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BIBLIOGRAPHIC RECORD TARGET
Graduate Library
University of Michigan
Preservation Office
Storage Number:
ABR2669
ULFMTBRTaBLmT/C DT 07/18/88 R/DT 07/18/88 CC STATmmE/Ll
010: : I a 03025534
035/1: : |a (RLIN)MIUG86-B51391
035/2: : |a (CaOTULAS)160123997
040: : I c MiU | d MiU
050/1:0 : | a QA669 | b .H66 vol.1
100:1 : I a Hinton, Charles Howard, | d 1853-1907.
245:10: | a Scientific romances, | c by C. H. Hinton. |n 1st series.
260: : | a London, | b S. Sonnenschein & cc, lim., |cl886.
300/1: : | a 229 p. jb incl. illus.,diagrs. |cl9cm.
505/1:0: | a What is the fourth dimension?--The Persian king. A plane world.—
A picture of our universe.—Casting out the self.
650/1: 0: | a Fourdi dimension
740/1:4 : | a The Persian king.
998: : IcWFA Is 9124
Scanned by Imagenes Digitales
Nogales, AZ
On behalf of
Preservation Division
The University of Michigan Libraries
Date work Began: _
Camera Operator: _
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SCIENTIFIC ROMANCES.
C. H. HINTON, B.A.
SWAN SONNENSCHEIN, LOWREY & CO.,
Paternoster Squark.
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Wl^at h % J0wri| gimmHon?
CHAPTER I.
r the present time our actions are largely in-
fluenced by our theories. We have aban-
doned the simple and instinctive mode of life
of the earlier civilisations for one regulated
by the assumptions of our knowledge and supplemented
by all the devices of intelligence. In such a state it is
possible to conceive that a danger may arise, not only
from a want of knowledge and practical skill, but even
from the very presence and possession of them in any one
department, if there is a lack of information in other
departments. If, for instance, with our present knowledge
of physical laws and mechanical skill, we were to build
houses without regard to the conditions laid down by
physiology, we should probably — to suit an apparent
convenience — make them perfectly draught-tight, and the
best-constructed mansions would be full of suffocating
chambers. The knowledge of the construction of the
body and the conditions of its health prevent it from
suffering injury by the development of our powers over
nature.
In no dissimilar way the mental balance is saved from
the dangers attending an attention concentrated on the
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4 What is ike Fourth Dimension ?
laws of mechanical science by a just consideration of the
constitution of the knowing faculty, and the condition* of
knowledge. Whatever pursuit we are engaged in, we are
acting consciously or unconsciously upon some theory,
some view of things. And when the limits of daily
routine are continually narrowed by the ever-increasing
complication of our civilisation, it becomes doubly impor-
tant that not one only but every kind of thought should
be shared in.
There are two ways of passing beyond the domain of
practical certainty, and of looking into the vast range of
possibility. One is by asking, "What is knowledge?
What constitutes experience ? " If we adopt this course'
we are plunged into a sea of speculation. Were it not
that the highest faculties of the mind find therein so
ample a range, we should return to the solid ground of
facts, with simply a feeling of relief at escaping from so
great a confusion and con trad ictoriness.
The other path which leads us beyond the horizon of
actual experience is that of questioning whatever seems
arbitrary and irrationally limited in the domain of know-
edge. Such a questioning has often been successfully
applied in the search for new facts. For a long time four
gases were considered incapable of being reduced to the
liquid state. It is but lately that a physicist has succeeded
in showing that there is no such arbitrary distinction among
gases. Recently again the question has been raised, " Is
there not a fourth state of matter ? " Solid, liquid, and
gaseous states are known. Mr, Crookes attempts to
demonstrate the existence of a state differing from all of
these. It is the object of these pages to show that, by
supposing away certain limitations of the fundamental
conditions of existence as we know it, a state of being
can be conceived with powers far transcending our own.
When this is made clear it will not be out of place to
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What is the Fourth Dimension ? 5
n vestigate what relations would subsist between our
mode of existence and that which will be seen to be
a possible one.
In the first place, what is the limit-ation that we must
suppose away ?
An observer standing in the comer of a room has three
directions naturally marked out for him ; one is upwards
along the line of meeting of the two walls ; another is
forwards where the fioor meets one of the walls ; a third
is sideways where the floor meets the other wall. He
can proceed to any part of the floor of the room by
moving first the right distance along one wall, and then
by turning at right angles and walking parallel to the
other wall. He walks in this case first of all in the
direction of one of the straight lines that meet in the
corner of the floor, afterwards in the direction of the
other. By going more or less in one direction or the
other, he can reach any point on the floor, and arty move-
ment, however circuitous, can be resolved into simple
movements in these two directions.
But by moving in these two directions he is unable to
raise himself in the room. If he wished to touch a point
in the ceiling, he would have to move in the direction of
the line in which the two walls meet. There are three
directions then, each at right angles to both the other,
and entirely independent of one another. By moving
in these three directions or combinations of them, it is
possible to arrive at any point in a room. And if we
suppose the straight lines which meet in the corner of
the room to be prolonged indefinitely, it would be
possible by moving in the direction of those three lines,
to arrive at any point in space. Thus in space there
are three independent directions, and only three ; every
other direction is compounded of these three. The
question that comes before us then is this. "Why
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6 What is the Fourth Dimension ?
should there be three and 011I3' three directions ? " Space,
as we know it, is subject to a limitation.
In order to obtain an adequate conception of what
this limitation is, it is necessary to first imagine beings
existing in a space more limited than that in which we
move. Thus we may conceive a being who has been
throughout all the range of his experience confined to a
single straight line. Such a being 'would know what it
was to move to and fro, but no more. The whole of
space would be to him but the extension in both direc-
tions of the straight line to an infinite distance. It is
evident that two such creatures could never pass one
another. We can conceive their coming out of the
straight line and entering it again, but they having
moved always in one straight line, would have no con-
ception of any other direction of motion by which such
a result could be effected. The only shape which could
exist in a one-dimensional existence of this kind would
be a finite straight line. There would be no difference in
the shapes of figures ; all that could exist would simply
be longer or shorter straight lines.
Again, to go a step higher in the domain of a con-
ceivable existence. Suppose a being confined to a plane
superficies, and throughout all the range of its experience
never to have moved up or down, but simply to have kept
to this one plane. Suppose, that is, some figure, such
as a circle or rectangle, to be endowed with the power
of perception ; such a being if it moves in the plane
superficies in which it is drawn, wil! move in a multitude
of directions ; but, however varied they may seem to be,
these directions will all be compounded of two, at right
angles to each other. By no movement so long as the
plane superficies remains perfectly horizontal, wil! this
being move in the direction we call up and down. And
it is important to notice that the plane would be different,
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Wliai is the Fourth Dimension ? 7
to a creature confined to it, from what it is to us. We
think of a plane habitually as having an upper and a
lower side, because it is only by the contact of solids
that we realize a plane. But a creature which had been
confined to a plane during its whole existence would
have no idea of there being two sides to the plane he
lived in. In a plane there is simply, length and breadth.
If a creature in it be supposed to know of an up or down
he must already have gone out of the plane.
Is it possible, then, that a creature so circumstanced
would arrive at the notion of there being an up and down,
a direction different from those to which he had been
accustomed, and having nothing in common with them ?
Obviously nothing in the creature's circumstances would
tell him of it. It could only be by a process of reasoning
on his part that he could arrive at such a conception. If
he were to imagine a being confined to a single straight
line, he might realise that he himself could move in two
directions, while the creature in a straight line could only
move in one. Having made this reflection he might ask,
" But why is the number of directions limited to two ?
Why should there not be three ? "
A creature (if such existed), which moves in a plane
would be much more fortunately circumstanced than one
which can only move in a straight line. For, in a plane,
there is a possibility of an infinite variety of shapes, and
the being we have supposed could come into contact
with an indefinite number of other beings. He would
not be limited, as in the case of the creature in a straight
line, to one only on each side of him.
It is obvious that it would be possible to play curious
tricks with a being confined to a plane. If, for instance,
we suppose such a being to be inside a square, the only
way out that he could conceive would be through one of
the sides of the square, if the sides were impenetrable,
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8 What ts the Fourth Dimension ?
he would be a fast prisoner, and would have no way
out.
What his case would be we may understand, if we
reflect what a similar case would be in our own existence.
The creature is shut in in all the directions he knows of.
If a man is shut in in all the directions he knows of, he
must be surrounded by four walls, a roof and a floor, A
two-dimensional being inside a square would be exactly
in the same predicament that a man would be, if he were
in a room with no opening on any side. Now it would
be possible to us to take up such a being from the inside
of the square, and to set him down outside it. A being
to whom this had happened would find himself outside
the place he had been confined in, and he would not have
passed through any of the boundaries by which he was
shut in. The astonishment of such a being can only be
imagined by comparing it to that which a man would feel,
if, he were suddenly to find himself outside a room in
which he had been, without having passed through the
window, doors, chimney or any opening in the walls,
ceiling or floor.
Another curious thing that could be effected with a
two-dimensional being, is the following. Conceive two
beings at a great distance from one another on a plane-
surface. If the plane surface is bent so that they are
brought close to one another, they would have no con-
ception of their proximity, because to each the only possible
movements would seem to be movements in the surface.
The two beings might be conceived as so placed, by a
proper bending of the plane, that they should be absolutely
in juxtaposition, and yet to all the reasoning faculties of
either of them a great distance could be proved to inter-
vene. The bending might be carried so far as to make one
being suddenly appear in the plane by the side of the other.
If these beings were ignorant of the existence of a third
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What is the Fourth Dimension ? 9
dimension, this result would be as marvellous to them, as
it would be for a human being who was at a great
distance — it might be at the other side of the world—
to suddenly appear and really be by our side, and
during the whole time he not to have left the place in
which he was.
CHAPTER II.
The foregoing examples make it clear that beings can
be conceived as living in a more limited space than ours.
Is there a similar limitation in the space we know?
At the very threshold of arithmetic an indication of
such a limitation meets us.
If there is a straight line before us two inches long,
its length is expressed by the number 3. Suppose
a square to be described on the line, the number
of square inches in this figure is expressed by the
number 4, i.e., 2X2. This 2 X 2 is generally written 2^,
and named " 2 square."
Now, of course, the arithmetical process of multiplica-
tion is in no sense identical with that process by which
a square is generated from the motion of a straight line,
or a cube from the motion of a square. But it has
been observed that the units resulting in each case,
though different in kind, are the same in number.
If we touch two things twice over, the act of touching
has been performed four times. Arithmetically, 2 x 2 = 4,
If a square is generated by the motion of a line two inches
in length, this square contains four square inches.
So it has come to pass Ihat the second and third powers
of numbers are called "square" and "cube."
We have now a straight line two inches long. On
this a square has been constructed containing four
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lo What is the Fourth DimensioM?
square inches. If on the same line a cube be constructed,
the number of cubic inches in the figure so made is 8,
I.e., 2 X 2 X 3 or 2^. Here, corresponding to the numbers
2, 2^, 2^, we have a series of figures. Each figure con-
tains more units than the last, and in each the unit is of
a different kind. In the first figure a straight line is the
unit, viz., one linear inch ; it is said to be of one
dimension. In the second a square is the unit, viz., one
square inch. The square is a figure of two dimensions.
In the third case a cube is the unit, and the cube is of
three dimensions. The straight line is said to be of one
dimension because it can be measured only in one way.
Its length can be taken, but it has no breadth or thick-
ness. The square is said to be of two dimensions because
it has both length and breadth. The cube is said to have
three dimensions, because it can be measured in three
The question naturally occurs, looking at these num-
bers 2, 2^, 2^, by what figure shall we represent 2*, or
2X2X2X3. We know that in the figure there must be
sixteen units, or twice as many units as in the cube. But
the unit also itself must be different. And it must not,
differ from a cube simply in shape. It must differ from
a cube as a cube differs from a square. No number of
squares will make up a cube, because each square has no
thickness. In the same way, no number of cubes must
be able to make up this new unit. And here, instead of
trying to find something already known, to which the
idea of a figure corresponding to the fourth power can be
affixed, let us simply reason out what the properties of
such a figure must be. In this attempt we have to rely,
not on a process of touching or vision, such as informs us
of the properties of bodies in the space we know, but on a
process of thought. Each fart concerning this unknown
figure has to be reasoned out ; and it is only after a number
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Whal is the Fourth Dimension ? 1 1
of steps have been gone through, that any consistent
familiarity with its properties is obtained. Of all applica-
tions of the reason, this exploration is perhaps the one
which requires, for the simplicity of the data involved, the
greatest exercise of the abstract imagination, and on this
account is well worth patient attention. The first steps
are very simple. We must imagine a finite straight line
to generate a square by moving on the plane of the paper,
and this square in its turn to generate a cube by moving
vertically upwards. Fig. I represents a straight line ;
Fig. 2 represents a square formed by the motion of that
Straight line ; Fig. 3 represents perspectively a cube
formed by the motion of that square A B C D upwards.
It would be well, instead of using figure 3, to place a cube
on the paper. Its base would be A B C D, its upper
surface E F G H.
The straight line A B gives rise to the square A B C D
by a movement at right angles to itself. If motion be
confined to the straight line A B, a backward and forward
motion is the only one possible. No sideway motion is
admissible. And if we suppose a being to exist which
could only move in the straight line A B, it would have
no idea of' any other movement than to and fro. The
square A B C D is formed from the straight line by a
movement in a direction entirely different from the direc-
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12 W/ial is ike Fottrth D\
tion which exists in A B, This motion is not expressible
by means of any possible motion in A B. A being which
existed in A B, and whose experience was limited to what
could occur in A B, woald not be able to understand the
instructions we should give to make A B trace out the
figure A B C D.
In the figure A B C D there is a possibility of moving
in a variety of directions, so long as all these directions
are confined to one plane. All directions in this plane
can be considered as compourided of two, from A to B,
and from A to C. Out of the infinite variety of such
directions there is none which tends in a direction perpen-
dicular to Fig. 2 ; there is none which tends upwards
from the plane of the paper. Conceive a being to exist
in the plane, and to move only in it. In all the move-
ments which he went through there would be none by
which he could conceive the alteration of Fig. 2 into what
Fig. 3 represents in perspective. For 2 to become 3 it
must be supposed to move perpendicularly to its own
plane. The figure it traces out is the cube ABCDEFGH.
All the directions, manifold as they are, in which a
creature existing in Fig. 3 could move, are compounded
of three directions. From A to B, from A to C, from A
to E, and there are no other directions known to it.
But if we suppose something similar to be done to
Fig. 3, something of the same kind as was done to Fig. i
to turn it into Fig. 2, or to Fig. 2 to turn it into Fig. 3,
we must suppose the whole figure as it exists to be moved
in some direction entirely different from any direction
within it, and not made up of any combination of the
directions in it. What is this ? It is the fourth direction.
We are as unable to imagine it as a creature living in
the plane Fig. 2 would be to imagine a direction such
that moving in it the square 2 would become the cube 3.
The third dimension to such a creature would be as un-
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What is the Fourth Dimension ? 1 3
intelligible as the fourth is to us. And at this point we
have to give up the aid that is to be got from any present-
able object, and we have simply to investigate what the
properties of the simplest figure in four dimensions are,
by pursuing further the analogy which we know to exist
between the process of formation of 2 from i, and of 3
from 2, and finally of 4 from 3. For the sake of conveni-
ence, let us call the figure we are investigating — the
simplest figure in four dimensions — a four-square.
First of all we must notice, that if a cube be formed
from a square by the movement of the square in a new
direction, each point of the interior of the square traces
out part of the cube. It is not only the bounding lines
that by their motion form the cube, but each portion of
the interior of the square generates a portion of the cube.
So if a cube were to move in the fourth dimension so as
to generate a four-square, every point in the interior of
ttie cube would start de novo, and trace out a portion of
the new figure uninterfered with by the other points.
Or, to look at the matter in another light, a being in
three dimensions, looking down on a square, sees each
part of it extended before him, and can touch each part
without having to pass through the surrounding parts,
for he can go from above, while the surrounding parts
surround the part he touches only in one plane.
So a being in four dimensions could look at and touch
every point of a solid figure. No one part would hide
another, for he would look at each part from a direction
which is perfectly diiferent from any in which it is possible
to pass from one part of the body to another. To pass
from one part of the body to another it is necessary to
move in three directions, but a creature in four dimensions
would look at the solid from a direction which is none of
these three.
Let us obtain a few facts about the fourth figure.
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14 What is the Fourth Dimension ?
proceeding according to the analogy that exists between
I, 2, 3, and 4. In the Fig. i there are two points. In 3
there are four points — the four corners of the square. In
3 there are eight points. In the next figure, proceeding
according to the same law, there would be sixteen points.
In the Fig. I there is one line. In the square there
are four lines. In the cube there are twelve lines. How
many lines would there be in the four-square ? That is
to say that there are three numbers — i, 4, and 12. What
is the fourth, going on accordingly to the same law ?
To answer this question let us trace out in more detail
how the iigures change into one another. The line, to
become the square, moves ; it occupies first of all its
original position, and last of all its final position. It
starts as A B, and ends as C D ; thus the line appears
twice, or it is doubled. The two other lines in the square,
A C, B D, are formed by the motions of the points at
the extremities of the moving line. Thus, in passing
from the straight line to the square the lines double
themselves, and each point traces out a line. If the
same procedure holds good in the case of the change of
the square into the cube, we ought in the cube to have
double the number of lines as in the square— that is eight
■ — and every point in the square ought to become a line.
As there are four points in the square, we should have
four lines in the cube from them, that is, adding to the
pi-evious eight, there should he twelve lines in the cube.
This is obviously the case. Hence we may with con-
fidence, to deduce the number of lines in a four-square,
apply this rule. Double the number of lines in the pre-
vious figure, and add as many lines as there are points
in the previous figure. Now in the cube there are twelve
lines and eight points: Hence we get 2 x 12 + 8, or
thirty-two lines in the four-square.
In the same way any other question about the four-
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What is the Fourth Dimension ? 15
square can be answered. We must throw aside our
realising power and answer in accordance with the
analogy to be worked out from the three figures we know.
Thus, if we want to know liow many plane surfaces the
four-square has, we must commence with the line, which
has none ; the square has one ; the cube has six. Here we
get the three numbers, o, \, and 6. What is the fourth ?
Consider how the planes of the cube arise. The square
at the beginning of its motion determines one of the faces
of the cube, at the end it is the opposite face, during the
motion each of the lines of the, square traces out one
plane face of the cube. Thus we double the number of
planes in the previous figure, and every line in the
previous figure traces out a plane in the subsequent one.
Apply this rule to the formation of a square from a
line. In the line there is no plane surface, and since
twice nothing is nothing, we get, so far, no surface in the
square ; but in the straight line there is one line, namely
itself, and this by its motion traces out the plane surface
of the square. So in the square, as should be, the rule
gives one surface.
Applying this rule to the case of the cube, we get,
doubling the surfaces, I3 ; and adding a plane for each
of the straight lines, of which there are I3, we have
another 12, or 24 plane surfaces in all. Thus, just as by
handling or looking at it, it is possible to describe a figure
in space, so by going through a process of calculation it
is within our power to describe all the properties of a
figure in four dimensions.
There is another characteristic so remarkable as to
need a special statement. In the case of a finite straight
line, the boundaries are points. If we deal with one
dimension only, the figure I, that of a segment of a
straight line, is cut out of and separated from the rest of
an imaginary infinitely long straight line by the two points
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1 6 Whai is the Fourth Dimension ?
at its extremities. In this simple case the two points
correspond to the bounding surface of the cube. In the
case of a two-dimensional figure an infinite plane repre-
sents the whole of space. The square is separated off
by four straight lines, and it is impossible for an entry
to be made into the interior of the square, except by
passing through the straight lines. Now, in these cases,
it is evident that the boundaries of the figure are of one
dimension less than the figure itself. Points bound fines,
lines bound plane figures, planes bound solid figures.
SoHds then must bound four dimensional figures. The
four-square will be bounded in the following manner.
First of all there is the cube which, by its motion in the
fourth direction, generates the figure. This, in its initial
position, forms the base of the four-square. In its final
position it fonns the opposite end. During the motion
each of the faces of the cube give rise to another cube.
The direction in which the cube moves is such that of
all the six sides none is in the least inclined in that
direction. It is at right angles to all of them. The base
of the cube, the top of the cube, and the four sides of
the cube, each and all of them form cubes. Thus the
four-square is bounded by eight cubes. Summing up,
the four-square would have l6 points, 32 lines, 24
surfaces, and it would be bounded by 8 cubes.
If a four-square were to rest in space it would seem to
us like a cube.
To justify this conclusion we have but to think of
how a cube would appear to a two-dimensional being.
To come within the scope of his faculties at all, it must
come into contact with the plane in which he moves. If
it is brought into as close a contact with this plane as
possible, it rests on it by one of its faces. This face is a
square, and the most a two-dimensional being could get
acquainted with of a cube would be a square.
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What is the Fourth Dimension ? 1 7
Having thus seen how it is possible to describe the
properties of the simplest shape in four dimensions, it is
evident that the mental construction of more elaborate
figures is simply a matter of time and patience.
In the study of the form and development of the chick in
the egg, it is impossible to detect the features that are
sought to be observed, except by the use of the microscope.
The specimens are accordingly hardened by a peculiar
treatment and cut into thin sections. The investigator
going over each of these sections, noticing all their pecu-
liarities, constructs in his mind the shape as it originally
existed from the record afforded by an indefinite number
of slices. So, to form an idea of a four-dimensional figure,
a series of solid shapes bounded on every side differing
gradually from one another, proceeding, it may be, to the
most diverse forms, has to be mentally grasped and fused
into a unitary conception.
If, for instance, a small sphere were to appear, this to be
replaced by a larger one, and so on, and then, when the
largest had appeared, smaller and smaller ones to make
their appearance, what would be witnessed would be a
series of sections of a four- dimensional sphere. Each
section in space being a sphere.
Again, just as solid figures can be represented on paper
by perspective, four-dimensional figures can be represented
perspectively by solids. If there are two squares, one
lying over the other, and the underneath one be pushed
away, its sides remaining parallel with the one that was
over it, then if each point of the one be joined to the
corresponding point of the other, we have a fair represen-
tation on paper of a cube. Fig. 3 may be considered to
be such a representation if the square C D G H be con-
sidered to be the one that has been pushed away from
lying originally under the square A B E F. Each of the
planes which bound the cube is reoresented on the paper.
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1 8 PVAa/ is ike Fourth Dimension ?
The only thing that is wanting is the three-dimensional
content of the cube. So if two cubes be placed with their
sides parallel, but one somewhat diagonally with regard to
the other, and all their corresponding points be supposed
joined, there will be found a set of solid figures, each
representing {though of course distortedly) the bounding
cubes of the four-dimensional figure, and every plane
and line in the four-dimensional figure will be found to
be represented in a kind of solid perspective. What is
wanting is of course the four- dimensional content.
CHAPTER III.
Having now passed in review some of the properties of
four- dimensional figures, it remains to ask what relations
beings in four dimensions, if they did exist, would have
with us.
And in the first place, a being in four dimensions would
have to us exactly the appearance of a being in space,
A being in a plane would only know soUd objects as two-
dimensional figures— the shapes namely in which they
intersected his plane. So if there were four- dimensional
objects, we should only know them as solids — the solids,
namely, in which they intersect our space. Why, then,
should not the four-dimensional beings be ourselves, and
our successive states the passing of them through the
three-dimensional space to which our consciousness is
confined ?
Let us consider the question in more detail. And for
the sal<e of simplicity transfer the problem to the case of
three and two dimensions instead of four and three.
Suppose a thread to be passed through a thin sheet of
wax placed horizontally. It can be passed through in two
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What is the Fourth Dimension ? 19
ways. Either it can be pulled through, or it can be held
at both ends, and moved downwards as a whole. Suppose
a thread to be grasped at both ends, and the hands to be
moved downwards perpendicularly to the sheet of wax.
If the thread happens to be perpendicular to the sheet
it simply passes through it, but if the thread be held,
stretched slantingwise to the sheet, and the liinds are
moved perpendicularly downwards, the thread will, if it
be strong enough, make a slit in the sheet.
If now the sheet of wax were to have the faculty of
closing up behind the thread, what would appear in the
sheet would be a moving hole.
Suppose that instead of a sheet and a thread, there
were a straight hne and a plane. If the straight line were
placed slantingwise in reference to the plane and moved
downwards, it would always cut the plane in a point, but
that point of section would move on. If the plane were
of such a nature as to close up behind the line, if it were
of the nature of a fluid, what would be observed would
be a moving point. If now there were a whole system of
lines sloping in different directions, but all connected
together, and held absolutely still by one framework, and
if this framework with its system of liiies were as a whole
to pass slowly through the fluid plane at right angles to
it, there would then be the appearance of a multitude of
moving points in the plane, equal in number to the number
of straight lines in the system. The lines in the frame-
work will ail be moving at the same rate — namely, at the
rate of the framework in which they are fixed. But the
points in the plane will have different velocities. They
will move slower or faster, according as the lines which
give rise to them are more or less inclined to the plane.
A straight line perpendicular to the plane will, on passing
through, give rise to a stationary point A straight line
that slopes vei"y much inclined to the plane will give rise
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20 What is the Fourth Dimension ?
to a point moving with great swiftness. The motions and
paths of the points would be determined by the arrange-
ment of the lines in the system. It is obvious that if two
straight lines were placed lying across one another like
the letter X, and if this iigure were to be stood upright
and passed through the plane, what would appear
would be at first two points. These two points would
approach one another. \yhen the part where the two
strokes of the X meet came into the plane, the two
points would become one. As the upper part of the
figure passed through, the two points would recede from
one another.
If the line be supposed to be affixed to all parts of the
framework, and to loop over one another, and support
one another,* it is obvious that they could assume all
sorts of figures, and that the points on the plane would
move in very complicated paths. The annexed figure
represents a section of such a framework. Two lines
X X and Y Y are shown, but there must be supposed
to be a great number of others sloping backwards and
forwards as well as sideways.
Let us now assume that instead of lines, very thin
threads were attached to the framework : they on passing
through the fluid plane would give rise to very small
spots. Let us call the spots atoms, and regard them as
• A B C D framework, X and Y two lines iiiterimkecl
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What is the Fourth Dimension ? 21
constituting a material system in tlie plane. There are
four conditions whicti must be satisfied by these spots if
they are to be admitted as forming a material system such
as ours. For the ultimate properties of matter (if we
eliminate attractive and repulsive forces, which may be
caused by the motions of the smallest particles), are — i,
Permanence; 2, Impenetrability; 3, Inertia; 4, Con-
servation of energy.
According to the first condition, or that of permanence,
no one of these spots must suddenly cease to exist.
That is, the thread which by sharing in the general
motion of the system gives rise to the moving point,
must not break off" before the rest of them. If all the
Hnes suddenly ended this would correspond to a ceasing
of matter.
2. Impenetrability. — One spot must not pass through
another. This condition is obviously satisfied. If the
threads do not coincide at any point, the moving spoti.
they give rise to cannot.
3. Inertia. — A spot must net cease to move or cease
to remain at rest without coming into collision with
another point. This condition gives the obvious condition
with regard to the threads, that they, between the points
where they come into contact with one another, must be
straight. A thread which was curved would, passing
through the plane, give rise to a point which altered in
velocity spontaneously. This the particles of matter
never do.
4. Conservation of energy.— The energy of a material
system is never lost ; it is only transferred from one form
to another, however it may seem to cease. If we suppose
each of the moving spots on the plane to be the unit of
mass, theprinciple of the conservation of energy demands
that when any two meet, the sum of the squares of their
several velocities before meeting shall be the same as the
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2 2 What is the Fourth Dimension ?
sum of the squares of their velocities after meeting. Now
we have seen that any statement about the velocities
of the spots in the plane is really a statement about the
inclinations of the threads to the plane. Thus the
principle of the conservation of energy gives a condition
which must be satisfied by the inclinations of the threads
of the plane. Translating this statement, we get in
mathematical language the assertion that the sum of
the squares of the tangents of the angles the threads
make with the normal to the plane remains constant.
Hence, aU complexities and changes of a material
system made up of similar atoms in a plane could result
from the uniform motion as a whole of a system of threads.
We can imagine these threads as weaving together
to form connected shapes, each complete in itself, and
these shapes as they pass through the fluid plane give
rise to a series of moving points. Yet, inasmuch as the
threads are supposed to form consistent shapes, the
motion of the points would not be wholly random, but
numbers of them would present the semblance of moving
figures. Suppose, for instance, a number of threads to
be so grouped as to form a cylinder for some distance,
but after a while to be pulled apart by other threads
with which they interlink. While the cyhnder was pass-
ing through the plane, we should have in the plane a
number of points in a circle. When the part where the
threads deviated came to the plane, the circle would
break up by the points moving away. These moving
figures in the plane are but the traces of the shapes of
threads as those shapes pass on. These moving figures
may be conceived to have a life and a consciousness of
their own.
Or, if it be irrational to suppose them to have a con-
sciousness when the shapes of which they are momentary
traces have none, we may well suppose that the shapes
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What is the Fourth Dimension ? 23
of threads have consciousness, and that the moving
figures share this consciousness, only that in their case
it is limited to those parts of the shapes that simul-
taneously pass through the plane. In the plane, then,
we may conceive bodies with all the properties of a
material system, moving and changing, possessing con-
sciousness. After a while it may well be that one of
them becomes so disassociated that it appears no longer
as a unit, and its consciousness as such may be lost.
But the threads of existence of such a figure are not
broken, nor is the shape which gave it origin altered in
any way. It has simply passed on to a distance from
the plane. Thus nothing which existed in the conscious
life on the plane would cease. There would in such an
existence be no cause and effect, but simply the gradual
realisation in a superficies of an already existent whole.
There would be no progress, unless we were to suppose
the threads as they pass to interweave themselves in
more complex shapes.
Can a representation, such as the preceding, be applied
to the case of the existence in space with which we have
to do ? Is it possible to suppose that the movements and
changes of material objects are the intersections with a
three-dimensional space of a four- dimensional existence ?
Can our consciousness be supposed to deal with a spatial
profile of some higher actuality ?
It is needless to say that all the considerations that
have been brought forward in regard to the possibility of
the production of a system satisfying the conditions of
materiality by the passing of threads through a fluid
plane, holds good with regard to a four-dimensional
existence passing through a three-dimensional space.
Each part of the ampler existence which passed through
our space would seem perfectly limited to us. We should
have no indication of the permanence of its existence.
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24 Wkal is the Fourth Dimension ?
Were such a thought adopted, we should have to imagine
some stupendous whole, wherein all that has ever eome
into being or will come co-exists, which passing slowly
on, leaves in this flickering consciousness of ours, limited
to a narrow space and a single moment, a tumultuous
record of changes and vicissitudes that are but to us.
Change and movement seem as if they were all that
existed. But the appearance of them would be due
merely to the momentary passing through our conscious-
ness of ever existing realities.
In thinking of these matters it is hard to divest our-
selves of the habit of visual or tangible illustration. If
we think of a man as existing in four dimensions, it is
hard to prevent ourselves from conceiving him as pro-
longed in an already known dimension. The image we
form resembles somewhat those solemn Egyptian statues
which in front represent well enough some dignified sit-
ting figure, but which are immersed to their ears in a
smooth mass of stone which fits their contour exactly.
No material image will serve. Organised beings seem
to us so complete that any addition to them would deface
their beauty. Yet were we creatures confined to a plane,
the outline of a Corinthian column would proTjably seem
to be of a beauty unimprovable in its kind. We should
be unable to conceive any addition to it, simply for the
reason that any addition we could conceive would be of
the nature of affixing an unsightly extension to some part
of the contour. Yet, moving as we do in space of three
dimensions, we see that the beauty of the stately column
far surpasses that of any single outline. So all that
we can do is to deny our faculty of judging of the ideal
completeness of shapes in four dimensions.
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What is the Fourth Dimension ?
CHAPTER IV.
Let us now leave this supposition of framework and
threads. Let us investigate the conception of a four-
dimensional existence in a simpler and more natural
manner — in the same way that a two-dimensional being
should think about' us, not as infinite in the third dimen-
sion, but limited in three dimensions as he is in two. A
being existing in four dimensions must then be thought
to be as completely bounded in all four directions as we
are in three. All that we can say in regard to the possi-
bility of such beings is, that we have no experience of
motion in four directions. The powers of such beings
and their experience would be ampler, but there would be
no fundamental difference in the laws of force and motion.
Such a being would be able to make but a part of him-
self visible to us, for a cube would be apprehended by a
two-dimensional being as the square in which it stood.
Thus a four-dimensional being would suddenly appear as
a complete and finite body, and as suddenly disappear,
leaving no trace of himself, in space, in the same way that
anything lying on a flat surface, would, on being lifted,
suddenly vanish out of the cognisance of beings, whose
consciousness was confined to the plane. The object
would not vanish by moving in any direction, but disap-
pear instantly as a whole. There would be no barrier no
confinement of our devising that would not be perfectly
open to him. He would come and go at pleasure ; he
would be able to perform feats of the most surprising kind.
It would be possible by an infinite plane extending in all
directions to divide our space into two portions absolutely
separated from one another ; but a four-dimensional being
would slip round this plane with the greatest ease.
To see this clearly, let us first take the analogous case
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26 What is the Fourth Di
in three dimensions. Suppose a piece of paper to represent
a plane. If it is infinitely extended in every direction, it
will represent an infinite plane. It can be divided into
two parts by an infinite straight line. A being confined
to this plane could not get from one part of it to the other
without passing through the line. But suppose another
piece of paper laid on the first and extended infinitely, it
will represent another infinite plane. If the being moves
from the first plane by a motion in the third dimension,
it will move into this new plane. And in it it finds no
line. Let it move to such a position that when it goes
back to the first plane it will be on the other side of the
line. Then let it go back to the first plane. It has
appeared now on the other side of the line which divides
the infinite plane into two parts.
Take now the case of four dimensions. Instead of
bringing before the mind a sheet of paper conceive a solid
of three dimensions. If this solid were to become infinite
it would fill up the whole of three-dimensional space.
But it would not fill up the whole of four-dimensional
space. It would be to four- dimensional space what an
infinite plane is to three-dimensional space. There could
be in four-dimensional space an infinite number of such
solids, just as in three-dimensional space there could be
an infinite number of infinite planes.
Thus, lying alongside our space, there can be conceived
a space also infinite in all three directions. To pass from
one to the other a movement has to be made in the fourth
dimension, just as .to pass from one infinite plane to
another a motion has to be made in the third dimension.
Conceive, then, corresponding to the first sheet of paper
mentioned above, a solid, and as the sheet of paper was
supposed to be infinitely extended in two dimensions,
suppose the solid to be infinitely extended in its three
dimensions, so that it fills the whole of space as we know it.
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What is the Fourth Dimension ? 27
Now divide this infinite solid in two parts by an infinite
plane, as the infinite plane of paper was divided in two
parts by an infinite line. A being cannot pass from one
part of this infinite solid to another, on the other side of
this infinite plane, without going through the infinite
plane, so long as he keeps within the infinite solid.
But suppose beside this infinite solid a second infinite
solid, lying next to it in the fourth dimension, as the
second infinite plane of paper was next to the first infinite
plane in the third dimension. Let now the being that
wants to get on the other side of the dividing plane move
off in the fourth dimension, and enter the second infinite
sofid. In this second solid there is no dividing plane.
Let him now move, so that coming back to the first
infinite solid he shall be on the other side of the infinite
plane that divides it into two portions. If this is done,
he will now be on the other side of the infinite plane,
without having gone through it.
In a similar way a being, able to move in four dimen-
sions, could get out of a closed box without going through
the sides, for he could move off in the fourth dimension,
and then move about, so that when he came back he
would be outside the box.
Is there anything in the world as we know it, which
would indicate the possibility of there being an existence
in four dimensions ? No definite answer can be returned
to this question. But it may be of some interest to point
out that there are certain facts which might be read by
the light of the fourth dimensional theory.
To make this clear, let us suppose that space is really
four dimensional, and that the three-dimensional space we
know is, in this ampler space, like a surface Is in our
space.
