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Full text of "Project Physics Reader: Classical & Modern Physics"

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PRQierr PHYSICS mmi 



Readings in Classical and Modern Physics 




PROjea PHYSICS rg/idgr 



Readings 

in 

Cbssical and Modern 

Physics 



A Component of the 
Project Physics Course 




HOLT. RINEHART AND WINSTON. PUBLISHERS 
New York • Toronto 



This publication is one of the many 
instructional materials developed for the 
Project Physics Course. These materials 
include Texts, Handbooks, Resource 
Book, Readers, Programmed Instruction 
Booklets, Film Loops, Transparencies, 16mm 
films and laboratory equipment. Development 
of the course has profited from the help of 
many colleagues listed in the text units. 



Directors of Harvard Project Physics 

Gerald Holton, Department of Physics, 

Harvard University 
F. James Rutherford, Chairman of the 

Department of Science Education, New York 

University, New York 
Fletcher G. Watson, Harvard Graduate School 

of Education 



PICTURE CREDITS 

Cover photograph: Open Modular Cube, 1966, sculpture 
by Sol LeWitt, American. Born 1928. Painted aluminum, 
60" X 60" X 60". Art Gallery of Ontario. Photographed 
by Norman Goldman. 



2 ^ 

5 I 

3 * 



Picture Credits for frontispiece 

(1) Photo by Glen J. Pearcy. 

Jeune fille au corsage rouge lisant. Jean Baptiste 
Camille Corot. Painting. Collection Bu'hrle, Zurich. 
Harvard Project Physics staff photo. 
Femme lisant. Georges Seurat, Conte Crayon 
drawing. Collection C. F. Stoop, London. 
Portrait of Pierre Reverdy. Pablo Picasso. 
Etching. Museum of Modern Art. N.Y.C. 
Lecture au lit. Paul Klee. Drawing. Paul Klee 
Foundation, Museum of Fine Arts. Berne. 



(2) 

(3) 
(4) 

(5) 

(6) 



Copyright ©1975, Project Physics 
All Rights Reserved 
ISBN: 03 089794-7 

56789 005 987654321 
Project Physics is a registered trademark 



SOURCES AND ACKNOWLEDGMENTS 
Readings in Classical and Modern Physics 

1. A Hole in the Sky, by Walter Sullivan. From 
The New York Times Magazine, July 14, 1974. 
Used by permission. 

2. The Drive for Power. Chapter 8 of The Ascent 
of Man by J. Bronowski. Copyright © 1973 by 

J. Bronowski. Used by permission of Little, Brown 
and Company. 

3. Modeling from The Engineering Concepts Cur- 
riculum Project: Man and His Technology. Copy- 
right © 1973 by Research Foundation of the State 
University of New York. Used by permission of 
McGraw-Hill Book Company. 

4. Exponential Process in Nature. Donald F. 
Holcomb & Philip Morrison, My Father's Watch: 
Aspects of the Physical World, copyright © 1974. 
Used by permission of Prentice-Hall, Inc., 
Englewood Cliffs, New Jersey. 



5. Physics in Biology - Physics Survey Committee 
NRC-NAS. From Physics in Perspective, Volume 1. 
Copyright © 1973 by the Physics Survey Committee. 
Used by permission of the National Academy of 
Sciences, Washington, D.C. 

6. Observations of an Early Morning Cup of Coffee, 

by Vincent J. Schaefer, American Scientist 59, 
No. 5, 1971. Used by permission o^ American 
Scientist. 

7. The Decision to Study Physics (1920) from 
Physics and Beyond: Encounters and Conversa- 
tions by Werner Heisenberg, Vol. 42 of World 
Perspectives, edited by Ruth Nanda Anshen. Copy- 
right © 1971 by Harper & Row, Publishers, Inc. 
Used by permission of the publishers. 

8. Science and Modern Art from Physics and Its 
Fifth Dimension: Society by Dietrich Schroeer. 
Copyright © 1972 by Addison-Wesley, Reading, Mass. 
Used by permission of Addison-Wesley. 

9. Symmetry. Donald F. Holcomb & Philip Morrison, 

My Father's Watch: Aspects of the Physical World, 
Copyright © 1974. Used by permission of Prentice- 
Hall, Inc., Englewood Cliffs, New Jersey. 
The Nature of Physics - Physics Survey Committee 
NRC-NAS. From Physics in Perspective, Volume 1. 
Copyright © 1973 by the Physics Survey Committee. 
Used by permission of the National Academy of 
Sciences, Washington, D.C. 
The Decision to Drop the Atomic Bomb from 
Physics and Its Fifth Dimension: Society by 
Dietrich Schroeer. Copyright © 1972 by Addison- 



10 



11 



12. 



13. 



14. 



15. 



Wesley, Reading, Mass. Used by permission of 
Addison-Wesley. 

The Conception of Nature in Japanese Culture, by 
Masao Watanabe. The Japan Christian Quarterly, 
published by Kyo Bun Kwan, Tokyo, and Science, 
Vol. 183, pp. 279-282, January 25, 1974. Used by 
permission. 

Facts on Household Appliance Energy Use from 
Annual Energy Requirements of Electric Household 
Appliances, EEA 201-73. Used by permission of the 
Electric Energy Association. 
Breeder Reactors by Walter Sullivan. From The 
New York Times July 22, 1973. Used by permission. 
Reflections of a Working Scientist. Reprinted 
by permission of Daedalus, Journal of the 
American Academy of Arts and Sciences, Boston, 
Massachusetts. Summer 1974, Science and Its Public: 
The Changing Relationship. 
Strzeino to the Golden West. Reprinted by per- 
mission of Charles Scribner's Sons from The Master 
of Light b\ Dorothy Michelson Livingston. Copy- 
right © 1973 by Dorothy Livingston. 
17. Energy and the Environment by John Fowler from 
The Science Teacher, December 1972. Used by per- 
mission. 

The Lens, A Most Imperfect Eye by Norman Gold- 
berg. Copyright © 1970 by Ziff-Davis Publishing 
Company. Reprinted by permission ofPopular Photo- 
graphy Magazine and Ziff-Davis Publishing Company. 
Science, Technology, and the Arts: A Reference 
Bibliography for Students by William H. Davenport. 



16 



18 



19. 



Ill 







IV 




This is not a physics textbook. Rather, it is a physics 
reader, a collection of some of the best articles and 
book passages on physics. A few are on historic events 
in science, others contain some particularly memorable 
description of what physicists do; still others deal with 
philosophy of science, or with the impact of scientific 
thought on the imagination of the artist. 



There are old and new classics, and also some little- 
known publications; many have been suggested for in- 
clusion because some teacher or physicist remembered 
an article with particular fondness. The majority of 
articles is not drawn from scientific papers of historic 
importance themselves, because material from many of 
these is readily available, either as quotations in the 
Project Physics text or in special collections. 

This collection is meant for your browsing. If you follow 
your own reading interests, chances are good that you 
will find here many pages that convey the joy these 
authors have in their work and the excitement of their 
ideas. If you want to follow up on interesting excerpts, 
the source list at the end of the reader will guide you 
for further reading. 




Readings in Classical and Modern Physics 
Table of Contents 



1 A Hole in the Sky 1 

Walter Sullivan 

2 The Drive for Power 12 

J. Bronowski 

3 Modeling 32 

The Engineering Concepts Curriculum Project 

4 Exponential Process in Nature 71 

Donald F. Holconnb and Philip Morrison 

5 Physics in Biology 88 

Physics Survey Connnnittee NRC-NAS 

6 Observations of an Early Morning Cup of Coffee 100 

Vincent J. Schaefer 

7 The Decision to Study Physics 104 

Werner Heisenberg 

8 Science and Modern Art 1 1 6 

Dietrich Schroeer 

9 Symmetry 131 

Donald F. Holconnb and Philip Morrison 

10 The Nature of Physics 149 

Physics Survey Connmittee NRC-NAS 



VI 



1 1 The Decision to Drop the Atomic Bomb 1 73 

Dietrich Schroeer 

12 The Conception of Nature in Japanese Culture 187 

Masao Watanabe 

13 Facts on Household Appliance Energy Use 194 

Electric Energy Association 

14 Breeder Reactors 195 

Walter Sullivan 

15 Reflections of a Working Scientist 197 

Steven Weinberg 

16 Strzeino to the Golden West 210 

Dorothy Michelson Livingston 

17 Energy and the Environment 224 

John Fowler 

18 The Lens, a Most Imperfect Eye 236 

Norman Goldberg 

19 Science, Technology, and the Arts: A Reference Bibliography for Students 239 

Wiiliann Davenport 



VII 



Nothing in the art of the medieval alchemist or the science- 
fiction writer is more bizarre than the concept of the "black 
hole". And yet, as the New York Times science editor 
points out, this new idea is receiving the attention of many 
scientists and is important to an understanding of our 
universe. 



1 A Hole in the Sky 

Walter Sullivan 

An article from The New York Times Magazine, July 14, 1974 



At 7:17 A.M. local time on June 30, 
1908, something frightful occurred in the 
Tunguska area of central Siberia. As 
though a catastrophic mid-air explosion 
had taken place, virtually all trees within 
a radius of 20 miles were blown down. As 
recently as the nineteen-sixties, the char- 
red tree trunks, many of them with the 
bark torn off, could still be seen from the 
air, forming a striking pattern of Hnes 
radiating from the explosion site. 

Residents of the region who were alive 
at the time of the blast have reported that 
just beforehand they spotted a fireball 
crossing the sky that was so bright "it 
made even the light from the sun seem 
dark." From Kirensk, 250 mUes away, a 
"pillar of fire" was seen, followed by 
three or four claps and a crashing sound. 

Such was the force of the explosion 
that horses were thrown down in an area 
south of Kansk, more than 400 miles dis- 
tant. Equally remarkable were the flash 
burns sustained by residents of this 
sparsely populated region. A farmer, S. B. 
Semenov, was sitting on the steps of his 
house, 40 miles away, when he saw the 
flash. He instinctively lowered his eyes, 
but the heat was searing. "My shirt was 
almost burned on my body," he told later 
visitors. When he raised his eyes again, the 
fireball had vanished. Moments later, the 
blast hurled him from the steps, leaving 



him briefly unconscious. When he re- 
covered, a great thundering sound was 
audible. His neighbor, P. P. Kosolopov, 
was facing away from the fireball and the 
first he knew of it was when his ears 
burned painfully. He covered them with 
his hands and ran into the house. 

A Tungus tribesman told scientists who 
reached the site long afterward that a 
herd of 500 reindeer had been wiped out: 
"The fire came by and destroyed the for- 
est, the reindeer and all other animals." 
In one herdsman's storage hut, everything 
had been burned including his clothing, 
and his samovar as well as his silverware 
had melted. 

Five widely divergent explanations for 
this event have been advanced: 

■ The first hypothesis was that a giant 
meteorite had fallen, exploding from the 
intense heat generated by its impact. 
Such a meteorite hit Arizona in prehistor- 
ic times, leaving a crater three-quarters of 
a mile wide. But when expeditions reach- 
ed the remote Tunguska region, they 
could not find even a small impact crater. 

■ In the nineteen-fifties, it was suggest- 
ed that a distant, highly advanced civiliza- 
tion may have somehow instigated a mid- 
air nuclear explosion. That the blast did, 
in fact, take place high in the air was 
shown by the dissection of tree branches 
that had been growing in 1908; the upper 



surfaces of the layer that had been ex- 
posed to the sky in that year had been 
scalded. In addition, recordings of fluctu- 
ations in the earth's magnetism at the 
time showed an effect strikingly like that 
produced by an atomic-bomb explosion 
in the atmosphere. And an expedition to 
the site in 1958 reported that unusually 
high levels of radioactivity had been de- 
tected there. However, a careful study of 
the area in 1961 showed that report to 
have been spurious. 

■ The explanation still favored by 
many scientists is that a comet head 
plunged into the atmosphere at such high 
velocity that it exploded in mid-air from 
heat generated by its entry into the atmo- 
sphere. Comet heads are widely beheved 
to be huge "dirty snowballs," formed of 
frozen gases such as ammonia and water, 
with an admixture of dust, including par- 
ticles of meteoritic iron. While such iron 
particles have been found in the soil of 
that region, they were not substantially 
more abundant than the accumulations of 
meteoric dust from the sky that are slow- 
ly deposited worldwide. Moreover, skep- 
tical scientists have asked how a comet 
could have exploded without leaving even 
a trace of its own substance. And how 
could it have approached the earth with- 
out being seen? 

■ A more recent theory is that an "an- 
tirock" made of antimatter plunged into 
the atmosphere and was annihOated on 
contact with atoms of ordinary matter, 
producing a fireball of gamma rays and an 
explosion. This would account for the 
flash burns, the apparent absence of a 
mushroom cloud like those generated by 
ordinary chemical and atomic explosions, 
and the lack of any residual material. 

■ The latest proposal is that a tiny 
"black hole" hit Siberia, passing through 
the entire earth and emerging in the 
North Atlantic. 

Nothing in the art of the medieval al- 
chemist or the contemporary science- 
fiction writer is more bizarre than the 
concept of a black hole. Yet in the last 
year or two a number of physicists have 



come to beheve that such "objects" re- 
present a substantial - perhaps even the 
major — part of our universe. A black 
hole would be an assemblage of matter 
that has shrunk — more properly, col- 
lapsed — to a state so extremely dense 
that it has become invisible. Because of 
its density, it would generate gravity in its 
vicinity of such extraordinary strength 
that no light — or anything else — could 
escape from it; any light rays coming near 
it would be irretrievably drawn in. 

Gravity is the weakest force in nature; 
for example, it takes the whole mass of 
the earth to make a feather fall. But if the 
earth were compressed to the size of a 
Ping-Pong ball, its gravity would become 
so concentrated that nothing could resist 
it — not even Ught. Visually, therefore, 
such a body would be a "black hole." 

Because of the extreme conditions 
within such an object, the laws of nature 
with which we are familiar would be over- 
whelmed, and, many theorists beheve 
"crazy" effects predicted by relativity 
theory (and to some extent already dem- 
onstrated) would prevail. Inside the black 
hole, time and space would be inter- 
changed, so that, like AUce's experience 
in "Through the Looking-Glass," it would 
be no more possible to remain in one 
place than to stop the forward march of 
time in our world. Anyone who fell into a 
black hole would be stretched out Uke a 
string of spaghetti, then would disinte- 
grate. Finally, even the atomic particles 
of the unfortunate person's body would 
lose their identity. Yet, theoretically, his 
or her image would hnger, ghost-like, on 
the outer fringes of the hole, where hght 
does not have quite enough energy to es- 
cape, preserving indefinitely the last 
gUmpse available to an outside observer. 

In contemplating such exotic explana- 
tions for the Tunguska event as antirocks 
or black holes, we realize how far our ideas 
about nature have gone beyond what we 
can see, hear and feel. The concept of an- 
timatter arose as scientists learned more 
and more about the behavior of atomic 
particles. It was evident that there are 
striking symmetries in such behavior, and 
in 1928 the British theorist P. A.M. Dirac, 



A Hole in the Sky 



whom many physicists rank with Einstein 
suggested that to complete the sym- 
metries there must be a particle identical 
to the electron but with an electric charge 
that is positive instead of negative. Four 
years later, such a particle - the positron 

- was discovered in laboratory experi- 
ments, and it is now evident that for 
every particle of ordinary matter, there is 
an "equal-but-opposite" particle (the an- 
tiproton is another example). If such 
particles were assembled into atoms, and 
the atoms assembled into stones, people 
and worlds, they would constitute anti- 
matter. Throughout our environment par- 
ticles of antimatter are constantly formed 
by the impact on atmospheric atoms of 
high-energy particles (cosmic rays) raining 
on the earth from space. The antiparticles 
can be observed by sophisticated labora- 
tory techniques, but they survive less 
than a millionth of a second. For as soon 
as they encounter an atom of ordinary 
matter — and there are plenty of those in 
our atmosphere — they are annihilated, 
leaving only a tiny but briUiant flash of 
Ught at the invisible but highly energetic 
wave lengths known as gamma rays. 

While ordinary matter dominates our 
part of the universe, conceivably there 
are galaxies of antimatter with their own 
antiworlds and antipeople far out in space 

— antigalaxies, so to speak. Light gene- 
rated by antimatter would be indistin- 
guishable from our kind of Ught, so it 
would be impossible to identify an anti- 
galaxy through a telescope. The physicist 
Harold P. Furth once wrote a ditty about 
Dr. Edward Teller, the "father of the 
hydrogen bomb," who had suggested that 
worlds may exist where antimatter pre- 
dominates. In the poem, "Perils of 
Modern Living," Dr. Teller voyaged to a 
world where everything is opposite (for 
example, antimacassars became macas- 
sars) : 

Well up beyond the tropostrata 
There is a region stark and stellar 
Where, on a streak of antimatter. 
Lived Dr. Edward AntiTeller. 

Remote from Fusions's orgin. 
He lived unguessed and unawares 



With all his antikith and kin, 
And kept macassars on his chairs. 

One morning, idling by the sea. 
He spied a tin of monstrous girth 
That bore three letters: A.E.C. 
Out stepped a visitor from Earth. 

Then, shouting gladly o'er the sands. 
Met two who in their alien ways 
Were like as lentils. Their right hands 
Clasped, and the rest was gamma rays. * 

The possibility that the Siberian explo- 
sion was caused by a meteorite of anti- 
matter was examined by no less a physi- 
cist than Willard F. Libby, former mem- 
ber of the Atomic Energy Commission 
and winner of a Nobel Prize for his dis- 
covery of radioactive carbon dating. 
Libby and two other physicists observed 
in Nature, a British journal of worldwide 
repute, that since both antimatter and 
matter would be converted into energy if 
such a meteorite fell into the atmosphere 
(a far more efficient conversion than that 
of an atomic bomb), only a small amount 
of antimatter would be needed to pro- 
duce a blast equal to that of 30 million 
tons of TNT — the estimated force of the 
Siberian explosion. They also pointed out 
that the disintegration of an antirock 
would briefly enrich the amount of car- 
bon 1 4 in the air, which is normally man- 
ufactured at a fairly steady rate by the 
rain of cosmic rays from space. If there 
was more carbon 14 in the air than nor- 
mal in 1908 and soon afterward, then 
wood formed in trees anywhere in the 
world during that period would be un- 
usually rich in that form of carbon. 

The amount of carbon 14 in successive 
rings of a 300-year-old Douglas fir from 
Arizona and a venerable oak from near 
Los Angeles were measured — and, in- 
deed, the highest level in the wood was 
created in 1909, the year after the blast. 
Had the object been made entirely of an- 
timatter, however, the effect would have 
been more marked. Thus the three scien- 
tists concluded that the evidence was in- 
conclusive. 

© 1956, The New Yorker Magazine, Inc. 



— It was last September that two scien- 
tists then at the University of Texas, A. 
A. Jackson 4th and Michael P. Ryan Jr., 
suggested that the 1908 devastation was 
caused by a "mini" black hole. The "con- 
ventional" black hole is the residue of a 
giant star that has collapsed, leaving a su- 
perdense remnant with a mass compar- 
able to that of the sun. In 1971, however, 
Stephen Hawking of Cambridge Universi- 
ty had proposed that "mini" black holes 
might have been created during the initial 
"big-bang" phase of the universe's birth. 
Hawking pointed out that if the earUest 
period of the universal explosion were 
turbulent, there must have been areas of 
great compression, as well as regions 
where expansion was taking place. The 
compression would have squeezed materi- 
al into mini black holes that would still 
permeate the universe. Writing in Nature, 
Jackson and Ryan proposed that the 
penetration of the atmosphere by such a 
mini black hole and its passage through 
the earth could account for all the report- 
ed effects. 

The more conventional idea of a comet 
impact obviously makes scientists hap- 
pier. But, in truth, no explanation satis- 
fies everyone, and we are left with the 
real possibility of a recurrence. Should it 
take place without warning in a popu- 
lated region and resemble a nuclear blast, 
could it trigger an atomic war? A better 
understanding of such phenomena could 
minimize the risks. In any case, the dis- 
cussion of black holes as a possible cause 
demonstrates to what extent some scien- 
tists are rushing to explain various puzzles 
in astronomy and physics with this be- 
wildering concept. Astronomical observa- 
tions in the past year or two have made 
black holes seem a reality, although, as 
one physicist put it, they are "as per- 
vasive in theory as they are evasive in ob- 
servation." 

The roots of the concept lie far back in 
the history of astronomy. In 1844, at the 
observatory in Konigsberg, Prussia (now 
Kaliningrad in the U.S.S.R.), F. W. Bessel 
found that the path of Sirius, the sky's 
brightest star, was slightly irregular. To 
casual observers, it had always seemed to 



remain in the same spot, but being one of 
the nearest stars to the solar system its 
motion relative to distant objects in the 
universe could be traced through a tele- 
scope. Sirius, Bessel's data demonstrated, 
moves in a wavy line rather than a 
straight one. 

This indicated to him that Sirius had an 
unseen companion, and that the two stars 
were circling each other as they flew 
through the void, "held in each other's 
arms" by their mutual gravity. Since the 
mass — that is, the weight — of Sirius 
could be estimated, it was possible, using 
the laws of gravitationally controlled mo- 
tion speUed out by Newton, to estimate 
the weight of the seemingly invisible com- 
panion. It turned out to be about the 
same as that of our own sun. Why, then, 
was the companion star invisible? 

It wasn't — not completely. Nineteen 
years after Bessel's observation, an Ameri- 
can telescope maker named Alvan Clark 
spotted the companion while testing a 
new instrument. The star's intrinsic 
brightness proved to be one-four-hun- 
dredth that of the sun. The real surprise 
came, however, when Ught from the star 
was analyzed. By the early decades of this 
century it was recognized that the whiter 
the light from a typical star, the hotter, 
brighter and bigger it is. Small stars burn 
cooler, are dimmer and redder. But this 
faint star was as white as Sirius — which is 
whiter than the sun. If so white and hot, 
why was it so dim? 

The only plausible explanation was that 
the star was very small and yet, to ac- 
count for its matching the weight of the 
sun, extremely dense. As Sir Arthur Ed- 
dington wrote in 1927: "The message of 
the companion of Sirius when it was de- 
coded ran: 'I am composed of material 
3,000 times denser than anything you 
have come across; a ton of my material 
would be a little nugget that you could 
put into a matchbox.' What reply can one 
make to such a message? The reply which 
most of us made in 1914 was — 'Shut up. 
Don't talk nonsense.' " 

Skeptics now similarly exhort the pro- 
ponents of the black-hole theory to si- 
lence. But that is getting ahead of our 



A Hole in the Sky 



story. Sirius's companion was a "white 
dwarf not a black hole, and with only 
one such object on the register, it could 
be dismissed as a freak. In time, though, 
other white dwarfs were found. In fact, 
they proved to be fairly common, al- 
though so dim that only those close to 
earth could be detected. 

The explanation became apparent in 
the late nineteen-twenties when scientists 
not only began to understand atomic 
structure but got their first inklings of 
what it is that makes stars shine — a ma- 
jor puzzle. The sun, it was evident, had 
been shining for billions of years. But no 
one knew what process could possibly ac- 
count for such an enormous and continu- 
ous output of energy. Einstein had pro- 
posed, in theoretical terms, an equiva- 
lence between matter and energy. His for- 
mula suggested that conversion of even a 
small amount of matter would release 
vast amounts of energy. Although there 
was then no evidence that such conver- 
sions really take place, Eddington and 
others considered the possibility that the 
fusion of hydrogen nuclei to form hehum 
nuclei might occur within stars. Since the 
hehum nucleus would weigh 0.8 per cent 
less than the hydrogen nuclei from which 
it was formed, this small residue of mat- 
ter would emerge as energy. 

If fusion — such as the conversion of 
hydrogen into hehum — were responsible 
for energy generation within stars, what 
would happen when the fuel for these nu- 
clear fires burned out? Stars are made of 
gas, and as long as they are hot inside — 
as long as their "fires" burn — that gas 
tends to expand. Put another way, the en- 
ergy generated in their cores fights its 
way out through the star in the form of 
radiation, exerting an outward pressure 
that counter-acts the massive weight of 
the star's own substance. But R. H. Fow- 
ler in Britain proposed in 1926 that when 
a star has burned up aU its fuel, this resis- 
tance to the inward pressure of the star's 
own weight vanishes and the star col- 
lapses upon itself, forming an object of 
great density — like one gigantic, frigid 
molecule. This would be the superdense 
stuff of a white dwarf. 



Was this appUcable to all stars, no mat- 
ter how large? In 1930 a young Indian, 
newly graduated from the University of 
Madras and on his way to do graduate 
work at Cambridge University in England, 
sought during the long passage to cal- 
culate what forces within an atom resist 
compression. On his arrival in England, 
Subrahamanyan Chandrasekhar, now 
known throughout the astronomical 
world as "Chandra," showed his calcula- 
tions to Fowler, his doctoral supervisor. 
He had come to the startling conclusion 
that, for any star much larger than the 
sun, there was no known force that could 
halt the coUapse. Contraction to a white 
dwarf was possible because of the hollow 
nature of atoms. According to the tradi- 
tional (but schematic) description of an 
atom, it resembles the solar system, with 
a nucleus in place of the sun and elec- 
trons in place of planets. Like the solar 
system, it is largely formed of empty 
space. However, Chandra realized, when 
something is squeezed in a powerful 
press, there are forces within the atoms 
that resist. One arises from a basic law, 
the "exclusion principle," that had been 
enunciated by Wolfgang Pauh a few years 
earlier. The electrons occupy certain 
"slots" (not really comparable to plane- 
tary orbits) and only one is permitted in 
such a slot at any one time. Under high 
temperatures or great compression (as 
within a star) the electrons are forced out 
of their slots, forming a plasma of inde- 
pendently moving electrons and atomic 
nuclei. But the electrons still repel one 
another in the manner defined by Pauh 
and it is this effect that finaUy stops the 
coUapse of a white dwarf. 

Chandra, however, calculated that the 
weight of any star much larger than the 
sun would overcome this "electron pres- 
sure." There are giant stars 50 times more 
massive than the sun. They burn so in- 
tensely that their hfetimes are hmited to 
10 or 20 miUion years, and countless 
numbers of them must have burned out 
during the biUions of years that have pass- 
ed since, for example, the MUky Way was 
formed. What happens to them? "A star 
of large mass cannot pass into the white- 



dwarf stage," wrote the youthful Chan- 
dra, "and one is left speculating on other 
possibilities." 

The leaders of the scientific estabUsh- 
ment reacted with indignation to this sug- 
gestion that there is no Umit to the col- 
lapse. Eddington pointed out that if a star 
kept on contracting, once it has shrunk to 
within a few miles' radius, its gravity 
would become "strong enough to hold 
the radiation" — that is, it would be a 
black hole. But Eddington refused to take 
the idea seriously. He turned Chandra's 
reasoning "almost a reductio ad absur- 
dum. " 

The first clue as to what actually hap- 
pens when a large star collapses came 
from analysis of the most spectacular 
event that the heavens offer — a "super- 
nova." In 1885 astronomers had observed 
an extraordinary flareup of a star in the 
great swirl of star clouds known as the 
Andromeda Nebula, which is the nearest 
galaxy resembling our Milky Way. For 25 
days that single star shone more brightly 
than 10 million suns. Then it faded to 
such an extent that it was no longer visi- 
ble through the most powerful telescopes. 
Astronomers noted that in 1572 a simi- 
lar flare-up, known as "Tycho Brahe's 
Nova," had occurred in our own Milky 
Way, (It was called a "nova" because it 
seemed to be a "new" star.) Two Mount 
Wilson Observatory astronomers, Walter 
Baade and Fritz Zwicky, pointed out that 
the star associated with the nova had 
seemingly vanished. It appeared that such 
a "supernova" occurs once in every few 
centuries within any one galaxy, gener- 
ating radiation that probably would be 
fatal to any inhabited worlds nearby. 

Baade and Zwicky theorized that a su- 
pernova marked the death of a very mas- 
sive star whose collapse was so cata- 
strophic that a large part of the star's sub- 
stance was converted into energy, leaving 
something of considerably smaller mass. 
This residual star, they said, must have 
been compressed to such a degree by the 
explosion that it consisted almost entirely 
of tightly packed neutrons. Neutrons and 
protons are the two particles that form 
the atomic nucleus, but neutrons, being 



electrically neutral, could be packed to- 
gether more tightly than protons, which, 
carrying a positive charge, repel one an- 
other. Also, since a neutron (when free of 
an atomic nucleus) eventually sheds an 
electron and turns into a proton, it seem- 
ed reasonably to suppose that, reversing 
the process, the compression of a sea of 
protons and electrons could produce neu- 
trons. 

Meanwhile, attention had been drawn 
to the most spectacular remnant of a su- 
pernova in the sky — the Crab Nebula, 
which today still looks like the high-speed 
photograph of an explosion. By compar- 
ing pictures of the nebula taken over a 
span of years, it was possible to trace the 
expansion of its luminous gas clouds. 
Running this "moving picture" back- 
wards indicated that the original explo- 
sion must have occurred — that is, light 
from it must have reached the earth — in 
about 1054 A.D. That was a time when 
the Chinese were keeping careful astro- 
nomical records and in that year, accord- 
ing to chronicles of the Sung Dynasty, a 
star appeared so brilliant that for 23 days 
it could be seen in full daylight. If the 
Crab Nebula was a product of that explo- 
sion, Baade argued, perhaps it had left a 
neutron star at its center. Indeed, a faint 
and rather strange-looking star was ob- 
served in that region. 

There was a strong suspicion, however, 
that the neutron star was a figment, an 
absurdity derived from theoretical manip- 
ulations. Whereas the concept of a white 
dwarf, a nugget of which would weigh a 
ton, had been considered pure nonsense, 
the idea of a neutron star, one cubic inch 
of which would weigh a biUion tons, was 
preposterous. A white dwarf was formed 
from the material of a star as large as the 
sun compressed into the size of the earth, 
but a neutron star, formed from a star 
somewhat larger than the sun, would be a 
comparable amount of material crushed 
into a body with a five-mile radius. 

Even greater skepticism greeted the pro- 
posals of a young physicist at the Univer- 
sity of California in Berkeley named J. 
Robert Oppenheimer. Oppenheimer later 
became known for his leadership of the 



A Hole in the Sky 



atomic-bomb project and for his profes- 
sional martyrdom during the cold-war 
hysteria. However, his chief theoretical 
work was in the nineteen-thirties and led 
to the black-hole concept. 

Taking off from the speculations of 
George Gamow, Edward Teller, the 
Russian Lev Landau and others, he and 
his students explored what would happen 
if the weight of the collapsing star was 
too great even for neutrons to resist. Put 
another way, what if the compression 
were sufficient to overcome the strongest 
force in nature — that exerted by such 
nuclear particles as neutrons upon one an- 
other at close range. The calculations of 
Oppenheimer and his group culminated in 
a 1939 paper that he wrote with Hartland 
Snyder "On Continued Gravitational 
Contraction." There was nothing, they 
said, in Einstein's theory of gravity — the 
so-called "general" theory of relativity — 
suggesting any reason why such a collapse 
should stop. As the contraction proceeded, 
the intensity of gravity in the heart of the 
star would increase, causing the collapse 
to run at an ever-increasing rate until fi- 
nally the density would become so great 
that the gravity would be strong enough 
to prevent anything, including light, from 
escaping. 

Because gravity, when very intense, 
slows time, the collapsing process, insofar 
as it could be followed from a distance, 
would seem to a distant observer to slow 
down as the gravity field increased in 
strength until, on the outer fringes of the 
black hole, the process would appear to 
have stopped altogether. The progression 
to total collapse could take as long as the 
lifetime of the universe. But to someone 
unfortunate enough to be falling into the 
stellar abyss, cut off from all contact with 
the outside, the collapse would seem to 
be running its course in about a day. 

The ultimate destiny of such a black 
hole, derived from the Einstein equations, 
would be infinitely powerful gravity con- 
centrated in an infinitely dense, infinitely 
small spot where time and space have lost 
their meaning — what is known as a "sin- 
gularity." Whether "things" really go to 
that extreme in the heart of a black hole 



is one of the basic problems confronting 
theorists today. When proposed by 
Oppenheimer, however, the concept was, 
many thought, little more than an oddity 
with which to titillate physics students. 

Then, in 1963, the discovery of quasars 
suddenly thrust the idea of gravitational 
coUapse into the forefront, helping to 
bring Oppenheimer out of intellectual ex- 
ile and reviving speculation about black 
holes. Quasars are bodies that seem far 
more distant than any other observable 
objects in the sky — so far away that it 
must have taken bilUons of years for their 
Ught to reach us, which means we see 
them as they were when the universe was 
relatively young. No ordinary process 
could make them shine so brightly. The 
nuclear reactions believed to occur inside 
a star seemed totally inadequate and so 
scientists inaugurated a series of annual 
meetings (initially in Texas) to explore 
how collapse processes involving enor- 
mous amounts of matter might be the an- 
swer. 

Further evidence that matter sometimes 
collapses to extraordinary densities came 
from a new branch of science — radio as- 
tronomy. Until recently our knowledge 
of the heavens has depended almost 
entirely on looking through optical tele- 
scopes, that is, on observing visible wave 
lengths of light that penetrate the blanket 
of air covering our planet. But it has be- 
come possible with radio telescopes, 
space vehicles and other methods to view 
the heavens through other wave-length 
"windows" which are ordinarily invisible 
— radio waves, X-ray, gamma rays, ultra- 
violet and infrared emissions. 

Surveying the heavens with radio anten- 
nas, astronomers at Cambridge University 
in England reported in 1968 that for sev- 
eral months they had been recording ex- 
tremely rhythmic radio signals from four 
points in the sky. Each source generated 
pulses at a characteristic rate, all being in 
the range from one pulse per quarter- 
second to one every two seconds. 
Rhythmic phenomena were not new to 
astronomy, being typically associated 
with the spinning of stars, planets and 



moons, but nothing was known to spin as 
fast as once every second. "Our first 
thought," said Sir Martin Ryle, leader of 
the British group, "was that this was an- 
other intelUgence trying to contact us." 
Then, however, the scientists began pon- 
dering what would happen if a star col- 
lapsed to a superdense state such as a 
white dwarf or - for those willing to en- 
tertain such a thought — a neutron star. 

There is a basic law known as the con- 
servation of angular momentum which is 
instinctively familiar to every figure skat- 
er or ballet dancer. In a pirouette, if the 
arms are extended, the spin rate slows. If 
they are held close to one's sides, the rate 
is fastest. Thus, if a star "pulls in its 
arms" by contracting, its spin rate will in- 
crease. Many stars spin roughly once a 
day, and it was calculated that if they col- 
lapsed to a superdense state, their spin- 
ning would accelerate enormously. If 
such a collapsed star had a magnetic field 
of great strength - as seemed likely - 
this field would cause emissions, includ- 
ing those at radio-wave lengths, to form 
directional beams that, with each rota- 
tion, would sweep the sky like an airport 
beacon, accounting for the pulses. 

Many astronomers clung to white 
dwarfs as the explanation, avoiding so ex- 
treme a concept as the neutron star. But 
then came evidence that not all of the 
pulsing radio sources, or "pulsars," are 
beeping at sedate tempos. From the Crab 
Nebula, radio astronomers detected 
pulses at 30 times a second. Could Baade 
and Zwicky, then, have been right? Was it 
conceivable that the pecuhar star in the 
heart of that supernova remnant was, in 
fact, a neutron star, spinning 30 times a 
second? 

To test the possibility, special light- 
monitoring and stroboscopic television 
systems were aimed at the star. The as- 
tonishing discovery was made that it 
does, indeed, "switch itself off" 30 times 
a second — an optical as well as a radio 
pulsar. 

It was hard to believe that even so com- 
pact an object as a white dwarf could spin 
that fast. Centrifugal force would tear it 
apart. The pulse rate of the Crab Nebula 
pulsar, moreover, was found to be slow- 



ing in a manner indicating that the origi- 
nal spin rate, right after the explosion 
seen in 1054, wasat least 50 times a sec- 
ond. Assuming that it slowed more rapid- 
ly in the early years than recently, its ini- 
tial spin could have been hundreds of rev- 
olutions per second. A neutron star seem- 
ed the only plausible explanation. 

By now scores of pulsars have been 
detected, and, since we presumably can 
observe only those whose radio beams 
sweep in our direction, there must be 
many more in the MUky Way Galaxy. 
With such powerful evidence of neutron 
stars, the possibility of even more ex- 
treme forms of contraction — black holes 
— began to seem reasonable. A number of 
physicists, notably John W. Wheeler and 
Remo Ruffini at Princeton University, 
started thinking about how they could be 
detected despite their "blackness." 

Mindful of the discovery of the first 
white dwarf through the effect of its 
gravity on an easily visible star, they pro- 
posed that a two-star system in which one 
member was a black hole might be found. 
Two-star systems are more common than 
single stars like our sun, and hundreds 
have been found in which one member 
cannot be seen. While light or matter can- 
not escape a black hole, its gravity should 
reach out an indefinite distance, making 
it possible for it to waltz through space 
with another star. 

A further clue would be the detection 
of emissions from material falling into 
the hole. This material, being drawn in at 
extremely high velocity, would become so 
hot that it would "shine" at X-ray wave 
lengths. Whereas hot things glow red and 
very hot things become white-hot, this 
extreme heat would generate brilliant 
X-rays before the material vanished into 
the hole. 

Where a black hole was circling with 
an ordinary star, robbing it of gas, the 
X-ray emission should be particularly in- 
tense. It has been calculated that this 
"sucking in" of gas by a black hole's grav- 
ity would be the most efficient of all pro- 
cesses that convert matter to energy 
(apart from the mutual annihilations of 
matter and antimatter). Energy radiated 



A Hole in the Sky 



away, chiefly as X-rays, would equal the 
conversion into energy of 10 per cent of 
the mass of rnfalling material. This con- 
trasts with the conversion of only 0.8 per 
cent in the fusion reactions of stars. It 
would therefore be many times more 
powerful a process than that of an atomic 
or hydrogen bomb. 

As pointed out by Yakov B. Zeidovich 
and his collegues at the Institute of Ap- 
phed Mathematics in Moscow, the gas in 
such a situation would not fall directly 
down the hole. Because the entire two- 
star system was in rotation, the gas would 
first swirl around the black hole, forming 
an "accretion disc." Because of the enor- 
mous speeds and pressures as the gas 
swirls down the hole, it would be heated 
until its X-ray emissions were 10,000 
times as luminous as the sun. 

The first hint that such X-rays were com- 
ing from certain points in the sky came in 
the nineteen-sixties. Seeking to glimpse 
the universe at wave lengths that cannot 
penetrate the atmosphere, scientists first 
sent balloons into the upper atmosphere, 
then fired rockets on short flights into 
space above the White Sands Proving 
Ground in New Mexico. Pinpointing the 
X-ray sources on these flights was diffi- 
cult because ordinary optical systems 
could not be used; such rays, for ex- 
ample, tend to go through a mirror in- 
stead of being reflected. It was neverthe- 
less evident that certain objects in the sky 
are extraordinarily brilliant at X-ray wave 
lengths. Four of the brightest were in 
Cygnus, the Swan, which decorates the 
evening sky in summer. They were given 
numerical designations, the most power- 
ful being Cyg X-1. 

Then, in 1970, a baby earth satellite 
built in the United States and launched 
from an Itahan platform in equatorial 
waters off East Africa brought revolution- 
ary discoveries. The sateUite, named 
"Uhuru" (from the Swahili word for free- 
dom), circled the equator sweeping both 
the northern and southern hemispheres of 
the sky with its X-ray detector. By the 
start of this year, it had located close to 
100 sources of X-ray emission, but Cyg 
X-1 still ranks as the strongest. With Cyg 



X-l's precise location pinned down, C. T. 
Bolton of the University of Toronto 
pointed out that it coincides with a two- 
star pair — one of whose members is in- 
visible. Such pairs can be identified, not 
only because of the wavy motion of the 
visible partner, but in many cases because 
the visible star seems (from the periodic 
alterations of the wave lengths of its 
light) to be moving more toward us and 
then away from us, as though circling 
something we cannot see. In the case of 
Cyg X-1, the visible star, a so-called super- 
giant known as HDE 226868, is circling 
something once every 5.6 days. 

Just as it had been possible years earlier 
to deduce the mass of the invisible white 
dwarf circling with Sirius from its effects 
on Sirius, so Bolton and others have esti- 
mated that the unseen companion of 
HDE 226868 is eight times heavier than 
the sun — far too massive to be either a 
white dwarf or neutron star. Moreover, 
X-ray emissions from this spot in the sky 
seem to vary in tempo with the waltz of 
the two stars — in a cycle of 5.6 days. 
The brightness of the visible member 
varies at double that tempo. If the invisi- 
ble companion, though very smaU, were 
drawing large amounts of luminous gas 
from the visible one, this would make the 
visible star appear elongated so that its 
brightness, as seen from earth, would 
reach a maximum twice during each rota- 
tion. 

While some scientists now argue that 
many of the X-ray sources seen by Uhuru 
and more recent satellites are black holes, 
the erratic behavior of such sources re- 
mains to be fully explained. Cyg X-1 may 
vary fivefold in brightness within a few 
minutes. Other sources flare up to spec- 
tacular brightness within a day or two, 
then fade slowly away. Whether such 
eruptions could be associated with black 
holes is not clear. 

Indeed, not all astronomers are con- 
vinced that the existence of black holes 
has been demonstrated. The evidence is, 
perforce, indirect. The proponents, on 
the other hand, are extremely eager to 
find such objects. As one of them puts it. 



"Either there are holes in the sky, or 
there are holes in the general theory of 
relativity." 

All of the strange effects of black holes, 
such as the slowing of time, the tight cur- 
vature of space and the influence of gravi- 
ty on light, were anticipated by Einstein's 
theory and have been confirmed by obser- 
vation — but not on the scale that would 
occur in a black hole. As early as 1919, 
for example, Einstein's prediction that 
gravity would bend light was demon- 
strated when a star whose light had 
skirted the echpsed sun appeared out of 
place. The powerful gravity of the sun at 
such close range had bent the light. Like- 
wise, the effect of gravity on time has 
been demonstrated by carrying high- 
precision clocks in jet airlines at eleva- 
tions where the earth's gravity is sub- 
stantially weaker than at sea level. The 
chief reason for doubting that black holes 
exist, therefore, has not been uncertainty 
about relativity as much as the suspicion 
that, when one of the giant stars burns 
out, it blows off so much material in its 
death throes that the remainder is not 
massive enough for total collapse. There 
is still much uncertainty about what re- 
ally happens in such a collapse. 

Nevertheless, black holes have been her- 
alded as a possible answer to two basic 
problems in cosmology: What is it that 
holds the universe together, and what 
binds the clusters of galaxies? 

Einstein's theory predicted that there 
must be enough mass within the universe 
to keep it from flying apart indefinitely. 
In other words, although all of the gal- 
axies (or clusters of galaxies) are flying 
apart, as though blown asunder by some 
primordial "big bang" it appears that 
they do not have sufficient velocity to es- 
cape one another's gravity. Their dispers- 
al, like the flight of a ball thrown upward, 
seems to be slowing enough so that it 
must ultimately reverse itself, initiating a 
"falling back" that, many theorists be- 
lieve, will plunge the entire universe into 
a single black hole. The trouble is that 
adding up all the material that can be 
seen or readily inferred accounts for only 



about 2 per cent of what would be need- 
ed to prevent eternal expansion. Black 
holes and the dark cinders of stars that re- 
main after a white dwarf or neutron star 
has cooled off might make up for much, 
if not all, of this deficit. 

The problem concerning clusters of gal- 
axies is similar. Millions of galaxies like 
our own Milky Way can be seen through 
powerful telescopes. They are not ran- 
domly scattered through space but orga- 
nized into clusters within which each gal- 
axy is moving so fast with respect to its 
companions that the clusters should long 
ago have flown apart. Something is hold- 
ing them together. Yet, again, not enough 
material can be observed to provide the 
necessary "glue" — the required amount 
of gravity. Black holes could be doing the 
job. 

Cosmologists have seized upon the 
hypothesis in a variety of other ways. For 
example, if the universe was formed from 
a "big bang" and, confined by its own 
gravity, is destined to fall back together 
again, then we are living inside an incipi- 
ent black hole from which, even now, no 
light can escape. As Kip Thome, theorist 
at the California Institute of Technology, 
has put it, we are within a universe com- 
posed of space and time created by the 
explosion, "and we are trapped inside its 
gravitational radius. No Ught can escape 
from the universe." 

It has been proposed that when the ex- 
pansion gives way to contraction, the "ar- 
row of time" will change direction. From 
the viewpoint of an observer outside the 
universe (although denied the ability 
to make such an observation) our lives 
would seem to begin with the grave and 
end in the womb. Yet to those inside the 
collapsing universe, time's arrow would 
appear normal. In that case we would 
have no way to know whether or not the 
collapse has already begun. 

Also being discussed is the possibility 
that enormously massive black holes, 
comparable to millions or billions of suns, 
form the cores of some (or all) galaxies. 
Since such objects should be able to gen- 
erate vast amounts of energy — for ex- 



10 



A Hole in the Sky 



ample by "swallowing" stars - it has 
been proposed that they could account 
for some of the breathtaking discoveries 
made by astronomers in recent years, 
such as the quasars, or the castastrophic- 
ally explosive events that seem to occur 
in the cores of galaxies, sometimes blow- 
ing them apart. 

A major dilemma is what happens with- 
in the black hole as it nears the ultimate 
— a "singularity." Some beheve that just 
as Newton's laws break down under the 
extreme conditions where relativity be- 
comes dominant, so relativity itself 
breaks down within the even more ex- 
treme conditions of a black hole, the laws 
that govern there being totally unknown. 

It may also be, as noted by Roger Pen- 
rose of Birkbeck College at the University 
of London, that the black-hole contrac- 
tion in some cases is sufficiently lopsided 
so that all sides are not closed off. This 
would permit one to peek into the forbid- 
den sanctum — theorists call it a "naked 
singularity." What would we see there? Is 
it possible that such wild things happen 
to space and time that a singularity would 
constitute a window into some other uni- 
verse, some other realm of space and time 
far removed from our own? 

Several theorists, including Igor 
Novikov in the Soviet Union and Yuval 
Ne'eman in Israel, have proposed that a 
star which goes down the drain through a 
black hole may emerge in some other 
place and time as a quasar. Are the bril- 
Uant quasars, then, really "white holes" 
in which material (in energy form) is 
pouring into the here and now from 
"somewhere else" — perhaps even an- 
other universe? 

That other universes may exist is cer- 
tainly possible, in the view of John 
Wheeler at Princeton, who has probably 
pondered such questions as deeply as any- 
one of our time. Each universe would 
have its own dimensions, its own physical 
"constants" and laws. These universes 
would have their home in a "super-space" 

indefinite in space and time. 

Efforts to understand black holes and 
related phenomena are drawing theorists 
over the horizon into new realms of 



speculation that may not be entirely eso- 
teric. The effort to explain what made 
stars shine anticipated the discovery of 
nuclear energy. If we find out that black 
holes are the energy source in quasars and 
other superenergetic objects, it could be a 
revelation of comparable significance. 

According to Chandra, the precocious 
graduate student of 1930 who, at the 
University of Chicago, is now a dominant 
figure in astrophysics: "The present situa- 
tion is not unlike that in the twenties 
when the conversion of hydrogen into 
helium was contemplated as a source of 
stellar energy, with no sure knowledge 
that it could be accomplished; only years 
later were well-defined chains of nuclear 
reactions that could accompUsh it formu- 
lated." To achieve an understanding of 
even more exotic phenomena, such as 
black holes, he beUeves, "we may similar- 
ly have to wait some years." 

Chandra likes to cite an Indian parable, 
learned in his childhood, about dragonfly 
larvae at the bottom of a pond: "A con- 
stant source of mystery for these larvae 
was what happens to them when, on 
reaching the stage of chrysalis, they pass 
through the surface of the pond, never to 
return." Each larva, as it feels impelled to 
rise to the surface and depart, according 
to the parable, "promises to return and 
teU those that remain behind what really 
happens, and to confirm or deny a rumor 
attributed to a frog that when a larva 
emerges on the other side of their world 
it becomes a marvelous creature with a 
long slender body and iridescent wings. 
But on emerging from the surface of the 
pond as a fully formed dragonfly, it is un- 
able to penetrate the surface no matter 
how much it tries and how long it 
hovers." As with someone who might fall 
into a black hole, communication is irre- 
vocably cut off. 

The parable ends with the endless and 
hopeless cry of the larvae: 

. . . Will none of you in pity, To 
those you left behind, disclose the 
secret? 

Perhaps, in the long run, we will be 
more fortunate and wiU not have to fall 
into a black hole to guess what is there. 



11 



In this essay on the Industrial Revolution, Josiah Wedgewood, 
The Marriage of Figaro , Benjamin Franklin, The Lunar Society, 
and a zoetrope are featured, along with such key scientists 
and engineers as Joseph Priestly, Jannes Watt, Sadi Carnot and 
James Prescott Joule. 



2 The Drive for Power 

J. Bronowski 

A chapter from The Ascent of Man , 1973 

Revolutions are not made by fate but by men. Sometimes they 
are solitary men of genius. But the great revolutions in the 
eighteenth century were made by many lesser men banded 
together. What drove them was the conviction that every man is 
master of his own salvation. 

We take it for granted now that science has a social respon- 
sibility. That idea would not have occurred to Newton or to 
Galileo. They thought of science as an account of the world as it 
is, and the only responsibility that they acknowledged was to tell 
the truth. The idea that science is a social enterprise is modern, 
and it begins at the Industrial Revolution. We are surprised that 
we cannot trace a social sense further back, because we nurse the 
illusion that the Industrial Revolution ended a golden age. 

The Industrial Revolution is a long train of changes starting 
about I 760. It is not alone : it forms one of a triad of revolutions, 
of which the other two were the American Revolution that 
started in 177s, and the French Revolution that started in 1 789. 
It may seem strange to put into the same packet an industrial 
revolution and two political revolutions. But the fact is that 
they were all social revolutions. The Industrial Revolution is 
simply the English way of making those social changes. I think of 
it as the English Revolution. 

What makes it especially English? Obviously, it began in 
England. England was already the leading manufacturing nation. 
But the manufacture was cottage industry, and the Industrial 
Revolution begins in the villages. The men who make it are 
craftsmen: the millwright, the watchmaker, the canal builder, 
the blacksmith. What makes the Industrial Revolution so 
peculiarily English is that it is rooted in the countryside. 



12 



The Drive for Power 



During the first half of the eighteenth century, in the old age of 
Newton and the decline of the Royal Society, England basked in a 
last Indian summer of village industry and the overseas trade of 
merchant adventurers. The summer faded. Trade grew more 
competitive. By the end of the century the needs of industry were 
harsher and more pressing. The organisation of work in the 
cottage was no longer productive enough. Within two genera- 
tions, roughly between 1760 and 1820, the customary way of 
running industry changed. Before i 760, it was standard to take 
work to villagers in their own homes. By i 820, it was standard 
to bring workers into a factory and have them overseen. 

We dream that the country was idyllic in the eighteenth century, 
a lost paradise like The Deserted Village that Oliver Goldsmith 
described in i 770. 

Sweet Auburn, loveliest village of the plain, 

Where heahh and plenty cheared the labouring swain. 

How blest is he who crowns in shades like these, 
A youth of labour with an age of ease. 

That is a fable, and George Crabbe, who was a country parson 
and knew the villager's life at first hand, was so enraged by it that 
he wrote an acid, realistic poem in reply. 

Yes, thus the Muses sing of happy Swains, 
Because the Muses never knew their pains. 

O'ercome by labour and bow'd down by time. 
Feel you the barren flattery of a rhyme ? 

The country was a place where men worked from dawn to dark, 
and the labourer lived not in the sun, but in poverty and dark- 
ness. What aids there were to lighten labour were immemorial, 
like the mill, which was already ancient in Chaucer's time. The 
Industrial Revolution began with such machines ; the mill- 
wrights were the engineers of the coming age. James Brindley of 
Staffordshire started his self-made career in i 7 3 3 by working at 
mill wheels, at the age of seventeen, having been born poor in 
a village. 

Brindley's improvements were practical : to sharpen and step 
up the performance of the water wheel as a machine. It was the 
first multi-purpose machine for the new industries. Brindley 
worked, for example, to improve the grinding of flints, which 
were used in the rising pottery industry. 



13 



Yet there was a bigger movement in the air by i 750. Water 
had become the engineers' element, and men Hke Brindley were 
possessed by it. Water was gushing and fanning out all over the 
countryside. It was not simply a source of power, it was a new 
wave of movement. James Brindley was a pioneer in the art of 
building canals or, as it was then called, 'navigation'. (It was 
because Brindley could not spell the word 'navigator' that work- 
men who dig trenches or canals are still called 'navvies'.) 

Brindley had begun on his own account, out of interest, to 
survey the waterways that he travelled as he went about his 
engineering projects for mills and mines. The Duke of Bridge- 
water then got him to build a canal to carry coal from the Duke's 
pits at Worsley to the rising town of Manchester. It was a 
prodigious design, as a letter to the Manchester Mercury recorded in 
1763- 

I have lately been viewing the artificial wonders of London and natural 
wonders of the Peak, but none of them gave me so much pleasure as the Duke 
of Bridgewater's navigation in this country. His projector, the ingenious Mr 
Brindley, has indeed made such improvements in this way as are truly 
astonishing. At Barton Bridge, he has erected a navigable canal in the air ; for it 
is as high as the tree-tops. Whilst I was surveying it with a mixture of wonder 
and delight, four barges passed me in the space of about three minutes, two of 
them being chained together, and dragged by two horses, who went on the 
terrace of the canal, whereon I durst hardly venture ... to walk, as I almost 
trembled to behold the large River Irwell underneath me. Where Cornebrooke 
comes athwart the Duke's navigation . . . about a mile from Manchester, the 
Duke's agents have made a wharf and are selling coals at three pence halfpenny 
per basket . . . Next summer they intend to land them in (Manchester). 

Brindley went on to connect Manchester with Liverpool in an 
even bolder manner, and in all laid out almost four hundred 
miles of canals in a network all over England. 

Two things are outstanding in the creation of the English 
system of canals, and they characterise all the Industrial Revolu- 
tion. One is that the men who made the revolution were practical 
men. Like Brindley, they often had little education, and in fact 
school education as it then was could only dull an inventive 
mind. The grammar schools legally could only teach the classical 
subjects for which they had been founded. The universities also 
(there were only two, at Oxford and Cambridge) took little 
interest in modern or scientific studies ; and they were closed to 
those who did not conform to the Church of England. 

