 
once. (5) So far we have been conceptually extending 
our sense-histories by removing certain limits imposed 
by sensation and memory. It now remains to proceed 
in the opposite direction. We cannot sense fields of 
no duration. But we can sense events of shorter and 
shorter duration. We can thus conceive any slab of 
a sense-history as cut into thinner and thinner slabs. 
In the end we can conceive of slabs of no duration, 
and can imagine the whole sense-history analysed into 
an infinite series of such instantaneous slices, just as 
we can conceive a cylinder as analysed into an in- 
finite series of parallel plane circular sections. Such 
momentary slices are not of course existents, and they 
are not literally parts of the sense-history ; but they can 
be defined by Extensive Abstraction, and a Pickwickian 
meaning can be given to the statement that the sense- 



460 SCIENTIFIC THOUGHT 

history is composed of thorn. These momentary slices 
will be purely spatial, whereas the sense-history as a 
whole and any finite real part of it are spatio-temporal. 
We may call each of these momentary sections a 
momentary sense-space in the given sense-history. By 
further applications of Extensive Abstraction within 
a single momentary sense-space, we could evidently 
define momentary sense-planes^ momentary sense-lines, and 
;// 1 ) m e n tt i ry sense-poin ts . 

It is pretty evident that, if the physical world be 
analogous to a sense-history at all, it will be analogous 
to an idealised visual sense-history, extended concep- 
tually in the ways described. And I think there is very 
little doubt that this is the original of the concept of the 
physical world as a whole in Space and Time. We 
must now consider more in detail the geo-chronometry 
of an idealised visual history. In the section that 
follows I am more than usually indebted to Whitehead, 
and I shall be contented if I provide the reader with 
" first aid " to the study of Whitehead's two great works 
on the philosophy of Nature. 

The Geo-chronometry of an Idealised Visual History. — 
The idealised visual history is a four-dimensional spatio- 
temporal whole, formed by the continual addition of 
successive slices, which are idealised fields. Each of 
these slices has duration, and the duration of the whole 
history is the sum of the durations of the successive 
slices up to and including the last that has become. 
Now we can regard all these successive fields as normal 
to a certain straight line in the history, just as successive 
circular slabs of a cylinder are all normal to its axis. 
This common normal to all the fields may be taken as 
the time-axis of the history. By Extensive Abstraction 
we then reduce the temporal thickness of the successive 
slabs to zero, and we thus get a series of momentary 
three-dimensional spaces, all normal to the time-axis of 
the history. 

Now the geo-chronometry of the history might, 



SPACE-TIME 



461 



apart from all wilder alternatives, be either Euclidean 
or elliptic or hyperbolic. According to which of these 
alternatives is realised, the geometry of its momentary 
spaces will be Euclidean or elliptic or hyperbolic. On 
either of the two latter alternatives the successive 
momentary spaces will not be parallel to each other. 
In elliptic geometry (which is analogous to the geometry 
of the surface of a sphere) there are no parallels, for all 
co-planar straight lines intersect each other twice. In 
hyperbolic geometry there are parallels and there are 
non-intersecting co-planar straight lines which are not 
parallel. And the common normals to a given straight 
line are not parallel to each other, though they do not 
intersect each other. It is only on the Euclidean alterna- 
tive that the momentary spaces will be parallel. The 
three alternatives may be very roughly illustrated in two 
dimensions and on a Euclidean plane by the three 
diagrams below. 



.t' 



s, s g 




i)£uc/ideanCase (it) £//tpfic Cose (//;) tfypcr6o//e Case 

(It must, of course, be remembered that what appears in 
these diagrams as lines normal to the time-axis represent 
three-dimensional spaces in the four-dimensional sense- 
history. Also that the curves in diagrams (ii) and (iii) 
are attempts at representing non-Euclidean straight lines 
on a Euclidean plane.) 

We may perhaps dismiss the elliptic alternative at 
once. If the geo-chronometry of a sense-history were of 
this type, its time-axis, like all other straight lines in this 
geometry, would be a closed curve, like a great circle 
on a sphere. Whilst I see no theoretical impossibility 
in the time of Nature being of this kind, I think that 



}<>_> SCIENTIFIC THOUGHT 

there is no evidence to support the suggestion. If it 
were so, the course of Nature would continually repeat 
itself in cycles. These might, of course, be of enormous 
duration ; and so the fact that we have no empirical 
evidence for this alternative cannot be counted as 
evidence against it ; we may make a present of the 
suggestion to the Dean of St Paul's and the Neo- 
platonists. 

We will therefore confine ourselves to the Euclidean 
and the hyperbolic alternatives. On the Euclidean 
alternative there would be an infinite number of equally 
permissible time-axes for the sense-history, and these 
would all be parallel to each other. The line t' in (i) 
is an example. On the hyperbolic alternative, so far 
as my very limited knowledge of four- dimensional 
hyperbolic geometry may be trusted, I should say that 
there could only be one time-axis for the sense-history. 
It is true that there are plenty of straight lines in the 
history, parallel to /. The line pp' in (iii) is an example. 
But none of them will be normal to the momentary 
spaces which are normal to /, and therefore none of 
them could be taken as time-axes. Again, there are 
plenty of lines beside t which are normal to all the 
momentary spaces. The line nri in (iii) is an example. 
But none of them are straight lines, and therefore none 
of them can be taken as time-axes. They are, in fact, 
curves called horocycles, and horocycles are to hyperbolic 
straight lines much as small circles are to great circles 
on the surface of a sphere. I do not think that the 
uniqueness of the time-axis suffices to show that the 
geo-chronometry of an idealised sense-history could not 
be hyperbolic ; but we shall see later that the Space- 
Time of Nature could hardly be supposed to have one 
single unique time-axis, even apart from the Theory 
of Relativity. Hence, we had better work out the 
geo-chronometry of the idealised sense-history on the 
Euclidean hypothesis, since we want it only as a basis 
for the geo-chronometry of physical Space-Time. 



SPACE-TIME 463 

There is a more positive reason for rejecting the 
hyperbolic alternative for the idealised sense-history. 
In the Euclidean case, since the normals to the time- 
axis are parallel to each other, and since Euclidean 
parallels are everywhere equidistant from each other, 
any slab of the sense-history, bounded by two such 
normals, has the same thickness throughout (see Fig. (i) 
above). In the hyperbolic case the normals diverge 
from each other on both sides of the common time-axis. 
The result is, that it is only on the Euclidean alternative 
that a Specious Present would have one definite limited 
duration. On the hyperbolic alternative sensa, far from 
the centres of a field, could last for enormous stretches 
of time, remaining in a single Specious Present. This 
seems to be contrary to fact. So, on every ground, 
it seems reasonable to take the geo-chronometry of the 
idealised sense-field as of the Euclidean type. 

We can now advance to the very important con- 
ception which Whitehead would call the timeless space 
of the idealised sense-history. When we talk of objects 
resting or moving in a space, we clearly cannot be 
thinking of a momentary space. For both rest and 
motion involve lapse of time. We must, in fact, be 
thinking of some kind of space which lasts for the 
whole time under consideration, and does not change 
as the time flows on. This is what Whitehead means 
by a timeless space. We have now to define such a space 
for the idealised sense-history. 

Let us imagine a completely uniform sense-object 
which lasts throughout the whole of the sense-history. 
As we slice the history up into thinner and thinner 
sections we shall, ipso facto, be slicing this sense-object 
into thinner and thinner sections, all exactly alike and 
all occupying precisely similar positions in these fields. 
Finally, by Extensive Abstraction, we shall reach a 
series of successive momentary spaces, each containing 
a momentary section of the uniform sense-object. All 
these momentary sections will be exactly alike, and 



464 SCIENTIFIC THOUGHT 

exactly similarly situated in their respective momentary 
spaces. If, now, we imagine the spatial dimensions of 
the uniform sense-object reduced more and more, so 
that, finally, it is the history of a mere point, it is clear 
that the object reduces to a line parallel to the time- 
axis of the sense-history. Each point in this straight 
line is in one of the momentary spaces of the history, 
and each of the momentary spaces contains one of the 
points. And these points are in corresponding- places in 
their respective momentary spaces. Thus any straight 
line in the sense-history which is parallel to the time- 
axis, is the history of a sense-object of punctual spatial 
dimensions, which rests in a single "place" through- 
out the duration of the history. 

We may therefore say that every straight line, parallel 
to the time-axis of a sense-history, is a pomt of the time- 
less space of the history. The timeless space of the 
history thus consists of the whole bundle of straight 
lines in the history which are parallel to its time-axis. 

We have now to define the straight lines of the timeless 
space. To do this, let us imagine a sense-object which 
is positionally non - uniform and of punctual spatial 
dimensions. It is evident that it will consist of a series 
of points, one in each of the successive momentary spaces. 
But these points will not occupy corresponding positions 
in their respective momentary spaces, since the object is 
positionally non-uniform. Thus the whole assemblage 
of them will be a curve of some kind in the sense-history. 
It will, in general, be a tortuous curve ; and it will, of 
course, never be a straight line parallel to the time-axis, 
for that would be the history of a positionally uniform 
punctual object. Again, it will, of course, never be a 
line in any one momentary space, for it would then not 
be the history of any enduring object whatever. Now, 
through each of the points of this curve, there goes one 
and only one straight line parallel to the time-axis of 
the history. And each of these lines, as we have seen, 
is one point in the timeless space of the history. It 



SPACE-TIME 465 

follows that the assemblage of all these lines is the 
course traced by the moving object in the timeless space. 
Such an assemblage of parallel straight lines will form 
a surface in the sense-history, which will not in general 
be fiat. But, if the moving object happens to describe 
a straight line in the timeless space of the history, this 
surface will flatten out into a plane parallel to the time- 
axis. The easiest way to see this is the following : It 
is admitted that the points of the timeless space of a 
sense-history are straight lines in the history, parallel to 
its time-axis. Now a straight line is uniquely determined 
by two of its points. Now the only figure in the sense- 
history, which is uniquely determined by two straight 
lines parallel to the time-axis, is the plane which contains 
them both, and is, of course, itself parallel to this axis. 
It is thus evident that a straight line in the timeless space 
of a sense-history is a plane in the sense-history, parallel 
to its time-axis. 

It remains to define the planes of a timeless space. 
A plane in the timeless space will be a figure uniquely 
determined by a straight line in that space, and a point 
which is in the space but not on the straight line. Now, 
we have already seen that a straight line in the timeless 
space is a plane in the history, parallel to its time-axis ; 
and that a point in the timeless space is a straight line 
in the history, parallel to its time-axis. The fact that 
the point is outside the line in the timeless space is 
identical with the fact that the corresponding line is 
outside the corresponding plane in the sense-history. 
It follows at once that a plane in the timeless space of a 
sense-history is a three-dimensional region in the history, 
uniquely determined by a plane, parallel to the time- 
axis, and a straight line, also parallel to the axis but 
not contained in this plane. This is an unlimited region, 
which plays a corresponding part in a four-dimensional 
manifold to a plane in an ordinary three-dimensional 
space. 

We have thus defined the points, straight lines and 



4 66 



SCIFXTIFIC THOUGHT 



planes of the timeless space of a given idealised sense- 
history in terms of certain special types of figures in the 
Latter. These definitions are wholly due to Whitehead. 
It will be noticed (i) that the timeless point is something 
more complex than the momentary point, since it consists 
of a whole series of the latter ; (2) some straight lines in 
the sense-history are also momentary straight lines in 
one of the momentary spaces ; but no straight line in 
the history is also a straight line in the timeless space. 
At best, it can only be a point in the latter ; (3) a timeless 
straight line is a set of straight lines in the sense-history, 
of a certain kind. Once the timeless concepts have been 
defined, the geometry of the timeless space can be worked 
out. It will be of the same character as the geometry 
of the momentary spaces of the history. For there is a 
one-to-one correspondence (though never an identity) 
between the timeless points, straight lines and planes, 
as defined above, and the momentary points, straight 
lines and planes of any one of the momentary spaces. 