We should then be in this ampler space like beings
confined to the surface of a plane would be in ours. Let
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2 8 What is the Fourth Dimension ?
us suppose that just as in our space there are centres of
attraction whose influence radiates out in every direction,
so in this ampler space there are centres of attraction
whose influence radiates out in every direction. Is there
anything to be observed in nature which would correspond
to the effect of a centre of attraction lying out of our space,
and acting on all the matter in it ? The effect of such a
centre of attraction would not be to produce motion in
any known direction, because it does not lie off" in any
known direction.
Let us pass to the corresponding case in three and two
dimensions, instead of four and three. Let us imagine a
plane lying horizontally, and in it some creatures whose
experience was confined to it. If now some water or
other liquid were poured on to the plane, the creatures,
becoming aware of its presence, would find that it had a
tendency to spread out all over the plane. In fact it
would not be to them as a liquid is to us — it would rather
correspond to a gas. For a gas, as we know it, tends to
expand in every direction, and gradually increase so as
to fill the whole of space. It exercises a pressure on
the walls of any vessel in which we confine it.
The liquid on the plane expands in all the dimensions
which the two-dimensional creatures on the plane know,
and at the same time becomes smaller in the third dimen-
sion, its absolute quantity remaining unchanged. In like
manner we might suppose that gases (which by expansion
become larger in the dimensions that we know) become
smaller in the fourth dimension.
The cause in this case would have to be sought for in
an attractive force, acting with regard to our space as the
force of gravity acts with regard to a. horizontal plane.
Can we suppose that there is a centre of attraction
somewhere off in the fourth dimension, and that the gases,
which we know are simply more mobile liquids, expand-
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What is the Fotirth Dimension ? 29
ing out in every direction under its influence. This view
receives a certain amount of support from the fact proved
experimentally that there is no absolute line of demarca-
tion between a liquid and a gas. The one can be made
to pass into the other with no moment intervening in
which it can be said that now a change of state has taken
place.
We might then suppose that the matter we know
extending in three dimensions has also a small thickness
in the fourth dimension ; that solids are rigid in the fourth
as in the other three dimensions ; that liquids are too
coherent to admit of their spreading out in space, and
becoming thinner in the fourth dimension, under the
influence of an attractive centre lying outside of our
space; but that gases, owing to the greater mobility of
their particles, are subject to its action, and spread out in
space under its influence, in the same manner that liquids,
under the influence of gravity, spread out on a plane.
Then the density of a gas would be a measure of the
relative thickness of it in the fourth dimension: and the
diminution of the density would correspond to a diminu-
tion oi the thickness in the fourth dimension. Could this
supposition be tested in any way ?
Suppose a being confined to a plane ; if the plane is
moved far off from the centre of attraction lying outside it",
he would find that liquids had less tendency to spread out
than before.
Or suppose he moves to a distant part of the plane so
that the line from his position to the centre of attraction
lies obliquely to the plane; he would find that in this
position a liquid would show a tendency to spread out
more in one direction than another.
Now our space considered as lying in four- dimensional
space, as a plane does in three-dimensional space, may be
shifted. And the expansive force of gases might be
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30 What is the Fourth Dimension ?
found to be different at different ages. Or, shifting as we
do our position in space during the course of the earth's
path round the sun, there might arise a sufficient difference
in our position in space, with regard to the attractive centre,
to make the expansive force of gases different at different
times of the year, or to cause them to manifest a greater
expansive force in one direction than in another.
But although this supposition might be worked out at
some length, it is hard to suppose that it could afford
any definite test of the physical existence of a fourth
dimension. No test has been discovered which is decisive.
And, indeed, before searching for tests, a theoretical point
of the utmost importance has to be settled. In discussing
the geometrical properties of straight hues and planes, we
suppose them to be respectively of one and two dimen-
sions, and by so doing deny them any real existence.
A plane and a line are mere abstractions. Every portion
of matter is of three dimensions. If we consider beings
on a plane not as mere idealities, we must suppose them
to be of some thickness. If their experience is to be
limited to a plane this thickness must be very small
compared to their other dimensions. Transferring our
reasoning to the case of four dimensions, we come to a
curious result.
If a fourth dimension exists there are two possible
alternatives.
One is, that theze being four dimensions, we have a
three-dimensional existence only. The other is that we
really have a four-dimensional existence, but are not
conscious of it. If we are in three dimensions CTily,
while there are really four dimensions, then we must be
relatively to those beings who exist in four dimensions, as
lines and planes are in relation to us. That is, we must
be mere abstractions. In this case we must exist only in
the mind of the being that conceives us, and our experience
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What is the Fourth Dimension? 31
must be merely the thoughts of his mind — a result which
has apparently been arrived at, on independent grounds,
by ati idealist philosopher.
The other alternative is that we have a four-dimensional
existence. In this case our proportions in it must be
infinitely minute, or we should be conscious of them.
If such be the case, it would probably be in the ultimate
particles of matter, that we should discover the fourth
dimension, for in the ultimate particles the sizes in the
three dimensions are very minute, and the magnitudes in
all four dimensions would be comparable.
The preceding two alternative suppositions are based
on the hypothesis of the reality of four-dimensional ex-
istence, and must be conceived to hold good only on that
hypothesis.
It is somewhat curious to notice that we can thus con-
ceive of an existence relative to which that which we
enjoy must exist as a mere abstraction.
Apart from the interest of speculations of this kind they
have considerable value ; for they enable us to express in
intelligible terms things of which we can form no image.
They supply us, as it were, with scaffolding, which the
mind can make use of in building up its conceptions.
And the additional gain to our power of representation
is very great.
Many philosophical ideas and doctrines are almost
unintelligible because there is no physical illustration
which will serve to express them. In the imaginary
physical existence which we have traced out, much that
philosophers have written finds adequate representation.
Much of Spinoza's Ethics, for example, could be symbo-
lized from the preceding pages.
Thus we may discuss and draw perfectly legitimate
conclusions with regard to unimaginable things.
It is, of course, evident that these speculations present
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32 Whai is the Fourth Dimension ?
no point of direct contact with fact. But this is no reason
why they should be abandoned. The course of knowledge
is Like the flow of some mighty river, which, passing
through the rich lowlands, gathers into itself the contribu-
tions from every valley. Such a river may well be joined
by a mountain stream, which, passing with difficulty
along the barren highlands, flings itself into the greater
river down some precipitous descent, exhibiting at the
moment of its union the spectacle of the utmost beauty
of which the river system is capable. And such a stream
is no inapt symbol of a line of mathematical thought,
which, passing through difficult and abstract regions,
sacrifices for the sake of its crystalline clearness the
richness that comes to the more concrete studies. Such
a course may end fruitlessly, for it may never join the
main course of observation and experiment. But, if it
gains its way to the great stream of knowledge, it affords
at the moment of its union the spectacle of the greatest
intellectual beauty, and adds somewhat of force and
mysterious capability to the onward current.
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PART I
CHAPTER I.
In Persia there was once a king. On one
occasion when he was out hunting he came
to the narrow entrance of a valley. It was
shut in on either side by vast hills, seemingly
the spurs from the distant mountains. These great
spurs spread out including a wide tract of land. To-
wards the entrance where he stood they approached
one another, and ended in abrupt cliffs. Across the
mouth of the valley stretched a deep ravine. The king,
followed by courtiers, galloped along, searching a spot
where the deep fissure might be shallower, so that
descending into it he might reach the valley by ascending
oti the opposite side,
But at every point the ravine stretched downwards
dark and deep, from cliff to cliff, shutting off all access
to the valley.
At one point only was there a means of crossing.
There were two masses of rocks, jutting out one from
either side like the abutments of a natural bridge, and
they seemed to meet in mid air.
The mass trembled and shook as the king spurred
his horse over it, and the dislodged stones reverberated
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34
The Persian Km
from side to side of the chasm till the noise of their
falling was lost.
Before the first of his courtiers could follow him one
of the great piers or abutments gave way — the whole
mass fell crashing down. The king was alone in the
valley,
"So ho," he cried, "the kingdom of Persia is shrunk
to this narrow spot ! " and without troubling himself for
the moment how he should return, he sped onward.
But when he had ridden far into the valley on his
steed that could outnumber ten leagues in an hour, and
had returned to the entrance of it, he saw no trace of a
living soul on the opposite brink of the clefl. No sign
was left, save a few reeds bent down by the passage of
the mounted train, that any human being had stood on
the opposite side for ages.
The evening came on apace. Yet no one returned.
Again he rode far into the valley. For the most part it
was covered with long grass, but here and there a thick
and tangled mass of vegetation attested to a great
luxuriance of soil, while the surface was intersected here
and there with rivulets of clear water, which finally lost
their way in the dark gorge over which he had just so
rashly adventured. But on no side did the steep cliffs
offer any promise of escape.
When the night came on he stretched himself beneath
one of the few trees not far from the ravine, while his
faithful horse stood tranquilly at his head.
He did not awake till the moon had risen. But then
suddenly he started to his feet, and walking to the edge
of the cleft, peered over to the iand from whence he had
come. For he thought he heard sounds of some kind
that were not the natural ones of the rustling wind or
the falling water. Looking out he saw clearly opposite
to him an old man in ragged clothing, leaning against
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The Persian King. 35
a rock, holding a long pipe in liJs hands, on which he
now and again played a few wild notes.
" Oho, peasant ! " cried the king. " Run and tell the
head man of your village that the king bids him come
directly, and will have him bring with him the longest
ropes and the strongest throwers under him."
But the old man did not seem to give heed. Then
the king cried, " Hearken, old man, run quickly and tell
your master that the king is confined here, and will
reward him beyond his dreams if he deliver him quickly."
Then the old man rose, and coming nearer to the
edge of the ravine stood opposite, still playing at inter-
vals some notes on his long pipe. And the king cried,
" Canst thou hear .' Dost thou dare to refuse to carry
my commands .' For I am the king of Persia, Who art
thou ? "
Then the old man made answer, putting his pipe aside:
" I am he who appears only when a man has passed for
ever beyond the ken of all that have known him. I am
Demiourgos, the maker of men."
Then the king cried, " Mock me not, but obey my
The old man made answer, " I do not mock thee ; and
oh, my Lord, thou hast moved the puppets I have made,
and driven them so to dance on the surface of the earth
that I would willingly obey thee. But it is not per-
mitted me to pass between thee and the world of men
thou hast known."
Then the king was silent.
At length he said, "If thou art really what thou
sayest, show me what thou canst do ; build me a
palace."
The old man lifted his pipe in both his trembling
hands, and began to blow.
It was a strange instrument, for it not only produced
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36 The Persian King.
the shriller sounds of the lute, and the piercing notes of
the trumpet, but resounded with the hollow booming of
great organ pipes, and amongst all came ever and again
a sharp and sonorous clang as of some metal instrument
resounding when it was struck.
And then the king was as one who enjoys the delights
of thought. For in thought, delicate shades, impalpable
nuances are ever passing. It is as the blended strains of
an invisible orchestra, but more subtle far, that come and
go in unexpected metres, and overwhelm you with their
beauty when all seemed silent. And lo, as the strains
sound, outside — palpable, large as the firmament, or real
as the smallest thing you can take up and know it is
there — outside stands some existence revealed — to be
known and returned to for ever.
So the king, listening to this music, felt that something
was rising behind him. And turning, beheld course
after course of a great building. Almost as soon as he
had looked it had risen completed, finished to the last
embossure on the windows, the tracery on the highest
pinnacles. All had happened while the old man was
blowing on his pipe, and when he ceased all was perfect.
And yet the appearance was very strange, for a
finished and seemingly habitable building rose out of
waste unreclaimed soil, strewn with rocks and barren.
No dwellings were near the palace to wait on it, no roads
led to it or away from it,
"There should be houses around it, and roadways,"
said the king ; " make thera, and fields sown with corn,
and all that is necessary for a state."
Blowing on his pipe in regular recurrent cadences, the
old man called up houses close together, than scattered
singly along roads which stretched away into the dis-
tance, to be seen every here and there perfectly clearly
where they ascended a rising ground. And near at
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The Persian King. 37
hand could be distinguished fields of grain and pasture
land.
Vet as the king turned to walk towards the new scene,
the old man laughed. "All this is a dream," he cried ;
"so much I can do, but not at once," And breathing
peals of music from his pipe, he said, " This can be, but
is not yet."
" What," asked the king, " is all a delusion .'" and as he
asked everything sank down. There was no palace, no
houses or fields, only the steep precipice-locked valley,
whither the king had ridden ; and his horse cowering
behind him.
Then the king cried, " Thou art some moonstruck
hermit, leading out a life of folly alone. Get thee to
the village thou knowest, and bring me help."
But the old man answered him saying, " Great king, i
am bound to obey thee, and all the creative might of
my being I lay at thy feet ; and lo, in the midst of this
valley I make for thee beings such as I can produce.
And all that thou hast seen is as nothing to what I can
do for thee. The depths of the starry heavens have no
limit, nor what I do for thee. Hast thou ever in thy
life looked into the deep still ocean, and lost thy sight
in the unseen depths.' Even so thou wilt find no end
in what I will give thee. Hast thou ever in thy life
sought the depths of thy love's blue eyes, and found
therein a world which stretched on endlessly .' Even so
I bring all to thy feet. Now that all the gladness of the
world has departed from thee, behold, I am a more
willing servant than ever thou hast had."
And again he played, and a hut rose up with a patch
of cleared soil around it, and a spring near by.
Then the king said, "Here will I dwell, and if I am
to be cut off from the rest of the world, I will lead a
peaceful life in this valley,"
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38 7
The sun was rising, the sounds had ceased, and the
old man had disappeared.
CHAPTER II.
He made his way slowly to the patch of cultivated
ground, he knocked at the door of the hut, and then he
called out. No answer was made to the sound of his
voice, he entered, and saw a rude, plain interior. There
were two forms half lying, half propped up by the walls,
and some domestic implements lay about, But when
he spoke to the beings they did not answer, and when
he touched their arms they fell powerless on the ground
and remained there. A terrible fear came on the king
lest he should become such as these. He left them and
again sought a possible outlet, but fruitlessly. And that
evening he sought the old man again and inquired what
sort of beings these were.
" For though in form and body like children out-
wardly," said the king, " they do nothing and seem
unable to move ; are they in an enchanted slumber ? "
Then the old man came near to the edge of the ravine
and, speaking solemnly and low, said :
" O king, thou dost not yet know the nature of the
place wherein thou art. For these children are like the
children thou hast known always both in form and body.
I have worked on them as far as is within my power.
But here in this valley a law reigns which binds them in
sleepfuincss and powerlessness. For here in everything
that is done there is as much pain as pleasure. If it is
pleasant to tread a downward slope there is as much
pain in ascending the upward slope. And in every action
there is a pleasant part and a painful part, and in the
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The Persian King. 39
tasting of eveiy herb the beings feel a bitter taste and a
sweet taste, HO indistinguishably united that the pleasure
and the pain of eating it are equally balanced. And
as hunger increases the sense of the bitterness in the
taste increases, so it is never more pleasant to eat than
not to eat. Everything that can be done here affords
no more pleasure than it does pain, from the greatest
action down to the least movement. And the beings as
I can make them, they follow pleasure and avoid pain.
And if the pleasure and the pain are equal they do not
move one way or the other."
"This is impossible," said the king.
" Nay," said the old man, " that it is as 1 have said I
will prove to thee." And he explained to the king how
it would be possible to stimulate the children to activity,
for he showed him how he could divest anything that
was done of part of its pain and render it more plea-
surable than painful. " In this way thou canst lead the
beings I have given thee to do anything," said the old
man, "but the condition is that thou must take the painful
part that thou sparest them thyself." And he bade the
king cut himself of the reeds that grew by the side of
the ravine, and told him that putting them between
himself and any being would enable him to take a part
of the pail) and leave in their feeling the whole of the
pleasure and the pain diminished by that part which he
bore himself.
Then the king cut of the reeds that grew by the side
of the ravine. He went to the hut where these beings
lay, and, taking the reeds in his hand, he placed one
between the child's frame and himself. And the child
rose up and walked, while he himself felt a pain in his
limbs. And he found that by taking a pain in each
part of him the child would exercise that part ; if he
wished the child to look at anything he, by bearing a
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40 The Persian King.
pain in his eyes, made looking at it pleasurable to the
child, and accordingly the child did look at the object
he wished him to regard. And again, by bearing a
bitter taste in his mouth he made the child feel eating
as pleasant, and the child gathered fruits and ate
them.
Then the king by using two reeds made both the chil-
dren move, and they went together wheresoever he
wished them. But they had not the slightest idea of the
king's action on them. They recognized each other, and
played with each other. They saw the king and had a
certain regard for him, but of his action on them they
knew nothing. For they felt his bearing the pain as this
thing or that being pleasurable. They felt his action as
a motive in themselves.
And all day long the king went with them, leading
them through the valley, bearing the pain of each step,
so that the children felt nothing but pleasure. But at
nightfall he led them back to the rude dwelling where
he had found them. He led them by taking the pain
from their steps in that direction, and not taking any of
the pain from steps in any other direction.
And when they had entered the dwelling-place he
removed his reeds from them. Immediately they sank
down into the state of apathy in which he had found
them. They did not move.
And the king at nightfall sought again the side of the
ravine.
Gazing across it he saw the sandy waste of the land
from which he had come, he saw the great stones which
were scattered about, looking pale and grey in the
moonlight. And presently in the shadow of a rock
near the opposite brink he discerned the form of the old
man.
And he cried out to him, and bade him come near.
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The Persian King. 41
And when the old man stood opposite to him, he be-
sought hira to tell him how he could make the beings
go through their movements of Hfe without his bearing
so much pain.
And the old man took his staff in his hand, and he
held it out towards the king, over the depth.
" Behold, O king, thy secret," he cried. And with his
other hand he smote the staff which was pointing down
into the depths. The staff swung to and fro many times,
and at last it came to rest again.
Then the king besought him to explain what this
might signify.
" Thou hast been," replied the old man, " as one who,
wishing to make a staff swing to and fro, has made every
movement separately, raising it up by his hand each time
that it falls down. But, behold, when I set it in move-
ment it goes through many swings of itself, both down-
ward and upward, until the movement I imparted to it
is lost. Even so thou must make these beings go through
both pleasure and pain, thyself bearing but the difference,
not taking all the pain."
"Must I then," asked the king, "by bearing pain give
these beings a certain store of pleasure, and then let
them go through their various actions until they have
exhausted this store of pleasure .' "
Then the old man made answer. " Can I have any
secrets from thee.' Hearken, O king, and I will telithee
what lies behind the shows of the world. What I have
shown thee is an outward sign and symbol of what thou
shouldst do, but it lies far outside those recesses whither
I shall lead thee. Thou couldst indeed give these beings
a store of pleasure, and they would go through their
actions until it was all spent ; but then thou wouldst
be as one of themselves. Thou wouldst have to per-
form the painful part of some action and let them per-
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42 The Persia7t ICing.
form the pleasant part, and thus thou wouldst be
immersed in the same chain of actions wherein they
were. For regard my staff" as it begins to swing. It is
not I that malie the movement that is imparted to it ;
that movement lay stored up in my arm, and when I
struck the staff with my arm it was as if I had let
another staff fall which in its falling gave up its move-
ment to the one I held in my hand."
"Where, then, does the movement go to when the
staff ceases to swing," asked the king.
" It goes to the finer particles of the air, and passes on
and on. There is an endless chain. It is as if there were
numberless staffs, larger and smaller, and when one falls
it either raises itself or passes on its rising to another or
to others. There is an endless chain of movement to
and fro, and as one ceases another comes. But, O king,
I wish to take thee behind this long chain and to place
thee where thou mayest not say, I will do this or that;
but where thou canst say. This whole chain of movement
shall be or shall not. For as thou regardest this staff
swinging thou seest that it moves as much up as it does
down, as much to right as to left. And if the move-
ments which it goes through came together it would be
at rest. Its motion is but stillness separated into equal
and opposite motions, And in what thou callest rest
there are vast movements. It shall be thine, O king,
to strike nothingness asunder and make things be. Nay,
O king, I have not given thee these beings in the valley
for thee to move by outward deeds, but I have given
them to thee such that thou canst strike their apathy
asunder and let them live. And know, O king, that
even as those beings are whom thou hast found, so are
all things in the valley down to the smallest. The
smallest particle there is in the valley lies, unless it
were for me, without motion. Each particle has the
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The Persian King-. 43
power of feeling pain and of feeling pleasure, but by the
law of the valley these are equal. Hence of itself no
particle moves. But I make it move, and all things in
the valley sooner or later move back to whence they
came. The streams which gather far off in the valley I
lead along to where they fail into the depths between
us. There they shiver themselves into the smallest frag-
ments,and each fragment I cause to return whence it first
came. And, O king, in all this movement, since it ends
where it began, there is no more pleasure than pain. It
is but the apathy of rest broken asunder. But the par-
ticles will not go through this round of themselves. I
bear the pain to make them go through, each one the
round I appoint it,"
" How then," exclaimed the king, thinking of the pain
he had felt in directing the movements of the children,
"canst thou bear all this pain ?"
" It is not much," answered the old man ; " and were
it more I would willingly bear it for thee. For think of
a particle which has made the whole round of which I
spoke to you — it will make this journey if on the whole
there is the slightest gain of pleasure over pain ; and
thus, although for each particle in its movement at every
moment I bear the difference of pain, the pain for each
particle is so minute that the whole course of natural
movements in the valley weighs upon me but little.
And behold all lies ready for thee, O king. I have
done all that I can do. I can perfect each natural pro-
cess, each quality of the ground, each plant and herb I
make, up to the beings whom thou hast found. They
are my last work, and into your hands I give them."
And when he had said this, the old man let drop his
staff, and placing both hands to his breast he seemed
to draw something therefrom, and with both hands to
fling it to the king-
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44 The Persian King.
For some moments' space the king could distinguish
nothing, but soon he became aware of a luminousness
over the mid ravine. Something palely bright was
floating towards him. As the brightness came nearer
he saw that it was a centre wherein innumerable bright
rays met, and from which innumerable bright rays went
forth in every direction.
" Take that," the old man cried, " The rays go forth
unto everything in the valley. They pass through
everything unto everything. Through them thou canst
touch whatsoever thou wilt."
The king took the rays and placed them on his
breast ; thence they went forth, and through them he
touched and knew every part of the valley. And think-
ing of the hut where the children lay, the king perceived
through the rays that went thither that the walls were
tottering, and like to fall on the children. And through
his rays he knew that the children perceived this in a
dull kind of way ; but since in their life there was no
more pleasure than pain, they did not feel it more
pleasant to rise up and move than to be still and be
buried.
But the king through the rays, as before through the
reeds, took the pain of moving, and the children rose
and came out of the hut ; and soon they were with the
king, running and bounding as never children leapt
and ran, with ecstasy of movement and unlimited
exuberance of spirit. But as they leapt and ran the
king felt an increasing pain in all his limbs. Still he
liked to see them in their full and joyous activity, and
he wished them to cast off that dull apathy in which
they lay. So all through the night he roamed about
with them thinking of all the wildest things for them to
do, and leading them through dance and play, every
movement and activity he could think of.
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The Persian Kmg, 45
At length the rising sun began to warm the air, and
the king, exhausted with pain, left off bearing it for
them.
After a few languid movements the children sank
down on a comfortable bank into a state of absolute
torpor. The king looked at them ; it seemed incon-
ceivable that they could be the same children who had
been running about so merrily a few moments ago.
Thus far he had received no advantage from the rays
the old man had given him, except that he could touch
the childi'en more easily.
He turned wearily and looked around. His horse
stood there. But instead of whinnying and running up
to greet him, the faithful animal stood still,looking across
the ravine.
" Perchance without my burden, and with the strength
these rays may impart," thought the king, " he might
manage the leap."
The horse was standing opposite the remains of the
natural bridge over which the two had so rashly crossed
the day before. The king touched the horse with his
rays. As with a sudden thrust of the spur, the noble
animal rushed forward and leapt madly from the frag-
ments of the arch. His fore feet gained the opposite
brink, and with a terrible struggle he raised himself on
the firm ground. Then he stood still. With a crash
the remaining fragments of the bridge fell into the gulf,
leaving the vast gap unnarrowed at any part. The
horse stood looking over the ravine. But though the
king called him by name, the faithful creature who used
to come to him at the slightest whisper paid no heed.
In a few moments he galloped off along the track the
courtiers had pursued.
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46 The Persian King.
CHAPTER III.
The king being left thus with the children, applied
himself to thought. He directed his rays to one of
the children and caused it to stand up, and, following
the counsel of the old man, he thought of an action.
The action he thought of was that of walking, and he
separated it into two acts ; the one act moving the
right foot, the other act moving the left foot. And he
separated the apathy in which the child was into pleasure
and pain ; pleasure connected with the act of moving
the right foot, pain connected with the act of moving
the left foot. Immediately the child moved forward its
right foot, but the left foot remained motionless. The
child had taken the pleasure, but the pain was left ; or,
since the king had connected the pleasure and pain with
two acts, it may be said, had done the pleasant act and
left the painful act undone.
After waiting some time to see if the child would
move, the king took the pain of moving the left foot ;
instantly the child moved it, and as soon as it had come
to the ground again it moved the right foot, which was
the pleasant act. But then it stopped. And by no
amount of taking pains in the matter of the left foot
could the king get the child into the routine of walking.
As soon as he ceased to take the pain of moving the
left foot, the child remained with the right foot forward.
At last he removed his attention from the movement of
the child, and it sunk back again torpor.
The rest of the day the king spent in reflection, and
in making experiments with the children. But he did
not succeed any better. Whatever action he thought
of they went through the pleasant act, but made no sign
of going through the painful act
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The Persian King. 47
When darkness came the king perceived the faint
luminousness of his rays : unless he had known of thetn
he would hardly have perceived it.
And now he tried a new experiment. He took one
of the rays, and, detaching it from the rest, he put it
upon the body of one of the children, going out from its
body and returning again to its body, so that it went
forth from the child and returned to the child again.
He then caused the child to stand up, and again tried
it with the action of walking. His idea was this : the
child required a power of bearing its own pain in order
to go through a painful act, and as the rays enabled
him to bear their pain, the ray proceeding from the
child and coming back to it might enable it to bear its
own pain. And now he separated the apathy into
pleasure and pain as before. The child moved the
right foot, and then when it had moved it, he saw that
it actually began to move the left foot. But it did not
move it a complete step, and after the next movement
of the right foot the left foot did not stir.
Again and again the king tried the children, but his
attempts came to nothing. One halting step of the
left foot he could get them to go through, but no
more.
He spent many hours. Suddenly the cause of his
failure flashed upon him. "Of course," he said to him-
self, "they don't move, for I have forgotten to take part
of the pain. If they went on moving their left feet they
would have no balance of pleasure."
And he tried one of them again. The child moved
the right foot, then began to move the left foot. The
king now by means of his rays took part of the pain of
the movement of the left foot, and the child completed
the step with it. Then of course it moved the right
foot, for that was pleasant, and again the king took part
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48 The Persian King.
of the pain of moving the left foot, and the child com-
pleted its second step. It walked.
The difficulty was surmounted. Soon both the chil-
dren were moving hither and thither like shifting
shadows in the night, and the king felt just a shade of
pain.
The children would come up to him and talk with
him, if he took the difference of pain which made it
pleasant for them to do so. But they had no idea of
his action on them, for by his taking the difference of
pain they found an action pleasant, and felt a motive
in themselves to do it, which they did not in the least
connect with the being outside themselves to whom they
spoke. They looked on him as some one more power-
ful than themselves, and friendly to them.
As soon as he was assured of the practical success of
his plans, the king let the children relapse into their
apathy while he thought. He conceived the design of
forming with these children a state such as he had
known on earth — a state with all the business and affairs
of a kingdom, such as he had directed before. The
vision of the palace which the old man had shown him
rose up. He saw in imagination the fertile fields, with
the roads stretching between them ; he saw all the
varied life of a great state. Accordingly from this time
he was continually directing their existence, developing
their powers, and learning how to guide them. And
just as on first learning to read whole words are learnt
which are afterwards split up into letters by the combi-
nations of which other words are formed ; so at first
he thought of actions of a complicated nature, such as
walking, and associated the moments of pleasure and
pain with the acts of which such actions were composed.
But afterwards he came to regard the simpler actions by
the combination of many of which the beings were made
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The Persian King, 49
to walk, and with the separate acts of these simple
actions he associated pleasure and pain.
And at first the beings were conscious of these simple
acts and nothing else, but in order that they might carry
out more complicated actions, he developed the dim ap-
prehension which they had, and led it on to the conscious-
ness of more complicated actions. The simplest actions
became instinctive to these beings, and they went
through them without knowing why. But if at any
time the Icing ceased to take the difference of pain, these
actions, seemingly automatic as they were, ceased.
At certain intervals the king found his plans incon-
venienced. Every now and then the beings went off into
a state of apathy. Enough pain was borne for them to
make it just worth their while to go through the actions
of each routine. But any additional complication or
hindrance unforeseen by the king was too much for
them, and they sank under it. To remedy this he took in
every action a slight portion of pain more than he had
done at first. Thus he expended a certain portion of
pain-bearing power to give stability to the routines.
And the margin of pleasure over pain thus added was
felt by the beings as a sort of diffused pleasure in
existence, which made them cling to life.
Now in guiding these beings towards the end he
wished to obtain, the king had to deal with living moving
beings, and beings whose state was continually changing,
And this led him to adopt as the type of the activity of
these beings not a single action, but a succession of
actions of the same kind, coming the one after the other.
Thus a being having been giver] a certain activity, it
continued going on in a uniform manner until the king
wished to alter it.
Again it was important to keep the beings together,
to prevent their being lost in the remote parts of the
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go The Persian King.
valley, and consequently the king tooK, other things
being equal, a certain amount of the pain of motion
towards the centre, and took none of the pain in any
movement away from the centre of the valley. Thus
the inhabitants had a tendency to come towards the
centre, for there was a balance of pleasure in doing so,
and thus they were continually presenting themselves
to his notice, and not getting lost.
Of course, if- there was any reason why he wanted
them away from the centre, the king ceased his bearing
of the pain of motion towards the centre, and then they
were under the other tendency solely, which he imparted
to them, in virtue of his bearing pain in another respect.
And in everything that he did the king had regard to
the circumstances in which the beings were placed, and
the objects which he wanted to obtain. He did not spare
any of his pain-bearing power to give them pleasure
purely as a feeling, but always united the pleasure he ob-
tained for them by his suffering with some external work.
And as time went on and the number of the in-
habitants increased, he introduced greater order and
regularity into the numberless activities which he con-
ceived for them. The activities formed regular routines,
conditioned by the surroundings of the being and the
routines of those around it. A routine did not suddenly
cease without compensation ; but if the king wished it
to stop he let another activity spring up at once in
place of it, so that there was no derangement. The
beings gradually became more intelligent, so that they
could be entrusted with more difficult routines, and
carried them out successfully, the king, of course, always
taking the difference of pain necessary to make it worth
their while. And they even became able to carry out
single activities on a large scale, involving the co-opera-
tion of many single routines. For they had a sense of
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The Persian King. 51
analogy, and observing some activity which the king
had led them through on a small scale, and in which
they had found a balance of pleasure, they were ready
to try a similar one on a larger scale.
There was one feature springing from the advanced
intelligence of the inhabitants which it is worth while to
mention. Many of the possible activities which the beings
could go through, instead of consisting of a pleasurable
part first and a less painful part afterwards, consisted of
a painful part first and a pleasurable part afterwards.
This might happen by the particular arrangement of the
acts of which the compounded activity consisted, the
acts having already moments of pain or pleasure affixed
to them, and happening to occur in such dispositions
that the first part of the activity was painful, the next
part pleasurable.
Now when the intelligence of the inhabitants was
developed, the king, by leading them to think of such
an activity, could induce them to go through with it.
For the idea of the pleasure which would accompany
the second part of the activity lightened the pain of
the first. And this, combined with the portion of the
pain which the king bore, almost counterbalanced the
pain connected with the first part of the activity. Thus
the beings were enabled to go through the painful part
of the activity. But when they came to the second part
of the activity the creatures were much disappointed. For
by the law of the valley pleasure and pain were equal
(except for the small part which the king bore). Now the
pleasures of expectation had been so great that when the
time camefor the act usually associated in their minds with
pleasure, the pleasure due had most of it been used up.
From this circumstance a saying arose amongst the
inhabitants which was somewhat exaggerated, but which
had a kernel of truth in what has just been described.
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52 The Persian King.
The saying was that " The pleasure for which a labour
has been undertaken flies away as soon as the labour
has been finished, and nothing is left but to begin a new
labour." And, again, another saying : " The enjoyment
of a thing lies in its anticipation, not in its possession,"
All this which has been so briefly described had in
reality taken a long time. And now fields were culti-
vated, better houses were built. The inhabitants of the
valley had increased greatly in number, and were divided
up into several tribes, inhabiting different parts of the
valley. But the most favoured position was the centre,
and for the possession of the centre there were con-
tentions and struggles. There the king's activity in
bearing was greatest, and the life was most developed.
All around the outskirts of the valley dwelt the ruder
and less advanced people, who were called barbarians
and savages bv those nearer the centre.
CHAPTER IV.
Now when the king saw the inhabitants becoming more
like the human beings he had known, he felt that he
was solitary, and he desired to have some intercourse
with them. But when he appeared amongst them they
recognized him at once as some one more powerful than
themselves, and were afraid of him. In their alarm they
tried to lay hands on him. When he, to prevent their
attacks, withdrew his continued bearing the difference of
pain in their actions, those who were attacking him
sank into apathy and became as the children whom he
had first found.
And a horrible report sprang up amongst the inhabi-
tants of a terrible being whu came amongst them, and
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The Persian King. 53
who struck all who looked on him with torpor and
death, So the king ceased to walk amongst them.
Still it was long since he had heard the sound of a voice
speaking to him, and he wished for a companion. He
sought again the old man, and standing at the edge of
the chasm he called upon him.
And the old man appeared. "Art thou weary, O
king, of thy task ? "
" Nay," replied the king ; " but I wish to make myself
known to the inhabitants that I may speak with them
and they with me."
And the old man counselled him to give some of his
rays to one amongst the beings, for then this being
having these rays and the power of bearing pain for
another other than himself, would be like the king, and
being like him would understand him.
Now the king sought over the whole of the valley,
and of all the inhabitants he found one most perfect in
form and in mind. He was the son of a king, and
destined to reign in his turn over a numerous people.
And the king gave him some of his rays, straight rays
going forth from the prince to others.
And immediately the prince awoke as it were from a
dream. And he comprehended existence, and saw that
in reality the pain and the pleasure were equal. And
when he had seen this, and knew the power of the rays,
and how by bearing pain he could make others pass
through pleasure and pain, and call those sleeping into
activity ; when the prince knew this, he cried out :
" One thing succeeds another in the valley ; pain
follows pleasure, and pleasure follows pain. But the
cause of all being is in bearing pain. Wherefore," he
cried, " let us seek an end to this show. Let us pray to
be delivered, that at last, pain ceasing, we may pass into
nothingness."
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54 The Persian King.
Thus the prince, apprehending the cause of existence,
felt that it was pain, and dimly comprehending how the
king was bearing pain, and himself feeling the strenu-
ousness of the effort of using the rays for which the
frame of the inhabitants was unstrung, longed that
existence itself might cease.
Yet all his life his deeds were noble, and he passed
from tribe to tribe, bearing the burdens and calling forth
the sleeping to activity.
CHAPTER V.
It is now the place in which to give a clear account of
the king's activity, and explain how he maintained the
varied life of the valley.
And the best plan is to take a typical instance, and to
adopt the Arabic method of description. By the Arabic
method of description Is meant the same method which
the Arabs used for the description of numerical quantities.
For instance, in the Arabic notation, if we are asked the
number of days in the year, we answer first 300, which
is a false answer, but gives the nearest approximation
in hundreds ; then we say sixty, which is a correction ;
last of all we say five, which makes the answer a correct
one, namely, 365. In this simple case the description is
given so quickly that we are hardly conscious of the
nature of the system employed. But the same method
when applied to more difficult subjects presents the
following characteristics. Firstly, a certain statement is
made about the subject to be described, and is impressed
upon the reader as if it were true. Then, when that
has been grasped, another statement is made, generally
somewhat contradictory, and the first notion formed
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The Persian King. 55
nas to be corrected. But these two statements taken
together are given as truth. Then when this idea has
been formed in the mind of the reader, another state-
ment is made which must hkewise be received as a
correction, and so on, until by successive statements
and contradictions, or corrections, the idea produced
corresponds to the facts, as the describer knows them.