The other outstanding feature is that the new inventions were 
for everyday use. The canals were arteries of communication : 
they were not made to carry pleasure boats, but barges. And the 



14 



The Drive for Power 



TheDukeofBridgewater. 

A medallion by 

Josiah Wedgwood. 




barges were not made to carry luxuries, but pots and pans and 
bales of cloth, boxes of ribbon, and all the common things that 
people buy by the pennyworth. These things had been manu- 
factured in villages which were growing into towns now, away 
from London ; it was a country-wide trade. 

Technology in England was for use, up and down the country, 
far from the capital. And that is exactly what technology was not 
in the dark confines of the courts of Europe. For example, the 
French and the Swiss were quite as clever as the English (and 
much more ingenious) in making scientific playthings. But they 
lavished that clockwork brilliance on making toys for rich or 
royal patrons. The automata on which they spent years are to 
this day the most exquisite in the flow of movement that have 
ever been made. The French were the inventors of automation : 
that is, of the idea of making each step in a sequence of move- 
ments control the next. Even the modern control of machines by 
punched cards had already been devised by Joseph Marie 
Jacquard about 1800 for the silk-weaving looms of Lyons, and 
languished in such luxury employment. 

Fine skill of this kind could advance a man in France before 
the revolution. A watchmaker, Pierre Caron, who invented a new 
watch escapement and pleased Queen Marie Antoinette, pros- 
pered at court and became Count Beaumarchais. He had musical 
and literary talent, too, and he later wrote a play on which 
Mozart based his opera The Marriage of Figaro. Although a comedy 
seems an unlikely source book of social history, the intrigues in 
and about the play reveal how talent fared at the courts of Europe. 

At first sight The Marriage of Figaro looks like a French puppet play, 
humming with secret machinations. But the fact is that it is an 
early storm signal of the revolution. Beaumarchais had a fine 
political nose for what was cooking, and supped with a long 
spoon. He was employed by the royal ministers in several 



15 



double-edged deals, and on their behalf in fact was involved in a 
secret arms deal with the American revolutionaries to help them 
fight the English. The King might believe that he was playing at 
Machiavelli, and that he could keep such contrivances of policy 
for export only. But Beaumarchais was more sensitive and more 
astute, and could smell the revolution coming home. And the 
message he put into the character of Figaro, the servant, is 
revolutionary. 

Bravo, Signer Padrone - 

Now I'm beginning to understand all this mystery, and to appreciate your 
most generous intentions. The King appoints you Ambassador in London, I go 
as courier and my Susanna as confidential attachee. No, I'm hanged if she does 
-Figaro knows better. 

Mozart's famous aria, 'Count, little Count, you may go dancing, 
but I'll play the tune' (Se vuol ballare, Signor Contino . . .) is a chal- 
lenge. In Beaumarchais's words it runs : 

No, my lord Count, you shan't have her, you shan't. Because you are a great 
lord, you think you're a great genius. Nobility, wealth, honours, emoluments ! 
They all make a man so proud! What have you done to earn so many 
advantages? You took the trouble to be born, nothing more. Apart from that, 
you're rather a common type. 

A public debate started on the nature of wealth, and since one needn't own 
something in order to argue about it, being in fact penniless, I wrote on the 
value of money and interest. Immediately, I found myself looking at . . . the 
drawbridge of a prison . . . Printed nonsense is dangerous only in countries 
where its free circulation is hampered ; without the right to criticise, praise 
and approval are worthless. 

That was what was going on under the courtly pattern of French 
society, as formal as the garden of the Chateau at Villandry. 

It seems inconceivable now that the garden scene in The 
Marriage of Figaro, the aria in which Figaro dubs his master 'Signor 
Contino', little Count, should in their time have been thought 
revolutionary. But consider when they were written. Beaumar- 
chais finished the play of The Marriage of Figaro about i 780. It took 
him four years of struggle against a host of censors, above all 
Louis XVI himself, to get a performance. When it was per- 
formed, it was a scandal over Europe. Mozart was able to show it 
in Vienna by turning it into an opera. Mozart was thirty then; 
that was in 1786. And three years later, in 1789 - the French 
Revolution. 

Was Louis XVI toppled from his throne and beheaded because 
of The Marriage of Figaro? 'Of course not. Satire is not a social 
dynamite. Bat it is a social indicator: it shows that new men are 



16 



The Drive for Power 



knocking at the door. What made Napoleon call the last act of 
the play 'the revolution in action' ? It was Beaumarchais himself, 
in the person of Figaro, pointing to the Count and saying, 
'Because you are a great nobleman, you think you are a great 
genius. You have taken trouble with nothing, except to be born'. 

Beaumarchais represented a different aristocracy, of working 
talent : the watchmakers in his age, the masons in the past, the 
printers. What excited Mozart about the play ? The revolutionary 
ardour, which to him was represented by the movement of 
Freemasons to which he belonged, and which he glorified in 
The Magic Flute. (Freemasonry was then a rising and secret society 
whose undertone was anti-establishment and anti-clerical, and 
because Mozart was known to be a member it was difficult to get 
a priest to come to his deathbed in i 79 1 .) Or think of the greatest 
Freemason of them all in that age, the printer Benjamin Franklin. 
He was American emissary in France at the Court of Louis XVI 
in 1784 when The Marriage of Figaro was first performed. And he 
more than anyone else represents those forward looking, force- 
ful, confident, thrusting, marching men who made the new age. 

For one thing, Benjamin Franklin had such marvellous luck. 
When he went to present his credentials to the French Court in 
1778, it turned out at the last moment that the wig and formal 
clothes were too small for him. So he boldly went in his own 
hair, and was instantly hailed as the child of nature from the 
backwoods. 

All his actions have the stamp of a man who knows his mind, 
and knows the words to speak it. He published an annual, Poor 
Richard's Almanack, which is full of the raw material for future 
proverbs: 'Hunger never saw bad bread.* 'If you want to know 
the value of money, try to borrow some.' Franklin wrote of it : 

In 1 732 I first publislied my Almanac ... it was continued by me about 2^ 
years ... I endeavoured to make it both entertaining and useful, and it 
accordingly came to be in such demand that I reaped considerable profit from 
it ; vending annually near ten thousand . . . scarce any neighbourhood in the 
province being without it. I considered it as a proper vehicle for conveying 
instruction among the common people, who bought scarcely any other books. 

To those who doubted the use of new inventions (the occasion 
was the first hydrogen balloon ascent in Paris in i 783) Franklin 
replied, 'What is the use of a new-born baby?' His character is 
condensed in the answer, optimistic, down to earth, pithy, and 
memorable enough to be used again by Michael Faraday, a 



17 



Benjamin Franklin represents those forward-looking, forceful, confident, 
thrusting, marching men who made the new age. 
Benjamin Franklin, by Joseph Duplessis. Painted in Paris, 1778. 




The Drive for Power 



greater scientist, in the next century. Franklin was alive to how 
things were said. He made the first pair of bifocal spectacles for 
himself by sawing his lenses in half, because he could not follow 
French at Court unless he could watch the speaker's expression. 

Men like Franklin had a passion for rational knowledge. Look- 
ing at the mountain of neat achievements scattered through his 
life, the pamphlets, the cartoons, the printer's stamps, we are 
struck by the spread and richness of his inventive mind. The 
scientific entertainment of the day was electricity. Franklin loved 
fun (he was a rather improper man), yet he took electricity 
seriously ; he recognised it as a force in nature. He proposed that 
lightning is electric, and in i 7 5^ 2 he proved it — how would a man 
like Franklin prove it? - by hanging a key from a kite in a 
thunderstorm. Being Franklin, his luck held ; the experiment did 
not kill him, only those who copied it. Of course, he turned his 
experiment into a practical invention, the lightning conductor ; 
and made it illuminate the theory of electricity too by arguing 
that all electricity is of one kind and not, as was then thought, 
two different fluids. 

There is a footnote to the invention of the lightning conductor 
to remind us again that social history hides in unexpected places. 
Franklin reasoned, rightly, that the lightning conductor would 
work best with a sharp end. This was disputed by some scientists, 
who argued for a rounded end, and the Royal Society in England 
had to arbitrate. However, the argument was settled at a more 
primitive and elevated level : King George III, in a rage against the 
American revolution, fitted rounded ends to the lightning 
conductors on royal buildings. Political interference with 
science is usually tragic; it is happy to have a comic instance 
that rivals the war in Gulliver's Travels between 'the two great 
Empires of Lilliput aiid Blefuscu' that opened their breakfast egg at 
the sharp or the rounded end. 

Franklin and his friends lived science ; it was constantly in their 
thoughts and just as constantly in their hands. The understanding 



A lightning conductor dating 
from Franklin's day. 



19 



of nature to them was an intensely practical pleasure. These were 
men in society : Franklin was a political man, whether he printed 
paper money or his endless racy pamphlets. And his politics 
were as downright as his experiments. He changed the florid 
opening of the Declaration of Independence to read with simple 
confidence, 'We hold these truths to be self-evident, that all men 
are created equal'. When war between England and the American 
revolutionaries broke out, he wrote openly to an English poli- 
tician who had been his friend, in words charged with fire : 

You have begun to burn our towns. Look upon your hands ! They are stained 
with the blood of your relations. 

The red glow has become the picture of the new age in England - 
in the sermons of John Wesley, and in the furnace sky of the 
Industrial Revolution, such as the fiery landscape of Abbeydale 
in Yorkshire, an early centre for new processes in making iron 
and steel. The masters of industry were the ironmasters: power- 
ful, more than life-size, demonic figures, whom governments 
suspected, rightly, of really believing that all men are created 
equal. The working men in the north and the west were no 
longer farm labourers, they were now an industrial community. 
They had to be paid in coin, not in kind. Governments in 
London were remote from all this. They refused to mint enough 
small change, so ironmasters like John Wilkinson minted their 
own wage tokens, with their own unroyal faces on them. Alarm 
in London : was this a Republican plot ? No, it was not a plot. 
But it is true that radical inventions came out of radical brains. 
The first model of an iron bridge to be exhibited in London was 
proposed by Tom Paine, a firebrand in America and in England, 
protagonist of The Rights of Man. 

Meanwhile, cast iron was already being used in revolutionary 
ways by the ironmasters like John Wilkinson. He built the first 
iron boat in 1787, and boasted that it would carry his coffin 
when he died. And he was buried in an iron coffin in 1 808. Of 
course, the boat sailed under an iron bridge ; Wilkinson had 
helped to build that in 1 779 at a nearby Shropshire town that is 
still called Ironbridge. 

Did the architecture of iron really rival the architecture of the 
cathedrals ? It did. This was a heroic age. Thomas Telford felt that, 
spanning the landscape with iron. He was born a poor shepherd, 
then worked as a journeyman mason, and on his own initiative 



20 



The Drive for Power 



Ironmasters like John 
Wilkinson minted their 
own wage tokens, with 
their own unroyal faces 
on them. 
.4 Wilkinson token, i 788. 




became an engineer of roads and canals, and a friend of poets. 
His great aqueduct that carries the Llangollen canal over the 
river Dee shows him to have been a master of cast iron on the 
grand scale. The monuments of the Industrial Revolution have a 
Roman grandeur, the grandeur of Republican men. 

The men who made the Industrial Revolution are usually 
pictured as hardfaced businessmen with no other motive than 
self-interest. That is certainly wrong. For one thing, many of 
them were inventors who had come into business that way. And 
for another, a majority of them were not members of the Church 
of England but belonged to a puritan tradition in the Unitarian 
and similar movements. John Wilkinson was much under the 
influence of his brother-in-law Joseph Priestley, later famous as a 
chemist, but who was a Unitarian minister and was probably the 
pioneer of the principle, 'the greatest happiness of the greatest 
number'. 



21 



The monuments of the 
Industrial Revolution 
have a Roman grandeur, 
the grandeur of Repub- 
lican men. 



The little bridge at Coalbrook- 
dale, the first great iron span to 
be erected over the Severn 
between i 775 and / 779. 



"4 




22 



The Drive for Power 




Josiah Wedgwood's pyrometer, 
for which he was elected a 
Fellow of the Royal Society 
of London. 



Joseph Priestley, in turn, was scientific adviser to Josiah 
Wedgwood. Now Wedgwood we usually think of as a man who 
made marvellous tableware for aristocracy and royalty : and so 
he did, on rare occasions, when he got the commission. For 
example, in i 774 he made a service of nearly a thousand highly 
decorated pieces for Catherine the Great of Russia, which cost 
over £2000 - a great deal of money in the coin of that day. But 
the base of that tableware was his own pottery, creamware ; and 
in fact all the thousand pieces, undecorated, cost less than £50, 
yet looked and handled like Catherine the Great's in every way 
except for the hand-painted idylls. The creamware which made 
Wedgwood famous and prosperous was not porcelain, but a 
white earthenware pottery for common use. That is what the 
man in the street could buy, at about a shilling a piece. And in 
time that is what transformed the kitchens of the working class 
in the Industrial Revolution. 

Wedgwood was an extraordinary man : inventive, of course, 
in his own trade, and also in the scientific techniques that might 
make his trade more exact. He invented a way of measuring the 
high temperatures in the kiln by means of a sort of sliding scale 
of expansion in which a clay test-piece moved. Measuring high 



23 



temperatures is an ancient and difficult problem in the manu- 
facture of ceramics and metals, and it is fitting (as things went 
then) that Wedgwood was elected to the Royal Society. 

Josiah Wedgwood was no exception; there were dozens of 
men like him. Indeed, he belonged to a group of about a dozen 
men, the Lunar Society of Birmingham (Birmingham was then 
still a scattered group of industrial villages), who gave them- 
selves the name because they met near the full moon. This was so 
that people like Wedgwood, who came from a distance to 
Birmingham, should be able to travel safely over wretched roads 
that were dangerous on dark nights. 

But Wedgwood was not the most important industrialist 
there : that was Matthew Boulton, who brought James Watt to 
Birmingham because there they could build the steam engine. 
Boulton was fond of talking about measurement ; he said that 
nature had destined him to be an engineer by having him bom 
in the year i 728, because that is the number of cubic inches in 
a cubic foot. Medicine was important in that group also, for 
there were new and important advances being made. Dr William 
Withering discovered the use of digitalis in Birmingham. One 
of the doctors who has remained famous, who belonged to the 
Lunar Society, was Erasmus Darwin, the grandfather of Charles 
Darwin. The other grandfather ? Josiah Wedgwood. 

Societies like the Lunar Society represent the sense of the 
makers of the Industrial Revolution (that very English sense) 
that they had a social responsibility. I call it an English sense, 
though in fact that is not quite fair ; the Lunar Society was much 
influenced by Benjamin Franklin and by other Americans 
associated with it. What ran through it was a simple faith : the 
good life is more than material decency, but the good life must be 
based on material decency. 



Wedgwood, by George Stubbs. 




24 



The Drive for Power 



It took a hundred years before the ideals of the Lunar Society 
became reality in Victorian England. When it did come, the 
reality seemed commonplace, even comic, like a Victorian 
picture postcard. It is comic to think that cotton underwear and 
soap could work a transformation in the lives of the poor. Yet 
these simple things — coal in an iron range, glass in the windows, 
a choice of food - were a wonderful rise in the standard of life 
and health. By our standards, the industrial towns were slums, 
but to the people who had come from a cottage, a house in a 
terrace was a liberation from hunger, from dirt, and from 
disease ; it offered a new wealth of choice. The bedroom with the 
text on the wall seems funny and pathetic to us, but for the 
working class wife it was the first experience of private decency. 
Probably the iron bedstead saved more women from childbed 
fever than the doctor's black bag, which was itself a medical 
innovation. 

These benefits came from mass production in factories. And 
the factory system was ghastly ; the schoolbooks are right about 
that. But it was ghastly in the old traditional way. Mines and 
workshops had been dank, crowded and tyrannical long before 
the Industrial Revolution. The factories simply carried on as 
village industry had always done, with a heartless contempt for 
those who worked in them. 

Pollution from the factories was not new either. Again, it was 
the tradition of the mine and the workshop, which had always 
fouled their environment. We think of pollution as a modem 
blight, but it is not. It is another expression of the squalid 
indifference to health and decency that in past centuries had 
made the Plague a yearly visitation. 

The new evil that made the factory ghastly was different : it was 
the domination of men by the pace of the machines. The 
workers for the first time were driven by an inhuman clock- 
work : the power first of water and then of steam. It seems insane 
to us (it was insane) that manufacturers should be intoxicated by 
the gush of power that spurted from the factory boiler without a 
stop. A new ethic was preached in which the cardinal sin was not 
cruelty or vice, but idleness. Even the Sunday schools warned 
children that 

Satan finds some Mischief still 
For idle Hands to do. 

The change in the scale of time in the factories was ghastly and 
destructive. But the change in the scale of power opened the 



25 




A factory token stamped with 
Watt's Steam Engine, 1786. 



future. Matthew Boulton of the Lunar Society, for example, built 
a factory which was a showplace, because Boulton's kind of 
metalwork depended on the skill of craftsmen. Here James Watt 
came to build the sun-god of all power, the steam engine, 
because only here was he able to find the standards of accuracy 
needed to make the engine steam-tight. 

In 1776 Matthew Boulton was very excited about his new 
partnership with James Watt to build the steam engine. When 
James Boswell, the biographer, came to see Boulton that year, 
he said to him grandly, 'I sell here, sir, what all the world desires 
to have - power'. It is a lovely phrase. But it is also true. 



Power is a new preoccupation, in a sense a new idea, in science. 
The Industrial Revolution, the English revolution, turned out to 
be the great discoverer of power. Sources of energy were sought 
in nature : wind, sun, water, steam, coal. And a question suddenly 
became concrete: Why are they all one? What relation exists 
between them? That had never been asked before. Until then 
science had been entirely concerned with exploring nature as she 
is. But now the modern conception of transforming nature in 
order to obtain power from her, and of changing one form of 
power into another, had come up to the leading edge of science. 
In particular, it grew clear that heat is a form of energy, and is 
converted into other forms at a fixed rate of exchange. In 1 824 
Sadi Camot, a French engineer, looking at steam engines, wrote 
a treatise on what he called Ta puissance motrice du feu*, in which 
he founded, in essence, the science of thermodynamics - the 
dynamics of heat. Energy had become a central concept in 
science ; and the main concern in science now was the unity of 
nature, of which energy is the core. 

And it was a main concern not only in science. You see it 
equally in the arts, and the surprise is there. While this is going on, 
what is going on in literature? The uprush of romantic poetry 
round about the year 1 800. How could the romantic poets be 
interested in industry ? Very simply : the new concept of nature 
as the carrier of energy took them by storm. They loved the word 
'storm' as a synonym for energy, in phrases like Sturm und Drang, 
'storm and thrust'. The climax of Samuel Taylor Coleridge's 



26 



The Drive for Power 



Rime of the Ancient Mariner is introduced by a storm that breaks the 
deadly calm and releases life again. 

The upper air burst into life ! 
And a hundred fire-flags sheen, 
To and fro they were hurried about ! 
And to and fro, and in and out. 
The wan stars danced between. 

The loud wind never reached the ship. 
Yet now the ship moved on ! 
Beneath the lightning and the Moon 
The dead men gave a groan. 

A young German philosopher, Friedrich von Schelling, just at 
this time in i 799, started a new form of philosophy which has 
remained powerful in Germany, Naturphilosophie - philosophy of 
nature. From him Coleridge brought it to England. The Lake 
Poets had it from Coleridge, and the Wedgwoods, who were 
friends of Coleridge's and indeed supported him with an 
annuity. Poets and painters were suddenly captured by the idea 
that nature is the fountain of power, whose different forms 
are all expressions of the same central force, namely energy. 

And not only nature. Romantic poetry says in the plainest way 
that man himself is the carrier of a divine, at least a natural, 
energy. The Industrial Revolution created freedom (in practice) 
for men who wanted to fulfil what they had in them - a concept 
inconceivable a hundred years earlier. But hand in hand, 
romantic thought inspired those men to make of their freedom a 
new sense of personality in nature. It was said best of all by the 
greatest of the romantic poets, William Blake, very simply: 
'Energy is Eternal Delight'. 

The key word is 'delight', the key concept is 'liberation' - a sense 
of fun as a human right. Naturally, the marching men of the age 
expressed the impulse in invention. So they produced a bottom- 
less horn of plenty of eccentric ideas to delight the Saturday 
evenings of the working family. (To this day, most of the appli- 
cations that lumber the patent offices are slightly mad, like the 
inventors themselves.) We could build an avenue from here to 
the moon lined with these lunacies, and it would be just about as 
pointless and yet as high-spirited as getting to the moon. Con- 
sider, for example, the idea of the zoetrope, a circular machine 
for animating a Victorian comic strip by flashing the pictures 



27 




So they produced a bot- 
tomless horn of plenty of 
eccentric ideas to delight 
the Saturday evenings of 
the working family. 
The Zoetrope ; a patent elevator- 
platform ; and patent Viennese 
Folding Bedroom Furniture. 




28 



The Drive for Power 



past the eye one after another. It is quite as exciting as an 
evening at the cinema, and comes to the point rather quicker. 
Or the automatic orchestra, which has the advantage of a very 
small repertoire. All of it is packed with homespun vigour which 
has not heard of good taste, and is absolutely self-made. Every 
pointless invention for the household, like the mechanical 
vegetable chopper, is matched by another superb one, like the 
telephone. And finally, at the end of the avenue of pleasure, we 
should certainly put the machine that is the essence of machine- 
ness : it does nothing at all ! 

The men who made the wild inventions and the grand ones 
came from the same mould. Think of the invention that rounded 
out the Industrial Revolution as the canals had begun it: the 
railways. They were made possible by Richard Trevithick, who 
was a Cornish blacksmith and a wrestler and a strong man. He 
turned the steam engine into a mobile power pack by changing 
Watt's beam engine into a high-pressure engine. It was a life- 
giving act, which opened a blood-stream of communication for 
the world, and made England the heart of it. 




We are still in the middle of the Industrial Revolution ; we had 
better be, for we have many things to put right in it. But it has 
made our world richer, smaller, and for the first time ours. And I 
mean that literally : our world, everybody's world. 

From its earliest beginnings, when it was still dependent on 
water power, the Industrial Revolution was terribly cruel to 
those whose lives and livelihood it overturned. Revolutions are - 
it is their nature, because by definition revolutions move too fast 
for those whom they strike. Yet it became in time a social revolu- 
tion and established that social equality, the equality of rights, 
above all intellectual equality, on which we depend. Where 
would a man like me be, where would you be, if we had been 
born before i 800? We still live in the middle of the Industrial 
Revolution and find it hard to see its implications, but the future 
will say of it that _in the ascent of man it is a step, a stride, as 
powerful as the Renaissance. The Renaissance established the 
dignity of man. The Industrial Revolution established the unity 
ofnature. 

That was done by scientists and romantic poets who saw that 
the wind and the sea and the stream and the steam and the coal 
are all created by the heat of the sun, and that heat itself is a form 
of energy. A good many men thought of that, but it was establi- 



29 



Richard Trevithick 
turned the steam engine 
into a mobile power pack. 




30 



The Drive for Power 



shed above all by one man, James Prescott Joule of Manchester. 
He was born in i 8 1 8, and from the age of twenty spent his life in 
the delicate detail of experiments to determine the mechanical 
equivalent of heat - that is, to establish the exact rate of 
exchange at which mechanical energy is turned into heat. And 
since that sounds a very solemn and boring undertaking, I must 
tell a funny story about him. 

In the summer of 1847, the young William Thomson (later 
to be the great Lord Kelvin, the panjandrum of British science) 
was walking - where does a British gentleman walk in the Alps ? - 
from Chamonix to Mont Blanc. And there he met - whom does a 
British gentleman meet in the Alps ? - a British eccentric : James 
Joule, carrying an enormous thermometer and accompanied at a 
little distance by his wife in a carriage. All his life, Joule had 
wanted to demonstrate that water, when it falls through 778 feet, 
rises one degree Fahrenheit in temperature. Now on his honey- 
moon he could decently visit Chamonix (rather as American 
couples go to Niagara Falls) and let nature run the experiment for 
him. The waterfall here is ideal. It is not all of 778 feet, but he 
would get about half a degree Fahrenheit. As a footnote, I should 
say that he did not - of course - actually succeed ; alas, the 
waterfall is too broken by spray for the experiment to work. 

The story of the British gentlemen at their scientific eccen- 
tricities is not irrelevant. It was such men who made nature 
romantic ; the Romantic Movement in poetry came step by step 
with them. We see it in poets like Goethe (who was also a 
scientist) and in musicians like Beethoven. We see it first of all in 
Wordsworth : the sight of nature as a new quickening of the 
spirit because the unity in it was immediate to the heart and 
mind. Wordsworth had come through the Alps in i 790 when 
he had been drawn to the Continent by the French Revolution. 
And in 1798 he said, in Tintern Abbey, what could not be said 
better. 

For nature then . . . 
To me was all in all - 1 cannot paint 
What then I was. The sounding cataract 
Haunted me like a passion. 



'Nature then to me was all in all.' Joule never said it as well as 
that. But he did say, 'The grand agents of nature are indestructible', 
and he meant the same things. 



31 



Models are not themselves the same thing as the real world 
objects or ideas they represent, but nevertheless they do help 
scientists and engineers learn about the real world. This article 
shows how. 



The Blind Men and 

the Elephant (J. G. 

Saxe, 1816-1887). 

The poem is given in 

Question 1 5 at the 

end of the chapter. 



Modeling 

The Engineering Concepts Curriculum Project 

A selection from Man and His Technology , 1973 

i I THE NATURE OF MODELS 

According to an old story, six blind men who had never seen 
an elephant tried to decide what it was.* The first man, feeling the 
elephant's flat, vertical side, concluded that the beast was similar 
to a wall. The second man touched a round, smooth, sharp tusk 
and decided that an elephant is similar to a spear. Grasping the 
squirming trunk, the third blind man said that the animal resembled 
a snake. The fourth man, who touched a knee, observed that 
elephants resembled trees. From an exploration of the ear of the 
elephant, the fifth man was convinced that the animal had the 
shape of a fan, while an examination of the tail convinced the 
sixth blind man that an elephant was similar to a rope. 

Each, of course, was partially correct, but insofar as a complete 
representation of the elephant was concerned, all were wrong. 
Each man, after observing the "real world," formulated a descrip- 
tion, or model. But since the observations were incomplete, the 
models were incorrect. 

Every time we describe an object, we are really making a model. 
We use our senses to find information about the real world. From 
this information, we decide what the object is. Then we pick out 
the important features. These make up the model. 

The model is an efficient way of viewing things. A good model 
includes only those parts which are useful. But, by restricting our 
thoughts to a few features, we are able to understand the object 
or system. We can anticipate the eff"ects of actions we might take. 
On this basis, we can select the best action. Thus, man's ability 
to control his environment and to build useful systems depends 
directly on his capacity to find models. 

Models Are Usually Quantitative 

Models begin as conceptions; they are ideas about the struc- 
ture and nature of something. Before we can go very far with the 
model, we usually have to develop a quantitative model, one which 



32 



Modeling 



tells how much, where, and when in terms of numbers. In other 
words, we use the language of mathematics to describe our situation. 

The importance of a quantitative model can be illustrated by 
the task of the man who is in charge of scheduling elevators in a 
twenty-story office building from 8:45 to 9 a.m. every weekday 
morning as people arrive for work. There are six elevators, each 
able to stop at every floor. 

When the building is first opened, the elevator supervisor 
simply loads each elevator in turn. As soon as it is loaded, it 
departs. Our supervisor notices that service is extremely slow. 
Occasionally, an elevator is loaded with one passenger for each of 
15 diff'erent floors. The poor passenger who works on the highest 
floor has a ten-minute ride. (Especially since the passengers at the 
back of the elevator as it starts up always seem to be the ones who 
want to get off" first.) 

As the complaints about service become more and more bitter, 
our supervisor wonders if service might be improved by using a 
better plan. He might, for example, use two elevators for floors 
2-8 only, two others for floors 9-15, and the other two for 16-20. 
He might stop only at even-numbered floors and force employees 
to walk down one flight of stairs to reach the odd-numbered 
floors. Obviously, there are many possible strategies which could 
be tried to improve service. 

The choice of a desirable strategy depends on the way employees 
arrive in the morning for each of the floors. For example, the 
fifteenth floor holds the executive suite for the top officers of the 
company. If any of them should arrive during this busy period, 
they must be delivered as rapidly as possible. This priority for 
Floor 15 means that at least one elevator should go directly to 
this floor. Similarly, certain floors may have many employees and 
should be given preference. In other words, to derive a sensible 
plan or strategy our supervisor needs at least a rough quantitative 
picture of the flow of people. This is the model. 

The model may be very approximate and rough, guessing only 
that the number of employees is the same for each floor. Or it 
may be very detailed with the number for each floor, their probable 
arrival times, and their relative importance to the company. If 
the model is very simple, the supervisor may be able to decide 
intuitively on a strategy; if the model is very detailed, a computer 
may be required to evaluate and compare the possible strategies. 

The important feature of this example is that no intelligent 
decision is possible unless a model is used, whether or not the 
supervisor calls his picture a model. 

2 I THE GRAPH AS A DESCRIPTIVE MODEL 

To form a model, we need to collect data about some aspect of 
the real world. We might wish to determine whether a simple 
relationship exists between the heights and the weights of twenty- 



33 



1,000 



Number of fatalities 



1 million people x hours exposed 




1/10 
1900 



Weight =W 
(pounds) 

200 



150 




W' 



100 



50 



■ 
■ 








L 




20 



40 



60 



Fig. 4-2. 

A different model which 

shows the willingness of people 

to accept risk. The vertical axis 

is a measure of the risk involved 

in different activities {the number of 

deaths in the U.S. divided by the total 

number of hours a million people are 

exposed to the risk). For example, 10 

means that there are ten deaths every hour 

a million people engage in this activity. 

The interesting part of this model is 
that just living {with possible disease) has 
about the same risk as driving a car or 
flying a commercial airplane. {Only about 
3% of the people ever fly ; 85 % ride in a 
car.) People seem willing to accept this 
risk of 1. Cigarette smoking has a 
risk of 3, skiing about I, and normal 
railroad travel fUO. This model gives 
us some idea how safe we must make 
new forms of transportation {moving 
sidewalks or 300-mph trains). 

The model is discouraging if 
we are interested in cutting down 
traffic accidents. It suggests that 
the average person may be 
willing to accept today's 
death rate. {Chauncey 
Starr, '''Social benefit 
versus technological 
risk,'" UCLA 
report, 1969.) 



80 



Height = H 
(inches) 



Fig. 4-3. Height-weight data 
for 20-year-old men. 



year-old men. After making several experimental measurements, 
we may secure a set of related numbers such as 5'6", 130 lb; 
6'1", 180 lb; 5'7", 155 lb. But it is difficult to discover any systematic 
relationship in this way. Even though we may have a reasonable 
expectation that as height increases, weight will increase, this 
verbal model is vague and imprecise. 

In order to present the data in a way which we can interpret 
more easily, we make a graphical plot, as in Fig. 4-3. Each point 
represents the height-weight data for one man. We notice now that 
the points are not scattered, but seem to be closely grouped. What 
can we say about the relationship between height and weight? 



34 



Modeling 



A straight line can be drawn through the points to represent 
averages for these data (Fig. 4-4). This picture of the data is a 
graphical model of the relationship between height and weight. 

This graphical model presents a clear but simplified description 
of the real world. It can be used as the basis for some reasonable 
predictions. From the straight-line average we can estimate the 
probable weight of a twenty-year-old man even though we know 
only his height. Let us suppose that we wish to estimate the weight 
of someone who is 73" tall. The corresponding weight for this 
height can be immediately obtained from our graph. The graphical 
model permits us to estimate the weight of such an individual, 
even if our original data did not include any individual of this 
height. Thus, we may predict from our graphical model that an 
individual who is 73" tall probably weighs about 180 pounds. 

An Equation As a Model 

While the graph of Fig. 4-4 is an appropriate model for our 
weight-height relationship, it is also often convenient to have a 
mathematical equation. The straight-line graph is exactly equiva- 
lent to an equation, which in this case happens to be 

W=%H- 407 

(We derive this in the next paragraph.) Even though the graph and 
the equation say exactly the same thing, it is often a nuisance to 
have to redraw the graph every time we want to tell someone what 
the model is. Furthermore, it is frequently easier to work with the 
equation. For example, what is the height expected for a 150-pound 
man? From the equation, 

150 = 8// -407 ov H= 70" 

Since our graph is a straight line, we know from algebra that 
the equation has the general form y = mx + b, or in this case, 

W =mH+b 

where W is the weight, H is the height, m is the slope, b is the 
vertical axis intercept. To complete the equation, we must there- 
fore determine the values of the constants m and b. Since b repre- 
sents the W, or vertical intercept of the line. Fig. 4-5 reveals that 
the line cuts through the li^-axis at a value of —407. Hence, 

W =mH~ 407 

We can measure the slope m directly. When H increases by 
10 inches (for example, from 60 to 70), W increases by 80 pounds. 
The slope is thus f^ or 8, and the equation is 

W=SH- 407 

Once the equation is determined, the weight IV can be found 
for any given height, or the height for any given weight. 




Fig. 4-4. 
73" tall. 



Weight =W 
(pounds) 

200 



150 



100 



Weight expected from a man 



•/• straight- 
line 
average 




-407 



Fig. 4-5. Straight line extended 
until it hits the W axis. 



Households 
1964 



Automobiles 




1985 




I ^ 54% 



Fig. 4-6. 

A completely 

different form 

of graphical 

model. In this case, 

we are interested 

in showing the changes 

expected from 1964 to 

1985. The ''pie'' charts show 

how the suburbs will grow, 

primarily as the central city 

becomes less important {if 

present trends continue). 

Thus, a model can be 

portrayed in many 

different forms. 

(Technology 

Review of 

M.I.T.) 



Central City |p Outside Central City Q Non-Metropolitan Areas 



We can use this model to predict points which were not orig- 
inally in our data sample. But these predictions must be carefully 
examined. For instance, the line we have drawn tells us that an 
individual who is 54" tall will weigh about 25 lb; worse yet, a 
24" person can be expected to tip the scale at an impressive nega- 
tive 215 lb! Surely these are curious figures for twenty-year-old 
men. What is wrong with our model? 

The straight-hne average that we drew was extended so that 
the W^ intercept (-407) could be found. But we are not entitled to 
say that all points on the entire line must represent real situations. 
Actually, the only use we can make of this model is to predict 
within our data field. We know that anywhere inside of the cluster 
of measured points we are in the neighborhood of a real-world 
possibility. However, we run into the danger of unrealistic prediction 
if we apply the model beyond the region that has been measured. 
This danger applies to either the graph or the equation. 

Our model, therefore, has its limitations. It must not be used 
to predict beyond the region of results experimentally obtained 
unless there are very good reasons to believe that real-world laws 
are not being violated. To test this model requires that we obtain 



36 



Modeling 



a fresh sample of twenty-year-old men, either the data from the 
same school for other years or from other schools or from the 
army. Then we either enter them on the plot or compare them with 
predictions made from the algebraic model. 

The equation is a mathematical model which says exactly the 
same things as the graphical model. Both of these models are more 
useful than the verbal model with which we started. 

One of the most interesting aspects of this model is that it 
turns out to be so simple. This is quite unexpected. If we think of 
the people we meet while walking down a busy city street, we know 
that all sizes and weights are combined. It is true that the sample 
studied was passed through two strainers (age and sex) to make it 
more manageable. 

We should give one final word of caution. We must remember 
where our original data came from. If we had measured the heights 
and weights of the members of the Kansas City Chiefs professional 
football team, we probably could not expect to use the model to 
predict the weight of a six-foot, 25-year-old starving artist. At 
least, we should be suspicious of the prediction. The model is only 
useful as long as we stay with the part of the world from which the 
model was derived. 

3 I A DESCRIPTIVE MODEL OF TRAFFIC FLOW 

A key urban problem is the question of how to handle motor 
traffic in the streets. Some cities have gone so far as to ban all auto- 
mobiles from a few streets. This does not so much solve the prob- 
lem as eliminate it — at least from those streets. Furthermore, it 
sometimes substitutes other problems, for example for the elderly 
and infirm, or for the shopkeeper trying to attract customers. It 
also increases the cost of goods since delivery expenses rise. 

If a traffic engineer is to improve present conditions he must be 
able to predict the results of changes. To do this he must construct 
a model of the traffic flow in and around the city. Since such a 
model is too complicated, we use a study of the simpler circum- 
stances within a school; even this we limit to what goes on at a 
single corridor intersection, such as that shown in Fig. 4-8. The 
limited model we derive for a single intersection could be extended 
to a whole building. The resulting larger model can be of practical 
use to school administrators, schedule-makers, and architects. 

In order to construct our model, we must determine what 
affects the behavior of the system. We are primarily interested in 
the rate at which people (including teachers and custodians) pass 
from one corridor to another, in other words, in the density of 
traffic as measured in people per minute. The measurement will 
be made by sensors, devices which respond in some way whenever 
a person passes. An example would be the device often called an 
electric eye, but for short-term service a much more practical sensor 
is a person stationed at the proper spot 



37 



North 
corridor 




Main 
corridor 



South 
corridor 





Fig. 4-8. A school corridor intersection. 



Fig. 4-9. Where traffic density is measured. 



Figure 4-9 shows the intersection with measurement points 
identified. Traffic problems usually arise at intersections rather 
than in the main corridors.* What we need for the present is a 
count, minute by minute during the time when classes are being 
changed, and for a minute (or more) before and after. 

Table 4-1 shows a possible result of such a set of measurements. 
The actual number of people who go through the intersection dur- 
ing the counting period is about half that shown because each 
person was counted twice, once when he entered and once when 
he left (if we forget people like Joe and Susan). 



Minute 






Counting station 




Total 


number 




T, 


7^2 




7-3 


counts 


1 


26 


counts 


50 counts 




30 counts 


106 


2 


42 




63 




47 


152 


3 


61 




102 




55 


218 


4 


112 




184 




73 


369 


5 


38 




42 




28 


108 


6 


22 




17 




9 


48 










Total for period 


1001 



The data can be shown more effectively if we present them in 
a plot, rather than a column of numbers. One form of plot which is 
often used in displaying a count of events is called a histogram. 
It has the form shown in Fig. 4-10 for the total number of indi- 
viduals passing through this intersection. 



As Joe passes position T^ going east, he sees 
that Susan is going south past Tj. He 
reverses his field and meets her in the middle 
of the intersection. Therefore, they both 
hold up traffic and he is counted three 
times at Tj; he might even stroll a few 
yards down the south corridor with Sue and 
add two more tallies to his total. 



Table 4-1. 
Detailed traffic 
count at one 
intersection, 
end of first 
period. 



38 



Modeling 



Counts 

per 
minute 



200 



150 



100 




Fig. 4-10. 

Bar graph of traffic 

at one intersection at the 

end of the first period. 



Class-changing period 



The height of each vertical column is proportional to half the 
total count for the minute indicated below it, half the total for the 
reason just explained. It is evident that most of the traffic, but not 
all, occurred during the interval between classes. The school ad- 
ministrator confronted with such a bar graph might well be sus- 
picious of the large traffic during the minute before the bell rang for 
class changing: Are some teachers dismissing their classes early? 
He might also be disturbed by evidence of a good deal of tardiness. 

Further information, useful to the scheduling officer, can be 
obtained if another bar graph is made, this time of total counts at 
the end of each period during the day (Fig. 4-11). Here the peaks 
shown for traffic at the ends of the first and fourth periods might 
suggest altering the room assignments in such a way as to lessen 
the traffic through this intersection at these times. For example, 
more students might be scheduled for successive classrooms in the 
same corridor to avoid the intersection. 

A full study of a school's traffic pattern requires that data be 
obtained at every intersection for every class-changing period 
throughout the day or even the entire week. If there are ten im- 
portant intersections, the total data can be portrayed in fifty histo- 
grams similar to Fig. 4-1 1 (ten for each of five days) or similar 
curves on a minute-by-minute basis. Inspection of these data then 
reveals the times and locations of major congestion. 

In processing data of this type, it is common practice to indicate 
those particular data points which are either unusually large or 
notably small. We might show in red all parts of the histograms 
which are larger than a predetermined amount (corresponding to 
troublesome congestion). We may choose to make up a small 



39 



Total 

counts 

500 



400 



300 



200 



100 






Fig. 4-11. 

Bar graph 

of total daily traffic 

at one intersection. 



6 Period 



separate list showing critical data only. Such selective presentation 
of critical data is called "flagging"; we flag data which are es- 
pecially important. 

This type of traffic-flow study is closely related to the queueing 
problem described in Chapter 3. Queues occur when traffic density 
increases. In the city traffic problem, the results are obvious. Ex- 
cessively long travel time ruins emergency services (ambulances, 
fire trucks, and police cars), lowers the income of taxi drivers, 
raises the cost of goods, and causes lost time for workers. One of 
the reasons some small businesses are moving out of the cities to 
the suburbs is the consistent tardiness of workers because of trans- 
portation problems. In one recent study, a manufacturing business 
employing 700 workers measured tardiness in the morning, lost 
time at the lunch hour, and early departures in the afternoon. 
The model showed that if the company moved to the suburbs, 
production would increase 12% with the same size labor force. 
Even if all employees were given free lunches, profits would in- 
crease 4% just from the greater production. 

Studies based on such models reveal the importance of ade- 
quate transportation in the life of any town or city. They also are 
a commentary on the way business is carried out in a city. When 
commuting trains, buses, and subways so often bring the business- 
men to work an hour late, one has to wonder whether most organ- 
izations don't employ more men than they really need. 



40 



Modeling 



4 I MODELS FOR RESOURCE MANAGEMENT 

Management of resources is a fertile area for the use of models 
and decision making. In this section, we illustrate this by looking 
at the history of the buffalo in the western United States. Then 
we show how this resource could have been managed with some 
simple models and logical decisions. 

The ideas which we present are currently being used in many 
different ways. In the northwestern United States, the salmon 
population is being modeled in detail in order to determine how 
to regulate salmon fishing and changes in water to ensure that the 
salmon supply will continue in the future. France has several pro- 
grams for sea "gardening," growing fish and shellfish for food. 
The invasion of the Great Lakes by lampreys (eels) and the re- 
sulting changes have been under study for more than two decades, 
with a variety of decisions made to restore the fishing industry 
and sport. 

The buffalo provide an interesting example of what is apt to 
happen with no national policy for resource management — no 
model, no logical decision. 



A Model for 1830 

In 1830, there were 40 million buffalo roaming the western 
United States. In terms of weight (at 1000 pounds each), there 
were 40 billion pounds of buffalo compared to only 24 billion 
pounds of human beings today in the entire United States. The 
buffalo dominated the western plains to an extent unknown for 
any other animal in history, including human beings. 

In 1830, the railroad arrived and the rapid westward expansion 
of the United States began. By 1887, there were only 200 buffalo 
left. In this slaughter, animals were often killed for only the tongues 
and hides. An average of only 20 pounds of meat (of a possible 
500) per buffalo was eaten. The peak was reached in 1872 when 
national heroes like "Buffalo Bill" Cody led the killing of more 
than seven million. 

In less than sixty years, the lack of any sort of policy led to the 
destruction of what could have been a major source of meat for 
today's population of this country. A single buffalo could provide 
the entire meat supply for at least five people for a year. 

Had the nation been aware of the potential problem in 1830, a 
model could have been constructed. In order to decide how many 
buffalo can be killed each year, we first must know how the popu- 
lation rises or falls from natural causes. Recent studies of buffalo 
have indicated the following facts: 

1 . Buffalo reach maturity at age 2. 

2. 90% of the females age 2 or older have one calf a year. 

3. 53% of the calves are male, 47% female. 



41 



4. 30% of the calves live for two years, or to maturity (infant 
mortality is high for most animals). 

5. 10% of the mature beasts die each year (from tuberculosis, 
drowning, predation, and so on). 

From these observations, we can construct a model in mathe- 
matical form to show the number of mature females alive at the 
beginning of each year.* For example, let's look first at year seven. 
How many females are there at the beginning of year seven? Of 
course, this can be any year picked at random. 

First, the answer depends on the number there were at the 
beginning of year six. Ten percent of those have died. Some other 
fraction have been harvested (killed for meat and hides). Let us 
call this fraction k. Then, of those who started year six, (0.9 - k) 
as many start year seven. 

This is not quite the whole story. During year six, some female 
buffalo have reached maturity (two years old). For every 100 
mature females at the beginning of year five, 90 calves are born; 
47% of these, or 42.3, are female; 30% of these, or 12.69, Hve to 
be two years old. Thus, 0.1269 of the female population at the 
start of year five become mature females at the start of year seven. 
Therefore, the number at year seven is (0.9 - k) times the 
number at year six plus 0.1269 times the number at year five. If 
we call F-j the number of females at the start of year seven, we 
can summarize this model very simply by an equation 

F7 = (0.9 -A:) 7^6 + 0.1269 Fs 

We can change the 7, 6, 5 to any three consecutive years. All this 
equation says is that the mature population depends on the size 
a year earlier and also two years earlier. The first term arises 
from the total death rate, the second term from the births two 
years ago. 

* 

The same general sort of model is used for 
males. The total population is, of course, 
the sum. To simplify the discussion, we 
consider only the females. (The male calves 
born depend on the number of females, so 
it is easiest to find the number of females 
first.) 



Fig. 4-15. 
Seal of the U.S. 
Department of the 
Interior. It is ironic that 
the animal we slaughtered 
so enthusiastically is the 
symbol of a government 
department and even 
appears on our coins. 




42 



Modeling 



A Decision Policy 

Once the model is known, we can choose k to control the 
population. We might want the population to increase, stay con- 
stant, or decrease. 

As an example, if the decision in 1830 had been to keep the 
population constant at 20 million mature females, how should k 
be chosen? Now in the preceding equation, we want F^, Fg, and 
F5 to be the same (20 million). Then we can cancel these F's or 
divide each term by F. This leaves an equation 

1 =(0.9- A:) + 0.1269 

which states that k should be 0.0269. This means we can harvest 
2.69% of the mature females each year. The population will not 
change. Since 0.0269 times 20 million is 538,000, we can harvest 
for food and hides 538,000 mature females each year. (Even more 
males can be harvested, since more males are born.) 

If both males and females are counted, we could have provided 
enough meat for 6 million people a year since 1 830 and still had a 
buffalo population of 40 million. All that was missing was an 
intelligent decision policy. 

If we were actually managing the buffalo population, we would 
have to measure the death and birth rates each year. If there were 
an epidemic, we might want to decrease the harvest until things 
were back to normal. 

We could also construct a more detailed model. Birth rates 
depend on the age of the mature females, the weather, and other 
factors. Infant mortality varies with location (the number of 
predators, the food supply, and so forth). 

The interesting feature of the example is the obvious benefit 
from a very simple model. Even if the numbers in the model are 
slightly in error, the decision (or policy) ensures that the population 
changes will be slow. If after several years we find the population 
is decreasing, we can reduce the harvest slightly. Over a period of 
years, we can reach a policy which gives a stable population. We 
can continually improve our model and our policy with experience. 

5 I A POPULATION MODEL 

While we worry about saving the buffalo or the falcon from 
extinction, there is much greater concern today about trends in 
the population of human beings. A model of the world's popula- 
tion is interesting because it represents a dynamic situation (one 
in which events change with time). Furthermore, the derivation of 
the model illustrates how we often need to refine or improve our 
model after it is initially determined. 

It has been estimated that since the appearance of man on the 
earth, a total of 15 billion human beings have existed. With a 
world population of nearly 3 billion today, 20% of all the people 



43 



who have ever hved are ahve today. Our population is growing 
at an explosive rate. 

Demography, or the study of population, is of increasing con- 
cern to economists, ecologists, sociologists, political scientists, 
engineers, and many others who must understand the present and 
plan for the future. Models of population change are exceedingly 
important to such study. They make possible analysis and pre- 
diction which can lead to more effective planning for the many 
goods and services that people need. 

We wish to obtain a simple model which would let us estimate 
the world population at some future date. The present average 
rate of population increase for the entire world is estimated to 
be close to 2% per year, and we assume in this section that this 
rate of increase does not change. At the start of 1960, population 
was approximately 3 billion (that is, 3 followed by nine zeros, or 
3 X 109). 

If the rate of increase is 2% per year, by the start of 1961 the 
increase is 0.02(3,000,000,000), or 60,000,000 people, to make a 
total of 3,060,000,000. We can then calculate the increase for the 
next year and for all succeeding years. The results are shown in 
Table 4-2. 





Population at 




Population at 


Year 


start of year 


Increase 


end of year 


1960 


3,000,000,000 


60,000,000 


3,060,000,000 


1961 


3,060,000,000 


61,200,000 


3,121,200,000 


1962 


3,121,200,000 


62,424,000 


3,183,624,000 


1963 


3,183,624,000 


63,672,480 


3,247,296,480 


1964 


3,247,296,480 


64,945,930 


3,312,242,410 


1965 


3,312,242,410 


66,244,848 


3,378,487,258 


1966 


3,378,487,258 


67,569,745 


3,446,057,003 


1967 


3,446,057,003 


68,921,140 


3,514,978,143 


1968 


3,514,978,143 


70,299,562 


3,585,277,705 


1969 


3,585,277,705 


71,705,554 


3,656,983,259 



Table 4-2. 

Estimated world 

population, 1960 to 1969. 

These data can be compared 

with more recent estimates: In 

July 1967, the Population Reference 

Bureau used United Nations and 

other statistics to estimate 

that, in the summer of 

1966, world population 

was 3.34 billion, an 

increase in one year 

of 65 million. 



The table shows that the increase is greater each year The 
growth IS always 2% of the population at the beginning of the 
year. As the population rises, the growth also increases. In fact 
if we contmued Table 4-2, we would find a population of 6 biUion 
by 1995. That is, the population will double in about 35 years. 

Carrying the calculation further, we would notice that this 
doubling occurs every 35 years. This would be true for any popula- 
tion number we start with, as long as the rate of increase is ly 



44 



Modeling 



per year. If the rate of increase were 3 %, the doubling would occur 
in 23.5 years.* 

Are these numbers in our table really accurate? From the entry 
in Table 4-2 for the population at the beginning of 1966, the 
model predicts exactly 3,378,487,258 people, a precise value. We 
have, however, ignored the fact that the numerical values with 
which we started were only approximations: The 3 billion initial 
population was a rounded number, and the 2% was an estimated 
average growth rate. If the initial population was exactly 3,000,- 
000,000 and the rate of increase was exactly 2.000,000,000%, then 
we should obtain ten meaningful digits in our answer. But since 
precision was lacking in our micasurement of both the starting 
population and the rate of increase, the results can have only a 
limited number of significant figures. We must, therefore, be con- 
tent to use rounded numbers. The extent of precision when two 
numbers are multiplied is restricted by the number with the smaller 
precision. If in this case it is the 2 % figure, and we assume that we 
are certain of its value to three significant figures (2.00%), then the 
rounded number having acceptable accuracy is not 3.378487258 
billion, but 3.38 biUion. 

If we continue our example with a 2 % rate of increase, we find 
that in the year 2060, just one hundred years from our starting 
date, the population will be nearly 22 billion. By the year 2160, 
it will reach an enormous 157 billion! With a doubling of popula- 
tion in 35 years, the growth after two centuries results in a popu- 
lation which is more than fifty times the original population. 

Plots of Population Growth 

We have already seen that a plot or graph is much easier to 
understand than a table of numbers. We now construct such a 
plot. For this, we use the predicted population at the beginning 
of each decade from 1961 to 2060 (Table 4-3). 





Population 


Decade 


(in billions) 


1961-1970 


3.06 


1971-1980 


3.72 


1981-1990 


4.55 


1991-2000 


5.55 . 


2001-2010 


6.77 


2011-2020 


8.20 


2021-2030 


10.06 


2031-2040 


12.2 


2041-2050 


15.0 


2051-2060 


18.3 



This is the same growth as compound in- 
terest gives. A rough rule is that the time 
to double is 72 divided by the rate of 
increase or interest in 9f • Thus, 5 "^c interest 
doubles the money in ^-f- or a little over 
14 years. 



Table 4-3. 

Estimated 

world population at start of 

each decade, 1961-2060. 



45 



As a matter of convenience, we have used the population for 
the first year of the decade, although the actual number continually 
grows. In the United States, where a census is made every tenth 
year, the count obtained is often considered to be the legal popu- 
lation until the next census is completed, even though the Census 
Bureau issues an annual estimate of the current number of our 
people. These values are plotted as a bar graph in Fig. 4-16. The 
height of each vertical column is proportional to the population 
at the start of that decade as given by the table. Not only do the 
heights of the bars go up in each ten-year period, but the steps 
become increasingly larger. 

The bar graph is one way of plotting the population growth. 
At the beginning of each decade (the start of 1961, 1971, and so 
forth), the figure is an accurate estimate or prediction. Then for 
the next ten years (Fig. 4-16), we show the population as constant 




1961 1981 2001 2021 2041 

10- Year interval 



2061 



Fig. 4-16. 
Estimated 
growth of world 
population. 



1 



until the start of the next decade. Actually, we know that the 
population tends to increase fairly smoothly year by year, month 
by month, and day by day. 

This steady growth in population can be portrayed if we 

Plot the points corresponding to the start of each decade 
(the points shown in Fig. 4-17). 

Draw a smooth curve through these points, as shown in 
the figure. This smooth curve gives only an approximate 
model of the real situation, since the population growth 
does fluctuate from year to year due to famine, epidemics, 



46 



Modeling 



c 

c 
g 

« 

O. 

o 

Q. 





1961 



Fig. 4-17. 

Fitting a smooth 

average line to the population 

growth graph. 



1981 



2001 2021 

Year 



2041 



2061 



wars, and so forth. The curve does represent a prediction 
of world population if we assume: 

a starting figure of 3,060,000,000 in 1961 (or 3.06 billion 
at the start of 1961) and 

a growth of 2 % per year. 

Now the extremely fast growth of population is clear. Even 
though the percentage increase remains constant at 2% per year, 
the larger increases each year produce a curve which becomes 
steeper and steeper. This curve is different from those we found in 
our previous models. The previous plots were linear. The popula- 
tion curve of Fig. 4-17, however, is not a straight line. 