As a visual sense-history is a four-dimensional 
whole, it is not possible completely to illustrate all this 
on paper. But we can help the reader to understand 
the four-dimensional case by imagining a sense-history 
which has only three dimensions, two spatial and one 
temporal. The momentary spaces will then be planes 
at right angles to the paper, and we can illustrate the 
relations between sense-history, momentary spaces, and 
timeless space in the drawing given below. 
Y, Y 2 

Q 



>t 




In this picture S L and S., are two momentary sections 
of such a sense-history. The dotted line p x q. 2 is the 
straight line in the sense-history which represents the 



SPACE-TIME 467 

history of a point-object, moving along a certain straight 
line in the timeless space of the history with a certain 
uniform velocity. The first momentary section of this 
object is the momentary pointy in the momentary space 
S r The last section of it is the momentary point q 2 
in the momentary space S 2 . Intermediate sections are 
momentary points in intermediate momentary spaces. 

The dashed line p x p 2 is the point P in the timeless 
space of the sense-history. The dashed line q x q 2 is the 
point Q in the timeless space of the history. P would 
have represented the history of the punctual sense- 
object if the latter had stayed in its original position. 
Q would have represented the history of this object if 
the latter had always been in the position which it 
finally occupies. The plane p x q x q. z p», which is deter- 
mined by the two straight lines P and Q, is the timeless 
straight line in the timeless space of the history which 
the moving punctual object traverses. It is uniquely 
correlated with the momentary straight lines p x q x in S 2 
and p 2 q 2 in S 2 , which might be called the "instantane- 
ous directions of motion of the moving object at the two 
moments t x and £,." These are of course similar, in 
the present case, since the object is moving all the time 
in one direction in the timeless space. 

The angle between the dotted line p x q 2 and the dashed 
line p x p 2 depends on the velocity of the moving point- 
object in the timeless space. The histories of all moving 
points which traverse this particular line in the timeless 
space will be straight lines in the plane p x q x q.±p. z , but their 
directions in this plane will depend on the velocity with 
which the object traverses the line. If the velocity be 
non-uniform, they will, of course, no longer be straight 
lines ; but they will still be plane curves in this plane. 
Naturally we cannot illustrate timeless planes in our 
diagram ; for we can only get them in connexion with 
a four-dimensional sense-history, whose momentary 
sections are not planes, as in the diagram, but three- 
dimensional spaces. Also, there are no momentary 



468 SCIENTIFIC THOUGHT 

planes in our diagram, except the timeless spaces 
themselves. 

(</) Physical World'lines and their Mutual Relations. — 
It is evident that such an idealised sense-history as we 
have just been describing would be a kind of "world," 
with a time, a timeless space, and objects which move 
or rest in the latter as the former Hows on. The question 
now is : How far can the world of physical objects and 
events be regarded as forming a spatio-temporal whole, 
analogous in character to an idealised sense-history ? If 
the analogy be complete, the physical world will have one 
time-direction (though many parallel time-axes), and one 
timeless Space, which will be of the Euclidean type. 
In this Space all physical objects will rest or move as 
the one physical Time Hows on. 

We must be prepared to recognise at once that it is 
by no means obvious that any such view of the structure 
of the physical world will fit the known facts. After all, 
why should the physical events and objects which are 
connected with a number of different sense-histories 
form a spatio-temporal whole which is exactly analogous 
in structure to a single sense-history? Even if there 
should be a certain analogy, we have not the slightest 
right to expect it to extend to every detail ; i.e., we have 
no right to be surprised if the geo-chronometry of 
physical Space-Time should not be exactly like that 
of the idealised sense-history. We shall see in a moment 
that most of the apparent paradox of the Theory of 
Relativity is due to the fact that it disappoints our simple- 
minded expectation that the geo-chronometry of physical 
Space-Time shall be exactly like that of a single ideal- 
ised sense-history. But, on reflection, we see that this 
expectation is absolutely groundless, and that it would 
be rather a queer coincidence if the geo-chronometries 
of two such different wholes were exactly alike. 

After these general preliminaries, let us see how far 
the analogy can be carried. A physical object is a 
succession of scientific events, just as a sense-object is 



SPACE-TIME 469 

a series of successive sensa in a sense - history. A 
punctual sense-object, whether positionally uniform or 
non-uniform, is a line of some kind in its sense-history. 
If it be positionally uniform, and therefore rests in the 
timeless space of the sense-history, it is a straight line, 
parallel to the time-axis ; if it moves, it is a curve of 
some kind on a surface generated by lines parallel to the 
time-axis, and so on. If then a punctual physical object 
can be regarded as analogous to a sense-object, we 
must suppose that it (or its history, if you prefer it) is a 
curve of some sort in physical Space-Time. We will call 
such a curve a " world-line," following Minkowski. All 
other material particles must equally be regarded as 
curves in physical Space-Time. We must next consider 
the intrinsic characters and mutual relations of world- 
lines, for the whole question of whether it is worth while 
to talk of a physical Space-Time at all depends on the 
nature of these. 

Suppose that B, the body of observer /3, appears as 
a resting sense-object in the visual sense-history of 
another observer a. We know that A, the body of a, 
will appear as a resting sense-object in the visual sense- 
history of /3, provided that a's and /3's kinesthetic 
sensations are alike. The complete symmetry between 
a's experiences in connexion with B, and /3's experiences 
in connexion with A, suggests that there is some great 
similarity in the world-lines of A and B. (Or rather in 
the world-lines which would represent their histories if 
they were reduced to punctual spatial dimensions.) It 
seems reasonable to suppose that, in such cases, we are 
dealing with pairs of intrinsically similar and similarly 
situated world-lines in physical Space-Time. We can 
conceive of groups of observers whose bodies form sets of 
similar and similarly situated world-lines. We will call 
these sets of relatively resting physical objects. We know 
that, if a certain body appears as a sense-object which 
moves in the timeless space of any one member of the 
set, it will appear as a sense-object which moves in the 



470 SCIENTIFIC THOUGHT 

timeless space of each member of the set. If it happens 
to be the body of an observer, we know further that his 
translatory kinesthetic sensations will differ from those of 
all members of the set. Moreover, all the bodies of the 
set will appear to this observer as sense-objects which 
move absolutely, but rest relatively to each other, in 
the timeless space of his sense-history. It seems reason- 
able to suppose that the world-line of this observer's 
body is in some way different from those of the set in 
question. There might be an intrinsic difference in the 
nature of the curve, or some kind of difference in its 
situation or direction in physical Space-Time. A geo- 
metrical illustration of the first kind of difference would 
be given by a straight line and a hyperbola ; an 
illustration of the second kind of difference would be 
given by two non-coplanar straight lines, or by two 
coplanar straight lines at an angle to each other. 

We can now extend these suggestions in the usual 
way from the bodies of observers to physical objects 
in general. We can suppose that a set of relatively 
resting particles is a set of similar and similarly situated 
world-lines, and that any particle which moves relatively 
to this set is a world-line which differs, either intrinsic- 
ally or in its situation in physical Space-Time, from 
the members of this set. 

{e) Straight and Tortuous World-lines. — World-lines 
might be curves of many different kinds ; some might 
be intrinsically very complex (like highly tortuous 
curves in ordinary space) ; others might be intrinsically 
very simple (like ordinary straight lines). It will be 
remembered that a punctual sense-object, which rests 
in the timeless space of its sense-history, is a straight 
line parallel to the time-axis of the history. Punctual 
sense-objects, which move in the timeless space of the 
sense-history, may be straight lines (though they need 
not be) ; but they are never parallel to the time-axis. 
We must see how far there is analogy to this in physical 
Space-Time. 



SPACE-TIME 471 

If any analogy at all can be drawn between a sense- 
history and the physical world, we must assume (1) that 
at least some particles are straight world-lines ; (2) that 
at least some of these straight world-lines are per- 
missible directions for time-axes for physical Space- 
Time ; and (3) that, by taking certain particles as having 
the characteristics (1) and (2), and by using suitable 
criteria of simultaneity, we can account for all the known 
general rules of spatio-temporal correlation among 
physical events. We will now see how far the analogy 
can be carried on this assumption. 

A straight world-line which is a permissible time- 
axis for physical Space-Time will be analogous to the 
time-direction of a sense-history. If the whole physical 
world is to be analogous to a single sense-history, every 
momentary physical event must have one and only one 
straight world-line passing through it, parallel to the 
given time-direction. The whole of such a bundle of 
parallel world-lines may be called a physical reference 
frame. From what has been said in the last section it 
is clear that every line of such a bundle is a point in the 
timeless space of the frame, and conversely. Each line 
of the bundle is, in fact, the history of a hypothetical 
particle, which rests at a certain place in the timeless 
space of the frame as the time of the frame flows on. 
The place of any momentary point-event in the timeless 
space of the frame will be the particular line of the 
bundle which passes through this point-event. The 
date of this event in the frame will be its particular 
position on this line. 

Particles which move uniformly in straight lines in 
the timeless space of this frame will be world-lines 
which (1) are straight, and (2) are contained in a certain 
plane parallel to the time-axis, but (3) are not themselves 
parallel to it. Particles which move non-uniformly but 
rectilinearly in the timeless space of the frame will be 
world-lines which (1) are not straight, but (2) are 
contained in some plane parallel to the time-axis. This 



472 SCIENTIFIC THOUGHT 

plane in Space-Time is, of course, the straight line in the 

timeless spaee of the frame along- which the particle 
moves. Particles which move non-uniformly and non- 
rectilinearly in the timeless space of the frame will be 
lines which (i)are not straight, (2) are not plane, but 
(3) are confined to a surface generated by straight lines 
parallel to the time-axis of the frame. Finally, the 
momentary spaces of the given frame will be sections 
of physical Space-Time, normal to the time-axis of the 
frame. Momentary events in the same momentary space 
will be contemporary with respect to the frame. 

(/) The Point of Separation between the Traditional 
View and the Special Theory of Relativity. — There is thus 
a complete analogy between a physical reference frame 
and an idealised sense-history, on the assumptions 
which we are at present making. On these assumptions 
every event in Nature has its place and date in such a 
frame. But now there arises a question to which there 
is nothing analogous in a sense-history. The question 
is this : Are all straight world-lines permissible time- 
axes for physical Space-Time, or are some of them 
permissible and others not? And, if the latter be true, 
what distinguishes those which are, from those which 
are not permissible? 

In a given sense-history there is one and only one 
Ume-direetion. This is because the simultaneity or 
successiveness of sensa in the same sense-history is 
actually sensed, and we have therefore no choice as to 
which we shall group together as simultaneous, and 
which we shall group apart as successive. The succes- 
sive slabs of the sense-history are given to us in the form 
of sense-fields, and the only possible time-direction is 
that of their common normal. The only choice allowed 
to us is that we could take any straight line in the sense- 
history, parallel to the time-direction, as a permissible 
time-axis, assuming that the geo-chronometry of the 
sense-history is Euclidean. 

If there were an exact analogy between physical 



SPACE-TIME 473 

Space-Time and an idealised sense-history, there would 
be one and only one direction in physical Space-Time 
which could be taken as the time-direction. If this were 
so, there would be one and only one frame of reference 
in which all the events of Nature could be consistently 
placed and dated. The only latitude allowed us would 
be that any frame which rested in the timeless space of 
the first would itself be a permissible frame. For this 
would merely amount to taking another world -line, 
parallel to the original one, as our new time-axis. 

Now this is exactly the assumption which the 
classical mathematical physics did make. It assumed 
that there was one and only one fundamental frame of 
reference in which all the events of Nature could be 
consistently placed and dated. The timeless space of 
this is the ''stagnant ether," and the one permissible 
time-direction is the history of any particle of the ether 
or of any particle that rests in it. No straight line which 
makes an angle with the one outstanding time-direction 
will be a possible time-axis ; the sections of physical 
Space-Time normal to such a line will not be momentary 
spaces, and the whole bundle of lines parallel to such 
a line will not form the points of a timeless space. 

Now there is nothing antecedently absurd in such 
a view. Temporal and spatial characteristics are 
different, for all observers ; and therefore it might well 
be that there is one and only one outstanding direction 
in Space-Time which can be taken as a time-direction. 
Moreover, it is certain that the assumption is not far 
wrong ; since it is the assumption of the traditional 
physics, and this has proved capable of dealing with 
all the more obvious spatio-temporal correlations of 
physical events in a single spatio-temporal scheme. 
We can, in fact, at once reject the opposite extreme 
view, viz., that all straight world-lines are equally per- 
missible as time-axes. For this would be inconsistent 
with the admitted difference between spatial and tem- 
poral characteristics for all observers, and with the 

2 H 



474 SCIENTIFIC THOUGHT 

very great measure of success which has attended the 
diametrically opposite assumption, that there is only 
one direction in Space-Time which can be taken as a 
time-axis. 