Thus the activity of the king will be here described
by a series of statements, and the truth will be obtained
by the whole of the statements and the corrections
which they successively bring in.
When the king wished to start a being on the train
of activity he divided its apathy into pleasure and pain.
The pleasure be connected with one act which we will
call A. The pain he associated with another act which
we will call B.
These two " acts," A and B, which together form what
ive call an " action," were of such a nature that the
doing of A first and then of B was a process used in the
organization of the life in the valley.
Thus the act A may be represented by moving the
right foot, B by moving the left foot, then AB will be
the action of taking a step. This however is but a
superficial illustration, for the acts which we represent
by A and B were fundamental acts, of which great
numbers were combined together in any single outward
act which could be observed or described.
Suppose for the present that there is only one creature
in the valley. The king separates his apathy with
regard to the action AB. Let us say he separates his
apathy into looo pleasure and looo pain. Of the
pleasure he lets the being experience the whole, of the
pain he bears an amount which we will represent by 2,
Thus the being has 1000 pleasure and 998 of pain, and
the aclion is completed. His sensation Is measured by
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56 The Persian King,
the number lOOO in the first act, and by 998 in the
second act.
But the king did not choose to malce the fundamental
actions of this limited and finishing kind, As the type
of the fundamental activity, he chose an action, and
made the being go through it again and again. Thus
the being would go through the act A, then the act B.
When the action AB was complete it would go through
an act of the kind A again, then through an act of the
kind B. Thus the creature would be engaged in a routine
of this kind, AB, AB, AB, and so on.
And if the creature had been alone, and this had been
the sole activity in which it was concerned, the king
would have gone on bearing 2 of pain in each of these
actions. The king would have kept the routine going
on steadily, the creature bearing 1000 of pleasure in
each A, and 998 of pain in each B.
At this point it may be asked that an example should
be given of one of these elementary routines which the
king set going. And this seems a reasonable request,
and yet it is somewhat too peremptory. For in the
world we may know of what nature the movements of
the atoms are without being able to say exactly what
the motion of any one is. In such a case a type is the
only possible presentation. Again, take the example
of a crystal. We know that a crystal has a definite law
of shape, and however much we divide it we find that
its parts present the same conformation. We cannot
isolate the ultimate crystalline elements, but we infer
that they must be such as to produce the crystal by
their combination.
Now life on the valley was such in its main features
as would be produced by a combination of routines of
the Itind explained. There were changes and abrupt
transitions, but the general and prevailing plan of life
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The Persian King. 57
was that of a routine of alternating acts of a pleasurable
and a painful kind. It was just such as would be built
up out of elementary routines, on which the king could
count, and which, unless he modified their combinations,
tended to produce rhythmic processes of a larger kind.
And even the changes and abruptnesses had a recurrent
nature about them, for if any routine in the valley
altered suddenly, it was found that there were cases oi
other routines altering in like manner, when the condi-
tions under which they came were similar. Thus the
fundamental type of the action which the king instituted
was that of a routine AB, AB, as described above. But
there were two circumstances which caused a variation,
so that this simple routine was modified.
Firstly, there was not one being only but many.
Secondly, the king wished to have some of his pain-
bearing power set free from time to time. He did not
wish to have to be continually spending it all In main-
taining the routines he had started at first, and those
immediately connected with them.
When he first began to organize the life of the beings
he did not consciously keep back any of his pain-bearing
power, but threw it all in the activities which he started.
Still from time to time he wished to start new activities
quite unconnected with the old, and for this reason he
withdrew some of his pain-bearing power, as will be
shown afterwards.
There were many beings. The king chose that the
type of activity in each should be a routine. In that
way he could calculate on the activity, and hold it in
his mind as a settled process on whose operation he
could count. But as the routines of the beings proceeded
they came into contact with one another, and made, even
by their simple co-existence, something different from
what a routine by itself was. They interwove
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58 The Persian King.
ways. Then, in order to take advantage of the com-
binations of these routines, or to modify them, it was
necessary to set going other routines.
In order to be able to originate these connected
routines the king adopted the following plan.
In the first action AB he separated the creatures'
apathy into looo pleasure and looo pain, bearing 2 of the
pain himself The creature thus went through 1000 oi
pleasure and 998 of pain. In the next action AB he did
not separate the beings' apathy up into so much pleasure
and pain. He separated it up into 980 pleasure and 980
pain, that is, each moment of feeling was 20 less in sensa-
tion than the moments of feeling were in the first action.
Now it is obvious that if the bearing 2 of pain will
make it worth while for a being to go through 1000
pleasure and 99S pain, then the bearing on the king's
part of i of pain would make it worth while for the
being to %o through 500 pleasure and 499 of pain.
And a similar relation would hold for different amounts
of pleasure and pain. Thus clearly for the being to go
through 980 of pleasure and the corresponding amount
of pain, it would not be necessary for the king to bear
so much as when the being went through 1000 of
pleasure and the corresponding amount of pain.
Consequently when the king divided the beings'
apathy into 9S0 pleasure and 980 pain, it would not be
necessary for hlra to bear 2 of pain to make it worth
the beings' while to go through the action. The king
would not bear so much as 2 of pain, and thus he
would have some of his pain-bearing power set free.
He would have exactly as much as would enable him to
make it worth a being's while to go through an action
with the moments of 20 of pleasure and 20 of pain.
And this — with a correction which will come later—
is what the king did. He employed the pain-bearing
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Tlie Persian King. 59
power thus set free in starting other routines. Thus
in the routine AB, AB, AB there would be first of all
the action AB. Then along with the second action
AB, the king (with the pain-bearing power set free)
started an action CD — the beginning of a routine CD,
CD, CD. Thus as the first routine went on and came
into connection with other routines, new and supple-
mentary routines sprang up which regulated and took
advantage of the combinations of the old routines.
The amount of the moments of pleasure in the routine
CD, was (with a slight correction explained below)
measured in sensation, equal to 20, Thus the moment of
pleasure in the first A being lOOO, the moment of pleasure
in the second A was 980, the moment of pleasure in
the first C was 20 (subject to the correction spoken of).
Thus the total amount of sensation in the second A and
and the associated act C, taken together (but for a small
correction) was equal to the sensation in the first A.
Hence the three points which were characteristic of the
activity of the beings in the valley are obvious enough.
1. There is as fundamental type a routine AB, AB.
AB, the sensation involved in which goes on diminishing.
2. There are routines CD, CD, &c., connected with
AB, AB, in which the sensation which disappears in the
routine AB, AB seems to reappear.
3. In the action AB itself there is a disappearance of
sensation. The sensation connected with A is 1000, that
connected with B is 998. Thus 2 of sensation seems
to have disappeared. This 2 of sensation is of course
the pain which the king bore, and which was the means
whereby the creature was induced to go through the
action at all. But looked at from the point of view of
sensation, it seems like a diminution of amount. This
diminution of amount, owing to the correction spoken of
above, was to be found regularly all through the routine.
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6o The Persian King.
And now, with the exception of the final correction,
the theory of the king's activity is complete. There are
certain mathematical difficulties which render an exhaus-
tive account somewhat obscure in expression. When
we take a general survey of a theory we want to see
roughly how it all hangs together ; but if we mean to
adopt it, the exactitude of the numerical relations
becomes a matter of vital importance.
It must be added that the numbers taken above were
taken simply for purposes of illustration. In reality the
pain born by the king was less in proportion.
The exhaustive account which follows deals with small
numerical quantities. It had better be omitted for the
present, and turned to later on for reference.
EXHAUSTIVE ACCOUNT.
We keep for the time being to the numbers used
above. When the king had enough pain-bearing power
set free in the second action of the routine AB, AB to
start another routine CD, of 30 pleasure 20 pain, he did
not use it all. He only used enough of it to set a routine
going the moments of pleasure and pain in which were
16 in sensation. The routine CD was made up of acts
with 16 of pleasure and 1(5 of pain.
The sensation in the first A was locxj, in the first B it
was 998, giving a disappearance of 2. In the second
A it was 980, and in C, which starts concurrently with
the second A, it was not 20 as might have been ex-
pected, but 16, giving a loss of 4. The second A is less
than the first A by 20. Searching for that 20 we find
16 in C. But there has been a disappearance of 4.
Looking now at the successive acts in the series we
have in A 1000 sensation, in B 99S sensation, in A and
C together 996 sensation.
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The Persian King.
6i
The cause of the loss between A and B has already
been explained. That between B and the second A with
C remains to be accounted for.
It has been already said that the king withdrew some
of his pain-bearing power from the routine AB and all
routines connected with it, thus he was enabled to start
activities altogether unconnected with those which he
had originated, and was with regard to the products of
his own activity as he had been at iirst, with regard to
the beings in the valley before he started them on the
path of life. And it was in consequence of his with-
drawal of his pain-bearing power that the amount of
sensation in C was not 20 but was less. This loss of
4 of sensation to the being corresponded to a setting
free of a certain portion of pain-bearing power on the
part of the king. And thus as the process went on, a por-
tion of his power was continually being returned to him.
In the table below the first line of figures contains the
amount of sensation in the actions AB, AB. The
second line of figures contains the amount of sensation
in the actions CD, CD. The third line of figures relates
to another connected routine EF, EF, which originates
in a manner similar to CD. The fourth line of figures
represents the amount of pain borne by the king, the fifth
line represents his pain-bearing power set free.
(l) 1000 998
A B
980 978,Sfc
A B
960 958i»Si
A B
w
16 iST"«r
C D
iSiWsV iSiVAVA
C D
(3)
■6 ISA%
E F
(4) 2
i-fA'i
lAV, + i.8!8».
(5)
TWff
jouo "r TOtrflSoo
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62 The Persian King.
If the total amount of sensation which is experienced
by the being in the original routine. and the connected
routines in the consecutive stages be summed up, it will
be found to be
1000, 998, 996, 994TMTr. 99irAV
and so on.
Finally, the proportion of pain borne by the king was
so small compared with the sensation experienced by
the being, that A and B were apparently equal in sensa-
tion. Thus the sensation in the second A and in C
together becomes apparently equal to that in B. And
instead of the sensation diminishing quickly as shown
above, it was only after a great many acts of the primary
and connected routines had been gone through that any
diminution of sensation in the form which the being
could experience it was to be detected Thus, as before
stated, there was :
1. A routine of continually diminishing sensation.
2. Connected routines the sensation in which was ap-
parently equal to that lost in A,
3. There was a continuous disappearance of sensation
from the experience of the beings accompanying every
step of the routine. The sensation which they could
experience was less in every subsequent step and con-
nected steps than in any one in which it was measured.
CHAPTER VI.
The history of the events which took place in the valley
in their due order and importance must be sought else-
where. But let us return and look at the condition of
the valley and its inhabitants. Let us see what has
become of them after a great lapse of time.
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I'he Persian King. 63
It is a fair, a beautiful land. The greater part of it is
cultivated. There is no war — even to the extremest
confines of the valley there is peace. Passing from the
remote confines where still dwell a barbarous race, we
come, as we approach the metropolis, amongst a more
and more polite and refined people. In the metropolis
itself the buildings are numerous and of great size. The
palace which the king saw rise under the old man's music
is there, but another ruler dwells in it. Near the palace
are two vast buildings standing on each side of a wide
open court. There is no other building near save one
between them, a comparatively small edifice of brick.
These buildings are the assembly halls of the two most
important councils in the valley. In the one on the left-
hand side of the palace met the most distinguished
of the inhabitants who from a special inclination or
fitness were entrusted with the regulations about the
pleasure and pain of the inhabitants. They framed
the rules according to which each inhabitant must
conform in his pursuit of pleasure, and they made the
regulations whereby the whole body of inhabitants were
supposed to gain an increase in pleasure and to avoid
pain.
In the building on the right hand of the palace met
those of the inhabitants who had studied the nature ot
feeling most deeply, and who from temperament or for
other reasons had in their course of study not paid so
much attention to whether feelings were painful or
pleasurable, but who had studied their amount and
regularity of their recurrence. They were the thinkers
from whom all the practical inhabitants derived their
rules of business. They devised the means and manner
of putting into execution what was decided on in the
other assembly. They did not often propose any positive
enactment themselves, but were always able to show
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64 1'he Persian King.
how the proposals of the other council could be carried
into effect.
Their power was derived in this manner. The king
had connected the feelings of pleasure and pain with
certain acts, and liad given each being a routine. Now
as he himself made ^use of this routine and combined
the routines of different ^dividuals to bring about the
results he desired, so also did the ruleVs of the valley.
The routines of the individuals were studied and classi-
fied, and if any work was required to be done, those
individuals whose routines were appropriate were selected
and brought to the required spot. Now to effect this a
careful study of the different routines was necessary,
and also a knowledge of what stage they were at. For
it would be no use bringing an individual whose routine
was almost at an end to a work which was just begin-
ning. Hence the most delicate instruments and pro-
cesses had been devfsed for measuring the amount of
feeling experienced by any individual, whether of plea-
sure or of pain, and a careful classification had been
made of all routines.
But it is best to study the constitution of the state in
a regular order, and the questions of pleasure and pain
considered as such were esteemed the most important.
The inhabitants knew that they sought pleasure and
avoided pain, and the great object was to make their life
more pleasurable. Two means were adopted, the banish-
ing of the causes of pain, and the obtaining causes of
pleasure.
By causes of pain and pleasure they meant those
objects with which the king had associated the feelings
of pleasure and pain in the equal and opposite moments
into which he had divided their apathy.
But in this respect they were in error to a certain
extent, for it was not so much in respect to things as in
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The Persian King. 65
respect to actions that the king separated their apathy
into pleasure and pain. For instance, there was a peculiar
species of shell which was found in many parts of the
valley, covered with strange and involved lines and
marks. Now the king had struck the apathy of the
inhabitants into two moments with regard to this shell,
one of pain connected with tracing out the twistings
and interweavings of the hues on the shell, one of pleasure
in contemplating the shell when the twistings and inter-
weavings had been deciphered. Now it was the custom
of the inhabitants to call the shell in its undeciphered
condition a painful object, in its deciphered condition a
pleasant object. And whoevercould, would get as many
deciphered shells as possible and experience the wave
of pleasure in looking at them.
Now in the earlier ages those who deciphered the
shells, or did work of a similar kind, had been forced to
do it ; they were a kind of slaves dependent on the will
of their masters, who took away all the pleasures of
their life. But in these earlier ages a great danger arose,
for when all the pleasure was taken away by their
masters, great masses of these slaves sank into apathy,
and it seemed as if the valley was sinking into deadness.
Now this was a great terror with the inhabitants whose
life was pleasurable, and at length they determined that
there should not be any more of these slaves. But each
of the inhabitants when he worked for another had to
have it made worth his while.
In this way a great diminution took place in the
pleasure-giving power of the so-called pleasurable things.
For if a man had had it made worth his while to decipher
one of these shells, he had had a great deal or nearly all
of the pain he spent in doing it counterbalanced by the
pleasure given him to induce him to do it. Hence when
the shell was handed over there was not much to enjoy
5
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66 The Persian King.
in it ; for by the law of the valley the pleasure and the
pain were equal, and the decipherer, not having gone
through so much pain on the whole, there was but little
pleasure to be got.
In fact, at this time the fashion of filling- the houses of
the more powerful of the inhabitants with the so-called
pleasurable things had somewhat gone out, and it had
passed into a proverb, "It is better to decipher your
own shells."
Now it may be considered strange how it was that
some of the inhabitants could get other of the inha-
bitants to decipher the shells for them at all, or, at any
rate, to decipher them so that there was any balance of
pleasure left with the shells at all. But this power on
the part of some of the inhabitants depended on the
general action of the king. For by bearing the differ-
ence of pain in innumerable respects in the life of each
he made life a pleasure (on the whole) to each, and they
strove each to preserve their own life which was a source
of pleasure. And some of the more powerful inhabi-
tants had the power of denying to the rest, unless they
laboured for them, the means of continuing to exist.
Consequently it was possible for things to be obtained
by the more powerful which had a balance of pleasure in
them.
But the authorities who had studied the life of the
valley in relation to pleasure and pain, saw that there was
a danger in this relation of the more powerful to the less
powerful. For as the numbers of the inhabitants increased
the power grew more and more concentrated in the hands
of a few, and there was a tendency for the inhabitants
in general to be compelled more and more to go through
the painful part of actions, leaving the pleasurable parts
for the more powerful. And every now and then, before
the council of wise men regulated the matter, great masses
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The Persian King. 67
of the inhabitants passed off in a state of apathy. So they
had many laws to restrict the action of the more power-
ful of the inhabitants ; and, indeed, the more powerful
of the inhabitants were ready to frame these laws them-
ijelves, and were willing to obey them, for they did not
like to see portions of the inhabitants going off into a
state of apathy.
But not only in this respect, but also in every other,
the wise men regulated the affairs of the valley so as to
make life more pleasurable. They had severe laws
against any one who deprived another of pleasure with-
out his consent, by violence or deceit. They did all
they could to ward olf a state of apathy. But in one
respect beyond all others they were full of care and
precaution. And this was in guarding against such
sources of trouble, anxiety, and pain which could be
removed from the community as a whole. Anything
tending to lower the standard of comfort as a whole
was carefully removed. Irregularities were reduced as
much as possible ; and, in one respect, a great step had
been taken. It had not been carried in the council of
wise men without great opposition, but it had at length
been passed into law.
Any child born in the valley which had any incurable
disease, or any gross deformity, or which by its delicacy
seemed likely to cause more pain than pleasure in the
valley, was at once put out of existence. The gain to
the inhabitants of the valley of this was in their eyes
immense ; for their sight was offended by no deformities,
and the painful ofiices of attending to the sick had
undergone a considerable diminution since this edict
had been passed into law.
The important duty of deciding on the claims of every
infant that was born to a painless extinction was con-
fined to a band of inspectors, who stayed for a short
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68 The Persian King.
time only in any one part of the valley, lest they should
become biassed by personal acquaintance with the indi-
viduals for whose children their offices were called into
requisition
CHAPTER VII.
Passing on to the other great building, wnere the other
wise men meet, it is right to describe what may be
called the intellectual development — as the foregoing
was the moral development of the valley. The course
which the opinions of the thinkers in the valley had
gone through was the following.
At first they had no clear ideas, but all manner of
mere opinions and fancies. At last they apprehended
certain general tendencies — such as that towards the
centre of the valley, and they explained many inclina-
tions which had before been puzzling to them by this.
And stimulated by this great discovery they examined
more and more closely. And they found many special
tendencies like that towards the centre of the valley,
which the king had called into existence, and which he
let go on as a general rule, unless he wished the con-
trary. And they also succeeded in nearly isolating the
simplest routines, and so practically could observe the
type of the king's plan.
They saw that one act A was succeeded by another
act B. And not taking into account that one was plea-
sant the other painful, they measured the amount of
sensation present in the two acts. And then they took
the next pair of acts, namely, A and B over again, and
measured the amount of sensation present in them ; and
they found that the amount of sensation gradually
diminished. And at first they thought that sensation
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The Persian King, 69
gradually came to a stop ; but afterwards they noticed
that other actions were started in the neighbourhood of
tlie routine A B as that diminished in point of feeling.
Now, of course, these other actions were started by
the king with the pain-bearing power set free from the
routine A B,as above described. Rut not knowing any-
thing about this action on the part of the king, or about
the king at all, the conclusion arrived at was this : That
sensation transmits itself If it does not continue in
the routine A B, that part which does not continue
passes on to the other routines, C D, E F, &c.
Then they measured very carefully; and they found,
as nearly as they could measure, the routines which
sprang up as the routine A B died away were equal in
sensation to the loss in the routine A B, A B. And from
this they concluded that the amount of sensation or
feeling ivas constant. They called it living force, and
said that it must transmit itself and, wherever it ap-
peared, be equal in its total amount to what it was at
first. But after a time, with more delicate measure-
ments and more patient thought, they found that some
of the sensation was still unaccounted for.
For consider any routine consisting of the acts A, B ;
A, B ; A, B. In order to make any pair of acts A, B
worth while, the king bore a certain amount of pain.
Referring to the numbers which we took before, if
there were 1000 of pleasure in A there would only be
998 of pain in B, Thus the sensation was not equal in
the two acts A and B. Some of the sensations had
gone, and tlie portion of sensation we are now consider-
ing — the portion by which B was less than A— had not
gone in starting other routines. This loss could not be
accounted for as they accounted for the difference in
sensation between the first action A B and the second
action, consisting of the acts A and B in the routine.
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•JO The Persian King.
There was a loss of sensation which was counter-
balanced by the gain in sensation in othev routines.
But besides this there was a furtlier loss. Some
sensation went off, not to be recovered in any routine
they knew.
Now it was the bearing on the part of the king which
produced the appearance of the passing away of sensa-
tion altogether, so that the act B was less in amount of
sensation than the act A. But the inhabitants — at least
the wise ones— were firmly convinced that sensation
could not be annihilated or lessened. So they came to
the conclusion that sensation was passing off into a form
from which it never reappeared, so that it could affect
them. They conceived it still to exist, but to be irre-
coverably gone from the life of the inhabitants of the
valley.
Taking the numbers we have taken, and the simple
instances we have supposed, this course of reasoning
appears straightforward enough. But in reality so com-
plicated was the state of things in the valley, and the
proportion of pain which the king bore in each single
action so minute, that to have arrived at this result
implied powers of investigation of no mean order.
It is interesting to mention the names which these
investigators gave in the valley. In the performance of
the pleasant act A, they said that the being acquired
greater animation. In going through the painful act B,
they said that he passed into a position of advantage.
They used the term advantage because, having completed
the painful act B, he was ready to begin the pleasant
part of the action A over again. And in this part he
manifested more animation.
And now although acts of greater animation and
greater advantage succeeded one another, and although
the new total of the sensation in the act of a being was
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The Persian King. 71
very nearly equalled by that in a subsequent act, still there
was not — -they had to confess there was not — a com-
plete equality. Some of the sensation had certainly
gone from the sphere in which the inhabitants could feel
it
We see that this sensation which was gone was in
reality the pain-bearing of the king, which set all their
life going.
But they knew nothing of this, and formed a very
different conclusion. They said : " If some of the sensa-
tion is continually going and disappearing from the life
of the inhabitants of the valley — if this is the case,
although the sensation may not be destroyed, it is
certainly lost to us."
And then they thought : " Surely the amount of sen-
sation must be always the same ; if some of it continu-
ally goes off into a form in which we cannot feel it, that
portion which is left behind, and which we feel, must be
continually growing less."
Hence they concluded that the sensation in the valley
was gradually running down. Less and less was being
felt. After a time, which they calculated with some
show of precision, all feeling will have left the inhabi-
tants and gone off in some irrecoverable form. All the
beings of the valley will sink into apathy.
Thus coming in the course of their investigations upon
the action of the king, which was the continual cause
of all life, they apprehended it as the gradual annihila-
tion of life.
The small building between the two council halls
remains to be noticed.
Now when the king had connected pleasure and pain
with different acts to be performed by the inhabitants of
the valley, he had of necessity to let the pleasant one be
the one that came first in the order of its possible per-
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72 The Persian King.
formance. And then by the device of the curved rays
he had brought it about that the inhabitants went
through the painful act consequent on the pleasurable
one, the two together forming the complete action which
the king had designed. But this chain was not very
secure. The inhabitants had a tendency to go through
the pleasurable act and leave the painful act undone,
Now in things which necessarily concerned their life,
the king would, by repeatedly bearing the pain of the
painful act, continually set the beings going again ; for
when they had performed the pleasant act they were
landed in a state of torpor, until the pain of the painful
act had been borne by them or for them. Now if this
act of which they took the pleasant and left the painful
part undone was in the main current of their lives, the
king would over and over again, by bearing the pain,
bring those who had shirked the painful part into a
position of advantage again, so that they could begin
the routine afresh with another pleasant act, And often
when thus started again they would take to the routine,
and bear the pain in the painful act themselves. But
many, after assisting them again and again, the king
was obliged to let sink into apathy, such namely as
always left the painful part of the action undone.
Now the little building was the council hall or inves-
tigation chamber of the searchers out of new pleasures.
And by new pleasures they meant something of the
following kind. With the pleasant and painful acts
which made up the main routines of their life, it was not
safe to take the pleasant and leave the painful acts, for
that gradually led to their sinking into apathy. But
there were many routines which the king had instituted
besides the main ones. And if the pleasant part of the
action constituting these secondary routines were taken,
then there followed no tendency to lethargy in the main
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current of their lives, but they simply had a pleasure the
more. Of course the pain of the painful act had to be
borne, but they not going through with it left it for the
king to bear.
Long ago, through one of the inhabitants of the valley
with whom he had communicated, the king had sent a
message, asking the inhabitants not to take the pleasant
part of an action without the connected painful part. But
now all memory of this message was lost, and the Httle
building had been built, as a council hall or investigation
chamber for the searching out of pleasurable acts. In
it all possible novelties of action were discussed. And
the pleasant parts of them being described, exactly how
far they were pleasurable, and in what degree they were
pleasurable, the information was made public throughout
the land.
CHAPTER VIII,
Besides these two principal buildings in the metro-
polis, there were other public buildings devoted to
various purposes. And some of the most important
were colleges devoted to the education of the young
inhabitants.
Now there was in the college of applied sensations
a student who, though outwardly as proficient as the
average of his companions, was in reality the most
backward of all. He learned by a kind of rote all the
doctrines they understood, and he could explain appa-
rently how one feeling caused another. But in himself
he had no particle of understanding. He seemed de-
ficient in the sense of cause and effect which the others
had. Of this the following instance will suffice to show
the nature.
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74 Ty^^ Persian King.
The king had, in order to prevent the inhabitants
from straying too far from the metropolis, kept a
constant watchfulness over their movements, and had
uniformly taken somewhat of the pain from any effort
which they made to move towards the metropolis, and
had not taken any of the pain in efforts whose tendency
was to remove them to a distance from the metropolis.
If there was any purpose to be served in going away
from the metropolis, he took enough pain from these
movements to make it worth the beings' while to go
away from the metropolis. But when other things
were equal, it was a pleasurable thing to go towards
the metropolis. The king made this general inclination,
because if it had not been so, beings lying out of the
way of his immediate attention might have drifted
away and gone to the confines of the valley, away from
where the busy life he was calling out was manifested,
and so have been lost to others and themselves. As it
was by imparting this general pleasurableness of moving
towards the metropolis he held ail the inhabitants
together, and knew the direction in which each would
tend, unless for any special reason he had made it more
pleasurable for the person to move away from the
metropolis.
Now, as has been mentioned above, this general ten-
dency had been observed by the inhabitants ; and they
knew quite well that every individual tended towards
the metropolis, and was only prevented from coming
into it by strong local interests, or by all available posi-
tions in it or near it being already occupied. If any
situation was vacant in the metropolis, it was easily
filled up by those from the surrounding country, for
they all felt this tendency to press in.
Now, the learned men in the valley had long recog-
nized this as one of the most important laws of the
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The Persian King. 75
valley. And tne students in the college of applied sen-
sations felt this law to be true law, and anything which
followed from it they felt to be self-evident. But the
student of whom we speak had not this happy, settled
feeling with regard to this law. He could not feel as if
it were necessarily true.
One day the head of the college was talking to the
foremost students — those who had nearly finished their
course and who would take their places in the valley
shortly— and he said incidentally in the course of his
remarks, that those who were moving away from the
metropolis were as much attracted to it as those who
were moving towards it.
"Why do they move away, then?" asked the back-
ward student, who had by great diligence, after a long
time, plodded his way by force of remembering by heart
into the top class. He forgot his usual caution and his
acquired habit of only asking questions he had heard
asked before in order to refresh his memory with the
answers he had heard given before.
The professor frowned at the stupid question. " The
supposed being," he answered, " while he is attracted to
the metropolis in accordance with the general law, may
yet have some stronger inducement at the time to move
away from the metropolis. That he does move away
shows of course that his temporary inducement to move
away is stronger than his permanent attraction towards
the metropolis."
The student said that he was obliged for the explana-
tion. " But— — "
" Well ? " said the professor.
"The only reason you have for supposing that the
being is attracted towards the metropolis is that he does
move towards the metropolis. I don't see why you
should say it was pleasant for him to move towards the
metropolis when he does not do so."
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76 The Persian King.
" But we Know," said the professor.
" No," said the student, " you only suppose ; because
you find it so on a great many occasions, you suppose it
is so always. You are like a savage who attacks the
house of a civilized man. And he tries the window, the
civilized man meets him there ; so he tries the door, the
civilized man meets him there ; so he goes back to the
window, and is met there again. And he concludes
there are two men in the house; and after a time he
concludes there are as many men in the house as there
are ways by which he tries to get in."
The student had forgotten himself in speaking like
this ; and the comparison to a savage, though made
in haste and in good part as an illustration, offended
the professor, so he said :
" You do not believe that the law of attraction towards
the metropolis is universal, and affects all the inhabi-
tants ? "
■' I cannot," said the student.
"Then you shall go to a place where you will feel it,"
said the professor. " You will go to-morrow to the ex-
treme confines of the valley, and stop there until you are
of a different mind."
He said this in a superior and gentle manner. But it
was a terrible blow to the prospects of any student to
be thus exiled. And yet the professor was within his
strict legal right, and the student knew it. He had
avoided this danger all through his college course, and
now it came with crushing effect on him. For just as
long ago in the valley they had had doctrines about the
king, and had punished any one who did not feel them
as true, and who was found out, so now when all the
ideas about the king had been disproved, they had severe
regulations about the belief in the laws. The learned
class was a sect of priests, and whoever ':hreatened to
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The Persian King. 77
bring confusion and trouble by denying any of the
known laws, and to lead the ignorant people to disregard
them and deny them, was subject to severe punishments.
In the case of this student, the error did not so much
matter, because he had committed his offence in the
presence of well-instructed people, who would only smile
at his folly. But he had in his presumption insulted the
head of the college, and his punishment was universally
considered to be mild and just. And yet he was not
altogether in the wrong. For it was not as though the
king {when he wanted a being to move away from the
metropolis) took as usual a portion of his effort in going
there; and at the same time counterbalanced this by
taking a still larger portion of the pain involved in his
moving away from the metropolis. By no means. When
the king willed a man to move away from the metro-
polis, he let him start afresh, as it were, according to the
conditions which every being was subject to in the
valley — that it was just as pleasant as painful to move
in any way, and he took a portion of the pain involved
in moving away from the city.
Now the student, when he was sent away, tried ear-
nestly to see wherein he had been wrong. The place
where he was exiled was on the confines of the valley,
where a peaceable race of savages lived, engaged in
agriculture. In the quiet, monotonous life of the place
he thought over his whole course of life, but could not
obtain any different feeling. And while thus buried in
thought, he fell into the way of going about with the
savages and doing as they did. Much to his surprise,
when his preoccupation of mind passed away, He found
himself singularly at home with them. Their tastes
seemed to agree with his. And he came to the conclu-
sion that he was in reality a savage who by some mis-
take had been admitted to the college. Having formed
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78 The Persian King.
this conclusion, lie threw himself into the life around him
heartily. In course of time he won the confidence of
the rude, uncultivated people, and they talked to him
unreservedly.
Many curious traditions were handed down amongst
tliem. There were some which proceeded from the time
when the king had walked and talked with the children
he called into activity. There were others proceeding
from times when there had appeared amongst them one
to whom the king had given some of his rays, so that that
person had the power of making the pain less in actions
for others, and of giving them motives to act, and of
rousing them thus to an active state. And all these
traditions they told to the exiled student.
Now their own belief was this. They thought that
there was a power over them, and in this they recog-
nized the king ; but how it was that this power
prompted them they did not know. Yet they connected
him in some way with pleasure and pain. They thought
it pained him when they had pleasure, but not in the
way in which was really the case. They thought simply
that it was pain to him to see them taking pleasure.
They thought, moreover, that he would, if they dis-
pleased him much, take away all their pleasure and
leave them nothing but pain.
Now the student saw clearly some errors, some con-
tradictions in their belief. For instance, he knew that
beings only followed pleasure, and directly pleasure was
equalled by pain, sanlt into apathy, and then gradually
vanished away. Hence he knew there need be no ap-
prehension of the power's acting as they thought. But
the thing they said, that their taking pleasure pained
this power, struclc him. He did not approve the results
in their life, for it was in consequence very gloomily
framed, though with a good deal of unconscious cheeri-
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The Persian King. 79
ness. But he knew as a scientific fact that there was a
constant diminution of feeling ; and since he also knew
that beings in the valley did nothing except it was more
pleasant, he concluded that although pleasure and pain
might both be disappearing, still pain must be disappear-
ing to a greater extent. Now since the feeling did not
become nothing, but passed away out of the perception
of the inhabitants, it followed that it must pass to some
being. It did not disappear as feeling, but passed away
from the sensation of the inhabitants. Is there a being,
then, he asked himself — the power of whom these simple
folks tell— who bears the difference of pain, and so
makes existence pleasant to us } And is that the mean-
ing of what they say that our pleasure pains him .' Is
it just the truth read backwards— the truth, namely, that
by his taking pain we have pleasures, which they have
had handed down to them as this — that our taking
pleasure pains him.
When he had thought thus far he remembered one of
his books in which the ancient beliefs of the valley were
discussed. It happened to be one of the books which
he had brought into his exile with him, He took it down,
and in the evening set himself to search through it. And
in a footnote towards the end of the book he read ;
" The existence of a power shaping the valley for the
good of the beings in it is clearly disproved. First, by
the amount of suffering there is in the valley. Secondly,
by the fewness of the types of Ufe, and the constant
modification of one plan to secure different results —
which would be much better achieved by the use of
radically different types and means. Thirdly, by the
absence of any indication of such a power, except in the
traditions of uncultivated tribes."
When the student had read this he rose up and paced
his chamber. For he saw clearly that if it was in bear-
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8o The Perszan King.
ing part of tne pain that the power of the being lay, the
first of these arguments fell to the ground. The presence
of the pain in the valley would prove that this power
took only some of the pain and not all. As to the
second argument, all it would come to was that the
being who, bearing pain, gave existence to the inhabi-
tants, used economy in his actions — he chose to effect
his objects with the least possible expenditure of means.
Reflecting thus he went out.
Now it may be considered surprising that the king
did not communicate in some way with the student, for
by means of his rays he was in possession of all that
had gone on in his mind. But the king had found over
and over again that if he manifested himself to any one
of the inhabitants of the valley, the effect, though good
at the immediate time, was most disastrous for the fol-
lowing time. For the ends he was working towards,
and leading the inhabitants towards, were much greater
than any one of them could grasp or conceive. And the
inhabitants, as soon as they had communication with
him, at once thought they knew his final will. And
they were a set most peculiarly stiff in their notions, and
with the kind of sanction which communication with
him gave them, even the most absurd ideas if once con-
ceived took a very long time to eradicate.
So when the student went out into the open air be
saw nothing except the stars, and heard nothing except
the wind. The way was so well known to him, however,
that he walked on quickly without stumbhng in the dark-
ness. He had not gone far when he saw a kind of
luminousness. Is it the moon beginning to rise? he
thought. Rut he found he had passed the light and was
leaving it behind. He could not have passed the moon
thus. He went towards the light, and when he had
reached it, it seemed like a slender staff of light. He
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The Persian King, 8i
touched it with his hand, and although he did not feel
anything, yet he could take hold of it, and he walked
on with the slender beam in his hand.
He had not gone very far when in his walk he touched
on something lying in the path. Bending down and
touching it with his hand he found that it was the form
of a fellow creature. " Pie is overcome with fatigue ;
can I help him along ? " he thought. He rose up to
look round, and let the beam of light which he held in
his hand touch the prostrate form. " I wish he could
get up by himself," he thought. No sooner had he felt
this wish than he had a sensation of pain in his limbs,
and the figure rose up.
" I could not move," it said, " until you came, with all
my reasons to get along ; the pain was as much as the
pleasure."