Furthermore, this is a particular kind of curve. Each new value 
of the variable is obtained by adding a constant percentage of the 
previous value to that value. We have a growth that is proportional 
to the accumulated size: "the bigger it gets, the faster it grows." 
A snowballing relationship of this type is called exponential. The 
curve of Fig. 4-17 is Known as an exponential curve. This very 
important curve represents a model which is encountered fre- 
quently, and we find other examples later in this chapter. 

Population Plots Over Longer Time Scales 

We now consider another plot of population increase, from 
1700 to 2165. This is shown in Fig. 4-18. The eye tends to follow 
the curve upward to the right; but it is also important to note that 



47 



the graph drops as we look to the left, or as we go backward in 
time. In fact, prior to 1800 the height of the curve on the scale of 
this graph is so small that it is difficult to measure its value. This 
reflects the fact that a "population explosion" has occurred: The 
population of the earth in the past was extremely small compared 
to the present population. The curve makes more reasonable the 
earlier statement that approximately 20% of all the people who 
have ever lived are alive today. From a larger scale copy of the 
curve we could find the even more striking fact that the popula- 
tion increase from 1940 to 1963 (just 23 years) was greater than the 
total population of the world in 1800! 

Since we have extended our look backward in time, it is appro- 
priate also to look further into the future. We might attempt to look 
ahead to the year 2700, a period only slightly more than 700 years 
from now. This represents about the same time difference as that 
between the present and the time of Marco Polo. The graphical 
results of the computations are shown in Fig. 4-19. 

Can this really be expected? The curve shoots up at a fantastic 
rate. The vertical scale on the left is much larger than in the pre- 
ceding figure — so much so that the steeply rising curve to the year 
2165 (Fig. 4-18) cannot even be seen. Our new exponential curve 
has reached such proportions by the year 2700 that, if we tried to 







Fig. 4-18. 
The growth of 
world population 
from 

1700 to 2165. 
Prior to the 
present time the 
curve is based 
on historical fact. 
Later values 
are predicted 
from a model. 



1800 



1900 2000 2100 2200 
Year 



48 



Modeling 



5,500,000 
5,000,000 

CO 

c 

° 4,000,000 



c 

•° 3,000,000 



a. 
o 

Q. 

:o 2,000,000 

o 

^ 1,500,000 

1,000,000 



250 




500,000 

,000 > 

100,000 
25,000 ^ 




Fig. 4-19. 

Modeling prediction 
of world population to 
the year 2700. 



One person 

for every 
square foot 



One person 

for every 
square yard\ 



1950 2000 2100 2200 2300 2400 2500 2600 2700 
Year 



plot it on the scale of Fig. 4-18, we would need a sheet of paper 
27 thousand times as high, or 11 thousand feet (more than two 
miles) high instead of five inches. 

What does this curve of Fig. 4-19 tell us? By the year 2510 we 
should expect to have a world population of nearly 200,000 bil- 
lion people, by 2635 about 1,800,000 billion people. Thirty-five 
years after that it will have doubled to approximately 3,600,000 
billion. In the year 2692, the model predicts a 5,450,000 billion 
population. 

How large is 5,450,000 billion? We can express it in many ways. 
The number when written completely would appear as: 

5,450,000,000,000,000 

It may be written as 5.45 X 10'^ but this form does not give one 
a good "feeling" for the enormous size. 

Here is one picture that helps to visualize the magnitude of the 
number. There are roughly 31 million seconds in each year. If we 
counted one thousand persons per second, it would take us 176,000 
years to complete the census. 

There is yet another way to grasp the significance of this esti- 
mate of 5,450,000 billion population. Let us ask where these people 
will be: How much room will they have? The surface of the earth 
contains approximately 1,860,000 billion square feet. About 80% 
of this area is covered by water, but let us suppose that all of the 
surface were land. We can calculate that in the year 2510 when the 
population is 200,000 billion, there will be 9.3 square feet per per- 



49 



son, or about one person per square yard all over the earth. Worse 
yet, in 2635 each person will only have one square foot on which 
to stand, and in 2670 if they insist on retaining that much real 
estate, they will be standing on each other's shoulders two deep. 
And only 22 years later they will be three deep. Now, if we do not 
assume that these people can tread water but instead must occupy 
the land area only (i of the total area), in 2692 we should expect to 
see totem poles 15 persons high on every square foot! 



6 I EXPONENTIAL GROWTH 

The model of the last section obviously is not useful for pre- 
dicting population too far into the future. The model is based on 
a 2% increase every year. Once the land becomes too crowded, 
this growth rate certainly will fall. The population will level off. 
In the next section, we will consider how to change our model to 
include this fact. 

The model is useful, however, to predict what will happen in 
the next thirty years. If the present growth rate is 2% per year, we 
can guess that this will not change very much in the near future. 
Regardless of the international efforts to control births, any real 
change requires educating masses of people. Even if reasonable 
laws were passed to limit the number of children a family could 
have, years would pass before the laws could be enforced effectively. 
Furthermore, there is a time lag involved in any program of 
population control. This is a factor in the model which is often 
overlooked when people write or speak about the population 
problem. To reduce the number of babies born each year, we need 
to reduce the number of women of child-bearing age. But the 
number of women 20 to 40 years old depends on the number of 
babies born more than twenty years ago. 

Consequently, even if the number of babies born this year were 
reduced, it would be more than twenty years before the effects were 
really noticeable. In other words, the population growth rate is 
fairly well determined already for the period from now until the 
year 2000. The real effects of any population-control program 
would not show up until about the year 2000. 

Such a time lag is found in problems where we are trying to 
control the environment. For example, even if all new cars built 
from today on were made to have no lead compounds in the ex- 
haust gases, it would be several years before there was a notice- 
able change in the lead in the air simply because of all the cars 
already on the road. Ten years would pass before almost all of the 
cars on the road were "clean." 

Because of this time lag, the model based on 2% growth per 
year gives a reasonable prediction of population for the next thirty 
years. (We assume there will be no world war, great epidemic, or 



50 



Modeling 




Fig. 4-20. 

The growth of 

world population 

from 

1700 to 2165. 



mass starvation.) In this section, we want to look in more detail 
at models which have such a constant growth rate. 

A Plot with Constant Growth Rate 

A signal (or a quantity such as population) with a constant 
growth rate is called an exponential. This simply means that the 
percentage change in each year (or hour or second) is the same. 
Each year the population increases by 2%. 

When we try to plot population, we run into the problem shown 
in Fig. 4-20. A plot which shows what is beginning around the 
year 2000 is useless before 1800 (where the curve is almost zero on 
our vertical scale). Also, the curve starts to rise so rapidly after 
2100 that it quickly goes off the paper. The trouble is clear. Our 
vertical scale only allows us to plot values from perhaps 2 billion 
to 200 bilUon. Over the years of interest, the population varies 
over a much wider range than this. 

When we have a constant growth rate, we can simplify the 
plotting if we use a different vertical scale. The population is 3 
billion in 1960 and we are interested in the years from 1760 to 2160. 
How do we plot? 

We first take a sheet of paper and mark the years off m the 
regular way. 1960 is in the middle, and every 50 years are shown 



51 



from 1760 to 2160. We know the population in 1960 is 3 billion, 
so the middle of the vertical axis is set at 3. 

In the last section we saw that the population doubled every 35 
years (with a 2% increase per year). Hence, we have the points 



Year 


Population 


1995 


6 


2030 


12 


2065 


24 


2100 


48 


2135 


96 



Along the vertical scale, we show a doubling every equal space 
(Fig. 4-22). In other words, the distance from 3 to 6 is the same as 




Fig. 4-21. 
Years marked 
off for the 
population 
plot. 



1760 



1810 



1860 



1910 



1960 
Year 



2010 



2060 



2110 



2160 



Q. 
O 
CL 




1760 1810 



2160 



Fig. 4-22. 
Points into the 
future shown 
with an unusual 
vertical scale. 



52 



Modeling 




Fig. 4-23. 
Plot of population 
growth from J 760 
to 2160 with 
increase of 2% 
each year. 



2160 



from 6 to 12. Once the vertical axis is labeled in this "odd" way, 
we can mark the above points. 

The usefulness of this plot is now obvious. The points are on a 
straight line. The population doubles every 35 years. If the vertical 
axis is marked to show a doubling corresponding to a constant 
distance up, the curve moves up this same amount every time it 
moves across by 35 years. This is just the property of a straight 
line. If we draw the rest of the curve back to 1760, we obtain the 
complete graph of Fig. 4-23. 

Once the horizontal and vertical scales are labeled, we need 
only two points to determine the straight line. For example, the 
1960 population is 3, and the 1995 is 6. We can just draw a straight 
line through these two points. 



An Economic Model 

The plot of Fig. 4-23 is useful whenever there is a constant 
rate of growth. The economic plots of the United States gross 
national product, for instance, show an average increase of 5% 
each year. If the total is 1 trillion dollars in 1970, the future can 
be predicted from Fig. 4-24. We construct this plot as follows. 

The years of interest are 1960 to 1990, so we label the horizontal 
axis. The 5% rise each year means we double every ^ or about 
every 14 years. We now have two points (1 trillion in 1970, 2 
trillion in 1984). The straight line can then be drawn. 

The graph shows that in 1990 the gross national product will 
be almost 3 trillion dollars. Since the United States population in 
1990 is expected to be about 300 million, the average per person 
income should be 3 trillion 300 miUion or $10,000. (In 1970 it 
was about $5,000.) 



53 



1/2 




1960 1970 1980 1990 
Year 



Fig. 4-24. Expected 
gross national product 
of the United States. 




Fig. 4-25. Vertical scale for an 
exponential plot (a is 1.4, b is 2.8). 



One word of caution should be given here. To make Fig. 4-24, 
we have used an odd vertical scale (Fig. 4-25). The distance from 
1 to 2 is the same as from 2 to 4. Each time we move this distance, 
the quantity being measured doubles. When we asked in Fig, 4-24 
what the gross national product would be in 1990, we had to 
estimate a value between 2 and 4 (point A in Fig. 4-24). 

To make this estimate, we must recognize in Fig. 4-25 that 
if a is halfway from 1 to 2, a does not correspond to 1.5 trilUon. 



GROWTH TRENDS IN U.S. AIRLINE PASSENGER TRAFFIC 

liiiiiiiiiMmiif"ji 




Fig. 4-26. 

Another example of 

a plot of exponential 

growth. The way in which 

the actual data follow the 

straight lines promises that the 

changes in the next few years can 

be predicted with reasonable confidence. 

These particular curves are used by 
airport planners, airlines, travel agencies 
government agencies, and companies 
building equipment for the air-travel 
industry. 

The straight line for international 
travel shows that the travel doubles 
every 5 years {1962 to 1967). 
Thus, the annual increase is 
72/5 or 14%. (Aviation 
Week and Space 
Technology) 



1946 48 50 52 54 56 58 60 62 64 66 68 70 1972 



54 



Modeling 



300 



09 
0) 

>. 

Q. 
(0 

c 
Q 

c 
o 



200 



ii 100 



BH 


[| 


B 


BH 


m 


mm 


H 


H 


HH 


B 


Bin 


B 


Pi 


^^^H 


B 


im 


p 


>^ 


Over 150 
million tons 


■ 


i^^i 


^^0^ in 1965 


B 




■■ 


■ 



Fig. 4-27. 
United States 
solid waste. 




1920 



1940 



1960 



1980 



Year 



If it did, going from 1 to a would mean multiplying by 1.5. Going 
from a to 2 would mean multiplying by -^^ or 1.33. But we said 
equal distances on the vertical scale correspond to equal multi- 
plying factors. If this is to be true, the point a corresponds to 
V2 trillions, or 1.4 trillions; b midway between 2 and 4 is 2-^/2 
trillions or 2.8 (not 3). 

The Solid-Waste Problem 

If the United States is considered as one vast system (containing 
as elements the manufacturing plants, the transportation vehicles, 
the people, and the natural and man-made devices), one of the 
important signals which can be measured is the solid waste. Such 
soUd-waste material includes all the material which we throw away: 
the 6 million cars which are scrapped every year, the appliances 
discarded, the refuse from construction and demohtion of build- 
ings, and the garbage. Our highly advanced technology and the 
associated high standard of hving lead to a national problem of 
increasingly serious magnitude. How can we dispose of this solid 
waste economically and without dangerously fouling the en- 
vironment? If we take a longer range viewpoint, how can we re- 
cycle this trash? In other words, how can we conserve our natural 
resources by using again the materials we are throwing away? 

The magnitude of the problem is vividly portrayed in Fig. 
4-27,* which shows the quantity of solid waste produced per year 

Figures 4-27 and 4-28 are taken from the 
report, "A Strategy for a Livable En- 
vironment," published for the U.S. De- 
partment of Health, Education, and 
Welfare, June, 1967. 



55 




Fig. 4-28. 

Annual deaths from lung 
cancer per 100,000 population 
as a function of the size of the 
community in which the 
people live. 



in the United States since 1920. The significance of this particular 
signal is perhaps clearer if we note that in 1965 nearly five pounds 
were produced each day for each person in the country. Further- 
more, the rate of increase is appreciably greater than the rate of 
population increase. (Indeed, the United States is by far the most 
efficient producer of rubbish in the history of civilization. With 
less than 10% of the world's population, we generate well over 
half of its rubbish.) 

The importance and urgency of the problem derive from two 
principal factors: 

1. In most cities, available land for dumps is being rapidly 
exhausted. At the same time, the nature of the solid waste 
is changing. A few decades ago, the rubbish was primarily 
garbage and ashes. Today it includes vast quantities of 
metals, plastics (e.g., non-returnable containers), and other 
new products, many of which cannot be economically 
burned without contributing to air pollution. 

2. We know very little about the eff"ects of environmental 
pollution on our physical and mental health. To what 
extent are polluted air or mounds of junked automobiles 
responsible for the increases observed in mental illness, in 
urban unrest, and in such physical illnesses as lung cancer? 
Even data such as shown in Fig. 4-28 are not easily inter- 
preted. Individuals living in the city may smoke more 
heavily, may lead lives under greater nervous tension, and 
so forth. The problem of evaluating the importance of 



56 



Modeling 



environmental pollution is further complicated by the 
realization that major effects on the balances of nature 
and the characteristics of man are unlikely to become 
evident for a generation or more, when it may well be too 
late to reverse the established trends. (The problem of the 
time lag enters again.) 

Whether we are worried about a single city or a whole region, 
the intelligent planning of new methods for disposing of waste 
requires that we predict how much waste will be produced in the 
future. For example, if we decide to build a new incinerator to 
burn the rubbish, six years may be required until the incinerator 
is operating. Thus, if a decision is made in 1970, the incinerator 
which is built should be designed for the quantity and type of 
rubbish which will appear after 1976. 

In this discussion, we consider only the quantity of solid waste 
produced. Figure 4-27 shows the past history of the system over 
the years 1920 to 1965. We wish to use the data to predict the signal 
at least a few years in advance. This need for prediction arises for 
two reasons: 

1. Data are usually available only some time after they are 
valid (in problems of this broad a nature, a year or two 
may be required). Thus, the curve of Fig. 4-27 runs only to 
1965, even though it was published nearly two years later. 

2. Design and construction of the faciUty require several years, 
so that the system is truly being built for the future. 

Before we try to use the data of Fig. 4-27 to predict solid waste 
in the future, we notice that the quantity is increasing at a constant 
rate. Every 12 years, the amount increases by 50%. This is exactly 
the property of an exponential. Consequently, we can change the 
plot of Fig. 4-27 to the exponential form. 

In 1950, there are 100 million tons generated. In 1962, the 
figure is 150 million tons. We label the time axis from 1920 to 
2000. The vertical axis includes 100, and then successive hnes 1.5 
times as much (Fig. 4-30). 




Fig. 4-30. 
Solid waste 
generated with 
vertical scale 
chosen to 

show soyi 

every 12 years. 



2000 



57 



Once the straight Hne is drawiii we can predict the quantity 
probably generated at any future date. For example, by the year 
2000 we can expect almost 500 million tons per year. With 300 
miUion people, this is about 1.6 tons or 3200 pounds per person 
per year. (Almost 10 pounds a day!) 

One proposal has been to build an artificial mountain of rub- 
bish from New Jersey to CaUfornia. When it is completed, it 
could be covered with grass and landscaped so it would provide a 
recreation area for future generations. The proposal does not sug- 
gest how to compensate the people who happen to live nearby and 
have to watch it grow. 

More attractive proposals are to raise the cost of goods so that 
the manufacturer has to reclaim them. Automobiles are a prime 
target. In 1969, more than 50,000 cars were simply abandoned on 
the streets of New York City. Any person driving through the 
United States soon encounters automobile junk yards steadily 
growing in size and ugliness. 

The Exponential As a Planning Device 

In this section, we have seen that exponentials can be plotted 
as straight lines if the vertical scale is marked as follows. Each unit 
distance up corresponds to multiplying the quantity by the same 
factor. 

Because exponentials occur so often, this form of plot is par- 
ticularly important. In using such plots for prediction of the future, 
it is important to recognize that we usually do not need great 
accuracy. Whether the solid waste generated in the United States 
in the year 2000 is 500 million tons or 450 miUion tons is not very 
important. Regardless of what the number will actually be, we 
need to start planning immediately if we are not to be swamped 
by rubbish. Either we have to stop its growth or we must find 
better ways to recycle it or dispose of it. 

This type of prediction is called extrapolation. We extrapolate 
(or extend) what has happened in the past into the future. We 
assume that the growth rate will not change. We should recognize 
that such extrapolation is not necessarily vaHd. New changes may 
occur in our way of living which may increase or decrease the rate 
of population growth or solid-waste generation. (See Box 4-1.) 

7 I AN IMPROVED POPULATION MODEL 

Obviously the population model with 2% growth is incorrect, 
at least after some time in the future. Quite clearly there are some 
limiting factors which prevent such a population increase. Actually 
our model is too simple because we did not take into account 
several important factors that tend to limit our predictions. 

To learn more about these factors, it is helpful to examine 
functional models of the world population. Such models are easy 



58 



Modeling 



Box 4-1 

EQUATIONS FOR EXPONENTIALS 

For those who hke to live by mathematics, we can write an 
equation for an exponential growth curve. The solid- waste 
generation data are used as an example. 

The general equation for an exponential is 

y=A r'/^ 

Here y is the quantity we are measuring (the solid waste 
generated per year in millions of tons), r is the factor by which 
y is multiplied in T years. In our case, r is 1.5 and Tis 12 years. 
/ is the time (in years) measured from any reference point. 
If we select the 100 value in 1950 as the reference, / is measured 
from 1950. (Thus, a / of 7 represents 1957, a r of -21 repre- 
sents 1929.) Finally, A is the quantity at the time / is zero. 
(In our case, /i is 100 since that is the solid waste in 1950.) 

Thus, the equation for United States solid-waste generation 
is 

y= 100 (1.5)'/'^ 
where / is measured from 1950. In 1998, / is 48 and 

;;= 100(1.5)^ = 506 

The equation predicts 506 million tons generated in 1998. 

The equation gives exactly the same information as our 
straight-line graph. 



to find in a biology laboratory. Any small organism that repro- 
duces rapidly will do. Fruit flies, yeast, and bacteria are commonly 
used examples. Here we describe a population model using yeast. 
First the experimenter must prepare a food supply, a "nutrient 
medium," For many yeast species, this may be simply a weak 
sugar syrup slightly modified by addition of other substances. Then 
there is need for a jar in which to keep the yeast as they gorge 
themselves, and for Adam and Eve, so to speak: the syrup must be 
inoculated with a few yeast cells to start with. The temperature 
should be kept constant, and the medium should be gently but 
constantly stirred. 

It is hardly possible to take a census of yeast cells as one does 
of people. Instead, a sampHng technique is used. Knowing the 
starting volume of his experiment, the investigator can withdraw 
a definite, very small percentage of it and count the yeast cells in 
that. Since the solution of food has been stirred, he can safely 
assume that his sample is typical, and that he can simply multiply 
by the proper factor to learn the total population. Such models as 
this one are particularly convenient because they take up very little 



59 



t 




Fig. 4-32. 
Exponential 
growth curve. 



1900 2000 

Year 



space; moreover, it is easy to try different circumstances ("to vary 
the parameters" as the professional puts it). It becomes possible 
to answer such questions as these: What is the rate of increase of 
population when the experiment begins? Does this rate remain 
constant as the population becomes larger? Does it matter whether 
the available space for the organisms remains constant or is made 
to increase as the population grows? Yeast cells produce an 
alcohol (there are many kinds of alcohol) from the sugar they 
consume; what is the effect of leaving the alcohol to accumulate 
in the nutrient medium? Of removing all but a constant fraction? 
Of removing all of it as it forms? (Removal can be rather easily 
accomplished by continually pumping fresh nutrient medium in 
and at the same time allowing the used medium to trickle out 
through a filter.) 

Which of these possible experiments cast light on our graphical 
model of world population? First, we know that the entire land 
surface of the earth is not inhabited but that it is not unlimited. 
(There is room for population to increase but the space will be 
used up someday.) This is modeled in the yeast case by using 
bigger jars (and more medium) up to a certain point, but then no 
more. Second, we know that food production can be increased 
for human beings but not without limit. We can supply more 
sugar to the yeast on a schedule that we think is comparable to 



60 



Modeling 



the future history of the world; even better, we can try many 
schedules. In short, we can test our model and thus refine it, by 
comparing it with what we already know about the course of 
development of the human population. 

Now it turns out that such experiments as those described are 
practically always alike in one feature. Growth is roughly exponen- 
tial at first; the rate of increase is not necessarily constant, but the 
population curve is closely similar to that of Fig. 4-32. If the 
experiment lasts long enough, however, the rate of growth sooner 
or later begins to decrease and in time reaches zero. The curve 
stops its exponential growth and tends to level out, as suggested in 
Fig. 4-33. Because this curve has a kind of S-shape, it is known as 
a sigmoid (from the Greek word sigma for the letter S). 

The basic reason for the change of shape shown is overcrowding. 
Without unlimited space in which to grow and unlimited food to 
support life, the individual yeast cell has neither room nor food to 
allow it to reach normal size. No doubt there are other reasons, 
but they are less important. 

In the case of small animals and insects tested in a laboratory 
or carefully controlled environment, the same leveling off of popu- 
lation has been observed. The rate of growth tends to decrease as 
the animals become badly overcrowded because of both physical 
and mental deterioration resulting from inadequate supplies of 
food, air, and water, excessive nervous tension associated with 
inability to move freely, and so forth. In actual experiments with 
rats, once severe overcrowding occurs, mothers reject their young, 
adults kill females, and reproduction falls rapidly. Whether such 
experiments have any meaning for human beings is not at all clear. 

Certainly nature ultimately limits population growth, although 
typically with a serious deterioration of the species as suggested 
in the preceding paragraph. One would assume that man will limit 
his population growth significantly before serious damage has been 
done to his general physical and mental condition. Indeed, the 



Fig. 4-33. Population growth 
in laboratory studies. 




Time 



61 



focus of the recent worldwide emphasis on population control is 
to limit the population to levels at which adequate food resources 
and land are available to ensure happy and healthy individuals. 

Perhaps the first man to recognize the sigmoid character of 
population growth (although he did not express it in this way) was 
Thomas Robert Malthus (1766-1834). He was an Enghshman who 
wrote a gloomy essay pointing out that a time must come when 
population will outrun food. Then the growth of population would 
be stopped, he believed, by widespread epidemics, or starvation, or 
war, or some combination of these. Instead of a truly sigmoid 
curve, however, his curve would probably actually turn down- 
ward. He predicted that the end of the growth period would come 
during the nineteenth century. That it did not was the result of the 
discovery of chemical fertilizers. With these an acre of ground 
brings forth several times as much food as was possible in Mal- 
thus' day. We can see, however, that some limit, at some time, 
must be reached in the number of pounds of food that can be won 
from an acre of ground or of sea. The supplies of potash and phos- 
phate easily recovered must someday disappear, so the cost of 
fertilizers must rise. The third major fertilizer element, nitrogen, is 
available without foreseeable limit from the air. The current re- 
search in development of food from the sea promises to provide 
the possibility of feeding adequately a great number of people, 
but not an unHmited number. 

A Model with Decreasing Growth 

Even if we agree that the population model of the preceding 
section (with 2% annual growth rate) is impossible, we can still 
use this exponential growth curve to predict moderately into the 
future. The sigmoid characteristic of Fig. 4-33 does behave as an 
exponential in the early portion. Recent population data indicate 
that we are indeed still in this part of the curve. 

If we desire to peer further into the future, we need a model 
which shows the eventual slowing of growth. To obtain such a 
model, we need to assume that the growth rate will eventually de- 
crease as the population increases. 

In the population model, we worked with a growth rate of 2 % 
a year. The population in any year is 1.02 times the population a 
year earlier. In a stable situation, with the population constant, the 
value in any year is just 1.00 times the value the preceding year. 

Thus, to obtain a sigmoid curve, we need to reduce the 1 .02 to 
1.00 as the population increases. Exactly how do we put in this 
change? When does the factor change from 1.02 to 1.01, for ex- 
ample? Then when from 1.01 to 1.00? Where will the population 
start to level off? 

Obviously, we can only guess. Today we are still in the region 
of exponential increase. This growth will eventually be slowed, but 
we do not know what factors will cause the leveling off. 



62 



Modeling 



Box 4-2 

MATHEMATICS OF A SIGMOID MODEL 

The man who rehshes mathematical language can derive 
a model for the sigmoid characteristic as follows. 

Exponential growth in the exponential case, the population 
in any year is a constant (1.02 in our case) times the value a 
year earlier. If P„+i is the population in the year (« + 1), 
Pn in the year («), then 

P.+i = r P., 

Thus, if Pi96o is 3 billion and r is 1.02, 

/'i96i= 1.02X3 = 3.06 billion 

Sigmoid behavior To obtain the leveling off, the factor r must 
decrease as population increases. This change occurs if we 
choose 

r = ro— c Pn 

ro is 1.02. This value is reduced by c Pn where c is a constant. 
As the population P„ increases, the r decreases. Then 

/>„+! = (ro - C Pn)Pn 

Example If ro is 1.029 and c is 0.003, and we measure popu- 
lation in billions, we obtain 

ro- c Pn= 1.029 - 0.003 X 3 = 1.02 

when the population is 3 billion. That is, in 1960 the growth 
rate is 2%. 

As Pn increases, the factor (ro — c Pn) decreases steadily. 
This factor becomes one when 

1.029-0.003 XPn= I 

or 

Pn = 9.7 billion 
According to this model the population levels off at 9.7 billion. 
This value depends critically on what we choose for the con- 
stant c, which represents the rate at which the growth decreases. 
Since we do not know what factors will hmit population, 
we really can only guess at c. 



The particular population model of this section is not especially 
important; indeed, major political or social changes may make our 
predictions of future world population look ridiculous to the his- 
torians of the year 2000. Our purpose in this section, however, is 
to introduce the idea of model refinement. We discovered that our 
2% model is ridiculous if we try to predict hundreds of years into 
the future. On the basis of our rather superficial understanding of 



63 



population growth, we then found an alternative model which at 
best has the property of leading to a limited ultimate population. 
(See Box 4-2.) Since we know we cannot predict population 
accurately too far into the future, our simple models are probably 
as good as much more complicated ones. 

8 I USES OF MODELS 

Predictive population models are often used with great success 
in governmental planning at all levels — town, state, and federal. 
For example, the design of a transportation system for a region 
requires that we have reasonably reliable predictions of population 
distribution in order to assess future transportation needs (for 
transporting people and the materials which people require). 

In such a problem, the complete system model includes popu- 
lation models for hundreds or thousands of separate towns. The 
complete model is often a mathematical model composed of many 
equations. Some of these are similar to the equations we have used 
and some are more complicated. Not only must birth and death 
rates (net growth) be considered, but the relationships among other 
factors must be included. There are also influences which make the 
populations of towns interdependent. If one town becomes unduly 
crowded, there is a strong tendency for neighboring towns to grow 
more rapidly. Immigration and emigration rates thus are important 
considerations for the development of an accurate dynamic model: 
a model in which the interrelationship of factors changes with time. 

Many Models for One System 

It is possible for one system to be represented by a number of 
different models. As in the case of the blind men and the elephant, 
no one model describes the real thing completely, but separate 
models of sub-systems are often necessary and useful. 

An air-conditioner provides an example of this characteristic. 
One model can be developed which is based on heat flow: how 
heat is extracted from a room, how the fluid in the unit changes 
its temperature as it absorbs heat, and how this heat is then trans- 
ferred outside of the room. This model must include such factors 
as expected temperature ranges, characteristics of the refrigeration 
unit and blower, and intake and outlet duct air flows. 

Another model to describe the same system might be a control 
model which includes the thermostat, the various relays and con- 
tacts, and the electrical network which links the electrical parts of 
the system. 

Yet another model of an air-conditioner could be developed 
for a study of its mechanical behavior. For example, we may wish 
to know how much noise and vibration the equipment will produce 
and how to design the air-conditioner to minimize the noise and 
vibration. For this objective the model would include a number of 



64 



Modeling 




Fig. 4-34. 

An initial model for 
the planning of a new 
town — in this case Twin 
Rivers, New Jersey, with a 
planned population of 10,000. 
This first model shows the 
general planning to include the land 
uses and the highways and lakes. {The 
two irregular areas are lakes.) Once this 
overall model is adopted, each section 
can be planned in detail. When the 
town is designed in this way, schools, 
parks, and shopping areas can be 
located within walking distances 
of most residential areas. Streets 
can be planned to avoid too many 
pedestrian crossings. The goal is 
to create a town which avoids 
many of the annoyances and 
difficulties of existing towns 
which have grown without 
overall planning. (© 1970 
by The New York Times 
Company. 
Reprinted by 
Permission) 



factors such as the characteristics of the moving parts, their 
mountings, the location of shock absorbers, and the geometrical 
arrangements of the^ openings, the absorbent surfaces, and the 
baffles. 

One Model for Many Systems 

What is there in common among the way in which a cup of 
coflFee cools, the way in which the numbers of chain letters increase, 
and the way in which a human head grows? Just as it is possible 



66 




Fig. 4-35. 

Three 

examples of exponential 

systems. 



Room temp. 



i 



mmmmmmmL 

10 15 20 25 30 35 40 



Time in minutes 
(a) 




)m 



Head and 
brain size ^^ 
in percent 
relative to 
size at 50 
age 20 



2 4 6 8 10 
Number of steps 

(b) 




for one system to be described by several different models, so one 
model frequently is applicable to many kinds of systems. In Fig. 
4-35 there are models of three different processes which one 
would not ordinarily think of as being similar. In (a) is shown 
how the temperature of a cup of coffee drops as the coffee cools 
to room temperature. The initial temperature is just below the 
boiling point. It drops rapidly at the start, then more and more 
slowly. After a half hour, the temperature of the coffee has dropped 
to within a few degrees of room temperature. 

The illustration in (b) describes a system in which the produc- 
tion of an item doubles at each step. During the early part of the 
curve the values are not readily observed because of the scale of 
the graph axis, but as the number of steps goes from 1 to 2 to 3 
to 4, the number of items increases from 2 to 4 to 8 to 16. The 
increases become larger with each step; for instance in going from 
9 to 10 steps the number of items doubles from 512 to 1024, This 
is a model for the chain-letter process, where an individual writes 
to two people, each of these writes to two others, and so on. 
After 20 steps in such a process the number of letters (items) 
being written is more than one million, and after 30 steps the 
number becomes greater than one billion. 



66 



Modeling 



This rapid growth of an exponential is the basis for the famihar 
story of the golf game between Mike and Dick. On the first tee, 
Mike suggested they play for a penny on the first hole and then 
double the bet each hole. By the eighteenth hole, Dick was so 
nervous he missed his drive completely, while Mike played with 
total relaxation. It was only after the match was over that the 
mathematically slow Mike realized that the bet on the last hole 
was more than $1300. 

Figure 4-35c shows how the size of a human head grows 
from birth to age twenty. At birth it is a little less than \ its full 
size, and it is growing very rapidly. At the age of five the growth 
begins to slow down appreciably, and at the age of fifteen the 
head is within a few percent of its ultimate size. 

We can see what is common to the cooling of a cup of coffee, 
the rate of increase in a chain-letter situation, and the growth of 
the human head. Each displays an exponential rate of change. 
In each of the processes, as in the population expansion, growth 
either increases or decreases exponentially. 

Our exponential curve thus fits many systems. Such things as 
the rate at which an automobile coasts to a stop, the growth of 
plants, and the accumulation of bank interest can also be repre- 
sented approximately by an exponential curve. All these examples 
show that one model may represent many different systems. 

Another remarkable aspect of modeling is how often we can 
find mathematical relationships among important quantities. As a 
final example, violent storms are of four general types: tornadoes, 
thunderstorms, hurricanes, and cyclones. There is a relationship 
between the size of the storm and its duration: the larger the 
storm, the longer it lasts. Indeed, if we call D the diameter of the 
storm in miles and T the duration in hours, the model is given by 
the equation: 

£)3 = 216 P 

Once we have found such a model from observation of many 
storms, we can answer such questions as: 

How long does a cyclone with a diameter of 600 miles last? 

How large is a thunderstorm which lasts one hour? 

If a hurricane has a diameter of 100 miles, what would be the 

anticipated duration in days? 

A tornado lasts 11.5 minutes; what is the expected size? 

The answers are lOOOliours, 6 miles, 2.8 days, and 2 miles. 

Such a model is only approximate. Any given storm may 
deviate from our equation just as any particular seventeen-year-old 
boy may be 5 feet 2 inches tall and weigh 300 pounds. In spite of 
such occasional deviations, however, the model yields a picture 
of typical average relationships among physical quantities. 



67 



Determination of Models 

Once an idea of the structure and nature of a thing is conceived, 
it may be expressed in many different ways. We may have diflferent 
models. Some, as we have seen, are verbal models. A map is a 
model, a graphical model. Other models are mathematical in 
which quantitative expressions are used to describe relationships 
in a precise way. Some models are developed using computers. 

An aircraft represents so complicated an aerodynamic problem 
that a complete mathematical description may be impossible. 
Therefore, it is usually modeled by constructing a small-scale 
version of metal or wood for testing in a wind tunnel. 

Models are used, not only to describe a set of ideas, but also 
to evaluate and to predict the behavior of systems before they are 
built. This procedure can save enormous amounts of time and 
money. It can avoid expensive failures and permit the best design 
to be found without the need for construction of many versions 
of the real thing. Models evolve, and it is customary to go through 
a process of making successive refinements to find a more suitable 
model. 

For example, in the development of a model for a nerve cell, 
there is need for successive refinement. A preliminary model is 
designed, it is tested against the real nerve cell, then the model is 
modified so that it becomes more realistic in its behavior. In the 
process of model construction it is essential to alternate back and 
forth between the real world and the model. 

The essential parts of the model-making process are shown in 
Fig. 4-36. Measurements or observations of the real world are 
used to develop a model. After a preliminary model is made, 
measurements made using the model are compared to the behavior 
of the real world. In most cases these tests show that the model is 
not completely satisfactory, so that it must be refined. This process 
is repeated until the model is acceptable. 

In the modeling of a nerve cell, or the modeling of the growth 
of a population of people, the real-world measurements are made 
on a system which already exists. In this case our model-making 
process is intended to produce a model which accurately matches 



Acceptable 

model 





















- 


Real 
world 




Model 




Test 




/' 


/ ■ 






Me 


/ 
asureme 


nts 


■ 


Vie 


1 
asureme 


Its 










Rpfinp 





















Fig. 4-36. 
The model-making 
process, shown as a 
block diagram. 



■Unsatisfactory 



Modeling 



the real world. In the case where scale-model airplanes or space- 
craft are modeled, the real-world object may not yet exist, and the 
box marked "Real World" in Fig. 4-36 theoretically contains the 
real object which we imagine and wish to achieve, as well as all 
pertinent facts about the real world (such as the properties of air, 
characteristics of flight systems which have already been built, and 
the characteristics of various materials and fuels). The model- 
building procedures are no different from those already discussed. 
Models can be descriptive, as in verbal, graphical, or mathe- 
matical representations. They can also be functional (they "really 
work"), as in scaled-down airplanes for use in wind tunnels or 
working replicas of nerve cells. The model includes only those 
parts of the system which are important for our purposes. The 
model guides our thinking and suggests how we can improve the 
system. 



Questions for Study and Discussion 



1. "No model is ever complete." Would it be helpful 
if one could in fact construct a complete model? 
Explain briefly. 

2. Discuss the difi'erences between 

a) functional and descriptive models. 

b) dynamic and static models. 
Give an example of each. 

3. Suggest two reasons why a mathematical model 
may be desirable. 

4. When a model is first designed, what is the next 
step which should be taken with it? 

5. Figure 4-3 shows the height-weight data for twenty- 
year-old men as a somewhat scattered cloud of 
points. Explain why it is reasonable and useful 
to draw a particular straight line through these 
points. 

6. The greatest height shown by the graph line of 
Fig. 4-4 is about 6'5". Would you be justified in 
using the graph line to predict the weight of a 
candidate for center on the basketball team if he 
is 6'10" tall? Why, or why not? 

7. From the equation for the relationship between 
weight and height of twenty-year-old men, find 
the expected height of a young man who weighs 
145 lbs. 



8. A forester might use a method similar to that of 
Section 2 to study the relationship between the 
height of a tree and the diameter of its trunk. It 
was pointed out that the height-weight data had 
been "passed through two strainers (age and sex)." 
What "strainers" would the forester have to use? 

9. How do highway engineers take a traffic count? 

10. To use an electric eye as a sensor in a corridor, a 
beam of light is arranged to shine from one wall 
(where the light source is) to the other wall (where 
the electric eye is). Whenever the light beam is 
interrupted by a person passing, the circuit of the 
electric eye operates a counter. Why would such 
a device give an incorrect count in the situation 
shown in Fig. 4-8? Can you think of a way to make 
it count correctly? 

1 1 . The text discussion on the uncontrolled harvesting 
of buff'alo is but one example of how man has 
willfully brought a species of animal to the point 
of extinction. Describe five other examples of how 
man has either willfully or unwittingly produced 
this eR"ect. 

12. The movements of the elk pictured in Fig. 4-14 
are monitored from a satellite. Describe how this 
is done and explain what elements of the life habits 
of an animal can be learned in this way. 



13. In the text, several factors which affect the growth 
rate of a town are listed: birth rate, death rate, 
nearness of other crowded towns, transportation 
system. Suggest five other factors which might in- 
fluence the growth rate of a town. In each case, 
explain briefly why the factor would be likely to 
increase or to decrease the growth rate. 

14. We have seen that it is possible for one system to 
have a number of diff"erent models which apply to 
it. Many times an engineer finds it necessary to 
have models of sub-systems. Suggest three models 
which could be used to describe a submarine. 

15. The poem on the blind men is: 



THE BLIND MEN AND THE ELEPHANT 

It was six men of Indostan 

To learning much inclined. 
Who went to see the Elephant 

(Though all of them were blind), 
That each by observation 

Might satisfy his mind. 

The First approached the Elephant, 

And happening to fall 
Against his broad and sturdy side. 

At once began to bawl: 
"God bless me! but the Elephant 

Is very like a wall!" 

The Second, feeling of the tusk, 
Cried, "Ho! what have we here 

So very round and smooth and sharp? 
To me 'tis mighty clear 

This wonder of an Elephant 
Is very like a spear!" 

The Third approached the animal. 

And happening to take 
The squirming trunk within his hands, 

Thus boldly up and spake: 
"I see," quoth he, "the Elephant 

Is very like a snake!" 



The Fourth reached out an eager hand. 

And felt about the knee. 
"What most this wondrous beast is like 

Is mighty plain," quoth he; 
" 'Tis clear enough the Elephant 

Is very like a tree!" 

The Fifth who chanced to touch the ear, 

Said: "E'en the blindest man 
Can tell what this resembles most; 

Deny the fact who can, 
This marvel of an Elephant 

Is very like a fan!" 

The Sixth no sooner had begun 

About the beast to grope. 
Than, seizing on the swinging tail 

That fell within his scope, 
"I see," quoth he, "the Elephant 

Is very like a rope!" 

And so these men of Indostan 

Disputed loud and long. 
Each in his own opinion 

Exceeding stifi" and strong. 
Though each was partly in the right 

And all were in the wrong! 

John Godfrey Saxe 
American Poet 1816-1887 

A modern version of the six blind men and the 
elephant is suggested by the following problem. A 
printed capital letter of the English alphabet is 
scanned photoelectrically and the resultant signal 
is read into a digital computer. Seven subroutines in 
the digital computer inspect it. The first states that 
the letter is like a U because it has at least one pock- 
et to hold rain coming from above; the second shows 
that it is like a K because it has at least one pocket 
to hold rain from below; the third and fourth find 
that it is like an A because it has no pockets on right 
or left; the fifth shows that it is like a V because it 
has two ends; the sixth shows that it is like an S be- 
cause it has no junctions; the seventh shows that it 
is like a D because it has two corners. Combining 
these models of the letter, determine what it is. 



70 



The idea of exponential growth and decay can help you under- 
stand nnany natural events — the expansion of hunnan and 
animal populations, connpound interest, and geological dating 
are sonne of the examples treated in this article. 



Exponential Process in Nature 

Donald F. Holcomb and Philip Morrison 

A chapter from My Father's Watch: Aspects of the Physical World, 1974 



Figure 4. 1 shows sketches of the population of a rabbit colony at 
successive times. The time interval between each frame and the next is 
the same, 6 mo. We are immediately struck by the several features of 
the population growth of the rabbit colony. The first feature is the 
legendary ability of the bunny to reproduce himself in copious numbers. 
The second feature thrusts itself upon us with nearly the same force. 




1 . 5 y rs 



Z^rs 



Z.Syvs 



Figure 4.1 

Sketches of the inhabitants of an imagined 
rabbit colony, at the successive times 
indicated. 



71 



It is the related fact that the total number of rabbits seems to be rapidly 
getting out of control at the later times. Suppose we plot the number of 
rabbits as a function of time. Figure 4.2 displays such a plot. We see 
that the number of rabbits is certainly not a linear function of time. 

Let us now try to isolate the key feature of the growth of the num- 
ber of rabbits that tends to produce the "runaway" numbers. Each 
pair of rabbits will produce some number of offspring. Let us assume 
that the rabbits are all indistinguishable from one another, so that each 
pair will produce about the same number of offspring in a given period 
of time. Suppose that this reproduction rate results in the rabbit 
population doubling in a time period of 190 days> Since reproduction 
is a pairwise phenomenon, we shall expect that doubled number of 
rabbits to double itself again in a second time period of 190 days. Here 
is the key! We are dealing with a fundamentally multiplicative process 
rather than an additive process. That is, if the population changes from 
N to 2N in a certain interval of time, we expect it to change to 4N in 
the next equal interval of time, and to SN in the next succeeding interval. 
If the basic process were additive, the population would change only to 
3N in that second interval, and to 4N in the subsequent one. 



Figure 4.2 

A graph of the growth of the rabbit 
population shown in Fig. 4.1 




0.5 1,0 1.5 2,0 2.5 
Time, in \/zars ^ 



A MATHEMATICAL MODEL We can now produce a mathe- 
FOR POPULATION matical model that encompasses 

GROWTH our analysis of the rabbit problem. 

What we have said about rabbits 
in the previous paragraph leads us to realize that the increase of popula- 
tion in a certain time interval is directly proportional to the total 
population which existed at the beginning of that interval. For the 
population at the beginning of the interval we use the symbol N. The 
time interval is labeled At, and the population increase in that interval 



72 



Exponential Process in Nature 



is called AN. Then the mathematical statement of our proposition is 
given by the relation 

AN 



At 



oc N. 



(4.1) 



If we choose to write an equation rather than a proportionality, 
the equation becomes 



AN 



kN 



(4.2) 



where k is some proportionality constant. 

With our unprepossessing rabbits, we have described an example 
of what we can call an exponential growth process. An exponential 
growth process is defined as one which is described by an equation of 
the type represented by Eq. (4.2). The reason for the choice of the 
word "exponential" will appear later on, after we follow through a 
variety of examples and analyses of similar population problems. 

Q. Because of concern for exhaustion of the earth's resources, 
there are those who urge the earth's peoples to plan for ZPG — 
"zero population growth." If A' is the population of the earth, 
what value of ^ in Eq. (4.2) will yield ZPG? 



Graphing with Logarithmic Scales 

But before going to other examples, we want to use the rabbit 
colony to develop a graphical technique that turns out to be particularly 
powerful in analyzing these exponential processes. Let us take the data 
shown in Fig. 4.2 and make another graph. For the vertical axis in our 
new graph, we shall take the logarithm (using base 10) of the number of 
rabbits rather than the number itself — retaining the time axis unchanged. 
Figure 4.3 includes the small table of logarithms that we need. These 
were extracted from numerical tables. The numbers are followed by a 
graph of these data. We see a remarkable mathematical feature of the 
rabbit population. Although Fig. 4.2 shows us that the total number 
of rabbits certainly does not grow Unearly with time, Fig. 4.3 shows us 



3.0 - 



f 



2.0 f- 

ofp 




Figure 4.3 

A graph of the logarithms of the rabbit 
numbers of Fig. 4.1. as a function of time. 



0.fc02 
0.954 
I .iTfe 
1.544 
I .778 
Z. 130 



73 



2000 




Figure 4.4 



A reproduction of a sheet of semi- 
logarithmic graph paper. 



that the logarithm of this total number does follow a straight line quite 
closely. If we think a bit about the character of logarithms, we may not 
be surprised at the situation. As a number changes from 1 to 10, its 



74 



Exponential Process in Nature 



logarithm (base 10) changes from to 1. As the number goes on to 100, 
its logarithm increases to a value of 2. We see that the logarithms of the 
numbers turn out to be the natural representation of the fundamental 
property of the rabbit population. The population grows by a fixed 
multiplicative factor in each interval of time so that the logarithm of 
the population number will grow by a fixed additive factor. 

In the box, we write the central feature of the rabbit problem. It 
is the key organizational principle, which we shall use in the remainder 
of this chapter. 

Key to Exponential Processes: If the growth or decay 
of a population over some fixed interval of time or distance 
is proportional to the population that existed at the be- 
ginning of the interval, then the population will follow the 
exponential growth or decay curve, and the logarithm of 
the population will increase or decrease linearly with the 
dependent variable, be it time or distance. 



■f 



For cases such as the rabbit population, Eq. (4.2) is a compact 
mathematical statement of the words in the box. 

A graph of the sort that we made in Fig. 4.3 is often called a 
"semilogarithmic plot," so called because one axis of the graph remains 
a hnear plot whereas the other axis uses a logarithmic scale. Use of these 
plots is sufficiently common that graph paper manufacturers have found 
it profitable to produce a special paper in which the vertical scale is 
marked according to the logarithms of the numbers rather than the 
numbers themselves. Figure 4.4 shows a section of such paper. The key 
feature of the logarithmic scale is that equal divisions on the scale 
correspond to multiplication by a certain factor. For the linear scale, 
we reflect that equal divisions correspond to addition of a certain num- 
ber. Thus, in Fig. 4.4, the horizontal axis uses a linear scale and the 
vertical axis uses a multiplicative scale. Appendix 4A explores in more 
depth how the graph paper designer figures out how to place the 
numbers on the logarithmic scale in Fig. 4.4. 



Applications of the Exponential Model 

to Description of Social and Physical Phenomena 

Popu/ation 

Example 1 : Suppose we maroon 1,000 people on an unhealthy desert 
island. It turns out that there is subsequently a net decrease (births 
minus deaths is negative) in the population of about 20 /<, each 
year — i.e., if we start observation at any date, we will find the 
population decreased by \ over the next 12 mo from the value it 
had at the beginning of that 12-mo period. Thus, the population 
data might look like the table shown in Fig. 4.5. Let us graph these 
data in two ways. In the first plot in Fig. 4.5a, we make a simple 



75 



graph of population as a function of time, using a linear scale on 
both axes. In the second plot, Fig. 4.5b, we use a logarithmic scale 
for the population axis. As we found with the growing rabbit 
population, a straight line graph results from the use of the 
logarithmic scale. 




Example 2: Suppose the climate on our island becomes suddenly 
salubrious at year 10, and the population starts to grow at 5°o per 
year. Now the yearly multiple shifts to 1.05, and the curve turns 
around. Figure 4.5c shows what happens. (Note that the time 
scale is compressed in comparison to that of Fig. 4.5a and 4.5b.) 

In the preceding examples, the key feature that leads to the ex- 
ponential decay or growth is present. That is, the change in the popula- 
tion in any interval of time is proportional to the value of the population 
number at the beginning of the interval, and we expect Eq. (4.2) to 



looo 

800 

t 

Popula+ioM 

400 




Population 




2 345fc 78«}I0 



Figure 4.5 

a. Declining population on an island, at 
successive years. 

b. A semi-logarithnnic plot of the data 
of a. 

c Population data for later years is added 
to that of b. after an improvement in 
environment at year 10. 



Population 




76 



Exponential Process in Nature 



describe the problem. Specifically, for the first 10 years on the island, 
if we choose the value of At to be one year, then k = -0.20/year. 

Q. For Example 2, for times greater than 10 years, what is the 
value of k if we again choose the interval At to be 1 yr? 

If you are interested in demography, you may already have been 
saying to yourself, "But the exponentially growing population cannot 
really follow the exponential model forever, growing without limit." 
Quite right. Eventually, in any real physical, biological, or social system, 
the exponentially growing population will run into some limiting factor 
that causes the growth curve to flatten out. In our example of the 
maroonees on the desert island, after the change from shrinking to 
growing population, the population would probably eventually be 
hmited by food supply. The world population is presently growing 
exponentially, which is a reason for great concern. When populations 
or other exponentially growing functions begin to bump into some 
natural ceiling, such as food supply, great strains may develop in the 
system in the process of accommodating itself to the new conditions. 

Compound Interest 

Another familiar example of an exponentially growing quantity is a 
sum of money invested at compound interest. We see the inexorable 
power of the pure exponential if we imagine Queen Elizabeth I investing 
the English equivalent of 1,000 dollars at compound interest of 5 % in 
1576 AD. Her accumulation, if that rather modest exponential growth 
factor continued unchanged, would be about 10' dollars in 1990, the 
approximate present value of the U.S. gross national product. 

Air Pressure at Various Altitudes 

Population problems in various forms provide the majority of the 
ready examples of exponential processes. In these problems, it is gener- 
ally equal intervals of time which are to be associated with multiplica- 
tion of the interesting population number by a constant factor. How- 
ever, in certain physical and biological phenomena, there is one other 
common situation. In it, intervals oUistance are associated with multi- 
plication of the quantity of interest by equal factors. We look at one 
example of such a process— the air pressure in our atmosphere as a 
function of altitude. 

The table shows data obtained with pressure gauges carried m a 
rocket fired from White Sands, New Mexico. 

In Fig. 4.6a, we plot the data on a linear scale. If we suspect that 
an exponential model might describe the situation, we then plot the 
pressure on a logarithmic scale, as in Fig. 4.6b. The exponential model 
seems to work. We shall not attempt to explore the physics of why this 
should be so, but we have already made the first step to testing any 
physical description. We know that, since the exponential model seems 
to describe the data correctly, the decrease in pressure for each unit 



77 



Air 

iw 400 




10 20 30 40 50 fcO 
Attitude in Km > 

(a) 



Properties of the Earth's 
Atmosphere at Elevations 
up to 1 00 Kilometers* 



10 20 30 40 50 

Altitude in kiYi — 

(b) 

Figure 4.6 

Rocket data of air pressure as a function 
of altitude. The inset shows a linear graph, 
the larger graph a semi-logarithmic plot. 



fco 



70 

-> 



80 



Altitude (km) 


Pressure (mm Hg) 





760 


10 


210 


20 


42 


30 


9.5 


40 


2.4 


50 


7.5 X 10-^ 


60 


2.1 X 10"' 


70 


5.4 X 10" = 


80 


1.0 X 10" = 


90 


1.9 X 10" ^^ 


100 


4.2 X 10-* 



•R J Havens, R T Koll, and H E 
LaGow. "The Pressure. Density, and 
Temperature of the Earth's Atmo- 
sphere to 1 60 kilometers." Journal of 
Geophysical Research. March, 1952, 
p 59. Data were obtained with rockets 
above White Sands, New Mexico. 



increase in height is proportional to the pressure existing at the given 
original height. (We are simply rephrasing the boxed statement given 
on p. 91 m words appropriate to this example.) Any physical model 
we propose must be consistent with the observed fact that the exponential 
mathematical model correctly describes the situation 



Q. 



The height of Mt. Everest is 8.9 km. Assuming the exponential 
model holds, what is the air pressure at the top of Mt 
Everest, according to Fig. 4.6b, expressed in the units of the 
graph, mm Hg? 



78 



Exponential Process in Nature 



RADIOACTIVE DECAY We now return to a very particular 

AS A NATURAL CLOCK kind of population phenomenon, 

which was introduced in Chapter 2, 
and explore it in some detail. We investigate the population of radio- 
active atoms that are decaying through radiation and, thus, changing 
to a different kind of atom. (Review the material of pp. 50-51.) 

Radioactive decay processes of various nuclei have been put to an 
enormous variety of uses in modern applied science. About 42 different 
naturally occurring nuclei, and a much larger number of artificially 
produced radioactive nuclei, undergo the decay process. Some of the 
uses depend upon the fact that the "radiation" sent out during the 
decay process itself can serve as an identification signal. In this chapter, 
we shall explore a use more directly coupled to our topic of interest. 
By following the population of a radioactive nuclear species, one can 
tell something about the chronology of the material in which the nuclei 
are imbedded. This scheme is called "radioactive dating." 

The basic idea of radioactive dating is simple. Suppose a popula- 
tion of radioactive atoms was encapsulated in some fashion at a reason- 
ably well-defined time in the past. Then, the fraction of those which 
remain undecayed at any given time will measure the time interval since 
the encapsulation, provided one knows the characteristic decay rate. 