(g) 7 he Hypothesis of a UmitedRange of 'lime-directions. — 
The only alternative worth discussing is that all straight 
world-lines whose directions lie within certain limits, 
and only these, are permissible time-directions. The 
traditional physics makes physical Space-Time exactly 
analogous in structure to a single idealised sense-history. 
The present suggestion makes it considerably different 
in principle, though not necessarily very different in 
practice. Nothing but the observable correlations 
between physical events, as betrayed by correlations 
between sensible events in various sense-histories, can 
decide between these alternatives. 

A little reflection shows that there is a certain 
incoherence in the traditional view, as regards mechanical 
phenomena. It is admitted that axes which move uni- 
formly in straight lines in the timeless space of the 
supposed fundamental frame will do equally well for 
placing events for mechanical purposes. And such 
axes will be represented by straight world-lines which 
make an angle with those which represent the funda- 
mental frame. If there were only mechanical phenomena 
to be considered, it would be natural to suppose that 
all such world-lines would do equally well as time-axes, 
and that all the corresponding frames would do equally 
well for placing and dating physical events. The only 
reason for thinking that there must be one fundamental 
frame connected with a certain unique direction in 
Space-Time, was the notion that any pair of events must 
be either simultaneous or successive, and that they could 
never be both. It was thought that the phenomena of 
light, electricity and magnetism, would show us the 
one fundamental frame, which was merely concealed in 
mechanical phenomena by the particular form which the 
laws of motion happen to have. Thus the traditional view 



SPACE-TIME 475 

holds that there is only one permissible time-direction, 
which can and must be used for dating all physical 
phenomena. But it allows you to place mechanical 
phenomena by reference to any axes which move 
uniformly and rectilinearly in the timeless space of 
the fundamental frame. 

Now the experiments on which the Special Theory 
of Relativity is based, show that this supposed difference 
between mechanical and electro-magnetic phenomena 
is a pure myth. Electro-magnetic phenomena fail to 
reveal any unique fundamental frame. Their laws 
remain of exactly the same form if you refer the events 
to axes which move uniformly and rectilinearly in the 
space of one fundamental frame, provided that you take 
the straight world-line which represents these moving 
axes as a permissible time-direction, and use it for dating 
your electro-magnetic events. 

The Special Theory of Relativity may, in fact, 
be summed up in the following statement: There is a 
whole set of different directions in Space-Time, equally 
permissible as time-directions for dating physical events. 
But all the permissible time-directions are confined 
within certain limits. Corresponding to any one of 
these will be a timeless space, whose points are the 
world-lines parallel to it. Every physical event has 
a unique place and date in any one such frame. Its 
place in the timeless space of any frame is determined 
by the line, parallel to the time-direction of the frame, 
which passes through it. Its date in the frame is deter- 
mined by its position on this line. The laws of all 
physical phenomena have precisely the same form, no 
matter which of these frames is used for placing and 
dating them. 

All the characteristic features of the Special Theory 
of Relativity follow at once from this supposition as to 
the geo-chronometry of physical Space-Time, as I will 
now show in brief outline. 

(i) There is nothing that can be called the timeless 



47^ 



SCIENTIFIC THOUGHT 



Space of Nature. There will be as many different 
timeless spaces as there are different permissible time- 
directions. 

(2) Two events which are contemporary in one frame 
will not be contemporary in another, unless they happen 
to occupy the same place in the timeless space of the first 
frame. The figure below will make this clear. 

M\fz 



rnz 






X 



t, 



m, 



/> 



^ 



•&.- 



+*, 



5fy 

Call the two frames F x and F 2 . Since they differ, they 
will consist of two bundles of parallel world-lines, 
inclined to each other. Since the two events are not to 
be at the same place in the timeless space of F 1( they 
will be on two different world-lines of the bundle, say 
l x and m v Since they are to be contemporary in F 1} 
they must both be in some one momentary space of F x . 
This will be a section of Space-Time, normal to the time- 
direction of F r Call this momentary space S\/x. Then 
the points A and /*, in which the lines l x and m x cut S\u, 
will represent our two events, which are simultaneous 
in the frame F x , but spatially separated in its timeless 
space. Now let X lie on the line / 2 of the frame F 2 , and 
let p. lie on the line ;« 2 of the frame F 2 . In this frame, 
instead of being in a single momentary space S\u, they 
are in the two successive momentary spaces S\ and S M . 
They are therefore successive in F 2 , though simultaneous 
in F r Moreover, their distances apart in the two time- 
less spaces are not the same. In the former, it is the 
distance between l x and m x ; in the latter, it is the smaller 
distance between 1. 2 and ni 2 . 

(3) Conversely, two events which are in the same 
place in the timeless space of F x will not be in the same 



SPACE-TIME 



477 



place in the timeless space of F 2 , unless they happen to 
be also contemporary in F r The diagram below will 
show this. 




The two events are on a certain line l v parallel to t Xi 
since they are in the same place in the timeless space 
of Fj. Since they are not to be contemporary in F x , they 
must be in different momentary spaces S\ and Sx' of F r 
The two events will be represented by the two points 
X and X', in which the line l x cuts these two momentary 
spaces respectively. In F 2 the two events X and X' are 
necessarily on two different lines, / 2 and /' 2 , parallel to 
t 2 , the time-direction of F 2 . They are therefore at 
different places in the timeless space of F 2 . Moreover, 
their temporal separation is different in the two frames. 
In Fj it is represented by the line XX', in F 2 by the shorter 
line between the two dotted normals to %, which represent 
the momentary spaces of F 2 , in which the two events are 
respectively situated. 

(4) We have still to consider some implications of 
the fact that not all straight world-lines are permissible 
time-axes, but only those whose directions lie within a 
certain limited range in physical Space-Time. Take 
any straight world-line t, which is a permissible time- 
axis, and consider any other non-parallel straight world- 
line/'. There will be one and only one plane in Space- 
Time which is parallel to t and contains p. In this 
plane take a line t' , parallel to /. Then / and t' will 
cut each other at an angle. This plane will be a straight 
line in the timeless space of the frame of which t is the 
time-axis. The line p will represent a particle moving 



478 SCIENTIFIC THOUGHT 

along this straight line in the timeless space with a 
uniform velocity. As we saw in the last section, the 
greater the velocity of this particle the greater will be 
the angle between/ and /'. Now we know that, if the 
angle between p and t' exceed a certain size,/ will not 
be a permissible time-axis. This would imply that there 
is no frame in whose timeless space the particle, whose 
history is the line/, rests. This would be contrary to 
the complete relativity of physical rest and motion. 
There is thus a certain maximum possible relative 
velocity, whose magnitude is determined by the size 
of the angle in Space-Time within which all permis- 
sible time-directions lie. If a straight world-line make 
a greater angle than this with any permissible time- 
direction, it cannot be the history of an actual particle 
or physical process. Such a world-line will, of course, 
cut each momentary space of any one frame at a point ; 
but you cannot take these successive momentary points 
as sections of the history of any one object, though of 
course each may be a section of the history of a different 
object. Now this notion of a certain maximum relative 
velocity is characteristic of the Special Theory of Rela- 
tivity, which, on empirical grounds, identifies this 
velocity with that of light in vacuo. 

(5) We cannot, so far as I can see, determine any- 
thing about the actual magnitude of the angle of the 
four-dimensional cone in physical Space-Time, within 
which all permissible time-directions lie. The tangent 
of its half-angle will indeed be the velocity of light. 
But we must beware of supposing that, because c, the 
velocity of light in centimetres per second, is a very 
large number, therefore the half-angle of the funda- 
mental cone must be very nearly a right angle, and 
therefore that there is a very wide range of possible 
time-directions. For the numerical value of the velocity 
of light obviously depends entirely on the units that 
we choose for measuring distance and duration. The 
largeness of c may simply mean that the centimetre 



SPACE-TIME 



479 



is a very small space-unit, or that the second is a very- 
large time-unit ; it tells us nothing about the size of 
the ansfle of the fundamental cone. 

(6) It follows at once from what has just been said 
that, whilst all the points in any timeless space are 
straight world-lines, there are many straight world- 
lines which are not points in any timeless space. It 
follows also that some pairs of momentary point-events 
are intrinsically separated spatially, i.e., occupy different 
positions in all timeless spaces, whilst others are not, 
i.e. , they occupy the same place in some timeless space. 
The diagram below will make this clear : 



X X' 



P 



-I 



■ m 



e , 



■**, 



Let X and X' be two momentary point-events at the 
same point / of the timeless space of the frame F r 
Let hi be another momentary point-event at the point m 
of the same frame, and let X, X', and /u, all have different 
dates in this frame. Draw the straight world-lines X/x 
and XV« ^ both fall within the fundamental cone, both 
are permissible time-directions. If so, X and^u will occupy 
the same place in the timeless space of the frame corre- 
sponding to X/x, and X' and p. will occupy the same place 
in the timeless space of the frame corresponding to XV- 
But it may happen that XV falls inside the cone, whilst 
X/x falls outside it. If so, X/x is not parallel to a possible 
time-axis, and therefore is not a point in any timeless 
space. Hence the momentary point-events X and /x will 
have an intrinsic spatial separation. It will be noticed 
that the question whether two momentary point-events, 
which occupy different places in the timeless space of a 
certain frame, are intrinsically separated in space or not, 
depends on whether their dates in the frame are much 
or little separated. X and /x, which are intrinsically 



480 SCIENTIFIC THOUGHT 

separated in space, are much nearer together in date 
than V and p, which are not spatially separated in all 
timeless spaces. 

(7) Almost exactly similar remarks apply, mutatis 
mutandis^ to temporal separation. This is sometimes 
intrinsic and sometimes not. The diagram below will 
explain how this happens. 



,"3 ■'"& 



X 



-// 



■ m > \ /v 



S&L », 



-*-/, 



X and jjL are two momentary point-events, which are 
simultaneous in the frame F x , and occupy the two points 
/j and iii 1 respectively in the timeless space of this 
frame, v is a third point-event, which differs both in 
place and in date from both X and /x in the frame F x . 
Join \y and fxv by straight world-lines. Draw the 
straight world-lines n 2 and n 3 , normal to \v and jxv 
respectively. If both u 2 and n z be permissible time- 
directions, \v and fxv will both represent momentary 
spaces, one in the frame corresponding to ;/ 2 , and the 
other in the frame corresponding to n z . If so, X and 
v will be contemporary in one of these frames, and fx 
and v will be contemporary in the other. Their tem- 
poral separation is therefore non-intrinsic. But it may 
happen that, whilst ;/ 2 falls inside the fundamental cone, 
and is therefore a permissible time-direction, ;/ 3 falls 
outside it, and therefore is not a permissible time- 
direction. If so, Xv will be a momentary space, and 
ixv will not. It will follow that fx and v are intrinsically 
separated in time, i.e., that there is no frame in which 
they are simultaneous. Here, again, the difference 
depends on the fact that X and v are further apart in 
the timeless space of F t than are fx and v. Hence, two 
point-events, which are successive in a certain frame, 



SPACE-TIME 481 

are intrinsically successive if they be near enough 
together in the timeless space of the frame. If they 
be far enough apart in the timeless space, they will 
not be intrinsically successive, i.e., it will be possible 
to find a frame in which they are simultaneous. 

All these seven consequences of the view that more 
than one, but not all, directions in physical Space- 
Time are permissible time-directions, are characteristic 
results of the Special Theory of Relativity ; and, as 
this certainly fits the facts better than the traditional 
views, we may assume that physical Space-Time has 
this particular kind of structure, at least to a very high 
degree of approximation. Thus the physical world as 
a whole is not completely analogous to a single idealised 
sense-history, since the latter has only one possible 
time-direction, whilst the former has several. Instead 
of being surprised at this difference, we ought rather 
to be impressed by the remarkable amount of similarity 
which exists between the structures of two such wholes. 