" Who are you ? "
" I am a wanderer, and am trying to reach the place
where I was born ; they will help me there."
Now in the valley there was a certain set of people
called wanderers, who had proved themselves unfit for
any real work. These, if inoffensive, were allowed to
roam about subsisting on charity. The student walked
alongside this wanderer ; and every step the wanderer
made he felt a sensation of pain in his limbs. But the
two walked quickly on till they came to the dwelling he
had left so shortly before. The student led him in and
let him rest in his chamber. And then he himself left
the dwelling again, taking with him a few necessaries.
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The Persian King.
CHAPTER IX.
When he had seen the wanderer safely housed he de-
termined to go and visit a friend who had Hved in a
town not very far from the metropolis. This friend had
been his most intimate companion when he first became
a student, but being- older had finished his studies
sooner, and had left the metropolis before the student's
misfortune. In leaving his place of exile the student
rendered himself liable to punishment, and he gave up
the means of subsistence which had been provided for
him there. He was obliged to go as a wanderer, and
trust to the liberality of the people on the way.
He was hospitably received as a rule. The region was
remote from the metropolis, the inhabitants were glad to
talk with a stranger— and the wanderers were, in general,
held to have a stock of exchangeable talk and news.
But he did not speak with any one of what lay present
to his mind, till one occasion.
As he was walking along early in the day, he was
hailed by an inhabitant who looked like a well-to-do
farmer. Something in the student's appearance attracted
him, for, learning that he was on his way to a distant
town, he asked him to stay and take the tirst meal of the
day with him. This inhabitant had been a clerk em-
ployed in the council of pleasure and pain. But the
sedentary life had been too trying for him ; he had come
to live in the country on a small possession of his till he
had overcome the strain.
" Did you not find it very dull in the part you come
from .'"
" No ; I found that the people had much of interest
to tell me."
"They have singular traditions. I remember when
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The Persian King. 83
a deliberation was held in our council as to whether they
were pernicious or harmless ; it was decided that they
were harmless and little likely to spread,"
" I have talked a good deal with them since I have
lived amongst them, and have come to the conclusion
that in what they believe a great deal is true."
" Indeed ! you cannot surely believe that our pleasure
is distasteful to any being outside us."
" No ; but I go back to the old notion of which you
have heard, that there is a being who calls us into being,
and who is over us ; and I believe that this being takes
pain, and so makes life pleasurable to us. You know
that some sensation is passing away, and you know that
there must be more pain that passes away than pleasure.''
" How can I know that ? "
" We know that there is not such a very great excess
of pleasure over pain. Now if in all the course of time
that has been, the sensation that has been passing away
was pleasure, there would by this time have been left an
excess of pain, and before now we should all have sunk
into apathy. So it is either pleasure and pain mixed
which passes away, or pain alone. I conceive that it is
pain alone. These strange doctrines are true, only
curiously expressed. The being over us is continually
bearing pain and so making existence pleasant to us,
thus causing us to move and live. So the pain of our
life is that remaining pain which he does not take."
"This seems tome a very dismal doctrine. I can
imagine some poetry in the idea of a being of infinite
power, strong and- glorious, but none in the idea of a
suffering being."
"When you were a child you thought your father
could do everything ; but as you grew up and found that
he too had his difficulties, was your regard for him les-
sened, or your thankfulness for that which he did for you ? "
"No. And you mean that If we do not regard this
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$4 The Persian King.
being in the same way, granting his existence, still we
should feel gratitude towards him."
" Certainly we should feel gratitude to him ; and, con-
sidering the attitude we have taken towards him, this
feeling of gratitude comes over us with a kind of revul-
sion. But besides gratitude I do not see why we must
lose any other feeling such as you seem to miss. Do
you not remember how, in the course of the studies we
have all been through, we were told that there were two
parts in knowledge — one corresponding to reality, one
introduced by the action of our own minds — so that
certain characteristics which we at first think to be due
to the nature of things in themselves we find out on
reflection are only our apprehension of our own mental
action ? "
" Yes ; we do not perceive the reality absolutely, we
apprehend it subject to the mind's mode of perceiving."
"And of course the mode of the mind's action makes
it perceive certain qualities as parts of the real existence,
which do not belong to real existence at all. These
qualities spring from our mind's own action. In old
times these qualities were considered to be qualities of
the reality instead of introduced there. And much of the
impressiveness of the idea formed of the being of whom
we speak was due to a mere magnification and extension
of these qualities — qualities which do not correspond to
anything in reality. So the impressiveness of the idea
of this being was due to the magnification of qualities
which originate solely in our minds."
" This accounts for the idea having faded away. But
tell me definitely in an instance. Explain by taking
some particular quality what you mean."
"I cannot do that, the thought but floats in my mind ;
still it is always good to embody. Something of this sort.
When we observe any object we always attribute to it
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The Persian King. 85
a certain power. Everything has its own powers of
resistance, of moving, of affecting us in certain ways.
Thus whatever we apprehend, we appreiiond as power-
ful. Now since this quality of powerful comes in with
regard to everything, it is probably introduced by the
mind, and is rather a part of the mental action in giving
an idea of reality than a quality of reality. If so, when
we suppose a being to have the quality of ' all powerful,"
we are not supposing anything at all about the being,
but are only extending a quality quite barren of any
correspondence with the absolute nature of things. We
have left off talking about the being, and ar^' extending
a conception which springs solely from the only way in
which we can perceive."
" Surely you would say that this being was powerful."
" Of course, if we think of him at all, we must conceive
of him as powerful ; the nature of our mental action
demands this. But to dwell on the notion of his power-
fulness is quite barren, the only subject of thought which
has content is to inquire what kind of power he has.
There has been a tendency on the part of those who
have thought about this being to represent his greatness
in every respect. But they have not always been judi-
cious in so doing, because being unable to separate his
real qualities from those which they attribute to him in
virtue of their own mode of perception, they have come
to lay stress on descriptions which on the one hand
correspond to nothing in reality, and on the other hand
fail to move those whom they are intended to impress.
A cloak has been woven. The nature of this being is
hidden. His nature has been connected with introspec-
tive questions about the origin — of, of all things, the way
in which we perceive. All this must be dashed aside.
This being is the cause of all our life, and yet he needs
your help as you understand help."
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86 The Persian King.
" I should like to accompany you to your friend and
hear what he has to sa*' "
" Come, certainly."
So they went together to the town. On the way the
clerk felt a brightness of existence such as he had not
enjoyed for a long time. They talked together, and
confided in one another. At length they came near the
town where the student's friend lived. They separated,
the clerk going into the town, the student to the house
of his friend. On his way there the path led through
a small wood of very thick growth. Passing along, he
found that he had left the path. Pausing to reflect in
which direction he ought to go, he thought he heard a
sound. It was repeated. Penetrating deep into the
obscurest part of the wood, he searched till at length he
found — carefully concealed — a child, a mere infant.
The child was nearly perished with exposure. He
took it up and warmed it. When the child was a little
l>ettei- the cause of its having been hidden away was
apparent. Its breathing was distressed and laboured.
It suiTered under some affection of the lungs, which
made it gasp at every breath. Still in other respects
the child was well developed and seemed strongly made.
It seemed to have been left too long without care to
recover. The pain of exhaustion from the neglect, and
added to this the pain of its breathing, was too much
for it, it was sinking,
" If I could bear the pain of its breathing," thought the
student, "it might not sink till I could get some nourish-
ment for it"
He looked up, for it seemed to him as if some one
struck him in the chest. There was no one there. The
pain continued. He did not drop the child but con-
tinued on his way to the house of his friend. When he
got there he noticed a stillness unusual in the houses
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The Persian King. 87
of the inhabitants. He entered, and was met by his
friend's sister. He saw at once that something must
have happened. She tooli hira into a dimly lighted
room, where he saw his friend lying motionless and his
face quite white.
" He has been suffering great pain for long," she said ;
" it was hoped that if he could bear up the pain would
have run its course and he would not sink. But all we
could do was no use." The room was full of all thing's
accounted pleasurable, and she looked round as she
spoke. "It was no good." Taking the child from his
arms she left hira with the form of her brother.
Sitting down by his side the student felt the strange
oppression on his chest continue. He went out and
found that the child had completely revived. It had
still the appearance of being agonized in its breatliing,
but its eyes were bright, and it laughed.
" It will be all right soon," said his friend's sister.
" Tell me what was the matter with your brother,"
When he had heard about his malady he returned to
the room. After he had sat there for some time he felt
more and more the sorrow for the loss of his friend, and
the need of his counsel. This aimless, inert form, this
lifeless mass, was that which he had come to seek — was
the being with whom he had longed to confer.
He bent over him. " Could I but snatch him back
into life ; could I but have one hour's intercourse with
him. If I had been with him I might have borne some
of the pain of his complaint before he was overpowered
with it." He touched the lifeless hands, they were cold
and damp. He gazed into the expressionless face. He
seemed to feel the pain of the inner struggle his friend
had waged against the disease. The quiet of that still
chamber was gone for him ; in his own person he felt the
pangs of the struggle for life. A mist came over his
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88 The Persian King.
eyes, and he sank down holding his friend's hands.
Suddenly he heard a voice. He rose and looked about
him. The sound came faintly from the lips of his
friend.
" I have been very ill," were the words he caught.
" I am so glad you have come ; I was thinking of you in
my worst moments. You have come just as I am getting
better."
Indeed the features were regaining expression, the
hands were warm. It was his living friend again.
After a few hours he was sufficiently recovered to
hear about all that had happened. They talked together
long and earnestly. His friend was convinced.
"Let us go to your companion," he said.
They went into the town together. They found that
the clerk had gone to the magistrates' hall where a trial
was being held. They did not see the clerk at first, so
they listened to the proceedings. A woman was brought
in who had been kept in prison for some days, accused
of concealing her child. The case was clearly proved.
The woman received her sentence with an appearance
of apathy,
" She will not come out of prison aiive," said the
student's friend, noting her expression.
But he called out to her from where they stood in the
body of the court, " Do not fear, your child is safe."
The woman's face brightened, and she went with her
jailers buoyantly.
The magistrate had remarked who it was that had
spoken, and was about to give orders for the disturber
of order to be brought up for punishment. But the
clerk, who was sitting near to the magistrate with whom
he was acquainted, said :
" This is the one I have told you about ; pray do not
punish him."
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The Persian King. 89
The magistrate accordingly contented himself with
warning the audience in general terms.
But he said to the clerk, " Something about him is
very repulsive to me, do not tell me anything more
about him."
The three returned together, and together they de-
liberated as to how the new idea about the king could
be made known. It seemed best to go to the metropolis
and talk with the wisest and most learned there.
The student asked about the child. His friend's
sister came and told him that its breathing was not any
better, but that the child itself was strong and playful.
" It belongs to the woman who was tried to day,"
said the student, "and must be kept safely til! she is
out of prison."
His friend after some deliberation gave it in charge
to a faithful servant to take to the metropolis. A suffer-
ing child there would be much more likely to be over-
looked, "and you," he said, "will be able to look after it."
As the student and the clerk were about to set out on
their way to the metropolis his friend took him apart.
" My sister tells me that I had sunk into apathy when
you came."
" Yes."
" And that you called me back ? "
" Yes."
" How can I thank you 1 had it not been for you I
should never have enjoyed life again. I am grateful to
you."
" Do not say grateful to me, but rather to that power
which does for you all your life that which I do for you
momentarily now. And even now it is not to me that
you should be grateful, but to him, for it is only because
he has enabled me to do so that I have taken of your
pain."
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90 The Persian King.
With this he took farewell of his friend, and with the
clerk proceeded on their way.
They had not got very far when a train of servants
came up behind them. They stood by on one side, bii1
from the midst of his attendants a youth stepped
forward.
" I have learned what you have done, and I have over-
taken you with great haste."
" What is your wish ? "
"I want to come with you. I know that you have
restored your friend from apathy to life. No power is
so great as that. I have riches in abundance, All that I
have is at your service ; teach me your power."
Now in the valley riches meant abundance of pleasant
things. At the time the student was bearing the con-
stant pain which he took of the child's breathing, and
the pain also of his friend's illness. He felt that be-
fore beginning to take pleasure — which was the mean-
ing of having pleasant things— it would be necessary,
to give up the power which he was exercising, so he
said to the youth somewhat harshly t
. " You cannot compare riches and that which I do,
nor can you exchange the one for the other. First give
up all your riches, then you can begin to learn what
I do."
The youth turned back, but once again spoke, saying :
" I will give up a great part of my riches if you will
teach me."
" If you want to keep any, however small a portion,
you cannot do what I do."
Then the youth with all his attendants passed away.
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'- Persian King,
CHAPTER X
When they came to the metropolis the clerk brought
many of his acquaintances to see the student. From
his position in the council chamber, he was able to
address and induce many of the ablest of the councillors
to come and inquire. But as soon as they came into
the presence of the student a sort of constraint sprang
up between them. They did not take his words as
having any real meaning. They were occupied all the
time on speculating what motive it was that made
him say these things, and as to what kind of differ-
ence it was which they felt existing between him and
them.
In fact, as time passed on, no one of any position or
power would be brought into any sort of approximation
to him. On the other hand he used to speak continu-
ally with the poorer people. Those that were sick
especially delighted in his presence. There seemed to
be in him a power of stimulating those that were sinking
into apathy back again into life. Those who were worst
off in the city seemed to feel when he spoke to them
a promise of an alleviation of their sufferings.
One day the clerk asked him
" How is the child ? "
"It is welL"
" But it still seems to breathe with as much difficulty."
" Yes, but see how happily it runs about."
" How do you manage to preserve it? Any child which
I have seen would be pining miserably with such an
affliction. What is the power which the being you tell
of has given you .' "
" It is no power in the sense you mean."
" Surely it must be. Have I not folloived you faith-
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92 The Persian King.
fully and done all I could to get the wisest in the city
to listen to you ? Surely the time has now come when
you will tell me what this power is, and, if you can, let
me share it."
" You do not know what you ask,"
" Tell me, I pray."
" It is simply this, when I became aware through
thought of the being that is over us I had no message
or command from him. But I found that I could when
I stood by any suffering being take some of the suffering
and bear it myself. So as he of whom I tell does with
us each moment of our lives 1 do occasionally and in a
little manner."
"But what pleasure do you get that makes all this
worth your while ) "
" There is no pleasure. I am glad to see the being
freed from suffering, and living instead of sinking,"
" Do you mean to sa\- that there is nothing to hope
for > "
"I hope the time will come when I shall have a fuller
knowledge of the being I know."
The clerk was silent. He went out. While he was
still thinking over what he had heard in answer to his
inquiries, a messenger came to him from the chief o(
the councillors of pleasure and pain, asking him to an
interview.
When the clerk had been ushered into the presence of
the chief councillor, and was alone with him, the latter
said :
'' I should like a little quiet conversation with you
about your companion."
" I shall be glad."
" When you gave up your office and retired you had
no expectation of being concerned in affairs of state
again so soon."
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The Persian King, 93
"I did not expect, certainly, and I do not know what
your meaning may be about my being concerned in
affairs of state."
" What I mean is very simple. The continued deliber-
ations, generation after generation, of the wise men who
assemble in the council chamber have been the cause of
the continued progress of the inhabitants. Nothing is
done by them hurriedly or violently, but gradually im-
provement after improvement is worked out. But
besides this, there have always been at every age
certain disturbances in the state ; certain doctrines are
brought forward, and sometimes these tend to good,
and should be encouraged ; sometimes they are of
unknown import, and must be studied ; sometimes they
are against the happiness of the state, and then the
grave responsibility rests upon us of checking them.
Now from your position you have more opportunity of
knowing than any one else in what direction your com-
panion's doctrines tend. I have sent for you to ask
yoj to share with me this grave responsibiUty."
" I do not think I can help you. I am sure he does
not wish to do any harm. What harm can there be. in
his doctrines ? "
" It is not so much about his doctrines which I want
to speak to you as about another subject. Many of
those who have talked with him have agreed with one
another in ascribing a singular oppressiveness to his
presence. The expression was even used by a very
worthy friend of mine, ' He made me feel like a puppet'
Now what right had he to inflict such a sensation on a
very worthy individual ? I want to ask you yourself if
you have ever felt this ? "
The clerk hesitated.
" At least, tell me, have you ever found it easv to
influence him ?"
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94 Tlie Persian King.
" No ; I do not feel as if I could influence him in the
least. He seems to lack the ordinary springs of motive."
" Now, should you say that it would be a gain to the
community if many should become like him? Would
not they be difficult to govern?"
" Certainly they would be difficult to govern,"
"Would it be a gain in pleasure to the rest of the
inhabitants or to themselves?"
" It would not be a gain to themselves," said the
clerk, recalhng the pain which his companion bore,
" but it might be good for the rest of the inhabitants."
"Yes," said the chief councillor, "that is where his
strength lies ; he is a very skilful physician or an impos-
tor, and he has the people on his side from the cures he
has effected. Can you tell me anything about his life?"
" I have heard from him that he was a student, and
was exiled ; and that in his place of exile he found out
the new doctrines, and he left the place he was sentenced
to. On his way I joined him."
"So much we know, and it is within our power,
according to the regulations, to compel him to go back,
and to punish him for having left the region he was
banished to."
"If you have that power, why do you not send him
back if you think it would be best for the state for him
to disappear ? "
" Ah, my good friend, you have heard a great deal ol
our public deliberations from your place in the council ;
but now that we are conmlting together, I must tell you
that there are deeper secrets in the art of government,
which you will readily apprehend. Suppose we arrested
this individual and sent him away, the people would not
see the justice of it. They want him now, and they
would say that the forms of law were being used to get
rid of him. Of course if his partizans became violent
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TJu Persian Kmg. 95
something of this kind would have to be done. But it
is only a decree that seems just in the eyes of the people
that we can prudently carry out in such a case without
attracting even more attention to him than there is at
present."
The clerk said nothing. The chief councillor went
on :
" I am sorry that our conference has come to so little.
I was hoping that I might have found in you a successor
to the vacant seat in the chamber. I know you have
the ability to fill it well. But before the advancements
are made some proof of the wisdom of the successor is
required. Hitherto you have not had the chance, but I
thought that in this difficult case, where you have so
much better opportunities of observation than any one
else has, you might have shown your mental power and
confirmed my opinion of you. Still, no doubt, on sorne
future occasion you will have another opportunity when
this affair, difficult as it is, is forgotten."
The chief councillor made a sign that the interview
was at an end, but the clerk remained.
" All that we want," the chief councillor resumed, " is
to form an opinion from inside knowledge of whether
this innovator is likely to cause more pain or more
pleasure if he gains a hearing. Can you advise us ? any
particle of knowledge of his inner life, apart from his
public professions, is valuable."
" There is a singular fact which I should like to tell
you of, as it has been, somewhat of a burden to me."
The chief councillor made a sign of assent, and the
clerk told him about the child, and how it had been
preserved.
" And with this child," he said, " he and I sit when
the day's work is done."
" It is indeed a strange story," said the chief councillor ;
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96 The Persian King.
"you are quite right In telling me. I was sure you were
one on whose discretion confidence might be placed.
You have given me the highest proof I could have ex-
pected. The bearings of this matter must be thought
That evening, as the clerk entered the room where
they lived, the student was leaning over the child with
a wearied expression. He went up to him and laid his
hand on his shoulder. The child looked up at them
and laughed, It was quite happy despite the apparent
struggles of its breathing. The student looked at his
companion's face. His weariness vanished at once, and
a strong warm light came into his eyes,
" You seem oppressed, my friend. I know you regret
the way in which all the wise and important people you
have brought here look on me, and you must feel some
sorrow for the partial loss of esteem they have showed
you in consequence. Can I help you to bear it ? "
At that moment the door opened, and a messenger
came in and gave the clerk a sealed packet. He
opened it and saw that it was his appointment to the
vacant seat in the council chamber. But his face did
not brighten. He answered his companion r>oodiIy,
and thus the day ended
CHAPTER XI.
On the next day the student rose early and went forth
aione. He did not, as was his wont, go amongst the
people, but he passed through the streets towards the
open country. On his way he was stopped by an old
woman, bent with age and many infirmities. She had
no place amongst the people, and had so many pains
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The Persian King. 97
and such a barrenness of existence that any one who
had thought of her would have wondered that she
remained aUve.
She stopped him and said, " Master, I have heard
that you can take my pain. Help me."
But he answered, looking at her, " No, I cannot, but I
have a message for you."
And she said, " A message for me ? I do not know
any one who would send me a message."
But he answered, " Nevertheless, I have a message to
you from my lord, and he bids me thank you."
She answered, " It cannot be. You must have made
a mistake."
But he said, " I have made no mistake ; he thanks
you."
He could not explain to her how by her bearing pain,
according to the law of the valley, she took it from that
which the king bore. Instead of saying that, he gave
her the message, and somehow the old woman believed it.
The rest of the day he spent in the open country.
When he returned it was getting towards dusk. There
was an unusual movement in the streets. On passing
into the public market-place he saw a crowd collected ;
and when he had penetrated to their midst, he saw
lying on the ground the child he had kept so long. It
had been lying uncared for and exposed for many hours ;
and the want of food, the fright, and its gasping breath-
ing made it the most pitiable object. He at once
stepped towards it and took it up in his arms.
" Is that your child ? " said one of the crowd.
" It is not my own," he answered, " but I take care of
it"
" Then it is you that are bringing pain upon us all,"
shouted several voices from the back of the crowd.
And some one shouted out :
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g8 The Persian King.
" I know you. You pretend to take pain away and
you really bring much more in secret."
And moved with a feeling of indignation against the
one who had caused such a painful object to exist as the
child was, the crowd closed on him, and barred his way
to his own place. But they did not lay hands on him.
As he stood with the child it gradually began to regain
its composure. But with a sudden movement the crowd
swept towards the council chamber. And when they
had come there they demanded that this cruel and
wicked act of keeping pain in existence should be
punished.
There happened to be several of the chief magistrates
on the spot, and in obedience to the voices of the crowd
they proceeded to sit in judgment at once. It was not
known how the child had come into the streets ; but it
was admitted by the prisoner to be his doing that it had
been kept aliva The doctors unanimously said that it
ought to have been put out of existence directly it was
born. There was practically no defence. The charge
of subverting the laws was established. The people
clamoured for the extreme penalty. The judges passed
sentence on the student,
Before morning he was put to death.
He met his fate without sorrow, even with gladness.
The pain in his life had for long been as much as he
could bear. He did not, like the prince of long ago,
look upon nothingness as the desired end of existence.
He felt the presence of the one whom he had dis-
cerned through thought, and this seemed more real to
him than life or death.
On the following day, whether in reaction from the
excitement of the previous evening, or from some other
cause, an unusual quiet pervaded the streets of the city.
There was not much discussion as to the event which
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The Persian King. 99
had happened. The prevailing feeling was one of
wonder that there should have been so much commo-
tion about an unimportant affair. For the most part
before the next evening the whole circumstances were
on the way to be forgotten. And yet every here and
there were persons in whose lives the loss of their friend
was deeply felt. Thejoy and spring of life seemed gone.
The poor child lay pale and motionless, save when every
now and then it gasped convulsively for breath. None
felt the despondency more than the clerk, The interest
and value of Ufe seemed to have gone. He did not care
for his new honours.
That day some most unexpected news went through
the town. The chief of the council of sensation had
sunk into apathy. He was in the prime of his life. It
was most unexpected. Every one was astonished at
the news, but were still more astonished at how little
they felt concerned.
Following on these tidings came others. Many of
the inhabitants of the metropolis whose lives were most
strenuous suddenly succumbed. The clerk had made
up his mind to go into the country. But tidings came
from there also that the poorer labourers, and those who
were exposed to the fatigue of long journeys or exposure
were in many cases sinking. The wave of torpor seemed
passing over the whole valley and not to be confined to
the metropolis. The rich and unoccupied classes only
were comparatively unaffected. They betook them-
selves to the store of enjoyable things at their service,
and so replaced the natural spring of life which seemed
tending to fail in every one.
On the confines of the valley, where the ravine struck
it vast depth between this land and that, vast and end-
less as the sea stretched the plain whence the king had
come. It was struck silvery grey by the light of the
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lOO The Persian King.
moon, dark shadows marked the nearer strands, and
gradually the rocks which cast them showed their sharp
outlines, hardly distinguishable from the ground out of
which they rose.
Over the great gulf floated the sounds of a pipe, the
strains were low, winning the soul with the sweetness of
an unearthly melody, throbbing as with a call to a
distant land away and beyond.
And when the eye found the source of the sounds,
there stood, once more, solitary in the untenanted vast,
the king's devoted friend, the same old man who before
had hailed him. Gradually the music sank lower and
lower, till at length silence spread in folds unruffled.
Then on the edge of the valley a form appeared. It
came and seemed to gaze across the gulf, standing
motionless and intent. At length a voice came.
" Art thou there ? "
" Yea, O king, what wouldst thou ? Art weaiy ? "
No answer came.
Then the old man spoke. " Behold the roads where
they stretch gleaming white in the moonlight ; behold
the fields, the villages ; see in the distance the great walls
of the palace. Have not these risen up for thee, O
king."
Then the king made answer ; " I am weary."
Suddenly the old man raised his pipe with both his
hands to his lips. Wave after wave of triumphant
sound pealed forth. Great harmonics such as marching
nations might hear and rejoice, noble notes of unbounded
gladness.
Then, crossing by an unknown way, he came and
stood by the king's side. After a while the two moved
on together, and by a secret path passed away from the
valley — whither I know not.
As soon as the king had departed from the valley the
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The Persimi King. loi
beings in it be^an to sink into the same state of apathy
as those were whom he had first found there. Those
who sank first were the ones in whose lives the stress of
labour or thought was the most intense, for they first
felt the loss of that bearing of pain by one beyond
themselves which gave them a difference of pleasure.
And slowly as the accumulated enjoyment was ex-
hausted, a chill death in life crept over the land. 'Tis
useless to ask after the fate of any one of those that
were there, for each was involved in the same calamity
that overwhelmed all. Every hand forgot its cunning.
The busy hum of life in the streets was hushed. In the
country the slowly moving forms gradually sank to rest.
At every spot was such unbroken quiet as might have
been had all the inhabitants gone to some great festival.
But there was no return of life. No watchful eye, no
ready hand was there to stay the slight but constant
inroads of ruin and decay. The roads became choked
with grass, the earth encroached on the buildings, till in
the slow consuming course of time all was buried —
houses, fields, and cities vanished, till at length no trace
was left of aught that had been there.
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CHAPTER I.
There are certain respects in whichi our world resembles
the valley. Instead of regarding pleasure, pain, and
feeling, let us examine the world we live in with regard
to motion in one direction and another, and in respect
of energy.
If we observe the movements which go on in the
world, we find that in great measure they consist of
movements which if put together would neutralize each
other.
A pendulum swings to and fro. If the two move-
ments took place at the same time the pendulum would
be still. Taking a more ample motion — that of the
earth round the sun. The earth moves in the course of
its orbit as much towards the sun as away from it, and
as much towards the east as towards the west. If all
the motion were to be gone through at one and the
same time the earth would not move with regard to
the sun.
Again, if we notice what goes on on the surface of the
earth, we see that there is a motion of rising up and
of sinking down. There is an approximation of the
chemical elements into some compounds, and a separa-
tion of them again. Of all the myriad processes which
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Our World. 103
go on, the swing of a pendulum is the type. But the
downward swing may be very different to the upward
swing. It may be that the downward swing is repre-
sented by the violent action of the chemical affinities in
a charge of gunpowder when exploded, and the upward
swing may be represented by the swift motion imparted
to a cannon bail, and the swift motion of the cannon
ball in its turn comes to rest, and as it comes to rest
slowly or quickly other changes take place.
And what we notice in our world is similar to what
the inhabitants of the valley noticed about pleasure and
paiii — that they do not neutralize one another as a
matter of fact.
The contrary motions on the earth which, if they were
put together, would neutralize one another, do not as a
matter of fact neutralise one another. We call motion
in one direction positive — in the opposite direction
negative. But in the world as a matter of fact positive
and negative motion do not together come to nothing.
As in the valley the states of pleasure and of pain did
not coalesce into a state of apathy, but always succeeded
one another, in simple or complicated fashion, so on
the earth it is impossible from two opposite moving
bodies to get stillness. If the two come into contact in
opposite directions the movement does not stop, but
makes its appearance in an alteration of the shape of
the bodies, in a disturbance of their particles, or in some
such fashion.
Again in the valley, by measuring the pleasure and
pain simply as feeling, and not taking into account
whether it was pleasure or pain, the inhabitants found
that the feeling was always the same in amount.
So we on the earth, measuring the amount of move-
ment, and leaving out of account whether it is positive
or negative, come to the conclusion that the quantity of
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104 Energy.
movement, recltoned in the way in which we call it
energy, is always the same. The principle of the con-
servation of energy has become a fundamental one in
science.
But besides the discovery that the amount of sensation
as such was always constant, the inhabitants of the
valley discovered that a portion of the sensation was
passing away from a form in which they could feel it.
And there is an analogous discovery in science, We
know that a portion of the energy of our system is
passing away. It is not being annihilated, but is dis-
appearing. With tlie energy which can be collected
from the falling of a stone, the same stone cannot be
raised to its former level again. Some of the energy
has disappeared from the form in which it can be known
as the energy of moving masses. The energy has in
some measure irrecoverably passed off in the form of heat.
Hence, just as the inhabitants of the valley came to
the conclusion that in point of sensation they were
"running down," and that after a time all sensation
would have passed away from the form in which they
could feel it, so we have come to the conclusion that
the energy of the system in which we live is running
down, that the energy is passing out of the form in
which it can be manifested as moving masses, that
finally all movement of masses will come to a standstill,
and there be nothing left save motionless matter, with
warmth equally diffused through it.
Now in coming to the conclusion about the valley,
that the amount of sensation was gradually passing away,
the inhabitants, as we have seen, had come upon the
very secret and cause of all the life in the valley. But
coming upon it from the outside they had not recognized
the significance of what they had found. The cause
and prime mover of all their existence indicated itself to
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Fermissioit. 105
them, coming thus upon it, as a process whereby all that
went on was doomed to a distant but certain extinction.
Now, is this process of the passing of mechanical
energy into the form of heat to be interpreted by us in
a way analogous to that in which the inhabitants of the
valley could have interpreted the process they found ?
In this cessation of sensation in the form in which
they could experience it lay the central fact of the life of
the valley. Has this passing away of energy from the
form in which we can experience it an analogous signiti-
caiice to us )
In order to examine into the possibility thus suggested
there are four convergent lines of thought which it will
be well to follow up separately. Each of these lines of
thought bears in an independent manner on the central
question — the significance of the passing away of energy.
These lines of thoufjht may be connected with the
following words, which indicate their significance: 'i)
Permission ; (2) Causation ; (3) Conservation of Energy ;
(4) Level.
CHAPTER II.
When we observe any movement taking place we ask
what is the cause of it ? what is the force which produces
it ? But surely, if we confine our inquiry to this point, we
have made an omission. That we are not conscious of
having made an omission may perhaps come from our
living in the air which yields so easily to any moving
body. If we lived in a rigid medium we should, when
we became aware of any moving body, ask two questions.
First, what urges it along ? secondly, what prepared the
channel for its motion ?
But seriously, without laying any stress on the above
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io6 Permission.
illustration, we see that to every movement two condi-
tions are necessary : a pushing and a yielding, a force
and a permission. If the particles of the air could not
yield, a pendulum could not swing through it. If again
the air could not pass on the motion it has received, it
could not yield to the motion of the pendulum.
Now since every motion requires a permission, we are
ted to ask the question. What is the ultimate per-
mission ? What again is that which by yielding allows
motion at all to take place ?
If we trace any movement scientifically we find an
indication of what the ultimate permission is.
A body swings through the air. Currents in the air
are set up. These currents impinge on the objects with
which the air is in contact, and in them produce heat —
producing heat also by friction with other portions of
the same air. Every motion thus passes off finally, at
however long an interval, in the form of heat. Motion
may reappear as motion through myriads of phases, but
at each change of form some of it passes off into the
form of heat, and finally all passes off into the form of
heat, Thus, unless matter admitted of being warmed,
there would be no ultimate permission. A motion once
started would never come to rest. Or, rather, no motion
could take place at all.
The tendency of the above remarks is to avoid the
conception of there being absolute laws of motion, true
of bodies when surrounded by no medium, modified
when a medium is present. Surely such a conception is
an instrument of the mind for exploring nature, not an
absolute fact in nature. The abstract laws of motion
are mental aids in creating knowledge; like scaffolding
for the builder, even from their very usefulness they
have probably but little to do with the permanent
edifice.
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Permission. 107
This passing into the form of heat supplies a place
analogous to that of the " void " in the speculations of
the Epicurean philosophers. They argued that motion
was not possible without a void. Given a void, some-
where into which matter could move, then any amount
of motion could be accounted for. But without a void
into which a portion of matter could move, how was it
possible for motion to begin ?
Thus repeating their inquiry with our altered concep-
tions, we ask this question about motion, or energy
(which is a particular way of reckoning motion).
Unless motion can in some way pass off, how can
there be all these transformations of energy ?
Now the ultimate transformation of all energy of
motion is into the form of heat. In this change into the
form of heat is to be sought the ultimate permission
which makes all transformations of energy, all motions,
possible. It is this being acted on of the finer particles
of matter which permits the movements of the larger
This passing of energy into the form of heat must not
be regarded as a side circumstance, as less essential to
the laws of nature than that law which we call the con-
servation of energy. It is at the same time the end oi
every motion, and that which makes every motion
possible.
The passing of energy into the form of heat takes
place in that which we call friction, and in all those
modes in which any movement is brought to a stand-
still. But so far from these being simply "hindrances"
to motion, it is through them that we learn that which
makes motion possible. It is with us as with the inhabi-
tants of the valley, the gradual cessation of feeling from
their life and the modes in which it ceased were the way
in which they regarded the action of the king who was
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ro8 Causation,
the cause of all. We have thought of motion as a thing
in itself impaired by the multitudinous obstacles it meets
in the world. Let us look on the circumstances more
impartially. Let us look on them as something co-equal
with motion. Let us find in that mode whereby all
motion comes to an end the originating cause also
whereby all motion comes to be.
The passing of the motion of masses into the form of
heat is the ultimate permission.
CHAPTER III.
If we reflect cautiously on the history of our opinions,
we find that we often fall into error in respect to our
freedom in attributing causes. If we are unfortunate we
are apt to look on our neighbours, or the world, or, if we
are of a self-depreciatory turn of mind, ourselves as the
cause.
Again in past times people really felt sure .about
certain things being causes which we now know had a
very slight connection with the result. Incantations
have been supposed to have an effect on physical phe-
nomena, such as eclipses. Numbers and their properties
have really been conceived as the causes of the modes of
existence. Ideas have been supposed to have causative
power over the order of the world.
We should be very careful in attributing the notion of
causation. If we see a stone lying on the ground, and
proceed to pick it up by the strength of the arm, we say
that the exertion of the arm is the cause of the stone
being lifted. But in this respect even we are too hasty.
The arm may exert itself and yet the stone not be lifted
up — -if it is too heavy. All that we can say about it is that
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Causation. 109
if the stone is lifted, a certain set of muscular actions
has gone on in the arm, and a certain movement of the
stone has taken place. If we look closely at the matter,
the movements in the arm are related to the movements
in the stone in a strictly measurable way. There has
been 50 much exertion corresponding to the weight of
the stone. But suppose the arm had done anything
else, there would have been the same relation traceable
between the movements in the arm and the actions
which followed its movements. The energy spent by
the arm would be equal to the energy imparted to the
object moved, whether it be a stone sent flying through
the air, or one lifted to a higher position (bearing in
mind always the small quantity of energy passing off in
the form of heat).
It does not seem advisable that the notion of cause
should be brought in to denote the relation of the move-
ment of the arm and the movement of the stone, These
are two sets of actions between which the regular rela-
tions which hold good between the consecutive states of
moving systems hold good.
The notion of " cause " should rather be applied to
that act of the will whereby the movements of the arm
are connected with the movement of that particular
stone rather than the movement of any other object.
We are the cause of the actions we will. The notion
of cause is derived from our " will " action, and the notion
of cause ought to be kept to this connection.