Half-Life 

The characteristic decay rate of a population is often stated in 
terms of the "half-life," the time for the population to drop to one-half 
from some chosen initial value. In mathematical language, if we use the 
symbol 7^12 for the half-life, and start with a population Nq at time 
t = 0, then the population N, at subsequent times t, will be given by the 
equation 

N = No-2-'/^"^ (4.3) 

Q. (1) By letting t = T^j^ , verify that Eq. (4.3) coincides with 
the word definition of T^^ given previously. 

Q. (2) From the graph ofFig. 4.4a or 4.4b, determine the half-life 
of the population of island inmates. 

We can now understand the source of the term "exponential 
process." It is any process in which the quantity of interest (such as our 
population, N) is proportional to some base number, such as 2, raised 
to a power which is itself a linear function of some running variable of 
interest, such as the time, t. The general form is 

where a is a constant, either positive or negative, y is some variable such 
as time or distance, and Q is the quantity of interest. Its value at >- = 
isCo- 



79 



Experiment shows us that each nuclear species has a particular 
half-life, determined by the degree of internal stability of the nucleus. 
Fortunately, for the purposes of applications, these half-lives span an 
enormous range of times. We shall here discuss only two particular 
species used in dating. Even within the area of dating measurements, 
there is a wide range of different species used, depending on the particular 
application. 

Radiocarbon Dating of Materials 
Removed from the Biosphere 

One dating scheme with some quite spectacular archaeological 
implications depends on measurement of the decay of a particular 
variety of carbon nuclei, labeled O*. The half-life of this nuclear species 
is 5,700 yr. When a C^* atom decays, it becomes a nitrogen atom, N^*. 

The C^"* species is itself produced in the Earth's atmosphere as 
the corpse of another radioactive decay process, which is stimulated 
by cosmic ray bombardment from outerspace. The parent of the C^* 
atoms is a nitrogen species, labeled N^^ The amount of C^* in the atmo- 
sphere, and hence the ratio of the C^"^ to the common carbon species 
C^^, is maintained at a stable value by the balance between C^* produc- 
tion and C*"^ decay suggested in the diagram of Fig. 4.7. We find that 

Figure 4.7 

Production of C* nuclei in the atmosphere 
and subsequent passage through the bio- 
sphere to interment. 

Cosvn ic Rays 



^--■^iw^osp 



itere 



.14 
■ 14 I. 



Equi libyjuvn 

Pt-oduCing 

Process 



BioSplaero. 

(Living Yr\a.He.v 
y\Q.a\r surface) 



In here 
I* 




No. C'^ 7.8X10" 



'/57OO y^s. 



WHere 6 is fhe 
time ( in years) since 
the matl-er left- the 
biosphere 



80 



Exponential Process in Nature 



the carbon nuclei, C^^ or C^'^, are carried about primarily as ingredients 
of carbon dioxide molecules. Since all living matter undergoes a con- 
tinual carbon exchange process through inspiration or respiration of 
carbon dioxide, all living matter has the same ratio C^*/C^^ as the 
equilibrium value maintained in the atmosphere by the cosmic ray 
bombardment. 

Now comes the "encapsulation process." When living matter 
dies — a tree is cut down or the flax for linen is harvested — the carbon 
exchange process stops. Then the C^VC^^ ratio gradually decreases as 
the C^"* decays. If we take an ancient block of wood or piece of linen 
and measure this C^VC^"^ ratio, we shall then know what fraction of 
the C^* remains undecayed. We then have a time measure in terms of 
the known half-life of C^*. 

But, you immediately ask, how do you know what the C^VC^'^ 
ratio in the atmosphere was in the dim past, when the material of 
interest left the biosphere? The answer is : we don't know. Everything 
else we know suggests that the value should have been about the same 
as it is now for an indeterminate time into the past. Hence, a measure 
of the present atmospheric C^'^/C^-^ ratio gives us a working value for 
that equilibrium ratio. (Actually, the ratio is now changing somewhat. 
Burning of fossil fuel that is poor in C^* tends to decrease the ratio, 
and C^''^ produced in nuclear weapons tests tends to increase it: one 
more example of how man's tinkering alters his environment.) 

We note that, with a half-life of 5,700 yr, an initial C^'*^ population 
will decay to yg of its original value in 22,800 yr. This fact suggests that 



Table of Some Archaeological Objects Dated with C^* 

Place Sample Age in Years 

Tikal, Guatemala wood lintel from Mayan temple 481 ± 120 ad* 

N. Newfoundland! charcoal associated with iron and slag 1,060 ±70ad* 

at the site of a great hall at L'Anse aux 

Meadows 

linen wrappings from Dead Sea Scrolls 1 ,91 7 ± 200 

Book of Isaiah 
Gt. Britain charcoal sample from Stonehenge 3,798 ± 275 

(first phase) 
Egypt wheat and barley gram from site at 6,391 + 180 

Fayum 
Near Clovis, N M , charcoal from campfire hearth 11,260+360 

U.S.A. connected with elephant hunters 

France charcoal from Lascaux Cave (site of 15,51 6 ± 900 

famous cave paintings) 
Iraq charcoal ash sample from cave at »25,000 

Sulimaniyah 

* Actual date given here, rather than age 

t Scientific American. May. 1967, p 78 
Other References are from W. F. Libby, 
Radio Carbon Dating. Chicago: Uni- 
versity of Chicago Press, 1952 



81 



this method might run out of accuracy as the remnants of C^* become 
difficult to observe. Such is the case — 20,000 yr is about as far back as 
this method will take us. 

Geological Dating 

For measurement of long times into the past, and in particular 
for the purpose of establishing the time scale of the Earth's geological 
history, the use of radioactive elements incorporated into the Earth's 
crust when it formed has been invaluable. Several different elements 
have turned out to be useful. Perhaps the most popular have been 
uranium, potassium, and strontium. We shall discuss the scheme for 
using radioactive potassium atoms in enough detail so that the 
methodology is at least outlined. 

In 1935, A. O. C. Nier showed that the common chemical element 
potassium (symbol, K) contains a very small concentration of a particu- 
lar variety of potassium which is radioactive. This radioactive species 
of atom, labeled K*°, is rather rare, there being only one K*° atom to 
each 8,400 nonradioactive potassium atoms. However, instruments for 
detection of the radioactive decay process are extremely sensitive, and 
this small fraction of "tracer" atoms turns out to be sufficient for the 
purpose. A sample of K*° atoms, as it decays with a half-life of 1.3 
X 10^ years, produces atoms of argon gas, labeled A*°, as a decay 
product. It turns out that the K*° atoms may also change into a different 
chemical species, Ca*^. In fact, only 12% of the decaying atoms form 
argon, and the other 88% form calcium. However, that ratio, g|, is 
determined by the inner structure of the potassium nucleus and is, 
hence, always the same. Thus, for every 12 argon atoms produced, we 
know that, on the average, 100 potassium atoms have decayed, 88 of 
them producing calcium. Despite the fact that calcium atoms are more 
numerous, we are most interested in the argon atoms. The great 
advantage of the argon atoms over calcium atoms is that they form a 
chemically inert gas, which is trapped in interstices of the material 
containing the original potassium. A sample of the material may then be 
broken down, and the argon is released without further ado. Calcium, 
on the other hand, readily enters into formation of chemical compounds, 
which must then be chemically broken down before analysis. Figure 
4.8 sketches the sequence of reasoning steps and experiments used to 
find the formation date of a piece of potassium-containing material in 
the earth's crust. 

Example^ : Suppose a sample of mass 1 g is found, upon analysis, to 
contain 4.21 % potassium by weight, and 13.6 x 10^^ A*° atoms. 
At what time in the past was the material formed? 
1. First, we determine the number of K'^^ atoms remaining in 
the sample at the present time. It is known, using the ideas of 



' Taken from Patrick M. Hurley, How Old is the Earth? New York: Doubleday 
Science Study Series, 1959. 



82 



Exponential Process in Nature 



chemistry, that each gram of potassium contains a total number 
of potassium atoms given by the relation 

Avogadro's number 6.02 x 10^^ atoms 
atomic weight 39.1 g 

= 1.54 X lO^^atoms/g. 

Therefore, the number of potassium atoms in our sample is 

0.0421 g X 1.54 X lO^^atoms/g = 6.49 x 10^° atoms. 

But only g^ of these are the tracer K*^ atoms. Thus, 

T^4o 6.49 x 10^° atoms ^^ , ^.^j ^ 

no. K*° atoms = = 77.1 x 10^^ atoms. 

8400 



AssuMip^'ioms 



(I) All arqoM •fot-mcd is ttropped iVi irviale>'rols. ^^ 

^'' C2) TVie. ratio of A'*'* toCa'*''* \A^^^ic^\ is -fov-wcct in +lie decay of K hos 
yewointd co/\stavvt tWrougl^oat Yivm., fvoKvi if = 0. 



Tiirc Developvv\tw+ of Sawnple I 



v 



Event "^i*"'* 



Material^ *-9-j >*>tca, soli^ii^ift*/ 
contami Mq^o otows of K 

k'*° afows decoy vj'i'tfn Inalf-WIe 
of 1.3 X lo'' yeairs. 

Mateviol f v-aps A*° Qtows as f Viey 

fov-vw. 

Mote>-ial coMfaiws soi*<e n\i%\\xre 

of K."**^, A*°, awd Ca*'*Qto«^s. 




Present tiwe, 7^ 



Sawple Processed ond Analyzed 



(0 Nuvwbe*- of A**" atows is dateir»vimed — wuniber isyV^ 
(2> Nurwbev- of K'*° atoms rewaiMing, labeled /i^-, is 
fouMd by wieasuv-inq total amo^xn'c of potassiuwi 
av,dusmqrat.o, ov>e K^° afo»v./8400 total Kator^S. 



To Find Value of T 



CO FiMd>l^„ fro^tUe. Suvw,/l^o =^7- ^^A+ 8.47/Va. 

WuvMber of k4°'S w^1.c^l wust havC decayed to torw 

Ca^° — wot directly wieasured. 
(2) We also know tliat 

/^^^y^z exp [ — -^-77-) 

~ ° I. Sit \o'* 

^7- T 

log 



2yj/^ ' ^ 1-3x109 



or 



r= 1.3x10' log. ^ = i.3xio^(3.3z iog,o-ir-) 

Qwd botti vKq and /J^ were previously deferwiincd. 



Figure 4.8 

Flow diagram for K*° dating scheme. 



83 



2. Now we can compute the total original number of K"^" atoms 
to have been 

77.1 X 10^^ + 13.6 X 10^^+ (8.47 X 13.6 x 10^^ ) = 205.6 x 10^^ 

remaining no. A*° atoms no. K'*°'s which must 

K*° created since have decayed to Ca*", 

atoms material which we do not 

formed measure 

3. Therefore, our basic exponential decay law becomes, inserting 
the known numbers, 

77.1 x 10'^ atoms = (205.6 x 10^^) atoms 

t 
X 2exp 

Solving for t, we have 



1.3 X 10^ yr 



205.6 X 10^^ atoms 

/ = 1.3 X 10^ yr log2 ^z^r^; ,„i5 , 

^ 77.1 X 10^^ atoms 

= 1.3 X 10' yr (3.32 logio 2.67)= 1.3 x 10' x 1.42 
= 1.8 X 10' yr. 

The material was laid down into solid form 1.8 x 10' years ago. 

Q. This K'^^ method does not depend on any assumptions about 
what fraction of potassium atoms were K''^^ atoms at the 
time the material was laid down. Explain what features of 
this scheme differentiate it from the carbon dating scheme 
described previously, which does depend on an assumption 
about C^yC^^ ratio at the time the material in question 
left the biosphere (see Fig. 4.7). 

In our discussion of C^* dating of objects removed from the 
biosphere, we noted that the value of the half-life of the particular 
radioactive species chosen tends to set the scale of times which can be 
accurately measured. After several half-lives, it is difficult to determine 
precisely the amount of the mother species remaining. The half-lives 
of K'^^ and several other species used for geological dating are of order 
of magnitude 10' yr, which turns out to be the natural time unit for 
treating the whole history of the earth (and, for that matter, of the solar 
system). Actually, this apparent coincidence of the half-lives of several 
prevalent radioactive species and the geological time scale is not really 
a coincidence at all. The nuclear species were themselves apparently 
formed not too long before the birth of the solar system, and the radio- 
active species that remain in substantial amounts are those whose 



84 



Exponential Process in Nature 



half-lives roughly match the present age of the solar system. (In case 
the reader has substantial interest in the interlocked questions of the 
age of the Earth, our solar system, and. indeed, our universe, he is 
referred to the introductory discussion for Special Topic B, Geological 
History of the Earth p. 363.) 

In conclusion, we note that the basic justification for our radio- 
active dating schemes depends upon our deeply held belief that the 
intrinsic properties of the atoms have been unchanged since the dawn 
of time. For the exponential decay depends upon the steady work of 
the law of equal fractional change in equal time, and only if the prob- 
ability of any given atom decaying in the next year remains always 
fixed does that law hold over all of the time scale. Appendix 4B, which 
discusses various aspects of radioactive decay processes that we have 
bypassed so far, examines that belief. 



CONCLUSION The main purpose of this chapter has been to 

show how a mathematical model of the ex- 
ponential processes can be exploited as an organizing principle for a 
wide variety of natural phenomena. There remains one important 
feature that we should call to your attention, if you have not already 
wondered about it. 

The mathematical model, embodied either in Eq. (4.2), which gives 
the primary condition for validity of the exponential model, or in Eq. 
(4.3), which gives the population as a function of time for a decaying 
population, would predict population numbers that exactly fit a 
straight line on a semilogarithmic plot of the sort given in Figs. 4.3 and 
4.5. In fact, the natural systems all have small deviations from the exact 
fit. Does such a situation invalidate the model? Of course not. We 
simply have another case of the abstraction process described in our 
Prologue. We abstract the essential element of a set of natural phenom- 
ena, find that a mathematical model is an excellent description of those 
abstracted systems, and so we use it fully. In the back of our minds we 
always remember that, for a variety of reasons which vary for different 
systems of interest, the true population numbers will fit the predictions 
of the mathematical model only in a statistical sense, not in an exact 
numerical sense. 



EXERCISES ^3^e Population 



Suppose a particular human population is described by Eq. (4.2), 
with a certain value of the constant k. If a birth-control campaign 
is instituted, is k likely to become larger or smaller? 

Consider the accompanying rounded-off figures for the popula- 
tion of the U.S., 1790-1870. Do these numbers show a roughly 
exponential growth of population? State briefly the reasoning ]^^° 
behind your answer. 



1790 


3 93 X 


10« 


1800 


5.31 X 


10^ 


1810 


7 24 X 


10« 


1820 


9 64x 


10« 


1830 


12 87 X 


10^ 


1840 


17 07 X 


10« 


1850 


23 19 X 


10^ 


1860 


31 44 X 


10^ 


1870 


38 56 X 


10^ 



85 



Year 


GNP in 
1929 Dollars 


1869 


9 X 10^ 


1879 


161 


1889 


240 


1899 


37 1 


1909 


550 


1919 


742 


1929 


104 


1939 


111, 


1949 


171. 


1959 


230 (est ) 


1969 


380 (est ) 



Species Half -Life \ 



3. The accompanying table gives the U.S. gross national product at 
10-year intervals from 1869 to 1969. The units are 1929 dollars, 
that is, the raw figures are corrected for changes in value of the 
dollar, so they presumably represent some real measure of goods 
and services produced. Do the numbers show a roughly ex- 
ponential growth in GNP? If there are fluctuations, can you 
correlate these with any other significant happenings in the 
society? 

4. During the Summer Olympics at Mexico City, 1968, there was 
considerable agitation about the eff"ect of the altitude (7,350 ft 
= 2.24 km) on runners unaccustomed to thin air. If the oxygen 
content of one breath is directly proportional to the air pressure, 
find, using Fig. 4.6, by how much the oxygen intake per breath 
was reduced for these runners. Does the effect appear significant 
to you? 

5. The atoms most used for geological dating, along with their half- 
lives, are listed. Suppose we started with equal numbers of these 
three species at f = 0. Potassium*° i 3 x io 
After a time equal to 5.0 x 10^° years, what would be the ratios Rubidium^' 5 x io 
of remaining populations of the three species? Uramum^^^ 45xio 

6. It is believed that formation of the Earth's crust took place about 
2.8 X 10^ years ago. If we assume that the potassium in the crust 
was all deposited at about this time, and we know that there is, at 
present, one radioactive K*° atom to 8,400 inert K^^ atoms, 
what was the approximate value of the ratio of number of K*° 
atoms to number of K^^ atoms at the time the crust formed? 

The following two problems extend the material in the text, 
rather than just exercising your knowledge of it. 

7. In the case of money gathering compound interest, Eq. (4.3) 
would have the form 

$ = $o2''^'/^ 

where T^i2 is now the doubling time rather than the half-life, since 
we are dealing with growth rather than decay. The doubling time, 
^1/2' if expressed in years, is simply related to the compound 
interest rate, /?, expressed in percent, by the following equation : 
^ _ 69.3 

Note that if, for example, the interest rate is 5 %, the doubling 
time is 13.9 yr. At a simple interest of 5 %, the doubling time would 
be 20 yr. Explain to your own satisfaction why the doubling time 
is so much shorter than the 20-yr figure. 

8. (An extension of the previous problem.) The population of the 
U.S. grew from 180,000,000 in 1960 to 203,000,000 in 1970. If this 
growth rate were to continue at a constant value, in approximately 
what year would the U.S. population double its 1960 value? 

9. (This problem introduces another example of a very common 
exponential process. The first part of the problem describes the 



86 



Exponential Process in Nature 



physical situation and how it can be connected to the exponential 
model. A question about a specific experiment is asked in the last 
paragraph.) 

Consider the following common situation in natural pro- 
^^ cesses. A stream of some kind of particles impinges upon a layer 
of material that absorbs or deflects some of the particles. If the 
material is uniform, so that the probability of any given particle 
being absorbed or deflected in a given thickness of material, Ax, 
is a constant, then we have the following relation, 

impinge OM Ax Ax 

in which N is the number of particles per unit cross-sectional area 
impinging on a layer of thickness Ax, and AN is the number of 
these that are knocked out of the stream in thickness Ax by 
absorption or deflection. We see that we have just the condition 
for an exponential decay of the particle density in the stream. In 
this case, it is equal intervals of distance which lead to decrease 
by equal multiplicative factors, similar to the air pressure problem 
discussed on p. 94. 

If a stream of high-energy electrons has its particle density 
cut in half by passing through a piece of aluminum 1 cm thick, 
what density would be necessary to insure that its density would 
be less than j^ of the original value? (This is a common prac- 
tical problem in shielding against high energy radiation of one 
sort or another.) 
10. (A difficult problem, combining scaling ideas with the exponential 
problem.) Consider the situation in which the weight of a raindrop 
increases as it falls through fog. Assume that the weight of fog that 
is added to the drop in each unit of time is proportional to the 
surface area of the drop. Under these circumstances, will the 
weight of the drop increase with time as an exponential curve? 



SUPPLEMENTARY READINGS 

Brown, Harrison, Age of the Solar System. Scientific American, April, 1957. 

CiPOLLA, Carlos M., The Economic History of World Population. Harmonds- 
worth, England: Penguin Books, Ltd., 1965, 117 pp. Cipolla discusses 
particularly clearly some of the important perturbations (e.g., agricultural 
and industrial revolutions) that have caused large departures from 
exponential growth of the world's population. 

Hurley, Patrick M., How Old is the Earth? New York: Doubleday Science 
Study Series, 1959. 

Price, Derek J. DeSolla, Little Science, Big Science. New York: Columbia 
University Press, 1963. This short book, based on a lecture series, analyzes 
many aspects of the growth of modern science, since the time of Newton, 
in terms of exponential models. In particular. Chapter 1, A Science of 
Science, is a very useful example of how one develops an application of the 
exponential model to natural population problems. Among other things. 
Price discusses some examples of possible behavior of a natural system 
that has been growing exponentially but then approaches some natural 
limit to its size. 



87 



The modern sciences are becoming more and more interwoven. 
Here we see some of the ways in which the methods and 
concepts of physics contribute to the advancement of biology. 



Physics in Biology 

Physics Survey Committee NRC-NAS 

An excerpt from Physics in Perspective, 1973 



Biology has become a mature science as it has be- 
come precise and quantifiable. The biologist is no 
less dependent upon his apparatus than the physicist. 
Yet the biologist does not use distinctively biologi- 
cal tools — he is always grateful to the physicists, 
chemists, and engineers who have provided the 
tools he has adapted to his trade. 

Until the laws of physics and chemistry had been 
elucidated it was not possible even to formulate 
. the important penetrating questions concerning the 
nature of life. 

PHILIP HANDLER 

Biology and the Future of Man (1970) 
(Chapter I, pages 3 and 6) 

Physics in Biology 

Nature of the Interface 

An especially active scientific interface, and one that is attracting an increas- 
ing number of physicists, is that between physics and biology. The problems 
posed relate to fundamental questions of life and hold the promise of sub- 
stantial contributions to the alleviation of human ills and misery. This inter- 
face combines fundamental science and both immediate and long-range 
social goals in a close and balanced relationship. Growing application of 
the methods, devices, and concepts of physics to some of the central biologi- 
cal problems should result in increasingly rapid progress. The scientific 
returns from such applications are already impressive. 

The title of this section, "Physics in Biology," rather than the more usual 
biophysics, is indicative of the Committee's approach to the interface. 
Rather than a survey of all biophysics, this report focuses on the role of 
physics and physicists in attacking some of the major problems of modern 
biology. The implications of such a role for physics education and the over- 
all physics enterprise also receive attention. 



88 



Physics in Biology 

To describe the interaction of physics with biology requires study of the 
flow of manpower, ideas, and procedures through the interface. The title, 
"Physics in Biology," implies a flow from left to right. It is convenient to 
divide the subject into three parts: (a) the flow of physicists into biology; 
(b) the flow of physics into biology, which includes the flow of ideas, tech- 
niques, and equipment, often through the intermediaries of engineering and 
chemistry; and (c) the interface called biophysics, in which the powers of 
physics are merging with the problems of biology in new ways that require 
nonstandard combinations of skills from both disciplines. 

The goal of biophysics is to be biologically useful. When it is successful, 
it merges with other branches of biology, such as biochemistry and molecu- 
lar biology, a major goal of which is to understand, in molecular terms, how 
genetic information is transmitted. The following example illustrates the 
contributions of biophysics to molecular biology. In 1944, it was shown 
that DNA, rather than proteins, contained the genetic information with 
which molecular biology is principally concerned. In 1953, J. Watson and 
F. Crick, working in the Cavendish Laboratory, developed from the accu- 
mulated chemical studies of dna and a consideration of its biological func- 
tion an interpretation of the x-ray studies of M. Wilkins in terms of the now 
famous double helix. Since then, molecular biology has developed rapidly, 
and biological function is now so interwoven with the structure of dna that 
the term "structure and function" has become a platitude. 

At the same time, and in the same laboratory in Cambridge, the crystal 
structures of the proteins were first being determined by x-ray crystal- 
lography, with a parallel influence on enzymology and biochemistry. In all 
these cases the isolation of the molecules and the definition of their bio- 
logical functions were accomplished after roughly a century of chemical 
research. The physicists who determined the crystal structures were attack- 
ing a biologically important problem. Their boldest and most original step 
was their starting assumption that these large biological molecules had 
unique structures that could be determined by x-ray crystallography. Physi- 
cists are accustomed to this kind of simplicity in science; assuming such 
simplicity is a reflection of their previous training and research style. The 
revolutionary nature of their findings depended on the originality of their 
assumptions. However, given their background as physicists, trained m 
x-ray crystallography under Bragg, and their interest in biology, their 
directions of attack were almost predetermined. Thus, in these illustrative 
and illustrious cases, physicists and physics created an exciting field of 
research in biophysics, which has now been merged with biochemistry and 

molecular biology. 

Determination of the structure of large biological molecules will con- 
tinue to be an active field of research. In addition to x-ray crystallography, 
other physical techniques such as nuclear magnetic resonance, electron spin 
resonance, Mossbauer studies, and optical studies are being used more and 
more These techniques, when used for structural studies, often complement 
x-ray data by giving information on a finer scale. This research is directed 
toward structural determinations of larger molecular aggregates, that is to 
say membranes and membrane-mediated enzyme systems; ribosomes, 



89 



which are the site of protein synthesis, composed of nucleic acids and pro- 
tein, with a molecular weight of ~10"; mitochondria, the membrane-bound 
volume in which the chemical energy of nutrients is converted to more 
usable forms by electron transfer reactions; and the photosynthetic unit in 
which photons are converted to chemical energy. In all of these systems, 
scientists are trying to understand biochemical functions in terms of the 
structure of the molecules and the physical interactions among them. 
Beyond the structures of isolated biological molecules lie the complicated 
questions of intermolecular interactions, which should challenge physical 
methods for many years. The collision techniques, which are only now 
beginning to be applied to the elucidation of elementary chemical reaction 
kinetics of simple inorganic molecular complexes, were developed in atomic 
and nuclear physics. Application of these approaches to molecular systems 
of biological interest is an exceedingly difficult but highly promising field. 

When structure is examined at finer levels than the molecular, it is quite 
clear that quantum-mechanical understanding of the electronic structure of 
certain parts of biological molecules will become increasingly important. 
The advances made through electronic understanding of the molecules of 
interest to chemists and condensed-matter physicists show the promise of 
this approach. Recently, as experimental molecular physicists have studied 
biological molecules with the goal of understanding their electronic proper- 
ties, the amount of systematic data has approached the point needed for 
theoretical synthesis and advances. This synthesis could lead in the future 
to a larger role for theoretical studies. Previously, the theorist's contribution 
to molecular biophysics has been very small, because, unlike the best experi- 
menters, he generally has not learned enough biology to be able to ask good 
questions. 

An exception occurs in the case of the theoretical models that are playing 
an increasingly important role in biology. This trend reflects the physicist's 
typically different viewpoint on biological problems. One of these differ- 
ences is the physicist's desire for a simple, comprehensive model, capable 
of providing a first-order explanation of a wide variety of observations. It 
is often baffling to a physicist when biologists insist on the complexity of 
nature and the uniqueness of each result. It is, of course, equally unappeal- 
ing to a biologist, struggling with complexities of dna replication, to be 
informed by a physicist that the Ising model, or enough molecular quantum 
mechanics, would solve his problem. However, in the middle ground be- 
tween these two extremes of oversimplification lies the productive applica- 
tion of physical models, based as always on experimental observations. For 
example, the concept of a genetic code proposed by physicists and theo- 
retical chemists such as Crick, Orgel, Gamow, and Griffith appealed to a 
mind trained in physics. Various theoretical models were examined. One 
question that was proposed and answered was how much information had 
to be stored. The answer was that there were 20 amino acids that had to be 
coded by the dna. Because dna has only four possible bases as coding 
units, a minimum of three bases is required. Was the code overlapping? 
This question was answered negatively by considering the known mutations 
that had been observed. 



90 



Physics in Biology 



Another useful model was that of Monod, Wyman, and Changeux, on 
allosteric proteins, whose function with respect to one small molecule can 
be affected by other small molecules. They proposed a generalized molecu- 
lar basis for feedback in biological molecules and thus stimulated many 
experiments and analyses to determine the crucial facts. 

A ctivity 

Perhaps the most active research area at the interface between physics and 
biology is that involving the study and determination of the molecular bases 
for biophysical processes. This work has engaged some of the best people 
in the subfield and uses a variety of physical techniques and probes, from 
x-ray crystallography through nuclear magnetic resonance and Mossbauer 
techniques (see Figure 4.93) to nanosecond fluorimetry. 

An older research area, but one that retains excitement and interest, is 
neural physiology. In part, this interest reflects the hope that such research 
can lead eventually to the understanding of the mysterious processes of 
human thought and memory, one of the remaining frontiers of man's under- 
standing. In part, it reflects the physicist's assumption that when informa- 
tion is transmitted and processed by essentially electrical mechanisms, the 
problem should be amenable to physical analysis. 

A striking example of physical reasoning in elucidating a particular 
property of a biological cell is the analysis of the electrical state underlying 
excitability in the giant axon of the squid. Its virtually unique diameter 




10 -8 -6 



-4-2 2 

VELOCITY (MM /SEC) 



6 8 10 



FIGURE 4 93 Human lung material from healthy lung (a) and from lung of hemo- 
siderosis victim (b). Mossbauer spectrum of diseased lung indicates an abnormally 
large amount of iron (note the difference in absorption scales in the spectra), which 
appears to be in the form of a finely divided, low-molecular-weight compound. 
[Source: C. E. Johnson, "Mossbauer Spectroscopy and Biophysics," Physics Today 
24,40 (Feb. 1971).! 



91 



(500-100 fim) enabled Hodgkin and Huxley, in 1949, to conduct a series 
of fundamental electrical measurements that, in turn, made it possible to 
establish for the first time an adequate quantitative description of the elec- 
trical state associated with the nerve impulse. Both the design and execu- 
tion of the experiments required a thorough knowledge of electronic cir- 
cuits, in which feedback plays a crucial role, and of the theory of ionic 
electric currents. Moreover, the interpretation of the data demanded an 
ingenious mathematical analysis. This achievement was in large measure a 
product of Hodgkin's and Huxley's training in physics. 

One of the basic findings of their analysis was that the ionic currents in 
the axonal membrane display strikingly nonlinear behavior in that the 
conductances are voltage-dependent and time-variant. The property of 
nonlinearity implies that, in a single neuron and chains of neurons (neural 
circuits), the elaborate calculations required to treat the excitable state 
can be carried out in general only with modern computers. And the 
statistical physics underlying the conductance changes in the cell mem- 
brane and at the junction between two cells (the synapse) presents a 
problem requiring highly sophisticated analysis. 

The study of neural physiology is typical of the advanced research con- 
ducted on macromolecular aggregates in modern biophysics. It involves 
the design and development of new measurement techniques, computer 
simulation of neural behavior, and the study of signal-transmission char- 
acteristics of biological media. It continues to provide important surprises. 
Recent work on the brains of primitive animals, in which the brain contains 
at most only a few hundred cells, has shown that, even here, a remarkable 
symmetry of structure and function has developed. 

Neural physiology stimulated some of the earliest physicists to move into 
biophysics; probably it will continue to attract them. Progress in neuro- 
biology will demand advances in the biochemistry and ultrastructure of the 
neuron; but, in any event, the elucidation of physical mechanisms, for ex- 
ample, the analysis of excitability in the giant axon of the squid, will con- 
tinue to play a crucial role. 

A third major activity at the interface involves the interaction of radiation 
with high- and low-level biological systems. The types of radiation em- 
ployed range from ultraviolet light to very-high-energy, heavy nuclear 
particles and mesons. The transfer of the techniques of nuclear physics — 
radioactive tracers, accelerator radiations, and nuclear instrumentation — 
has brought about a revolution in biophysics and in both clinical and re- 
search medicine. 

Radioactive isotopes have contributed enormously to the general im- 
provement in diagnosis, and a large number of radioisotopes are now in 
routine use. Isotopes commonly used include: ^^^I, ^"I, ^*'Fe, ^'""In, •■'9'"Tc, 
'^'Cr, '^Co, «°Co, '^Se, ^'Sr, ^^-^Hg, '^T, and ^^-^Au. These are used for 
visualization of the thyroid, brain, liver, lung, kidney, pancreas, spleen, 
heart, bone, and placenta and for a variety of physiological tests in which 
the rate of disappearance or rate of uptake of a particular labeled substance 
reflects the function of a given organ system (see Figures 4.94 and 4.95). 
In 1968, there were some four million administrations of labeled com- 



92 



Physics in Biology 





FIGURE 4.94 This is a bone scan made with short-lived strontium-87m (half-life 
2.8 h). The patient was a 13-year-old girl with a bone sarcoma of the right tibia. The 
greater strontium uptake in the right leg indicates the presence of the lesion. [Source: 
J. H. Lawrence, B. Manowitz, B. S. Loeb, Radioisotopes and Radiation (Dover, New 
York, 1969).] 



pounds to patients, and the rate of use has been growing rapidly. These 
isotopes are employed routinely in practically every hospital in the United 
States. 

Increasing attention is being given to the use of very-short-lived isotopes, 
particularly "C, which should be especially useful because of the enormous 
potential for incorporation into a wide variety of biological compounds, 
with consequent extension of the range of diagnostic procedures. The short 
half-life, some 20 min, markedly limits the time for synthesis of the isotope 
into the desired compound and the time available for use. Thus the source 



93 




94 



Physics in Biology 



FIGURE 4.95 Left: The autofluoro- 
scope detector shown with its 2-in. lead 
shield removed. A bank of 293 sodium 
iodide crystals is in the lead-encased en- 
closure at bottom. This bank is separated 
from the 12 photomultiplier tubes by a 
4-in. Lucite light pipe. The data are 
transferred electronically and recorded on 
Polaroid film. 

Below: Four neck scintiphotos of dif- 
ferent individuals made with the gamma- 
ray scintillation camera 24 h after admin- 
istration of 25 to 50 /uCi of iodine-131. 
Upper left: Normal, butterfly-shaped, 



thyroid gland. Upper right: Solitary toxic 
nodule in right lobe. This "hot" nodule 
takes up the iodine-131 to a greater extent 
than the normal thyroid tissue. Lower left: 
Degenerating cyst seen as a dark area in 
lower left of picture. This "cold" nodule 
is nonfunctioning, hence does not take up 
the radioisotope. Lower right: This patient 
had undergone a "total" thyroidectomy 2 
years previously. The photo shows regrowth 
of functioning tissue, right, and also a metas- 
tasis, lower center. 

[Source: J. H. Lawrence, B. Manowitz, 
and B. S. Loeb, Radioisotopes and Radia- 
tion (Dover, New York. 1969).] 







95 



of the isotope (an accelerator), facilities for rapid synthesis, and clinical 
facilities must be in close juxtaposition. A closely cooperating team of 
physicists, chemists, and clinicians is required for effective application. Use 
of this isotope, although still in its relatively early stages, is increasing 
rapidly and has great promise. 

Another rapidly developing diagnostic procedure involves the determi- 
nation of the entire amount of a given element, for example, calcium, in the 
body by means of activation analysis. The entire body is exposed to a beam 
of fast neutrons, which thermalize in tissue and are captured by the element 
in question. The patient is then placed in a whole-body counter and the 
total amount of the given element deduced from the total induced activity. 
The entire procedure can be accomplished with the delivery of only a small 
fraction of 1 rad to the patient. 

Isotopes are now used widely in radiotherapy in a variety of ways. 
High-intensity external sources, such as cobalt-60 and cesium-137, have in 
many instances replaced x-ray machines for routine radiotherapy. The 
depth-dose characteristics of radiations from these sources are more favor- 
able than those of most x-ray beams, and the units have the advantage of 
ease of operation and maintenance. As a specific example, the cure rate 
in cases of mammary cancer increased dramatically when cobalt-60 therapy 
replaced that with 100-kV x rays. The reason was that the higher energy 
"••Co radiations were able to penetrate the sternum to a lymph node behind 
it, whereas the x rays could not. In addition, beta emitters such as 
strontium-90 are beginning to be used more frequently for the therapy of 
some superficial external lesions. 

Physiological localization of radioactive isotopes is used in some forms of 
therapy, for example, iodine for treatment of hyperthymism and thyroid 
tumors and *-P for treatment of some diseases of the bone marrow. These 
procedures represent optimal therapy only in a relatively few situations. 

Accelerators have contributed greatly to the improvement of radio- 
therapy. Early accelerators allowed transition from the use of relatively 
low-energy x rays for radiotherapy to the use of supervoltage x rays, per- 
mitting the delivery of a relatively large dose to the tumor in depth, with a 
minimal dose to the intervening normal tissues. Electron accelerators such 
as the betatron have permitted an additional distinct improvement in the 
therapeutic ratio, or dose-to-tumor, dose-to-normal-tissue ratio. 

Somewhat in the future is the therapeutic use of beams of negative pions, 
which currently are produced only in elementary-particle and very-high- 
energy nuclear-physics facilities. These have the enormous advantage of 
delivering not only their ionization energy but also their entire rest mass 
energy to their final destination in matter. Thus, while traveling to the 
therapy site, they do relatively little damage to surrounding tissues; their 
capture then releases some 200 MeV of energy at the treatment site. 

Currently, there is much interest in the use of accelerators to produce 
beams of fast neutrons for radiotherapy. The rationale is that all tumors 
quickly develop small foci of poorly oxygenated or hypoxic cells. These 
hypoxic cells are markedly resistant to damage by x or gamma radiation 
but are much more susceptible to damage by neutrons or other densely 



96 



Physics in Biology 



ionizing radiations. Although a variety of reactions and neutron spectra 
might be used, the approximately 1 4-MeV neutrons from the D-T reaction 
are optimal in terms of penetrating characteristic and density of ionization. 
The procedure is experimental, and several years will be required to evalu- 
ate its efficacy. Man-made transuranium isotopic sources of neutrons, such 
as -"-Cf, have just recently become available and are also being used, with 
the same rationale. 

Not only are radiations in the high-energy or nuclear realm used in such 
studies and applications but also ultraviolet and infrared radiation (see 
Figure 4.96). For example, Setlow and his collaborators at Oak Ridge 




FIGURE 4.96 Detection of breast cancer by infrared thermography. [Photograph 
courtesy of the Lovelace Foundation for Medical Education and Research.] 



97 



very recently discovered that a particular species of skin cancer can be 
traced not only to a specific damage site in the human cell dna induced by 
ultraviolet radiation but also to the lack, in susceptible individuals, of a 
rather rare enzyme the function of which is to repair such damage. Already 
a test has been developed that can detect the total lack of this enzyme 
in utero and make possible therapeutic termination of the pregnancy; 
otherwise, with total lack of the enzyme, the normal life-span of a child 
would be brief. It is hoped that further research will result in a technique 
for the detection of, and compensation for, the partial lack of this enzyme 
in the population. 

The use of infrared photography as a diagnostic tool is now rather well 
developed. Reflecting the increasing metabolism of cancer cells is a local 
temperature elevation that shows clearly in an infrared photograph; this 
technique is extremely simple, over 90 percent effective, and widely 
employed. 

The long-term effects of very-low-level radiation on a population is, of 
course, a matter of continuing concern and controversy. The controversy 
arises largely because, at the levels now under consideration, even granting 
the validity of the mouse-man extrapolation, it has been estimated that an 
8-billion-mouse colony would be required to yield statistically significant 
results. This situation shows the importance of understanding mechanisms 
not just doing statistical experiments. It is an example of a situation that 
Weinberg has defined as "trans-science," * a problem in which it appears 
superficially that in principle science should be able to give concrete 
answers but, when examined in greater detail, exceeds the scope of any 
economically feasible scientific study. 

Although now of somewhat less importance than in past decades, the 
overall questions of thermodynamic energy balance and stability in bio- 
logical systems continue to occupy the attention of a small group of physi- 
cists in biology. Although the broad outlines of the physics involved in the 
intricate energy-transfer mechanisms have been established, major ques- 
tions remain unanswered. 

In fluid physics and rheology there also are problems. The dynamics of 
human body fluids are still inadequately understood and can pose significant 
problems in vascular surgery and repair and in the more ambitious organ- 
replacement projects now in developmental phases. In rheology, a wide 
range of open questions in regard to bone growth, muscle attachment, and 
the like need answers. 

Biomedical engineering has become a specialty in its own right, stimu- 
lated by the pressures for improved man-machine interface designs in 
supersonic aircraft, space vehicles, and precision industrial production lines, 
as well as by more prosaic needs such as improved kitchen appliances. The 
design of artificial organs, prosthetic devices, and the like is another part 
of this field. Progress in the development of long-lived portable power 



Science, 174, 546-547 (Nov. 5, 1971). 



98 



Physics in Biology 



sources and parallel progress in ultraminiaturization of semiconductor elec- 
tronic components should lead to a greatly increased capability to mitigate 
human infirmities. Much of this work represents applied physics at its best. 

One of the most difficult tasks in the biomedical engineering areas of 
bacterial colony analysis, brain scintigram analysis, blood-cell identification, 
chromosome analysis, and heart image extraction from a cardioangiogram 
is the extraction of relevant objects from an irrelevant background. The 
principal reason is that the pictures in these fields are often complicated by 
unwanted background, and object images are poorly defined. In recent 
years, computer processing of radiographic images has emerged as a highly 
promising technique. 

Three aspects of biophysical instrumentation merit attention. The first 
involves instrumentation for clinical application in both diagnosis and 
treatment. Major progress is under way in clinical instrumentation; a 
modern hospital's intensive-care wing illustrates the vital role that physics 
research plays here. A second aspect of instrumentation involves biological 
and biochemical laboratories in which new techniques, devices, and ap- 
proaches permit massive increases in both the speed and quality of measure- 
ment, thus making possible the extension of the most modern diagnostic 
aids to a much larger segment of the population. The techniques also facili- 
tate ongoing research in biology, biochemistry, and biophysics. Third, 
advances in instrumentation open entirely new areas of biophysical research. 
Examples of devices that have led to major breakthroughs are the scanning 
electron microscope, the ultracentrifuge, and nuclear magnetic resonance. 



99 



There is more to a cup of coffee than you thought. 



Observations of an Early Morning Cup of Coffee 

Vincent J. Schaefer 

An article from the American Scientist. 1971 



If a cup of very hot black coffee is illumi- 
nated with a strong beam of light parallel 
to the surface, a number of extremely in- 
teresting chemical, physical, and optical 
phenomena can be observed. I first 
noticed these effects ten years ago along 
the edge of boiling hot pools at Yellow- 
stone Park in the wintertime (i). A few 
years later I encountered them again 
while havmg coffee with my wife shortly 
after sunrise at the Research Center of 
the Museum of Northern Arizona, near 
Flagstaff. 

At Yellowstone, the effects were often 
hard to see because moisture from the 
hot water condensing in the air obscured 
the surface of the pool much of the time. 
At Flagstaff, on the other hand, the clean 
air of the early morning and the brilUance 
of the rising sun provided ideal conditions 
for viewing the multiple effects which I 
will now describe. 

When a cup is filled to the brim with 
black coffee (instant or otherwise) which 
is close to boiling and is viewed with good 
illumination, the first thing noticed is 
that the surface of the steaming coffee 
displays an irregular cellular pattern. The 
cells, in polygonal array, show cross 
sections of approximately 1 to 3 cm and 
appear to consist of dusty white areas 
outlined by narrow dark lines. These vis- 
ible cells mark areas of rising columns of 
hot water, and the dark lines mark the 
region where the spreading, slightly cool- 
ed liquid is descending into the body of 
the coffee to form what are called Benard 
cells. 



These convection cells are present in all 
liquids and gases that are unstable be- 
cause they are hotter at the bottom than 
at the top. It doesn't matter whether the 
air or liquid is heated at the bottom or 
cooled at the top, so long as the temper- 
ature decreases toward the top. Related 
phenomena range in size from the micro- 
scopic dimensions first observed by the 
Frenchman Henri Benard in 1 900 under 
his microscope to certain cloud patterns 
of the earth, water patterns in the sea, 
and even the granular structures of the 
sun. 

On the surface of the hot coffee, the 
Benard cells are observable because of the 
phenomenon called Stefan flow. In fact, 
this is one of the most elegant ways to see 
the elusive phenomenon named after 
Joseph Stefan (1835-1893). The intense 
flux of water vapor molecules rising from 
the hot surface of the coffee exerts a 
positive upward force on the cooler 
atmosphere immediately above the 
surface of the liquid. Most of the water 
droplets that condense in the saturated 
air tend either to fall back into the Uquid 
or to drift away into the air above and 
evaporate. 

However, there is a certain size of droplet 
that is too large to escape from the micro- 
environment but too small for gravity to 
overcome the positive force of the up- 
ward thrust of vapor molecules arising 
from the surface of the hot liquid. These 
condensed particles are thus balanced 
between the field of gravity fall and the 
upward molecular thrust in such a way 



100 



Cup of Coffee 




Holt, Rinehart and Winston Photo by Russell Dian 

that they are literally balanced or 
levitated above the surface of the hot 
coffee. At the boundaries of the cells, 
however, there is a negative vapor flux 
that prevents the balance of droplets and 
thus reveals the black surface of the 
coffee. 

If observed under a low-powered binoc- 
ular microscope, the dust-Uke patches of 
tiny water droplets over the rising current 
of hot coffee will be seen to consist of 
arrays of highly uniform, densely packed 
water droplets. Their size and height 
above the hot liquid is controlled by the 
combination of upward force, the 
number of effective nuclei in the region, 
and gravity fall. 

That they are highly charged and thus 
stabihzed can be shown by moving a 
charged object, such as a hard rubber 
comb, above the surface. Under these 
conditions all the suspended droplets 
suddenly disappear. 

That their size and number are controlled 
by the presence of ambient condensation 
nuclei is shown by generating a larger 
number of nuclei by holding a hghted 



match below the edge of the coffee cup. 
When this is done, the concentration of 
particles suddenly increases, but they are 
noticeably smaller and are suspended 
closer to the surface of the hot hquid. 

If, instead of a charged comb, a radio- 
active source is brought near the particles, 
they will also disappear as they coalesce 
and fall back into the liquid. However, 
the effect is much less dramatic than with 
the charged comb. 

When illuminated with a strong beam of 
parallel light, such as the rising sun, a 
slide projector, or a strong flashlight, 
beautiful colors will be observed over the 
surface of the dark liquid when viewed in 
the direction of the illumination and 
close to the axis of the hght beam. This 
phenomenon (2), called the High Order 
Tyndall Spectra, also produces the color 
in the corona surrounding the sun or 
moon when seen through a cloud com- 
posed of nearly uniform droplets and the 
so-called mother-of-pearl clouds occasion- 
ally seen when lenticular and other wave 
clouds, made up of small, uniform drop- 
let size that appear red, blue, and green, 
are viewed in the direction of the sun. 



101 



Close observation of the surface of the 
hot, black coffee showing a nice array of 
Benard cells will often disclose another 
phenomenon. With the cells delineated by 
the dark lines that mark the descending 
current of liquid, a dark line will 
suddenly cut across the grayish zones of 
levitated droplets. This is caused by a tiny 
whirlwind that develops in the rising hot, 
moist air, which locally possesses a super- 
adiabatic lapse rate. The transient vortex 
is generally of very short duration, having 
a Lifetime of milliseconds. 

A very special and quite fascinating elec- 
trical phenomenon can be seen by the 
careful and adept experimenter. With a 
stable zone of balanced particles in equi- 
librium with the hot Uquid and its 
surroundings, a charged object such as an 
electrified hard rubber comb, if not too 
highly charged, will produce a very dense 
stream of droplets that originate in an 
electric wind generated by the proximity 
of the charged object. Depending on the 
geometry of the charged object, this 
strange effect may consist of one or more 
streams of small droplets condensing on 
ions coming from the charged object. 
When I first observed this effect, it was 
generated by several teeth of a charged 
hard rubber comb. 

While a cup of hot, black coffee is an 
ideal arrangement to see some or all of 
these phenomena, the effect dies away as 
the coffee cools. In order to study the 
effects for extended periods of time, I 
arranged the following set-up. An empty 
sardine can was cleaned, filled with water 
blackened with ink, and heated on a hot 
surface. A discarded but usable electric 
iron, held upside down with a clamp, was 
used as a hot plate. This arrangement per- 
mitted me to conduct experiments for as 
long as desired. A lantern slide projector 
served as an excellent light source, and a 
binocular microscope made it possible for 
me to see the packing size and other fea- 
tures of the floating droplets. Subse- 
quently, I found that hot glycerine pro- 
vided an improved substance for ex- 
tended studies. The higher refractive 



index and very low vapor pressure permit 
experiments not easily carried out with 
water. 

When the Uquid becomes sufficiently 
heated so that droplets appear above the 
surface of the liquid, they may be re- 
moved by Lifting them off in a vortex in- 
duced by holding a flat, stiff card or thin 
sheet of metal in a vertical position near 
the surface of the hot Liquid, A very sUght 
drift of air curhng around the vertical 
edge of the thin sheet will start a vortex 
that wiU continue in the highly unstable 
air above the hot Liquid. 

If the surface of the Liquid becomes con- 
taminated, it sometimes wiU faiL to show 
the phenomena. The surface may be 
cleaned by dropping a small piece of 
newsprint or other paper onto the surface 
of the liquid and immediately removing 
it. The contaminating monolayer, dust or 
other substance, will plate out onto the 
paper surface and adhere to it upon re- 
moval. Several successive applications of 
fresh paper may be necessary to clean the 
hot liquid surface. While the paper plating 
method is a very simple and effective 
method for cleaning films from liquid sur- 
faces, a small Langmuir trough (J, 4) is 
more efficient for extended research 
studies. 

It is, of course, quite easy to contaminate 
intentionally the coffee or other hot 
Uquid surface in order to explore the 
effect of molecular coatings on the 
phenomena described. One might anti- 
cipate that a monolayer of hexadecanol 
(5), which is so effective in reducing the 
evaporation of water from water re- 
servoirs, would prevent the formation of 
the floating droplets, but such a mono- 
layer has no apparent effect on the 
evaporation of hot water. This apparently 
is due to the Uquidity of the film. Since 
the melting point of hexadecanol is 
49.3°C, hexadecanol in excess of a mono- 
layer appears as a Uquid lens rather than 
the smaU "islands" of powder which 
exude a very effective evaporation- 
reducing film when placed on cold water. 



102 



Cup of Coffee 



A visible film of indicator oil, however, 
which conversely is quite ineffective in 
reducing the evaporation of water from a 
water reservoir, is immediately effective 
in cutting off the Stefan flow effect. 



One word of warning! It may be desirable 
to use glycerine or ink-colored water 
from the start. A number of my friends 
have accused me of conspiring to prevent 
them from enjoying their hot cup of 
coffee; they tell me that the effects are 
not only intriguing but they last until 
their coffee has lost that hot tang that 
tastes so good early in the morning! 



References 

1. Schaefer, V, J. 1963. Report of the Third 
Yellowstone Field Research Expedition, 
Jan. 8-Feb. 5, 1963. ASRC Pub. #13, p. 79. 
Atmospheric Sciences Research Center, 
State University of New York at Albany. 

2. Minnaert, M. 1954. The Nature of Light and 
Colour in the Open Air. New York: Dover 
Publications. 

3. Langmuir, I., and V. J. Schaefer. 1937. The 
effect of dissolved salts on insoluble mono- 
layers. /. Amer. Chem. Soc. 59:1762. 

4. Schaefer, V, J. 1966. The detection of sur- 
face active molecules on airborne particu- 
lates. /. de Recherches Atmospheriques 
11:141. 

5. Langmuir, I., and V. J. Schaefer. 1945. 
Rates of evaporation of water through com- 
pressed monolayers on water. /. Franklin 
Inst. 235:119. 



103 



As a young man, Werner Heisenberg, later to become a 
famous physicist, was advised to choose music as a career. He 
explains here why he turned to science instead. 



7 The Decision to Study Physics 

Werner Heisenberg 

A selection from Physics and Beyond: Encounters and Conversations, 1971 



From school I did not go straight on to the university; there was 
a sharp break in my life. After my matriculation, I went on a 
walking tour through Franconia with the same group of friends, 
and then I fell seriously ill and had to stay in bed for many 
weeks. During my long recuperation, too, I was locked away with 
my books. In these critical months I came across a work that I 
found extremely fascinating, though I was unable to understand 
it fully. The author was the famous mathematician, Hermann 
Weyl, and the book was entitled Space, Time and Matter. It was 
meant to provide a mathematical account of Einstein's relativity 
theory. The difficult mathematical arguments and the abstract 
thought underlying that theory both excited and disturbed me, 
and, in addition, confirmed me in my earlier decision to study 
mathematics at the University of Munich. 

During the first days of my studies, however, a strange and, 
to me, most surprising event took place, which I should like to 
report in brief. My father, who taught Middle and Modern Greek 
at the University of Munich, had arranged an interview with 
Ferdinand von Lindemann, the professor of mathematics, famous 
for his solution of the ancient problem of squaring the circle. I 
intended to ask permission to attend his seminars, for which I 
imagined my spare-time studies of mathematics had fully prepared 
me; but when I called on the great man, in his gloomy first-floor 
office furnished in rather formal, old-fashioned style, I felt an 
almost immediate sense of oppression. Before I could utter a 



104 



The Decision to Study Physics 



word of greeting to the professor, who rose from his chair very 
slowly, I noticed a little black dog cowering on the desk, and was 
forcefully reminded of the poodle in Faust's study. The little 
beast looked at me with undisguised animosity; I was an unwel- 
come intruder about to disturb his master's peace of mind. I was 
so taken aback that I began to stammer, and even as I spoke it 
dawned on me that my request was excessively immodest. Linde- 
mann, a tired-looking old gentleman with a white beard, ob- 
viously felt the same way about it, and his slight irritation may 
have been the reason why the small dog now set up a horrible 
barking. His master tried to calm him down, but the little beast 
only grew more hysterical, so that we could barely hear each 
other speak. Lindemann asked me what books I had recently 
been reading, and I mentioned Weyl's Space, Time and Matter. 
As the tiny monster kept up his yapping, Lindemann closed the 
conversation with "In that case you are completely lost to mathe- 
matics." And that was that. 

Clearly mathematics was not for me. A somewhat wearing 
consultation with my father ended with the advice that I ought 
to try my hand at theoretical physics. Accordingly, he made an 
appointment with his old friend Arnold Sommerfeld, then head 
of the Faculty of Theoretical Physics at the University of Munich 
and generally considered one of the most brilliant teachers there. 
Sommerfeld received me in a bright study with windows over- 
looking a courtyard where I could see a crowd of students on 
benches beneath a large acacia. The small squat man with his 
martial dark mustache looked rather austere to me. But his very 
first sentences revealed his benevolence, his genuine concern for 
young people, and in particular for the boy who had come to ask 
his guidance and advice. Once again the conversation turned to 
the mathematical studies I had pursued as a hobby while still at 
school, and to Weyl's Space, Time and Matter. Sommerfeld's 
reaction was completely diflFerent from Lindemann's. 

"You are much too demanding," he said. "You can't possibly 
start with the most difficult part and hope that the rest will 
automatically fall into your lap. I gather that you are fascinated 
by relativity theory and atomic problems. But remember that 
this is not the only field in which modem physics challenges basic 
philosophical attitudes, in which extremely exciting ideas are 



105 



being forged. To reach them is much more difficult than you 
seem to imagine. You must start with a modest but painstaking 
study of traditional physics. And if you want to study science at 
all, you must first make up your mind whether you want to 
concentrate on experimental or theoretical research. From what 
you have told me, I take it that you are much keener on theory. 
But didn't you do experiments and dabble with instruments at 
school?" 

I said that I used to like building small engines, motors and 
induction coils. But, all in all, I had never been really at home in 
the world of instruments, and the care needed in making rela- 
tively unimportant measurements had struck me as being sheer 
drudgery. 