(h) The Facts imderlying the above Theory of the Geo- 
chronometry of Physical Space-Time. — If the above view 
of the structure of physical Space-Time is to be verifi- 
able, as it is to a high degree of approximation, we 
must have some empirical means of (i) distinguishing 
straight from tortuous world-lines, and (ii) distinguish- 
ing those straight world-lines which are permissible 
time-directions from those which are not. We find 
that we can unify the facts by assuming that the history 
of any particle which rests relatively to the fixed stars 
is a straight-world line, and that the history of any 
particle which moves in a straight line with respect to 
the fixed stars, and with uniform velocity as judged 
by clocks set by the method of light-signals described 
in Part I, Chapter IV, is another straight world-line 
inclined to the first. And the history of a wave of light 
is the limiting kind of straight world-line which we can 
take as a permissible time-direction. It is important 
to notice that, although any one permissible reference- 



482 SCIENTIFIC THOUGHT 

frame for physical Space-Time is strictly analogous, on 
the present theory, to an idealised sense-history, yet 
we have to treat the two from rather different stand- 
points. The temporal relations between events in the 
sense-history are cognised directly by sense and 
memory. Certain events are given simultaneously and 
others are given in succession. Moreover, the sense- 
history has an intrinsic unit of duration in the constant 
sensible duration of all the successive Specious Presents. 
In dealing with the physical world we have to set up 
c?iteria for the simultaneity or succession of physical 
events ; and it is not until we have done this that we 
can say which physical events are to be put into the 
same momentary space and which into different 
momentary spaces of a given frame. Moreover, there 
is no intrinsic standard of equality of physical duration, 
and so we have to set up some criterion for equality 
of time-lapse. Until we have done this, we cannot 
decide whether the motion of a certain particle in the 
timeless space of a certain frame is uniform or not. 
And, until this has been decided, we cannot say whether 
the history of this particle is or is not to be regarded as 
a straight world-line, inclined to the time-direction of 
the frame in question. 

(/) The Difference between the Special and General 
Tlieories of Relativity. — The traditional physics and the 
special Theory of Relativity agree in making the geo- 
chronometry of physical Space-Time Euclidean. Or, 
to put it more accurately, the geo-chronometry of the 
one permissible frame on the traditional theory is 
Euclidean, and that of each of the many permissible 
frames on the special Theory of Relativity is also 
Euclidean. This amounts to saying that, on both 
views, all straight world-lines are Euclidean straight 
lines. This implies that the geometry of the one 
timeless space of the traditional theory and of the 
many timeless spaces of the special Theory of Relativity 
is Euclidean. 



SPACE-TIME 483 

Now in both theories we have taken the history of 
a particle which rests or moves relatively to the fixed 
stars with a uniform rectilinear velocity, as judged by 
properly adjusted clocks, to be a straight world-line. 
Similarly, on both theories, we have taken the history 
of a wave of light to be a straight world-line. But, 
even on the traditional theory, it would have to be 
admitted that the universality of gravitation prevents 
the history of any actual particle from being an exactly 
straight world-line, on this definition, if the geo- 
chronometry of physical Space-Time be Euclidean. 
For, however far a particle may be from the fixed stars 
and from all other bodies, it is, even on traditional 
views, subject to gravitational forces, though these may 
be practically negligible. We have now to add to this 
the newly discovered fact that light, and all other forms 
of radiant energy, are themselves affected by gravita- 
tional fields. Thus it turns out that, if the geo- 
chronometry of physical Space-Time be Euclidean, it 
must be admitted that the history of no particle or 
process that we could possibly meet with is, in fact, a 
straight world-line. Thus both the traditional physics 
and the Special Theory of Relativity are in the odd 
position of holding that the geo-chronometry of physical 
Space-Time is Euclidean, and that therefore all straight 
world-lines are Euclidean straight lines, and then 
admitting that the history of no actual particle or 
process is a Euclidean straight line. The universal 
force of gravitation thus appears as a hypothesis to 
account for this universal divergence. It must be 
admitted that this hardly inspires confidence. 

Now the Euclidean hypothesis is only one of three 
possibilities ; the other two being the hyperbolic and 
the elliptic, as described earlier in this chapter. These 
three types of hypothesis agree in the important respect 
that anv manifold which has either of these three 
structures is homaloidal. This means roughly that the 
structure of any finite region of the manifold will be 



484 SCIENTIFIC THOUGHT 

the same as that of any other, no matter where that 
region be situated within the whole. It is only on these 
three hypotheses that this is true. Obviously then, the 
next step would be to suppose that the geo-chronometry 
of physical Space-Time is not Euclidean, but is, never- 
theless, homaloidal. We might then suppose that the 
histories of actual particles and processes in gravi- 
tational fields are straight world-lines, though these 
are not Euclidean, but hyperbolic or elliptic, straight 
lines. If this view of the structure of physical Space- 
Time would account for all gravitational phenomena, 
without our having to introduce gravitation ad hoc as 
a special but universal force, it would obviously be 
reasonable to adopt it. 

Now we can deal with gravitational fields on such 
a hypothesis, so long as we confine ourselves to 
regions of physical Space-Time which are not occupied 
by physical events. For here we are concerned with 
regions for which the analogy to Laplace's equation 

Wv d*v <^ = 

dx 2 d/ 2 ds* 

holds. This analogy, as we saw in Part I, is the 
vanishing of the Modified Riemann-Christoffel Tensor 
throughout the region. But, when we are concerned 
with regions occupied by physical events, we require 
an analogy, not to Laplace's, but to Poisson's equation 

d 2 v d' 2 v d 2 v _ 

where p is the density of the " filling " of the region. 

Now the analogy to this is not the vanishing of the 
Modified Tensor, but the equating of it to another 
tensor, which expresses the " filling " of the region under 
discussion. And we must remember that, under the 
heading of " occupied regions" of physical Space-Time 
we have to include not merely those which contain 
matter in the ordinary sense of the word, but also those 



SPACE-TIME 485 

which contain only radiant energy of any kind, since 
this also gravitates. 

It is evident then, that if we want to explain gravi- 
tational phenomena by reference to the spatio-temporal 
structure of Nature, we cannot do this by ascribing a 
homaloidal structure to physical Space-Time. We must 
assign different values to the Modified Tensor for 
different regions ; since some regions are physically 
occupied and others are not, whilst of those which are 
physically occupied, some are more densely filled than 
others. The vanishing of the Unmodified Tensor, every- 
where and everywhen, would imply that physical Space- 
Time is homaloidal and Euclidean ; the vanishing of 
the Modified Tensor only, everywhere and everywhen, 
would imply that physical Space-Time is homaloidal, 
though not Euclidean ; but, since it is certain that 
neither of these alternatives is compatible with explain- 
ing gravitational phenomena in terms of the structure 
of physical Space-Time, any such theory must assume a 
non-homaloidal structure for physical Space-Time. The 
only property which remains common to all regions of 
physical Space-Time is that the square of the spatio- 
temporal separation of any pair of adjacent events is a 
homogeneous quadratic function of the differences 
between the values of their four corresponding co- 
ordinates in any frame. 

Now it does seem to me immensely important that 
we should not slur over this last transition. The 
passage from one to another view of the structure of 
physical Space-Time, so long as this structure is assumed 
still to be homaloidal, is of no particular philosophical 
importance. But the jump from a homaloidal to a 
non-homaloidal structure ought not to be taken lightly. 
It does involve, so far as I can see, the definite abandon- 
ment of a certain concept of Nature, which has so far 
been universally held. This is, roughly speaking, 
the concept of Space and Time as inert indifferent 
"containers," distinguishable from the material which 



,S.. SCIENTIFIC THOUGHT 

happens to occupy them. This view appears in a very 
crude form in the Absolute theories of Space and Time. 
But it survives, and can be restated, in the Relational 
theories and in the Special Theory of Relativity. The 
cash value of the distinction between physical Space- 
Time and its contents is that the sum total of physical 
events has a certain spatio-temporal structure which is 
the same always and everywhere, and is independent 
of qualitative differences between events. One region 
of Space-Time is differentiated from another only by 
qualitative differences in the filling of the two regions. 
Now any such view vanishes altogether on the General 
Theory of Relativity. It has been said that the Special 
Theory broke down the distinction between Space and 
Time, and that the General Theory broke down the 
distinction between both and Matter. The first part of 
the statement seems to me very loose, since the distinc- 
tion between spatial and temporal isolation remains 
for every observer. The Special Theory breaks down, 
not the distinction, but the isolation of space and time. 
But, in a very real sense, the general theory does break 
down the distinction between Space-Time and events. 

Now I do not make this an objection to the General 
Theory. All theories are but ways of unifying the 
observable facts under concepts ; and any theory that 
succeeds in doing this is permissible. I only want the 
reader to be quite clear that there is here a radically 
new way of looking at Nature. I think it will always 
be possible to unify the same facts by the more usual 
scheme of a homaloidal Space-Time and suitable fields 
of force. In so far as this fits in better with our 
traditional way of looking at things, this is to be 
preferred. But I should suppose that its advantages 
are only temporary ; thai they will vanish as we become 
more familiar with alternative concepts ; and that our 
preference for homaloidal Space-Time,//^ material and 
fields of force, has no greater ultimate significance than 
our preference for beginning dinner with hors d'ceuvres 



SPACE-TIME 487 

and ending it with coffee over taking it in the opposite 
order. 

The following additional works may be consulted 
with advantage : 

A. N. Whitehead, Principles of Natural Knowledge, 

Chaps. IX. to XIII. 
,, Concept of Nature, Chaps. V. to IX. 

,, Mathematical Concepts of the Material 

World. (Proc. Roy. Soc, vol. 205.) 
,, ,, The Principle of Relativity.* 

H. Minkowski, Raum und Zeit. 
H. Weyl, Space, Time, and Matter. 

A. S. Eddington, Report on the Relativity Theory of 

Gravitation. 
,, ,, Space, Time, and Gravitation. 

A. A. Robb, A Theory of Time and Space. 

,, ,, Absolute Relations of Time and Space. 

S. Alexander, Space, Time, and Deity, Bk. I. 

B. Riemann, Ueber die Hypothesen welche der Geometrie zu 

Grunde liegen. 

D. M. Y. Sommerville, Non-Euclidean Geometry. 

E. H. Neville, The Fourth Dimension. 



* This most important work appeared while the present book was in the 
press. Whitehead argues that Space-Time must be homaloidal ; and he 
deduces the characteristic results of the General Theory of Relativity from 
a modification of the traditional law of gravitation, and not from supposed 
variations in the structure of different regions of Space-Time. 



CHAPTER XIII 

" . . . . quam scdcm Somnia vulgo 
Vana tcncrc fcrunt, foliisque sub omnibus hacrent. 
Multaque praeterea variarum monstra ferarum, 
Centauri in foribus stabulant, Scyllaeque biformes, 
Et centumgeminus Briareus, ac bellua Lernac 
Horrendum stridens, flammisque armata Chimaera. 

• ••■•• • * 

Et ni docta comes tenues sine corpore vitas 
Admonuit volitare cava sub imagine formae, 
Trruat, et frustra ferro diverberet umbras." 

(Virgil, Mneid, VI.) 

The Physiological Conditions of Sensations, and the 
Ontological Status of Sensa 

At the end of Chapter VIII we said that the Critical 
Scientific Theory of physical objects and our perception 
of them left two main problems on hand. One was to 
clear up the meanings of physical place, shape, size, date, 
diiration, etc., and to establish their cash value in terms 
of those corresponding characteristics of our sensa, on 
which they must ultimately be founded. This task I 
have performed to the best of my ability in the last 
four chapters. The other problem was to elucidate the 
very obscure statement that external physical objects 
and our own bodies "jointly produce in us the sensa 
by which these external bodies appear to us." Probably 
any solution of this problem will be found to favour 
(if not actually to require) some particular view as to 
the nature of sensa and their ontological status in the 
universe. So this book will fitly end with an attempt 
to define the meaning and estimate the truth of the 
above statement. 

488 



CONDITIONS AND STATUS OF SENSA 489 

Almost every phrase in this statement bristles with 
ambiguities. (1) The notion of "joint" production 
will be found to be far from clear, and its possible 
alternative meanings will have to be analysed. (2) We 
shall have to raise the question whether the conditions 
jointly produce sensations, or sensa, or both. (3) The 
word "production" is highly ambiguous, even when 
we have settled what we mean by "joint production." 
It may mean a kind of creation out of nothing, or a 
process of ordinary causation, or a process of selection 
out of a mass of pre-existing material. 