All that goes on outside us can only be apprehended
as consecutive states following on one another. Between
certain sets of consecutive events we notice that the same
relation holds good which we have observed in other
consecutive states. If some water is heated in England
it passes off into steam ; if water is heated in another part
part of the world it also passes off into steam. There is
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no Causation.
an exact analogy in the behaviour of water under the
action of heat wherever we observe it. But all that we
have obtained as knowledge is the fact that we may
practically be confident of an analogous behaviour on
the part of water wherever circumstances are similar.
We may use the expression that heat is the cause of
water boiling for convenience. But the expression
should not be used as containing any deep meaning.
To say one external event is the cause of another is
to put an absolutely unknown and spiritual relation in
place of impartial observation.
To cause a motion is the name for the action of our
soul on matter— a thing shrouded in mystery. To be
the antecedent in a chain of movements is the fact which
we can observe about any movement in the external
world. We cannot strictly say what movements of
gases, water, &c., cause this volcano. We can only say
what movements of gases, water, &c., precede this
volcanic eruption analogous to movements which have
preceded other volcanoes.
There are invariable sequences in the external world to
which we do not affix the notion of cause and effect — day
and night, summer and winter. Why we should do so
in any case is not clear, except that by familiarity and
mystery the sequences have become to us something like
our own will action. Indeed, is it not the case that when
we can trace intermediate links we say so and so comes
from so and so in such a manner. But when no inter-
mediate links can be traced we say one event causes
another.
If, however, we omit the feeling of causation from the
external chain of events, it does not follow that there is
no causation to be apprehended in the external world.
Let us not introduce the notion of causation at hap-
hazard. But if we find in the external world signs of
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Conservation of Energy. 1 1 1
an action like our own will action, let us then say, Here
is causation.
The inhabitants of the valley would not have been
right in saying that one act of a routine caused another;
But they were right in saying that the amount of sensa-
tion was constant, and that some of it passed off in a
form in which they could not feel it.
And so let us not say that one action causes another.
Let us not say, for example, that the downward swing of
a pendulum is the cause of its upward swing. But !et
us simply say that the one follows the other ; that the
amount of energy present is the same except for the
small portion that passes off into the form of heat,
CHAPTER IV.
Suppose certain sets of numbers were being presented
to us one after the other, and amongst these three con-
secutive sets were the following. First set : 3, 5, 6.
Second set : 8,-2,— i, I. Third set : 7, 4, 2,— i.
A little consideration will show us that there is a
certain uniformity in these sets.
Take the square of each of the numbers in the iirst
set and add them together, the result is 70. Thus
3Z + 52 4. 62 = 9 + 25 + 36 = 70,
The sums of the squares of the numbers in the second
set come to the same. 8^ + (—2)2 4- (-1)2 -i- i^ = 64
+ 4 + I + I ^ 70. Also in the third, 72 + ^a + 22+
{- 1)* = 49 + 16 + 4 + I = 70, and so on.
Having noticed this we should regard it as a purely
formal law, having nothing to do with why the num-
bers were presented to us. But we should consider
it likely that it would characterize all the numbers that
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112 Conservation of Energy.
were presented to us. And if this expectation were
found to be realized, we should after a time feel a cer-
tain assurance that the next set of numbers presented
would satisfy the same law. If this assurance was
indefinitely satisfied we should get to regard the satisfy-
ing this law as an invariable condition of the numbers
presented. But we should never regard this purely
formal law— that is, a law about the particular charac-
teristics of the numbers — we should never regard this
formal law as the cause of the next set of numbers
appearing after the first had gone.
When, however, we talk about the conservation of
energy we are apt to think of it as more than a merely
formal law, more than a statement about numbers which
has been found to hold true.
Yet it is no more. The law of the conservation of
energy asserts that in any system in motion the sura of
the squares of the velocities of the particles at any one
moment is equal to the sum of the squares of the velo-
cities of the particles at the next moment.
The conservation of energy is but a mode of reckon-
ing motion, by which it is found to be constant in all
changes of a system. The system must emorace all
the particles concerned in the motion. It may be made
as large as we like.
The principle of the conservation of energy as here
stated is confined to the case of moving bodies. Some-
times the energy is said to disappear from the form of
motion and become potential energy. That case will be
treated under the fourth consideration of level, but it
introduces no alteration in what has been said.
As to the practical truth of the law of conservation of
energy there can be no doubt ; nor as to the value of
the results obtained from tracing its validity in obscure
actions. But there is nothing final about it. It is a
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Conservation of Energy. 113
numerical statement of extreme value, and it introduces
a mode of reckoning by which motion can be looked
upon as indestructible as matter is.
There is a possible objection to the law of conserva-
tion of energy.
It is no less a law in nature that in every one of
a series of changes some of the energy passes off into
the form of heat. Now heat is reckoned as a mode oi
energy. And there is in science a method of calculat-
ing how much energy any given quantity of heat is
the equivalent of. And this equivalence is calculated
on the supposition that no energy is lost. When heat
is produced and motion passes away, the proportion
between the motion that disappears and the heat that
appears is represented by a number calculated on the
assumption that no energy is lost. Thus whenever
any quantity of energy takes the form of heat, the quan-
tity of heat which is produced is exactly given by the
calculation. But the reverse process is not possible.
It is not possible to turn back all the energy in the form
of heat into the form of motion. Consequently it can-
not be proved that the energy in the form of heat would,
if all turned into motion, produce as much motion as
that from which it was produced. There may be an
absolute loss of energy^ — only a very small one. The
law of the conservation of energy may be the expression
that this loss is a minimum.
This objection is not essential to the line of argument
pursued above with regard to the conservation of energy.
It forms no necessary part of the line of thought we are
pursuing. It merely tends to show that the law of the
conservation of energy is no axiom which we cannot
suppose not true. The real conclusion to which this
part of our line of thought tends is that the conserva-
tion of energy is a purely formal law.
S
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Level.
CHAPTER V.
The most apparently simple movements are those
which we see taking place on the surface of the earth,
connected with the agency which we call gravitation.
We see the rivers flowing from a higher to a lower level,
rocks when loosened from a mountain side rolling
down, rain falling, and many minor changes of this sort.
But there are many actions besides these. For in-
stance, suppose before us a spring coiled up. When it
unwinds it "exerts force," it transmits movement. In
its first state it is like a stone at the top of a mountain.
In its second state it is like a stone which has fallen to
the bottom of the mountain. It had a power of move-
ment and of communicating movement, now it has lost
that power.
Again, the powder in a gun when it explodes expands
and imparts movement to the shot. When the gun has
been fired off the powder enters a different state. Before,
the chemical affinities of its constituents were in a state
of tension, now that it is fired off, they have formed
fresh combinations. The power of transmitting move-
ment has been lost by that which was the powder. It
is like a portion of water at the top of a fall of water.
If it remains at the top it has at any time the power of
producing a shock, and of effecting, say, the movement
of a water-wheel under it. But if it falls it has exerted
and lost that power.
The difference of level associated with gravity is
familiar to us. But we have no right, other than our
own familiarity with it, to look on gravity as less in
need of explanation than any other phenomenon of the
external world. Newton did not suppose that there
was any force inherent in matter which attracted other
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Level. 115
matter inversely as the square of the distance. He
showed that a great many astronomical facts were
capable of being explained and calculated on this
hypothesis. He left the explanation of how it is that
matter gravitates unsolved, and it remains unsolved to
the present day.
But gravitation affords us a useful term — " Level."
Let us agree to call the following on a high level — -a
stone at the top of a precipice, a wound-up spring,
oxygen and hydrogen mixed in the proportion to form
water. Let us call the following at a low level — the
stone at the foot of the precipice, a spring straightened
so far as it tends to straighten, oxygen and hydrogen
united in the form of water.
In passing from their first state to their last ail these
have manifested a power of movement and of communi-
cating movement. They have now relatively to their
former state lost that power.
Difference of level in this general sense is the most
universal distinction of matter.
No motion takes place unless matter passes from a
higher to a lower level.
The universal cause of motion is that which produces
this difference of "level" in the general sense.
If there were no difference of level the state of things
in nature would be as if one spring in order to unwind
had to wind up an exactly equal spring of the same
amount ; as if a stone falling from a height had to raise
an exactly equal stone to the same height from which it
fell. Under such conditions of things no motion would
begin. In such a state of things all nature would be
like the inhabitants of the valley when the king bore
no pain, for no course would be preferable to any other
course.
What is the cause of the " Difference of Level ? "'
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ii6 Level.
Whenever matter passes from a higher to a lower level
some of the energy which is given out passes away in
the form of heat. This passing away of some of the
energy into the form of heat is an invariable accompani-
ment of the transition from a higher to a lower level.
Is it the cause of the difference of level ?
In the valley the king by bearing some pain made
action worth while. Is there any indication in nature of
the production of a lower level which makes the course
of things run on.
It is certain that energy in every action passes off into
the form of heat, and unless it is through the power of
the finer particles of matter to absorb the energy, it is
difficult to see how any action can take place.
As with the other lines of thought, this line also ter-
minates with a possibility. Nothing has been proved,
but a place has been provided.
In the first part of this paper a possible mode of
action was exhibited in the imaginary relations of a world
subject to certain laws of pleasure and pain.
In the second part it has been shown that something
is wanting in our conception of the natural processes.
There is room for a central idea. No scientific doctrines
properly understood would clash with one properly
located.
Can the mode of action exhibited in terms of sensation
in the fictitious world be applied to the case of the world
of force and matter ?
Before passing on, however, it is worth while to exa-
mine a little more closely into what is meant by the
expression so often used ; " Passing off into the form of
heat."
The modes in which energy passes off into the form of
heat are in general those modes by which movement is
brought to a standstill such as friction. And we are apt
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Heat. 1 1 7
to think motion the primary fact, the cessation of motion
a secondary and disagreeable fact. But both are equally
existent phenomena, and the convenience to ourselves is
not to mislead us as to their relative importance.
But what is this passing off of energy into the form
of heat ? The phrase is unsatisfactory, for we are told
by science almost in the same breath that heat is the
motion, the mechanical motion, of the particles of matter.
So the statement resolves itself into this. Only when
some of the motion passes off into the form of motion
of the smaller particles of matter does motion take place
in larger masses.
As a corollary it follows that at some date, however
distant, all the motion of masses will have passed away
into the form of motion of smaller masses,
It may be urged that when the larger masses move,
the smaller particles also move. This is true ; but
motion in this sense is used to denote change of position
amongst the smaller particles with regard to one another.
The particles in a flying cannon-ball are relatively still
with regard to one another as far as the motion of the
cannon-ball as a whole is concerned.
We thus arrive at the following principle : The con-
dition of the motion of masses taking place is that some
of the motion passes off into the motion of the .smaller
particles.
But if the motion of the smaller particles is just the
same as that of the larger portions, we are obviously not
at the end. The very same principle just applied must
be applied again.
These motions of the small particles of matter cannot
take place unless some of their movement is transmitted
and passed on, and transformed into the motion of still
finer particles of matter.
But here obviously we are brought to the beginning of
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1 1 8 Ultimate Medium.
an infinite series. An infinite series passing from finer
matter to still finer matter, and so on endlessly.
The assumption by which we are led to this endless
series of transmissions must be clearly apprehended.
We take the law — that the motion of masses only takes
place when some of the motion passes off into the
motion of the finer particles of matter, and we assume
that it holds always.
In a lever there is a fixed point, the fulcrum, which
supports it, and the power raises the weight ; but the
weight may be fixed, and then the fulcrum can be lifted
by the power. So wo obtained this law from the con-
sideration of material relations ; and now we suppose
this law to be the fixed point, and shift our notions
of material relations.
Thus we are landed on an endless series. Before pro-
ceeding, however, to inquire what the significance of this
endless series may be, let us assume an end to it. Let us
assume that we come at last to a final transmission. Let
us assume that the energy is transmitted to the ultimate
particles of matter.
Or, if we have gone beyond matter, let us suppose an
ultimate medium which hy its modifications builds up
matter, and which is the last and ultimate substance.
Let us suppose this ultimate medium absolutely to
receive some of the energy. Let it absolutely receive
and absorb some of the energy, and thereby give rise to
the difference of level, to give the ultimate permission
which sets all things going.
What are the properties of this medium ? We obtain
an indication of what they are when we examine the
properties of the finer kinds of matter. Compared with
the motions of masses, motions which affect the smaller
particles of bodies are infinitely quick. Light and elec-
tricity are actions affecting the smaller particles of
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Ultimate Medium. 1 19
bodies, and by them distances are speedily traversed,
which relatively to moving masses are very great.
Now in point of speed of transmission the properties
of this ultimate medium m'Xist be infinitely beyond those
of luminiferous ether.
To this ultimate medium all movements at any dis-
tance from each other must be almost equally present at
every part At whatever distance from one another two
affections of this ultimate medium be supposed to take
place, the effect of the one will travel to the place of
action of the other instantaneously.
Such a medium is a kind of visible symbol of the
universe, being one system in which all motions should
be co-determined.
To make this clear, suppose a transformation of energy
was produced in one part of space of an absorption of
energy on the part of this ultimate medium, this trans-
formation of energy would be produced by a medium in
instantaneous contact with every other part of space, and
the transformation of energy thus originated would har-
monize with, and have reference to, the transformations
of energy in every other part of space.
There are two infinities — -the infinite of space extend-
ing out each way, the infinite of the smaller and smaller
divisions of matter. The ultimate medium we have sup-
posed partakes of both infinities. It is infinite in extent,
and infinitely fine in its particles.
Now this medium by absorbing energy sets move-
ments going. And that movements do not neutralize
one another — i.e., that movements in opposite directions
do not mutually destroy one another — has this result, that
a given amount of this absorption produces the greatest
possible amount of motion. If motion came to a rest
in any other way, more of this absorption by the ultimate
medium would be needed. Hence, by a given amount
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120 Infiniie Series.
of absorption in the ultimate medium the greatest pos-
sible amount of motion is produced. That is, the
absorption of motion into the ultimate medium is a
minimum, and the law of the conservation of energy is
the expression of this being a minimum.
But here again a further remark is called for. We start
by assuming energy to be an absolute existence. But
why not assume this action on the part of the ultimate
medium to be the real action, and consider the pheno-
mena of motion and energy as the mode nf its action.
What this action of the ultimate medium may be
needs examination. All that we can say at present is
that relatively to that which we call energy, the action
of this medium is that of being acted on.
CHAPTER VI.
In the preceding, Iiowever, it must be remembered that
this conception of an ultimate medium was merely a
supposition to enable us to see and roughly map out the
relations of the things we are investigating. Where we
were really landed was in an infinite series— we were
brought logically to the conception of an infinite scries
of media, one behind the other.
What does an infinite series indicate ?
Let us turn to a region of thought where infinite series
are familiar objects, and we can learn about them.
In algebra infinite series are common. Thus take
series i— — 1- - and so on for ever. This is the attempt
in algebra to represent a trigonometrical idea. In trigo-
nometry it is expressed as cos. x. But in algebra it
needs this infinite series.
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Infinite Series. 1 3 1
In algebra infinite series occur when tlie object wliich
it is wanted to represent in algebraical terms cannot be
grasped by algebra. When there is no single term o!
set of them in algebra which will serve, the object is
represented by means of an infinite series. Thus we
may say that in any calculus, when the object to be
treated of cannot be expressed in the terms of the cal-
culus, it is represented by means of an infinite series.
Now, dealing with material considerations, going on
in the calculus of matter, we have come to an infinite
series. This indicates that we have gone as far as the
material calculus will carry us. We have now to bring
ill an idea from a different quarter if we will simplify
our expression.
It may well be that within our experience there is
nothing which will serve. But let us suppose that that
which in material terms we represent as an infinite series
is a will^a will in contact with all existence, as shown
by the properties it had when we conceived it as an ulti-
mate medium. For, regarding It as an ultimate sub-
stance, we found that it would be affected by pulsations
infinitely quicker than light and electricity ; considered as
a substance, it was such that distance to it tended to be
annihilated. Hence as a will we must say of it that to
it all that is is present^a will which by a fiat that to our
notions is being acted on rather than acting, accepting
pain rather than taking pleasure, sets the course of the
world in motion, vi-hich holds all in one system, which
creates all activities. For although we apprehend this
will relatively to the appearances which we suppose we
know, mechanical energy and feeling, still we see that
both are caused by it, and that the sum of both is
nothing, save for that which this will is in them.
Is there any other way of apprehending this will than
through the external world ?
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12 2 Recapitulation.
We have two apprehensions of nature — one of ex-
ternal things, the other of our own wills.
Does this will not exist in those who are true per-
sonalities, and not mere pleasure-led creatures? — have
they not some of this power, the power of accepting,
suffering, of determining absolutely what shall be? — a
creative power which, given to each who possesses it,
makes him a true personality, distinct, and not to be
merged in any other— a power which determines the
chain of mechanical actions, of material sequences —
which creates it in the very same way in which it seems
to be coming to an end — by that which, represented in
material terms, is the absorption of energy into an ulti-
mate medium ; which, represented in terms of sensation,
is suffering ; but which in itself is absolute being, though
only to be known by us as a negation of negations.
CHAPTER VII.
In conclusion let us remark that we have supposed two
different worlds — one of sensation in the fir.st part, one
of motion in the second part. And these have been
treated as distinct from one another. And especially in
the first part, by this avoidance of questions of move-
ment, an appearance of artificiality was produced, and
occasionally inconsistencies, for sometimes sensations
were treated as independent of actions, sometimes as
connected with them. But it remains to be decided if
these inconsistencies are in themselves permanent, or
whether, when we remove the artificial separation, and
let the world of sensation and the world of motion
coalesce, the inconsistencies will not disappear, thereby
showing that their origin was merely in the treatment.
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Recapitulation. £ 23
not in the fact ; that they came from the particular plan
adopted of writing about the subject and are not in-
herent in the arguments themselves.
The king in the first part was supposed to have all the
material problems of existence solved. There was a com-
plete mechanism of nature, He took up the problem of
the sentient life. But this problem can only artificially
be separated from that of the material world. The gap
between our sensations and matter can never be bridged,
because they are really identical.
Let us then allow this separation to fall aside. Let
us suppose the king to have all the reins of power in his
own hands. Let us moreover suppose that he imparts
his rays to the inhabitants so that they have each a por-
tion of his power. And let us suppose that the inhabi-
tants have arrived at a state of knowledge about their
external world corresponding to that which we have
about the world which we know.
Let us listen to a conversation between two of them.
A. The energy of the whole state of things is running
down.
B. How do you prove that r
A. Whenever any motion of masses takes place a
certain portion of the energy passes irrecoverably into
the form of heat, and it is not possible to make so large
a movement with those same masses as before, do all
that is possible to obtain the energy back again from
the heat into which it has passed,
B. Well, what about the heat ? Energy in the form
of the motions of the masses passes off into the energy
of heat. But what is heat ?
A. It is the motion of the finer particles of matter.
B. Well, 1 would put forward this proposal. We
have by observation got hold of a certain principle that
where any movement takes place some of the energy
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1 24 Recapitulation.
goes in working on the finer particles of matter. Let us
now take this principle as a universal one of motion,
and apply it to the motions of the finer particles of
matter themselves, which are simply movements of the
same kind as the movements of the larger ones. This
principle would show that these movements are only
possible inasmuch as they hand over a portion of their
energy to work on still finer matter.
A. Then you would have to go on to still finer matter.
B. Yes, and so on and on ; but to fix our thoughts,
suppose there is an ultimate fine matter which is the last
worked on. Now I say that we may either suppose that
this is being gradually worked on and all the energy is
dissipating, or else we may put it in this way. When
we regard so much energy we are apt to think that it is
the cause of the next manifestation in which it shows
itself. But this is really an assumption. Energy is a
purely formal conception, and all that we do is to trace
in the actions that go on a certain formal correspondence,
which we express by saying that the energy is constant.
A. Rut I feel my own energy.
B. Allow me to put your feeling to one side. If we
take then the conservation of energy to be merely a
formal principle, may we not look for the cause of the
movements in the invariable accompaniment of them,
namely, in the fact that a certain portion of the energy
is expended irrevocably on the finer portions of matter.
If now we take this ultimate medium which suffers the
expenditure of energy on it, may we not look on it as
the cause, and the setter in action of all the movements
that there are. By its submitting to be acted on in the
way in which it does submit, it determines all the actions
that go on. For what is all else than a great vibration, a
swinging to and fro. When we count it as energy, we
by reckoning it in a particular manner make it seem to
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Recapitulation. 125
be indestructible, but that the energy should be inde-
structible would be a consequence from the supposition
which we could very well make, that to produce a given
series of effects the submitting to be worked on of this
ultimate medium must be a minimum. If it were a
minimum no movements could neutralize one another
when once set going, for if they did there would be a
waste, of the submission of this ultimate medium,
A. But what do you suppose this ultimate medium
would be?
B. That I cannot tell, but we seem to have indications.
For the more fine the matter which we investigate, the
more its actions seem to annihilate distance : light and
electricity produce their effects with far greater rapidity
than do the movements of masses. We might suppose
that to this ultimate matter all parts were present in
their effects, so that anything emanating from the ulti-
mate matter would have the appearance of a system
comprehending everything,
A. But you have not got any evidence of an ultimate
matter.
B. No, all that we can think of is an endless series of
finer and and finer matter. But is that not an indication
rather, not that the direction of our thoughts is false, but
that there are other characteristics of this ultimate, so
that when looked at under the form of matter it can
only be expressed as an infinite series.
Let us omit the considerations brought forward in the
preceding conversation and examine more closely the
philosophy of the inhabitants of the valley in so far as it
corresponds with ours.
They laid great stress on a notion of vis viva, or what
we should term energy, but said it was gradually passing
away from the form of movements of large bodies to
that of movements of small bodies. So that in the
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T 26 Recapitulation.
course of time the whole valley would consist of nothing
but an evenly extended mass of matter moving only in its
small particles — and thjs motion of the small particles
they called heat. Now they had very clearly arrived
at the conviction that with every mechanical motion
there was a certain transference of vis viva to the
smaller particles of matter, so that it did not appear
again as mechanical motion. But they did not accept
this as a principle to work by. They did not consider
that the motions of the smaller particles of matter were
just the same as those of the larger masses. They did
not see that if a condition held universally for the move-
ments of the visible world, it must also hold for the
smaller motions which they experienced as heat. So
the conclusion which they should logically have come to
that there was a transference of vis viva on and on was
not held. But the step was a very little one for them to
take from regarding an invariable condition as always
there to regarding it as a cause. For the causes they
assigned were all purely formal relations, and only got
to assume an appearance of effective causes by familiarity
with them, and a throwing over them of that feeling of
effectiveness which they derived from the contact which
they had with the king.
They might have reasoned. This universal condition
of anything happening must be the cause. Energy goes
from a higher to a lower level. That which causes the
difference of level is the cause, and the cause of the dif-
ference of level must be that which invariably accom-
panies such a transference of energy from a higher to a
lower level. Now this invariable condition is the passing
of a portion of the energy into the form of motions of
the finer parts of matter. Hence there is an apparently
endless series. But to reaJize the matter, suppose an
ultimate medium, suppose there is a kind of matter of
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Recapiiulatton. 127
infinite fineness distributed everywhere wiiich let itself
be worlced on, and so determines differences and wakens
the sleeping world. What are the qualities of this fine
matter ? We see them in the properties of the finer
kind of matter which we know, such as light, electricity.
The property of the finer kind of matter is in general
that it tends to bring distant places together, so that a
change in one part is rapidly communicated to every
other part. If they followed this indication they would
have supposed that the ultimate fine matter was of such
a nature as to make all parts of the valley as one, so that
there was no distance, and any determination of a differ-
ence of level on the part of this ultimate matter would
have reference to all the conditions everywhere. It
would be in immediate contact vifith every part, so that
anything springing therefrom would present the appear-
ance of a system having regard to the whole. Now if
they had imagined such an ultimate medium doing that
which to them would seem bearing rather than exerting
force, suffering rather than acting, they would not have
been far from a true conception of the king who directed
them all. For he himself by reason of his very omni-
presence could not be seen by them. There was
nothing for them to distinguish him by. But they could
have discovered somewhat of the means fay which he
acted on them, which can only be described from the
appearances they present to the creatures whom the
king calls into life.
But of truth they would have had another and perhaps
a truer apprehension of the king in a different way. For
when he acted on them so that they took one course
ratlier than another, it was his action in themselves that
they felt. If they were mere pleasure-led creatures then
they were shaped outwardly, but if in their inner souls
he acted and through them suffered, then they were true
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128 Recapitulation.
personalities conscious of being true selves, the oneness
of all of them lying in the king, but each spontaneous in
himself and absolute will, not to be merged in any other.
Thus they had two modes of access to the king, one
through their own selves where he had made them exist,
one through the outer world. And in the outer world it
was but a direction in which they could look. They
could never behold the personality of the king, but only
an infinite series of different kinds of matter, one sup-
porting the other as it were and underlying it, but doing
more also than this, for in proportion as they "considered
the kinds of matter that laydeeper they found that distant
became near, absent, present, that time gave no longer
such distinctions, but from the phenomenal side they
seemed by a gradual diminution of the limitations of
experience to arrive at an external presentation of that
absolute which exists in the fulness of things, which they
knew more immediately in themselves when they truly
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INTRODUCTION.
SN the next two or three of these papers certain
questions connected with the subject of a
space higher than our own will be treated,
is well, therefore, first to recede and to
form definite conceptions about a world of plane space,
about a world in which the beings can only move in two
independent directions. Then, proceeding thonce to our
own world, we may gain the means of passing on to a
higher world. And I should have wished to be able to
refer the reader altogether to that ingenious work, " Flat-
land." But on turning over its pages again, I find that
the author has used his rare talent for a purpose' foreign
to the intent of our work. For evidently the physical
conditions of life on the plane have not been his main
object. He has used them as a setting wherein to place
his satire and his lessons. But we wish, in the first
place, to know the physical facts.
With this aim it is necessary to form a clear idea of
what matter would be in a world of two dimensions, and
the following illustration is a convenient one.
Place on the smooth surface of a table a half-crown
piece, and suppose it to slide on the table perfectly
freely. Imagine it to exercise an attractive force along
the surface of the table in all directions round itself
By it and near it place a sixpence, and let the sixpence
also slide freely on the table. It will, however, not be
9
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1 30 InlroducHon.
so free to move equally in all directions as the half-
crown was, for it will be attracted by the half-crown. It
will slip over the surface of the table under the influence
of this supposed force, and will come into contact with
the half-crown. Now if we suppose that both the half-
crown and the sixpence are very thin, that they are both
of them only the thickness of the ultimate particles of
matter, then we shall have a representation of what
material bodies will be in a plane world.
We must suppose that the particles cannot lift them-
selves or be lifted up from the plane so as to lie upon
each other. Under no circumstances can they quit the
surface of the plane.
Moreover, at no point must the particles adhere to the
plane, nor must there be any friction impeding their
movements over it. The only purpose which the sup-
port serves is to lf:eep them on the same level surface
and to convey influences from one particle to another.
The gravity which we know, and which acts at right
angles to the table on which the coins rest, will not
have any effect on the particles in their motions on the
plane, but will simply keep them to the plane. Any
force of attraction which concerns their motions proceeds
from one particle to another. Thus, conceive the half-
crown to be a very large disk of matter, and the six-
pence to be a sentient being. This being would feel a
force of attraction towards the centre of the half-crown,
and this force of attraction would keep him to the rim
of the half-crown. If he weighed anything it would be
by balancing it with his weight against the force which
tended to pull it to the centre of the half-crown. He
would not feel the gravity which keeps hira against the
surface of the table ; he would not know that there was
a hard, smooth surface on which he rested. He would
always have been in contact with it, and so he could not
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Introduction. 131
tell what it would be like to be free from it. He would
have no contrast whereby to apprehend its effect on him.
Moreover, he would only know of movements in di-
rections along the plane. He would not conceive that
such a thing was possible as movement in another
direction than to and fro, hither and thither on the
plane. It is difficult to suppose that a being would be
supported on one side by a plane, and not be in contact
with anything on the other side, even atmosphere. - Yet
if we suppose a being of real matter free to move on the
plane, this is what must be conceived. If the sixpence is
conceived as such a being, it must receive its impressions
through its rim. The rim represents its skin.
And if it be supposed to be surrounded by air for its
respiration, this air must not be able, any more than the
particles of solid matter, to rise away from the plane.
The plane being must be conceived to have a different
air to that which we know. The particles of its air,
however free to move amongst themselves, must not
have the power of moving away from the surface of the
plane, as if so they would be able to pass to the interior
of the body without passing through the skin. Any
passage leading to the interior of the body would have
to terminate in an opening in the rim, otherwise it would
be completely shut up from the exterior.
Now it is obvious that if the table is struck so that it
quivers, this movement will be communicated to the
coins lying on it. Either the coins as a whole will
move, or their particles will be disturbed.
Again, if we suppose there to be some particles loosely
cohering together, lying on a smooth sheet of iron, it is
evident that the quivering and jostHng of the iron, if it is
struck, would have an effect on the particles, and may
cause the breaking up of the thin masses in which the
particles cohere. Thus, if the material of which the
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132
Introduction.
sheet is composed be very dense and rigid, compared
to the substances lying on it, they may undergo many
alterations, being broken up and coming together again,
while the supporting matter which bears them all up
simply moves and vibrates.
It is evident that just as the particles are affected by
PAPER
the vibration and shaking of the sheet of metal on which
we suppose them, so they might in turn possibly affect the
sheet of metal and cause vibrations and shakings in it.
These shakings and vibrations would go forth from a
particle which excited them in every direction along
the sheet. They would not pass out into the air^ except
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Introdticiion. 133
secondarily and in a very minute degree. The shake
would be transmitted in the sheet. And the effect on
neighbouring particles would be great, on more distant
particles it would be less, and on those at a great dis-
tance barely perceptible.
The following is a good plan for obtaining in a defi-
nite way the feeling of what existence in a plane would
be like ; it enables us to realize the conditions in such
a way as to lay the basis for subsequent thought.
Let the reader take a sheet of note-paper and hold it
before himself edgewise, so that he sees it with one eye
aa a single line. And let him hold it so that this line
runs downwards from his eyebrows to his mouth, as
shown in Diagram I. Now on this sheet of paper, on
one side of it, let a straight line be drawn running across
it, away from the observer. Suppose all below this lino
to be a thin layer of particles which, keeping compactly
together, form a solid sheet of particles, every one of
which touches the paper. This would be the solid earth
to a being in the plane world.
Let the surface of the paper above this be covered
by a layer of particles which move freely amongst each
other, but which do not rise from the surface of the
paper. These particles form the air of such a world.
On the surface of the earth draw a line standing up-
right. Let this line represent a man. Another line will
represent a wall which the man could not pass except
by getting over it.
It will be found that the objects on the paper are felt
to be subject to the action of gravity. The question will
occur, Why will not this thin layer of particles slip off
the paper ?
Now, the sense of gravity must not be got rid of, but
it must be connected with the matter in the sheet of
paper.
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1 34 Introduction.
Suppose, then, that the sheet were to grow bigger and
bigger till it filled out reaching through the whole world
and cutting the globe in two. Then let all the earth be
removed except a thin layer on one side of this enlarged
sheet of paper. This thin layer will be the only portion
of matter left. And such a thin layer will represent a
plane world. The force of gravity must be conceived as
remaining, but as coming from a large and thin disk.
Now to keep this thin layer on the paper it would be
necessary to have some force acting sideways, so as to
keep the particles to the paper.
And the paper itself may be conceived to exercise
such a force : it is many particles thick, while the thin
layer of matter is only one particle thick, and thus it
will keep the layer of matter, which covers one side of
it, in its place by virtue of its own attraction.
We suppose that the paper exerts an attractive force
which keeps the thin layer of matter to it. This attrac-
tive force is not felt by the sentient beings on the paper,
nor does it influence the movements of the particles of
matter amongst themselves. We also suppose another
attractive force proceeding from particle to particle
of the matter on the plane. This would be felt by the
heings and produce movements of matter.
Thus the conception of a plane world necessarily
involves that of something on which it is.
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!lam mtmib.
I ^iyflwr^ HERE the sun's rays grazing the earth in
■ hShII January pass off and merg-e into darkness lies
&jLyu|| a strange world.
mA^t^^ 'Tis a vast bubble blown in a substance
something like glass, but harder far and untransparent.
And just as a bubble blown by us consists of a dis-
tended film, so this bubble, vast beyond comparison,
consists of a film distended and coherent.
On its surface in the course of ages has fallen a thin
layer of space dust, and so smooth is this surface that the
dust slips over it to and fro and forms densities and
clusters as its own attractions and movements determine.
The dust is kept on the polished surface by the
attraction of the vast film; but, except for that, it moves
on it freely in every direction.
And here and there are condensations wherein have
fallen together numbers of these floating masses, and
where the dust condensing for ages has formed vast disks.
And these disks are glowing hot^yct no light comes
from them into our universe.
For this world lies beyond the JEther — far beyond. And
however hot or glowing the masses are, if there is no
medium to transmit the vibrations of heat the influence
cannot travel.
Thus the only directions in which the heat can travel
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136 A Plane World.
are on the film. From each of these glowing disks the
luminous influence streams forth carried by the vibrations
of the film which supports everything. For the heat and
intense agitation of these glowing disks shakes and dis-
turbs the bubble, and just as a thin soap bubble quivers
and shakes, so this film quivers and shakes. And so
elastic is it, and so rigid, that it carries the light and heat
to all surrounding regions. Yet so vast is the bubble, so
tremendous in its dimensions, that the agitation from
these glowing disks travels almost in straight lines, till,
spreading out on every side, it merges into darkness-
like the ripples in the centre of a vast calm lake gradually
become indistinguishable.
And round these central orbs of fire — for orbs of fire
they are, though they only transmit their fire along the
film of the bubble — round these orbs pass in due order
and succession other disks, which, cold or warm, have not
that energy of light and heat which the central orbs
possess.
These disks, though large, are so immeasurably small
compared with the vast surface of the all-supporting
bubble, that their movements seem to lie on a plane flat
surface; the curving of the film on which they rest is so
slight compared to their magnitude, that they sail round
and round their central fires as on a perfect level
surface.
And one of these orbs is fitted by nature to be the
habitation and home of living beings. For it is neither
so hot as it was for long ages after it had condensed from
the film of dust wherefrom all orbs are made, nor has it
so cooled down as to render life unsupportable.
And, moreover, it is full of vast crevices and channels,
for in many places the interior in cooling after the rim
had set from its molten condition has left long caverns
and passages, not only in one layer, but in many.
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A Plane World. 137
And on the rim artd in these passages and caverns
live the inhabitants of whom I speak.
They do not rise from the surface of the film, but as
all matter lies on the smooth surface but one particle
deep, so their, bodies formed out of matter lie, as we
should say, on this smooth surface.
Yet of this they know nothing. They say that they
stand and walk.
For this orb has an attractive force.
By that very same impulse of coming together whereby
it gathered its particles out of the dust on the bubble,
by that very same force it draws towards its centre ail
Diagram II;-
that is near it or on it. Thus " up" is to these inhabi-
tants a movement from the centre of the disk on the rim
of which they live and away from it. " Down" is a move-
ment from the rim towards the centre. The thin layer
which forms the mass of the disk is their solid matter.
They are not able even in thought to rise away from the
surface of the bubble, and look from space upon their
mode of existence. They ever pass to and fro upon a
line, upon a rim ; and no two can walk except after one
another. If you look at the rude 'picture you will see
that the two beings represented by two triangles cannot
pass one another if they are unable to lift themselves up
from lying on the surface of the paper. The surface of
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13S A Plane World.
the paper represents the surface of the bubble, and sliding
freely on it, but unable to lift up from it, are tenuous
shapes that are the inhabitants, and that thin layer of
particles that is to them solid matter.