"Still, even if you study theory, you will have to pay particular 
attention to what may appear trivial little tasks. Even those who 
deal with the larger issues, issues with profound philosophical 
implications— for instance, with Einstein's relativity theory or 
with Planck's quantum theory— have to tackle a great many 
petty problems. Only by solving these can they hope to get 
an over-all picture of the new realms they have opened up." 

"Even so, I am much more interested in the underlying philo- 
sophical ideas than in the rest," I said rather bashfully. 

But Sommerfeld would have none of this. "You must remem- 
ber what Schiller said about Kant and his interpreters: 'When 
kings go a-building, wagoners have more work.' At first, none of 
us are anything but wagoners. But you will see that you, too, will 
get pleasure from performing minor tasks carefully and con- 
scientiously and, let's hope, from achieving decent results." 

Sommerfeld then gave me a few more hints about my pre- 
liminary studies, and said that he might well come up with a 
little problem connected with recent developments in atomic 
theory on which I could try my mettle. And it was decided that I 
would join his classes for the next few years. 

This, my first conversation with a scholar who really knew his 
way about in modern physics, who had personally made impor- 
tant discoveries in a field impinging on both relativity and 
quantum theory, had a lasting effect upon me. Though his call 
for care in small details struck me as eminently reasonable— I 
had heard it often enough from my own father— I felt dejected at 



106 



The Decision to Study Physics 



the thought that I was still such a long way from the field that 
really interested me. No wonder that this interview became the 
subject of many discussions with my friends. I remember one of 
these particularly well: it bore on modern physics and the cul- 
ture of our time. 

That autumn, I saw a great deal of the boy who had played 
Bach's Chaconne so magnificently in Prunn Castle. We would 
meet in the house of our mutual friend, Walter, himself a fine 
cellist, and practice for a private recital of Schubert's B Major 
Trio. Walter's father had died at an early age, and his mother 
had been left to care for her two sons in a large and very 
elegantly furnished house in Elisabeth Strasse, just a few min- 
utes* walk from my parents' house in Hohenzollern Strasse. The 
magnificent Bechstein grand in the living room was an added 
reason for our frequent visits. After we had finished playing, we 
would often talk deep into the night, and it was on one such 
occasion that the conversation came round to my proposed 
studies. Walter's mother wondered why I had not decided to 
make music my career. 

"From the way you play and speak about music, I get the 
impression that you are much more at home with art than with 
science and technology, that you prefer the muses to scientific 
instruments, formulae and machinery. If I am right, why ever 
have you chosen natural science? After all, the future of the 
world will be decided by you young people. If youth chooses 
beauty, then there will be more beauty; if it chooses utility, then 
there will be more useful things. The decision of each individual 
is of importance not only to himself but to the whole of man- 
kind." 

"I can't really believe that we are faced with that sort of 
choice," I said rather defensively. "Quite apart from the fact that 
I probably wouldn't make a very good musician, the question 
remains in which field one can contribute most. Now I have the 
clear impression that in recent years music has lost much of its 
earlier force. In the seventeenth century music was still deeply 
steeped in the religious way of life; in the eighteenth century 
came the conquest of the world of individual emotions; in the 
nineteenth century romantic music plumbed the innermost 
depths of the human soul. But in the last few years music seems 



107 



to have quite deliberately entered a strange, disturbed and 
rather feeble stage of experimentation, in which theoretical 
notions take precedence over the desire for progress along estab- 
lished paths. In science, and particularly in physics, things are 
quite different. Here the pursuit of clear objectives along fixed 
paths— the same paths that led to the understanding of certain 
electromagnetic phenomena twenty years ago— has quite auto- 
matically thrown up problems that challenge the whole philo- 
sophical basis of science, the structure of space and time, and 
even the validity of causal laws. Here we are on terra incognita, 
and it will probably take several generations of physicists to dis- 
cover the final answers. And I frankly confess that I am highly 
tempted to play some part in all this." 

My friend Rolf, the violinist, demurred. "As far as I can see, 
your remarks about modern physics apply equally well to mod- 
em music. Here, too, the path seems to be dearly mapped. The 
old tonal barriers are collapsing and we find ourselves on promis- 
ing virgin soil, with almost complete freedom to choose what 
sounds and rhythms we like. Hence the musician has every 
chance of discovering as many riches as the scientist." 

Walter now raised several objections of his own. "I don't really 
know whether 'freedom of expression' and 'promising virgin soil' 
are necessarily the same thing. At first sight it admittedly looks as 
if greater freedom must necessarily mean enrichment, wider 
possibilities; but this I know to be untrue in art, with which I am 
more familiar than with science. I would think that progress in 
art takes place in the following way: First a slow historical pro- 
cess transforms the life of men in spite of themselves, and thereby 
throws up fresh ideas. A few talented artists then try to give these 
ideas a visible or audible form by wresting new possibilities of 
expression from the material with which they work— from colors 
or musical instruments. This interplay or, if you like, this 
struggle between the expressive content and the limitations of the 
expressive medium is, I think, a sine qua non of the emergence of 
real art. If the limitations of the expressive medium were taken 
away— if in music, for instance, we could produce any sounds we 
liked— then the struggle would be over, and the artist's effort 
would reach into a void. For that reason I am skeptical about too 
much freedom. 



108 



The Decision to Study Physics 



"In science," Walter continued, "a continuous flow of new 
experiments is made possible by new techniques; there are new 
experiences and as a result new contents may be produced. Here 
the means of expression are the concepts by which the new ideas 
are grasped and made explicit. For instance, I have read that 
Einstein's relativity theory, which interests you so much, was 
born from the failure of certain experiments designed to demon- 
strate the motion of the earth through space by means of the 
interference of light rays. When this demonstration misfired, it 
became clear that the new results, or, what amounts to the same 
thing, the new ideas, called for an extension of the means of 
expression, i.e., of the conceptual system proper to physics. Quite 
likely, no one anticipated that this would demand radical 
changes in such fundamental concepts as space and time. It was 
Einstein's great achievement to appreciate before anyone else 
that the ideas of space and time were not only susceptible to 
change but, in fact, had to be changed. 

"What you have said about recent developments in physics 
could reasonably be compared with developments in music in the 
middle of the eighteenth century. At that time, a gradual his- 
torical process had led to a growing awareness of the emotional 
world of the individual— as all of us know from Rousseau and 
later from Goethe's Werther—SLnd it was then that the great 
classicists— Haydn, Mozart, Beethoven and Schubert— succeeded 
in extending the means of expression and so discovered the 
musical language needed for depicting this emotional world. In 
modern music, on the other hand, the new contents appear to be 
highly obscure and implausible, and the plethora of possible 
expressions fills me with deep forebodings. The path of modern 
music seems to be determined by a purely negative postulate: the 
old tonality has to be discarded because we believe that its 
powers have been exhausted, and not because there are new and 
more forceful ideas which it is incapable of expressing. Musicians 
are entirely in the dark about the next step; at best they grope 
their way forward. In modern science the questions are clearly 
posed, and the task is to find the right answers. In modem art, 
however, even the questions are uncertain. But perhaps you had 
best tell us a bit more about the new fields you intend to explore 
in the world of physics." 



109 



I tried to convey what little bits of knowledge I had gleaned 
during my illness, mainly from popular books on atomic physics. 

"In relativity theory," I told Walter, "the experiments you 
have mentioned, together with other experiments, caused Ein- 
stein to discard the prevailing concept of simultaneity. That in 
itself was exciting enough. Every one of us thinks that he knows 
precisely what the word 'simultaneous' means, even if it refers 
to events that take place at great distances. But we are mis- 
taken. For if we ask how one determines whether two such 
events are, in fact, simultaneous and then evaluates the various 
means of verification by their results, nature herself informs us 
that the answers are not at all clear-cut but depend on the ob- 
server's state of motion. Space and time are therefore not inde- 
pendent of each other, as we previously believed. Einstein was 
able to express the 'new' structure of space and time by means of 
a simple and coherent mathematical formula. While I was ill, I 
tried to probe into this mathematical world, which, as I have 
since learned from Sommerfeld, has already been opened up 
fairly extensively and has therefore ceased to be unexplored 
territory. 

"The most interesting problems now lie in a different field, in 
atomic physics. Here we come face to face with the fundamental 
question why the material world manifests ever-recurring forms 
and qualities— why, for example, water with all its characteristic 
properties is invariably reproduced during the melting of ice, the 
condensation of steam or the combustion of hydrogen. This has 
been taken for granted in physics, but has never been fully ex- 
plained. Let us suppose that material bodies— in our case, water 
—are composed of atoms. Chemistry has long made successful use 
of this idea. Now, the Newtonian laws we were taught at school 
cannot tell us why the motions of the particles involved should 
be as stable as they, in fact, are. Only quite different natural laws 
can help us to explain why atoms should invariably rearrange 
themselves and move in such a way as to produce the same sub- 
stances with the same stable properties. We first caught a glimpse 
of these laws twenty years ago, in Planck's quantum theory. Since 
then, the Danish physicist, Niels Bohr, has combined Planck's 
theory with Lord Rutherford's atomic model. In so doing, he was 
the first to throw light on the curious stability of atoms which I 



110 



The Decition to Study Physics 



have just mentioned. But Sommerfeld believes that in this sphere 
we are still a long way from a clear understanding of the ways of 
nature. Here we have a vast unexplored field, in which new 
relationships may be discovered for decades to come. By the ap- 
propriate reformulation of natural laws and with correct new 
concepts we might, for instance, be able to reduce the whole of 
chemistry to atomic physics. In short, I firmly believe that in 
atomic physics we are on the track of far more important rela- 
tions, far more important structures, than in music. But I freely 
admit that 150 years ago things were the other way round." 

"In other words," Walter asked, "you believe that anyone con- 
cerned with cultural progress must necessarily make use of the 
historical possibilities of the age in which he lives? That, if 
Mozart had been born in our day, he, too, would be writing 
atonal and experimental music?" 

"Yes, I suspect just that. If Einstein had lived in the twelfth 
century, he would not have been able to make important scien- 
tific discoveries." 

"Perhaps it is wrong to keep bringing up such great men as 
Mozart and Einstein," Walter's mother said. "Few individuals 
get the chance to play such decisive roles. Most of us must con- 
tent ourselves with working quietly in a small circle, and ought 
to ask simply whether playing Schubert's B Major Trio is not 
more satisfactory than building instruments or writing mathe- 
matical formulae." 

I agreed that I myself had quite a few qualms and mentioned 
Sommerfeld's quotation from Schiller: "When kings go a-build- 
ing, wagoners have more work." 

"We all feel the same way about it," Rolf declared. "Those of 
us who want to become musicians have to take infinite pains to 
master their instruments, and even then can only hope to play 
pieces that hundreds of better musicians have played much more 
proficiently. And you yourself will have to spend long hours with 
instruments that others have built much more competently, or 
retrace the mathematical thoughts of the masters. True, when all 
this has been done, the musical wagoners among us are left with 
no small sense of achievement: constant intercourse with glorious 
music and the occasional delight of a particularly successful 
interpretation. Likewise, you scientists will occasionally manage 



111 



to interpret a relationship just that little bit better than anyone 
before you, or determine a particular process more accurately 
than your predecessors. But none of us ought to count on the fact 
that he will be doing trail-blazing work, that he will make deci- 
sive discoveries. Not even when he works in a field where a great 
deal of territory has still to be opened up." 

Walter's mother, who had been listening attentively, now said 
something, more to herself than to us, as if she were trying to 
formulate her thoughts as she spoke: 

"The parable of the kings and the wagoners may have quite a 
different import. Of course, superficially it looks as if the glory is 
entirely the kings', as if the wagoners' work were purely sub- 
sidiary and unimportant. But perhaps the very opposite is true. 
Perhaps the kings' glory rests on the work of the wagoners, on the 
fact that the wagoners have put in many years of laborious 
effort, reaping joy and success. Perhaps men like Bach or Mozart 
are kings of music only because, for two long centuries, they have 
offered so many lesser musicians the chance of reinterpreting 
their thoughts with love and conscientious attention to detail. 
And even the audience participates in this careful work as it 
hears the message of the great musicians. 

"If you look at historical developments— in the arts no less 
than in the sciences— you will find that every discipline has long 
periods of quiescence or of slow growth. Even during these 
periods, however, the important thing is careful work, attention 
to detail. Everything that is not done with utter devotion falls 
into oblivion and, in fact, does not deserve to be remembered. 
And then, quite suddenly, this slow process, in which general 
historical developments introduce changes in the contents of a 
particular discipline, opens up new possibilities, quite unex- 
pected contents. Talented men feel an almost magical attraction 
for the process of growth they can sense at work here, and so it 
happens that, within a few decades, a relatively small region of 
the world will produce major works of art or scientific discoveries 
of the greatest importance. In the late eighteenth century, for 
instance, classical music poured forth from Vienna; in the fif- 
teenth and sixteenth centuries painting had its heyday in the 
Netherlands. True, great men are needed to express the new 
spiritual contents, to create the forms in which further develop- 



112 



The Decision to Study Physics 



ments can be molded, but they do not actually produce these new 
contents. 

"Of course, it is quite possible that we are on the threshold of 
an exceptionally fruitful scientific epoch, in which case it would 
be wrong to dissuade any young man from participating in it. It 
seems unlikely that important developments will take place in 
more than one branch of art or science at one time; we ought to 
be grateful enough if it happens in any one area, if we can share 
in its glory either as bystanders or as active participants. It would 
be foolish to expect more. That is precisely why I find popular 
attacks on modern art— be it painting or music— so unjust. Once 
music and the plastic arts had solved the great problems posed to 
them in the eighteenth and nineteenth centuries, there just had 
to be a more restful period, in which much of the old could be 
preserved and new things were tested by trial and error. To 
compare modern compositions with the finest achievements of 
the great epoch of classical music seems utterly unfair. Perhaps 
we ought to finish the evening with the slow movement of 
Schubert's B Major Trio. Let's see how well you can play it," 

We did as we were asked, and from the way in which Rolf 
played the somewhat melancholic C major figures in the second 
part of the movement, I could sense how sad he was at the 
thought that the great epoch of European music might be gone 
forever. 

A few days later, when I walked into the hall where Sommer- 
feld usually gave his lectures, I spotted a dark-haired student 
with a somewhat secretive face in the third row. Sommerfeld had 
introduced us during my first visit and had then told me that he 
considered this boy to be one of his most talented students, one 
from whom I could learn a great deal. His name was Wolfgang 
Pauli, and for the rest of his life he was to be a good friend, 
though often a very severe critic. I sat down beside him and 
asked him if, after the lecture, I might consult him about my 
preparatory studies. Sommerfeld now entered the hall, and as 
soon as he started to address us Wolfgang whispered in my ear: 
"Doesn't he look the typical old Hussar officer?" After the lec- 
ture, we went back to the Institute of Theoretical Physics, where 
I asked Wolfgang two questions. I wanted to know how much 
experimental work had to be done by someone interested chiefly 



113 



in theory, and what he thought of the respective importance of 
relativity and atomic theory. 

"I know," Wolfgang told me in reply to my first question, 
"that Sommerfeld lays great stress on experimental studies, but I 
myself am not cut out for them; I hate the whole business of 
handling instruments. I quite agree that physics is based on 
experimental results, but once these results have been obtained, 
physics, at least modern physics, becomes much too difficult a 
subject for most experimental physicists. This is probably so 
because the sophisticated instruments of modern physics take us 
into realms of nature that cannot be adequately described with 
everyday concepts. We are forced to employ an abstract kind of 
mathematical language and one that presupposes a considerable 
amount of training in modern mathematics. It is a sad fact but 
true that we all have to specialize. I find abstract mathematical 
language quite easy, and hope to put it to good use in my work. 
Needless to say, I realize that some knowledge of the experimental 
side is absolutely essential. The pure mathematician, however 
good, understands nothing at all about physics." 

I then repeated my conversation with old Lindemann, and 
told Wolfgang about his black lap dog and his reaction to my 
reading Weyl's Space, Time and Matter. My report obviously 
caused Wolfgang the greatest amusement. 

"That's just what I would have expected," he said. "Weyl 
really does know a lot about relativity theory, and for Linde- 
mann such knowledge is enough to disqualify anyone from 
bearing the title of serious mathematician." 

As to the respective importance of relativity and atomic 
theory, Wolfgang had this to say: "The so-called special theory of 
relativity is now a closed chapter; you simply have to learn it and 
use it like any other theory in physics. Nor is it of particular 
interest to anyone anxious to make new discoveries. However, the 
general theory of relativity, or, what comes to much the same 
thing, Einstein's theory of gravitation, is still wide-open. But it 
is rather unsatisfying in that, for each experiment, it will give 
you a hundred pages of theory with the most complicated 
mathematical derivations. No one can really say whether the 
whole thing is correct. Nevertheless it opens up new possibilities 
of thought, and for that reason must be taken seriously. I have 



114 



The Decision to Study Physics 



recently written a fairly lengthy article on the general theory of 
relativity; perhaps that is one of the reasons why I find atomic 
theory so much more interesting. 

"In atomic physics we still have a wealth of uninterpreted 
experimental results: nature's evidence in one place seems to 
contradict that in another, and so far it has not been possible to 
draw an even halfway coherent picture of the relationship in- 
volved. True, Niels Bohr has succeeded in associating the 
strange stability of atoms with Planck's quantum hypothesis— 
which has not yet been properly interpreted either— and more 
recently Bohr is said to have given a qualitative explanation of 
the periodic system of the elements and of their chemical prop- 
erties. But I can't for the life of me see how he could have done 
so, seeing that he, too, is unable to get rid of the contradictions I 
have mentioned. In other words, everyone is still groping about 
in a thick mist, and it will probably be quite a few years before it 
lifts. Sommerfeld hopes that experiments will help us to find 
some of the new laws. He believes in numerical links, almost in a 
kind of number mysticism of the kind the Pythagoreans applied 
to the harmony of vibrating strings. That's why many of us have 
called this side of his science 'atomysticism,' though, as far as I 
can tell, no one has been able to suggest anything better. Perhaps 
it's much easier to find one's way if one isn't too familiar with the 
magnificent unity of classical physics. You have a decided advan- 
tage there," Wolfgang added with a malicious grin, "but then 
lack of knowledge is no guarantee of success." 

Despite this little broadside, Wolfgang had confirmed every- 
thing I myself had been thinking before I decided to make 
physics my career. I was very glad not to have tried my hand at 
pure mathematics, and I looked back on Lindemann's little dog 
as "part of that power which still produceth good, whilst ever 
scheming ill." 



115 



Some artistic responses to science and technology - 
Expressionism, Futurism, and the Bauhaus. 



8 Science and Modern Art 

Dietrich Schroeer 

A chapter from Physics and Its Fifth Dimension: Society, 1972 



Blue is the masculine principle, robust and spiritual. Yellow is 
the feminine principle, gentle, serene, sensual. Red is matter, 
brutal and heavy. 

Franz Marc 

The suffering of a man is of the same interest to us as the suffering 
of an electric lamp, which, with spasmodic starts shrieks out the most 
heartrending expression of color. 

Umberto Boccioni 

Yellow light has a wavelength of 0.0000^2 centimeters. 

Textbook on optics 

This chapter contains an examination of the response of painters 
and aUied artists to science and technology in the early 20th 
century. The German Expressionists exemplify a retreat to an 
organic nature, while the Italian Futurists represent an explora- 
tion of the feelings induced by modern technology. The Bauhaus 
is presented as an example of a successful fusion of art and 
technology. 



INTRODUCTION 

This chapter will explore the impact of science and technology on 
painters and architects during the first third of this century. Need- 
less to say, it is not very easy to establish any direct connection 
between these very different human activities. In addition, the 
approach and interpretation will necessarily be quite personal and 
subjective. Since there is then the possibility that I may be try- 



116 



Science and Modern Art 



ing too hard to make the facts fit a preconceived conclusion, this 
whole discussion must not be taken too seriously. The overall 
objective will be to try to outline possible artistic responses to 
science and technology and, in the process, to convey the atmo- 
sphere in which the modem scientific revolution was taking place. 

TECHNOLOGY AND ART: 1900-1933 

The paintings I Hke best date from the period 1900- 1933. ^Y two 
favorite paintings were painted in 19 14; Three Riders, by Wassily 
Kandinsky, and Tyrol, by Franz Marc. I have at times wondered why 
my preference should lie there. One guess is that this is so because 
this period contains many varied responses to the ever-increasing 
pervasiveness of science and technology. 

Science has always had some interaction with painting; Goethe 
with his Theory of Colors is a prime example of this. There was, of 
course, a great change in painting in the later part of the 19th century 
due in part to the introduction of photography, which eliminated 
the need for painting as a faithful record of the visible (see, e.g., Ref. 
15.4). Painting then became more and more a subjective and ultimate- 
ly nonrepresentational picture of what the artist felt rather than a 
picture of the objects which he saw. The Impressionists were in some 
ways the forerunners of this subjectivity. Georges Seurat, for example, 
studied the separation of white fight into its component colors and 
found that color mixing could be done by the eye as well as directly 
on the canvas; thus his pointillism consisted of putting small spots 
of pure color on the painting and letting the observer's eye and brain 
carry out the fusion. Analysis of the observer's role in the visual pro- 
cess was carried even further by Van Gogh, particularly in his last 
pure-color pictures of 1888-90. The subjective trend then went 
through the French Fauvists (wild beasts), hke Andre Derain, to the 
German Expressionists hke Marc, Kandinsky, and Ernst L. Kirchner, 
and the Itafian Futurists fike Umberto Boccioni and Gino Severini. 
It has continued with the Cubists like Pablo Picasso, Georges Braque, 
and Fernand Leger and on to Bauhaus painters Uke Klee and Fein- 
inger. Contemporary with the latter painters is the art-artisan move- 
ment of the Bauhaus following the First World War, and the architec- 
ture of Le Corbusier, Mies van der Rohe, and Frank Lloyd Wright. 
All these movements put more and more of the painter's subjective 



117 




118 



Science and Modern Art 



impressions into the paintings, in particular his reaction to the 
increasingly more technological surroundings. And the three move- 
ments of the Expressionists, the Futurists, and the Bauhaus are par- 
ticularly interesting because they reveal the three alternate reactions 
of retreat, absorption, and integration. 

EXPRESSIONISM 

In Germany the Expressionistic movement after 1900, such as the 
Blaue Reiter in Munich, reacted to science and technology by re- 
treating to an organic nature, by painting landscapes and animals 
with background of fantasy. 

The attitude in 19 12 of the Russian-born painter Kandinsky 
(Fig. 1 5.1) may be characterized by his concern with the human soul: 

On the basis of a deeply felt criticism of the materiaUstic structure 
of the contemporary world, he strove to ferret out and combat 
every form of materialism in art. The modern sciences had 
transmuted the material substance of things into symbols of 
energy; in painting Matisse had liberated colour from its function 
of signifying objects and giving it a spiritual significance. Picasso 
had done the same for form. For Kandinsky these were 'great 
signs, pointing to a great goal.' From all this he drew his own 
conclusion: 'The harmony of colours and forms can be based on 
only one thing: a purposive contact with the human soul.' The 
expressive resonance of pure coloured forms provided the painter 
with a means of making visible the inner resonance of things, 
their vibration in the human soul. The vibrations of the soul 
can be raised to the surface and made visible by pure pictorial 
harmonies uncluttered by objective or metaphoric images, just as 

they are made audible by the pure sounds of music These 

were the ideas that moved Kandinsky's friends to cast off their 
ties with the images of the visible world and to discern the re- 
flections of a higher world in the responsive stirrings of their 
psyche. For these ideas did not revolve exclusively round 'art,' 



Fig. 1 5. 1 Lyrisches by Wassily Kandinsky (191 1). (Photo courtesy of 
Museum Boymans-van Beuningen, Rotterdam.) 



119 



but were embedded in a religious intimation of an encompassing 
Being, at the centre of which, between the earthly things of 
nature and the transcendent realities above them, stood man, 
endowed with antennae that enabled him to enter into com- 
munication with the whole. (Ref. 15.5, p. 117) 

So Kandinsky retained a sense of fairy-tale fantasy, combined it 
with the resonances of colors in the soul, and by 19 14 was able 
to break away completely from any representational content in his 
paintings. 

Marc was even more strongly motivated by a dread of the 
technological world, by a fear of losing any bonds with the reality of 
nature. So to him the key symbols were animals; he felt that animals 
were embedded in the great rhythms of nature (Fig. 15.2). The colors 
of his animals, as in the Tiger or the Blue Horses^ always represented 
the spiritual essence of their nature. As his paintings became more 
abstract, nature and world were not excluded, but rather transposed 
into the wider dimension of the whole modern spirit. Along with 
Marc at Verdun in 19 16, the whole Expressionist movement in paint- 
ing died in World War I. But its spirit continued in many other 
fields, particularly in architecture, as will be pointed out later. 

FUTURISM 

The ItaUan parallel to Expressionism was Futurism, lasting from about 
1908 to 19 14. "The Futurists were not only the first artists to take 
cognizance of the dynamism of a technological society, but they 
also produced works of art of extraordinary emotional impact. They 
translated the kinetic rhythms and the confused, intense sensations 
of modern life into potent visual form." (Ref. 15.1, p. 7.) Fillippo 
Tommaso Marinetti in Milan in 1909 wrote the founding mani- 
festo, which cried in part "burn the museum," "drain the canals of 
Venice," as a protest against the older styles of painting. Beyond this 
protest was a new ideal in art. The modern world was to be typified by 
the automobile with its violently pulsing, noisy Ufe; the staggering 
speed of this mechanical achievement was to replace the classical 
characterizations of the mythical horse Pegasus. As Marinetti put it: 

We declare that the world's splendour has been enriched by a new 
beauty; the beauty of speed. A racing motor car, its frame adorned 



120 



Science and Modern Art 




Fig. 15.2 Jumping Ponies by Franz Marc (1913)- (Photo courtesy of 
Bernard S. Myers.) The New York Public Library, Astor, Lenox and Tilden 
Foundations 



121 



with great pipes, like snakes with explosive breath ... a roaring 
motor-car, which looks as though running on shrapnel, is more 

beautiful than the Victory of Samothrace We shall sing of the 

great crowds in the excitement of labour, pleasure and rebel- 
lion ... of bridges leaping hke gymnasts over the diaboUcal 
cutlery of sunbathed rivers . . , (From the Sackville exhibition 
catalog, London, March 19 12, as quoted in Ref. 15.1, p. 124.) 

The painter Severini said: 

We choose to concentrate our attention on things in motion, 
because our modern sensibility is particularly qualified to grasp 
the idea of speed. Heavy powerful motor cars rushing through 
the streets of our cities, dancers reflected in the fairy ambiance 
of light and color, airplanes flying above the heads of the excited 
throng. . . . These sources of emotion satisfy our sense of a lyric 
and dramatic universe, better than do two pears and an apple. 
(From the Marlborough Gallery catalogue, London, April 191 3, 
as quoted in Ref. 15.1, p. 11.) 

And Boccioni: 

We cannot forget that the tick-tock and the moving hands of 
a clock, the in-and-out of a piston in a cyUnder, the opening 
and closing of two cogwheels with the continual appearance and 
disappearance of their square steel cogs, the fury of a flywheel or 
the turbine of a propeller, are all plastic and pictorial elements 
of which a Futurist work in sculpture must take account. The 
opening and closing of a valve creates a rhythm just as beautiful 
but infinitely newer than the bUnking of an animal eyelid. 
(Translated by R. Chase, as quoted in Ref. 15.1, pp. 131-132.) 
The Italian Futurists were fighting estrangement from the 

world — the lonely isolation of the individual that was not only the 
inheritance of the artist but a common threat to modern man. They 
wanted their art to restore to man a sense of daring, an assertive will 
rather than submissive acceptance. "We want to re-enter life," 



Fig. 15.3 Study for Dynamic Force of a Cyclist II by Umberto Boccioni 
{^9^3)- (Photo courtesy of Yale University Art Gallery, gift of Collection 
Societe Anonyme.) 



122 



Science and Modern Art 



^^ 




123 




Fig. 15.4 Street Light by Giacomo Balla (1909), oil on canvas, 68-3/4 ^ 
45-1/4". (Photo courtesy of the Collection of the Museum of Modern Art, 
New York, Hillman Periodicals Fund.) 



124 



Science and Modern Art 



they said, and to them Ufe meant action. "Dynamism" was the magic 
word to them. The Futurists wanted to put the spectator in the 
center of the picture. "We Futurists," said Carlo Carra, "strive with 
the force of intuition to insert ourselves into the midst of things in 
such a fashion that our 'self forms a single complex with their 
identities." This is like the Expressionists, but with more emphasis 
on the mechanical innovations rather than on an escape into the animal 
world. And their works bear such titles as Cyclist, by Boccioni (Fig. 
15.3), Abstract Speed — Wake of Speeding Automobile, by Giacomo 
Balla, Expansion of Lights, by Severini, and The Street Light — Study of 
Light (Fig. 15.4), by Balla. Dynamic action is indicated by multiple 
images, by rays of light interrupted by action, and by the conflict of 
separated colors. Balla, who was interested in all scientific matters, 
was so fascinated by astronomy that the vision of the planet Mercury 
passing before the sun as it might be seen through a telescope served 
in 19 14 as inspiration for one of his happiest series of paintings. 
"The form/force," said Boccioni, "is, with its centrifugal direction, 
the potentiality of real form"; obviously the language of the Futurists 
itself owes debts to the sciences. The confrontation with technology 
is direct; man clearly must bend technology to his own will. 

This attempt by the Futurists to absorb technology into art also 
came to an end with World War I. To them in 1914 the war promised 
to be the ultimate awakening and unifying force. Several of them 
signed up in the bicycle messenger corps; and some died in the war, 
terminating the movement, a movement which in any case could by 
its very nature probably not have survived the postwar period. 

THE POSTWAR BAUHAUS MOVEMENT 

After the war, there was a great confrontation of society with cruel 
reality; in Germany, for example, by 1924 it took a wheelbarrow full 
of bilUon-mark bills to buy a loaf of bread. In this atmosphere there 
could no longer be a complete retreat from technology. And an institu- 
tion developed in 19 19 — the Bauhaus, or House of Building — which 
attempted to unite the arts and industry/technology. The Bauhaus 
was founded by Walter Gropius in Weimar, the residence long before 
of Goethe, and the place where the constitution of the new German 
Repubhc was drawn up after the war. Although the Bauhaus move- 
ment included many artists, such as Kandinsky and Klee, who had 



125 



been involved in the Expressionist movement before the war, it 
was started by Gropius to become a consuhing art center for industry 
and the trades. In every subject the students were to be trained by 
two teachers, an artist and a master craftsman. And these students, 
once familiar with science and economics, quickly began to unite 
creative imagination with a practical knowledge of craftsmanship, and 
thus to develop a new sense of functional design. 

Not that the Bauhaus was the first to try the combination of art 
and design. There were, for example, in the middle of the 19th century 
attempts in Great Britain to provide this kind of synthesis. But those 
were failures because the products were not mass-producible. Some- 
how the genius of Gropius avoided this problem at the Bauhaus. The 
artistic instruction included the theory of form and color, mathematics, 
and physics; rigorous analyses of Unes and planes and space were 
attempted by Klee, Kandinsky, and Laszlo Moholy-Nagy. The tech- 
nical skills were produced both by workshops and by industrial experi- 
ence. The students were not just idealists, but included many veterans 
of the war who were searching for a meaning of life. It is this contact 
with reality, through industrial work, for example, which made the 
Bauhaus so successful. 

The fate of the Bauhaus was symboUc of its time. In 1925, when 
the poUtical climate in Germany was particularly bad, the Bauhaus 
left conservative Weimar and moved to Dessau. In 1 928 Walter Gropius 
left; in 1933 overnight the Nazi regime locked the doors. The impact 
of the Bauhaus — of the fusion of art with science/technology — is, 
however, still with us. Our modern tubular metal chairs are frequently 
based on Bauhaus designs, as are many of our advertisements, fabrics, 
and much of our architecture. 



OTHER EXAMPLES OF SCIENCE AND ART 

There are many other interesting traces of the sciences in art and 
architecture during the postwar period. Worthy of special note are 
three: 

I. There is the Expressionistic architect Erich Mendelsohn, who in 
the period 19 17— 1920 constructed the Einstein tower near 
Potsdam as an observatory to run tests on the general theory of 



126 



Science and Modern Art 



relativity, fusing Expressionism with the grandeur of the Einstein- 
ian concept (see Fig. 16.1.). 

2. There is the architect Rudolf Steiner, who in his younger years 
edited Goethe's works and whose views were hence strongly 
colored by Goethe's views on science. These viewpoints are incor- 
porated into Steiner's Expressionistic buildings Goethenaum I 
and II. 

And, finally, 

3. Le Corbusier took mathematical proportions along the Unes of 
Pythagoras, and the idea of modularity from crystallography, to 
form his concept of a modulator — a series of proportional sizes 
based on man to build up all dimensions of buildings. While he 
used technological products, Le Corbusier's architecture was very 
much man-oriented. 

Note the parallel in the interest of Goethe as a poet-scientist and in 
Einstein as a philosopher-scientist. 

We could also speak of Cubism in painting, with its attempts to 
modularize the areas of paintings, which then led to the work Mondrian 
and his squares and rectangles. As a final example there is the painter 
Leger. Before the First World War he tried many styles of painting, 
none of which seemed satisfactory. Then came his wartime service 
in an engineering unit, where he came in close contact with men who 
felt at home with technology. Their optimism about the machine 
world inspired him: 

He felt that as an artist his task was to discover forms of expres- 
sion appropriate to modern life. The shining, precise, abstract 
beauty of the machine provided a visual point of departure. He 
understood that the mechanical thing possessed a representative 
value as the truest creation of modem civiUsation and that the 
images derived from it could become evocative emblems of the 
modern industrial world. (Ref. 15.5, p. 253) 

After the war he integrated industrial objects into his art as motifs 
to evoke modern esthetics. The gleaming machine, the concreteness 
of wheels, and the dynamism of repeated motion — all these are 
reflected in Leger's works (Fig. 15.5). 



127 




Fig. 15.5 Three Women by Fernand Leger (1921), oil on canvas, 72-1/4 x 99". (Photo courtesy 
of the Collection of the Museum of Modern Art, New York, Mrs. Simon Guggenheim Fund.) 



128 



Science and Modern Art 



SUMMARY 

We might sum up this chapter as follows. Adding to the whole atmos- 
phere of the period 1900 to 1933 was a confrontation between the 
individual artistic intellect and science/technology. This confronta- 
tion profoundly influenced the arts of the period. Some artists, like the 
German Expressionists, rebelled against technology by retreating to 
a more organic view of nature, by making something fairy-tale-Uke of 
the technology; for example, in Expressionist pictures, railroads 
always look Uke toys. Other artists, Uke the Italian Futurists, tried 
to absorb technology rather than confronting or avoiding it; for 
example, the Futurist's railroads look Uke dynamic machines. Neither 
of these cases necessarily involved a deep understanding of the basic 
scientific trends. Nonetheless, these were profound cultural reactions 
to the new science-based industrial age. The third, and most successful 
approach, was the attempt by the Bauhaus to totally integrate the arts 
and industry. The resultant impact is still enormously visible in all 
of industrial designing. Nonviolent confrontations ofthe two cultures 
can indeed be quite productive. 



REFERENCES 

Prime references 

1 5. 1 J. C. Taylor, Futurism, New York: The Museum of Modern 
Art, distributed by Doubleday and Co. of Garden City, New 
York, 1 96 1. Many ofthe illustrations are Futurists' paintings, 

15.2 D. Sharp, Modem Architecture and Expressionism, London: 
Longmans, Green and Co., Ltd., 1966; Chapters IX and XI 
have Expressionist architecture illustrations, including the 
Goethenaum I and II. 

Interesting reading 

15.3 B. S. Myers, The German Expressionists, New York: Frederick 
A. Praeger, 1966. Has many Expressionist illustrations. 

15.4 A. Scharf, Art and Photography, London: Allen Lane, 1968. 
Discusses how photography modified art. 



129 



15-5 W. Haftman, Painting in the Twentieth Century, Vols. I and II, 
New York: A Praeger, 1965. Has Expressionist illustrations. 

15.6 H. Bayer, W. Gropius, and I. Gropius, Eds., Bauhaus 1919- 
1928, Boston: C. T. Bransford Co., 1959, 3rd printing. 

15.7 G. Kepes, Language of Vision, Paul Theobald and Co., 1959. 

15.8 G. Kepes, Ed., Module, Proportion, Symmetry, Rhythm, New 
York: George Brazillier, 1966. 

15.9 W. Scheiding, Crafts of the Weimar Bauhaus, New York: Rein- 
hold Publishing Co., 1967. 

15.10 L, Hirschfeld-Mack, The Bauhaus, Groyden, Victoria, 
Australia: Longmans, Ltd., 1963. 

QUESTIONS FOR DISCUSSION 

1 . It has been suggested that the impression we have of people's 
faces is actually a time average, and that this is the reason why 
paintings are better portraits than photographs (which record 
one instant). Is this indeed the difference? 

2. Painters use such words as "resonance" and "vibration." Do they 
know the scientific meaning of what they are saying? Does it 
matter whether they understand these words? 

3. What is Op art? Does contemporary art include a response to 
science? 

4. Is the artist's response primarily to science or to technology? 

5. Should we make artists study physics? 

6. Why do artists continually refer to the science of Goethe rather 
than to that of Newton? Why do artists such as Dali make por- 
traits particularly of Einstein? 



130 



What is symmetrical, what is not, and how you can tell is 
discussed in this article. The concept of symmetry turns out 
to be of surprising importance and continuing interest in 
physics. 



9 Symmetry 

Donald F. Holcomb and Philip Morrison 

A chapter from My Father's Watch: Aspects of the Physical World, 1974 



A. SYMMETRY* "Symmetry" is a word with pleasam and 
orderly connotations to the civihzed mind. 
But symmetry provides, as well, an organizing principle of considerable 
power in collecting certain knowledge about the behavior of the 
physical world. The purpose of this nearly self-contained special topic 
is to explore that knowledge. 



The Balance and Symmetry 

We begin with a dicussion of one of the simplest of all measuring 
instruments, the balance, and view it as seen by Archimedes. Archimedes 
(287-212 BC) was a resourceful scientist, but he was practically innocent 
of any knowledge of forces, weights, lever arms, and the like. He 
approached the "why" of the behavior of the simple, equal-arm 
balance on the basis of arguments about symmetry and the principle of 
insufficient reason. 

Consider the equal-arm balance shown in Fig. A.l with identical 
weights on the two sides. Archimedes took the position that since the 
physical system is initially completely symmetrical — i.e., the two sides 
are mirror images of one another — there is no reason why it should turn 
one way or the other. Hence, it remains balanced. (This is the meaning 
of the term "principle of insufficient reason" — there is insufficient 
reason for the system to go one way or the other.) 

Sy»wt»ie+ry 



Figure A.l 

The equal-arm balance shows symmetry 
on the two sides of a plane which passes 
through the pivot point. 



I 



Pivot 



131 



Q. We know very well that it is possible to have such a system 
balanced with weights that are not identical, at least in 
appearance. For example, one weight could be made of lead, 
the other of aluminum. Does this possibility destroy Archi- 
medes' argument? 

In passing, we note that the reflection symmetry (i.e., one-half the 
system is a mirror image of the other half) which we tacitly recognize 
in the case of the balance is everywhere around us. Most animals have 
approximate reflection symmetry about a central plane. We shall 
shortly discuss carefully the precise method of characterizing the 
reflection symmetry. For the moment, we ask, are animals really 
symmetrical? Is the reflection symmetry perfect? The answer is, of 
course, "No — there are many small asymmetries, as we note for the 
human animal if we look at ourselves in a double mirror." But we 
recognize the overwhelming validity of the approximation of symmetry, 
despite small deviations. 

Experiment : In the quiet of your room, try to arrange a set of mirrors 
so that you can see your face and its mirror image side-by-side. 
How true is your own reflection symmetry? 

Figure A.2 shows a sketch of one of the few animals that deviates 
significantly from reflection symmetry — the flounder. This fellow's 
mouth and eyes seem to us to be misplaced, so accustomed are we to 
the symmetrical appearance of animals. 

Recognizing that in this argument about symmetry Archimedes 
was dealing with the special case of reflection symmetry, we now return 
to further consideration of the balance, to develop his arguments a bit 
further.^ 



(Head-on View) 

Figure A.2 

A sketch of the flounder, a rare example of 
an animal that lacks reflection symmetry. 

Consider the arrangement of a balance beam and four identical 
weights sketched in Fig. A. 3a. Should this arrangement balance, on the 
basis of Mr. A's appeal to symmetry? It is clearly not an arrangement 
with exact reflection symmetry. But now we introduce an additional 
argument : "Symmetrical motion of two identical weights about the 
center line of the two maintains the balance condition." That is, by 



' Ernst Mach's famous book. The Science of Mechanics, London: Open Court 
Publishing Co., 1942, pp. 13-20, gives a careful discussion of the strengths and 
weaknesses of Archimedes' approach to the problem. 



132 



Symmetry 



Y 



T^ 



(j^) 












Figure A. 3 

(a) The beam loaded with four weights is 
in balance, but does not appear to have 
exact reflection symmetry with respect to 
the pivot. 

(b) Two of the weights are moved 
symmetrically with respect to the dotted 
line. 

(c) The movement of the two weights 
maintains balance, and also produces 
reflection symmetry. 



means of the operation suggested by Fig. A.3b, moving one weight one 
direction and an equal weight the other direction by the same distance, 
bringing us to the configuration of Fig. A.3c, we assert that we shall not 
change the balance condition. Since we have reduced the situation to 
one of obvious reflection symmetry, it must also follow that the con- 
figuration of Fig. A.3a was also in balance. Archimedes apparently used 
an argument of this sort in an attempt to reduce any situation to one of 
self-evident symmetry by means of what he considered a "reasonable" 
procedure. 

Q. Consider the initial situations shown in Fig. A.4a and A.4b. 
Apply the scheme outlined in the discussion of Fig. A.3 to 
move weights in each of the configurations of Fig. A. 4 in 
order to reduce these configurations to ones with clear reflec- 
tion symmetry. That is, move 2 weights at a time symmetrically 
about their midpoint, toward one another or apart, in an opera- 
tion similar to that of Fig. A.3b. Sketch the final configuration 
in each case. 



£~5' 



CO 



Cb) 



Figure A, 4 

The sketches labeled (a) and (b) show 
two examples of a beam which is balanced 
but has an apparently asymmetric arrange- 
ment of weights. Suitably symmetric 
movement of the weights, two at a time, 
can maintain balance and also move 
tqward a symmetrical arrangement of 
weights for either example. 



133 



Symmetry of Appearance vs. 
Symmetry of Physical Effects 

More extensive investigation of physical systems quickly shows 
us that we must be careful not to infer that visual reflection symmetry 
automatically guarantees reflection symmetry of all physical effects 
connected with the system. By implication, we have ascribed such a 
position to Archimedes. 

Suppose one has a wire that is to carry an electric current, as 
shown in Fig. A.5a. The Ught arrows indicate the direction the electric 
current will take when we turn it on. (One need know nothing about the 
nature of electric current to follow this example, only to accept the fact 
that the current consists of something which flows, and thus has a flow 
direction associated with it. In practice, one might produce the current 
by connecting two ends of the wire to a battery ; then the current could 
be reversed simply by reversing the connections to the two terminals of 
the battery.) Above the wire is placed a compass needle, which we align 
parallel to the wire before switching on the electric current. We could 
achieve this arrangement on the Earth's surface by aligning the wire in 
the direction in which the compass needle naturally points — i.e., toward 
magnetic north. This configuration. Fig. A.5a, appears to have reflection 
symmetry about the dotted plane shown ; as with the balance, there is 
nothing to distinguish right from left. However, when the current is 
passed through the wire, we find that the compass needle takes up a 
position something Uke that shown in Fig. A.5b. If the current is re- 
versed, fhe configuration in Fig. A.5c results. Neither configuration 
A. 5b nor A. 5c possesses the reflection symmetry of the original arrange- 
ment, and we appear to have a breakdown of the principle of insufficient 
reason. 



Figure A. 5 

(a) A compass needle and current- 
carn/ing wire are arranged so as to lie in a 
single vertical plane. 

(b) As the current is turned on, the 
compass needle swings in such a fashion 
that the initial reflection symmetry is 
destroyed 

(c) Reversing the current reverses the 
direction of the compass needle. 



Electric 
Cavrent 




1/ No»-it^-Se,ekiw9 
-' Pole 



ImagiwQry Vevtical RcHcction 
Plane 




134 



Symmetry 



What do the resuhs of this imagined experiment show? Two 
possibiHties are obvious. 

1. The principle of insufficient reason is itself fundamentally flawed. 

2. Some aspect of the system, not immediately apparent to the 
human eye, destroys the reflection symmetry that Fig. A.5a 
suggests. 

Possibility (2) turns out to be the correct one. We shall eventually 
return to discuss in some detail the property of the compass needle that 
is not immediately apparent. First, however, we discuss the common 
types of geometrical symmetry and their use in describing properties of 
natural systems. 



Geometrical Symmetry 

We now want to explore systematically the use of symmetry as a 
useful concept for organizing observations. Before doing so, we must 
engage in the very characteristic scientific activity of describing care- 
fully the meaning of the term in question. Rather than attempt to pro- 
duce a definition of symmetry in the Websterian sense, we shall define 
the term by answering the following question: "How can one describe 
unambiguously the symmetry properties of an object?" The answer gives 
our definition. 



The symmetry properties of an object are described by 
cataloging all the operations one can perform on the object 
which leave it indistinguishable from its original form. 



Some examples of operations one might perform on an object to test its 
symmetry properties are as follows : 

1. Movement through space without reorientation. 

2. Reorientation about some axis in space. 

3. Imaging in a mirror. 

4. Inversion (to be defined later — this term has a specific meaning 
that is difficult to render in everyday language). 

More formally, if one performed one of these operations and 
found the object's appearance to be indistinguishable from its appear- 
ance before the operation was performed, he would say, "The object 
does not change under the operation of 

1. translation, or 

2. rotation, or 

3. reflection, or 

4. inversion." 

(The numbers in the two lists correspond.) We shall investigate these 
four symmetry operations in varying degrees of detail. Our chief aim 



136 



will be to understand the interplay between the ideas of symmetry 
gained from dealing with abstract geometrical forms and the application 
of those ideas to the real physical world around us. 

Translation 

The operation of "translation" is perhaps the simplest of all — we move 
the object of interest through space without reorienting it. Suppose we 
perform a translation of a book by a distance X. Figure A.6a sketches 
the operation. Are the book's properties distinguishable from those it 
had before the operation? Yes and no. The book is obviously in a 
different position with respect to its background. However, various 
physical experiments would find the book to behave identically. The 
equivalence of one point in space to any other point, so far as the laws 
of physics are concerned, is at once a trivially obvious and deeply 
fundamental fact. 

Rather than pursue that one, however, we turn to a rather different, 
but practically more important example. Consider the three patterns 
shown in Fig. A.6b. We assume that these repeating patterns extend 
indefinitely far out of the figure to both left and right. Consider the first 
pattern, for example. A translation of the whole pattern by some dis- 



Figure A.6 

(a) A book is translated by distance X. 
No other change takes place. 

(b) Three repetitive patterns are sketched. 
We say that each of these patterns has 
symmetry under translation by some 
characteristic distance. 




CO 




Co^h^ues ^ x^v-v^vv-v-N/v^ Co«tiv,ues 



1 1 I 
Hi I 



-5jLL!lfljJUjLLi^ 



Cb) 



136 



Symmetry 



tance to right or left will, in general, produce a pattern visibility distinct, 
since the zigs and zags would be in different places. However, if we 
displace the pattern by a distance a, or any multiple thereof, it will 
appear not to have been changed, since all zigs and zags will appear in 
the same positions. Therefore, the first pattern of Fig. A.6b has transla- 
tion symmetry under displacement by distance a. 

Q. By what distances could you displace the second and third 
patterns in Fig. A.6b and stiU leave each of them indistinguish- 
able from its original form? 

Although they are interesting primarily to the artist and artistic 
analyst, we cannot resist the temptation to call attention to the many 
interesting examples of the use of translational symmetry to produce 
aesthetic effects in various forms of decoration. Figure A.7 shows two 
of these.^ Figure A.7a shows a photograph of the Doge's Palace in 



mm 




Two interesting examples of translation 
symmetry in designs of the past, (a) The 
facade of the Doges palace in Venice, 
(b) A row of Persian bowmen sketched 
from a frieze in Darius' palace in Susa. 



2 These examples are noted in Herman Weyl, Symmetry, Princeton : Princeton 
University Press, 1952, pp. 49, 50 



137 



Venice; Fig. A.7b is a sketch of a pattern in a frieze of Persian Bowmen 
from Darius' palace in Susa. 

Q. What is the repetition distance in the Bowmen pattern of Fig. 
A.7b? 

In physical science, perhaps the most useful application of the 
ideas of translation symmetry comes in the field of crystallography, 
which is the analysis and description of the forms taken by natural 
crystalline materials. These crystalline materials are made up of three- 
dimensional arrays of fundamental building blocks, and the specifica- 
tion of the translational repetition distances is an indispensable scheme 
for describing the characteristics of a particular crystal. Figure A.8 



gh-^-gF 

♦■-<>- i- 



(a) NqCI 
"^"T'l'^-Cr'^ [ 2 Kinds of 



^^^^ 



f.f;T 

I • I • I 

1 • I • ' 
I • I • * < 



,5c'-,V-.VT»i Cb)AluwiiMaw 

--f --f ' l»L-t 

• I * ;*>■•] ri '<l►ldo^^Q+o^^1l 

m I • \ ' L-'f 










Cfystal SKuctuvcs 

Figure A.8 

Crystal structures show repeating patterns, 
and thus have translational symmetry 
under certain movements, (a) Model of 
sodium chloride crystal structure, (b) 
Aluminum has a different but still simple 
structure, (c) The graphite structure is 
more complicated. 



shows models of sections of three different crystals, each of which is 
made up of one or two kinds of atoms. As with the one-dimensional 
examples in Fig. A.6, we assume that the models extend indefinitely in 
all directions. 

Q. Can you describe the translational symmetry properties of 
the atomic lattices of sodium chloride and aluminum shown 
in Fig. A.8? That is, what translation distances, in what 
directions, will cause the structure to overlay precisely its 
original configuration? 



138 



Symmetry 



Rotation About an Axis 

Another operation we can perform on an object is rotation about some 
chosen axis. Figure A.9 shows two plane figures, a square and an equi- 
lateral triangle. If we rotate the square about an axis through its center, 
which is perpendicular to the plane of the square, we find that the 
figure is indistinguishable from its original form whenever the rotation 
angle is some multiple of 90°. Thus, in one full revolution there are four 
indistinguishable positions. We describe this property by saying, "The 
square has a four-fold rotation symmetry about an axis through the 
center and perpendicular to the plane of the square." In the case of the 
equilateral triangle, the repetition period is 120° rather than 90°. We 
say, "The equilateral triangle has a three-fold axis through its center." 

^ Axis 



Ax'is 





Figure A 9 

We imagine rotating these simple figures 
about a vertical line passing through the 
axis spot. 

Q. 1. Do all triangles have this three-fold axis? If not, can one 
say anything in general about the rotational symmetry of 
triangles? 

2. Sketch a two-dimensional figure with a two-fold axis, 
and one with a six-fold axis. 

Note carefully that one must always specify the axis about which 
the rotation takes place. The axis is often so obvious in the case of 
highly symmetrical figures that one tends to forget its importance. 
But consider Fig. A. 10. We have chosen an axis through one corner of 




A«is 



Figure A.I 

An equilateral triangle rotated about an 
axis through one corner does not exhibit 
three-fold symmetry. 



139 



Figure All 

The operation of reflection with respect to 
the x-K plane is carried out by changing 
the sign of the z-coordinate for each point 
of the object. The cubical frame shown 
would be reflected by a series of nnove- 
ments such as that shown. 




ReflecfiOM 
Plane. 



the equilateral triangle and then have rotated by 120° about this axis — 
the threefold symmetry simply does not exist about this axis. The dotted 
triangle is obviously different from the original one, since it is in a 
different place. 

Reflection with Respect to a Plane 

A third familiar operation is that of reflection in some plane. This 
operation is particularly familiar because the reflection operation is 
precisely what a mirror does if placed in the chosen plane. Figure A. 11 
shows a cube and one of its reflection symmetry planes. Mathematically 
speaking, if we set up a coordinate system as shown in the figure with 
the reflection plane chosen to be the x-y plane, the reflection operation 
consists of taking a point at some z coordinate — say, Zj — and taking it 
to — Zj . This reversal of z coordinate is done for all points of the figure, 
and the mirror image is thus produced. Note particularly that one must 
always specify the plane with respect to which the reflection operation 
is performed, just as he must specify the axis for the case of rotation. 



Inversion with Respect to a Point 

Suppose we establish a coordinate system as shown in Fig. A. 12, with 
X, y, and z axes. If we now take each point of an object, with coordinates 
Xi, yi, and Zj, and move the point to coordinates — x^, — yi,and — Zi, 
we have performed the operation of inversion on the object, about the 
point 0, the origin of coordinates. If this operation leaves the object 
indistinguishable from its original state, then we say the object has 
inversion symmetry with respect to the point that is the origin of the 
xyz axes. For an easily visualized example, consider a two-dimensional 
example in Fig. A. 13, the letter A. In two dimensions, inversion with 
respect to the point takes all points at coordinates x, y to coordinates 



Figure A. 1 2 

In the operation of inversion, each point 
has the sign of all three cartesian coordin- 
ates reversed. In this figure, the point 
(x, , K, . z, ) goes to the point ( -x, . - /, . 
— z, ) shown. 



(-^.,-yi )-■?.) 




140 



Symmetry 



OtfiqiM 




iMverfed A 



O^-igiMol A 




iMolistinquis^iable 



Origin 



Figure A.I 3 

The letter A does not have inversion 
symnnetrY about a central point, but letter 
X does have this property. 



— X, —y. The figure sketches the inversion process for the letters A and 
X. We see that X has inversion symmetry about the given point. The 
inverted letter A is clearly different from the original. Hence, A does 
not have inversion symmetry about the chosen point — in fact, there is 
no point with respect to which A has inversion symmetry. For such a 
situation, we usually say, simply, "A does not have inversion symmetry." 
Two nominally different symmetry operations may sometimes be 
equivalent, in certain special circumstances. For example, consider a 
two-dimensional object such as the letter S in Fig. A.M. In two dimen- 
sions, rotation of 180° about the axis through point is identical with 
the inversion process taken with respect to point 0. This coincidence 
of rotation through 180° and inversion about cannot occur with 
three-dimensional figures, however. 