These questions are not, of course, independent of 
each other. It is pretty certain that any answer that is 
given to one of them will cut out certain answers to the 
rest, and will favour certain other answers to them. 
But we must start by treating each question separately, 
and then try to view the results of our separate discus- 
sions as a whole. 

Without prejudice to the conclusions that we may 
reach when we discuss question (2), we shall find it 
best to start by saying that processes in external bodies 
and in our own jointly condition sensations, rather than 
that they jointly condition sensa. On our view a 
sensation is a complex whole, in which an objective 
factor (the sensum) and a subjective factor (the act of 
sensing) can be distinguished. Whether either of these 
can exist apart from the other we do not at present 
either assert or deny. But this at least is certain ; all 
the sensa of whose existence I am directly aware are 
constituents of my sensations, and all the sensa of whose 
existence other observers tell me are constituents of 
their sensations. Hence any evidence that I may think 
I have that certain physical and physiological processes 
are necessary and sufficient to produce sensa is prima 
facie evidence that they are necessary and sufficient to 
produce sensations. It may be that they can only pro- 
duce sensations by producing sensa, but this question 

must be left aside for the present. So, to start with, 

2 1 



490 SCIENTIFIC THOUGHT 

we shall talk about the production of sensations, and 
shall leave it an open question whether this involves 
the production of sensa. 

The Notion of Joint Production. — I think that the 
view of educated common-sense is that there are certain 
events, very definitely localised in Time and Space, 
which happen in my brain and are the necessary and 
sufficient conditions of the occurrence of each of my 
sensations. If I sense a practically uniform sense-object, 
it is thought that there is a practically uniform process 
in some part of my brain, which lasts as long as the 
sensation, and is its necessary and sufficient condition. 
Some, but not all, of these brain-events are supposed to 
be due to external physical events, such as the striking 
of bells, the lighting of matches, etc. Others are 
supposed to be due to internal causes. It is held that, 
even when a sensation is due to some external cause, 
such as the striking of a bell, this is never a sufficient 
condition. Something must be transmitted from the 
external object to the sense-organ, and something must 
be transmitted from the sense-organ to the brain. 
Otherwise the brain-event, which is supposed to be the 
necessary and sufficient condition of the occurrence of 
the sensation, will not happen, and so the sensation 
will not be produced. I propose first to introduce some 
necessary technical terms for stating the common-sense 
view ; then to clear up certain ambiguities in the 
notion of necessary and sufficient conditions ; and 
then to ask in what sense, if any, there is reason to 
believe that certain definitely localised brain-events are 
the necessary and sufficient conditions of each of my 
sensations. 

(a) Originative, Transmissive and Productive Conditions. 
— On the ordinary view, the production of a sensation 
by an external physical event requires the fulfilment of 
at least three types of condition. Let us take the case 
of hearing a certain stroke of a certain bell, (i) The 



CONDITIONS AND STATUS OF SENSA 491 

bell must be struck, or I shall not hear any sound 
characteristic of it at the time. This may be called the 
originative condition. (2) Unless there be air or some 
other material medium between my body and the bell 
I shall hear nothing, even though the bell be struck. 
There are excellent reasons, some of which have been 
mentioned in Chapter X, for holding that something 
travels with a finite velocity from where the bell is, 
through the medium, to my body. This may be called 
an external transmissive condition for my sensation of 
sound. (3) We have reason to think that, even though 
the originative and the external transmissive conditions 
for the occurrence of a sensation be fulfilled, no sensa- 
tion will happen unless a certain nerve be intact, 
leading from the sense-organ to the brain. And it is 
generally held that the process in the nerve is trans- 
missive in character. The evidence for this is fairly 
good, (a) If the nerve be cut at any point, no sensation 
of the kind will henceforth be experienced. Its integrity 
is therefore a necessary condition. (/3) It is possible to 
note the time when an external stimulus acts on a sense- 
organ, and to get the patient to press a button as soon 
as he can after getting the sensation. If this button 
stops a clock, and the clock be delicate enough, there 
will always be a lapse of time between the two events. 
This, of course, does not conclusively prove that there is 
any lapse of time between the reception of the stimulus 
and the occurrence of the sensation, since the observed 
lapse might simply be the time between having the 
sensation and pressing the button. We have direct 
experimental evidence that a process, which takes time, 
travels along motor-nerves to muscles. So far as I am 
aware, we have no direct experimental evidence that 
a process which takes time travels up a sensory nerve 
from the stimulated organ to the brain. Still, it is 
reasonable to suppose that this is so, and it is in fact 
always assumed. On this assumption, we may say 
that there is an internal transmissive conditio)i which is 



492 SCIENTIFIC THOUGHT 

necessary if I am to have here and now a sensation of 
the sound characteristic of this bell. 

A transmissive condition might be defined as follows : 
It is a process which is practically uniform in character, 
and is immanent. This means that it is divisible into 
successive slices which are qualitatively very much 
alike. They differ only in date and place, and the 
nearer they are together in date the nearer they are 
together in place. And the character of each slice is 
the necessary and sufficient condition of the character 
of the next slice. 

(4) Now, at a certain stage, viz., when the process 
has reached a certain part of the brain, it is supposed 
that a transeunt causal relation supervenes. This means 
that there is a certain brain-event, which is continuous 
with the immanent process, and is the necessary and 
sufficient condition of an event of an entirely different 
kind, belonging to a different "substance" or strand of 
history. This event is a sensation, which is, of course, 
an event belonging to that substance or strand of 
history which we call the observer's mind. Even if 
the transmissive process in the body should continue 
beyond the point at which the sensation occurs (as it no 
doubt does when the sensation is followed by a motor- 
reaction), we should say that the sensation belonged to 
an entirely different series from the later events in the 
transmissive process in the body. If the internal trans- 
missive process ends up in the brain, we say that a 
certain slice, which ends it, is the productive condition of 
the sensation. If the internal transmissive process 
continues after the sensation has been produced, we 
must say that the productive condition of the sensation 
is a certain intermediate slice of this process. 

It seems to be commonly supposed that the slice of 
the internal transmissive process which is the productive 
condition of the sensation must be extremely thin in time, 
i.e., that it cannot stretch back from the date at which 
the sensation begins for any appreciable time. We shall 



CONDITIONS AND STATUS OF SENSA 493 

see in the next sub-section that this belief is based on 
tacit assumptions, which are far from self-evident and 
cannot be proved. 

It is held that all sensations have originative and 
productive conditions, even though the sensation be 
"hallucinatory." If I "see stars," this sensation is 
presumably due to a certain brain-event, which is its 
productive condition. If this event can be traced to 
changes of blood-pressure in my eyes or to something 
happening in my liver, these would count as originative 
conditions. Whether all sensations have transmissive 
conditions is uncertain. It is certain that most of them 
have, and probably the difference between those which 
obviously do, and those which apparently do not, is a 
difference of degree rather than one of kind. It is 
perfectly obvious that an ordinary sensation of light or 
of sound has a long train of transmissive conditions, 
both external and internal. It is fairly clear that a 
sensation of itching in the finger, or of stomach-ache, 
has internal, though not external, transmissive condi- 
tions. But, if an auditory or visual experience were 
started by a change of blood-pressure in a part of the 
brain immediately adjacent to that in which the pro- 
ductive conditions of such experiences are localised, 
the transmissive process would be so short as to be 
evanescent. Still, we are probably justified in saying 
that the vast majority of sensations have originative, 
transmissive, and productive conditions. 

We must next notice (a) that some kinds of sensa- 
tions have only internal originative (and therefore internal 
transmissive) conditions. These are the sensations con- 
nected with our somatic sense-histories, such as feelings 
of headache, stomach-ache, etc., and kinesthetic sensa- 
tions. It is a well-known fact that the places of somatic 
sensa in their fields are not always a safe guide to the 
places of their originative conditions in physical space. 
A toothache occupies a certain sensible place in the 
total somatic field of the moment, and it may go on 



494 SCIENTIFIC THOUGHT 

occupying similar places in successive somatic fields. 
These somatic places will be correlated, through past 
experience, with certain places in the movement-con- 
tinuum, which are optically occupied by the visual 
appearances of my tooth and physically occupied by 
certain scientific events which dentists profess to know 
about. As a general rule the part of my body which 
thus corresponds to a given sensible place in my somatic 
fields is the seat of those scientific events which originate 
the somatic sensum which occupies this sensible place. 
E.g. , if a feeling- of toothache be located in a certain 
sensible place in my somatic field, my dentist will 
generally find something wrong with the particular tooth 
which I point out to him as occupying the physical place 
correlated with this sensible place. Sometimes, how- 
ever, he will find that nothing relevant is happening in 
this tooth, but that the originative conditions of my 
toothache are located in a part of physical space which 
is correlated with a quite different part of my somatic 
field from that in which the feeling of toothache is 
located. 

(/3) Another important fact is that, although experi- 
ences of a certain kind may generally have external 
originative (and therefore partly external transmissive) 
conditions, yet experiences of the same general character 
may sometimes be originated by purely internal condi- 
tions. This is best illustrated by experiences of the 
visual type. Generally these are originated by some 
external luminous body, which starts waves that travel 
to the eye and there set up a disturbance which travels 
up the optic nerve to the brain. But in dreams we have 
perfectly distinct visual experiences, very much like 
those of waking life, although our eyes are shut and 
we may be in a perfectly dark room. Again, visual 
images are rather like visual sensa ; and we can 
apprehend them best in the dark and with our eyes shut. 
Thus it is evident that the originative conditions for 
experiences of the visual type need not be external to 



CONDITIONS AND STATUS OF SENSA 495 

the body in every case. It is worth noticing that here 
presumably the internal originative conditions are ex- 
tremely unlike the normal external originative condi- 
tions. The inside of the body is quite dark ; so that, 
whatever be the internal conditions which originate the 
visual experiences of dreams, they must be extremely 
different from the luminous events which are the origi- 
native conditions of normal visual sensations. 

I think that visual experiences provide the only 
perfectly clear case where very similar experiences are 
originated sometimes from without and sometimes from 
within, and where the two kinds of originative condition 
are extremely different in character. If we take auditory 
experiences, the facts are much less certain. It is quite 
true that I have auditory experiences in dreams, and 
that these are very much like those of waking life, 
which are originated by events outside my body. It 
is also true that many people can apprehend auditory 
images, and that these are a good deal like auditory 
sensa. So far, the facts about auditory experiences 
resemble those mentioned above about visual experi- 
ences. But now we have to notice two important 
differences : (i) It is much harder to be sure that the 
auditory experiences of dreams are not originated 
externally than to be sure that the visual experiences 
of dreams are not thus originated. Rooms are dark 
and our eyes are shut when we are asleep. But we 
cannot shut our ears, and few rooms are wholly free 
from those physical events which would suffice to 
originate auditory experiences in a waking man. It is 
therefore uncertain whether the auditory experiences 
of dreams be not originated externally. 

(ii) As I have said above, our bodies are dark inside, 
i.e., there are no physical events in them of a kind which 
would suffice to originate normal visual sensations in a 
waking man. But it cannot be said that our bodies are 
silent inside. All sorts of processes are going on in them, 
which would be quite capable of producing, in a mild 



496 SCIENTIFIC THOUGHT 

form, vibrations of the kind which strike a waking man's 
ears when he hears an externally originated sound. 
Moreover, our bones are capable of transmitting sound- 
waves just as well as air or any other material medium. 
Thus, even if there be auditory experiences which are 
originated internally, it cannot be confidently asserted 
that their originating conditions are different in kind 
from those of externally originated auditory sensations. 
E.g., " head-noises " may quite well be noises of perfectly 
normal origin, which are heard by the sufferer and not 
by others, simply because his brain is nearer to and 
better connected with their originative conditions than 
the brain of anyone else can be. Thus we are reduced 
to the apprehension of auditory images, as the one clear 
example of auditory experiences whose originative con- 
ditions are almost certainly internal and almost certainly 
different in character from the external originative con- 
ditions of normal auditory sensations. I am indeed 
prepared to believe that some of the auditory experiences 
of dreams and disease probably do originate internally, 
and trom events which are not like ordinary sound- 
vibrations ; but I take this view, rather on the ground 
of analogy with visual experiences, than on account of 
any purely auditory phenomena known to me. 