B y^ Now were it not
^ . .::r^-- ; ■ -""-^tv,; -. ., ^ for the fact that the
_.--.'.-'-'" "■■£ orb is reft into these
o'' chasms and pas-
showing a disk BD lying on it, and a creatnr. SageS,the onlymOVe-
'S^u'"'=^''^'i,?,?*'*'"^ ■ ■ ,S?'1-^'*,°B°'' tnent that these
Qf Ihe filni, BD is a section of the disk, AB is
a section of ihp creature. THe thickness is beings would have
enormously magnified and also the height AB ij u r „
of the crmlnrl compared with the dfameler WOuld be of pass-
BD of the disk. The attmction which ABfeeh ;„„ ^OUnd and round
keeps him to BD ; both AB and BD, the being ^
and the disk, slide freely on the film CE on the rim of their
without knowing of its existence. , ,
world.
Many words that we have, to them could bear no
meaning. Thus "right and left " is to them unknown.
For consider their faces bent in one direction along the
rim. In following this direction, they go forward, in
retracting from it they go backward. If they go away
from the centre they go up, towards the centre is down.
And by no means can they turn, raising themselves from
the surface whereon they are. They do not even know
that they have two sides ; their movements, thoughts, and
imaginations are all confined to that surface on which
they are. This they call their space, their universe;
nor does aught that lies beyond it, towards the interior
of the bubble or away from it, directed outwards, come
into their thoughts, even as an imaginary possibility of
existence.
Life is extremely limited on such a world. To take a
single instance, in order for two beings to pass each other,
a complicated arrangement is necessary, shown in Dia-
gram IV.
At intervals along the rim recesses and chambers are
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A Plane World.
139
constructed. Near the openings of these chambers lay
movable plates or rods. When two beings wish to pass,
one of them descends into the recess; the other one
pushes the rod
so as to form a
bridge over the
opening, walks
across it, and
then removes
the plate
that the one who has descended can get up and go on
his way.
If by any chance, while a being is in the recess, the
plate or rod which acts as a bridge gets fixed, he is in a
dangerous predicament. For suppose a being confined
as shown. If he, suffering from want of air, cuts through
the roof at AE, the whole part to the right of AB comes
tumbling down. For its only support Is severed when
AB is cut through. It is impossible to make a hole
which is not the whole width of matter as it lies on the
surface. And with
regard to this all con-
structions have to be
made. There cannot
be two openings in a
wall of a house, un-
less when the one is
open the other is so
fashioned as closing
_ to act as a rigid sup-
port to the wall.
A
liagram V. —A house .
which now depends for its upholding entirely on it.
Thus, in the diagram, the house is held up entirely by
the side opposite to the doorway EF, which is now open.
The roof is supported by the side CD. If an opening
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140 A Plane World.
AB be.made in the wall CD before the doorway EF is
closed, the roof will fall in. So, in order to pass through
the house, EF must be firmly shut up before AB is
opened. The houses are always built in the interior
passages so as to leave the rira of the disk free for
locomotion.
And there are many things to be said of the inhabitants
on this disk with respect to their social and political life.
It is hardly necessary for me to put down much about it
here, for any one by using the method of the historian
Buckle, and deducing the character of a people from
their geographical influences and physical surroundings,
could declare what the main features of their life and
history must be.
But one or two remarks may be made here. First of
all they are characterized by what I may venture to call
a crude kind of polarity.
In dwellers in our world this polarity, which shows
itself amongst other ways in the distinction of sexes, is
tempered and modified.
In every man there is something of a woman, and in
every woman there are some of the best qualities of a
man.
But in the world of which we speak there is no phy-
sical possibility for such interfusion. In a linear exist-
ence there would be no consciousness of polarity. It
makes its appearance first in the plane, and in a hard
and unmitigated form.
It is impossible to do otherwise than caricature these
beings when we write of them thus ih brief. So let us
accept the matter frankly, and, without scruple, look at
them in the broadest possible manner.
If the reader will cut out the triangles in the corners
of the two next pages he will obtain four plane beings,
two of which are men, two of which arc women. The
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DiEigtcim VII.
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A Plane World. 145
lines down which the cutting is to be made are marked
with a black Une. Now having cut out two men, whom
we will call Homo and Vir, draw a line on a piece of
paper to represent the rim of the world on which they
stand, and, remembering that they cannot slide over each
other, move them about. It must be remembered that
the figures cannot leave the plane on which they are put.
They must not be turned over. The only way in which
they can pass each other is by one climbing over the
other's head. They can go forwards or backwards.
Much can be noticed from an inspection of these figures.
Of course it is only symbolica! in the rudest way, but in
their whole life the facts which can be noticed in these
simple figures are buiit up and organized into compli-
cated arrangements.
It is evident that the sharp point of one man is always
running into another man's sensitive or soft edge. Each
man is in continual apprehension of every other man :
not only does each fear each, but their sensitive edges —
those on which they are receptive of all except the
roughest impressions — arc turned away from each other.
On the sensitive edge is the face and all the means of
expression of feeling. The other edge is covered with
a horny thickening of the skin, which at the sharp point
becomes very dense and as hard as iron. It will be
evident, on moving the figures about that no two men
could naturally come face to face with each other.
In this land no such thing as friendship or familiar
intercourse between man and man is possible. The
very name of it is ridiculous to them. For the only
way in which one man can turn his sensitive edge to
another man is if one of them will consent to stand on
his head. Fathers hold their male children in this way
when little, but the first symptom of manhood is con-
nected with a resentment against this treatment.
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146 A Plane World.
If now two women, Muiicr and Femina, be looked at,
the same relation will be seen to hold good between
them. By their nature they are predisposed, bj;- accident,
to injure one another, and their impressionable sides are,
by the very conditions of their being, turned away from
each other.
If now, however, Homo and Mulier be placed together,
a very different relationship manifests itself They can-
not injure one another, and each is framed for the most
delightful converse with the other. Nothing can be
more secure from the outside world than a pair of ap-
proximately the same height ; each protects the sensitive
edge of each, and their armoured edges and means of
offence are turned against all comers, either in one direc-
tion or the other. But, if the pair, through a mutual
misunderstanding, happen to be disadjusted, and, their
feet on the rim, turn their sharpnesses against one another,
they are absolutely exposed to the harms and arrows of
the world.
Still, even in this case they cannot wound one another
■ — -a happy immunity.
In the annals of this race which I have by me I find a
curious history, which, unintelligible for ages to them,
admits by us of a simple explanation.
It is said that two beings, the most ideally perfect
Vir and Mulier, were once living in a state of most
perfect happiness, when, owing to certain abstruse studies
of the Mulier, she was suddenly, in all outward respects,
turned irremediably into a man. Vir recognized her
as the same true Mulier. But she occupied the same
position with regard to him which any other man would.
It was only by standing on his head that he could, with
his sensitive edge, approach her sensitive edge. She
refused to explain how it was, or impart her secret to
any one, but she had, she said, undergone a great peril.
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A Plane World. 147
She manifested a atrange knowledge of the internal
anatomy of the race, and most of their medical know-
ledge dates from her. But no persuasion would induce
her to reveal her secret ; all the privacy of existence
would be gone, she said, if she revealed it She
was supposed to have acquired some magical know-
ledge.
This possession, however, did not make either of them
happy, and one day, with fear, she said that she would
either die or be restored to the outward semblance of
her sex.
She disappeared — absolutely ; although she was sur-
rounded by her friends, she absolutely vanished. And
had it not been that some days afterwards, cutting
through the solid rock for the purposes of some excava-
tions, they accidentally came on a chasm, they would
never have found her alive again. For she was found in
a cavity in the living rock, warm and beautiful — her old
self again.
Her secret died with her.
From our point of view it is easy to see what had
happened. If the figure Mulier be taken up and turned
over it will be easy to see that, though still a woman,
her configuration has become that of a man. To all
intents and purposes she is a man. She is rendered
incapable of that attitude which is the natural one
between the men and women in this land, and the
happy relationship between her and Vir is neces-
sarily and entirely broken off. Move about as you
will, keeping her figure turned thus on the plane, you
will not be able to make her a fitting helpmate for her
unfortunate Vir. She must have discovered the secret
of raising herself off the surface, and by some accident
been turned over. Perhaps she had used this new posi-
tion to study anatomy — for to an observer thus situated
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148 A Plane World.
the interior of every body would He perfectly open — and
in prosecuting her studies had overbalanced herself,
I have only mentioned this anecdote, however, for the
sake of a curious observation which was made at the
time. It was found that when she was in this trans-
formed condition she was absolutely without atmosphere.
To explain : ordinarily, apart from anything she said or
did, there was a kind of influence proceeding from her
which made her presence agreeable to Vir. When she
was turned over she lost this. Now the explanation of
this is obvious. To these people light is the agitation
of the surface of the bubble; transparent objects are
those which do not hinder this agitation in its course.
But most bodies and the physical frame of the inhabi-
tants amongst them were not transparent, but stopped
and reflected these agitations of the film, thus sending
off from their outer edge those vibrations which excited
sight in their fellows. But besides these vibrations of
light there were iiner ones still which were not damped or
deflected by the outer edge of the body, but came
through the greater part of their frame as if it was
transparent. In the interior, however, of their organiza-
tions there were certain regions which did arrest these
.subtler vibrations, and which had (as the eye of light)
the power of appreciating them. In connection with
these regions there were certain structures, extremely
minute, which had the converse power of agitating the
film, and so sending forth through the periphery of the
body these same minute vibrations. These organs were
not of any use, but they formed a sort of means of sym-
pathetic communication between the inhabitants, acting
in no very defined way, but certainly producing a sensa-
tion of a vague kind. Now when Mulier was turned in
the way described, the relation of her frame to the film
of the bubble was disarranged, and it was no wonder
that this " atmosphere " disappeared.
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A Plane World. 149
In many respects the inhabitants of this world are far
more advanced than we are, having a simpler problem —
how to deal with matter in one plane—they have advanced
more nearly to a complete knowledge of its properties.
Yet great as their knowledge is, their performance is
smal!. If you but reflect on one single fact, you will see
how limited all their efforts must be. They cannot fix
the centre of a wheel, so that it rotates
round an axis. For consider a wheel
-—a small disk lying on their plane.
The centre on every part of it/
touches the surface of the bubble on
which all things slide freely. To fix
this point they would have to drive
down into the film— a thing which
they cannot do, and which they are
far from even imagining.
If they make an opening in the
disk they can arrive at the centre of
it. But then the rod of matter which
they put in will prevent the disk «s1™pproachTo a wtect
from revolving.
The nearest approach to a wheel with a fixed centre
which they can attain is shown in Diagram VIII., a por-
tion of a circular disk which oscillates about the smooth
end of a rod built into the substance of the cut-away disk.
Their carts
are shown in the
■ ^ O C^ i) '
iccompanymg
Diagram IX,-A can. ^^^^^ They are
simply rods placed on rollers: as the rod is pulled
along, the rollers turn, and the rod slides along —
just as a boat does on the rollers whereby sailors help
themselves in hauling it up the beach. As soon as
these rollers roll from under the rod, as it goes on in its
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150 A Plane World.
forward motion, they have to be secured, and then lifted
over the cart and put down in front. Thus there are to
each cart a set of httle disks or rollers, and, as the cart
goes on, these rollers have to be lifted over the cart from
the back to the front.
There is no means by which this can be made a
continuous action. Each roller has to be waited for,
lifted separately, and carried over separately. And to
put it down in front, the rope by which the cart is dragged
along has to be unfastened and fastened up again.
Looking at the Diagram IX. it will be seen that there
is a hollow in the body of the cart. On the part A E
the driver sits. In the hollow from B to C is put the
load. The load cannot then slip out over the ends oP
the cart. There is nothing in the cart to prevent it from
falling out sideways.
But the contents, as the whole body of the cart, arc
kept to the smooth surface of the bubble, and are thus
supported by it on the side remote from the reader's eye,
and also are kept from rising away from this surface
by the force of attraction exerted by the film.
Thus the surface of the bubble and its attractive force
supply the other two sides of the cart.
But of these two sides, the beings are ignorant, and it
seems to them perfectly natural that loads of any kind,
even of fluids, should be kept securely in a cart with two
ends.
The method by which the rope is fastened to the cart
ft is this : C is the body
of the cart ; R is the
rope ending in a
wooden step B ; A ii
[ram X.— How n rope is fj.^ed 10 a cart, an obloUg piece of
wood. When the rope has to be taken out, A is lifted out
by its handle, B is slipped back and taken out of the recess
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A Plane World. 151
in C, and then the rope is free from the cart. And in a
similar way it is secured a^ain.
One very ordinary way of driving machinery with lis
is by shafting. A long rod is driven round arid carries
wheels at different places along its length. Now with
these inhabitants it was impossible to do this, because
the twisting motion round a rod could not be imparted
without going out of the thin layer in which they were.
Their methods of transmitting motion were by long rods,
by a succession of short rods, by pendulums attached to
one another, or finally by wheels which drove one another,
but which were held by smooth sockets fitting round the
rim far enough to steady them, but not so far as to
hinder them from touching each other.
As to their science, the best plan is to give a short
account of its rise.
They discovered that they were on a disk rotating
round an inner centre, and also proceeding in a path
round the source of light and heat.
They found that they were held in their path by a
force of attraction. But this attractive force was not
with them as it is with us. With us, since the effect
which any particle has on the surrounding particles
spreads out in our space if the distance is doubled from
a centre of attraction, the force it exercises becomes one-
quarter of what it was when at the less distance.
With them, however, when the distance doubled, the
force of attraction became only one-half of what it was
at the less distance. For the light, or attraction, or
force of any kind emanating from a particle, only spreads
along the filmj and does not pass out into the space above
or beneath. If they had been on a thick globe instead
of a bubble, the laws of attraction would have been -the
same as with us. But the bubble on which they were
was thin compared with the paths along which the radiant
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152 A Plane World.
foi'ces spread forth. And thus every force being kept
to one plane diminished as the distance from the centre
of !ts action. I
Now it was a great problem with them how the light
came from the central orb. Their atmosphere, they
knew, extended but a small distance above the surface of
their disk. And it was quite incapable, moreover, of con-
veying vibrations such as those of light and heat.
By studying the nature of light they became convinced
that to transmit it there must be a medium of extreme
rigidity between them and the great source of light.
It is easy enough to sec that what they thought was a
medium between them and their sun was in reality the
rigid surface on which they rested. This elastic film
vibrated in a direction transverse to the layer they
called matter, and carried the particles of matter with it.
But they, having no idea but that the surface on which
they were was the whole of space, thought that space
must be filled with a rigid medium. They found that
the vibrations of the medium were at right angles to the
direction in which a ray was propagated. But they did
not conceive of a motion at right angles to their plane ;
they thought it must be in their plane.
It was a puzzle to them how their disk glided with so
little friction through this medium. They concluded
it was infinitely rare. They were still more puzzled
when they had reason to believe it was an opaque sub-
stance; and yet that it could be anything else than a
medium which filled their space was inconceivable to
them. They could never get rid of it from a vacuum,
however perfect. Indeed we see that in producing a
vacuum they merely cleaned the surface on which they
were.
In one respect it might have been advantageous if
■ See Appendix.
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A Plane World. 153
they had known, for, their law of attraction beJn^ what it
was, their movement round their sun was not destined
to go on for ever ; but they were gradually falling nearer
and nearer. Now, if only they had made the attempt,
they might by some means have got a hold on the sur-
face on which they were, and, by means of a keel which
tended to furrow it, have guided their world and them-
selves in their path round their sun. Indeed, it is possible
to imagine them navigating themselves whither they
would through their universe —that is, on the surface of
their bubble.
It was also unfortunate in another respect that they
did not realize the fact of the supporting surface, for the
feeling which they came to have of being suspended in
space, absolutely isolated, wa.s a very unsettling one, and
tended to cause in them a certain lack of the feeling of
solidarity with the rest of the universe.
We have seen that their laws of mechanics were very
different from ours. But they had after all an experi-
ence of our mechanical principles, though in a curious
way. In all motions of any magnitude moving bodies
were confined to the surface of the plane. But where the
small particles were concerned there was more liberty of
motion. The small particles were free in their move-
ment ; although they could not go more than a very small
distance away from the film on which they rested, still
they were capable of motion perpendicular to it. Thus a
long line of particles connected together could rotate as
a whole, keeping straight lilce a twisting wire, and by
means of many strings of particles thus connected,
movements could be transmitted in a way which was
totally unlike the mechanical movements to be seen in
the case of large masses.
This motion of rotation round an axis lying in the
plane was to them what electricity is tons. It was quite
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154 ^ Plane World.
a mysterious force. But it was extremely useful in its
applications. Having no idea of a rotation which hi
taking place went out of their surface, they could not
conceive a reason for the results of such movements.
It can easily be seen how many kinds of forces they
could have. There was the spinning motion of the small
particles on the surface. This they were aware of— it
produced .many appearances, but it was not fitted for
transmission across great distances, as each particle was
apt to be hindered in its rotation by its neighbour.
Sometimes, however, when conditions were favourable,
many of these rotations were harmonious, and waves
were produced in their matter resembling the waves in
our ocean.
There were only two other kinds of motion. One was
an up and down vibration of the film carrying matter
with it ; the other was the twisting of strings of particles
which were rigidly connected together. The up and
down motion of the film was to them light. Those
kinds of matter which did not hinder this motion were
said to be transparent; those kinds which, lying on the
film, hindered the motion or threw it back were said to
be opaque.
The twisting motion round an axis was to them what
electricity is to us. And when this twisting motion in
one direction or another was conveyed to the particles
of small masses which were free to move, many curious
etfects were produced analogous to the movements of
electrified bodies. There are obviously no other rota-
tions or vibrations possible ; hence in that world there is
nothing corresponding to magnetism. Their light was
simple, and could not be split into two kinds as our light
can be — ^into two kinds of polarized light.
Was there no sign, then, by which the inhabitants of
this world could gain a knowledge of their own limita-
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A Plane World. 155
tion ? There was. There was both a sign and the inter-
pretation of it lying before them. They knew that they
could have two triangles precisely similar, and yet such
as could not be turned the one into the other by any
movement in the plane. How two, things could be so
alike, and yet differ in some mysterious way, was to them
a puzzle. As an instance of such triangles may be
taken those used in Diagram VL to represent the man
and the woman. They may be exactly equal, yet the
beings in a plane world cannot turn them so that one
would coincide with the other.
Yet had they but considered the case of a being
lower in the scale of space existence than themselves,
they would have seen the answer to their riddle.
For consider a being confined altogether to a line
c E' A' M A M c. ^^^ ^ be the being, and
let him observe the three points ABC, and let him
form an idea of them and their positions with regard to
each other, which he measures by the distance he has
to travel to reach one after passing the other.
Let him also become aware of the three points A' B'
C, forming a precisely similar set on the other side of
him.
It may be objected that the being in the line could
not conceive any point lying beyond A, but that his
experience would be limited to the points A and A'. If
A and A' are material particles this would be the case,
but we may suppose them to be places in the line
marked out by cold and heat, or some such means.
Then a being could conceive a series of positions in his
space such as A, B and C, A', B', C.
If now he remembers each set, and thinks about them,
he finds that they are alike in every respect. But he
cannot make them coincide with each other. For if he
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156 A Plane World.
pushes the set A B C along the line, when A B and
A' B' are together C is just where it ought not to be. It
is not on C. And if he gets C on C, then A B has gone
far away.
He would neither be able to make them coincide nor
to conceive their coincidence.
There would be no movement within the realm of his
experience which would make them coincide.
Yet the dweller in a plane world could easily make
these sets of points coincide, for he would bend the
whole line round in his plane so that A coming on A',
B should come on B', and C on C. There would be no
difficulty to him in doing this. And he does it in virtue
of there being to him a movement possible which is not
possible to the being in the line. He has a liberty of
motion unknown to the linear being.
And now why should he not reason thus, " Something
which to the linear being is inconceivable, to me is con-
ceivable. Then may not things inconceivable to me be
yet possible .' May it not be possible, that two triangles
which are like one another, but yet which cannot be
thought by me as coinciding — may not these triangles
be able to be made coincident " ?
In this simple fact of his perpetual observation was
really the proof of the whole matter if he had but looked
at St, the sign manual of his limitation, the promise of
his liberation from it in thought, the key to the explana-
tion of the mysterious minute actions by which he was
surrounded, and perchance a help to the comprehension
of a higher life.
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APPENDIX.
Bin our world a particle of matter which sends
forth influence on the surrounding matter
I doeij not send its radiant energy off along a
I plane, but from the particle all the influence
spreads out into space. And the most convenient in-
stance in our world to consider is that of a luminous
point from which rays spread out in every direction.
Let M in Diagram XL be such a point — a particle of
Diagram XI.— Patlkles in space and in a piane cjccrting force.
matter sending forth luminous rays in our three-dimen-
sional space.
Instead of studying how these rays spread out in every
way all around M, let us only consider tho.se which, pas.s-
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158 A Plane World.
ing out from M, fall on the square A B C D. A B C D
casts a shadow, and this shadow extends, and is found to
be bigger the further off from M it is measured. Suppose,
at the distance from M, M E, wc put a square in the path
of the shadow so as just to receive the shadow on it
exactly. Let E F G H be this square. As i.s shown
by the dotted lines, this square will be four times as
large as the square A B C D. So when the distance is
doubled, the shadow becomes four times as big.
Now those rays of light which fall on A B C D would,
if they were not interrupted by it, spread out so as to
exactly cover E F G H. Thus the same amount of
light which falls on the small square A B C D would, if
it were taken away, fall on the large square E F G H.
Now since the large square is four times the size of
the small square, and the same amount of rays fall on it
—for it only receives those which would fall on the small
square — ^there must be at any part of it an illumination
one-quarter as strong as there would be at any point on
the small square.
Thus the small square, if placed in its position, would
seem four times as bright as the large square.
Thus, when the distance from the origin of light i,-;
doubled, the amount of light received by a surface of
given area becomes one-fourth of what it was at the less
distance.
This is what is meant by varying inversely as the
square of the distance. When the distance is doubled
the intensity of the light is not simply less, but is halved
and ha4ved, and becomes one-quarter of its previous
intensity.
But in the case of a particle resting on a thin sheet of
metal, and shaking the metal — as, for instance, a metal
plate can be made to shake by a violin bow—then this
law would not hold.
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A Plane World. 159
Take the second figure. Let P be the particle, and
let the influence proceeding from it fall on the rod A B
lying on the plane, and let us suppose the rod to stop
the vibrations from going beyond it, to receive them and
to turn them back just as a body does the light. Then
the " shadow " of A B would spread out away from P ;
and if another rod E F were put in at the distance P E,
which is double of P A, then, to exactly fit the shadow,
it would have to be double the length of A B ; and the
vibrations which fell on A B would exactly fall on E F.
Now since E F is twice as long as A B, the vibrations
which fall on any part of it will be one-half as intense as
the vibrations which fall on a portion of matter of the
same size lying where A B lies.
Thus in a plane the influence or force sent out by any
particle would diminish as the distance. It would not
" vary inversely as the square of the distance," but would
"vary inversely as the distance."
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% "B'xdxm ai Qxxx ^Intkrse,
CHAPTER I.
BIT seems to mc that the subject of higher space
1 is becoming felt as serious, and fraught with
] much that is of the deepest interest, not only
' as a scientific problem, but in other ways also.
It seems also that when we commence to feel the
seriousness of any subject we partly lose our faculty of
dealing with it. The intellect seems to be overweighted
somehow, and clogged. Perhaps the suppositions we
make seem to us of too great importance, and we are
not willing enough to let them go, feairing to lose the
thing itself if we lose our hold of the means by which we
have first apprehended it.
But whatever may be the cause, it does seem un-
doubtedly the fact that the mind works more clearly
and more freely on subjects which are of slight im-
portance.
And I propose, that without ignoring the real im-
portance of the subject about which we are treating,
we should cast aside any tension from our minds, and
look at it in a light and easy manner.
With this object in view let us contemplate a certain
story which bears on our problem.
It is said that once in a certain region of Ireland
there took place a curious contest. For in Kilkenny
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i62 A Picture of Our Universe.
there were two cats so alike in si^e, vigour, determina-
tion, and prowess, that, fighting, they so clawed, scratched,
bit, and finally devoured each other, that nothing was
left of either of them save the tail.
Now, on reflecting on this story, it becomes obvious
that it originated when looking-glasses were first im-
ported into Ireland from Italy. For when an Irishman
sees for the first time anything new, he always describes
it in an unexpected and yet genial and interesting
manner. Moreover, we ail know what contentious fel-
lows they are, and how all their thoughts run on fight-
ing. And I think if we put this problem to ourselves,
how by bringing in fighting to describe a looking-glass,
we shall see that the story of the Kilkenny cats is the
only possible solution. For consider evidently how it
arose. Depositing his favourite shillaly in a corner, the
massively- built Irishman, to whom the possession was a
novelty, saw reflected in his looking-glass the image of
his favourite cat. With a scrutinizing eye he compared
the two. Point for point they were like. " Begorra if I
know which of the two would win ! " he ejaculates. The
combat becomes real to him, and the story of the Kil-
kenny cats is made.
Now, to our more sober mind, it is obvious that two
cats— two real material things—could not mutually an-
nihilate each other to such an extent. But it is perfectly
possible to make a model of the Kilkenny cats — to see
them fight, and to mark the issue.
And I propose to symbolize or represent the Kilkenny
cat by a twist. Take a pencil, and round it twist a strip
of paper — a flat .spill will do. Now, having fastened the
ends on to the pencil by two pins, so that it will not un-
twist, hold the paper thus twisted on the pencil at right
angles to the surface of a looking-glass : and in the look-
ing-glass you will see its image. In Diagram I., M repre-
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A Picture of Our Universe. 163
sents the mirror, and on the left hand is shown the twist,
on the right hand the image twist. Now take another
pencil and another piece of paper, and make a model of
what you see in the glass. You will be able to twist this
second piece of paper in a spiral round this second pencil
so that it is an exact copy of what you see in the glass.
Now put the two pencils together end to end, as they
would be if the first pencil were to approach the glass
until it touched it, meeting its image: you have the real
copy of the image instead of the image itself. Now pin
together the two ends of the pieces of paper, which are
near together, and you have your two Kilkenny cats
ready for the fray. To make them fight (remember that
the twists — not the paper itself, but the paper twisted —
represent the cat), hold firmly and pull the other ends (the
tail ends, so to speak), so as to let each twist exercise its
nature on the other.
You will see that the two twists mutually annihilate
each other. Without your unwrapping the paper the
twists both go, and nothing is left of them.
Now the image of the twist as a real thing was made
by us. It did not exist in nature other than as a mere
appearance.
But I want you to imagine this process of producing
a real image as somehow existing. I want you to lay
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164 A Picture of Our Universe.
aside for the present the question of how it could be
done, and to conceive twists and image twists.
This is the mechanical conception I wish you to adopt —
there are such things as twists. Suppose by some means
to every twist there is produced its image twist. These
two, the twist and its image, may exist separately ; but
suppose that whenever a twist is produced its image
twist is also produced, and that these two when put
together annihilate each other.
With this conception let us explore the domain of
those actions which are called electrical.
When a glass rod is rubbed with silk it becomes
excited, its state is different. It manifests many pro-
perties, such as that of attracting light bodies, giving off
a glow of light, &c. The silk also with which it was
rubbed manifests similar properties. It also attracts
light bodies, appears to glow in the dark, &c.
And yet there is a difference between the state of
excitement of the glass and of the silk. The electricity
which is in them is of different kinds. And If the
electricity of the silk and of the glass be brought together,
all electrical effect disappears ; they become glass and
silk in an ordinary condition.
It may seem strange that, if this is so, they should
become electrified when rubbed together. Yet this is
the case, and must be taken as a fact. It seems to
depend partly on the circumstance that glass and silk
are not what is called conductors. In a conductor, if
one part receives electricity, this electricity at once runs
over the whole of the conductor, whether it be an inch
!ong or many feet. And if any part of the conductor
be touched by another conductor which is in contact
with the earth, every trace of electricity leaves the con-
ductor, flowing, as it were, freely out of it.
Now both glass and silk do not let the electricity run
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A Picture of Our Universe. 165
from them so easily. To discharge a glass rod it has
practically to be touched in every part. Thus, when by
the rubbing with silk electricity is produced on it, it is
conceivable that this electricity should be kept to a
certain extent, and not combined immediately with the
electricity on the silk.
Besides, the same cause — the friction which produced
the electricity on the glass, and the other kind of elec-
tricity on the silk — would probably prevent their com-
bination as long as it was applied.
Now let us suppose that the electrical charge which
the glass has consists in this.
Let us suppose that the particles of the glass on the
surface of it are twisted, strained out of their natural
position, and twisted.
Let us also suppose that the particles of the silk are
twisted too, but let them have the image twist.
Now these two twists, the glass twist and the silk
twist, its image, when brought together, will run down.
In unwinding each other they will give off a certain
amount of energy, which will manifest itself as a spark,
make a crackling sound, and so on. But when they
unwind each other there is no more tension of the
particles.
This does not explain in the least why the glass
particles should receive a twist in one direction, the silk
particles a twist of the image kind.
But instead of inquiring into this, it is best to see if
this supposition is in accordance with other known facts
of electrical action ; because, if it is not, we may dismiss
it more easily than we could if we had to test it with
regard to the very inaccessible question of why some
bodies, when rubbed, get electritied in one way, others
in another.
When the glass and silk are near together the twist
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1 66 A Picture of Our Universe.
on the glass and that on the silk are related to each
other as twist and image twist, and there is no action on
surrounding bodies from either of them, as they, so to
speak, satisfy each other.
But when the glass rod and the silk are moved apart,
and brought near other objects, then each of them calls
up on those objects near which it is brought a twist of the
kind which is the image of its own twist.
If the glass rod is brought near a mass of metal,
which we will call a conductor, the following effect is ob-
served : — -The part of the conductor near the glass rod
becomes charged with electricity of the silk kind ; the
part of the conductor away from the rod becomes
charged with electricity of the glass kind.
Now lot us bring into play the supposition which wc
made before.
Let us suppose that there is some process in nature
which, when there is a twist, makes a real image of that
twist come into being. If we assume this process, wc
see that, opposite to the silk, on whatever objects are
near it, will be a twist of the glass kind, and opposite
the rod will be a twist of the silk kind. That is to
say, that oa the conductor there will be a twist of the
silk kind when the glass rod Is brought near it.
But there is nothing to make the particles of the
conductor twist as a whole. The glass rod is not sup-
posed to touch the conductor — it is simply brought near
it, and no actual communication takes place between
them. No force is actually applied to it, nor electricity
communicated to it. Hence, on the whole, the particles
of the conductor will not be twisted. That is to say,
since there is a twist of the glass kind on one end, there
will be at the other end a twist of the image kind — that
is, of the silk kind. And these two twists are like the
two twists on the pencil — if allowed to run together they
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A Picture of Our Universe. 167
will run each other out So if the conductor were re-
moved from the neighbourhood of the glass rod It would
be found to be no different from what it was at first It
would not be "charged."
Now this is what actually happens.
Thus we have, firstly, a glass rod with its twist ;
secondly, a mass of metal with two twists on it — one
near the glass rod, and of the image kind ; the other at
the other, end of the mass of metal, and related to the
original twist in the following way. It is the image of
its image.
Now it will be found by using a mirror that the image
of the image of a twist is the twist itself
Hence on the other end of the conductor there is a
twist of the same kind as that on the glass rod.
And it is obvious that the rod, with its twist, is con-
nected with the twist on the conductor nearest to it, and
the twist on the other end of the conductor will, by the
same arbitrary process which we have assumed as real,
call up a twist, the image of itself, on any object near it.
If it is touched by the object with this contrary twist
the two will run together, and the conductor will, if it is
left free, have only one twist — the silk kind, which has
come up opposite the rod.
If now the rod be moved away, the conductor will be
twisted as a whole ; that is, all the particles of which it
is composed will be slightly twisted with a twist of the
silk kind.
In this state it is said to be charged.
Thus the assumption which we have made, that there
is some process in nature in virtue of which, opposite
to any twist, its image twist is produced as a real thing
— this assumption is in harmony with the laws of
induction.
Instead of working with a glass rod it is more con-
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1 68 A Picture of Our Universe.
venient to use a metal rod. Suppose we take a poker
and attach a handle of sealing wax to its middle. See
A B below. This will be easily imagined, and its two
ends, the handle and the black end, will be easily re-
tained in the mind.
If now electricity be communicated from the glass
rod to the poker by touching the two together, what
happens is this : The particles of the glass being twisted
communicate their twist to the particles of the poker.
The twist on the poker is of the same kind as the
twist on the glass rod, and the amount of twisting
which the glass particles had is divided between the
glass rod and the poker. The use of the sealing-wax
handle is to keep the twist from communicating itself
to the body of the person holding it, and, through him,
to the earth. It is found that certain bodies, " non-
conductors," will not communicate the twist and convey
it along ; whereas metallic bodies, and conductors
generally, will communicate this twist at once to great
distances.
We will suppose that a metallic body consists of par-
ticles so arranged together that it easily acts as a set of
minute threads or chains of particles which will twist,
each thread or chain twisting as a whole. Thus the
conception which should be formed of a metallic body
conducting electricity along it is this : — Conceive a
bundle of very fine but very rigid wires, each wire twist-
ing separately but with the same kind of twist as all the
others, and each, as it twists, rotating amongst its fellow
threads. If we have a metal rod we can twist it between
the finger and thumb. This is not the kind of twist we
suppose, but that each separate string of particles is thus
twisted, so that each set twisting remains in the same
part of the metal rod — but is turning round in its fixed
position. This is a body conveying an electric current.
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A Pictttre of Our Universe. 169
If the current will not pass, the set of minute wires
must be conceived as held at the far end, and given a
twist, starting from the point where the electricity is
communicated. Now if a conductor is thus charged and
left, it is found that it retains its charge ; to be dis-
charged it must be touched with another conductor.
Hence this twist of minute threads differs from a twist
of a wire in that the threads cannot untwist of them-
selves unless other threads come into contact with them
to which they can impart the twist. That this should
be the case may depend on the fact that the twisting
strings are strings of molecules, and the ends of them
would thus be connected with other molecules with
something of the same tenacity as that with which the
strings themselves cohere together, and are unable to
unlock themselves from these insulating or untwisting
molecules.
Let us consider the state due to these twisting strings
of particles.
Place two pennies lying on the table before you, and
suppose them to be the sections in which two strings of
a conductor are cut across, so that you are looking at
two particles, represented by the pennies in the interior
of a conductor ; the strings, of which the pennies are
sections, come up towards your eye. Now twist the two
pennies each in the same direction — say that of the
hands of a watch. From the outer edges you can take
the motion off; the edges are moving in the same direc-
tion. But where the two pennies meet you will see that
the edge of each is going in a contrary direction to the
other. And if one penny tends to move an object in
one way the other tends to move it in the contrary
direction. Hence these motions tend to neutralize each
other in the interior of a conducting wire.
Having now formed a conception of the state of the
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particles in an electrified poker, suppose another poker
likewise held by an insulating handle is brought near
the first. Let the pokers be so arranged that the
handles both point one way, the black ends another way,
and let the second poker be in the same line as the
first, with its handle towards the black end of the first.
Now the first poker is charged, it contains electricity,
its particles are twisted. What effect will it have on the
second poker ?
It is found that the second poker undergoes a certain
change, but when it is removed to a di.stance from the
first poker all trace of this change disappears.
On the end nearest the first poker — on the handle — is
found silk electricity ; on the end furthest from the first
poker — on the black end — is found glass electricity.
+ +" — +
Let A B be oni; poker, Ihc + representing the i:harge of glass eleclricily.
Let C D represent the otiict poker, the — representing the induced
silk electricity, the -h the glass electricity in it.
Let A be the handle of the first, B its black end. Let
C be the handle of the second, and D its black end. To
explain this let us bring in our imaginary principle.
Let us suppose that when a charged body is brought
near an uncharged body, but is separated from it by
some medium through which electricity cannot pass — let
us suppose that by some agency the twist in the charged
body calls up an image twist in the body opposite it.
Thus, due to the twist in the first poker there will be an
image twist in the handle part of the second poker.
But the strings of particles in the second poker are
not twisted as a whole ; they are twisted in such a
way that if they are removed from the first poker, the
twist, whatever it be, disappears.
Now this would obviously be effected if we suppose
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the same thing to go on in the second pokei' as took
place between the first poker and the second. Let the
twist in the handle end C of the second poker be accom-
panied by the production of an image twist in the black
end D. And let us take this as a fair account of our
observations. If a body, which as a whole does not
undergo a twist, has one part of it twisted, then
there will be the image twist in the other part of it.