Figure A.I 4 

In two dimensions, inversion with respect 
to any point such as O is always equiva- 
lent to a rotation of 180° about en axis 
through that point. 



Inversion 
opevatiow 
on pointyO 




, ^ , 180" rotation 
/' ''jir operation 
^ , oboat axis 
point O 



Q. 1 . Consider the two letters A and H . Classify each according 
to the classes of symmetry operations — ^rotation, reflec- 
tion, and inversion — under which they remain unchanged. 
In figuring out the symmetry classes, consider the letters 
as constrained to remain in a plane — i.e., the letters 
cannot be rotated out of the plane of the paper. 

2. Describe the symmetry properties of a featureless sphere, 
using the language we have developed in this chapter. 

3. Is there anything symmetrical about a glove ? What about 
apair of gloves? 

4. Describe the symmetry properties of a helix with ends, 
such as an automobile coil spring. Assume the two points 
of the helix to be exactly diagonally opposite one another. 



141 



Figure A.I 5 

A right-handed helix (1) is the mirror 
image of a left-handed helix (2). 




(2) 



Right and Left Symmetry 



In the last question at the end of the previous section, we inquired about 
the symmetry properties of a helix. We now want to focus on one particu- 
lar property of the helix that is profoundly significant in determining 
certain properties of biological systems, and which leads us to deeper 
thoughts about the basic symmetry properties of nature. 

Figure A. 15 shows two helices; they are mirror images of one 
another. Perhaps, after your thinking about the previous question about 
helices, you can see that no conceivable rotation performed on No. 1 
will make it look like No. 2. By convention, No. 1 is called a right-hand 
helix, and No. 2 a left-hand helix. [The convention is the same as that 
used m labeling a right-hand screw thread (the usual kind) and a left- 
hand screw thread (which probably appears most commonly on the 
bolts used by certain manufacturers to fasten automobile wheels to 
hubs on one side of the car).] 

As a result of a long series of biological experiments, beginning 
with the work of Pasteur in 1848 on the forms of tartaric acid molecules 
and contmumg through the elucidation of the structure of the DNA 
molecule by Watson and Krick in 1953, it is known that many large 
chemical molecules of biological interest possess a full or partially 
developed helicity. This statement means that the molecule has a mirror 
image which is geometrically distinct. Much more importantly the 
mirror image molecule turns out to be chemically and biochemically 
different. This effect has the profound result that only one of the two 
mirror forms of certain types of molecules is employed by living matter 
Figure A.16 illustrates the two mirror forms of a simple compound of 
biological interest, alanine. These two molecular forms, called /-alanine 
and ^-alanine, are made up of precisely the same atomic constituents- 
3 carbon atoms, 7 hydrogen atoms, 1 nitrogen atom, and 2 oxygen 
atoms-formed with exactly the same internal relationships except 
that one form is the mirror image of the other. But on this subtle 
difference hangs a weighty matter. Alanine is a fundamental processing 
chemical present in the biological machinery of man. If you were to 
replace his normal supply of /-alanine with ^-alanine, he would die 
His body cannot use (/-alanine. Feynman has put the matter pungently. 

So far as we know, in principle, we could build a frog, for example, in 
which every molecule is reversed, everything is l.ke the "left-hand" mirror 



142 



Symmetry 




X -alanine 




aloviine 



Figure A.I 6 

A right-handed molecule, d-alanine, and 
its left-handed counterpart, /-alanine, are 
analogous to the pair of helices in Fig. 
A.I 5. Look upwards along the vertical line 
between two C atoms and imagine taking 
this line as a rotation axis. You can see 
that a left-handed tour around the upper 
part of the molecule for /-alanine will find 
the sequence: CH3 group, NH3 group, 
H atom, whereas one must do a right- 
handed tour for cy-alanine in order to 
generate the same sequence. 




Figure A. 1 7 



The huge DNA molecule, of genetic 
importance, is in the form of a double helix. 
The sketch shows only a portion of a 
DNA molecule, which is made up of 
three kinds of molecular building blocks. 
The small white circles are hydrogen 
atoms which serve as links between the 
"backbone" of sugar-phosphate groups 
and the nitrogen-based groups of the 
outer, double helix. 



image of a real frog; we have a left-hand frog. This left-hand frog would go 
on all right for a while, but he would find nothing to eat, because if he 
swallows a fly, his enzymes are not built to digest it— unless we give him a 
left-hand fly.^ 

Figure A. 17 shows a sketch of a model'^ of the DNA molecule, 
which carries the genetic code in animals. Only the form with the right- 



^ R. P. Feynman, Lectures on Physics, Reading, Mass. : Addison-Wesley Publishing 

Co., Inc., 1963, pp. 52-56. 
* Reproduced from Hugh Grayson-Smith, The Changing Concepts of Science, 

Englewood Cliflfs, N.J. : Prentice-Hall, Inc., 1967, by permission of the publishers. 



143 



hand helicity shown is found in nature despite the fact that its mirror 
image is equally stable chemically. 

Now comes the deeper question of the natural philosopher. What 
caused the choice in nature? Why do we not have left-helix people who 
use all of the left-helical molecules and build up a complete left-oriented 
(no political overtones, please) organism? The true reason for the fact 
that all known systems in nature use chemical molecules of the same 
helicity is lost in the misty beginnings of evolution. There is no evidence 
that there is any fundamental scientific reason for this choice, and one 
is led to believe that our present situation is the result of pure chance — 
at some stage early in the process, a chance fluctuation momentarily 
favored the population of molecules of one helicity, and a dominance 
was established that soon pervaded all the primitive biochemical forms 
and was sustained as they moved toward more complicated biological 
structures. 



Parity 

One implication of the previous discussion is that if we did succeed 
in building a left-handed biological world, it would function precisely 
according to the same natural laws as the world we have. In fact, for a 
very long time scientists believed that there was an immutable sym- 
metry property of nature at work here— namely, that any natural 
system has a conceivable mirror image whose properties would unfold 
in time so that the two would always be mirror images of one another. 
We quote Feynman again : 





Figure A.I 8 

in a parity-conserving 
world, a clock and 
its mirror image will 
run so as always 
to remain mirror images. 



Suppose we build a piece of equipment, let us say a clock, with lots of 
wheels and hands and numbers ; it ticks, it works, and it has things wound 
up inside. We look at the clock in the mirror. How it looks in the mirror 
is not the question. But let us actually build another clock which is exactly 
the same as the first clock looks in the mirror — every time there is a screw 
with a right-hand thread in one, we use a screw with a left-hand thread in the 
corresponding place of the other; where one is marked "2" on the face, 
we mark a "£" on the face of the other; each coiled spring is twisted one 
way in one clock and the other way in the mirror-image clock ; when we are 
all finished, we have two clocks, both physical, which bear to each other the 
relation of an object and its mirror image, although they are both actual, 
material objects, we emphasize. [Figure A. 18 shows Feynman's Clocks.] 
Now the question is : If the two clocks are started in the same condition, the 
springs wound to corresponding tightnesses, will the two clocks tick and 
go around, forever after, as exact mirror images? (This is a physical 
question, not a philosophical question.) Our intuition about the laws of 
physics would suggest that they would.^ 



' R. P. Feynman, Lectures on Physics, Reading, Mass. : Addison- Wesley Publishing 
Co., Inc., 1963, pp. 52-54. 



144 



Symmetry 



The faith of scientists in this so-called parity conservation principle 
(that the two clocks or their equivalents would evolve so as always to 
remain mirror images) was so strong that the demonstration of its 
failure in a remote realm of nature through an experiment by Wu, 
Ambler, Hay ward, Hoppes, and Hudson in 1956 led to a Nobel Prize 
for T. D. Lee and C. N. Yang, who had suggested the experiment and 
postulated the failure.^ 

So far as we presently know, this failure of the parity conservation 
principle is restricted to a particular class of subatomic phenomena 
that are almost completely isolated from interaction with the matter 
world as we know it. We do not have space to pursue the details of the 
Wu, Ambler, Hayward, Hoppes, and Hudson experiment and many 
subsequent investigations that have delimited the particular class of 
phenomena for which systems exhibit an innate and immutable handed- 
ness. An annotated list of references is given at the end of this section. 
But we should emphasize the distinction between this situation and the 
biochemical one. In the biochemical case, the predominance of one 
kind of molecule is believed to be a chance situation, and an otherwise 
identical chemical molecule of opposite helicity always exists. For the 
subatomic particles involved in the breakdown of the parity principle, 
the right or left helicity is an integral part of the makeup of the particle, 
and if the helicity is changed, the particle no longer evolves according 
to the same set of natural laws. In other words, the true mirror image of 
one of these particles does not exist in nature. 

We now return briefly to the question of the wire and compass 
needle (see Fig. A.5 and accompanying text). Can we identify the hidden 
property of the system shown in Fig. A.5a that causes the breakdown of 
the apparent reflection symmetry? Yes, we can. The physical eff"ect of 
the current through the wire is to generate magnetic eff'ects which 
intrinsically possess a helicity. Figure A. 19 is a modification of Fig. A. 5a, 
which includes imaginary magnetic lines of force drawn to represent 
the helicity. The arrangement has lost its mirror symmetry about the 
dotted plane as a result of addition of the magnetic lines of force, and 
we have no reason to apply the principle of insufficient reason. Figures 
A.5b and A. 5c become Figs. A. 18b and A. 18c. We now see that the 
configuration of Fig. A.18c is simply that of A. 18b rotated through 180° 
about the dotted axis AA', and there are no longer any surprises 
remaining. 

Not only Geometry! 

Our examples of the uses of symmetry have been drawn mostly 
from geometry alone. Left-right symmetry, symmetry of motion along 
a wire, symmetry of position along a line are typical. But physical 
objects have properties which cannot be described by geometry, of 



* A description of this experiment is given in the article entitled The Overthrow of 
Parity, by P. Morrison, Scientific American, April, 1957. 



145 



Figure A.I 9 

By adding loops representing the magnetic 
field to the sketches of Fig. A. 5, the 
apparent symmetry of A. 5(a) is destroyed. 
Now, (b) and (c) are seen to represent 
the same internal relationships among the 
current, magnetic field loops, and compass 
needle. The configuration of (c) is merely 
a 180° rotation of the configuration of 
(b). 





course, and sometimes symmetry goes with these. For example, electric 
charge is a property of many physical objects. Perhaps you recall the 
catch words, "like charges repel, unlike charges attract." That phrase 
correctly described the behavior of electric charge. Describing the 
forces between electric charges in this way implies a kind of symmetry. 
It doesn't matter how we choose to assign the names positive and 
negative to the two kinds of charge — plus works on plus just like minus 
on minus, and the force of plus on minus is indistinguishable from that 
of minus on plus. This feature means that you can exchange all plus 
charges for minus charges in a system, and vice versa, and nothing in 
simple electrical phenomena will change. Thus, charge exchange is a 
symmetry operation, and evidently an important one. 

When the twentieth century came around, physicists learned that 
the positive charges in ordinary matter are always carried by protons, 
and the negative charges always by electrons. The protons and electrons 
could be found combined in various ways. But protons are not at all 
like electrons. For example, they weigh about two thousand times more. 
So the symmetry between electrical charge types seemed to be lost, once 
you imagined exchanging the particles which really carry the charges. 

Then came some remarkable discoveries. In the early thirties, it 
was found both by experiments and in theory that there are particles 
called positrons which share all the properties of electrons except that 
they have positive charge, not negative. By 1960 we had also found 
particles which share all the properties of protons save that they have 
negative charge. Thus, the symmetry of charge was restored, but in 



146 



Symmetry 



modified form. It was now clear that if you changed the charge, sub- 
stituting positrons for electrons and negative protons for protons, both 
together, the whole system should behave as before. The symmetry is 
shown to be more elaborate than we guessed. Charge must go with 
mass in just the right way. The new particles are called anti-particles, 
and their world is the anti-world. We do not really know if the anti- 
particles occur anywhere in large numbers. If they do, the anti-matter 
they make there must behave just the same as the matter we know and 
are made of, at least in all electromagnetic ways. 

The restoration of that simple symmetry of charge in such a full 
fashion has given physicists even greater respect for the power of the 
idea. Symmetry still rules the domain of fundamental physics. But just 
as with the charge symmetry, the further symmetries which we now 
seek are more subtle and complex than those which appear easily in 
drawings. But all can be described by our basic test — if we specify some 
operation upon a physical system and find it unchanged in some 
fundamental way as a result of that operation, then the operation in 
question is a symmetry operation, and we have catalogued yet another 
symmetry property of nature. 



1. Consider all the letters of the alphabet (excepting A and H, which EXERCISES 
you have already worried about), and arrange them in groups 
according to the classes of symmetry operations — rotation, reflec- 
tion, and inversion — under which they remain unchanged. In 

figuring out the symmetry classes, consider the letters as con- 
strained to remain in a plane — i.e., the letters cannot be rotated 
out of the plane of the paper. 

2. Consider a tennis ball or baseball, complete with seams, and 
describe its symmetry properties. Assume that the interior is 
homogeneous. {Suggestion: The real thing is a big help here, 
rather than trying to visualize from a two-dimensional picture or 
sketch.) 

3. Describe the symmetry properties of a card table, including the 
leg-folding mechanism. (Again, direct observation will help.) 

4. Trace the sketch of the crystal structure of graphite given in Fig. 
A.8c. Imagine yourself located at the position of one atom. Find 
and show with arrows on your tracing the three possible transla- 
tional movements of the lattice structure that will bring another 
carbon atom to your position with its surrounding atoms in an 
identical configuration to that seen from your position before the 
move. (These movements are the elements of translational sym- 
metry of that lattice, since they generate configurations indis- 
tinguishable from the original one.) We emphasize again that the 
sketch shows only a fragment of a structure assumed to extend 
indefinitely far in all directions. 

5 Given the fact that the Earth is a sphere, can you argue rigorously 
on symmetry grounds that "gravity" should pull objects toward 
the center of the Earth (as it does) rather than pulling them parallel 
to the surface? 



147 



SUPPLEMENTARY Feynman, Richard P., ROBERT B. Leighton, and Matthew Sands, Symmetry 
READINGS in Physical Laws, The Feynman Lectures on Physics. Reading, Mass.: 

Addison-Wesley Publishing Co., Inc., 1963, Chap. 52. Feynman provides 
a lively discussion of the meaning of the phrase "symmetrical behavior of 
physical laws" in contrast to pure geometrical symmetry. The author 
concentrates on mirror symmetry, concluding with a discussion of con- 
servation of parity. With hard thinking by students and a bit of embroidery 
in the form of detailed facts furnished by an instructor, this chapter is 
largely accessible to nonscience students. 
Stapp, Philip, with Judith Bregman, R. Davisson, and Alan Holden; 5^^- 
metry, a film (1967). Available from Contemporary Films, Inc., 267 W. 
25th St., New York, N. Y. 10001 . This film, which grew as an experimental 
project, uses visual and sound channels in an imaginative way to com- 
municate the nature of geometrical symmetries. Its content will be per- 
ceived very differently by students with different frames of reference and 
may communicate better than the linear, printed, or spoken word channel 
to some students. It deals entirely with two-dimensional figures. 
Weyl, Hermann, Symmetry. Princeton: Princeton University Press, 1952. (A 
large portion of the book is reprinted in James R. Newman, ed.. The 
World of Mathematics, vol. 1, New York : Simon and Schuster, Inc., 1962.) 
In this 145-page book, Weyl gives a beautiful overview of the role that 
symmetry, in both its aesthetic and mathematical senses, plays in art, 
biological systems, and crystals. Most of the book is roughly at the mathe- 
matical level of this section, and is quite accessible to the general student. 

Wood, E. A., Crystals and Light . Princeton : D. Van Nostrand Co., Inc., Momen- 
tum Paperback, 1964. Chapter 1, Symmetry, provides a clear exposition 
of the scheme for classifying geometrical symmetries. If one wishes to 
make an excursion mto crystallography, the field that employs ideas of 
geometrical symmetries most extensively. Chapter 2, Symmetry in Crystals, 
1 8 pages long, provides a sensible introduction. 



148 



Only one person in several thousand is a physicist. Should it 
matter to the others what he or she does, or that he or she is 
there at all? 



1 The Nature of Physics 

Physics Survey Committee NRC-NAS 

An excerpt from Physics in Perspective, 1973 



scire — to know 
scientia — knowledge 

Nam et ipsa scientia potest as est 

FRANCIS BACON (1561-1626) 

Of Heresies 

Introduction 

Science is knowing. What man knows about inanimate nature is physics, 
or, rather, the most lasting and universal things that he knows make up 
physics. Some aspects of nature are neither universal nor permanent— 
the shape of Cape Cod or even a spiral arm of a galaxy. But the forces 
that created both Cape Cod and the spiral arm of stars and dust obey 
universal laws. Discovering that has enabled man to understand more of 
what goes on in his universe. As he gains more knowledge, what would 
have appeared complicated or capricious can be seen as essentially simple 
and in a deep sense orderly. The explorations of physical science have 
brought this insight and are extending it— not only insight but power 
For, to understand how things work is to see how, withm environmental 
constraints and the limitations of wisdom, better to accommodate nature to 
man and man to nature. . 

These are familiar and obvious generalities, but we have to begm there 
if we want to discuss the value of physics in today's and tomorrow's world 
Going beyond generalities evokes sharp questions from several sides. Will 
the knowledge physicists are now striving to acquire have intrinsic value 
to man, whether it has practical application or not? Is it possible to promise 
that material benefits will eventually accrue, at least indirectly, from niost 
of the discoveries in physics? How does technology depend on fur her 
advances in physics (and vice versa)? How does physics influence other 
sciences? Is vigorous pursuit of new knowledge in physics still beneficia las 
it demonstrably was in the past, to chemistry, astronomy, and the other 
sciences for which physics provided the base? Is physics P^^^aps approach- 
ing the end of its mission, without very much more to discover? Has the 
physicist himself an intrinsic value to human society? Must he justify his 



149 




(Above) Hurricane Gladys was stalled west of Naples, Florida, when photo- 
graphed from Apollo 7 on October 17, 1968. Its spiraling cumuliform-cloud bands 
sprawled over hundreds of square miles. A vigorous updraft hid the eye of the storm 
by flattening the cloudtops against the cold, stable air of the tropopause (then at 
54,000 feet) and forming a pancake of cirrostratus 10 to 12 miles wide. Maximum 
winds near the center were then 65 knots. [From National Aeronautics and Space 
Administration, This Island Earth. O. W. Nicks, ed., NASA SP-250 (U.S. Government 
Printing Office, Washington, D.C., 1970).] 

(Below) NGC 3031, spiral nebula in Ursa Major photographed with the 200-inch re- 
flector of the Palomar Observatory. [Courtesy Hale Observatories] 



150 



The Nature of Physics 



work by relating it to pressing social problems? Only one person in several 
thousand is a physicist; will it matter to the others what he does, or that 
he is there at all? Or is that the right test to apply, no matter how it comes 
out? 

We speak briefly to such questions in this and the following chapter. 
The entire Report, including the reports of the various subfield panels, 
provides in copious detail answers to some of these questions or facts 
from which a reader can form his own judgment, for these are not questions 
that even all physicists would answer in just the same way. 



Fundamental Knowledge in Physics 

Mathematics deals with questions that can be answered by thought and 
only by thought. A mathematical discovery has a permanent and universal 
validity; the worst fate that can overtake it is to be rendered uninteresting 
or trivial by enclosure within a more comprehensive structure. Mathema- 
ticians make up, or one could say discover, their own questions in the 
timeless universe of logical connection. In a science such as geology, on 
the other hand, the questions arise from local, more or less accidental 
features of nature. How was this mountain range formed? Where was 
Antarctica two billion years ago? To answer such questions one has to 
sift physical evidence. The answers are not universal truths. Geology, as 
its name attests, differs from planet to planet. 

Physics, like geology, is concerned with questions that cannot be decided 
by thought alone. Answers have to be sought and ideas tested by experi- 
ment. In fact, the questions are often generated by experimental discovery. 
But there is every reason to believe that the answers, once found, have a 
permanent and universal validity. All the evidence indicates that physics 
is essentially the same everywhere in the visible universe. A physicist who 
asks, "Does the neutron have an electric dipole moment?" and turns to 
experiment to find out, could as well perform the experiment on any planet 
in any galaxy — it is just more convenient here at home. The question itself 
concerns a fact as general as (and perhaps even more basic than) the size 
of the universe. Physics is the only science that puts such fundamental 
questions to nature. 

Take the question: Do all electromagnetic waves, including radio waves 
and light waves, travel through empty space at the same speed? Present 
theories assume so, but the contrary is at least conceivable. Perhaps there 
is a difference so slight that it has not been noticed. To decide, the physicist 
must turn to experiment and observation. In fact, this particular question 
has recently received renewed attention. As not infrequently happens, the 
most sensitive test was applied by asking what sounds like a different ques- 
tion but can be shown to be logically equivalent. Indeed, the experimental 
evidence shows that the speed of long and short electromagnetic waves 
is the same to extraordinarily high precision. The result implies that the 
light quantum, the photon, cannot have an intrinsic mass as great as 10-" * 

* Physicists commonly use powers of 10 as a '^°^3^«"if"t ^Jl°;;J^^"^^^^^^ 
large numbers Thus, for example, 1000 becomes 10^ and 1,000 000 becomes 10 The 
numeral foHowed by zeros equal in number to the value of the exponent is the rule 
of thumb. This notation is used throughout the Report. 



151 



of the mass of an electron. No one was astonished by the result. Most 
physicists have always assumed the photon rest mass to be exactly zero 
and can only be relieved that such peculiarly perfect simplicity has survived 
closer scrutiny. Those who examined the evidence may have been a little 
disappointed — but their time was not wasted. 

This quite unsensational episode is characteristic of fundamental in- 
quiries in several ways. Fundamental experiments in physics often — indeed 
usually — yield no surprises. However, had the result been otherwise, it 
would not have demolished electromagnetic theory. A generalization or 
enlargement of the theory would have been necessary. Finally, the test, sen- 
sitive as it was, could not settle the question once and for all, for no real ex- 
periment achieves infinite precision. So the question will doubtless be raised 
again, in one form or another, should a new experimental technique or a 
bright idea create the opportunity for a significantly more stringent test. 
An equally fundamental assumption, the proportionality of inertial and 
gravitational mass, was tested in experiments of successively higher preci- 
sion by Newton (1686),Bessel (1823), Eotvos (1922), and Dicke (1964) 
— in the last case to an accuracy of 10-^\ 

Thanks to such relentless probing of its foundations, even where they 
appear comfortably secure, physics has acquired a base far more solid 
than is popularly appreciated. When a physicist states that a proton carries 
a charge equal to that of the electron, he can point to an experiment that 
proved any inequality to be less than one part in 10-". When he expresses 
confidence in the special theory of relativity, he can refer to a multitude of 
experiments under ultrarelativistic conditions in which even a slight failure 
of the theory would have been conspicuous. Electromagnetic interactions 
are today more completely accounted for — that is to say, better under- 
stood — than any other phenomena in physics. Quantum electrodynamics, 
the modern formulation of electromagnetic theory, has now been tested 
experimentally over a range of distance from 10^ cm down to 10-^' cm, a 
range of 10-\ This theory was itself developed in response to experiments 
that revealed small discrepancies in the predictions of the much less com- 
plete theory that preceded it. No one will be much surprised if quantum 
electrodynamics in its present form fails to work for phenomena involving 
still smaller distances; that will not diminish its glory or its validity within 
the vast range over which it has been tested. Nor did the extension of 
electromagnetic theory into quantum electrodynamics deny the essential 
truth of Maxwell's equations for the electromagnetic field. Knowledge 
thus won is about as permanent an asset as mankind can acquire. 

The most fundamental aspects of the physical universe are manifest in 
symmetries. In the history of modern physics, the concept of symmetry 
has steadily become more prominent. The beautiful geometrical symmetry 
of natural crystals was the first evidence of the orderliness of their internal 
structure. Exploration of the arrangement of atoms in crystals by x-ray 
diffraction, begun 60 years ago, has mapped the structure of thousands 
of substances and is now revealing in detail the architecture of the giant 
molecules involved in life. Meanwhile, physicists became concerned with 
more than just geometrical symmetry. Symmetry, in the broadest sense, 
involves perfect indifference. For example, if two particles are distinguish- 



152 



The Nature of Physics 



ably different in some ways but show absolutely the same behavior with 
respect to some other property, a physicist speaks of symmetry. The notion 
of identity of particles is intimately related. All these ideas acquire their 
real importance in quantum physics, where an object, a molecule for in- 
stance, is completely characterized by a finite number of attributes. 

In probing questions of symmetry in the domain of elementary particles, 
the physicist is again, like the first crystallographers, seeking a pattern of all- 
pervading order. A sobering lesson learned from modern particle physics, 
a lesson the Greek atomistic philosophers would have found unpalatable, is 
that man is not wise enough to deduce the underlying symmetries in nature 
from general principles. He has to discover them by experiment and be 
prepared for surprises. No one guessed before 1956 that left and right 
made a difference in the interaction of elementary particles. After it was 
found that the true and perfect indifference in the weak interactions is not 
left/right but left-electron/right-positron, it was again disconcerting to 
find even this rule of symmetry violated in certain other interactions. But 
it has by no means been all surprises. Symmetry rules guessed from 
scattered clues often have been amply corroborated by later experiments; 
and in particle physics, thinking about symmetries has been enormously 
fruitful. A grand pattern is emerging, largely describable in terms of 
symmetries, that makes satisfying sense. 

The primary goal of research in fundamental physics is to understand 
the interactions of the very simplest things in nature. That is a basis, 
obviously necessary, for understanding larger and more complicated organi- 
zations of matter anywhere in the universe. The shape of a particular 
galaxy is not, from this rather narrow point of view, a fundamental aspect 
of nature, but the motion of an electron in a magnetic field is fundamental 
and has implications for many things, including life on earth and the shapes 
of galaxies. 

However, physics has to be concerned with more than the elementary 
few-body interactions of particles and fields. It can be a gigantic step 
from an understanding of the parts to an understanding of the whole. To 
appreciate the total task of physics, a broader view of what is fundamental 
is necessary. Consider, for example, man's practically complete ignorance 
of the evolution of the flat, patchily spiral distribution of gas and stars that 
he calls his own (Milky Way) galaxy. (Only very recently some plausible 
theories have been developing; it is too early to say how much they can 
explain.) The interaction of molecules, atoms, ions, and fields is now 
well enough known for this problem, and Newtonian gravitation, on this 
scale, is unquestionably reliable. With these simple ingredients, why doesn't 
the problem reduce to a mere mathematical exercise? One good reason — 
perhaps not the only reason — is that a complete and general theory of 
turbulence is lacking. It is not just a lack of efficient methods of calculation. 
There is a gap in man's understanding of physical processes, which remains 
unclosed, even after the work of many mathematical physicists of great 
power. This gap is blocking progress on several fronts. When a general 
theory of turbulence is finally completed, which probably will depend on 
the work of many physicists and mathematicians, a significant permanent 
increase in man's understanding will have been achieved. That will be 



153 



fundamental physics, using both fundamental and physics in a broad sense, 
as, to take an example from the recent past, was the explanation of the 
mystery of superconductivity by Bardeen, Cooper, and Schrieffer. Although 
pedantically classifiable as an application of well-known laws of quantum 
mechanics, it was truly a step up to a new level of understanding. 

These two examples, turbulence and superconductivity, stand near op- 
posite boundaries of a wide class of physical phenomena in which the 
behavior of a system of many parts, although unquestionably determined 
by the interaction of the elementary pieces, is not readily deducible from 
them. Physicists know how to deal with total chaos — disorganized com- 
plexity. Statistical mechanics can predict anything one might want to know 
about a cubic centimeter of hydrogen gas with its 10^® molecular parts. As 
for the hydrogen molecule itself, it presents the essence of ordered simplic- 
ity. Its structure is completely understood, its properties calculable by 
quantum mechanics to any desired precision. What gives physicists trouble, 
to continue the classification suggested by Warren Weaver, is organized 
complexity, which is already present in a mild form in so familiar a 
phenomenon as the freezing of a liquid — a change from a largely dis- 
ordered to a highly ordered state. Here a general feature is that what one 
molecule prefers to do depends on what its neighbors are already doing. 
How drastically that feedback changes the problem is suggested by the lack 
of a theory that can predict accurately the freezing point of a simple liquid. 
In the physics of condensed matter, many such problems involving coop- 
erative phenomena remain to challenge future physicists. A turbulent 
fluid, on the other hand, confronts the physicist with a system in which 
order and disorder are somehow blended. Complex it certainly is, but 
not wholly disorderly, admitting no clean division between the random 
flight of a molecule of the fluid and the organized motion of a row of eddies. 

The solution of these major problems of organized (or partly organized) 
complexity is absolutely necessary for a full understanding of physical 
phenomena. Extraordinary insight and originality will surely be needed, 
as indeed they always have been. The intellectual challenge is as formidable 
as that faced by Boltzmann and Gibbs in the development of statistical 
mechanics. The consequences for science of eventual success could be as 
far-reaching. 

Broadly speaking then, the unfinished search for fundamental knowl- 
edge in physics concerns questions of two kinds. There are the primary 
relations at the bottom of the whole structure. How many remain to be 
discovered and how small the number to which they can ultimately be re- 
duced are not yet known. Then there is the knowledge needed to understand 
all the behavior of the aggregations of particles that make up matter in 
bulk. Here the mysteries are perhaps not so deep, although the remaining 
unsolved problems are of formidable and subtle difficulty. It is easier to 
imagine how this part of the development of fundamental physics could 
be concluded, if the even more difficult problem of organized complexity 
in living organisms is left for the physiologist, assisted by the biochemist and 
biophysicist, to solve. 

What has been learned in physics stays learned. People talk about 
scientific revolutions. The social and political connotations of revolution 



154 



The Nature of Physics 



evoke a picture of a body of doctrine being rejected, to be replaced by 
another equally vulnerable to refutation. It is not like that at all. The 
history of physics has seen profound changes indeed in the way that 
physicists have thought about fundamental questions. But each change 
was a widening of vision, an accession of insight and understanding. The 
introduction, one might say the recognition, by man (led by Einstein) of 
relativity in the first decade of this century and the formulation of quantum 
mechanics in the third decade are such landmarks. The only intellectual 
casualty attending the discovery of quantum mechanics was the unmourned 
demise of the patchwork quantum theory with which certain experimental 
facts had been stubbornly refusing to agree. As a scientist, or as any 
thinking person with curiosity about the basic workings of nature, the reac- 
tion to quantum mechanics would have to be: "Ah! So that's the way it 
really is!" There is no good analogy to the advent of quantum mechanics, 
but if a political-social analogy is to be made, it is not a revolution but the 
discovery of the New World. 



The Question of Value 

Most people will concede that fundamental scientific knowledge is worth 
its cost if it contributes to human welfare by, even indirectly, promoting the 
advance of technology or medicine. It is easy to support a claim for much 
of physics. But now that some frontiers of fundamental research have 
been pushed well beyond the domain of even nuclear engineering, that 
justification is not always plain to see. A connection between many-body 
theory and the latest semiconductor device is not much more difficult to 
trace than the connection between thermodynamics and a jet engine. But 
it is not easy to foresee practical applications of the fundamental knowledge 
gained from very-high-energy experiments or, say, tests of general relativity. 

Two responses can be made, each of which has some validity. First, 
inability to foresee a specific practical application does not prove that there 
will be none. On the contrary, that there almost certainly will be one 
has become a tenet of conventional wisdom, bolstered by familiar examples 
such as Rutherford's denial of the possibility of using the energy of the 
nucleus. Applying this principle to strange-particle interactions will prob- 
ably raise fewer doubts among laymen than among physicists. Even here 
the conventional wisdom may be sound after all. High-energy physics is 
uncovering a whole new class of phenomena, a "fourth spectroscopy" as it 
is termed elsewhere in this Report. In the present state of ignorance, 
it would be as presumptuous to dismiss the possibility of useful application 
as it would be irresponsible to guarantee it. 

A secondary benefit that can be expected, as a return for supporting 
such research, is the innovation and improvement in scientific instrumenta- 
tion that such advanced experiments stimulate. (This point is discussed in 
a subsequent section of this chapter on the contributions of physics to 
technology.) Other sciences also benefit from the development of experi- 
mental techniques in physics. „,L ■ r J 

But these responses do not squarely face the question: What is funda- 



155 



mental knowledge itself worth to society? Elementary-particle physics 
provides an example. A permanent addition to physicists' knowledge of 
nature was the recognition, several years ago, that there are two kinds of 
neutrino. This fact, although compatible with then existing theory, was not 
predictable a priori, nor is the reason understood. The question was put to 
nature in a fairly elaborate high-energy experiment, at a total monetary 
cost that reasonable accounting might put at $400,000 (not including beam 
time on the Alternating Gradient Synchrotron Accelerator). The answer 
was unequivocal: The electron neutrino and the muon neutrino are not 
identical particles. 

For physics this was a discovery of profound significance. Neutrinos are 
the massless neutral members of the light-particle or lepton family, of 
which the familiar electron and its heavier relative, the muon, are the only 
other known members. Just how these particles are related — even why 
there is a muon — is one of the central puzzles of fundamental physics, a 
puzzle that is as yet far from solution. Obviously, it was not about to be 
solved while physics remained ignorant of the fact that there are two kinds 
of neutrino, not just one. 

Still, how does this bit of knowledge benefit the general public, interesting 
as it may be to the tiny fraction of scientists who know what "two kinds" 
means in this connection? The answer must be that the discovery was a 
step — a necessary step — toward making nature comprehensible to man. 
If man is going to understand nature, he has to find out how it really is. 
There is only one way to find out: Experiment and observe. If man does 
not fully understand the leptons, he cannot claim to understand nature. 

On the other hand, the neutrino is a rather esoteric creature. It would 
be absurd to expect wide and instant appreciation of this fundamental 
discovery. Even of fundamental knowledge there is too much for most 
people to absorb. Many a physicist who could calculate on the back of an 
envelope the neutrino flux from the sun remains complacently ignorant of 
the location and function of the pituitary gland in his body. The point is 
that the value of new fundamental knowledge must not be measured by 
the number of people prepared to comprehend it. To say that man 
understands this or that aspect of nature usually means that some people do, 
and that they understand it sufficiently well to teach it to any who care to 
learn and to maintain a reliable base from which they or others can explore 
still turther. The great thing about fundamental scientific knowledge is that 
it is an indestructible public resource, understandable and usable by anyone 
who makes the effort. When so used in its own domain, it is a thing of 
beauty and power. 

The great American physicist Henry Rowland once replied to a student 
who had the temerity to ask him whether he understood the workings of the 
complicated electrostatic machine he had been using in a demonstration 
lecture: "No, but I could if I wanted to." Knowledge of fundamental 
scientific laws makes for economy of human thought. It is the great simpli- 
fier in a universe of otherwise bewildering complexity. It is not necessary 
to analyze every cogwheel in an alleged perpetual motion machine to know 
that it will not work or to keep tracking all the planets to be sure that they 
are not about to collide. The revelation that the electron and muon neu- 



156 



The Nature of Physics 



trinos are different, although it might appear to have complicated matters, 
was in fact a step toward ultimate simplicity, because it brought closer the 
essential truth about leptons. 

Some of the fundamental ideas of physics have slowly become part of the 
mental furnishings of most educated people. The following statements 
probably would elicit general assent: All substances are composed of atoms 
and molecules; nothing travels faster than light; the universe is much larger 
than the solar system and much older than human life; energy cannot 
be obtained from nothing, but mass can be turned into energy; motions of 
planets and satellites obey laws of mechanics and gravity and can be pre- 
dicted precisely. That is surely a rather meager assortment, but, even so, 
what an immense difference there is between knowing these few things and 
not knowing them — a difference in the relation of a person to his world. 
A child asks his father "What is a star?" or "How old is the world?" 
In this century he can be answered, thanks to hard-won fundamental 
knowledge. What is that worth? The answers can hardly contribute to 
anyone's material well-being, present or future. But they do enlarge the 
territory of the human mind. 

Much of what modern physics has learned has not yet become common 
knowledge. Here is an example. Not only physicists but everyone who 
has studied quantum mechanics knows that all known particles, without 
exception, fall into one or the other of just two classes, called fermions and 
bosons, which differ from one another profoundly on a certain question 
of symmetry. The difference is as fundamental as any difference could be. 
Although usually expressed somewhat abstractly, the distinction is less 
recondite than some theological distinctions over which men have quarreled 
fiercely. Its concrete manifestations are vast, among them the astonishing 
properties of superfluid helium (a boson liquid), the electrical properties 
of metals, and, indeed, through the Pauli exclusion principle, the very 
existence of atoms and molecules, hence of life. Now it would seem that 
this profound, essentially simple truth about the physical universe ought 
to be known to most fairly well-educated persons, to as many, perhaps, as 
understand the difference between rational and irrational numbers. Yet, 
it is probably safe to say that a majority of college graduates have never 
heard of fermions and bosons, and that an even larger majority is not 
equipped to understand what the distinction means. Probably far less than 
10 percent of current college graduates have had a course in physics or 
chemistry in which the exclusion principle was mentioned. Perhaps 10 
percent will learn enough mathematics so that, if they are interested, they 
could be made to understand a statement such as "the wavefunction changes 
sign on exchange of particles." 

But can anyone except physical scientists be interested in such a ques- 
tion? History suggests that it is possible. Long before the atomic bomb 
made mc- a catchword, the theory of relativity (both special and general) 
engaged the public interest more intensely than anything else in twentieth 
century physics. The fascination lay not only in the enigmatic figure of 
Einstein and the notion of a theory that, as the newspapers were fond 
of claiming (quite erroneously), only 12 men could understand. There 
was at the same time a sustained, genuine intellectual interest, at all levels 



157 



of understanding commencing with zero, in the puzzling implications of 
new ideas about space and time. To this day, nothing beats the twin 
paradox for stirring up spirited argument in an elementary physics class. 
People who have any interest at all in ideas seem to be more interested, 
on the whole, in fundamental questions than in practical questions. It is 
usually easier to interest an intelligent layman in the uncertainty principle 
than in how the mass spectrograph works. Of course, that is true only 
if he or she can be given some idea, not wholly superficial, of the meaning 
of the uncertainty principle. This can be done; it has been accomplished 
many times, in different styles, by imaginative teachers and writers. Nor is 
it hard to convey to a thoughtful person the essential notion of antimatter, 
or the question of left- and right-handedness in nature, both ideas that 
intrigue many nonscientists. It may even turn out that nonphysicists of 
the next generation, many of whom were brought up with the new math 
and are on speaking terms with computers, will find the abstract rules of 
particle physics a more satisfying statement about nature than would an 
old-fashioned physicist. 

Admittedly, there are difficulties in engaging the active interest of non- 
scientists in some of the most fundamental ideas of physics. They 
are illustrated in the example of the fermion-boson distinction. Unlike 
relativity, this subject makes no connection with familiar concepts such as 
time, space, and speed. No paradox or controversy stirs the imagination in 
first acquaintance. The intelligent layman can only listen to the explanation 
of fermions and bosons as if he were hearing a story about another world. 
There is nothing to argue about. It may serve as brief intellectual enter- 
tainment; most likely it will not impinge on or disturb the ideas he already 
has. He may not be eager to tell someone else about it. In that case it 
can hardly be claimed that the person has gained something of permanent 
value to him. And yet, when followed to a slightly deeper level, this idea 
has a direct bearing on a question that has engaged human throught for 
2000 years — the ultimate nature of substance. It gives a most extraordinary 
answer to philosophical questions about identity of elementary particles, 
questions that were already implicit in the cosmology of Democritus but 
were never faced before quantum mechanics. Here, too, is a key to the 
wave-particle duality with which the quantum world confounded man's 
mechanistic preconceptions. The philosophical implications of the fermion- 
boson dichotomy are still, after 40 years, poorly understood by philosophers. 

So the problem is one of teaching. Very many people who are not 
scientists are interested or can be interested in the basic questions that have 
always attracted human curiosity. The discoveries of physics, even those 
presently described in abstruse language, bear directly on some of these 
questions — so directly that when understood they can transform a person's 
conception of the atomic world or the cosmos. To promote that under- 
standing is a task for the scientist as teacher, in the broadest sense of 
teacher. In the short run, drawing a potential audience from college 
graduates of the past 20 or 30 years, and perhaps the next 10, the physicist 
must apply his imagination and ingenuity to convey interesting and mean- 
ingful, and essentially true, accounts of some of the fundamental develop- 
ments in physics. It is to be hoped that some day the educated layman 



158 



The Nature of Physics 



he addresses will have had enough physical sciences and mathematics in 
his general education to turn a discussion of the symmetries of elementary 
particles into some sort of dialogue. 

The audience need not be of a size that would impress a national 
advertiser but only a few million people — a few hundred, say, for every 
physicist. Of course, the distribution of potential interest and comprehen- 
sion is a many-dimensional continuum. Everyone ought to be, and can be, 
given some glimpse of what fundamental physics is about. However, it is 
impossible to compare the value of a brief exposure of 10" people to news 
of a discovery in physics with the value of sustained and active interest on 
the part of 10® people. Both are valuable now, and both will help, in the 
long run, to make the fundamental knowledge that physics is securing mean- 
ingful and useful to all people. 

The value of new fundamental scientific knowledge is not, after all, 
contingent on its appreciation by contemporary society. It really does not 
matter now whether Clerk Maxwell's ideas were widely appreciated in 
Victorian England. Their reception is interesting to the historian of science, 
but mainly as a reflection of the attitudes and structure of the society in 
which Maxwell worked. The full value of a scientific discovery is concealed 
in its future. But even as the future unfolds, the value that one may set 
on an isolated piece of fundamental knowledge often becomes uncertain 
because of the interconnection in the growing structure. In the end, one is 
forced to recognize that there is just one structure; understanding of the 
physical universe is all of one piece. 



Physics and Other Sciences 

Physics is in many ways the parent of the other physical sciences, but the 
relation is a continually changing one. Modern chemistry is permeated with 
ideas that came from physics, so thoroughly permeated, in fact, that the 
sudden demise of all physicists — with the exception of an important class 
calling themselves chemical physicists — would not immediately slow down 
the application of physical theory to chemical problems. The last great 
theoretical contribution of physics to chemistry was quantum mechanics. 
For another such contribution there is no room, almost by the definition 
of chemistry. From the point of view of the physicist, chemistry is the 
study of complex systems dominated by electrical forces. Strong inter- 
actions, weak interactions, gravitation— these are of no direct interest to 
the chemist. There is no reason to doubt, and voluminous evidence to show, 
that quantum mechanics and electromagnetic theory as now formulated 
provide a complete theoretical foundation for the understanding of the 
interactions between atoms and molecules. 

An immense task remains for the theoretical chemist, a task that is in 
some part shared by the physicist interested in the same problems. One area 
of common interest is statistical mechanics, especially the theory of "coop- 
erative" phenomena such as condensation and crystallization, where, al- 
though the forces that act between adjacent molecules are known, the 
behavior of the whole assembly presents a theoretical problem of singular 



159 



subtlety. Other problems that attract both chemists and physicists include 
phenomena on surfaces, properties of polymers, and the fine details of the 
structure and spectra of simple molecules. A subject of very intense 
research in which physics and chemistry are thoroughly blended is the 
study, both experimental and theoretical, of reactions in rarefied partially 
ionized gases. This study has direct applications in plasma physics, the 
development of high-power lasers, the physics of the upper atmosphere, and 
astrophysics. 

There is really no definable boundary between physics and chemistry. 
There never has been. Approximately 5000 American scientists, on a rough 
estimate, are engaged in research that would not be out of place in either 
a physics or a chemistry department. Some call themselves physicists and 
their specialty chemical physics or just physics. Others are physical chem- 
ists. The label generally reflects the individual's graduate training and 
correlates with some differences of interest and style. These chemical 
physicists have illustrious predecessors, including Michael Faraday and 
Willard Gibbs. And those who, like them, have made a permanent mark 
on both sciences are likely to be thought of as physicists by physicists and 
chemists by chemists. 

Physics serves chemistry in quite another way. It is the source of most 
of the sophisticated instruments that the modern chemist uses. This 
dependence on physics has been, if anything, increasing. Perhaps the in- 
frared spectrograph and the x-ray diffraction apparatus should be credited 
to the physics of an earlier era; their present highly refined form is largely 
the result of commercial development stimulated by users. But mass spec- 
trographs, magnetic resonance equipment, and microwave spectrometers, 
all of which originated in physics laboratories in relatively recent times, 
are found in profusion as well as are the more general electronic com- 
ponents for detecting photons and atoms — electron multipliers, low-noise 
amplifiers, frequency standards, and high-vacuum instrumentation. One 
might follow a research chemist around all day, from spectrograph to com- 
puter to electronic shop to vacuum chamber, without deducing from ex- 
ternal evidence that he was not a physicist, unless, as might still happen 
today, the smell of his environment gave it away. 

Radiochemistry is in a class by itself. The radiochemist and the nuclear 
physicist have been partners indispensable to one another since before 
either specialty had a name. The dependence of experimental nuclear 
physics on radiochemical operations is perhaps less conspicuous, seen 
against the whole enterprise of nuclear physics, than it was 10 or 20 years 
ago. On the other hand, advances in the use of labeled elements and 
compounds in chemical, biochemical, and medical research continue to be 
paced by improvements in detection methods. These came directly from 
physics. A spectacular recent example is the solid-state particle detector, 
with parentage in nuclear physics and solid-state physics. 

Instead of viewing physics and chemistry as different though related 
sciences, it might make more sense to consider a science of substances, 
with its base in quantum physics and objects of study ranging from the 
crystalline semiconductor (now assigned to the solid-state physicist) to 
the alloys of the metallurgist, to the molecular chain of high-polymer 



160 



The Nature of Physics 



physics and chemistry, to the elaborate molecular structures of the organic 
chemist. Through this whole range of inquiry one can discern a remark- 
able convergence in theoretical treatment, and also in experimental meth- 
ods. The first comes about as fundamental understanding replaces phe- 
nomenology. When the properties of the complex system, be it a boron 
whisker or a protein molecule, can be systematically deduced from the 
arrangement of its elementary parts, which are nothing but atoms gov- 
erned by quantum mechanics, a universal theory of ordinary substances 
will be at hand. Such a theory has not yet been achieved, but as theoretical 
methods become more powerful, they become, as a rule, more general, 
and there is steady progress in that direction. Already the language of 
theory in organic chemistry is much closer than it used to be to the language 
of theory in solid-state physics. 

The convergence in experimental methods, which of course should never 
become complete, also reflects the tendency of more powerful analytic 
methods to be more general. The scanning electron microscope is equally 
precious to the biochemist and the metallurgist. The infrared spectrograph 
is almost as ubiquitous as the analytic balance. Radioactive labeling is 
practiced in nearly all the physical sciences. 

Notwithstanding the staggering accumulation of detailed information 
in the materials sciences, a drastic simplification of scientific knowledge 
is occurring in these fields. As the facts multiply, the basic principles 
needed to understand them all are being consolidated. To be sure, the need 
for specialization by individuals is not declining; the quantity of information 
vastly exceeds what one mind can assimilate. But the specialist is no longer 
the custodian of esoteric doctrine and techniques peculiar to his class of 
substances. Quantum physics is replacing the cookbook, and the mass 
spectrograph is replacing the nose. The future organic chemist acquires 
a rough working knowledge of quantum mechanics very early — often 
earlier, the physicist must concede with chagrin, than his roommate who 
is majoring in physics. Soon, if it is not already so, any single section of 
this enormously rich and varied picture will be understood at a funda- 
mental level by anyone equipped with a certain common set of intellectual 
tools. 

Well under way here is nothing less than the unification of the physical 
sciences. This unification is surely one of the great scientific achievements 
of our time, seldom recognized or celebrated, perhaps, because, having 
progressed so gradually, it cannot be seen as an event. Nor can it be 
credited to one science alone. The influence of quantum physics on 
chemistry was clearly a central development, and, if one wishes to sym- 
bolize that development by one of its landmarks, there is Linus Pauling's 
The Nature of the Chemical Bond. In physics there are many landmarks 
in the theory of condensed matter, from the first application of quantum 
theory to crystals by Einstein and Debye to the solution of the riddle of 
superconductivity, among them the quantum theory of metals, the under- 
standing of ferromagnetism, and the discovery of the significance of lattice 
imperfections in crystals. But the basic contribution of physics is the 
secure foundation on which all this knowledge is built— on understanding, 
confirmed by the most stringent experimental tests, of the interactions 



161 



between elementary particles and the ways in which they determine the 
structure of atoms and molecules. The fruits of this immense achievement 
are only beginning to appear. 

Biology obviously derives part of its nourishment from physics by way 
of chemistry. Biochemistry and molecular biology are equally dependent 
on physical instrumentation. X-ray diffraction, electron microscopy, and 
isotopic labeling are indispensable tools. Modern electronics is important 
in physiology, most conspicuously in neurophysiology, where spectacular 
progress has been made by observing events in single neurons, made ac- 
cessible by microelectrodes and sophisticated amplifiers. Other examples 
are described in the Report of the Panel on Physics in Biology. 

These are products of past physics. One might wonder whether future 
physics is likely to prove as fruitful a source of new experimental techniques 
for biology and medical science. There are two reasons for thinking that 
it will. First, there is no apparent slackening of the pace of innovation 
in experimental physics. In almost every observational dimension, short 
time, small distance, weak signal, and the like, the limits are being pushed 
beyond what might have been reasonably anticipated. If there is one thing 
experience teaches here, it is that quite unforeseen applications eventually 
develop from any major advance in experimental power. Through the 
Mossbauer effect, preposterous as it seems, motions as slow as that of the 
hand of a watch can be measured by the Doppler shift of nuclear gamma 
radiation. Even after this discovery, when Mossbauer experiments were 
going on in dozens of nuclear-physics laboratories, a physiological appli- 
cation would have seemed rather fanciful. In fact, the Mossbauer effect 
is being used today to study, in the living animal, the motion of the 
basilar membrane in the cochlea of the inner ear, perhaps the central 
problem in the physiology of hearing. 

There is another reason to look forward to contributions to the life 
sciences from inventions not yet made. It is the existence of some obvious 
and rather general needs, the satisfaction of which would not violate 
fundamental physical laws, for example, an x-ray microscope with which 
material could be examined in vivo with a resolution of, say, 10 A or a 
better way of seeing inside the body than the dim shadowgraphs, remark- 
ably little better than the first efforts of Roentgen, that medical science 
has had to be content with for half a century. But the breakthroughs prob- 
ably will again come in unexpected ways; one cannot guess what will 
play the role of Roentgen's Crookes tube. The physicist can only feel 
rather confident that an active, inventive period in experimental physics 
eventually will have important effects on the way research is done in the 
biological sciences. 

The intellectual relations between physics and biology are changing, 
perhaps more because of what is happening in biology than what is 
happening in physics. Most physicists who have any acquaintance with 
biology, if only through semipopular accounts of the latest discoveries, 
find the ideas of current biology, especially molecular biology, intriguing 
and stimulating. No physicist could fail to be stirred by the elucidation 
of the genetic code or by the other glimpses into primary mechanisms 
of life. This wonderful apparatus works by physics and chemistry after 



162 



The Nature of Physics 



all! But it is far more ingenious and subtle than any contrivance of wires, 
pulleys, and batteries. From the intricate engine of muscle fiber to the 
marvelous information processer in the eye, plainly there are hundreds of 
mechanisms in which physics, chemistry, and biological function are 
inextricably involved. Also, the evident universality of basic processes in 
the cell appeals strongly to a mind trained in the physicist's approach to 
structure and function. There is no doubt that biology is going to attract 
some students who would have made good physicists, which cannot be de- 
plored. It is to be hoped that there soon will be a growing number of biolo- 
gists who are not only well grounded in physics but who share, and possibly 
derive some encouragement from, the physicist's conviction that the be- 
havior of matter can be understood in terms of the interactions of its 
elements; this behavior and these interactions are the goals of experimental 
study. 

At the other end of the scale is astronomy. Physics began with astron- 
omy, but after the foundations of Newtonian mechanics were secured, 
astronomical observations (not counting as such the observations of cosmic 
rays) did not directly generate new fundamental physics. However, as- 
tronomy did provide a rich field for the application of physics. Great 
advances in astronomy such as the elucidation of the structure and evolu- 
tion of stars depended on an understanding of the structure of atoms. That 
came from the physics laboratory and from quantum theory as it developed. 
Then it was nuclear physics that supplied the keys to the generation of 
energy in the stars and to the production of the elements. These questions 
were highly interesting to physicists and inspired both theoretical and 
experimental work. But, broadly speaking, this work was merely physics 
applied to astronomical problems. 

At a different level, though, astronomy has always had a powerful intel- 
lectual influence on physics. The heavens confronted man with tantalizing 
mysteries. His conceptions of what he saw there strongly influenced 
philosophical attitudes toward nature. Astronomy has given the physicist 
confidence that the universe at large is governed by beautifully simple laws 
of physics, discoverable from earth by man. That belief gives the explora- 
tions of physics a wider purpose and significance. It attracts the physicist's 
attention to cosmological questions, to the physics of gravitation, and to 
phenomena occurring under conditions utterly unattainable in a terrestrial 
laboratory. 

Today the interaction of physics and astronomy is more vigorous than 
at any time since Newton. Astronomy has entered an astonishingly rich 
period of significant discovery. This is due, in part, to observing over a 
greatly widened spectrum, from the long waves of radio astronomy, which 
have in 25 years greatly increased the knowledge of the large-scale universe, 
to X rays and gamma rays, which are just beginning to produce interesting 
information. In part, too, it reflects the increased power and scope of 
astrophysical theory, working from a more complete base in atomic and 
nuclear physics. Also, nature has provided some incredibly marvelous, 
totally unexpected features for telescopes to discover, displaying on a grand 
scale phenomena that involve most of physics. Less than ten years after 
the maser was invented in a physics laboratory, the maser process was 



163 



found to occur in clouds of interstellar gas. It is typical of the present 
intensive involvement of physicists in astronomy that this discovery was 
made by some of the same physicists, now turned radio astronomers, who 
had participated in the microwave spectroscopy that led to the invention 
of the maser. 