(y) The question might be raised whether there be 
any type of sensible experience which is always originated 
by external conditions. I should not care to assert 
anything so sweeping ; but I think it may be said that 
tactual experiences have a fair claim to this position. 
Tactual experiences are far less common in dreams than 
are visual or auditory experiences. Tactual images are 
extremely rare. If they exist at all, I certainly do not 
apprehend them myself, and I have not met anyone else 
who admitted doing so. Moreover, it is quite impossible 
to prove that such "hallucinatory" tactual experiences 
as there are, do not originate through actual contact 
between the skin and other bodies. For it is certain 
that throughout the whole of our waking and sleeping 



CONDITIONS AND STATUS OF SENSA 497 

life parts of our skin are in contact with other bodies. 
Again, there must always be contact between various 
parts of our internal organs ; and between some of these 
and the blood, undigested food, and so on. Thus, I 
think it would be very difficult to show even that any 
tactual experience was not originated by contact with 
external objects, and impossible to show that such 
experiences are ever originated except by contact of 
some kind, either internal or external. This is doubtless 
why most of us agree with the Apostle Thomas, who 
thought that touch was the best test for distinguishing 
normal from hallucinatory perceptions. 

The theoretical importance of the points which we 
have just been raising will be seen in a later sub- 
section, where we shall consider how far we are justified 
in holding that certain brain-events are sufficient con- 
ditions of every sensation. Before ending the present 
sub-section we must discuss one point about originative 
and transmissive conditions. It is fairly obvious what 
part of the whole process is to be taken as the productive 
condition of a sensation. At least it is obvious where 
it ends ; for it ends where the sensation begins. Exactly 
how far back it stretches from this date is less de- 
terminate, and will need further discussion later on. 
But it is much less clear what stage in the long process, 
which ends up with a certain sensation, ought to be 
taken as the originative condition of that sensation. Let 
us return for a moment to the example of the striking 
bell. We took the stroke of the bell as the originative 
condition of the auditory sensation. But it mi-ght fairly 
be asked whether we should not have had just as good 
reasons for taking an earlier or a later stage in the total 
process as the originative condition. Whenever the 
process passes from one substance to another of a 
different kind, and changes sharply in character, there 
is an outstanding slice of it which might plausibly be 
taken as the originative condition. Now one such point 
is where and when the transmissive process of sound- 



4<)8 SCIENTIFIC THOUGHT 

waves in the air ends and the transmissive process of 
nervous disturbance in the auditory nerve begins. Why 
should we not take a terminal slice of the external 
transmissive process as the originative condition of the 
sensation? Again, the process, of which one stage is 
the stroke of the bell, does not begin at that stage. 
Probably a man struck the bell ; a contraction in his 
muscles caused the blow ; a nervous current in a motor- 
nerve caused the contraction ; and so on to infinity. 
Why should we not take one of the innumerable stages 
which precede the stroke as the originative condition 
of the sensation ? 

To these questions I answer (i) that we do recognise 
the last stage of the external transmissive process as 
important, and do mark it out by the special name of 
stimulus. For the physiologist and the physiological 
psychologist this is the earliest outstanding part of the 
total process which is of special importance. (2) The 
importance of the stage which immediately precedes 
the external transmissive process arises from its common 
relation to a number of different observers. If there be 
a number of observers listening to the same bell, there 
are as many different external and internal transmissive 
conditions, stimuli, and productive conditions, as there 
are observers. But all these different processes diverge 
from a common centre in Space-Time, and at this centre 
is located the physical event which is taken to be the 
common originative condition of all these very similar 
auditory sensations. (3) We can see how closely the 
notion of originative conditions is bound up with the 
fact of common optical and other centres for the corre- 
sponding sensa of different observers, by noting how 
difficult it becomes to apply this notion where the sensa 
of different observers are not correlated in this way. 
For instance, when we see a mirror-image we are 
doubtful what we ought to regard as the originative 
conditions of our visual sensations. The mirror-image 
is a partial optical object, and there is a certain place 



CONDITIONS AND STATUS OF SENSA 499 

behind the mirror which is optically occupied from 
many, though not from all, directions by sensa belong- 
ing to this object. A child or a cat might be inclined 
to suppose that this place is physically occupied by 
those events which are the common originative con- 
ditions of all the sensations whose sensa together make 
up the optical object. But the incompleteness of such 
optical objects prevents a grown man, even if he be 
ignorant of physics, from locating the originative con- 
ditions of his sensation in the optical place of these 
objects. We are left with the choice of events in the 
mirror or events in the reflected physical object, as the 
originative conditions of such sensations ; and, which- 
ever choice we make, we have to admit that the place 
which is optically occupied by our visual sensa and the 
place which is physically occupied by the originative 
conditions of our sensations are widely separated. If 
we say that the events in the mirror are the originative 
conditions of our sensation, we must remember that 
they will not originate similar sensations in observers 
in all directions, as the normal originative conditions 
of visual sensa do. If we say that the events in the 
reflected physical object are the originative conditions 
of our sensation, we must remember that, unless men- 
tion be made of the mirror as well, we cannot account 
either for the peculiar optical place or for the peculiar 
" inversion " of the image-sensa. 

(fr) Dependently and Independently Necessary Conditions. 
— As I have said, it is commonly held that certain 
brain-events are the necessary and sufficient conditions 
of the occurrence of all our different sensations. We 
have now to clear up the notion of "necessary and 
sufficient conditions," and to see in what sense, if any, 
it is true that brain-events are the necessary and 
sufficient conditions of all our sensations. A number 
of conditions a, b, and c, are said to be severally 
necessary and jointly sufficient to produce an event x, 
if (1) whenever they are all present .r happens, and (2) 



500 SCIENTIFIC THOUGHT 

whenever they are not all present x does not happen. 
It is obviously much easier to be sure that a, b, and care 
severally necessary than that they are jointly sufficient 
to produce x. If we can omit in turn a, b, and c, and 
find that x does not happen, we can be sure that each of 
these conditions is necessary. But it is far from safe 
to assume that, because abc has always been followed 
in our experience by x, therefore these conditions are 
jointly sufficient to produce x. It is never really 
possible to get abc in complete isolation from the rest 
of the world, and there may have been some fourth 
factor d, which was, in fact, present in all the cases that 
fell under our notice and was necessary for the pro- 
duction of x. Statements that such and such conditions 
are jointly sufficient to produce a certain result should 
therefore always be viewed with suspicion. 

If abc be sufficient to produce x, it follows that no 
other factor (unless it be simply a constituent of one of 
the factors a, b, or c, or a combination of them, such as 
ab), can strictly be necessary to produce x. For to say 
that abc is sufficient to produce ,r, is to say that whenever 
abc happens x follows. Hence both abed and abed will 
be followed by x, whatever d may be.* And if x follows 
in the absence of d, as it does in the case abed, d cannot 
be necessary for the occurrence of x. If then a certain 
brain-event be really sufficient to produce a certain 
sensation (say that of the sound characteristic of a 
certain bell), the existence of the bell and the air, and 
the occurrence of a stroke on the bell, and so on, cannot 
be strictly necessary to produce this sensation. Yet we 
should commonly say that the striking of the bell, and 
the other conditions which we have enumerated, are 
necessary, if that particular noise is to be sensed at 
that particular time. Our ground for this statement is 
that we believe that no such sensation would have 
happened then, if no bell had existed, and if it had not 
been struck shortly before. 

* Here " d" simply stands for " the absence of d." 



CONDITIONS AND STATUS OF SENSA 501 

It is clear from this that we use the word " necessary " 
in two different senses. In one of them, nothing can 
be necessary to produce an event unless it be contained 
in the smallest set of conditions which will jointly 
suffice to produce the event. In the other, many factors 
which are not contained in the smallest set of conditions 
which will jointly suffice to produce an event are yet 
said to be necessary for its production. We must, in 
fact, distinguish between independently and dependently 
necessary conditions. If a certain brain-event be really 
sufficient to produce the sensation of the sound of a 
certain bell, then the striking of the bell, the disturbance 
of the air, and so on, are only dependently necessary 
to the production of this sensation. That is, they are 
necessary to produce the sensation only in so far as 
they are necessary to produce the whole, or some part 
of, that brain-event which is sufficient to produce the 
sensation. We may say in general that a is a depend- 
ently necessary condition of the event jt, if a be necessary 
to produce the whole, or some part of, the conditions 
which are independently necessary and jointly sufficient 
to produce x. 

Now a very important question at once arises. 
Can a certain event a be both dependently and independ- 
ently necessary to produce x? I think that this would 
commonly be denied ; but we shall see in a moment 
that it can only be denied on the basis of certain 
assumptions about causation, which have very little 
plausibility when they are explicitly stated. What 
would it mean to say that a is both dependently and 
independently necessary to produce x? It would mean 
that a, b, and c (say) were all needed to produce x, and 
that they are all that is needed, but that a plays two 
parts. It produces b (say). And it co-operates with b and 
c to produce x. Supposing it to be possible that a should 
play both parts, and supposing it to be certain that a is 
dependently necessary, then it would always be impossible 
to know that a is not also independently necessary to 



502 SCIENTIFIC THOUGHT 

produce x. For, if a be dependently necessary to 
produce x, there is some factor b in the necessary and 
sufficient conditions of x, which cannot occur unless a 
has preceded. Since b never does occur without a 
preceding, we cannot, possibly know whether /; does not 
need the co-operation of a in order to produce x, unless 
we have some positive reason for holding that a 
dependently necessary condition of an event cannot 
also be an independently necessary condition of it. 

Let us apply this abstract logical argument to the 
concrete case of the auditory sensation of the noise of a 
i^rD* 1 bell. If the brain-event which produces this sensation 
fr'*^ could not occur unless t he bell had rung a litt le earlier, 
*k we cannot be sure that the brain-event is by itself a 

sufficient condition of this sensation, unless we are sure 
that a dependently necessary condition cannot also be 
an independently necessary condition of the same event. 
If the brain-event never happens without the bell-event 
preceding, we cannot possibly know that the brain- 
event, without the co-operation of the bell-event, would 
suffice to produce the auditory sensation, unless we 
have some a priori ground for this belief. For the only 
conclusive empirical ground for such a belief would be 
to get the brain-event without the bell-event, and to 
find that the sensation still followed. But, ex hypothesis 
we cannot get just this kind of brain-event without a 
bell-event preceding, and therefore this empirical argu- 
ment cannot be used. Conversely, of course, we cannot 
be sure that the bell-event is independently as well 
as dependently necessary for the production of the 
sensation. 

Now, is there any a priori argument against the 
possibility of a certain condition a being at once 
dependently and independently necessary to produce a 
certain event x? I know of one and only one way in 
which such a possibility could be refuted. If it be held 
that all the independently necessary conditions of an 
event must be contemporary with each other, it will 



CONDITIONS AND STATUS OF SENSA 503 

follow that the same factor cannot be both independently 
and dependently necessary to produce a certain event. 
For the dependently necessary condition will precede 
that one of the independently necessary conditions 
Which it produces. Consequently it could not itself be 
an independently necessary condition, if these have all 
to be simultaneous with each other. 

But I cannot accept the premise of this argument. 
(1) It does not seem to me to have the slightest trace 
of self-evidence. I think there is something to be said 
for the proposition that cause and effect must be 
continuous with each other in time, and that the 
complete cause must itself be a continuous process in 
time. This, however, is quite compatible with a and 
b being successive, and yet both of them being inde- 
pendently necessary conditions of x. Suppose that the 
end of b is simultaneous with the beginning of x, and 
that the end of a is separated by a lapse of time from the 
beginning of b. Then the principle of the temporal 
continuity of causation would only show that the com- 
plete cause of x consists, not merely of a and b, but also 
of some process which bridges the gap between the 
.wo. It has no tendency to show that b is the complete 
cause of x, and that a is only dependently necessary. 

(2) Apart from the lack of self-evidence in the 
principle that all the independently necessary conditions 
of an event must be simultaneous, there is a serious 
positive objection to it. We have seen that no two 
events are intrinsically simultaneous, unless they also 
have no spatial separation. Events which are separated 
in the timeless space of one permissible frame, and 
are simultaneous with respect to that frame, will be 
temporally separated with respect to any other frame 
which moves in the timeless space of the first. Thus 
the principle would presumably have to be stated in 
the much milder form that the independently necessary 
conditions of an event must not be intrinsically separated 
in time, i.e., that there is at least one permissible frame 



5o 4 SCIENTIFIC THOUGHT 

with respect to which they are all simultaneous. But, 
when it thus loses its original sweet simplicity, it seems 
to lose any trace of self-evidence which it may have 
had before. 