I say that the poker as a whole is not twisted, and all
that this means is that if it be removed from the elec-
trical influence it is found to be not charged ; and the
idea which we may form is this 1 the strings of particles
are twisted like the two strips of paper round the pencil ;
they are twisted so that they will exactly unwind if left
alone.
Now of course all these suppositions are merely pro-
visional, and must be dismissed unless seen to be
mechanically possible ; but for the present we are trying
to see if our assumption will fit in with facts. And our
assumption is that there is in nature a power which
amongst the molecules produces that as a real thing
which in our larger mode of existence only occurs as a
simulacrum and appearance. Our looking-glass images
are not real, but we suppose that real images are
produced amongst the molecules."
We have seen that if we make a certain supposition as
to the calling up of an image twist by a twist of
molecular matter, then the main facts of electricity are
capable of an explanation, which, involving merely the
motion of ordinary matter, is far preferable to the idea
of there being a mysterious fluid, and more in harmony
with our present ideas of electricity.
And yet it is impossible to retain this supposition
unless a clear mechanical explanation can be given of
' For delails, see Appendix III.
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how a real image of itself can be called up by the twist
which we suppose electricity to be.
We can by intelligent agency produce a twist which
is the real image of a given twist. But it would be
absurd to suppose amongst the molecules, an agency
which, acting with prescribed aim, gave in that domain
those real simulacra, those evident images, those phan-
toms with which we in our larger world of masses are
for ever mocked.
And yet it would be curious if such an hypothesis
were to claim a recognized position in our' mental
apparatus with which we think about nature.
For in that molecular world, if we imagine it to our-
selves, there would be a curious state.
If we consider a twist and its image, they are but the
simplest and most rudimentary type of an organism.
What holds good of a twist and its image twist would
hold good of a more complicated arrangement also. If
a bit of structure apparently very unlike a twist, and with
manifold parts and differences in it — if such a structure
were to meet its image structure, each of them would
instantly unwind the other, and what was before a
complex and compound whole, opposite to an image of
itself, would at once be resolved into a string of formless
particles. A flash, a blaze, and all would be over.
To realize what this would mean we must conceive
that in our world there were to be for each man some-
where a counter-man, a presentment of himself, a real
counterfeit, outwardly fashioned like himself, but with
his right hand opposite his original's right hand. Exactly
like the image of the man in a mirror.
And then when the man and his counterfeit met, a
sudden whirl, a blaze, a little steam, and the two human
beings, having mutually unwound each other, leave
nothing but a residuum of formless particles.
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CHAPTER n.
What physical explanation is possible of this produc-
tion of a real image ?
First of all we may note that the production of a real
image of any disturbance is one of the commonest phe-
If a piece of indiarubber lying on the table be pressed
downwards with the finger it will move up when the
finger is removed. The yielding and the resuming its
original form are movement and image movement.
If the disturbance is simply a displacement in one
line, then, if the medium in which this displacement is
produced is not permanently displaced, but on the whole
maintains its equilibrium, there invariably accompanies
any displacement its image displacement.
Moreover, to take the simple example of a wave propa-
gated through water — the particles of the water on the
whole move about a mean position ; they are not displaced
permanently in any one direction ; and, taking the dis-
tance from the crest to the hollow of a wave, then from
the hollow to the next crest, is the real image of the first
part. Thus in the complete movement in the wave
measured from crest to crest, there is displacement and
its real image.
Thus there seems some consistency about this suppo-
sition of an image, about the production of a real image
in nature.
But there are two observations which we can make.
Firstly, if it is true in these complicated cases it ought
to be true in simpler cases also. That is, if this suppo-
sition is in harmony with electrical actions, it ought to
fit in with other actions of a simpler kind.
Secondly, a supposition of this kind has no per-
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manent value; it is rather a feeler, by which we trace
out our way in the darkness, than any actual vision
itself. In default of an actual realization of what the
electrical relations are we can treat them by means of
a supposition. But we must be ready at any moment
to give up the supposition if it does not harmonize with
the facts.
And in the first case does the idea of a real image
hold good about the simplest possible actions ?
If we push our fist towards a glass the image is that of
a fist moving in the opposite direction.
Now, suppose a pressure exerted on a wall, as, for
instance, a hard stone hitting it. The wall undergoes a
displacement, but not as a whole— only that part of it
where the stone hits. And this displacement is followed
by the image displacement, for the wall in the part
where it has been hit and pressed back moves forward,
and by its reaction throws the stone off.
Every case of action and reaction is a case of a motion
and its image motion.
If a bullet strikes the wall and goes with such velocity
that it lodges in it, then the motion of the ball and the
image motion of the wall destroy one another, and the
result is a shattering of the wall in the path of the bullet.
Now in the case of a simple displacement of this kind
there is a rule by which we can form the image dis-
placement. Take a point on the wall, and about this
point as a centre turn the displacement half way round,
so that it does not come to be itself again, but is oppo-
site to itself.
By this turning, the displacement becomes the image
of itself; a movement into the wall becomes a move-
ment out from the wall ; and these follow .one another if
the wall is not injured. It should be noticed that the
displacement is moved round this point, using a direction
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A Picture of Our Universe. 175
which is not in the displacement itself. The displace-
ment goes straight into the wall. The turning motion,
which we suppose, needs another direction than this.
Now suppose, instead of a simple displacement like
this, we take a displacement involving two directions, as
in the case of a wave disturbance — it will be found that
the conditions are just the same. If a wave movement
falls on a medium which it does not destroy or move as
a whole, the displacement calls up its image displace-
ment. And the image displacement can be found, as
before, by twisting the displacement round so as to be-
come opposite to itself — by twisting it half-way round.
But in this case, too, a direction must be used which is
not used in the displacement itself.
Let us look at the wave disturbance more closely.
The horizontal central line in Diagram II. will re-
present the positions which a number of particles occupy
when at rest. That is, let us suppose there to be a num-
ber of particles lying in a series forming this line.
We can think of the portions of an elastic cord. An
indiarubber tube may be taken as an illustration, and
made to vibrate by a motion of the hand.
If now one of the particles be deflected from its
natural position — suppose it is moved to the position
M — then we should have one particle at M out of its
place, and all the others in their places.
But this does not happen. If the particle is pulled to
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M, the particles near it follow after it, and arc also dis-
turbed from their places, though not so much as the
particle at M.
We should have a set of particles forming a shape
like L M N, only much longer ; in fact, the particles all
along the cord would be raised.
If the cord is struck suddenly we do have a set
arranging themselves like L M N, but only for a limited
distance along the cord.
And here we notice a curious thing.
If a set of particles is forced to go like I.. M N,
removed from their position of repose, then at once a
set of particles goes like N O N'.
A displacement is accompanied by another displace-
ment which is the opposite of it. And this displacement
and opposite displacement travels along the elastic cord.
But the point of view which is the most natural one
to regard it from is a little different from this. Let us
consider a single point, P. When this is disturbed it
moves above its original position, to M, and below to
the other end of the dotted line. Its complete move-
ment is from one of these extremes to the other. And
if we take the complete disturbance as exhibited in all
its phases by different points, we ought to look at the
portion of the diagram M N O. For here at N we have
a point not displaced at all ; at M, one displaced to its
full extent upwards ; at O, one displaced to its full extent
downwards, And intermediate particles have interme-
diate displacements.
Now when a complex displacement of this kind is put
into a cord, its image at once springs up. The displace-
ment represented by M N O at once calls up the dis-
placement represented by O N' M', and this condition of
displacement and image displacement continues repeat-
ing itself till the cord comes to rest,
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A Picture of Otir Universe. 177
If the diagram be closely looked at, it will be seen
that it exhibits the Image relationship twice over. For
the movement of the particle P from P to M has its
image in the motion of another particle from its place
of repose to the position O. The disturbance itself,
M N O, consists of displacements and image displace-
ments ; and this disturbance, with its image O N' M',
makes the wave from crest to crest.
The "twist" which we consider in these pages is like
the wave motion, but with a third component added, so
that in the complete motion there is a displacement
coming out from the plane of the paper, as well as the
displacements in the plane of the paper itself
And just as the wave displacement produces a real
image of itself in a medium which it does not distort as
a whole, so there is nothing arbitrary in our assuming
that an electric twist calls up the real image of itself
in an insulating medium — that is, a medium which it
cannot twist as a whole.
If L M N O is a wave motion, then L' M' K' O is its
image, as produced by moving it round out of the plane
of the paper — Diagram II. If the wave disturbance is
moved round in the plane of the paper, the original wave
L M N O becomes L' M' N' O— Diagram III.— a shape
which bears no resemblance to the transmitted wave.
Consider O N M L to be a bent piece of wire lying on
the paper ; if it is moved round 0,, keeping on the paper,
it becomes O N' M' L'. To become like O N' M' L'
in Diagram II. it must move up from the paper and
down again on the right.
Thus adopting this artificial aid to thought — that a
displacement calls up an image displacement— we get
the rule that this displacement, the image, can be got
from the original displacement by moving the original
displacement half-way round, using as the plane in which
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A Picture of Our Universe.
the turning is made tliat plane which is given us by
taking these two directions — the direction in which the
wave is moving, and a direction at right angles to the
directions in which the displacements which form the
wave take place.
Thus, with the wave motion shown, if we take the
direction towards the top of the page to be the up di-
rection, and that from left to right to be the sideways
direction, then out of the paper towards us is the " hear "
direction. So, too, in this case we have to turn the wave
disturbance out of the plane of the paper, and each point
of it, to produce the image, must turn in a circle (going
half-way round it) lying in .a plane which has the two
directions near and sideways. The motions of the par-
ticles themselves are in the plane of the paper. So to
get the image by turning we use a direction — the
"near" direction, which is not involved in the wave
motion itself.
Hence we may state, as a tentative principle, that
when a disturbance takes place in a medium which will
not be disturbed as a whole, then such disturbance is ac-
companied by a real image of itself; and this real image
of itself is the configuration which would be obtained by
twisting the original disturbance round in a direction not
contained in the original disturbance.
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j4 Picture of Our Universe. 1 79
Thus the disturbance O N' M' L' is obtained by twist-
ing the disturbance L M N O round. The direction in
which it is twisted is the direction coming out from the
plane of the paper.
Now if this plane disturbance is in nature accompanied
by its real image, why should not a twist such as takes
place in the electric current also be accompanied by its
image twist when it impinges on a medium which it
cannot twist as a whole — that is, when it comes to an
insulator in its path?
The reason, obviously, is that we cannot conceive such
an image produced mechanically. And the reason of
this can be exhibited thus.
When we had a plane disturbance like L M N O wc
only used up two dimensions of space, and we have a
third coming up from the plane ; and this direction en-
ables us to imagine a turning which will alter A B into
its image.
But when we have a twist proceeding along an axis,
as in the case of electricity, we have no direction left
over in space whereby we may conceive the twist turned
round.
Now when the displacement itself involves all these
directions how will our rule hold ?
Hoiv shall we get the image displacement ? We can
find what it is by using a looking-glass ; but the same
rule which served in previous cases ought to work here
also.
We want a direction which is neither up and down,
right and left, towards and away.
Now let us adopt a mathematical device, and suppose
there is such a direction, and let us call it the X direction,
the unknown direction.
Then if we turn the twist round, using this X direction,
we shall get the image if our rule is correct. And as a
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matter of fact, by twisting a figure round in this way,
using a direction different from any of tlie three men-
tioned above, we do get its image.
Hence the rule we have formed worics consistently.
It will be found that if there was another direction so
that the spiral disturbance could be turned independently
of the directions used up in it, that just as a plane dis-
turbance can be turned into its image disturbance,
so the spiral disturbance of electricity could be turned
into its image spiral by a simple turning.
In this argument we have not looked at the matter
directly, but from the outside. To see it immediately
requires us to gain a familiarity with the properties of
space with four independent directions, and that would
take too long for the present paper. The same conclu-
sion can be arrived at mathematically ; but in these
papers as far as possible we avoid symbohsm. We
want to gain hold of scientiilc facts in a warm and
living way, to unwrap them from conventionalities and
formulse.
Thus if we suppose that in the minute motions which
go on about us there is a possibility-of moving in a four-
dimensional way, then it is perfectly legitimate to assume
that in a medium which cannot be twisted, but which is
clastic, a twist calls up a real image twist.
And thus the assumptions which we have made as the
basis of an electrical theory are justified on the assump-
tion of a four-dimensional space, are untenable except
on that supposition.
The matter is of course perfectly open. The only way
is this, by adopting the assumption of a higher space to
predict what the actions of the molecules will be, then if a
number of predictions are verified the evidence will be-
come strong. And I fee! sure that there are some very
curious things to be made out here. For my own part
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A Picture of Our Universe. iSi
the evidence of the reality of four-dimensional space — in
the sense in which we say that our space is real— does
not rest on the consideration of the molecular move-
ments about which it is not easy to get clear ideas,
but on the study of the facts of space. I hardly think
that any one who spent a few years in becoming familiar
with the facts of space, not by the means of symbolism
or reasoning but by pure observation, could doubt that
there are really four dimensions.
In noticing the simpler actions and their image actions
we find that the real image does not coexist with its
original, but rather follows and succeeds it. If we push
against a board the board yields, and springs back when
we leave off pushing. If the original displacement is
permanent as a point pressed against an elastic surface
and making the surface yield, then the image of this
displacement is potential ; it is not actually there, but
comes into play as soon as the original displacement is
removed.
Now in the electrical actions we have assumed both
the original twist and the image twist as concurrently
existing.
In certain cases there is no doubt that they are co-
existent as when a glass rod is rubbed by silk.
But if the case of the action of a charged poker on an
uncharged one be examined it will be found that there
is nothing to prove that the image twist comes into
existence until the original one is removed.
When the charged poker is brought near the other,
the remote end of the second is affected with the same
kind of electricity as is on the charged poker.
The appearance is just the same as if a thin wall were
exposed to a pressure on one side, and the other side
were to bulge out. The displacement is transmitted
through the conductor.
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It is only when the original charged body is removed
that the image charge is found to be in existence on the
second conductor. There are some peculiarities, how-
ever, which make electrical displacements different in
their appearances from ordinary displacements.
No body can be made to move in any direction with-
out imparting an equal motion in an opposite direction
to another body — e.g., the motion of a cannon ball is
equalled by the recoil of the cannon.
And so no twist can be given to the particles of a
body without an image twist being given to other
particles.
Now the image displacement or rectilinear motion,
in the case of a rectilinear motion, in straightforward
movement seems to remain in the place where it was
produced. The recoil of the gun carriage produces a
strain Qy\ its bearings and friction, which produce heat,
which gradually dissipates.
But the image displacement, in the case of electricity,
seems to have a marvellous facility for running through
the earth and meeting the original displacement. An
indefinitely long line of action seems in electricity to
take the place of a simple point. Our ordinary mechani-
cal forces arc located in centres, or points of action. In
electricity the line seems to take the place of the point.
Where the ordinary engineer deals with points the
electrical engineer deals with lines.
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A Picture of Our Universe. 183
CHAPTER ILL
THE ^.THER.
There are some expressions which, being somewhat
vaguely used, arc apt to cause confusion in the mind of
those who read or hear about higher space.
And perhaps the most mischievous is the expression,
a curvature of space. Now of space as It is generally
used, in its accepted significance, there can be no curva-
ture. For space means a system of positions extending
uniformly in the number of dimensions we choose to fix
upon.
If we take the straight line as our space, we may call
it I space ; then the set of positions follow one on after
the other without bending. If the line is bent it becomes
a line, not a straight line. It should not be called 1
space, but a thing in 2 space. That is, it is a bent line
in a plane.
A being who was on the line might not perceive the
fact of this bending, and it might not affect the measure-
ments he made. But if the line ran into itself again, and
he found that he was moving on what we should call a
circle, this would in no way affect his idea of space.
He would recognize that what he called space, namely,
his line, was not space, but a curved thing in 2
space.
Similarly, taking a plane — this is by definition not
curved in any way, known or unknown, and it can only
be conceived to be bent by ampler space being conceived,
and its being imagined as having force applied to it so
as to become a bent thing in this ampler space. In this
case the term " plane " is not the correct name.
And so about our three-dimensional space ; we cannot
be robbed of that idea, although it plight conceivably be
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184 A Pichire of Our Universe.
proved that our earth and our whole universe were on a
curved thing in 4 space.
We will then keep the term " space " for the ordinary
conception ; and call it i, 2, 3, 4 space, according to the
number of supposed independent directions.
A curved hne or surface or solid we will call a i, 2, or
3 thing, according to the number of dimensions in it.
A straight line is a i thing possible in i space. A
circle is a i thing possible in 2 space. At any point of
it a being in it is limited to motion in one direction,
while the circle itself involves two dimensions. The
surface of a sphere is a 2 thing possible in 3 space. The
rind of an orange, or the orange itself, is a 3 thing possible
in 3 space.
It will be observed that the surface of the sphere,
although only a 2 thing, involves the conception of
3 space, and cannot be understood without the use of the
idea of 3 space. It is a 2 thing because at any point of
the surface a being can only move in two independent
directions. A crooked line drawn on the surface of a
sphere is a i thing in a 2 thing in 3 space.
Another very common misconception is occasioned
by the use of a figure of this kind QC l^o represent a
" knot " in 3 space.
It obviously corresponds in 3 space to an iron rod
welded together at the crossing place of the loop, so that
it is indistinguishable which is the one free end, which
the other. At the crossing point the two lines repre-
sented by the two ink marks must be absolutely one and
the same.
If one line be supposed to go over the other, by how-
ever small a distance, it would leave the plane. It would
suddenly become invisible to the creature in the plane,
and it would appear again at the other side of the line it
crossed as if it came from nowhere.
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A Picture of Our Universe. 185
It would be as extraordinary a sight as if we saw a
pole going up to a brick wall, then beyond the brick
wall the rest of the pole appearing^not going through
the brick wall, nor coming round it— but somehow
appearing; part of the same pole moving when it
moved, obviously connected with it, and yet with no
joining part which we could possibly discover.
Again, it sometimes appears to be thought that the
fourth dimension is in some way different from the three
which we know. But there is nothing mysterious at all
about it. It is just an ordinary dimension tilted up in
some way, which with our bodily organs we cannot point
to. But if it is bent down it will be just like any ordinary
dimension : a line which went up into the fourth dimen-
sion one inch will, when bent down, lie an inch in any
known direction we like to point out. Only if this line
in the fourth dimension be supposed to be connected
rigidly with any rigid body, one of the directions in that
rigid body must point away in the fourth dimension
when the line that was in the fourth comes into a 3
space direction.
If the reader will refer back to the paper on the plane
world he will find a description of the means by which
a being there might know that he was in a Hmited
world, and that his conception of space was not of what
was really the whole of space, but of the limited portion
of it to which he was confined by his manner of being.
The test by which such a being could discover his limi-
tation was this. He found two things, each consisting of a
multitude of parts — two triangles ; and the relationship of
the parts of the one was the same as the relationship of
the parts of the other. For every point in the one there
was a corresponding point in the other. For every pair
of points in the one there was a corresponding pair of
points in the other. In fact, considered as systems made
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i86 A Picture of Our Universe.
up of mutually related parts, each was the same as the
other.
Yet he could not make these two triangles coincide.
Now this impossibility of bringing together two things
which he felt were really alike was the sign to him of his
limitation ; and by reflecting on the similar appearance
which would present itself to a being limited to a straight
line — by thinking of two systems of points which were
really identical, and which he could make coincide, but
which a line being could not make coincide, he would
be led to conclude that he in his turn was subject to a
limitation.
Now is there any object which we know which, con-
sidered as a whole consisting of parts, is exactly like
another whole, the two having all their parts similarly
arranged, so as to form in themselves two identical
systems, and yet the one incapable of being made to
coincide with the other, even in thought?
Let us look at our two hands.
They are (except for accidental variations) exactly
alike. And yet they cannot be made to coincide.
And here, if we reflect on it, is the sign to us that we
are limited in our notions of space — that we are really
in a four-dimensional world.
Watching a ship as it recedes from the shore we see
that it becomes hull down before it vanishes, and'^know
that the earth is round. And no less certainly do our
two hands, in their curious likeness and yet difference,
afford to us a perpetual proof of our limitation, and
indicate a larger world.
This sign really tells us more than the mere fact
of our limitation : it tells us where to look for the
possibility of four-dimensional movements. It tells us
that movements of any degree of magnitude relative to
us are not possible in the fourth dimension. It tells us
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A Picture of Our Universe. 187
to look for four-dimensional movements in the minute
particles of matter, not in the movements of masses of
about our own size.
The task before os is difficult. We have to make up
from the outside what the appearances of a higher space
existence are to us in our space, and then we have to
look at the facts of nature and see if they correspond to
these appearances.
Let us take a few isolated points and look at them
patiently.
To a being standing on the rim of a plane world a
straight line absolutely shuts out the prospect before
him. If the straight line is infinite it cuts his world in
two ; he can never hope to get beyond it.
It is to him what an infinite plane would be to us,
stretching impassably in front of us, cutting us off from
all that lies on the other side.
But we know that a point can move round this line.
It ca,n revolve round it by going out of the plane, and
coming down again into the plane on the other side of
the line.
This movement would be inconceivable to a plane
being ; for he can only conceive it possible to get to the
other side of the line by going to the end of it and
coming back along the other side of the line.
Now take a piece of paper and put a dot right in the
middle and suppose that it hag no means of passing
through the paper. We can only conceive the dot get-
ting to the other side of the paper by passing round the
edge and coming back again to the position underneath
where it was.
But by a four-dimensional movement it can slip round
the paper without going to the edge.
A set of words may help. In a plane a body rotates
round a point— rotation takes place round a point. In
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1 88 A Picture of Our Universe.
space rotation is always round a line — the axis. In
four-dimensional space rotation takes place round a
plane.
To take a farther consideration of this point — a plane
being can see one side or the opposite of a straight line.
He can only see it in one direction or in the reverse
direction. But we can look at a straight line from a
direction at right angles to that in which a plane being
looks at it. We can look at a straight line from points
which go all round it.
Similarly, a being in four-dimensional space can look
at a plane from a direction at right angles to that in
which we look at it. If we try to think of this we shall
imagine ourselves looking at the thin edge. But this is
not what a four-dimensional being would mean. He
would see the plane exactly as we see it, but it would be
from a direction at right angles to that in which we look.
In working with four-dimensional models it is a curious
sensation until we become used to it— that of looking at
a plane at one time, and then looking at it again ; and,
although it seems just the same- — as square in front of
us as before — realizing that we are looking at it from a
direction at right angles to that of our former view.
And in four dimensions a point which is quite close
to a plane can revolve round it without passing through
it, thus presenting to us the appearance of vibrating
across the plane, but not passing through it.
The appearance is as wonderful to us as it would be
for a plane being. to see a point which was in front of
a line quickly passing behind it without having gone
round the end. Such a point would appear to the plane
being to vibrate across his line without passing through it.
Now if we stand in front of a mirror we see the image
of ourselves. If we were to go round the mirror and
take behind it the position which our image seemed to
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189
occupy, we should not be able to make ourselves co-
incide with it. In the mirror opposite to our left hand
is the image of our left hand ; but if we passed round,
Diagram IV.
our right hand would be in the place in which we
imagined we saw the image of our left hand. And thus
we cannot make ourselves coincide with our image. But
by a rotation in four-dimensional space we could put
ourselves so as exactly to coincide with our image.
This can be seen by referring to the case of the straight
line, Diagram IV.
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190 A Picttire of Our Universe.
Let A B C be a triangle, and G a line. If A B C
moves round the end of the line, it can take up tho posi-
tion A' B' C ; but it cannot anyhow be made to take the
position shown in Diagram V., A' B' C.
But if we move the triangle ABC out of the plane
round the line G as axis, it will, in the course of its
twisting round this axis, come into the position A' B' C.
It will come into this position when it has twisted half-
way round. The point A, for instance, twists round in
a circle lying in a plane which contains the direction
A to A', and the direction at right angles to the paper.
Twisting half-way round in this circle, it becomes A',
and so on for the other points. Now a being who did
not know what a direction was which lay out of the
plane would not be able to conceive this twisting and
turning movement. It would be as impossible for him
to conceive the triangle ABC turned into the triangle
A' B' C, as it would be for us to suppose ourselves
turned into the looking-glass image of ourselves by a
simple twisting.
Yet just as a thing inconceivable to the plane creature
can be done, so we could be twisted round and turned
into our image. But this only holds theoretically; our
relation to the eether is such that we cannotbe so turned,
or any bodies of a magnitude appreciable to our senses.
If we consider the case of a being limited to a plane,
we see that he would have two directions marked out
for him at every point of the rim of matter on which he
must be conceived as standing. This is up and down,
and forwards and backwards — the up being away from
the attracting mass on which he is.
Now, if he were to realize that he was in three-dimen-
siojial spac^, but confined to a plane surface in it, his
first conclusion would be that there was a new direction
starting from every point of matter, and that this new
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A Picture of Our Universe, 191
direction was not one of those which he knew. This
new direction he could not represent in terms of the
directions with which he was famiHar, and he would have
to invent new terms for it,
And so we, when we conceive that from every particle
of matter there is a new direction not connected with
any of those which we know, but independent of all the
paths we can draw in space, and at right angles to them
all — we also must invent a new name for this new
direction. And let iis suppose a force acting in a definite
way in this new direction. Let there be a force like
gravitation. If there is such a direction, there will pro-
bably be a force acting in it; for in every known direction
we find forces of some kind or another acting. Let us
call away from this force by the Greek word ana, and
towards the centre of this force kata. Then from every
point in addition to the directions up and down, right
and left, away frqm and towards us, is the new direction,
ana and kata.
Now we must suppose something to prevent matter
passing off in the direction kata. We must suppose,
something touching it at every point, and, like it,
indefinitely extended in three dimensions.
But we need not suppose it — this unknown — to be
infinitely extended in the new direction ana and kata. If
matter is to move freely, it must be on the surface of
this substratum. And when the word surface is used it
does not mean surface in the sense that a table top is a
surface ; it is not a plane surface, but a solid space sur-
face. If from every point of a material body a new
direction goes off, the matter which fills up the space
produced by the solid moving in this new direction, will
have the solid it started from as its surface, and will be
to it as a solid cube is to the square which bounds it on
the top.
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192 A Picture of Our Universe.
Now this body which extends thus, bearing all solid
portions of matter in contact with its surface by every
point of them, may be thick in the kata direction or
thin.
If it is thick, then the influence of any point streaming
out in radiant lines will pass as in all space directions,
so out also in this new direction.
And then if its influence spreads out in this new
direction, its efl'ect on any particle near it will diminish
as the cube of the distance ; for, besides filling all space,
it will have also to fill space extended in this new direc-
tion.
But we know that the influence proceeding from a
particle does not diminish as the cube of the distance,
but as the square of the distance.
Hence the body which, touching all solid bodies by
every point in them, and supports them extending itself
in the kata direction — this body is not thick in this
direction, but thin. It is so thin that over distances
which we can measure the influence proceeding from a
body is not lost by spreading in this new kind of depth.
Thus the supporting body resembles, as far as we
know it, a portion of a vast bubble. But moving on the
surface of this bubble we can pass up and down, near
and far, right and left, without leaving the surface of the
bubble. The direction in which it is thin is in a direction
which we do not know, in which we cannot move. But
although we cannot make any movements which we can
observe with our eyes in this direction, still the thin film
— thin though infinitely extended in any way which we
can measure — this thin film vibrates and quivers in this
new direction, and the effects of its trembling and quiver-
ing ar& visible in the results of molecular motion. It
only affects matter by its movement in directions at right
angles to any paths ivhich we can point to or observe.
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A Picture of Our Universe. 193
and these movements are minute ; but still they are
incessant, all- pervading, and the cause of movements of
matter. It is smooth— so smooth that it hinders not at
all the gliding of our earth in its onward path. Hence
it does not transmit a direct pull or push in any direction
from one particle to another ; but by the twistings and
vibrations of the material particles it is affected, and
conveys from one to another these movements. Yet to
bear up all matter, and thus hold it on its vast solid
surface, it must be extremely rigid and imshatterable ;
and hence it cannot be permanently altered or twisted
by any force proceeding from matter ; but receiving from
matter any push or twist, it is impressed with it for some
distance ; then, reasserting itself, it produces an image
displacement or twist, and this image it transfers to the
particles of matter which it touches.
Sometimes, as when light comes from the sun, this
displacement and image is repeated and repeated in-
numerable times before at last we, receiving it, become
aware of the origin of the disturbance.
But the properties and powers of this solid sheet—
this film quivering and trembling, yet infinite and sohd—
are too many to begin to enumerate. The lether is
more solid than the vastest mountain chains, yet thinner
than a leaf ; undestroyed by the fiercest heat of any
furnace, for the heat of the furnace is but its shaking
and quivering ; bearing all the heavenly bodies on it,
and conveying their influence to all regions of what we
call space.
And by some mysterious action it calls up magnetism
from electricity ; by its different movements it gives the
different kinds of light their being.
Of itself untrammelled and unclogged by matter, it
vibrates and shakes with the speed and rapidity of the
vibrations of light. But when matter lies on it — when air,
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194 -^ Picture of Our Universe.
even in its rarest condition, lies on it— its proper move-
ment is damped and some of its quick shakings that are
light, slow down to the obscure vibrations of heat. Thus of
itself it will not take up the vibration of a hot body, but
selects only those orbs which are glowing with radiant
light wherefrom to take its thrilling messages. But
when matter lies on it, it takes obediently the less
vivacious movements of terrestrial fires.
A being able to lay hold of the a;ther by any means
would, unless he were instantly lost from amongst us by
his staying still while the earth dashes on — he would be
able to pass in any space direction in our world. He
would not need to climb by stairs, nor to pass along
resting on the ground.
And such a being, even as thin as ourselves, and as
limited, if not even in physical powers, but merely In
thought he became aware of his true relation to the
^ther, ho would see all things differently.
From all shapes would fall that limitation of thought
which makes us see them differently to what they are ;
and in largeness and liberty of possible movement his
mind would travel where ours but creeps, and soar and
extend where ours journeys and diverges.
It is impossible in contemplating the rudiments of
four- dimensional existence to prevent a sense of largeness
and liberty penetrating even through the profoundness
of our ignorance.
Whether we shall find beings other than ourselves,
when we have explored this larger space, cannot be said.
But there is a path which holds out a more distinct
promise.
When the conditions of life on a Jilane are realized it
becomes evident that much of that which is to us merely
natural— obvious from the very conditions of our life—
could only be attained by beings on the plane as the
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A Picttire of Oitr Universe. 195
result of ai-tificial contrivances and modifications of tiieir
natural tendencies. In their progress and development
they would, as it were, represent on the plane the features
of the normal and undeveloped life of three-dimensional
beings, and they would attain, as a result of moral labour
and energy, a position which children in our higher life
are born to without trouble or thought.
And so we in our advancing civilization may to the
eyes of some higher beings represent in our arrange-
ments and institutions an approach to the simplest
matters of fact in their existence. We are separated
from such a view by our bodily conditions, but we
are not to be prevented from taking it with our minds.
By building up the conception of higlier space, by
framing the mechanics of such a higher world, we may
arrive at a fairly accurate knowledge of the conditions
of life in it,
And then, with that element in our thought, with the
rcasoned-out characteristics present to our minds of
what life on a higher physical basis would be, we may
be able to judge amidst conflicting tendencies with more
certainty and calmness.
In one of the follovving papers of this series an account
will be given of some of the facts which we can discern
about the machinery and appliances of four-dimensional
beings.
But the work of real discernment belongs to those
who will from childhood be brought up to the concep-
tion of higher space,
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APPENDIX I.
\ SUPPOSITION can be made with regard to
the .ether which renders clearer an idea often
foiuid in literature,
This idea is that of the freedom of the will.
If the will is free, then it must affect the world so as to
determine chains of actions about which the mechanical
laws hold true. We knowthat these mechanical laws are
invariably true, Hence, if the will is an independent
cause, it must act so that its deeds produce to us the
appearance of a set of events determined by our known
laws of cause and effect. The idea of the freedom of
the will is intimately connected with the assertion that
apparent importance, command of power, greatness and
estimation, are outside considerations, not affecting the
real importance and value of any human agent These
ideas can easily be represented using the idea of the
jEther as here given.
For suppose the Eether, instead of being perfectly
smooth, to be corrugated, and to have all manner of
definite marks and furrows. Then the earth, coming in
its course round the sun on this corrugated surface,
would behave exactly like the phonograph behaves.
In the case of the phonograph the indented metal
sheet is moved past the metal point attached to the mem-
brane. In the case of the earth it is the indented srther
which remains still while the material earth slips along
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A Pichtrc of Our Universe. 197
it. Corresponding to each of the marks in the s;ther
there would be a movement of matter, and the con-
sistency and laws of the movements of matter would
depend on the predetermined disposition of the furrows
and indentations of the solid surface along which it slips.
The sun, too, moving along the ^ther, would receive
its extreme energy of vibration from the particular
region along which, it moved, and the furrows of the
intervening distancegive the phenomena actually observed
of our relationship to the sun and other heavenly bodies.
Thus matter may be entirely passive, and the history
of nations, stones of kings, down to the smallest details
in the life of individuals, be phonographed out accord-
ing to predetermined marks in the aether. In that case
a man would, as to his material body, correspond to cer-
tain portions of matter ; as to his actions and thouglits
he would be a complicated set of furrows in the Kther.
Now what the man is in himself may be left un-
determined ; but he would be more intimately connected
with the aether than with the matter of his body. And
we may suppose that the Jethcr itself is capable of
movement and alteration ; that it moulds itself into
new furrows and marks.
Thus the old woman smoking a pipe by the wayside
years ago, and whom I somehow so often remember, is
not much different from me— we are both corrugations of
the same tether.
Now our consciousness is limited to our bodily sur-
roundings. Yet it may be supposed that in an action of
our wills we, whatever we are (and for the present let us
suppose that we are a part of the sether), we may be
altering these corrugations of the sether. A single act
of our wills, when we really do act, may be a universal
affair with quite infinite relations. Thus it may be the
immediate presentation to us of an alteration proceeding
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igB A F.ichi.re of Our Universe.
from us of all that set of corrugations which represents
our future life ; it may be the whole disposition and lie
of events, which are prepared for the earth to phono-
graph out, being differently disposed. And it evidently
is quite independent of the particular furrows in which
such alteration first occurs. That long strip of ;Ethcr
which is a very humble individual may, by an act of self-
configuration, affect the neighbouring long strips and
produce great changes. At any rate the intrinsic value
of the will is quite independent of the kind of furrows
along which any material human body is proceeding.
APPENDIX .11.
It is a good plan in fixing our attention to give de-
finite names to the directions of space. Let U stand
for up. Then the up direction wc will call the U direc-
tion, or simply U-
Then sideways, from left to right, we will call V, so
that moving in the V direction, or moving V, means
moving to the right hand.
Then the away direction we will call W, so that a
motion which goes away from us we call aW motion,
and its direction we call W.
Then any other direction which we suppose indepen-
dent of these we will call the X direction. Now the
simple push or displacement takes place in direction V,
or !eft to right. It is turned into its image by turning
in the plane U Y—i.e., the plane of the paper.
The wave motion takes up the directions U V, and it
can be turned into its image by a turning in the plane
W V — i.e„ by turning out of the paper, as if the paper
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A Picture of Our Universe. 199
were folded over about the dotted line. Then finally
the twisting motion takes up the directions U V W, and
can be turned into its image by being turned in the plane
V X. That is, if each point is turned half-way round in
this plane it becomes the corresponding point in the
image twist. Thus on the supposition of the preceding
pages, if a positively electrified particle could be turned
in 4 space, it would become a negatively electrified
particle,
APPENDIX III.
It remains now to examine if the supposition that the
particles of a wire are twisting in strings fits in with
observed facts of electricity.
And firstly, if the particles arc twisting in this manner,
it is only reasonable to suppose that they vtouM take up
a little more room than they did when not subject to
this movement — that is, the wire would become a little
thicker. But its volume remaining the same, if it becomes
thicker it must compensate for this thickening by be-
coming shorter. And it is found that a wire through
which an electric current is sent tends to become shorter
when the current comes into it.