Nuclear physicists and astrophysicists have been engaged for more than 
20 years in a collaboration from which has come not only an understanding 
of the source of energy in stars but of the production of the chemical ele- 
ments found in the universe. This knowledge bears directly on the history 
of the universe, providing much of the solid evidence against which cosmo- 
logical theories can be tested. More surprising is the emerging importance 
to astronomy of elementary-particle physics. The opacity of matter to 
neutrinos turns out to be relevant not only to the reconstruction of a 
primordial big bang but to what is going on now at the centers of galaxies. 
Inside pulsars there is almost certainly "hyperonic" matter, composed of 
particles more massive than protons, known only in the laboratory as 
evanescent products of high-energy collisions. Perhaps a not negligible 
fraction of the matter in the universe is compressed into this state, a form 
of matter hardly speculated about before pulsars were discovered five years 
ago. It may be difficult to forecast commercial applications on planet Earth 
for high-energy physics, but its importance in the universe as a whole may 
have been greatly underestimated. 

Of course, cosmic rays have been studied by physicists, not astronomers, 
for 50 years; and these particles, still the most energetic a physicist can 
hope to see, have been transcendentally important in the development of 
modern physics. It is hard to imagine how elementary-particle physics 
would have progressed if the earth had been shielded from cosmic rays. 
Although the source of cosmic rays was obviously astronomical, it is only 
rather recently that the importance of cosmic radiation as a constituent of 
the interstellar medium has been appreciated. Something like a merger 
of cosmic-ray and related high-energy physics with astrophysics has taken 
place; the new Division of Cosmic Physics in the American Physical 
Society is one indication. Magnetohydrodynamics and plasma physics are 
very lively subjects of common interest to members of both groups. Beyond 
these obvious cases of interest, even solid-state physicists have been drawn 
into astrophysics by the discovery of neutron stars. 

In the same period, a resurgence of interest in gravitation has occurred 
among both astronomers and physicists — among astronomers because of 
the discovery of systems close to the theoretical conditions for gravitational 
collapse and among physicists because of experimental developments that 
bring some predictions of gravitational theory within the range of significant 
laboratory test. 

All these developments are bringing again to physics and astronomy a 
wonderful unity of interest. Never before have so many parts of physics 
directly concerned astrophysicists; seldom before have astronomical phe- 
nomena so stirred the imagination of physicists. 

The cosmos is still the place where man must look for answers to some 
of the deepest questions of physics. Were the fundamental ratios that 
characterize the structure of matter as found here and now truly pre- 



164 



The Nature of Physics 



cisely constant for all time? Observations of distant galaxies offer a 
view backward in time to an earlier stage of the universe. Is Einstein's 
general relativity an exact and complete description of gravitation? Is the 
visible universe a mixture of matter and antimatter in equal parts, or is 
what is called matter overwhelmingly more abundant throughout? Already 
astronomers have observations that bear on these questions. The conclu- 
sions are only tentative now, but it seems quite certain that the questions 
will be answered. 

As for the earth sciences, a gap no longer exists between astronomy 
and geology. A look at the relation of physics to the earth sciences shows 
a network of interconnected problems, stretching from the center of the 
earth to the center of the galaxy. The earth's magnetic field provides a 
good example. How it is generated has always been a puzzle. Now it 
appears, although the explanation is not complete, that magnetohydro- 
dynamic theory is about to produce a convincing picture of the electric 
dynamo that must be at work within the earth's fluid core. Furthermore, 
the same ideas may explain the generation of magnetic fields of stars and 
even, when applied on a very different scale, the magnetic fields that 
pervade the whole galaxy. These developments are the work of both 
geophysicists and astrophysicists, many of them people whose breadth of 
interest would justify both titles. In addition, the interplanetary magnetic 
fields in the solar system, which are dominated by the solar wind, are of 
interest to both the planetary physicist and the solar physicist. 

The theoretical base for these interrelationships is the dynamics of 
highly conducting fluids, including ionized gases, which is also the base for 
such potentially important engineering developments as the magnetohydro- 
dynamic generator. Not new fundamental physics but ingenious and in- 
sightful analysis and the development of more powerful theoretical tools are 
needed. 

From the point of view of physics, the other sciences might be grouped 
into four very broad divisions: a science of substances, including chemistry 
and also a part of physics; life sciences; earth sciences plus astronomy (for 
which a good name that will comprehend the range from meteorology to 
cosmology is lacking); and engineering science. These divisions are, of 
course, multiply overlapping, with a topology that would defy a two- 
dimensional diagram. A category of current interest, environmental science, 
would overlap all four. 

Engineering science is suggested as a fourth division, although it is not 
as extensive or as well recognized as the others, to emphasize a distinction 
between the products of technology and the growing body of knowledge — 
scientific knowledge — that constitutes the intellectual capital of engineering. 
To this knowledge both engineers and physicists contribute continually, 
with a mutual stimulation of ideas. To call different portions of this body 
of knowledge mere applied mathematics does not do justice to the imagina- 
tive work that goes on or to the potential influence on the other sciences 
of the ideas generated. A previously mentioned example is the important 
subject of fluid dynamics, with its ubiquitous problem of turbulence, in 
which engineering science naturally has a big stake. Consider, as another 
example, communication theory, developed in its many aspects by people 



165 



calling themselves variously engineers, mathematicians, and physicists. 
Sophisticated treatments of fluctuation phenomena, including quantum 
effects, the relation of information to entropy, and the rich ramifications — 
including holography — of Fourier duality are just a few of the ideas it 
encompasses. Or consider the theory of automatic control with feedback, 
which was developed mainly within engineering science but is now an indis- 
pensable aid in most experimental sciences, including physics. The point is 
that between physics and engineering science there are strong intellectual, 
one might even say cultural, links. That is only one aspect of the relation 
of physics to technology, a topic explored more fully in the following 
section. 

No one would question the importance of physics in the development 
of these fields of science. However, because chemistry needed physics does 
not necessarily imply that chemistry now needs help from physicists. 
Physicists have made fairly direct contributions to chemistry, even recently; 
and physics, at least as a source of new experimental tools and techniques 
for other sciences, may be as fruitful a source in the immediate future 
as it has been in the past. But can essential contributions from physics to 
the other sciences in the form of new and basic ideas be expected? Do the 
chemists or the earth scientists, who have fairly well assimilated the appar- 
ently relevant parts of physics, need the physicist for any service except to 
teach physics to their students? What is their interest in his hunt for quarks 
or gravity waves? 

There are two ways to answer such questions from the physicist's point 
of view. One can meet example with example, explaining, for instance 
(as will be done in Chapter 4 when this question is addressed with 
specific reference to high-energy physics), how the isolation of the quark 
could have immense practical consequences. Or one can make a more 
general reply along the following lines. The increasing unity of the 
physical sciences at the basic level and the proliferation of interconnec- 
tions among the fields, and especially with physics, make intellectual vigor 
widely contagious. New ideas tend to stimulate other new ideas. As 
long as physics has great questions to work on, its discoveries can hardly 
fail to excite resonances in neighboring fields. 



Technology and Physics: Their Mutual Dependence 

Everyone knows that today the main sources of new technology are 
research laboratories of physics and chemistry and not the legendary 
ingenious mechanic or Edisonian wizard. Actually, the relation of tech- 
nology, that is, applied science, to basic science has been close for more 
than a century. Think of Faraday, Kelvin, Pasteur. It is true that Morse 
and Bell were amateurs in electricity, while Maxwell, it is said, found 
the newly invented telephone not interesting enough to serve as a subject 
of a scientific lecture. But the sweeping exploitation of electromagnetism 
that began in the latter half of the nineteenth century was based directly on 
the fundamental understanding achieved by Maxwell. No one would suggest 
that today's semiconductor technology could have been created solely by 



166 



The Nature of Physics 



engineers ignorant of the relevant fundamental physics. Research in physics 
provided the base from which present technology is developing. 

But physics research did, and is doing, more than that. Research is a 
pov^^erful stimulator of fresh ideas. One reason is that in research, and 
especially in the most fundamental research, the scientist is often trying 
to break new ground. He may need to measure something at higher energy 
(remember Van de Graaff and the electrostatic generator) or closer to 
absolute zero (Kamerlingh Onnes discovering superconductivity) or in a 
previously inaccessible band of the spectrum. Years before World War II 
the magnetron was first exploited for the generation of 1-cm waves by the 
physicists Cleeton and Williams at the University of Michigan. They 
used it to make the first observation of the inversion resonance of the 
ammonia molecule. 

Also, and this applies to both experimental and theoretical research, to 
be challenged by a puzzling phenomenon stimulates the imagination. One 
is likely to try looking at things from a new angle, questioning assumptions 
that had been taken for granted. P. W. Bridgman once described the 
scientific method as "the use of the mind with no holds barred." The unin- 
hibited approach of the research scientist to a strange problem has even 
generated a whole discipline — operations research. Prominent among its 
creators were scientists like P. M. S. Blackett and E. G. Williams, who 
came from fundamental physics research, both experimental and theo- 
retical, of the purest strain. 

The research laboratory, including the theoretical physicist's blackboard 
or lunch table, provides the kind of freewheeling environment in which 
an idea can be followed for a time to see where it leads. Most new ideas are 
not good. In a lively research group these are quickly exposed and dis- 
carded, often having stimulated a fresh idea that may be more productive. 

In such a setting, physicists are not generally intellectually constrained 
by the distinction between fundamental science and technology. For one 
thing, experimental physics heavily depends on some very advanced 
technology. The research physicist is not only at home with it, he has 
often helped to develop it, adapt it, and debug it. He is part engineer by 
necessity— and often by taste as well. An experimental physicist who is 
totally unmoved by a piece of excellent engineering has probably chosen 
the wrong career. One cannot make such a sweeping statement about 
theoretical physicists, but even they, as was spectacularly demonstrated 
long ago in the Manhattan Project, frequently can apply themselves both 
effectively and zestfully to technological problems. Currently, in fields 
such as plasma physics and thermonuclear research, there are many theo- 
retical physicists, with a broad range of interest and expertise, some with a 
background in elementary-particle physics, intimately concerned with engi- 
neering questions. 

Ongoing basic research is necessary for the translation of scientific dis- 
covery into useful technology, even after the discovery has been made. 
As a rule the eventual value to technology of a discovery is seldom clearly 
evident at the time. It often emerges only after a considerable evolution 
within the context of fundamental research, sometimes as an unexpected 
by-product. Nuclear magnetic resonance (nmr) is now widely used 



167 



in the chemical industry for molecular structure identification. This pos- 
sibility was totally unforeseeable in the early years of nmr research. It 
came to light only after a major improvement in resolution had been 
achieved by physicists studying nmr for quite different purposes. How- 
ever, a backlog of unapplied basic physics is not all that it takes to gen- 
erate new technology; it may not even be the main ingredient. 

Some of the most startling technological advances in our time are 
closely associated with basic research. As compared with 25 years ago, 
the highest vacuum readily achievable has improved more than a thousand- 
fold; materials can be manufactured that are 100 times purer; the submicro- 
scopic world can be seen at 10 times higher magnification; the detection of 
trace impurities is hundreds of times more sensitive; the identification of 
molecular species (as in various forms of chromatography) is immeasur- 
ably advanced. These examples are only a small sample. All these develop- 
ments have occurred since the introduction of the automatic transmission 
in automotive engineering! 

On the other hand, fundamental research in physics is crucially depend- 
ent on advanced technology, and is becoming more so. Historical examples 
are overwhelmingly numerous. The postwar resurgence in low-temperature 
physics depended on the commercial production of the Collins liquefier, a 
technological achievement that also helped to launch an era of cryogenic 
engineering. And today, superconducting magnets for a giant bubble 
chamber are available only because of the strenuous industrial effort that 
followed the discovery of hard superconductors. In experimental nuclear 
physics, high-energy physics, and astronomy — in fact, wherever photons 
are counted, which includes much of fundamental physics — photomultiplier 
technology has often paced experimental progress. The multidirectional 
impact of semiconductor technology on experimental physics is obvious. 
In several branches of fundamental physics it extends from the particle 
detector through nanosecond circuitry to the computer output of analyzed 
data. Most critical experiments planned today, if they had to be con- 
strained within the technology of even ten years ago, would be seriously 
compromised. 

The symbiotic relation of physics and technology involves much more 
than the exchange of goods in the shape of advanced instruments traded 
for basic ideas. They share an atmosphere the invigorating quality of 
which depends on the liveliness of both. The mutual stimulation is most 
obvious in the large industrial laboratory in which new technology and 
new physics often come from the same building and, sometimes, from 
the same heads. In fact, physics and the most advanced technology are 
so closely coupled, as observed, for example, on a five- to ten-year time 
scale, that the sustained productivity of one is critically dependent on the 
vigor of the other. 



Experimental Physics 

An experimental physicist is usually doing something that has not been 
done before or is preparing to do it, which may take longer than the 
actual doing. That is not to say that every worthwhile experiment is a 



168 



The Nature of Physics 



risky venture into the unknown. Many fairly straightforward measure- 
ments have to be made. But only fairly straightforward! The easy and 
obvious, whether in basic or applied physics, has usually been done. The 
research physicist is continually being challenged by experimental problems 
to which no handbook provides a guide. Very often he is trying to extend 
the range of observation and measurement beyond previous experience. 

A most spectacular example is the steady increase in energy of accel- 
erated particles from the 200-keV protons, with which Cockcroft and 
Walton produced the first artificial nuclear disintegrations in 1930, to the 
200-GeV protons of the National Accelerator Laboratory — in 40 years a 
factor of a million! This stupendous advance was achieved not in many 
small steps but in many large steps, each made possible by remarkable 
inventions and bold engineering innovations produced by physicists. Al- 
though numerical factors of increase do not have the same implications 
in different technologies, few branches of engineering have come close to 
that record. A possible exception is communication engineering. Trans- 
mission by modulated visible light, now feasible, represents an increase 
in carrier frequency of roughly a million over the highest radio frequency 
usable 40 years ago. What is really more significant, the information 
bandwidth achievable has increased by a comparable factor. This great 
advance was, of course, made possible by development in basic physics 
and at many stages was directly stimulated by the basic research of physi- 
cists. Even accelerator physics contributed at one stage by stimulating 
the development of klystrons. The accelerator physicists have a remarkable 
record of practical success as engineers. From the time of the early 
cyclotrons to the present, no major accelerator in this country, however 
novel, has failed to work; most of them exceeded their promised per- 
formance. 

In other branches of experimental physics, too, people are doing things 
that would have appeared ridiculously impractical only 10 to 20 years 
ago. For example, a discovery in the physics of superconductivity (the 
Josephson effect) made it possible to measure precisely electric voltages 
and magnetic fields a thousand times weaker than could be measured 
previously. Electrons, also positive ions, can be electrically caged, almost 
at rest in space, for hours. By another technique, neutral atoms can be 
stored in an evacuated box for minutes without disturbing a natural internal 
oscillator that completes, in that time, about 10^- cycles of oscillation. 
One by-product is an atomic clock that is accurate to about a second in 
a million years. By recent laser techniques, light pulses of only 10-^- sec- 
onds' duration have been generated and observed. The local intensity of 
light that can be created with lasers is many million times greater than any- 
thing known in the laboratory ten years ago. Effects can be readily observed 
that in the past could be only the subjects of theoretical speculation, thus 
opening to investigation as entire field of basic research — nonlinear optics. 
Within the same decade, the highest magnetic-field strengths easily avail- 
able in the laboratory, which had hardly changed in a century, were 
roughly quadrupled by superconducting magnets. In the same period, low- 
temperature physicists extended downward by a factor of 10 the tempera- 
ture range usable for general experimentation. 

These developments and others mentioned subsequently in this Report 



169 



show that experimental physics is not running out of ideas or becoming a 
routine matter of data-gathering. In fact, experimental physics could be 
entering a new period, distinguishable (by criteria other than austerity of 
budgets!) from two preceding periods of conspicuous experimental advance 
in modern physics: the decade before World War II, which, in terms of 
tools and techniques, could be called the "cyclotron and vacuum tube" 
period, and the immediate postwar period, in which microwave electronics 
and nuclear technology, largely the fruits of wartime physics, made possible 
an enormous advance in experimental range. Within the past 10 to 15 
years, several postwar developments have come of age that, considered 
as a group, promise a comparable advance in experimental capability. 
These include cryogenics in all its ramifications, semiconductor tech- 
nology, laser-maser techniques, and the massive exploitation of computers. 
One trouble with any such historical formula, and the glory of physics as 
an adventure, is the existence of the important and unclassifiable exceptions. 
For example, the continuously spectacular progress in high-energy accelera- 
tors fits only very loosely into the scheme just outlined. A more modest 
exception is the simple proportional counter, one of the most elegant and 
sensitive devices of physics since the torsion pendulum, which has survived 
through all three periods, earning in each a new lease on life. 

Whether it signifies a new era or not, the enormous advance in observa- 
tional power that is occurring now will in all likelihood open still more 
fields of research in physics. It will certainly lead to applications yet 
unforeseen in other sciences and technology. 



Physics — A Continuing Challenge 

It is possible to think of fundamental physics as eventually becoming 
complete. There is only one universe to investigate, and physics, unlike 
mathematics, cannot be indefinitely spun out purely by inventions of the 
mind. The logical relation of physics to chemistry and the other sciences 
it underlies is such that physics should be the first chapter to be com- 
pleted. No one can say exactly what completed should mean in that 
context, which may be sufficient evidence that the end is at least not 
imminent. But some sequence such as the following might be vaguely 
imagined: The nature of the elementary particles becomes known in self- 
evident totality, turning out by its very structure to preclude the existence 
of hidden features. Meanwhile, gravitation becomes well understood and 
its relation to the stronger forces elucidated. No mysteries remain in the 
hierarchy of forces, which stands revealed as the different aspects of one 
logically consistent pattern. In that imagined ideal state of knowledge, no 
conceivable experiment could give a surprising result. At least no experi- 
ment could that tested only fundamental physical laws. Some unsolved 
problems might remain in the domain earlier characterized as organized 
complexity, but these would become the responsibility of the biophysicist 
or the astrophysicist. Basic physics would be complete; not only that, 
it would be manifestly complete, rather like the present state of Euclidean 
geometry. Such an outcome might not be logically possible. 



170 



The Nature of Physics 



One might be more seriously concerned with the prospect of reaching a 
stage short of that, in which all the basic physics has been learned that is 
needed to predict the behavior of matter under all the conditions scientists 
find in the universe or have any reason to create. From chemistry to 
cosmology, let us suppose, all situations are covered, but one cannot predict 
with certainty the scattering cross section for e-neutrinos on ^-neutrinos at 
10^" V. Suppose further that the experiments required to explore fully 
all the physics at 10^" V are inordinately costly and offer no prospect of 
significantly improving physics below 10-" V, which is already known to 
be sufficiently reliable. If some such state were reached, one might reason- 
ably expect that research in fundamental physics would be at least brought 
to an indefinite halt if not closed out entirely as being in the state of per- 
fection previously postulated. It would be said that all the physics that 
mattered had been learned. 

Some physicists are supposed to have made this statement about physics 
at about the end of the nineteenth century. That they were wrong, 
spectacularly wrong, is a reminder that human vision is limited; it proves 
nothing more. For the state of knowledge of physics today is essentially 
different from that in 1890, just before the curtain was pulled back, so to 
speak, from the atomic world. Where the problems lie is evident. As 
far as the behavior of ordinary matter is concerned, it is hardly con- 
ceivable that the detailed picture of atomic structure, the product of 
quantum theory and exhaustive experimentation, should turn out to be 
misleading or that the main problem in nuclear physics should suddenly 
be revealed as one hitherto ignored. There are mysteries, but they lie 
deeper. If it were possible to fence off a particular range of application, for 
example, chemistry at temperatures below 10'' deg, then a state in which 
all the relevant fundamental physics is essentially complete could be 
reasonably anticipated. Indeed, for a sufficiently restricted application, the 
day might already have arrived. 

The trouble is that the range of interests continues to widen, and in 
unexpected ways. Because of pulsars, the structure of atoms exposed to 
a magnetic field of lO^^ q (tg^ million times the strongest fields in labora- 
tory magnets) becomes a question of some practical concern, as does the 
shear strength of iron squeezed to a billion times its ordinary density. Just 
now astronomy seems to be making the most new demands on fundamental 
physics; there the end is not in sight. 

Even if the physicist could reliably and accurately describe any ele- 
mentary interaction in which a chemist or an astronomer might be inter- 
ested, the task of physics would not be finished. Man's curiosity would 
not be satisfied. Some of the most profound questions physics has faced 
would remain to be answered, if understanding of the pattern of order 
found in the universe is ever to be achieved. The extent of present 
ignorance still is great. 

It is far from certain that in the presently recognized elementary particles 
the ultimate universal building blocks of matter have been identified. The 
laws that govern the behavior of the known particles under all circum- 
stances are not known. It is even conceivable that the study of particle 
interactions at ever higher energy leads into an open domain of never- 



171 



decreasing complexity. Probably most physicists would doubt that. Cosmic 
rays afford an occasional glimpse of matter interacting at energies very 
much greater than particle accelerators provide, and no bizarre conse- 
quences have yet been observed. It seems rather that physicists now face 
not mere complexity but subtlety, a strangeness of relationship among 
the identified particles that might render the question of which of them 
is truly elementary essentially meaningless. 

Even if physicists could be sure that they had identified all the particles 
that can exist, some obviously fundamental questions would remain. 
Why, for instance, does a certain universal ratio in atomic physics have 
the particular value 137.036 and not some other value? This is an experi- 
mental result; the precision of the experiments extends today to these 
six figures. Among other things, this number relates the extent or size 
of the electron to the size of the atom, and that in turn to the wavelength 
of light emitted. From astronomical observation it is known that this 
fundamental ratio has the same numerical value for atoms a billion years 
away in space and time. As yet there' is no reason to doubt that other 
fundamental ratios, such as the ratio of the mass of the proton to that 
of the electron, are as uniform throughout the universe as is the geometrical 
ratio 7r= 3.141 59. Could it be that such physical ratios are really, like 
TT, mathematical aspects of some underlying logical structure? If so, physi- 
cists are not much better off than people who must resort to wrapping a 
string around a cylinder to determine the value of tt! For theoretical physics 
thus far sheds hardly a glimmer of light on this question. 

The question was posed in even sharper form 40 years ago by Eddington, 
who argued that the structure perceived in nature can be nothing but a 
reflection of the methods of observation and description that must be 
employed. That view would reduce fundamental physics to metaphysics. 
But Eddington's own conception of the structure did not survive. Such 
evidence as he had adduced was soon washed away in a flood of discovery. 
The whole history of physics since then gives no sign that physics is about 
to become an exercise in deduction. Every attempt to close the theoretical 
structure to all changes except refinements has been confounded by an 
experimental discovery. This has happened so often that there has been 
some accession of intellectual humility along with the vast increase in 
knowledge of the underlying structure of matter. Surely the end of the 
story is yet far off. 

The fundamental question survives, if not the attempts to answer it: 
Is there an irreducible base, or design, from which all physics logically 
follows? The history of modern physics warns that the answer to such a 
question will not be attained just by thinking about it. To be sure, brilliant 
theoretical ideas, probably many, will be needed, and some future Bohr 
or Einstein may become renowned for the flash of insight that eventually 
reveals a key to the puzzle (or the absence of a puzzle!). But without 
experimental exploration and discovery, new ideas are not generated. 
Physics will remain an experimental science at least until very much more 
is known about the fundamental nature of matter. 



172 



Some of the fundamental differences between science and 
politics are highlighted in this reexamination of what may 
have been the most momentous decision of World War II. 



1 1 The Decision to Drop the Atomic Bomb 

Dietrich Schroeer 

A chapter from Physics and Its Fifth Dimension Society, 1972 



. . . the physicists felt a particularly intimate responsibility for sug- 
gesting . . . and . . . for achieving the realization of atomic wea- 
pons. . . . In some sort of crude sense, which no vulgarity, no humor, 
no overstatement can quite extinguish, the physicists have known sin; 
and this is a knowledge which they cannot lose. 

J. Robert Oppenheimer in The Open Mind., p. 8o 

Some of the military, political, and emotional background to the 
decision to use the atomic bomb is presented. The interaction of 
the views of the nuclear physicists with those of the military and 
the President is discussed. 



INTRODUCTION 

In 1 94 1 the nuclear scientists proposed the atomic bomb, in 1945 
some of them were opposed to its use, and now there are those who 
consider the use of the bomb to be the event wherein scientists for the 
first time tasted sin. In this chapter we will examine the scientific, 
emotional, and miUtary-pohtical background behind the decision of 
the United States to actually use the atomic bomb as a weapon in the 
Second World War. 

This was a particularly interesting decision for at least two 
reasons. First, in the United States the atomic bomb was proposed by 
scientists primarily because of fear of German militarism. Yet it was 
finally used against an enemy who would have been easily defeated 
without it. Secondly, the bomb was proposed and built by scientists 
who were trained to think in terms of a consensus. Yet because of the 
secrecy of the Manhattan Project, only a very select group of persons 
was in a position to influence the final decision concerning use of the 
bomb — a group which did not even include the members of Congress. 



173 



We shall begin by considering the basis for the fear of a German 
atomic bomb. Then the attitudes of the scientists toward the use of 
the bomb on Japan will be outlined. Finally, the military and political 
situation which led to its use will be compared with the consequences 
of its use. Hopefully this review will make clear the resulting 
ambivalence in the attitude of the scientific community toward this 
mixture of great scientific, technological, and organizational achieve- 
ment combined with the horror of its wartime usage. 

THE FEAR OF THE SCIENTISTS 

The original motivation of the scientists in the United States for 
proposing the atomic bomb as a weapon was fear. The immigrant 
scientists had tasted Hitler's Germany firsthand; they knew the op- 
pression which an Axis victory would bring. Even Einstein, though 
basically a pacifist, knew there would be circumstances intolerable 
enough to negate his pacifism; and he knew that a war against Nazism 
was one of these. 

But beyond this general fear, the immigrant nuclear scientists 
had the more direct fear that Germany would be the first to build 
an atomic bomb and use it to win the war. This fear was the reason 
Einstein wrote his letter to President Roosevelt; his primary purpose 
was to get the President to convince the Belgians not to let Hitler 
capture their stock of uranium, and to thereby delay the Germans 
as long as possible in building the bomb. This fear led to the overriding 
concern of the scientists that the Allies should be the first to possess 
the bomb; until the German surrender this was the specter haunting 
the Manhattan Project. There was, in fact, so much fear at the end of 
1942 that some scientists convinced themselves that Hitler would 
attack Chicago with the radioactivity from a reactor (on Christmas 
day, of course); they so convinced themselves that they sent their 
families to the country. 

THE GERMAN ATOMIC BOMB 

It is interesting to examine this specter a little closer in order to see 
how substantial it may have been. When the curtain of wartime 
secrecy shut off contact between the two scientific camps, the Ger- 
mans were rapidly moving toward building the atomic bomb. Not only 
had fission first been observed in BerUn by Hahn, but in April of 1939 
a first meeting concerning an atomic bomb had already been held 
under the official auspices of the Reich Ministry of Education. There 
had also been a bomb proposal to the War Office; even the Postal 
Ministry began to perform nuclear research with such a bomb in 
mind. By September 1939, more than a fortnight before Sachs could 
obtain an interview with Roosevelt to transmit Einstein's letter, nine 
German nuclear physicists had met in the Army Weapons Office and 
drawn up a detailed program of research. The Uranium Club was then 



174 



The Decision to Drop the Atomic Bomb 



formed, with Heisenberg (the discoverer of the Uncertainty Principle) 
as head; and the Kaiser Wilhelm Institute for Physics in Berhn was 
made the club's Scientific Center. Negotiations were begun for all 
the uranium and radium from the Joachimsthal mines in Czech- 
oslovakia; a 3500-ton supply of uranium was captured when Germany 
overran Belgium; and when Norway was taken over by Germany, 
the Germans captured the world's only large-scale plant for manu- 
facturing the heavy water which would make a nuclear reactor an 
easy thing to build. As far as the Americans and the British could 
see, the Germans had then a two-year headstart toward an atomic 
bomb, had all the natural advantages, and were clearly moving rapidly 
in the right direction. This was a self- feeding fear. The lack of any 
nuclear-progress spy reports after 1939 surely meant simply that 
supersecrecy was instituted to hide tremendous German achieve- 
ments. And when the V-2 rocket construction started, the worry 
arose that, since the V-2 was too small to have much effect with 
ordinary explosives, it must be intended to dehver nuclear war- 
heads. 

The fear of the German atomic bomb evoked three different 
responses. First the British and later the American atomic-bomb pro- 
grams were pushed with great vigor. Secondly, the Norwegian heavy- 
water plant was bombed and sabotaged. The plant was promptly 
rebuilt; this indicated to the Allies that the German atomic-bomb 
program must have very high priorities. The third part of the response 
was the "Alsos" mission. ("Alsos" is Greek for "grove;" the mission 
was presumably named in honor of General Groves.) Alsos was an 
intelUgence group which included physicists whose assignment was 
to pick up German scientific secrets as Axis laboratories and univer- 
sities were captured by the Allies. The scientific chief of this operation 
was Dr. Samuel Goudsmit (now editor of the Physical Review Letters, 
perhaps the most prestigeous physics journal in the West). This group 
went along with the AlHed armies (sometimes even ahead of them) 
and examined the files at the universities and laboratories for hints 
about the nuclear operations. As the story uncovered, it became clear 
that not only was there no German atomic bomb, there wasn't even 
an operational nuclear reactor. 

There were many factors contributing to the German failure to 
build an atomic bomb. The first was the competition among the 
scientists participating in the program. Although Berhn had been 
set up as the center for the Uranium Club, most of the physicists 
preferred to do their work in their own institutes. There was constant 
competition between tJhe three agencies supporting the groups work- 
ing on the bomb — between the Educational Ministry, the War Office, 
and the Post Office. When the Postal minister informed Hider about 
his bomb project, Hitler joked, "Look here gentlemen, while you 
experts are worrying about how to win the war, here it is our Postal 
Minister who brings us the solution." In the United States a similar 
problem was finally terminated by Oppenheimer when he set up the 
centralized laboratory at Los Alamos. In Germany, however, the 



175 



competition continued, and its results were manifold. There were 
constant fights as to who was to be allowed to use the limited amounts 
of pure uranium and heavy water; even in the last days of the war 
these materials were still being shuttled from one laboratory to 
another, with no group ever having enough to run a conclusive 
reactor experiment. Splits between those groups came out also in 
discussions of separation processes, and as a result the priorities for 
programs were usually determined by the pecking order; in part as 
a consequence of this, no separation process had made any significant 
progress by the end of the war. 

One of the more powerful brakes on the program was a purely 
technical mistake. Very early in the war a measurement was carried 
out which indicated that carbon in the form of graphite could not 
be used as a moderator in a fission reactor using natural uranium. 
Presumably the carbon used in this measurement had impurities 
in it; after all, Fermi in the United States successfully built a graphite 
reactor in 1942. As a consequence of this error, the German physicists 
thought they needed heavy water for a reactor, and hence made them- 
selves totally dependent on that captured Norwegian heavy-water 
plant. The Allied sabotage and bombings of this plant then completely 
upset the program. 

Another significant reason for the lack of progress toward the 
bomb was the very nature of the German Nazi state and ideology. 
As indicated in Chapter 16, by 1937 nearly 40% of the German 
university professors had been dismissed, and many more had fled. 
Between 1932 and 1937 the number of university students in mathe- 
matics and the sciences had dropped to 36% of its former level. It 
was only in 1942, when it became clear that the end of the war was 
not imminent, that the government began to recognize this problem. 
Then Goering said: 

What the Fiihrer abhors is any strict regimentation of science, 
with results like this: "This invention may indeed be vital — 
extremely vital to us, and would bring things a long way for 
us; but we can't touch it because the fellow's got a Jewish wife, 
or because he's half- Jewish himself. . . ." 

I have discussed this with the Fiihrer himself now; we have 
been able to use one Jew two years longer in Vienna, and 
another in photographic research, because they have certain 
things which we need and which can be of the utmost bene- 
fit to us at the present. It would be utter madness for us to 
say now: "He'll have to go. He was a magnificent researcher, 
a fantastic brain, but his wife is Jewish, and he can't be 
allowed to stay at the University, etc." The Fuhrer had made 
similar exceptions in the arts all the way down to operetta 
level; he is all the more likely to make exceptions where really 
great projects or researchers are concerned. (As quoted in Ref 
18.3, p. 126.) 



176 



The Decision to Drop the Atomic Bomb 



And, as was pointed out in Chapter i6, political meetings had to be 
called to decide what physics was consistent with the party philosophy. 
This not only was discouraging to any real scientists; it further was 
very encouraging to all scientific quacks who were party members. 

But the final and perhaps most decisive reason for the failure 
of the German atomic- bomb program was the attitude of the German 
scientists. They felt no fear; they were not worried about an American 
atomic bomb; after all, German science was superior. The prompt 
rebuilding of the Norwegian hydro plant after the sabotage and bomb- 
ing and the prompt production of pure uranium made it clear that 
German industry and the war offices were prepared to support an 
atomic-bomb program. But the scientists never learned to ask for 
money; from either a lack of confidence or of desire, they never 
pushed the program very forcefully. When the scientists had a talk 
with the sympathetic Armaments Minister Speer, they asked for so 
little money that he was embarrassed. The German scientists them- 
selves claim that they never really wanted to build an atomic bomb 
(e.g., Refs. 1 8. 1 and 18.5). To them the program was an opportunity 
to preserve some German science for the postwar period; by doing 
defense work they were able to keep away from the front and to 
maintain a semblance of university teaching and research. Doubts 
have been expressed as to the correctness of this after-the-fact 
explanation (e.g., Ref. 18.3), but in any case, fission research was not 
pursued in Germany with enough energy to lead to significant pro- 
gress. 

THE ATOMIC BOMB AND JAPAN 

The Alsos mission and the surrender of Germany in May of 1945 
ended any fear of a German atomic weapon on the part of American 
scientists in the Manhattan Project. And Japan clearly had not the 
facilities, the resources, or the scientific estabUshment necessary to 
build such a weapon. Once the fear motive was removed, American 
nuclear scientists could then think about the longer-term implica- 
tions of the bomb and specifically about its possible application to the 
war with Japan. Should it be used, and if so, how? And what would 
happen to nuclear research and nuclear information once the war 
was over? To the military, including the man in charge. General 
Groves, there was no question that the weapon would be used if 
built; the only worry was that it might not be finished in time. So 
any change of plans had to occur at the very top; only the President 
could decide the ultimate use of the bomb. 

There were attempts to influence Roosevelt on this issue. 
Alexander Sachs, who had passed the Einstein letter to him, debated 
the question with him in December of 1944 and later claimed that 
Roosevelt at that time agreed to a rehearsal demonstration of the 
atomic bomb before international and neutral witnesses prior to 
any wartime use. But this agreement, if it indeed existed, was never 



177 



mentioned to Secretary of War Stimson, who on March 15, 1945, 
had his last talk on the subject with Roosevelt: 

I went over with him the two schools of thought that exist in 
respect to the future control after the war of this project, in case 
it is successful, one of them being the secret close-in attempted 
control of the project by those who control it now, and the other 
being international control based upon freedom of science. I told 
him that those things must be settled before the projectile is 
used and that he must be ready with a statement to come out to 
the people on it just as soon as that is done. He agreed to that. 
(Quoted for example in Ref. 18.1, p. 175.) 

A report by Szilard on the scientists' feelings about the bomb was 
lying on Roosevelt's desk when he died. After Roosevelt's death, any 
changes in the decision about the use of the bomb required convinc- 
ing the new President, Harry S. Truman, who hadnever heard of the 
weapon while he was Vice President. 

THE SCIENTISTS' VIEWPOINT 

The most general and wide-ranging discussions about the use of the 
bomb took place among the nuclear scientists in Chicago, where 
toward the end of the war there was not so much pressure since the 
production processes had already passed on to industry; this stood 
in contrast with Los Alamos where everyone continued to work at 
fever pitch until the very end to meet the bomb-construction and test- 
ing deadlines. It was in Chicago that the Jeffries Report, Prospectus 
on Nucleonics, was prepared — a report which contained discussions 
of a possible future armaments race as well as of the future applica- 
tions of nuclear fission. Early in 1945 several of the Chicago scientists 
became convinced that international control of nuclear knowledge 
would be the best way to ensure open dissemination of this new 
information. As James Franck put it in April of 1945: 

We read and hear about all the efforts which the best states- 
men devote to peace planning in Dumbarton Oaks, San Francisco, 
etc., and we hear about plans to control industries, etc. in the 
agressor states, but we know in our hearts that all these plans 
are obsolete, because the future war has an entirely different and 
a thousand times more sinister aspect than the war which is 
fought now. How is it possible that the statesmen are not in- 
formed that the aspect of the world and its future is entirely 
changed by the knowledge that atomic energy can be tapped, and 
how is it possible that the men who know these facts are prevented 
from informing the statesmen about the situation? One of the 
grave political decisions which will soon have to be made is how 
and when to inform the public, since in a democratic country 
effective political steps cannot be taken without enUghtened 
public opinion. (As quoted in Ref. 18.2, pp. 294-295.) 



178 



The Decision to Drop the Atomic Bomb 



A "Committee on the Social and Political Implications of 
Atomic Energy" was formed under Franck. It completed the 
Franck Report in early June of 1945, a report which was prompt- 
ly classified. A quotation from the preamble to this report is ap- 
propriate here because it shows that the scientists were aware 
that they could speak about the implications only as well-informed 
citizens, not as experts: 

The scientists on this Project do not presume to speak authori- 
tatively on problems of national and international pohcy. How- 
ever, we found ourselves, by the force of events, during the last 
five years, in the position of a small group of citizens cognizant 
of a grave danger for the safety of this country as well as for the 
future of all the other nations, of which the rest of mankind is 
unaware. We therefore feel it our duty to urge that the political 
problems, arising from the mastering of nuclear power, be 
recognized in all their gravity, and that appropriate steps be 
taken for their study and the preparation of necessary decisions. 
We hope that the creation of the Committee by the Secretary of 
War to deal with all aspects of nucleonics, indicates that these 
impUcations have been recognized by the government. We believe 
that our acquaintance with the scientific elements of the situation 
and prolonged preoccupation with its world-wide political im- 
plications, impose on us the obUgation to offer to the Committee 
some suggestions as to the possible solution of these grave prob- 
lems. (As quoted in Ref. 18.2, p. 302.) 

The objections raised in the report to the use of the atomic bomb 
were that it would be likely to induce an armaments race and 
thus reduce the possibility of an international control agreement. 
While the report was signed by all seven members of the committee, 
there were other scientists who felt that an all-out attack on 
Japan by the atomic bomb would significantly shorten the war. 
There were petitions and counterpetitions. A poll was carried out 
July 12, 1945, among 150 out of the 250 nuclear scientists at the 
Chicago Metallurgical Lab. The following alternatives were pre- 
sented: 

Which of the following five procedures comes closest to your 
choice as to the way in which any new weapons that we may 
develop should be used in the Japanese war: 

1. Use them in the manner that is from the military point of 
view most effective in bringing about prompt Japanese sur- 
render at minimum human cost to our armed forces. 

2. Give a miUtary demonstration in Japan to be followed by 
renewed opportunity for surrender before full use of the weapon 
is employed. 

3. Give an experimental demonstration in this country, with 



179 



representatives of Japan present; followed by a new oppor- 
tunity for surrender before full use of the weapon is employed. 

4. Withhold military use of the weapons, but make public experi- 
mental demonstration of their effectiveness. 

5. Maintain as secret as possible all developments of our new 
weapons and refrain from using them in this war. 

The results were as follows: 



Procedure indicated above 



Number voting 23 69 39 16 3 

Percent of votes 15 46 26 11 2 



(As quoted in Ref. 18.2, p. 304.) 



Clearly there was concern among the scientists, but there was no 
unanimity; some scientists wanted the weapon to be first demonstrated 
before being used in combat in Japan, but this view was not universal; 
there was concern about the moral and political asj>ects of being the 
first nation to use this weapon, but it was the concern of private in- 
dividuals. 

The new President, Truman, did ask for advice about the way to 
use the bomb; near the end of April 1945 he appointed the so-called 
Interim Committee. It included Stimson, Secretary of War; George L. 
Harrison, Stimson's assistant; James F. Byrnes, future Secretary of 
State; Ralph A. Bard, Undersecretary of the Navy; WiUiam L. 
Clayton, Assistant Secretary of State; Dr. Bush; Dr. Karl T. Compton, 
president of M.I.T; and Dr. Conant. A panel of four scientists was 
appointed to advise the committee: A. H. Compton, Fermi, Lawrence, 
and Oppenheimer. According to Stimson, after discussions with the 
scientific panel, the committee unanimously adopted the following 
recommendations: 

1 . The bomb should be used against Japan as soon as possible. 

2. It should be used on a dual target — that is, a miUtary instal- 
lation or war plant surrounded by or adjacent to houses and other 
buildings most susceptible to damage, and 

3. It should be used without prior warning [of the nature of the 
weapon] . One member of the committee, Mr. Bard, later changed 
his view and dissented from recommendation. 

In reaching these conclusions the Interim Committee carefully 
considered such alternatives as a detailed advance warning or a 
demonstration in some uninhabited area. Both of these sugges- 
tions were discarded as impractical. . . . (As quoted in Ref. 18.2, 
pp. 296-297.) 



180 



The Decision to Drop the Atomic Bomb 



Since President Truman ultimately followed the advice of this com- 
mittee, a critical point is whether indeed all possible alternatives had 
been considered or whether the agreement was not just an act of 
rubber-stamping. Apparently many different alternatives were con- 
sidered, such as a nighttime airflash several miles above Tokyo, the 
demonstration bombing of a forest area in the vicinity of Tokyo, or at 
least a detailed advance warning. But all the alternative uses of the 
bomb were rejected because they would not be impressive enough or 
their results could be hidden through military secrecy or they could 
be negated by moving prisoners of war into the area. The consensus in 
the committee was not quite as total as implied by Stimson. The 
scientific panel, for example, only advised; it did not vote on the re- 
commendations. And Mr. Bard had never heard of the Manhattan 
Project prior to this meeting; consequently, his agreement was so 
forced that he subsequently withdrew his consent to the recommenda- 
tions and a month later resigned his naval post to emphasize his 
opposition to the bombing (feeling that the Navy was quite able to 
bottle up Japan and that the Army just wanted to share in the glory of 
the final victory). There is, however, no question that Truman re- 
ceived the recommendation from this high-level committee (with a 
large representation from science and technology) that only a bombing 
of a live target would be convincing to the Japanese. The scientists 
certainly were not unanimously against the usage of the bomb. 



THE MILITARY SITUATION IN JAPAN 

In the meantime, the war situation was as follows. Okinawa had been 
invaded in a very bloody battle with suicidal kamikazi plane missions 
taking place on a large scale. On March 9, 1945, 325 B-29's bombed 
Tokyo with 2000 tons of incendiaries. The resulting fire storm killed 
approximately 100,000 people, flattened 16 square miles, and de- 
stroyed 250,000 buildings. In five months of bombing, the 21st 
Bomber Command had paralyzed 66 metropolitan centers and had 
made eight million Japanese homeless. Hunger was a constant torture; 
rice rations were down to one-fourth of the prewar level. And over- 
riding all this was fear; as the B-29's and the planes from the carriers 
dominated the people's very movement, the civilian population of 
Japan was on the edge of desperation. 

Attempts to negotiate concerning a surrender began as early as 
May, 1945 — through Switzerland, over radio propaganda broadcasts, 
and even through Russian intermediaries (since Russia still had not 
declared war on Japan). But the Japanese military was not prepared 
to surrender. The plans for the defense of the homeland were to kill 
as many invaders as possible and thus to shatter American morale 
enough to lead to a negotiated peace in place of the demanded un- 
conditional surrender. And the American military plans still called 
for an invasion of Japan; casualty estimates were hundreds of thou- 
sands of Americans, plus many more Japanese. 



181 



The Potsdam Conference was going on at this time, and on July 
24 Truman "casually" told Stalin that the U.S. had a new weapon 
of unusual destructive force. The Russian premier showed no special 
interest in this weapon. He only said that he was glad to hear it and 
hoped the U.S. would make "good use of it against the Japanese." 
He never asked a question about it. In the Potsdam Declaration of 
July 26 there was an ultimatum threatening complete destruction of 
Japan. For the Japanese the biggest stumbling block in the way of 
surrender was Point 6 of this declaration. This point said: "There 
must be eUminated for all time the authority and influence of those 
who have deceived and misled the people of Japan into embarking on 
world conquest." They interpreted this as requiring the abdication 
of the Emperor, which was an unacceptable condition. In his radio 
response to the Potsdam Declaration, Premier Suzuki tried to say 
that the government would "withhold comment," but he accidentally 
used the words meaning to "take no notice of, treat with silent con- 
tempt, ignore." Truman could only interpret this as a refusal to sur- 
render, so he authorized the use of the atomic bomb. On August 6 the 
B-29 named "Enola Gay" took off. The weather was good, so at 8:15 
a.m. local time, the "Little Boy" was dropped on Hiroshima. (The 
city of Kyoto had been struck from the original target Ust since it 
had been the ancient capital of Japan and was a shrine of Japanese 
art and culture.) Truman made a public statement: "It is an atomic 
bomb." Three days later, one day after Russia entered the war, a 
plutonium bomb was dropped on Nagasaki. As part of this flight, a 
letter was dropped by parachute, addressed by Professors L. Alvarez, 
R. Serber, and P. Morrison to their former colleague at Berkeley, 
Professor R. Sagane at the Imperial University of Tokyo: 

We are sending this as a personal message to urge that you use 
your influence as a reputable nuclear physicist, to convince the 
Japanese General Staff of the terrible consequences which will be 
suffered by your people if you continue in this war. 

You have known for several years that an atomic bomb could be 
built if a nation were willing to pay the enormous cost of pre- 
paring the necessary material. Now that you have seen that we 
have constructed the production plants, there can be no doubt 
in your mind that all the output of these factories, working 24 
hours a day, will be exploded on your homeland. 

Within the space of three weeks, we have proof-fired one bomb 
in the American desert, exploded one in Hiroshima, and fired the 
third this morning. We implore you to confirm these facts to your 
leaders, and to do your utmost to stop the destruction and waste 
of life which can only result in the total annihilation of all your 
cities if continued. As scientists, we deplore the use to which a 
beautiful discovery has been put, but we can assure you that 
unless Japan surrenders at once, this rain of atomic bombs will 
increase manyfold in fury. (See, for example, the facsimile in 
Ref. 17.7, p. 258.) 



182 



The Decision to Drop the Atomic Bomb 



The number of dead due to these two atomic bombs is not very ac- 
curately known, but is on the order of 150,000. Official Japanese 
statistics placed the number of dead at Hiroshima (out of a population 
of 400,000) at 70,000 up to September i, 1945, and the number of 
wounded at 130,000 with 43,500 severely wounded. The supreme 
AlUed Headquarters announced in February of 1946 that the casual- 
ties in Hiroshima were: 

dead — 78,150; 
missing — 13)983; 
seriously wounded — 9^428; 
slightly injured — 29,997. 
The horror of those days has been often described (as in Refs. 18.12 
through 18.15); the survivors still bear psychological scars (Ref. 
18.15). 




Fig. 1 8. 1 Remains of the Nagasaki Medical College after the A-bomb 
drop on August 9, 1945. (Photo courtesy of the United States Atomic 
Energy Commission.) 



183 



Even after the atomic bomb was used, the Japanese cabinet was 
still split on whether to surrender or not; one man who was basically 
committed to the policy of trying to get better surrender terms by 
bleeding the Americans on the beaches was the War Minister Anami, 
spokesman for the Army and the most powerful man in Japan. But 
finally Emperor Hirohito saved face for everyone by taking the onus 
of surrender on himself: ". . . the time has come when we must bear 
the unbearable." On the loth August, Japan offered to surrender. 
Members of the Army briefly tried to rebel and to destroy the Emperor's 
recording of the planned surrender radio broadcast; but Anami vacil- 
lated and the uprising failed. Included in the brief 300-word an- 
nouncement of August 15 (nine days after the first atomic bomb) 
were the following statements: 

. . . the war situation has developed not necessarily to Japan's 
advantage. . . . Moreover, the enemy has begun to employ a new 
and most cruel bomb, the power of which to do damage is indeed 
incalculable, taking the toll of many innocent fives. Should we 
continue to fight, it would not only result in an ultimate coUapse 
and obliteration of the Japanese nation, but would also lead to 
the total destruction of human civilization. (Quoted for example 
in Ref 18.7, p. 182.) 



SUMMARY 

In fear of a German atomic bomb, the U.S. scientists proposed such a 
weapon and built it. But then they lost control of it, as it inexoner- 
ably was used in defeating Japan. President Truman had to make 
the final decision concerning its use, and it is questionable whether 
he ever had any major doubts in his mind about the correctness of 
his ultimate choice. The bomb may or may not have significantly 
shortened the war, but now the world must live with that memory. 
For the scientists there is much irony in the course of events 
related to the atomic bomb. First, the fear of Germany was groundless 
insofar as the bomb ultimately was not necessary for the winning of 
the war. Secondly, the designing of the bomb was a technological feat, 
but it was not science since it was product-oriented. In fact, this war- 
time contact with secrecy and its consequent hampering of scientific 
activities impressed the participating scientists tremendously, and 
colored all their future political attempts at arranging the course of 
science. And finally, the instincts of the scientists were right when 
they tried to get the broadest possible audience for the discussions on 
the bomb's use — when they asked for a more general public con- 
sensus. Perhaps it would have been the very best possible thing if the 
discussion could have been made totally public; only in that way 
could the most socially responsible decision have been reached. But 
this was impossible under wartime secrecy, a secrecy which perhaps 
was not necessary but which did exist. The decision to drop the bomb 



184 



The Decision to Drop the Atomic Bomb 



could, therefore, in no sense be called a scientific decision. This whole 
exercise brought home to the nuclear scientists the difference between 
science and poUtics, a difference which they have had to continually 
relearn. They discovered that no consensus was possible in the latter 
field. 

REFERENCES 

Prime references 

1 8. 1 R. Jungk, Brighter Than a Thousand Suns, (Ref. 17.4); pp. 
156-210. 

18.2 A. K. Smith, "Behind the Decision to Use the Atomic Bomb, 
Chicago 1944-45," Bulletin of the Atomic Scientists 14, 288- 
312(1958). 

Interesting reading 

18 3 D. Irving, The German Atom Bomb, New York: Simon and 
Schuster, 1967; also published as The Virus House, London: 
William Kimber and Co., Ltd. 

18.4 S. A. Goudsmit, Alsos, New York: Henry Schuman, Inc., 1947. 

18.5 W. Heisenberg, Encounters and Conversations, (Ref. 13.2). 

18.6 W. L. Laurence, Men and Atoms, (Ref. 17. i); pp. 134-185. 

18.7 W. Craig, The Fall of Japan, New York: Dell Publishing Co., 
1968. 

18.8 J. Toland, The Rising Sun, New York: Random House, 1970. 

18.9 E. Fogelman, The Decision To Use the Atomic Bomb, New York: 
C. Scribner's Sons, 1964. 

18.10 M. Amrine, The Great Decision: The Secret History of The A tomic 
Bomb, New York: Van Rees Press, 1959. 

1 8. 1 1 H. Feis, The Atomic Bomb and the End of World War //, Prince- 
ton, N.J.: Princeton University Press, 1966. 

18.12 J. Hersey, Hiroshima, New York: Alfred Knopf, 1946. 

18.13 R. Jungk, Children of Ashes, New York: Harcourt, Brace and 
World, 1 96 1. 

18.14 M. Hachiya, Hiroshima Diary: The Journal of a Japanese Physi- 
cian, August 6-September 30, 1945, Chapel Hill, N.C.: Univer- 
sity of North CaroUna Press, 1955. 

18.15 R. J. Lifton, Death in Life: Survivors of Hiroshima, New York: 
Random House, 1968; it is the survivors who feel guilty for 
having been part of the complete social collapse which took 
place in the hours after the blast of the bomb. 

18.16 F. Diirrenmatt, The Physicists, New York: Grove Press, 1964; 
a play about scientists without social responsibility. 

18.17 K. Vonnegut, Jr., Cat's Cradle, New York: Dell Publishing Co., 
1963; a satirical book about scientific social responsibihty. 



185 



QUESTIONS FOR DISCUSSION 

1. Was it right for the German nuclear physicists to want to preserve 
some German physics (as opposed to some physics for Germany)? 

2. Do the reasons given seem to adequately explain the failure of the 
German atomic bomb as compared to the success of the American 
program? 

3. Can we say with hindsight that the decision to use the bomb was 
wrong? Is it not good that the world saw a demonstration of the 
effects of such a weapon? 

4. To whom belongs the glory of this magnificent achievement? To 
whom belongs whatever guilt may be associated with it? 



186 



Because of their traditional sense of coexistence with nature, 
the Japanese did not conne until recently to look upon nature 
as something to be investigated or exploited. 



12 The Conception of Nature in Japanese Culture 

Masao Watanabe 

An article from Science, January 1974 



Man's Harmony with Nature 

Some ten years ago, when I had the privilege 
of teaching at the University of Missouri, I read 
an old Japanese story to my class one day and 
asked each of the students to write a short 
corriment on it. It was a story related by Laf- 
cadio Hearn,^ a European-American journalist 
and writer who came to Japan in 1890 and de- 
cided to stay here permanently because he was 
fascinated by Japanese life and culture.- From 
the comments of my American students on this 
story, I learned that one point which most im- 
pressed them was that, in order to welcome his 
adopted brother home from a long journey, a 
Japanese warrior filled the vases in his guest 
room with chrysanthemum flowers. They ob- 
served that this was quite different from Amer- 
ican custom and perhaps was unique to Japan. 

As the students had noticed, this small incident 
pointed to something characteristic of Japan: a 
love of nature which has existed from very early 
days. This love of nature has resulted in a re- 
fined appreciation of the beauty of nature in, 
for example, landscapes, miniature gardens 
{hakoniwa), miniature trees {bonsai), flower 
arrangement {ikebana), the tea ceremony {cha- 
noyu), short poems called haiku, and even the 
art of cookery. 

Nature for the Japanese has not traditionally 
been an object of man's investigation or exploi- 
tation for human benefit as it has been for 
Westerners. For the Japanese and for other 
Oriental peoples, man was considered a part of 



nature, and the art of living in harmony with 
nature was their wisdom of life. 