(3) Lastly, it seems to me almost certain that the 
sufficient productive conditions of many sensations could 
not be momentary, and, therefore, must include non- 
simultaneous factors. I do not merely mean by this 
that " momentary " conditions are not existent facts and 
can only be defined by Extensive Abstraction. I mean 
that, if you tried to apply Extensive Abstraction to the 
conditions of many sensations you would find that these 
do not converge to a set of contemporary momentary 
states. It is practically certain, e.g., that the external 
originative and transmissive conditions of sensations 
of light and sound are periodic, and it is reasonable to 
suppose that the subsequent internal processes in nerves 
and brain are periodic too. There is a very accurate 
correlation between the colour or pitch of the sensum and 
the period of the external originative and transmissive 
events. Now it is impossible that the characteristic 
periodicity of red light, or of a certain note on the piano, 
should be carried by a purely momentary brain-event. 
Presumably the brain-event, which is the productive 
condition of even the shortest sensation of red, must last, 
at least as long as one complete vibration of red light. 
Or, if we prefer to express ourselves more guardedly, 
we must, at least, hold that the productive conditions of 
the shortest possible sensations of (say) red and blue 
must both have characteristic finite durations, and that 
these durations must have to each other the same ratio 
as the periods of a complete vibration of red light, and 
a complete vibration of blue light. If the productive 
conditions have durations, they must have non-simul- 
taneous parts. And, if the whole finite event be the 
least that is sufficient to produce the sensation, all its 
successive parts must be independently necessary to 
produce the sensation. If, further, the event in question 



CONDITIONS AND STATUS OF SENSA 505 

be transmissive in character (if, e.g., it be the passage of 
some kind of disturbance through a finite tract of brain 
and nerve) the earlier parts of it will also be dependently 
necessary conditions of the sensation, since the later 
parts will not happen unless the earlier ones happen and 
produce them. 

The upshot of this discussion seems to be that we 
cannot prove by any direct empirical argument that any 
condition which is dependently necessary to produce 
a sensation is not also an independently necessary 
condition of it. And we cannot prove a priori that 
dependently necessary conditions cannot also be inde- 
pendently necessary, except from a premise which is 
not self-evident, is of very uncertain meaning when the 
relativity of physical simultaneity is considered, and is 
almost certainly false as applied to the productive con- 
ditions of some of our most important sensations. It 
follows that it is rash in the extreme to expect to be 
able, even in theory, to isolate a momentary event at 
a definite place in the brain, and to say : "This is the 
necessary and sufficient condition of such and such a 
sensation." We cannot be absolutely certain that even 
such remote dependently necessary conditions as the 
stroke of the bell are not also independently necessary 
conditions of our sensation of the sound which is 
characteristic of the bell. And we can feel fairly 
confident that at least the later stages of the internal 
transmissive conditions of a sensation are independ- 
ently as well as dependently necessary conditions 
of its occurrence. To put it shortly : The productive 
conditions of a sensation almost certainly include the 
later stages of its internal transmissive conditions ; and, 
for all that we can certainly know, they might include 
the external transmissive and the originative conditions 
as independently necessary factors. 

I think it is possible to produce a more or less 
plausible indirect empirical argument, which renders it 
probable that the independently necessary conditions of 

2 K 



506 SCIENTIFIC THOUGHT 

some at least of our sensations do not extend so far 
back as the external transmissive or the originative 
conditions. But it is only an argument from analogy, 
and, as we shall see, the analogy is none too good. 
The argument would run as follows : Although the 
particular sensation s would not have arisen when it 
did, unless certain external originative and transmissive 
conditions had been fulfilled, there are sensible experi- 
ences s', very much like s, which happen {e.g., in 
dreams) when there is good reason to believe that no 
such external originative or transmissive processes are 
operating. If so, internal conditions are sufficient to 
produce /. And the analogy between s' and s may 
suggest that purely internal conditions are sufficient 
to produce s, though these cannot, in fact, arise unless 
certain external conditions be first fulfilled. If this 
be so, the external conditions are only dependently 
necessary for the production of s. To take a concrete 
example. Although I should not have sensed a certain 
flash at a certain moment unless someone had struck 
a match very shortly before in my neighbourhood, yet 
I do have visual experiences very much like this sensa- 
tion in dreams. The latter must have been produced 
by purely internal conditions. Hence purely internal 
conditions are sufficient to produce experiences very 
much like this particular sensation. Therefore probably 
the sufficient conditions of all visual experiences are 
internal ; and the external conditions, which are necessary 
for the production of many such sensations, are only 
dependently necessary. That is, the striking of the 
match is necessary only for producing the internal 
process which is the sufficient condition for the sensation 
of the flash ; it is not also necessary as a condition which 
co-operates with the later stages of this process. 

It is evident that such an argument could never 
establish more than a probability that external events 
are not independently necessary conditions of those 
sensations to which they are dependently necessary. 



CONDITIONS AND STATUS OF SENSA 507 

The strength of the argument in any particular case 
will depend on two factors, viz.: (1) the degree of analogy 
between the experiences /, which are alleged to be 
originated wholly from within the body, and the 
sensations s, which are externally originated ; and (2) 
the degree of certainty with which it can be asserted 
that the experiences s' are originated altogether inter- 
nally. When the experiences s' are apprehensions of so- 
called " mental " images I should not deem the analogy 
strong enough to bear any great weight of argument. 
For, although visual and auditory images are a good 
deal like visual and auditory sensa respectively, yet 
there are such marked differences between them that 
we hardly ever mistake one for the other in normal 
waking life. I should be inclined to say that only the 
experiences of dreams, and other forms of hallucination, 
bear enough likeness to auditory and visual sensations 
to support an argument such as I have outlined above. 
Now, in the last sub-section we saw that it is by no 
means certain that auditory experiences (other than 
images) are ever originated save by external physical 
events or by internal events of precisely the same 
character. It is therefore doubtful whether there be 
any facts about auditory experiences which the present 
argument could use as premises. With tactual ex- 
periences, as we saw, the position is still less favourable. 
In fact, it is only with visual experiences that there is 
really good evidence that something very much like 
normal sensations can be originated by events which 
are wholly internal and are quite unlike the external 
originative conditions of the normal sensations. Thus 
Ave can argue with a fairly high degree of probability 
that the sufficient conditions of visual sensations are 
internal, and that the external originative and trans- 
missive conditions are only dependently necessary ; but, 
for auditory and tactual sensations, a similar argument 
leads to only a weak probability. 

It must be remembered, on the other hand, that it 



5o8 SCIENTIFIC THOUGHT 

is equally impossible to prove (what the nai'ver Realists 
would like to believe) that the external originative con- 
ditions of our sensations are independently, as well as 
dependently, necessary conditions for the occurrence of 
these sensations. Thus, so far as I can see, empirical 
facts and a priori principles about causation justify little 
more than complete agnosticism on this subject. There 
is, therefore, an almost open field for different hypotheses, 
each carrying the independently necessary conditions 
backwards in Time and Space by different amounts. 
Each will lead to a somewhat different theory as to 
what is involved in the perception of external physical 
objects and events, and the hypothesis which leads to 
the theory of perception which best unifies all the 
known facts is the one to be preferred. 

Within the body I know of no means of setting even 
probable limits to the distance backwards in Space and 
Time to which the independently necessary conditions 
of a sensation may stretch. It may be that the events 
in the brain are sufficient, and that the process in the 
sensory nerve is merely transmissive. On the other 
hand, it is equally likely, so far as I can see, that the 
process in the nerve is an independently necessary, as 
well as a transmissive condition, for the occurrence of 
the sensation. The former alternative appears to be 
unhesitatingly taken by physiologists, and accepted, on 
their authority, by the general public. But this con- 
viction rests on no stronger basis than a failure to draw 
certain distinctions among " necessary conditions," and 
a simple faith in certain dogmas about causation which 
will not bear the light of common day. 

I will end this sub-section by considering a rather 
confused semi-popular argument, which tries to raise 
doubts about the existence of external objects and events, 
on the ground of physiological theories about the 
conditions of our sensations. I will call this position 
Physiological Scepticism. The argument would run some- 
what as follows. " My only ground for believing in 



CONDITIONS AND STATUS OF SENSA 509 

the existence of external physical objects is the occur- 
rence of certain sensations which I ascribe to them. But 
physiology proves that states of my body are siifficient 
conditions of all my sensations. Hence I have no right 
to conclude from the occurrence of sensations to the 
existence of external physical objects and processes, as 
their originative conditions." To this we may answer : 
(1) That, even if internal processes be sufficient condi- 
tions of our sensations, we do not know and have no 
reason to believe, that these internal processes would 
take place unless certain external events were happening 
and affecting our bodies. Thus we may still argue to 
the existence of such external objects, as, at least, the 
dependently necessary conditions of many of our sensa- 
tions. Moreover, the resemblance between many of the 
sensa which I sense and those which are sensed by 
other observers, the fact that visual sensa from different 
observers' sense-histories are in the same optical place, 
and the somewhat similar facts about auditory sensa, 
suggest strongly that there is often a remote external 
physical event, which is located in this place, and is 
a common dependently necessary condition of all these 
correlated sensations. (2) We have seen that it is im- 
possible to be sure that these dependently necessary 
external conditions are not also independently necessary. 
It is, therefore, quite uncertain whether internal pro- 
cesses ai'e sufficient conditions of all my sensations. If 
this be held at all, it can only validly be held as a 
probability based on certain partial analogies. (3) It 
is perhaps worth while to point out that Physiological 
Scepticism cannot consistently stop at the stage of 
doubting the existence of external physical objects. If 
such arguments be valid at all, they must finally be 
applied to one's own body and its supposed internal 
structure. All that anyone knows about the physiology 
and internal anatomy of his own body he has learnt by 
studying and dissecting other organised bodies. Now, 
for each observer, these are simply external physical 



510 SCIENTIFIC THOUGHT 

objects, of whose existence and inner structure he learns 
by sensations of sight and touch. If then he is forced to 
be wholly sceptical about external physical objects, he 
ought, if he wants to be consistent, to be equally sceptical 
about all statements which imply the existence of a per- 
manent inner structure and variable states of his own 
body. The conclusion of Physiological Scepticism blows 
up its own premises, and the only consistent result is 
complete scepticism about all physical objects and pro- 
cesses, including those with which physiology professes 
to deal. Physiologists with a tendency to philosophical 
speculation are liable to combine Naive Realism about 
the purely hypothetical states of their brains with Sub- 
jective Idealism about all other physical objects, includ- 
ing those which they have had to study in order to learn 
about their own brains. To parody Mr Gibbon's re- 
mark about the Jews : " In contradiction to every known 
principle of the human mind this singular people seems 
to have yielded a stronger and more ready assent to" 
the hypothetical entities of their science "than to the 
evidence of their own senses." 

(c) Occurrent and Continuant Conditions. — In the last 
sub-section I brought forward certain abstract logical 
considerations to show that it is impossible to tell how 
far the series of independently necessary conditions of 
a sensation must be carried in Space and Time. But, 
quite apart from these considerations, it is practically 
certain that no event in the brain is a completely sufficient 
condition for the occurrence of any sensation. Every 
event depends on two kinds of conditions, which 
we may call occurrent and continuant, borrowing two 
useful names from Mr W. E. Johnson. We are 
always very liable to notice the occurrent and to 
ignore the continuant conditions, and then to think 
that the former are sufficient to produce the event. 
It would commonly be said that the stroke of a bell is 
a necessary and sufficient condition of the occurrence 
of certain vibrations in the surrounding medium. So it 



CONDITIONS AND STATUS OF SENSA 511 

is, provided that there is a material medium in contact with 
the bell, and that it is capable of being set in vibration 
by a disturbance of this particular period. It is evident 
that the latter condition is as necessary for the setting 
up of vibrations as the former. But the striking of the 
bell is a short outstanding event in that long and fairly 
uniform strand of history which is the bell ; whilst the 
medium and its structure existed before the bell was 
struck, and will exist with very little change for long 
afterwards. Moreover, in our experience, bells are much 
more often than not surrounded with such a medium. 
The medium is thus such an unexciting and such a 
usual piece of physical history that we hardly think it 
worth mentioning. Now I should call the striking of 
the bell an occurrent condition, and the existence of a 
surrounding medium of suitable structure a continuant 
condition, of the setting up of the vibrations. Both are 
necessary, and neither by itself is sufficient. Together 
they are sufficient. We can, if we like, call the striking 
of the bell the necessary and sufficient occurrent condition of 
the vibrations, but we must on no account call it the 
necessary and sufficient condition without qualification. 