Again, suppose a wire through which a current has
been sent suddenly isolated. It has a twist in it, and
will keep this twist. But if it is connected up with any
other wire forming a complete circuit through which it
can untwist itself, it will probably do so, and in un-
twisting would very likely overshoot the mark and
become twisted in the opposite direction. Thus it would
make a series of twists, each less than the last before
becoming quiescent, And it is observed that a wire if
so isolated doe.s produce a rapidly alternating series of
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200 A Picture of Our Universe.
very minute currents before it comes to rest ; just as ii
it were untwisting itself and overshot the mark each way
many times before the electrical state has altogether
disappeared.
The question now comes before us, How is it that a
wii'c gets twisted ? Through what agency is a current of
electricity urged through a wire, or a twist put into it ?
This is often done by means of an electrical battery.
We will take a simple instance.
Suppose a dish of sulphuric acid, and a bit of carbon
and a piece of zinc put into it. Then the carbon and
the zinc are connected outside the liquid by a wire.
Along this wire electricity will pass. Now the twist put
into the wire must come from somewhere. And it is
found that the sulphuric acid, which is a very lively com-
pound, and contains a great deal of energy, becomes
quieted down, and is quite different after the battery has
finished working. On examination afterwards it is found
to consist of sulphate of zinc.
Sulphuric acid can be looked upon as consisting of two
bodies — hydrogen and a sulphur and oxygen compound.
This sulphur and oxygen compound is called SO4. Now
the SO4 comes to the zinc, and with zinc forms quite a
dead compound, with little energy in it, called zinc
sulphate, or Zn SO^. The hydrogen, on the other hand,
comes off at the carbon in an energetic state.
Hence evidently the SO., has given up its energy, the
hydrogen has not, So the twist in the wire probably
comes from the SO, ; and thus the twist is started
at the zinc end, and runs round the wire from zinc to
carbon.
At the same time we may suppose that an image
twist, starting also from the zinc, runs through the fluid
of the battery and then along the wire, till meeting the
twist the two mutually unwind each other.
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^ Picture of Out Universe. 201
Thus the battery will be as if one had a loop of tliread,
and at one point twisted it between one's finger and
thumb. Twist and image twist, starting from this point,
unwind each other on the opposite part of the loop.
And if the loop is not joined, but the threads are held,
each will become twisted with increasing tension til! they
can twist no longer. The objects which hold the ends
of the thread, and prevent them twisting, represent
insulators.
It is found that when a strong current of electricity
passes through some water which has had a little sul-
phuric acid added to it, two effects take place.
In the first place some of the current passes through
as through a wire. In the next place a part of the
current is used up in producing an effect on the water.
It splits the water up into two parts, each of them con-
taining very much more energy than the water. One
part is called hydrogen, and comes off at the wire which
comes from the zinc, which we will call the zinc wire.
The other part of the water comes off at the wire coming
from the carbon, or at the carbon wire, and is called
oxygen.
Let us now suppose that the twist of the zinc wire
calls up in the molecule of water next to it an image
twist. If it could pass on its twist at once, the water
would form an ordinary conductor ; but the water is not
a conductor. Hence we suppose the same relation tO'
hold good between the end of the zinc wire and the
water molecules as between the zinc wire and any other
body to which the twist cannot be communicated.
Now in the part of the molecule nearest the zinc wire an
image twist is called up. And hence the molecule, being
unable to twist as a whole, in the end of it away from
the zinc wire a twist is produced. Thus the water
molecule is strained into image twist and twist. Now
14
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202 A Picture of Our Universe.
let us suppose that by a powerful current it is wrenched
in two. It is separated into a part having an. inriage
twist " hydrogen," which comes off at the zinc wire, and
into a part with the twist " oxygen."
But this part with the twist calls up an image twist
in the molecule next to it, wrenches it in two. Thus
the oxygen of the first molecule separates up the next
molecule into hydrogen and oxygen. The oxygen has
a twist, the hydrogen an image twist. These twists run
each other out, and leave an oxygen part free.
This oxygen part does the same to the next molecule,
and so this action is transmitted througli the whole body
of the water till the carbon wire is reached^ — when, the
■oxygen part finding no other molecule to wrench asunder,
is left isolated, and comes off in the form of gas.
Thus we see. that oxygen and hydrogen would be
bodies having in them twist and image twist — that is,
that they would have an active rotation each of them ;
but the rotation would be different in the two cases, and
such that if put together they would run each other out :
the light and heat produced by the union of the two
beiijg probably the exhibition of the effects of this
If we adopt the supposition, which seems most in
accordance with facts, that there are in water two dif-
ferent elements occurring in distinct particles, the one
■called oxygen, theother hydrogen ; and if, moreover, we
suppose that these particles are perpetually changing
places, and that each oxygen particle is sometimes
linked with this hydrogen particle, sometimes with that,
then it is obvious that the oxygen and the hydrogen in
the water are in such a state that, if collected together
separately, they would form liquid oxygen and liquid
hydrogen ; and the effect of the electric twist is to give
them those active image rotations, or strains, which
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A Picture of Our Universe. 203
make them take the gaseous form, and assume that
peculiar relation to each other which exhibits itself so
strikingly in combustion.
With regard to magnetism, the same phenomenon of a
particular state or disturbance of matter and its image
state or disturbance is very strikingly obvious.
For take the case of a magnet. By the influence of
-an electric current passing round it, it can be turned into
a magnet with opposite poles. That is to say, the small
particles of the iron have been so shifted that, whatever
their disposition was in the first case, they have now the
reverse disposition. If we suppose the small particles to
be magnets like the whole magnet, and all to have their
north poles pointing in one direction, then after the
action of the current they have their north poles pointing
in the opposite direction. But they have not turned in
space, for, if they were to turn, each must turn about
some axis. But if there was some axis then, with regard
to this axis, the magnetic influence would have a definite
relation ; the turning of tlie particles would take place
in a certain plane, and there would be a certain plane in
the magnet which would have special properties.
But a magnet is perfectly symmetrical Jn all its pro-
perties round its axis. The magnet which has had its
poles reversed is, as an arrangement, the image of itself
in its first condition. In the solid mass of iron which
forms tlie magnet, by the action of electricity, a particular
arrangement and its real image are alternately pro-
duced.
There are some very important electrical phenomena
which have been left out of consideration altogether —
namely, the repulsions and attractions exercised by
electrified bodies.
Adopting the conceptions here laid down with regard
to electricity — that the two kinds arc in the relation of
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204 A PicHi-re of Our Universe.
twist and image twist— we find that certain conclusions
force themselves upon us.
A positively electrified body attracts a negatively
electrified body.
A positively electrified body repels a positively elec-
trified body.
Or, as it is put in a shorter form, one kind of electricity
attracts the opposite kind, and repels the same kind.
Now, if our theory is true, a twist ought to attract its
image twist, and repel a twist like itself
And as far as can be observed it is always a fact
that a movement of any kind taking place in a medium
does attract its image movement, and repel a movement
like itself.
Some very instructive experiments have been made
with bodies suspended in water, and caused to pulsate
or twist. It would be found, on referring to the details
of these experiments, that if two spheres are pulsating
or throbbing, so that the movements of the one are at
any instant what the movements of the other would
seem like, if looked at in a mirror, then these two spheres
will attract each other. If the one Is a real copy of
the other, then they repel each other. And this law
holds good not only for throbbing movements, but also
for twisting movements.
If now we supposed that what held good for move-
ments held good for tensions of the same nature as the
movements, these results would be in exact accordance
with our suppositions. If a twisting movement attracts
its image twisting movement, will a twist attract its
image twist by means of its effect on the medium in
which it is, and on which it exerts tension ? This point
must be left undecided.
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€mtmg ®ttt % S«lt
§nE words which I have chosen as the title
of this paper are the expression for a process
I which has been asserted to be one that occurs
aUke in our mental and in our moral life. It
has so happened that in certain of my own inquiries
I have applied this process ; and the details may be of
interest. But I must warn the reader not to expect any
wide views on hfe, or far-reaching thoughts, or any of
the warmth of human affairs. What I think about is
Space ; and it is the application of the principle of cast-
ing out the self in attaining a knowledge of Space about
which I have something to say.
And, firstly, as a bit of absolute human experience
is never without value, but that which we make up is
often so, I may as well cast the fear of ridicule aside
and enable the reader to take in, in a few lines, the
exact commencement of my inquiry.
The beginning of it was this, I gradually came to
find that I had no knowledge worth calling by that
name, and that I had never thoroughly understood any-
thing which I had heard. I will not go into the matter
further ; simply this was what I found, and at a time
when I had finished the years set apart for acquiring
knowledge, and was far removed from contact with
learned men. I could not take up my education again,
'5
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2o6 Casting out the Self.
but although I regretted my lost opportunities I de-
termined to know something. With this view I tried
to acquire knowledge in various ways, but in all of
them knowledge was too impalpable for me to get hold
of it: And I would earnestly urge all students to make
haste in acquiring real knowledge while they are in the
way with those that can impart it ; and not rush on too
quJcldy, thinking that they can get knowledge after-
wards. For out in the world knowledge is hard to find.
At length I came to find that the only thing I could
know was of this kind. If, for instance, there were
several people in a room, I could not know them them-
selves, for they were too infinitely complicated for my
mind to grasp ; but I could know if they were at right
or left hand of one another, close together, or far apart.
And the same of, to take another instance, botanical
specimens in a book. I could not grasp the specimens —
each was too infinitely complicated, and each part too
infinitely complex— but I could tell which specimen wa.s
next which.
Accordingly, being desirous to learn something
thoroughly, and since, in the arrangement of any dif-
ferent objects, there was such a lot of ignorance intro-
duced by the objects being different— each bringing in
its own ignorance and feeling of bewilderment — I deter-
mined to learn an arrangement of a number of objects
as much alike as possible.
Accordingly I took a number of cubes, which were as
simple objects as I could get, arranged them in a large
block, and proceeded to learn how they were placed with
regard to each other. In order to learn them I gave each
of them a name. The name meant the particular cube
in the particular position.
Thus, taking any three names, I could say, about the
three cubes denoted, how they were placed with regard
y Google
Casting out the Self. 207
to one another : one, say, would be straight above the
first with four intervening, the third would touch the
second on the right hand, or some similar arrangement.
Now in this way I got what I conceived to be know-
ledge. It was of no use or beauty apparently, but I had
no reason to use it or to show it
It is about this bit of knowledge that I want to speak
now — a block of cubes, and the cubes are known each
one where it is.
Sometimes I have been tempted to call this absolute
knowledge, but have been reminded that I did not know
the cube itself. Against this I have argued. But in argu-
ment we say many things which we do not understand,
and my conclusion is, on the whole, that the objection
is well founded. Still, if not knowledge absolute, the
knowledge of this block approaches more nearly to
knowledge absolute than any other with which I am
acquainted, because each cube is the same as its neigh-
bour, and instead of an arrangement of all sorts of
diverse ignorances we have only one kind of ignorance
— that of the cube. Each of the cubes was an inch each
way, and I learnt a cubic yard of them. That is to say,
when the name of any cube was said, I could tell at
once those which it lay next to ; and if a set of names
were said, I could tell at once what shape composed of
cubes was denoted. There were 216 primary names,
and these, taken in pairs, were enough to name the cubic
For the practical purpose of this paper, however, it
will suffice if the reader will imagine a block of twenty-
seven cubes, forming a larger cube, each cube being
denoted by a name {see Diagram I. below). Then it is
evident that two names mean a certain arrangement
consisting of two cubes in definite places with regard to
one another— three names denote three cubes, and so on.
y Google
2o8
Casting out the Self.
^^^ y^s y^^
y^y& y ^7 ^ y<9
/)5
And I would ask the reader not to mind taking a little
trouble at this point, and to look at the diagram for a
little while. If there is anything about which we can
form perfectly clear ideas, it is a little heap of cubes.
And if the reader will simply look at them for a little
space of time, he will realize clearly every word of what
I have to say ; for I am going to talk about nothing else
than this little block of cubes.
Thus, looking at the cube with the figure i upon it,
this numeral will serve for the name of the cube, and
similarly the number
written on every cube
will serve for its name.
So if I say cubes i
and 2, 1 mean the two
which lie next to each
other, as shown in the
diagram ; and the
numbers
4. 7,
DiELgrEim I, abkick™iiHitingoi27.;ubu3. Diagram I!. L a b 6 S
standing
above each other. If I say cubes I and iO, I mean
the first cube and one behind it hidden by it in the
diagram.
Now this is the bit of knowledge on which I propose
to demonstrate the process of casting out the self. It is
not a high form of knowledge, but it is a bit of know-,
ledge with as little ignorance in it as we can have ; and
just as it is permitted a worm or reptile to live and
breathe, so on this rudimentary form of knowledge we
may be able to demonstrate the functions of the mind.
And first of all, when I had learnt the cubes, I
7
S
9
4
5
6
1
2
3
7 8 9
4 Tie
i m
yGoosle
Casting out the Self. 209
found that I invariably associated some with the idea
of being above others. When two names were said, I
had the idea of a direction of up and down. But with
regard to the cubes themselves, there was no absolute
direction of up or down. I only conceive of an up
and down in virtue of being on the earth's surface, and
because of the frequent experience of weight. Now this
condition affecting myself I found was present in my
knowledge of the cubes. When certain of the names
were said, I conceived of a figure having an upper part
and a lower part. Now, considered as a set of cubes
related to one another and not to me, the block had
nothing to do with up and down. As long ago as
Ptolemy, men have known that there is no such thing
as an absolute up and an absolute down. And yet I
found that in my knowledge of the set of cubes there
was firmly embedded this absolute up and this absolute
down. Here, then, was an element arising from the par-
ticular conditions under which I was placed, and the
next step after recognizing it was to cast it out. This
was easily done. The block had to be turned upside
down and learnt over again with the cubes all in their
new positions. It was, I found, quite necessary to learn
them all over again, for, if not, I found that I simply went
over them mentally the way first learnt, and then about
any particular one made the alteration required, by a
rule. Unless they were learnt all over again the new
knowledge of them was a mere external and simulated
affair, and the up and down would be cast out in name,
not in reality. It would be a curious kind of knowing,
indeed, if one had to reflect what one knew and then,
to get the facts, say the opposite.
It may seem as if, when the cubes were known in an
upright position, they would be easily imagined in an
inverted position. But practice shows that this is, very
y Google
210 Casting oui ike Self.
far from being the case. It requires considerable mental
effort to determine the alterations in position, and to
get an immediate knowledge requires a considerable
time.
It may seem as if it were a dubious way of getting
rid of gravity, or up and down, just to reverse the action
of it.
But this way is the only way, for we, I have found,
cannot conceive it away ; we have to conceive it acting
every way, then, affecting each view impartially, it affects
none more than another, and is practically eliminated.
The cube had not only to be turned upside down, but
also laid on each of its sides and then learnt. There
were a considerable number of positions, twenty-four in
number, which had to be brought close to the mind, so
that the lie of each cube, relative to its neighbours and
the whole block, was a matter of immediate apprehen-
sion in each of the positions.
If a single cube be taken and moved about, it will be
found that there are twenty-four positions in which it
can be put by turning it, keeping one point fixed, and
letting each turning be a twist of a right angle. The
whole block had to be turned into each of these posi-
tions and learnt in each.
Thus the block of cubes seemed to be thoroughly
known.
At any rate, up and down was cast out. And we can
now attach a definite meaning to the expression "casting
out the self" One's own particular relation to any object,
or group of objects, presents itself to us as qualities
affecting those objects — influencing our feeling with
regard to them, and making us perceive something in
them which is not really there.
Thus up and down is not really in the set of cubes.
Now these qualities or apparent facts of the objects
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Casting out the Self. 2 1 1
can be got rid of one at a time. To cast out the self is
to get rid of them altogether.
As soon as I had got nd of Up and Down out of the
set of cubes I was struck by a curious fact.
If in building up the block of cubes one goes to the
left instead of to the right, keeping all other directions
the same, a new cube is built up having a curious rela-
tion to the old cube. It is like the looking-glass image
of the old cube. Every cube in the new block corre-
sponds to every cube in the old block, but in the new
figure it is as much to the left as before it was to the
right. And any set of names in the block so put up
gives a shape which is like the shape denoted by the
same set of names in the old block, but which cannot be
made to coincide with it, however turned about. It
is the looking-glass image of the old shape. The one
block was just like the other block, except that right
was changed into left, Now, was it necessary to cast out
right and left as had been done with up and down ? or
was right and left, as giving distinctions in the block and
in shapes formed of cubes, to remain ? It seemed as if
right and left belonged more to me than to the set of
cubes. And yet the right-handed set of cubes could not
be made by moving about to coincide with the left-
handed set of cubes. And this power of coincidence
was the test which had convinced me of the self nature
of" Up and Down,"
Let Diagram I. represent a small block of cubes. It is
itself in the form of a cube, and it contains 27 cubes.
For purposes of reference we will give a number to each
cube, and the number will denote the cube where it is.
In the front slice are cubes numbered from i up to 9,
in the second slice are cubes numbered from 10 to \'6,
and so on. Thus behind i is the cube lo. This cube
and the cube 11 are hidden, but the cube 12 is shown in
the perspective.
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2 12 Casting out the Self.
Now in this block of cubes there is a part which is
known and a part which is unknown. The part which
is known is how they come or the arrangement of them.
The part that is unknown is the cube itself, repetitions
of which in different positions forms the block.
The cube itself is unknown, because, being a piece of
matter, it possesses endless qualities, each of which grows
more incomprehensible the more we study it. It is also
unknown in having in it a multitude of positions which
are not known. The cube itself is, amongst other things,
a vastly complicated arrangement of particles. Hence,
putting all together, we are justified in calling the cube
the unknown part ; the arrangement, the known part.
The single cube thus is unknown in two ways. It is
unknown in respect to the qualities of hardness, density,
chemical composition, &c. It is also unknown as a
shape. If it really consisted of a certain number of
parts, each of which was clear and comprehensible in
itself, then we should know it if we grasped in our minds
the relationship of all these parts. But there are no
definite parts of which a cube can be said to be made
up. We can suppose it divided into a number of exactly
similar parts, and suppose that all are like one of these
parts. But this part itself remains, and the problem re-
mains just the same about this part as about the whole
cube-
Now there is a double perplexity: one about the nature
of the matter, the other about the cube as to the arrange-
ment of its parts. We will give up any question about
the matter of which the cube is composed ; to know any-
thing about that is out of the question. But, supposing
it to be of some kind of matter, it presents an inex-
haustible number of positions. It can be divided again
and again.
Let us look at the block again, and for the moment
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Casting out the Self. 2 1 3
dismiss from our minds the question just raised as to the
single cubes of which it is built up. Let us look on each
of these cubes as a unit. Then two of the units, taken
together, form a shape ; three or five of them would form
a more complicated shape, and so on.
We can also suppose the cubes away, and think
merely of the places which they occupied. In this
manner, by first thinking of the 27 cubes, and then
simply by keeping the places of them in our minds,
we get 27 positions, and in these positions we can
suppose placed any small objects we choose. Each of
these positions may be called a unit position, and we
can form different arrangements of small objects by
putting them in different ones of these positions. Now
in all this we do not divide the cube up. We simply
think of it as a whole— we think of it as a unit. Or if
we take the room of the cube instead of the cube, and
think of the place it occupies, which I call a position, we
do not divide that position up. We take it, if I may use
the expression, as a unit position. And without asking
any question as to tite nature of these positions, whether
they are complicated ideas or not, we have a kind of.
knowledge of the whole block, in that it consists of this
collection of 27 cubes, or of this set of 27 positions.
Thus in a rough and ready manner there is something
which we can take. If we do not inquire about one of
the cubes itself, we are all right ; that being granted we
can know the block.
But if we look into what each of these unit cubes, or
what each of these unit positions is, we find quite an
infinity opening before us. There is nothing definitely
of which we can say that the whole unit cube is built
up, and each of the positions has a perfectly endless
number of positions in it, if we come to examine it
closely. All that we can say is that our ignorance
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2 1 4 Casting out the Self.
about each of the unit positions is of the same kind
as our ignorance about every other, and, taking one as
granted, we may as 'well take the 27 as granted ; and
so out of a lot of similar ignorances we get a kind of
knowledge of the whole. And this knowledge is not
a mere indefinite thing, but it can be worked at, im-
proved, and made perfect after its kind. For suppose
we limit ourselves to the 37 positions numbered in
Diagram I. Two of these positions form one shape,
three of them will form another shape, and so on. And
in going over each of these arrangements we gradually
get to know the whole set of them which form the
block.
Having given up for the time any question as to the
possible subdivisions of the cube, and looking on each
cube as a unit position, we have 2J positions. These
positions can be taken in different selections, and each
selection is a shape. To know the block or set of
positions means to form a clear Idea of every shape, con-
sisting of selections of positions, which can be formed out
of the 27.
But each of the cubes, 27 of which form the whole
block, can be divided up. Each of these cubes contains
a great many positions. There must, for instance, be
positions in each cube for every one of its molecules.
Thus it is evident that the cube supplies an inex-
haustible number of positions to be learnt. I call the
cube unknown in the sense that there are a great number
of positions in it which are not clearly realized by the
mind.
By a very simple device it is possible to penetrate a
little into the unknown part. The whole set of cubes
forms a cube. Let us consider the small cube to be a
model of the whole cube. Let us consider It as consist-
ing of 27 parts, each related to the other as the 27 first
y Google
Casting out the Self. 215
cubes were related amongst themselves. Thus the un-
known part, the material cube, which is used to build up
the whole, becomes reduced in size. Fig. 31. represents
such a cube.
This is the theory. The practical work consisted in
learning the names denoting these smaller cubes in con-
nection with their positions, so that, the names being said,
the small cubes meant were present to the mind, and a
set of names being said, the shape, consisting of a set of
cubes in deSnite relations to each other, came vividly
before one. A complete knowledge of the block of cubes
would be a complete appreciation of all the possible
shapes which selections of the cubes would form, and
this I strove to attain. Here at length I found real
knowledge, and after a time I was able to reduce the
size of the unknown still further, and to obtain a solid
mass of knowledge fairly well worked all through.
And now it all seemed satisfactory enough. There
was real knowledge in knowledge of the arrangement ;
and the material cube, which must be assumed, could be
made smaller and smaller, it could be turned into know-
ledge, thus affording a prospect of obtaining endless
knowledge. Thus I found the real home of my mind, the
only knowledge I had ever had, and I hoped always to
continue to add to it, and always to reduce the unknown
in size.
Presently, too, the forms of the outward world began
to fall in with this knowledge ; and as the mass of known
cubes became larger in number, a group of them would
fairly well represent a wall, a door, a house, a simple
natural object such as a stone or a fruit.
Yet amidst all this delight I became conscious, dimly
enough, of a self-element in the knowledge of blocks.
If, putting up the block of cubes, wc go to the left
instead of the right, but in all other respects build up in
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2 r6
Casting out the Self.
the same way, we obtain a block which has a curiouR
relation to the first block.
The ordinary block is shown over again in Diagram
III. Diagram IV. is the new block. The new block is
like a looking-glass image of the old block. It is just
the same, but
7 8 9
4 5 6
1 2 3
that lett aj
right is ,
versed.
Also, if ^
take
selet
1 1 o n s of
blocks we get
figures which
are just re-
versed. Thus
4, 7,
T_B_9
4 _5__6
1 2 3
Block in.,
ans a figure
turned to the right;
DiagmmUl. ;„ Block IV, a figure
turned to the left.
Again, consider the two figures
formed by selecting the cubes
1,4,7,8, 17, from Diagrams III.
and IV. respectively. We get
two figures which are just like
Diagram V. one another as arrangements, but
which we cannot turn into one another by twisting.
Considered as arrangements in themselves, these
figures and these blocks seem to be identical, for the
relationships of cube to cube which are present in
the one are all present in the other. But considered
as shapes they are not identical. For they will not
coincide.
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Casting out the Self.
217
The whole matter becomes much more clear if we
■consider the relationship between the individual cube
.used and the block which it forms.
There are two starting-points, either of which we can
adopt. We can start with the real material cube, or we
can start with the act of arranging. When I speak of
the real material cube
I do not want to
attention 1
the kind of
matter of
which it is
composed, or
to the nature
of matter, but
to the fact
that it is to
be a real cube
such as can
be made, and
which, if one
edge or corner be
marked, will retain
that mark just where
is not a product of
but an object, with
objects in general,
the. real material
9 8 7
6 5 4.
3 2 1
/
L_L_Z
6__5__4
3 2 1
Diagram IV.
K its iDiage blodi.
it is — a cube which
the imagination,
the properties of
Let us start with
cube. Let us take
the cube shown in Diagram vi. Diagram V., which
is the model on a small scale of the Block IlL The
numbers in it show the small cubes of which we suppose
it to be built up after the pattern of Block IIL The
numbers also serve to show the distinction of positions —
that is, we can refer to the right-hand corner or edge, &c.,
by saying the numbers of the small cube which lies there.
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2 1 8 Casting out the Self.
Now, using the cube of Diagram V. to build up the
block in Diagram III. we get a perfectly orderly result,
as shown in Diagram VII., and we can go to bigger and
bigger blocks, or down to smaller and smaller ones with-
out any hitch. But if we use the cube of Diagram V.
to build up the block of Diagram IV., there is a disad-
justment which can be discerned in Diagram VIII. Thus,
when V. is used to build up III., the small cubes in V.
I, 4, 7, lie in same edge as the cubes i, 4, 7, in the big
Cube III. But when V. is used to build up IV., the small
7
8
9
9
8
7
4
5
6
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5
4
7
s
^
2
3
3
2
7
8
9
4
5
e
4
5
6
)
2
3
1
2
3
Cube V.
ikgram Vlll.— Block IV. bu
wiih Cube v.— a disadjustmi
cubes 3, 6, 9, lie on the edge which is occupied by the
cubes I, 4, 7, in big Cube IV.
Thus, if the same material cube is used, there is a
disadjustment, and the figure IV. cannot be considered
the same as the figure III. even as an arrangement, for
the same parts of the cubes do not lie in an analogous
manner. A certain corner of Cube V. is marked with
the figure 7 ; this corner would be on the outside in Block
III., but in building up Block IV. it would lie on the
inside.
It is somewhat difficult to express this fact, but if the
real cubes arc looked at it becomes perfectly obvious.
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Casting out the Self- 2 1 9
Imagine the whole Block III. to be built up of a num-
ber of cubes, every one of which is alike. If the sides of
these cubes be distinguished by any markings— if, for
instance, the left-hand side is blue and the other sides
are each of some special colour, then on building lip
the whole block the left-hand side of the whole block
will be blue.
If, now, the same cubes be taken, and the attempt be
made to build up the looking-glass image of the block
with them, it will be found that there will be a disadjust-
ment. If the blue sides are made to go to the right, a,s
they must, to form an image block, then some other sides
will be in different places to what they should be in order
to produce an image of the original block. Although
considered as an arrangement of cubes the new block
will be an image of the original block, still, looking at
the individual cubes of which it is composed, it will be
seen that the new block is not an exact image of the old
block.
If, however, we take the other starting-point, and, not
assuming any fixed fundarhental cube, look only at the
act of arrangement, the two Blocks, III. and IV,, are
found to be identical in every internal relationship.
For, taking the act of arrangement as the basis, if,
when we have built up the Block IV., we look upon each
of the cubes as an arrangement of the same kind as the
whole, then the cube i in Diag. IV, is represented in
Diag. VI. And it is evident that if Diag. IV. is built up
out of cubes like Diag. VI., the small cubes, i, 4, 7, lie
n the same edge as the cubes i, 4, 7, in Diag. IV. Thus
t will be found for every relationship in Diag. III. there
s an exactly similar relationship in Diag. IV.
In this case if, for the sake of material illustration, we
ise marked cubes, it seems that we must not suppose
:ach particular cube to have a fixed marking of its own,
y Google
2 20 Casting Old the Self.
but that we must suppose the markings to spring up on
the sides of the cubes in accordance with the places into
which they are put.
There is another manner of regarding the matter
which may help to bring out the point at issue.
If we suppose that we are putting up the cubes in one
room while another person is putting up cubes in an
adjoining room ; if we can tell him what we are doing,
using the words right and left, he will be able to put up
a block exactly like ours. But if we do not allow our-
selves to use the words right and left, but speak to the
other person as If he were simply an intelligence without
having the same kind of bodily organization as ourselves,
we should find that, supposing he could put up the block
of cubes, it would be a mere matter of chance whether he
had put up the block as we had put it, or whether he
had put it up in an image way. And the same with
regard to any shape. We could tell him that the cubes
should be put together, and we could tell him the
relationship which they should have with regard to one
another ; but the figure he put up would just as likely be
an image of our shape as not.
And we could go on for ever building more and more
complicated shapes and telling him to do the same,
and no hitch or difficulty would come. But at the end
all his shapes might be ours just reversed, as if seen in a
mirror.
And if, having put up the block, we coloured the sides
of the cube we used as the fundamental cube, and told
him how we had coloured it ; if he coloured his and
brought it to us, and we compared them, his would just
as likely be the image of our cube, and not able to be
turned into it. So that although, as arrangements, the
structures we had put up were alike, still neither of us
could use the other's fundamental cube ; and if we ex-
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Casting out the Set/. 2 2 \
changed the fundamental cubes there would be an in-
consistency in each of our arrangements.
Now, are these blocks of cubes really the same ? Arc
III, and IV. really the same in themselves, as all relation-
ships in the one are to be found in the other ? If so, the
feeling on my part that they are different, and the in-
conceivability of their coinciding, must be due to some
self-element which is mixed up with my apprehension
of the cube.
The Block IV. is like the Block III. in its known part-
in its arrangement. It is unlike Block III. in its un-
known part—the cube which must ultimately be supposed
as the fundamental cube, by using which over and over
again the whole is built up.
Now, the properties of the unknown part — the little
cube of matter which of some size or another, we must
assume, are so mysterious that one does not feci any
argument very safe which rests on it.
Moreover, there is a very obvious consideration which
reduces the importance of the part played by the
material cube very considerably.
It is possible to consider the Cube V., which is used to
build up III., as the total of 27 cubes.
But each of these cubes — -the small cubes in Diag. V.- —
can be considered to be made up of 27 still smaller cubes,
By going on In this way we can get our fundamental
cube very small indeed. The difference between the
Cubes III. and IV., in respect to this fundamental cube,
will still remain. But omitting this difference they will
be, considered as arrangements, identical.
To state the matter over again. We start with a real
cube, one inch each way, and build up the block in
Diagram III. with it. If we try to build up the block
in Diagram IV. with this same inch cube, we find that
there is a disadjustment.
16
yGoosle
22 2 Casting out the Self.
But we are not obliged to have oui' fundamental cube
5ne inch in size. We can take it as small as we like,
and build up the block, using a greater number of such
cubes. We can take it the twenty-seventh of the twenty-
seventh of an inch cube ; or, in fact, as small as ever we
like. And if we take a very small cube as the funda-
mental one with which we build up the Block III,, then,
using this same fundamental cube to build up Block IV.,
we should find a disadjustment, although this disad-
justment would only come in when we come down to
the very minute cube, and studied its relationship to
the whole Block IV.
Thus, apparently, the Block IV, could never be built
up consistently, using as its fundamental cube the fun-
damental cube out of Block III. But in saying this Vi'e
have really made an assumption.
It is obvious that Cubes V. and VI., just like Cubes
III. and' IV., considered as shapes made up of matter,
are very different, and could not be shifted one on to
the other.
But all our laws and feelings about movements and
possibilities are founded on the observation of objects
having a certain degree of magnitude.
But the fundamental cube, which we must assume,
may be supposed to be of a degree of magnitude less
than any known degree.
In cubes of a certain size V. and VI. are different, and
cannot be made to coincide.
But we are absolutely unable to say anything about
cubes beyond a certain degree of smallness. With cubes
of a certain degree of minuteness, V. and VI. might be
able to be made coincide.
Thus, for instance, we feel as if wc could divide a
piece of matter on and on for ever. But chemists tell
us that, after a certain number of divisions, the next
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Casting out the Self. 223
division would split it up into two different kinds of
matter. Since all our reasoning is founded on the
behaviour of objects of known size, we can tell nothinsj
at all by inference about the behaviour of very small
objects.
It is obvious that, from our' customary experience, we
can assert absolutely nothing at all about the extremely
minute or the extremely large. All reasoning which i.s
founded on the likeness between the extremely small
and the ordinary objects of our observation is absolutely
valueless as telling us any truth.
Of course, by saying this we have not got rid of the
argument for the difference of III. and IV. But wc
have put the thing from the observation of which that
argument is drawn out of the region of known things,
We have put it into the hazy land of the extremely
minute. Its argument is good, but it depends on its
being of a certain si^e. We suppose it less than that
size, and we can consider the subject without regard
to its argument.
The question then before me was, Is " Right and Left "
to be cast out ? And connected with this was the
consideration of whether it was possible for extremely
minute cubes to be " pulled through," that is, to be treated
somehow which would turn one like V. into one like VI.
Now, if " right and left " was a self-element, it could
be cast out ; if it was a permanent distinction in the
cubes themselves, it could not be cast out. The thing to
do was evidently to try. The method was to learn the
cubes over again, in a set of new positions. For every
one of the \vays in which they were learnt before, there
was an inverted or pulled through way to be learnt.
While I was engaged in this attempt another inquiry
suddenly coincided with this, and explained it all.
Much has been said about the fourth dimension of
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224 Casting out Ike Self.
space and the inconceivability of it to us. Now, if there
are beings who live in a four-dimensional world, they
must feel as habituated to it as we do to ours, and the
conceptions which seem so impossible to us must be
every-day matters to them. It would be impossible for
us to tiy to enter at once into the serious thoughts of
these denizens of higher space. But amongst them
there would probably be some with whose occupations
we might become familiar, and with whose ideas we
might gain some acquaintance. Amongst these beings
there must be children, and just as children on the
earth gain their familiarity with space by means of
bricks and blocks and toys, so these higher children must
have their own simple objects wherewith they grow into
familiarity with their complex world.
Now it is easy to make a set of simple objects such
as these higher children would use. And it seemed a
practical thing to do with regard to the conceivability
or inconceivability of the fourth dimension to give the
matter a fair trial, by going through those processes
and those experiences which must be gone through by
the beings in higher space to gain their acquaintance
with it.
When I say that it is easy to make a set of objects,
such as the higher children use, I do not mean to say
that they can be made completely in every part at once.
But we can make the ends and sides of them, and we
can look at the ends and sides of them as they appear
to us in space, and we can make up exactly what sides
come into space when the simple objects are twisted and
moved.
Just as a being living on a plane could tell about all the
faces and edges of a cube or other simple solid figure by
looking at what he could see when the cube was laid on
his plane, and when it was twisted and laid down again ;
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Casting out the Self. 225
so we can tell all about the sides, faceSj and edges of a
higher solid.
And the project seems less uninviting if we reflect on
how complicated a matter the formation of our own
conceptions of a solid are. What a lot of faces and
edges a cube has ! And, moreover, it must be remem-
bered that wc never touch or see a solid ; we only see the
surface and touch the surface. If we cut away the
surface that we first saw "or touched, we come on
another surface, and so on.
Now, of course, the surfaces of a solid are given to us
by nature in their right connection and relation. Each of
the edges of the cube, for instance, can be noticed and
remarked without any diiSculty, and they are all on the
same bit of space, to be looked at one at the same time
as another.
But the sides, faces, and edges of a higher solid cannot
be in our space all at once. They must come separately,
be looked at one by one.
Thus a being in a plane could not see the lower side
and fhe front of a cube at once. He would first have to
look at the lower side as the cube rested on his plane,
then if the cube were turned over he would see the
front, and the lower side would be gone. If he got the
set of right appearances which a cube would present to
him when, turning about in a systematic way, it came
at intervals into his plane, and if, moreover, he fixed
his mind on these appearances, he might at last, if it
was in him, rise to the conception of a cube as wc
know it.
Now, the parts by which a higher solid comes into our
space are solids, and what we have to form is a set of
solids coming and going in a systematic way, as the
higher figure is moved about in a systematic way.
This afforded a welcome exercise, for conceiving the
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