I do not pretend that an absolutely hard and fast 
line can be drawn between occurrent and continuant 
conditions. An occurrent condition is a short out- 
standing slice in some long strand of physical history, 
which is fairly uniform up to this slice and again shows 
uniformity, often of the same kind as before, after the 
slice. A continuant condition is a long and practically 
uniform strand, which stretches out with little varia- 
tion before, during, and after the occurrent condition. 
Obviously terms like "short," "outstanding," "uni- 
form," etc., are relative. But, for our purpose, all 
that we need to notice is that some of the conditions 
of an event are always of the continuant type, and that 
the more a condition is of the continuant type the more 
likely it is to be overlooked. 

Let us now apply these general considerations to 



512 SCIENTIFIC THOUGHT 

the necessary and sufficient conditions of our sensations. 
When a stimulus, which normally produces a certain 
kind of sensation, acts on a sense-organ, such as the 
eye or ear, no sensation will be produced unless the 
nerve be intact and the general structure of the brain 
be not disintegrated beyond a certain very small degree. 
Again, the structure of the sense-organ, sensory nerve, 
and brain may (so far as we know) be intact, and yet 
no sensation will be produced if the man be dead. If 
he be alive, but asleep or in a swoon or under the 
influence of a drug, the stimulus may also fail to produce 
a sensation in his mind. Again, there are such pheno- 
mena as " psychic" blindness, deafness, etc., which 
happen spontaneously in hysteria, and can be induced 
artificially by hypnosis. Here there is no reason whatever 
to suppose that there is any defect in the structure of 
sense-organs, nerves, or brain —indeed there is evidence 
to the contrary— and yet the external stimulus is not 
followed by any correlated sensation in the conscious 
mind of the patient. Lastly, we have seen in an earlier 
chapter that similar external stimuli will often produce 
in different observers sensations whose sensa are partly 
different in quality, and that these differences can be 
correlated with differences in the past histories of the 
observers. 

It is evident then that one general continuant con- 
dition for the production of sensations is that the sense- 
organ and the nerve which are specially concerned, 
and at least a considerable part of the brain, shall be 
structurally intact. Given this condition, it is also 
necessary that the body shall be "alive." This is 
probably a distinct condition from the one just men- 
tioned. Although the structure of the brain and nervous 
system does not remain intact for very long after the 
death of the body, it would be rash to say that it dis- 
integrates profoundly immediately after death. Motor 
nerves can certainly be kept alive for some considerable 
time after the death of the body. I should suppose that 



CONDITIONS AND STATUS OF SENSA 513 

"being alive" involves at least the maintenance of a 
certain moving equilibrium among bodily changes. We 
might therefore call it the general somatic occurrent con- 
dition of sensations. I suppose that "being awake" 
or " being conscious " involves at least a certain moving 
equilibrium among processes in the brain. This might 
therefore be called the general cerebral occurrent condition 
of sensations. Since a man can be alive without being 
awake, though he cannot be awake without being alive, 
there is a partial dependence and partial independence 
between these two sets of conditions. 

The bodily conditions on which psychic blindness or 
deafness depend, if such there be, are quite unknown to 
us. It seems to me theoretically possible that the 
conditions of such phenomena are wholly psychic, and 
have no bodily correlates at all. Whatever view we 
may take on this point, we can at least say that they 
are special, and not simply general conditions, such as we 
have so far been describing. A patient is not, as a rule, 
psychically blind to all lights or psychically deaf to all 
noises. Most usually he is blind or deaf only to those 
which have some special association for him, or to those 
about which suitable suggestions have been made to 
him by himself or by others. We may reasonably 
suppose that psychic blindness or deafness, if it have a 
bodily correlate at all, depends on certain disconnexions 
between the particular nervous process which would 
normally give rise to the sensation, and the rest of the 
brain. Thus the condition that we shall not be psychi- 
cally blind or deaf when a certain stimulus acts on us 
may be called a special connective condition for the occur- 
rence of the sensation. As it is a condition which 
usually holds, unless there be special causes to disturb 
it, it should presumably be counted as continuant rather 
than occurrent. Lastly, when the quality of the sensum 
partly depends on the past experiences of the observer, 
we may say (borrowing a useful expression from Mr 
Russell) that the sensation has mnemic conditions. (By 



514 SCIENTIFIC THOUGHT 

using this phrase I do not imply either the acceptance 
or the rejection of that peculiar kind of causation which 
Mr Russell calls " mnemic causation.") On the ordinary 
view that past experiences leave traces which persist, 
and that it is these which condition our present sensa- 
tions, I suppose that mnemic conditions would be partly 
continuant and partly occurrent. The trace, having 
become part of the permanent structure of the nervous 
system, would be a continuant condition. The con- 
nexions between this trace and other parts of the brain, 
which have been formed by association, will also be 
continuant connective conditions. But the excitement 
of this particular trace, when a certain part of the brain 
is excited by some external stimulus, is a special 
occurrent condition. 

All the conditions which I have just been enumerating 
must be fulfilled if a certain stimulus is to be followed 
by a characteristic sensation at a given moment. The 
mnemic conditions may, in a sense, be called "less 
necessary " than the others, since (a) there are probably 
some sensations in whose production they play little 
if any part ; and (/3) even if they be necessary to produce 
a certain sensation at a certain moment, it is probable 
that a rather similar sensation would be produced with- 
out them, provided that all the other conditions were 
fulfilled. On the other hand, if any of the other con- 
ditions be not fulfilled, no sensation at all will be 
produced in the conscious mind * of the observer. 

The question can now be raised as to which of these 
conditions are only dependently necessary, and which 
are also independently necessary, for the production of 
a sensation. The structural integrity of a special nerve, 

* I use the expression "conscious mind" here, because I think that it is 
theoretically possible that sensations may be produced in connexion with a 
certain brain and nervous system, which do not form parts of that mind which 
normally manifests itself through this organism. Such sensations (if they 
exist at all) might not form parts of anything that deserves to be called a 
mind ; or again, they might form parts of a mind which seldom or never 
manifests itself. 



CONDITIONS AND STATUS OF SENSA 515 

and its "being alive," are presumably dependently 
necessary conditions ; since, unless they be fulfilled, no 
disturbance will be produced in the brain. Whether 
they be or be not also independently necessary it seems 
impossible to tell, for the reasons given in the last sub- 
section. But I should suppose that, on any view, the 
substantial structural integrity of the brain as a whole, 
in addition to that of the particular part that is imme- 
diately connected with a special sensory nerve, is an 
independently necessary condition for the production 
of a sensation. In addition to this, I should suppose 
that the general balance ot cerebral processes, which is 
involved in the statement that the observer is "awake," 
is an independently necessary condition. The special 
connective conditions, which are needed for the absence 
of psychic blindness or deafness, are also independently 
necessary. And, if the sensation has mnemic conditions, 
these are independently necessary for the production of 
just this sensation, though a sensation a good deal like 
it might be produced in their absence. 

We see now how loose it is to talk of a certain brain- 
event, very definitely localised in time and place, as 
the sufficient condition for the occurrence of a sensation. 
Apart altogether from the fact, elicited in the last sub- 
section, that we do not know how many of the dependently 
necessary conditions are also independently necessary, 
we see that such assertions ignore many conditions, 
some occurrent and some continuant, which are inde- 
pendently necessary. At the utmost we can call a 
certain brain-event, fairly definitely localised in Time and 
Space, the necessary and sufficient special non-mnemic 
occurrent condition of a sensation. In addition to this, 
every sensation needs at least the following conditions : 
(1) the general continuant cerebral condition of structural 
integrity of the brain as a whole ; (2) the general occur- 
rent cerebral condition of "wakefulness"; and (3) a 
special continuant connective condition to prevent 
psychic blindness, deafness, etc. Moreover, many 



516 SCIENTIFIC THOUGHT 

sensations require further (4) mnemic conditions, which 
are partly OCCiirrent and partly continuant; (5) and all 
sensations require, as at least dependency necessary 
conditions, that the body as a whole, and especially the 
sensory nerve, shall be structurally intact (a continuant 
condition), and that the body shall be "alive" (a general 
occurrent condition). Beside all these, there may well 
be purely psychic conditions, having no bodily correlates, 
which must also be fulfilled if sensations are to arise in the 
mind. I am going to assume, for the sake of simplicity, 
in this book that there is such a complete parallelism 
between mind and body that it is enough to mention 
bodily conditions, because every psychic condition has 
its bodily correlate. I am very far from believing that 
this is true, and am not even sure that it has any very 
definite meaning which would survive analysis ; so I 
assume it here simply as an excuse for avoiding 
additional complications which are hardly relevant to 
our present purpose. 

Sensations, Sensa and Acts of Sensing. — For reasons 
given at the beginning of this chapter we have so far 
spoken of physiological and physical conditions as pro- 
ducing sensations. We have now to ask whether this 
involves the production of sensa, or of acts of sensing, 
or of both. Before we can hope to answer this, we must 
try to clear up the notion of a sensation a little more 
fully than we have yet had occasion to do. 

(a) The General Process of Sensing. — A sensation, on 
our view, is a complex in which an objective factor (the 
sensum) and a subjective factor (the act of sensing) can 
be distinguished. Whether either of these can exist 
without the other is a matter which has so far been left 
in decent obscurity. It is obviously logically possible, 
and indeed quite plausible, that there might be unsensed 
sensa. It is very much harder to believe that there 
could be acts of sensing which did not sense anything, 
because an act of sensing would seem to involve a 



CONDITIONS AND STATUS OF SENSA 517 

special relation between a sensum (which is thereby 
sensed) and something else. Let us begin by asking 
whether every different sensation involves a different 
act of sensing. 

It seems clear to me that we distinguish different 
sensations by means of the different sensa which are 
their objects. If two sensa be in different fields of the 
same sense-history we should say that the observer had 
two different sensations. If two sensa were in the same 
field, and completely overlapped in time, we should say 
that the observer had two sensations, provided the two 
sensa were separated spatially in the field by a back- 
ground which differed qualitatively from both of them. 
I think it would be reasonable to say that sensa in 
successive fields are sensed by different acts, which are 
themselves successive. But I see no reason to postulate 
different acts of sensing for different sensa in the same 
field. When we remember that sensa do not exist in 
isolation, but are simply outstanding features in sense- 
fields, any such view seems far from plausible. It 
seems more reasonable to suppose that the same act 
of sensing grasps a whole sense-field. We can then 
distinguish as many sensations as there are outstanding 
sensa in the field ; but there seems no need whatever to 
assume a special act of sensing for each of these sensa. 
To say: "I have two contemporary sensations, one of 
x and the other of y" would seem to mean simply : "I 
sense a field /, in which x and y are two outstanding 
parts, which may overlap in time but are separated in 
space." Thus, although every sensation involves an 
act of sensing, it does not follow that the production of 
every sensation involves the production of a special act 
of sensing. 

So far, we have been considering sensa which are in 
the same special field, e.g., in some one visual field. 
But my general sense-history consists of a number of 
parallel special sense-histories, e.g. , visual, tactual, 
auditory, etc. My general sense-history goes on 



518 SCIENTIFIC THOUGHT 

throughout the whole of my waking life at any rate, 
though there may be gaps in any one of my special 
sense-histories. Now I do not see any reason to 
suppose that there are as many contemporary acts of 
sensing as there are contemporary special sense-fields. 
The various special fields are joined up with each other 
by sensible temporal relations to give a general sense- 
field. If I am aware at once of a visual and a tactual 
field, I see no more ground for postulating two acts of 
sensing, one visual and the other tactual, than for 
postulating two acts of sensing for grasping a red patch 
and a blue patch in the same visual field. I would 
rather say that there is a single general act of sensing, 
which happens to be supplied with both a visual and a 
tactual field for its objects. Certainly a tactual sensation