I recall a story an American missionary to 
China once told me. Three men went to see 
Niagara Falls. One was an Indian from India, 
one a Chinese, and one an American. On see- 
ing the falls, the Indian, as a matter of course, 
thought of his god, manifested in this grandeur 
of nature. The Chinese simply wished to have 
a little hut beside the falls, where he might in- 
vite a friend or two, serve tea, and enjoy con- 
versation. The American, however, immediately 
asked himself what could be done to make the 
most of such an enormous amount of energy. 
Of course, the roar of Niagara Falls might have 
been too much for the Chinese, but the story 
illustrates the different attitudes of different 
peoples. 

To a Chinese or a Japanese, drinking tea and 
eating food are not merely matters of nourish- 
ment or meaningful companionship, but are also 
considered occasions for artistic appreciation of 
nature. Therefore, the landscape you look at 
while eating, the room in which you serve your 
meal, as well as the tableware you use and the 
food itself, must suit your altitude. This ap- 
preciative attitude toward nature has been a 
central theme of Japanese culture. 

During my first visit to America twenty years 
ago, one of my American friends saw the 
powdered tea leaves which I had brought from 
home, and he thought it was instant green tea. 



187 



In fact, it was for use in the tea ceremony, 
during which one sits formally on the floor for 
at least half an hour while the tea is being pre- 
pared. The Japanese people now have instant 
tea, but without Western influence would never 
have thought of making it in an instant form, 
as the tea ceremony is an inheritance from the 
medieval Japanese people, embodying their in- 
tuitive recognition of the beauty of nature and 
Ufe. 

Flower Arrangement and 
Western Cosmology 

A similar theme is expressed in the art of 
flower arrangement, which was developed pri- 
marily in the 15th century. The underlying 
principles of flower arrangement are indicated 
by three main stems or branches that symbolize 
Heaven, Man, and Earth. The "primary stem" 
is symbolic of Heaven and forms the central line 
of the whole arrangement. Therefore, the ar- 
ranger selects for it the strongest stem available. 
Next to the primary stem is the "secondary 
stem," which is symbolic of Man. It is placed 
in such a manner as to give the effect of grow- 
ing sideways and forward from the center line. 
It should be approximately three-quarters of the 
height of the primary stem and inclined toward 



it. The "tertiary stem," symbolic of Earth, is 
the shortest and is placed to the front or slightly 
to the opposite side of the roots of the first two. 
All are fastened securely in a holder to give the 
effect of growing from one stem. Additional 
flowers may be added to fill out each arrange- 
ment, but it is the correct arrangement of the 
three principal stems which is of paramount 
importance. 

Although the idea of a structured universe was 
alien to the Japanese mind in the 15th century, 
the composition of the flower arrangement may 
be compared with Western cosmology to illust- 
rate differing views of man and nature. 

Traditional Western cosmology originated in 
the Middle Ages. It was a creation of Christian 
theology, given form by the adoption and modi- 
fication of the Aristotelian-Ptolemaic theory of 
world structure. Not only did it represent the 
physical setting of the visible world, but it was 
also symbolic of spiritual truth. 

As exemplified by Dante in his Divine Come- 
dy, man was seen as the crucial intermediary 
in a world comprising a hierarchical chain of sub- 
stance that stretched from the inert clay of the 
center to the pure Spirit of the Empyrean. As 
described in Genesis, man was made of earth, 
and medieval scholars held that he therefore 




Fig. 1 (left). Japanese flower arrange- 
ment, an illustration from an old textbook 
by Ibiiki Sanjin Seiko, Sunahcichi Ikebana 
Den (1775). Fig. 2 (right). Medieval 

European co.sniDlogy. [From Apianus, 
Cosinoi^niphid (Antwerp. 1539)] 



188 



Nature in Japanese Culture 




-ni* 





Fig. 3. "Fisherman and Woodcutter" by Sesshu Toyo (1420-1506). 



gravitated naturally toward the center of the 
world, the locus of Hell. However, it was also 
written in Genesis that man was the only ter- 
restrial creature inspired by the Spirit of God. 
Therefore, he constantly aspired to ascend to 
the realm of God, the highest of the Heavens. 
The entire setting of medieval cosmology thus 
mirrored man's hope and fate. Although this 
physical structure was later altered by the so- 
called Copernican revolution, the basic idea 
of man which it portrayed remained little 
changed and continued to play an important 
role in the history of Western thought. 

Because the Japanese people did not adopt 
the sort of cosmology that can be expressed in 
terms of a geometrical structure, the form of the 
flower arrangement could be considered most 
comparable to the structure of Western cosmol- 
ogy. A comparison of the two reveals that they 
represent very different ideas of man and the 
world. It is true that, in either case, man's place 



was intermediate between heaven and earth. 
In the Western system, however, heaven and 
earth were, by definition, diametrically opposite, 
forming a dichotomous world in which man's 
place was absolutely crucial. On the other hand, 
there was no such dichotomy in the traditional 
Japanese ideas. There, nature was a unity, and 
man lived in it as a part of this unity. 

The Rise of Modern Science 

In the Western conception, man was not an 
ordinary part of nature. He was a specially 
privileged creature, and nature was subordinate 
to him and even to his sin. He was the master 
of the natural world, which was at his disposal to 
analyze, examine, and make use of. The rise of 
modern science in the West was premised on this 
sort of religious and philosophical view of nature. 

At the very moment when John Milton was 
preparing his long epic "Of Man's first dis- 
obedience, and the fruit/Of that forbidden tree" 



189 



which brought about the "loss of Eden,"^ in 
the same England, Robert Hooke the scientist 
started the Preface of his Micrographia (1665) 
with the following words: 

It is the great prerogative of Mankind 
above other Creatures, that we are not only 
able to behold the works of Nature, or barely 
to sustein [sic] our lives by them, but we have 
also the power of considering, comparing, 
altering, assisting, and improving them to 
various uses. . . . 

. . . And as at first, mankind fell by tasting of 
the forbidden Tree of Knowledge, so we, their 
Posterity, may be in part restor'd by the same 
way, not only by beholding and contemplat- 
ing, but by tasting too those fruits of Natural 
knowledge, that were never yet forbidden.'* 

This also illustrates how deeply and positively 
modem scientific investigation of nature was 
rooted in Western thought and culture. 

Moreover, since the natural world and the 
whole universe were manifestations of God's 
creation, the study of it was not only a useful 
but also a highly esteemed endeavor. Cotton 
Mather, an American colonial divine and scien- 
tist, stated that knowledge of "The Book of 
Creatures" was indispensable for an imder- 
standing of "The Book of Scriptures"^ — an idea 
shared by many scientists of the 17th and 18th 
centuries. Both the study of science and the 
utilization of science for the comfort of mankind 
were important items among Calvinistic "good 



works." Indeed, such an outlook provided some 
of the important religious motivation which 
fostered the development of modern science in 
the Western world. 

Nature for the Japanese was different. It was 
an object not of his mastery, but of his apprecia- 
tion, and was even his best companion. An il- 
lustration is a famous haiku, a verse of seven- 
teen syllables, composed by a young female Jap- 
anese poet of the 18th century, Kaga no Chiyo. 
Early one summer morning, when she went out 
as usual to draw water from her well, she found 
to her surprise that the pole of her well-bucket 
was entwined by the tendrils of a morning 
glory with fresh, dewy flowers. Instead of re- 
moving the plant from her pole, she went to a 
neighbor for water. Later, with brush in hand, 
she described the scene and her sentiments in 
haiku form. 

The well-pole taken by a morning glory, 
I went to a neighbor for water. 

Another illustration from Japanese literature 
may be drawn from "An account of my hut," 
an essay by Kamo no Chomei written in the 
early 13th century.^ The author presented a 
pessimistic view of the world by enumerating 
recent natural disasters, such as fires, typhoons, 
famines, and earthquakes, and he deplored the 
hardship and impermanence of life. His only 
escape was to "abandon the world" and retire 
to a lonely but quiet life in a small hut in the 



Fig. 4. Section from Clioju Jinhutsii Gii^a (scrolls of frolicking animals and people), 
attributed to Toba Sojo (Heian period, 12th century). 
The scrolls are owned by the Kozanji Temple, Kyoto, Japan. 




190 



Nature in Japanese Culture 



countryside. He wrote that "my only desire for 
this life is to see the beauties of the seasons" 
and "It is better to have as friends musical 
strings and bamboo and flowers and the moon." 
(A somewhat similar hermit tradition has ex- 
isted in the West also.) 

In the Japanese view, there existed varieties of 
beings and seasons, but there was no absolute 
division of heaven and earth, nor an absolute 
"onceness" of time in the Western sense. Every- 
thing came and went in cycles. Even though the 
violence of nature, together with the pessimistic 
teaching of the Buddhism of his time, made a 
man like Chomei so pessimistic, he still found 
his rest in nature. As pointed out by a contem- 
porary Japanese critic,"' similar attitudes of the 
Japanese people were revealed in their reactions 
to the great earthquake and consequent fire of 
1923, which almost completely destroyed Tokyo 
and Yokohama. 

Although the Japanese people have been fre- 
quently visited by earthquakes, they did not in- 
itiate the scientific study of earthquakes. Even 
though they were knocked down by typhoons, 
floods, or earthquakes, they were happy as soon 
as they realized in themselves that they were 
nestled in the bosom of nature. In this way, they 
were relieved and recovered without going on 
further to an objective clarification of these 
calamities. It was only after Japan was opened 
to the Western world in the late 19th century, 
and Western visitors were exposed to earth- 
quakes here, that seismology was initiated. With- 
out this beginning, Japan would not have be- 
come one of the leading countries in the study of 
seismoIogy,despite its high frequency of earthquakes. 

Unique Japanese Contributions to Science 

If the view of nature in Japan has tradition- 
ally been as I have outlined, is there any pos- 
sibility that traditional elements can make a 
positive and unique contribution to the science 
of today and of the future, rather than simply 
being presented as relics in arts and literature? 
This is an important but difficult question. 
When it was put to a group of Japanese people 
staying in America, one of them gave a figurative 
answer. Making a comparison with the construc- 
tion of a modern Western-style building, he 



suggested that for structure and materials we 
Japanese have to rely mainly upon Western 
methods, but in interior decoration we may con- 
tribute elements of our own. This was about as 
far as I too could see, until I met a more pro- 
mising sign in an article by John Frisch.^ 

Frisch, who studied anthropology at the Uni- 
versity of Chicago and now teaches at Sophia 
University in Tokyo, evaluated Japan's con- 
tribution to modern anthropology in the article. 
According to him, a group of Japanese scholars 
have gained worldwide recognition by their uni- 
que contributions to studies of the social be- 
havior of animals. From their many years of 
observation of the life of wild monkeys around 
feeding stations, these Japanese fieldworkers 
were able to discover much concerning the soci- 
al structure of the groups of monkeys, the vari- 
ability of behavior between different gioups, 
and the "inventive behavior" of the monkeys. 

The results of their investigation have been 
regarded as important in that they show that 
nonhuman primates can adapt to change con- 
ditions by spontaneously modifying their habits. 
In other words, they are able not only to modify 
or enlarge already existing behavioral patterns 
but also to create new ones. These discoveries, 
anthropologists consider, make a positive con- 
tribution to one of the key issues of modem 
anthropology, namely, the understanding of the 
origins of human culture and society. 

Even more interesting, however, is the fact 
that the approach used by the Japanese field- 
workers contains something original which is not 
often found in similar studies by Westerners. It 
may well reflect the traditional Japanese way of 
looking at nature, that is to say, an affinity and 
sympathy with all living things. To most ob- 
servers, all monkeys look very much alike, and 
it is difficult to identify individuals in a group. 
Therefore, most Western fieldworkers catch the 
animals and mark them with numbers. The 
Japanese, however, became acquainted with the 
faces, general appearance, and personalities of 
the monkeys, and succeeded in identifying in- 
dividuals not by numbers but by giving them 
names of popular and traditional figures from 
Japanese history. "This seems hard to imagine 
for Western scientists," wrote Frisch. 



191 



Thus, the Japanese observers were able to 
produce abundant and valuable data concerning 
the life and behavior of the animals. Such an 
approach might not have developed so naturally 
in the Western cultural zone, where the distinc- 
tion between man and other living things has 
been observed more strictly. In other words, to 
quote Frisch, "while the Western scientist tends 
to regard the animals as objects situated in front 
of him, somewhat as bacteria under the mic- 
roscope, his Japanese colleague tends to think in 
terms of a personal relationship with indi\iduals 
who have names and whose life stories arc often 
familiar to him."^ 

Frisch maintained that the intellectual and 
spiritual tradition of Japan constitutes a most 
favorable environment for the science of non- 
human primate behavior, and that "we may see 
in this particular example an indication of the 
nature of the contribution which Japan can be 
expected to make, not only to anthropology, but 
to our wider understanding of nature in its rela- 
tion to man."i^ 

Environmental Problems 

In his Nobel lecture entitled "Japan the Be- 
autiful and Myself" (1968), Yasunari Kawabata 
first quoted a poem of the Zen priest Myoe 
(1173-1232): 

Winter moon, coming from the clouds to keep 

me company, 
Is the wind piercing, the snow coldpn 

Then he commented on it, saying: 

Winter moon, going behind the clouds and 
coming forth again, making bright my foot- 
steps as I go to the meditation hall and 
descend again, making me unafraid of the 
wolf: does not the wind sink into you, does 
not the snow, are you not cold? I choose it 
as a poem of warm, deep, delicate compassion, 
a poem that has in it the deep quiet of the 
Japanese spirit. ^^ 

Thus, things in nature are intimate companions 
for the Japanese people. 

Since the nation itself has been highly in- 
dustrialized, the attitude of the people may be 
changing greatly. Basically, however, much of 



this attitude remains unaltered. A verse in one 
of the contemporary popular songs in Japan 
asks: 

Chimneys are so high that, you moon. 
Don't your eyes smart from the smoke? 

After a day's work, Japanese workers are happy 
drinking sake, singing this song, and addressing 
it to the moon. They are merged with nature, 
forgetting themselves and even forgetting the 
dreadful destruction constantly inflicted upon 
nature and themselves by the smoke from the 
chimneys. Such optimism seems, though, to have 
favored the too rapid growth of the gross nation- 
al product. 

Now, the underlying idea of Lynn White's 
article, "The historical roots of our ecologic 
crisis,"^^ is closely related to my view outlined 
above. In discussing the environmental crisis 
today, he asserts that "both modem technology 
and modem science are distinctively Occident- 
al," that "Human ecology is deeply conditioned 
by beliefs about our nature and destiny — that is, 
by religion," and that "Our science and tech- 
nology have grown out of Christian attitudes to- 
ward man's relation to nature. . . ." In the 
counterculture groups he discerns "a sound in- 
stinct in their affinity for Zen Buddhism," but he 
is doubtful of the viability of these faiths among 
Western people, an opinion with which I agree. 
White ends his article by proposing as "a patron 
saint for ecologists" St. Francis of Assisi, who 
"tried to depose man from his monarchy over 
creation and set up a democracy of all God's 
creatures." 

I do not know whether White would include 
Buddhist priests in a catalog of patron saints for 
ecologists. But let me cite two instances of 
Buddhist practice. When going out for the daily 
mendicancy, it was customary for Southeast 
Asian monks to wait until there was sufficient 
light to see the lines on the palms of their hands, 
lest they should tread on little worms and insects 
while walking. A second example comes from 
the life of Ryokan (1757-1831), a Japanese Zen 
priest and poet who had a particular following 
among farmers and children. He is said to have 
used a mosquito net in summer, not to protect 



192 



Nature in Japanese Culture 



himself from being bitten by mosquitoes, but to 
prevent his unconsciously slapping them while 
sleeping. He left one of his legs outside the net 
so that mosquitoes might live on him. 

Obviously, this kind of sentiment has been 
rapidly fading in Japan. Contemporary Jap- 
anese, while extensively utilizing modem science 
and technology, are not fully aware, however, 
that a view of nature considerably diflFerent 
from their own underlies these activities. In 
their hearts they are still immersed in nature, 
and their attitude is still one of relying upon 
nature. The urgent task before the Japanese 
people is, therefore, that they fully realize 
man's responsibility for nature, unite this reali- 
zation with their traditional closeness to nature, 
and endeavor to overcome the current environ- 
mental crisis. 

Notes 

1 "Of a Promise Kept," in Lafcadio Hearn, A 
Japanese Miscellany, Rutland, Vt. & Tokyo, 1954, 
pp. 11-19. 



2 Lafcadio Hearn (1850-1904) thus came to 
contribute a great deal to the introduction of 
Japanese culture to the Western world. 

3 John Milton, Paradise Lost, I, lines 1 & 4, in 
The English Poems of John Milton (World's 
Classics), Charles William, ed., London, 1971, p. 
114. 

4 Robert Hooke, Micrographia (1665), New 
York, 1938, Preface. 

5 Cotton Mather, The Christian Philosopher, 
London, 1721, p. 8. 

6 Kamo no Chomei, in Anthology of Japanese 
Literature from the Earliest Era to the Mid-Nine- 
teenth Century, Donald Keene, ed., New York, 

1955, p. 221. 

7 Ikutaro Shimizu, in Kindai Nihon Shisoshi 
Koza, Vol. 3, Tokyo, 1960, pp. 9-62. 

8 John Frisch, "Japan's Contribution to Mod- 
em Anthropology," in Studies in Japanese Cul- 
ture, Tokyo, 1963, pp. 225-244. 

9 Ibid , p. 240. 

10 Ibid., p. 243. 

11 Yasunari Kawabata, "Japan the Beautiful and 
Myself," translated by Edward G. Seidensticker. 

12 Ibid. 

13 Lynn White, Jr., Science, Vol. 155, March. 
10, 1967, pp. 1203-1207. 



193 



13 Facts on Household Appliance Energy Use 

Electric Energy Association 



How much energy do 
your appliances use? 

While all major appliances (excluding heat- 
ing and water heating) consume only about 
5% of our nation's total annual energy sup- 
ply, it is, nevertheless, still important that 
we use these appliances in the most effi- 
cient manner possible. 

To help you achieve this, we have reprint- 
ed here a listing* of the more common elec- 
tric appliances and their estimated yearly 
kilowatt hour consumption. These listings 
are based on normal use and may vary some- 
what depending on the size and location of 
your house, the efficiency of your equip- 
ment and the number and living habits of 
the people in your home. 

'Source: annual energy requirements of 
electric household appliances, (1973), Elec- 
tric Energy Association, New York, N.Y, 







Est. kwh* 




Average 


consumed 




wattage 


annually 


Food preparation 






Blender 


386 


15 


Broiler 


1,436 


100 


Carving Knife 


92 


8 


Coffee Maker 


894 


106 


Deep Fryer 


1.448 


83 


Dishwasher 


1,201 


363 


Egg Cooker 


516 


14 


Frying Pan 


1,196 


186 


Hot Plate 


1.257 


90 


Mixer 


127 


13 


Oven, microwave (only) 


1,450 


190 


Range 






with oven 


12,200 


1,175 


with self-cleaning 






oven 


12.200 


1,205 


Roaster 


1,333 


205 


Sandwich Grill 


1.161 


33 


Toaster 


1,146 


39 


Trash Compactor 


400 


50 


Waffle Iron 


1,116 


22 


Waste Disposer 


445 


30 



194 



Food preservation 

Freezer (15 cu ft) 341 1.195 

Freezer 

(Frostless 1 5 cu ft) 440 1 ,761 

Refrigerator (12 cu ft) 241 728 

Refrigerator (Frostless 

12cuft) 321 1,217 

Refrigerator/Freezer 

(14cuft) 326 1,137 

(Frostless 14 cu ft) 615 1.829 



Laundry 

Clothes Dryer 
Iron (hand) 
Washing Machine 

(automatic) 
Washing Machine 

(non-automatic) 
Water Heater 

(quick recovery) 

Comfort conditioning 

Air Cleaner 
Air Conditioner 

(room) 
Bed Covering 
Dehumidifier 
Fan (attic) 
Fan (circulating) 
Fan (rollaway) 
Fan (window) 
Heater (portable) 
Heating Pad 
Humidifier 

Health & beauty 

Germicidal Lamp 

Hair Dryer 

Heat Lamp (infrared) 

Shaver 

Sun Lamp 

Tooth Brush 

Vibrator 

Home entertainment 

Radio 

Radio/Record Player 
Television 
black & white 
tube type 
solid state 
color 
tube type 
solid state 

Housewares 

Clock 

Floor Polisher 
Sewing Machine 
Vacuum Cleaner 





Est. kwh* 


Average 


consumed 


wattage 


annually 


4,856 


993 


1.008 


144 



512 

286 

2,475 
4,474 

50 

860 

177 

257 

370 

88 

171 

200 

1.322 

65 

177 

20 

381 
250 

14 

279 

7 

40 

71 
109 



160 
55 

300 
200 

2 

305 

75 

630 



103 

76 
4,219 
4,811 

216 

860** 
147 
377 
291 

43 
138 
170 
176 

10 
163 

141 

14 

13 
1.8 

16 

0.5 

2 

86 
109 



350 
120 

660 
440 

17 
15 
11 
46 



'KWH is the abbreviation for kilowatt hour. A 
kilowatt hour is equal to 1000 watts of electri- 
city working for one hour. For example: a 
100-watt light bulb left on for 10 hours uses 
one KWH of electricity. 

'Based on 1000 hours of operation per year. 
This figure will vary widely depending on area 
and specific size of unit. 



Here described is an unusual device that generates useful 
energy and in the same process produces more fuel than it 
uses. 



14 



Breeder Reactors 

Walter Sullivan 



How the Breeder Reactor Works 

HEAVY SHIELDING 



.- •li^i^;^^^^^;^^^^^^^;^^^^^^ 







HEAT 
EXCHANGER 




T o Power 



1 * r 
PUMP 




PUMP 



I Iheat 

EXCHANGER 



The breeder reactor is a unique source of energy: In the process of generating 
power to produce electricity, it makes more fuel than it consumes. It uses U-235 
atoms (in short supply) or plutonium for its fuel. Neutrons produced by the 
fission of these elements react with U-238, which is in abundant supply but is 
nonfissionable and therefore useless. The reaction, however, converts the U-238 
into plutonium, which is fissionable and thus can be used as a fuel. This is how 
the breeder works: 

A pump (1) drives liquid sodium into reactor vessel. Neutron radiation from 
reactor core (2) generates heat, raising the temperature of the sodium. The 
neutrons bombard U-238 in the breeder blanket (3) and convert the U-238 into 
plutonium. Reflectors (4) divert neutrons back into reactor. The neutron shield 
(5) prevents any escape of radiation. The heated sodium is transferred (6) to a 
second circulation system (7) which is filled with sodium that is not radioactive. 
This sodium is then used to generate steam for the power plant (8). The original 
sodium i!s recycled back through the reactor. Thus sodium that has passed 
through the radiation environment of the reactor never leaves the heavily 
shielded inner plant. 



An article from The New York Times, July 22, 1973 



Itrkari CKrk 



In 1951 the world's first breeder reac- 
tor—a small, experimental device— went 
into operation at the reactor testing 
station near Idaho Falls, Idaho. In suc- 
ceeding years American atomic energy 
specialists became increasingly convinced 



that such reactors— which, in producing 
energy, manufacture more fuel than they 
consume— offer the best hope of avoiding 
a serious shortage of nuclear fuel, or of 
energy, until new power sources are de- 
veloped. 



195 



196 



Today, however, 23 years later, the 
United States still has not begun con- 
struction of a full-scale breeder plant, but 
other countries have. Last week the 
Soviet Union announced that its big 
breeder plant at Shevchenko, on the west 
shore of the Caspian Sea, had gone into 
commercial operation. 

Next month, the French hope to warm 
up their Phoenix reactor, the first of a 
number of projected European breeder 
reactors. At Kalkar on the Rhine another 
is being built, with West Germany footing 
70 per cent of the bill and Belgium and 
the Netherlands sharing the remainder. 

And at Dounreay, on the bleak north 
coast of Scotland, the British version is 
almost complete. Operating personnel 
have begun taking over some units of the 
complex, whose final cost is expected to 
be $l-billion. It is hoped that power gen- 
eration can start late this year or early in 
1974. 

More than 99 per cent of natural urani- 
um is U-238, whose atoms cannot be split 
in a reactor. That is, they are useless as 
reactor fuel. The attraction of a breeder 
reactor is that, while "burning" fission- 
able uranium (U-235) or some other 
nuclear fuel, it converts the U-238 pre- 
sent into Plutonium, and plutonium is 
useful as reactor fuel. In this way the 
reactor can produce more fuel than it 
consumes, as illustrated in the diagram. 

The reasons for the European progress, 
and American tardiness, are several. The 
United States, because of its huge atomic 
weapons program, has had ample facilities 
for extracting the tiny fraction of U-235 
in uranium as it occurs in nature. This 
provided the American nuclear energy 
program with ample fuel and thus there 
was no early pressure to build breeders to 
convert U-238. 

The Europeans, with meager facilities 
for extracting U-235, were early moti- 
vated to develop breeders. But now, in 
view of the world's limited uranium re- 
serves, the United States Atomic Energy 
Commission has been pressing for a fuU- 
scale prototype breeder plant. However, 
the project has been stalled by legal 
maneuvers of those who believe such re- 
actors could be hazardous. 

The projected prototype plant would 
be situated near Oak Ridge, Tenn., the 



site of various nuclear installations, but 
the construction has been blocked by the 
court action of the Scientists' Institute 
for PubUc Information. 

A major concern of those with mis- 
givings about this type of reactor is the 
large amount of plutonium involved. The 
Dounreay reactor is impressively large, 
although less than a quarter the size of 
those that, it is expected, must be built to 
be economical. And yet this plant will 
contain a ton of plutonium. 

The breeders foreseen for the future 
will produce many tons of this material 
each year. If even small amounts escaped 
into the air or water of a region, they 
could wreak havoc, for the substance can 
be lethal and retains its radioactivity for 
many years. Elaborate measures are taken 
in the breeder plants to avert any such 
escapes, but opponents of the program 
fear they are not foolproof. 

Another concern is the possibility that, 
with so much of the stuff in atomic 
plants around the world, some of it might 
be smuggled off to make atomic bombs. 
Only a small amount is needed for such a 
weapon. 

While those who have designed the 
breeders believe they have made adequate 
provision against any "credible" mishap, 
the technology is complex. It requires, 
for example, Uquid metal at a temper- 
ature as high as 1000 degrees Fahrenheit 
flowing at extreme speed to keep the re- 
actor from overheating. The flow rate in 
the Dounreay reactor will be 3.5 tons a 
second. The coolant used is liquid sodium 
because it does not boil at the high tem- 
peratures that give breeder reactors their 
superior efficiency. However sodium 
reacts almost explosively on contact with 
water, so the plumbing must be fool- 
proof. 

In those countries where the breeders 
are in operation or nearing completion- 
Britain, France and the Soviet Union— the 
pubUc seems largely to have been per- 
suaded that the precautions are adequate. 
It is, however, these same three countries 
that have pressed forward with supersonic 
transport development, whereas in the 
United States the SST program has been 
suspended because of environmental 
concerns. The parallel, so far as breeder 
reactors are concerned, is striking. 



A lively response to current characterization of the scientist 
as a Doctor Frankenstein, a Mandarin, or an Adding Machine. 



15 Reflections of a Working Scientist 

Steven Weinberg 

An article from Daedalus, 1974 



I ONCE HEARD the period from 1900 to the present described as "this slum of a cen- 
tury." Certainly the case could be made that the twentieth century fails to come up 
to the nineteenth in the grand arts — in music, in literature, or in painting. Yet the 
twentieth century does stand among the heroic periods of human civilization in one 
aspect of its cultural life — in science. We have radically revised our perceptions of 
space, time, and causation; we have learned the basic principles which govern the 
behavior of matter on all scales from the atomic to the galactic; we now understand 
pretty well how continents form and how the genetic mechanism works; we may be 
on the verge of finding out the over-all space-time geometry of the universe; and 
with any luck we will learn by the end of the century how the brain is able to 
think. It seems strange to me that of all the enterprises of our century, it should be 
science that has come under attack, and indeed from just those who seem most in 
tune with our times, with contemporary arts and ways of life. 

I take it that my role in this issue is not so much to defend science — if science 
turns you off, then a scientist defending science must absolutely disconnect 
you — but rather to serve as an exhibit of the "genuine article," the unreformed 
working scientist. I will therefore simply list three of what I take to be the common 
current challenges to science, and react to each in turn. 

These reflections arise from my own experiences as a theoretical physicist 
specializing in the theory of elementary particles, and I am not really certain how 
far they would apply to other areas of science. I intend most of my remarks to 
apply to the whole range of natural nonbehavioral pure sciences, but some of 
them may have a more limited validity. On the other hand, I explicitly do not in- 
tend my remarks to apply to the social or psychological sciences, which seem to me 
to face challenges of a special and different sort. 

The Scientist as Dr. Frankenstein 

I suppose that public attitudes toward science, favorable or unfavorable, are 
shaped far more by the expectation of good or evil technological developments, 
than by approval or disapproval of the scientific enterprise itself. This is much too 
big a problem to cover here in any but the most fragmentary way, and it can be 
logically separated from a judgment of science qua science, but it is a matter of 
such overriding public concern that it cannot be altogether passed over. I will dis- 
cuss it briefly under the headings of five criticisms of the part that "pure" scientists 
have played in the creation of new technology. 



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1. Scientists pursue their research, without taking due account of the harm that 
may be done by practical application of their work. 

This is in some degree true. There are even some scientists, though I think not 
many, who argue that it is their business to pursue knowledge wherever it leads 
them, leaving the question of practical application to businessmen, statesmen, and 
generals whose responsibility it is to worry about such matters. For example, many 
critics point to the nuclear weapon as the ugliest product of "pure" research. But 
this charge overestimates the degree to which the scientist can look into the future. 
The nuclear physicists who discovered fission at the end of the 1930's were not so 
much indifferent to the danger of nuclear weapons as they were unaware of it. 
(Meitner, Strassmann, and Hahn, for example, published their work in the open 
literature in 1938-1939.') Later, of course, nuclear weapons were developed in the 
United States and elsewhere by scientists who knew perfectly well what they were 
doing, but this was no longer for the sake of pure research, but in the hope of help- 
ing to win World War II. 

I do not see how my present work on elementary particles and cosmology could 
possibly have any applications, good or evil, for at least twenty years. But how can 
I be sure? One can think of many dangers that might arise from present pure 
research, especially research on genetics and the human mind, and I hope that the 
researchers will be able to hold back the most dangerous lines of research, but they 
will not have an easy time of it. For a scientist unilaterally to cut off progress along 
certain lines because he calculates that more harm than good will come out of it 
requires a faith in the accuracy of his calculations more often found among 
businessmen, statesmen, and generals than among natural scientists. And do the 
critics of science really want the scientist and not the public to make these 
decisions? 

2. In order to gain material support for their "pure" research or for themselves, 
scientists prostitute themselves to industry or government by working directly on 
harmful technological developments. 

Again, scientists being human, this charge is, in some measure, true. One has 
only to think of Leonardo's letter to the Duke of Milan offering his services in the 
construction of ingenious instruments of war. It seems strange to me, however, to 
single out scientists to bear the burden of this charge. Returning to the unavoidable 
example of nuclear weapons, Oppenheimer, Fermi, and the others who developed 
the nuclear fission bomb in World War II did so because it seemed to them that 
otherwise Germany would develop the bomb first and would use it to enslave the 
world. Since World War II a large fraction of the physicists whom I know personally 
have washed their hands of any involvement, part-time or full-time, in military 
research and development. I know of no other group, certainly not workers or 
businessmen, who have shown a similar moral discrimination. And what of those 
scientists who have not washed their hands? Admittedly; there are some who work 
on defense problems for money, power, or fun. There are a few others who are con- 
vinced on political grounds that any weapon that adds to military strength should 
be developed. However, most of the "pure" scientists in the U.S. who have been 
involved in military work have tried to draw a line at one point or another, and to 



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work only on a limited class of problems where, rightly or wrongly, they felt that 
more good than harm could be done. My own experience has been mostly through 
work in the JASON group of the Institute for Defense Analyses, and more recently 
for the U.S. Arms Control and Disarmament Agency. Many of the members of 
JASON, myself among them, simply declined to do work in support of the U.S. 
effort in Vietnam. Others worked on the so-called "electronic battlefield," because 
they believed (as it happened, wrongly) that by laying an impassible barrier 
between North and South Vietnam, they would induce the U.S. to stop bombing 
North Vietnam. In recent years many of us have tried to switch our work over en- 
tirely to problems of strategic arms control, but it is not easy; the Nixon administra- 
tion has recently fired or canceled the consultant contracts of many of those in the 
Arms Control Agency (including me) who had worked on SALT. 

I would like to be able to argue that academic scientists have had a humane 
and restraining influence on military poHcy, but looking back, it is hard to find 
evidence that I, or even those much more active and influential than myself, have 
had any influence at all. However, I am convinced at least that the world would 
not be better off if we had kept our hands out. 

3. Scientific research of all types is oppressive, because it increases the power of the de- 
veloped nations relative to the underdeveloped, and increases the power of the ruling 
classes relative to the ruled. 

This charge rests on such far-ranging political and historical assumptions that I 
cannot begin to do it justice. I am not convinced that new technology tends to sup- 
port old power structures more than it tends to shake them up and put power in 
new hands. I am also not convinced that one should always support un- 
derdeveloped nations in conflict with more modern ones; for instance, it is the Arab 
states that threaten the existence of Israel, not the other way around. Furthermore, 
this argument for stopping scientific research logically requires a permanent 
general strike by everyone whose work helps to keep modern industrialized society 
going, not just by scientists. Perhaps some do reach this conclusion, but they must 
have more faith in their abihty to look into the future than I have in mine. I would 
agree, however, that certain special kinds of technology are particularly liable to be 
used in an oppressive way, especially the modern computer with its capacity for 
keeping track of enormous quantities of detailed information. I would be in favor 
of cutting off specific kinds of research where specific dangers clearly present 
themselves, but decisions in this realm are always very hard to make. Usually, as in 
the case of computer technology, it is not possible, by closing off lines of research, 
to ward off the dangers of technology without at the same time giving up its oppor- 
tunities. 

4. Scientific research tends to produce technological changes which destroy human 
culture and the natural order of life. 

I am more sympathetic to this charge than to most of the others. Even apart 
from what has been done with new weapons of war, a terrible ugliness seems to 
have been brought into the world since the industrial revolution through the prac- 
tical applications of science. As an American, I naturally think of what I see from 
my car window: the great superhighways cutting cross the countryside, the subur- 



199 



ban strips with their motels and gas stations, and the ghttering Hfelessness of Park 
Avenue. 

I am not sure why this should have happened. Earlier new technology, such as 
the pointed arch and the windmill, created more beauty than ugliness. Perhaps it is a 
question of scale; so many people now have cars and electric appliances that the im- 
pact of highways, factories, and power stations is too great to be absorbed into the 
natural background — unlike an occasional windmill or cathedral. 

If this diagnosis is correct, then a cure will be extraordinarily difficult. When in- 
dustrialization offered cars and electric appliances to the general public, it offered a 
mobility and ease previously enjoyed only by the few who could keep carriages and 
servants, and people accepted with alacrity. Are we now going to ask them to go 
back to the status quo ante? I suppose that the only answer here, as before, is to 
make judgments as well as we can in favor of the civilizing technology and against 
the brutalizing. And there are examples of civilizing technology, like the bicycle, 
the LP record, and the railroad. As W. G Hoskins, himself a bitter enemy of the 
superhighway and the jet airport, says in his wonderful book. The Making of the 
English Landscape:' 

Indeed, the railways created as much beauty as they inadvertently destroyed, but of a totally 
different kind. The great gashes they inflicted on the landscape in their cuttings and em- 
bankments healed over, and wild flowers grew abundantly once more. Going down to the 
south-west in spring, the cuttings through Somerset and Devon sparkle with primroses. Even 
in Clare's own country, the railway has been absorbed into the landscape, and one can enjoy 
the consequent pleasure of trundling through Rutland in a stopping-train on a fine summer 
morning; the barley fields shaking in the wind, the slow sedgy streams with their willows 
shading meditative cattle, the early Victorian stations built of the sheep-grey Ketton stone 
and still unaltered. . . . 

The problem of identifying the civilizing technology and of regulating society so as 
to suppress the rest is far too complicated to go into here. In any case, it is not a 
problem on which scientists' opinions are worth more than anyone else's. 

5. While serious human needs go unfulfilled, scientists spend large sums on 
accelerators, telescopes, etc., which serve no purpose other than the gratification of 
their own curiosity. 

There is no doubt that a great deal of scientific work is carried out without any 
expectation of practical benefit, and indeed would be carried out even if it were 
certain that no practical benefit would result. It is also true that some of this work is 
very expensive, for the simple reason that in any given field the experiments that 
can be done with string and sealing wax tend to have been done already. 

I suppose that if one takes the strictly utilitarian view that the only standard of 
value is integrated public happiness, then scientists ought to be blamed for doing 
any research not motivated by calculations of how much it would contribute to 
public welfare. By the same reasoning, no one ought to support the ballet, write 
honest history, or protect the blue whale, unless it can be shown that this will max- 
imize public happiness. However, anyone who believes that knowledge of the uni- 
verse is, like beauty or honesty, a good thing in itself, will not condemn the scien- 
tist for seeking the support he needs to carry out his work. 

This does not mean that the support must be granted; the public has to weigh 
the practical benefits that will be "spun off' — the teaching that most pure scientists 



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do to earn their salaries and the general strengthening of technological capabilities 
that seems to accompany pure research. These are hard to calculate. As Julian 
Schwinger points outs,' 

And one should not overlook how fateful a decision to curtail the continued development of 
an essential element of the society may be. By the Fifteenth Century, the Chinese had 
developed a mastery of ocean voyaging far beyond anything existing in Europe. Then, in an 
abrupt change of intellectual climate, the insular party at court took control. The great ships 
were burnt and the crews disbanded. It was in those years that small Portuguese ships 
rounded the Cape of Good Hope. 

I do not want to argue here about whether the public gets its money's worth. My 
point is that, in seeking support for scientific research, scientists need not agree 
with the public as to why the work should be done. 



The Scientist as Mandarin 

There is a widespread suspicion that science operates as a closed shop, closed to 
unorthodox ideas or uncomfortable data, especially if these originate outside a 
small circle of established leaders. One recalls countless movies in which elderly 
scientists in white coats wag their grey goatees at the young hero and expostulate, 
"But what you propose is quite impossible, because. . . . If the public is receptive 
to Sunday supplement stories about unidentified flying objects or quack cures for 
arthritis, it is in part because they do not believe the scientific establishment gives 
the possibility of such things a fair hearing. In short, not everyone is convinced that 
the scientists are as open-minded as they ought to be. 

This is not one of the most important or profound challenges to science; 
nevertheless, I want to present some answers to it here, because this will give me a 
chance to explain some of my enthusiasm for the process of scientific research. Also, 
this is an easy challenge to meet, because it arises not so much from political or 
philosophical differences, as from simple misapprehensions of fact. For convenience 
I will discuss separately the questions of the receptivity of scientists to ideas from 
young or unestablished scientists; to ideas from outside the scientific profession; to 
unorthodox ideas from whatever source; and to uncomfortable data. 

1 . How open is science to new ideas from the young, unestablished scientist? 

Of course, there is a scientific cursus honorum, and those who are just starting are 
less influential than their seniors. The fact is, however, the system of communication 
in science, probably more than that in any other area of our society, allows the new- 
comer a chance at influencing his field.* 

In physics, my own field, the preeminent journal is the Physical Review. Almost 
all physicists at least scan the abstracts of the articles in their own specialties in 
each issue. The Physical Review has a panel of over a thousand reviewers who 
referee submitted papers, but in fact about 80 percent of all papers are accepted, 
and of the others a good proportion are rejected only because they are unoriginal. 
The Physical Review is an expensive operation, supported by subscriptions and 
page charges paid by the authors' institutions, but if an author cannot arrange to 
have the page charge paid, the paper is published anyway (though admittedly with 
a few months' delay). 



201 



There is also a more exclusive journal, Physical Review Letters, which publishes 
only short papers judged to contain material of special importance. As might be ex- 
pected, there is a crush of authors trying to get their papers published in Physical 
Review Letters, and every year sees several editorials in which the editor wrings 
his hands over the difficulty of making selections. Nevertheless, Physical Review 
Letters does a good job of judging the paper rather than the author. (In 1959, 
when I was an unknown research associate, I had several papers accepted by 
Physical Review Letters; in 1971, as a reasonably well-known professor at M.I.T., I 
had one rejected.) 

In addition to the Physical Review and Physical Review Letters, there are a 
great number of other physics journals in which it is even easier to publish. So well 
does this system work that it has become quite common for a physics department 
chairman who needs advice on the work of a young physicist in his own depart- 
ment to solicit comments from senior physicists in other universities who have 
never even met the young physicist, on the assumption that they will of course be 
familiar with his or her published work. 

Of course, the humanities and social sciences also have widely circulated jour- 
nals, but I have the impression that they do not provide anywhere near so effective 
a channel of communication for the young or unestablished scholar as do the 
natural science journals. The reason is that the natural sciences have more objective 
(though not necessarily more reliable) standards for judging the value of a piece of 
work. A young physicist who succeeds in calculating the fine-structure constant 
from first principles, or in solving any one of dozens of other outstanding problems, 
is sure of a hearing. For instance, my own subfield of theoretical physics was 
shaken up in 1971 by work of a previously unknown graduate student at Utrecht,* 
and then again in 1973 by a previously unknown graduate student at Harvard.' I 
suspect that a graduate student in history who has revolutionary ideas about the 
fall of the Roman Empire might have a harder time getting a hearing. 

The less academic professions such as law, medicine, business, the military, and 
the church, are even less open. In these, a young person's work is, I believe, 
directed to a small circle of superiors rather than to an international community, 
and it is natural for their judgment of his ideas to be colored by subjective factors, 
such as the degree to which he accommodates himself to their preconceptions. 
Only a few, after getting over these hurdles, reach a level from which they can 
communicate to their whole profession. 

None of this reflects any moral superiority in the scientists themselves. It is a 
natural outgrowth of the fact that they work in specialities small enough that a 
beginner has a chance to communicate with the whole international community of 
specialists, and with standards objective enough that they all can recognize the 
value of a piece of important research. However, it does seem peculiarly inap- 
propriate to charge the sciences with being closed to new ideas from the young and 
unestablished. 

For the sake of fairness, I should add here that these observations are strongly 
colored by my own experience as a theoretical physicist who works alone at his desk 
or at a blackboard with one or two colleagues. I concede that the scientific enter- 
prise may look very different to experimental scientists, and most especially to those 
experimentalists in high energy nuclear physics who work in large research teams. 



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Reflections of a Working Scientist 



For instance, a recent paper' reporting the discovery of an important new class of 
neutrino interaction iiad no less than fifty-five authors from seven different in- 
stitutions. I do not know to what extent a junior member of such a team can really 
get a hearing for an idea of his own. 

2. How open is science to new ideas from outside? 

My remarks so far only indicate the openness of the scientific community to ideas 
which are at least expressed in a language that is familiar to established scientists and 
deal with problems that they recognize as important. Otherwise, the work is unlikely 
to be published in a scientific journal or, if published, to be read. Then what about 
the prophet in the wilderness, the truly original genius outside the scientific com- 
munity whose ideas cannot be understood by the pedants in university science 
departments? 

I submit that there is no such person. I do not know of any piece of work in 
physics in this century which was originally generally regarded as crack-pot — as op- 
posed to merely wrong — which subsequently turned out to be of value. It is true 
that Einstein was only a patent clerk when he invented special relativity, but his 
work was on a recognized problem, was duly published in the Annalen der Physik, 
and was received with respect, though not with instant acceptance by the physics 
community. 

In reaching a judgment on the closed-mindedness of scientists to ideas from 
outside their ranks, it should be kept in mind that the system of scientific com- 
munication has evolved, not merely to transmit ideas and data, but to do so in a 
way that leaves the scientist time to get some of his own work done. If we had to 
struggle through every paper, even when the author did not accept the conventions 
of scientific language, we would literally have no time to do anything else. It may 
be that we miss a pearl of wisdom every century or so, but the price has to be paid. 

3. How open is science to truly revolutionary ideas? 

Even granting that the scientific communication system works as well as it ought 
to, are not scientists' minds closed to ideas, from whatever source, which challenge 
orthodox scientific dogma? (As Gershwin tells us, "They all laughed at Wilbur and 
his brother, when they said that man could fly. ") Many laymen and some scientists 
seem to believe that any number of scientific revolutions would immediately become 
possible if only scientists would give up some of their preconceptions. 

I believe that this is a mistake, and arises from a misconception as to the nature 
of scientific advance. The scientific principles which at any given moment are 
accepted as fundamental are like structural timbers which support a great 
superstructure of successful predictions. It is easy to imagine knocking down any of 
these timbers, but very hard to imagine what would then keep the roof from falling 
on our heads. 

For a major scientific advance to occur, it must become clear not only that fun- 
damental changes are necessary, but also how the successes of the previous theory 
can be saved. For example in 1957 T. D. Lee and C. N. Yang brought about a 
revolution in physics through their proposal that parity is not conserved— that is, 
that there is an absolute distinction in nature between left and right.' (It can be 
shown mathematically that if right and left are equivalent, then every physical 



203 



state can be classified as having odd or even parity, according to how it seems to 
change when viewed in a mirror. It can also be shown that the parity is con- 
served — that is, it does not change with time.) It was quite easy to imagine that 
parity is not conserved; what was hard to see was that parity conservation had to be 
violated, and that it could be violated without losing the spectroscopic selection 
rules and other consequences which had given rise in the first place to the idea of 
parity conservation. As it happened, Lee and Yang were led to their proposal by a 
puzzle in meson physics. Two different kinds of meson were identified as having 
positive and negative parity respectively, through their decay into states of positive 
and negative parity, and yet the masses and lifetimes of the two mesons were 
observed to be identical. Many solutions were tried, including fundamental 
changes in the principles of quantum mechanics. Finally, rejecting any such radical 
solution, Lee and Yang proposed that the two different mesons were really only 
one, that the meson had seemed like two because it could decay both into states of 
the same and of different parity. This proposal would have gotten nowhere if they 
had not pointed out at the same time that parity could be changed in these decays 
because they were "weak" (that is, they have rates only of order lO^/sec per par- 
ticle), thereby leaving unchallenged the successful predictions of parity conserva- 
tion in the much faster (say, 10*° to 10'*/sec) "strong" and electromagnetic 
processes. 

Even the greatest scientific revolutions show a similar conservatism. Einstein 
changed our understanding of space and time, but he did so in a way which was 
specifically designed to leave our understanding of electricity and magnetism in- 
tact. What the scientist needs is not a wide open mind, but a mind that is open just 
enough, and in just the right direction. 

4. How open is science to uncomfortable new data? 

One often reads in popular histories of science that "So and so's data showed 
clearly that this and that were false, but no one at the time was willing to believe 
him. Again, this impression that scientists wantonly reject uncomfortable data is 
based on a misapprehension as to the way scientific research is carried on. 

The fact is that a scientist in any active field of research is continually bom- 
barded with new data, much of which eventually turns out to be either misleading 
or just plain wrong. (I speak here on the basis of my experience in elementary par- 
ticle physics and astrophysics, but I presume that the same is true in other fields as 
well.) When a new datum appears which contradicts our expectations, the 
likelihood of its being correct and relevant must be measured against the total mass 
of previously successful theory which might have to be abandoned if it were 
accepted. 

During the latter half of the nineteenth century, for instance, there were known 
anomalies in the motions of the moon, Encke's comet, Halley's comet, and the 
planet Mercury, all of which seemed to contradict Newton's theory of gravitation. 
These anomalies might have caused a tremendous amount of effort to be wasted 
looking for alternative theories of gravitation, but most physicists either ignored the 
data or assumed that some less radical explanation would turn up.' As it happened, 
they were 75 percent correct; simple explanations (such as an improvement in the 
treatment of tidal forces) were later found for the anomalies in the motions of the 



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Reflections of a Working Scientist 



moon and the comets. The anomaly In the motion of Mercury did, in 1916, turn 
out to be of fundamental importance when Einstein showed how it arose from 
relativisitic corrections to Newtonian mechanics. But even this is an exception that 
proves the rule. If physicists had taken the anomaly in the motion of Mercury 
seriously from the beginning, presumably they would also have taken the 
anomalies in lunar and cometary motions seriously, and would thereby have been 
led away from rather than toward the discovery of general relativity. 

Here is a simpler and more recent example. At a high energy physics con- 
ference in 1962, data were reported to the effect that neutral K mesons and their 
antiparticles can both decay into a positive pi-meson, an electron, and a neutrino. 
If true, this would have overturned a theory of weak interactions, the "current- 
current model," which had served as the basis of a great number of successes in 
other contexts. I remember Murray Cell- Mann rising and suggesting to the 
meeting that since the experiments didn't agree with the theory, the experiments 
were probably wrong. The next generation of experiments showed that this was in- 
deed the case. 

I realize that it may seem to the reader that the theorists in these examples were 
merely closed-minded and lucky. However, no scientist is clever enough to follow 
up hundreds of clues that lead in hundreds of different directions away from exist- 
ing theories. (This is especially true of data of dubious provenance which would 
revolutionize scientific knowledge, such as evidence on unidentified flying ob- 
jects, psychokinesis, and copper health bracelets. ) What a scientist must do is to be 
open to just that piece of new data which can be integrated into a comprehensive 
new theory, and to file the rest. 

Above all, in judging the openness of science, one should remember its unique 
capacity for discovering its own mistakes. Most natural scientists have the ex- 
perience several times in their lives of being forced by new data or mathematical 
demonstrations to recognize that they have been seriously wrong about some im- 
portant issue. (For instance, I was sure that Lee and Yang were wrong when they 
first proposed that parity is not conserved, and became convinced only by subse- 
quent experiments.) On a larger scale, the physics community has many times been 
forced by new data to scrap large bodies of existing theory. If this takes away from 
our reputation for infaUibility, it should also take away the impression that our 
minds are closed. 

The Scientist as Adding Machine 

The most profound challenge to science is presented by those, such as Laing 
and Roszak, who reject its coldness, its objectivity, its nonhumanity, in favor of 
other modes of knowledge that are more human, more direct, more rapturous." I 
have tried to understand these critics by looking through some of their writings, 
and have found a good deal that is pertinent, and even moving. I especially share 
their distrust of those, from David Ricardo to the Club of Rome, who too con- 
fidently apply the methods of the natural sciences to human affairs. But in the end 
I am puzzled. What is it that they want me to do? Do they merely want the natural 
scientist to respect and participate in other modes of knowledge as well as the 
scientific? Or do they want science to change in some fundamental way to incor- 



205 



porate these other modes? Or do they want science simply to be abandoned? These 
three possible demands run together confusingly in the writings of the critics of 
science, with afguments for one demand often being made for another, or for all 
three. In accordance with my role here as a specimen of the unregenerate working 
scientist, I will try in what follows to keep the issues raised by these three demands 
logically distinct, and to analyze each in turn. 

1 . We should recognize the validity of other modes of knowledge, more human and 
direct than scientific knowledge. 

Roszak expresses this view in terms of a metaphor he attributes to Stephen 
Toulmin:*' 

When we insist on making scientific expertise the arbiter of all knowledge, it is exactly like 
believing that cartographers know more about the terrain than the natives who live there, or 
the artists who have come to paint its beauties, or the priests who tend its holy places. 

This does not seem to me to b? an issue which raises any problems for science. 
Scientists, like other folk, are perfectly willing to respect and participate in various 
kinds of mental activity — aesthetic, moral, even religious. Perhaps the hang-up is 
with the word "know." For my part, since I view all epistemological arguments 
with perplexity anyway, I am willing to describe the perceptions of the Lake of 
Nemi experienced by Turner or the priests of Diana as "knowledge." For certain 
practical decisions, such as where to have a picnic, I would even be guided by this 
"knowledge" rather than by a contour map of the lake. Continuing Toulmin's 
metaphor, the real problem is whether maps should all be redesigned to incor- 
porate aesthetic and moral information, or, if this is impossible, whether maps have 
any value at all? This is the problem I address below. 

2. Science should change so as to incorporate other modes of knowledge. 

To quote Roszak again," 

What should come of this ideally is not some form of separate-but-equal coexistence, but a 
new cultural synthesis. 

And again," 

It is a matter of changing the fundamental sensibility of scientific thought — and doing so 
even if we must drastically revise the professional character of science and its place in our 
culture. There is no doubt in my mind that such a revision would follow. Rhapsodic intellect 
would slacken the pace and scale of research to a degree that would be intolerable by 
current professional standards. It would subordinate much research to those contemplative 
encounters with nature that deepen, but do not increase knowledge. And it would surely end 
some lines of research entirely out of repugnance for their reductionism, insensitivity, and 
risk. 

My answer is that science cannot change in this way without destroying itself, 
because however much human values are involved in the scientific process or are 
affected by the results of scientific research, there is an essential element in science 
that is cold, objective, and nonhuman. 

At the center of the scientific method is a free commitment to a standard of 
truth. The scientist may let his imagination range freely over all conceivable world 
systems, orderly or chaotic, cold or rhapsodic, moral or value-free. However, he 
commits himself to work out the consequences of his system and to test them 
against experiment, and he agrees in advance to discard whatever does not agree 



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with observation. In return for accepting this discipMne, he enters into a 
relationship with nature, as a pupil with a teacher, and gradually learns its underly- 
ing laws. At the same time, he learns the boundaries of science, marking the class 
of phenomena which must be approached scientifically, not morally, aesthetically, 
or religiously. 

One of the lessons we have been taught in this way is that the laws of nature 
are as impersonal and free of human values as the rules of arithmetic. We didn't 
want it to come out this way, but it did. When we look at the night sky we see a 
pattern of stars to which the poetic imagination gives meaning as beasts, fishes, 
heroes, and virgins. Occasionally there is drama — a meteor moves briefly across the 
sky. If a correlation were discovered between the positions of constellations and 
human personalities, or between the fall of a meteor and the death of kings, we 
would not have turned our backs on this discovery, we would have gone on to a 
view of nature which integrated all knowledge — moral, aesthetic, and scientific 

But there are no such correlations. Instead, when we turn our telescopes on the 
stars and carefully measure their parallaxes and proper motions, we learn that they 
are at different distances, and that their grouping into constellations is illusory, only 
a few constellations like the Hyades and Pleiades representing true associations of 
stars. With more powerful instruments, the whole system of visible stars stands 
revealed as only a small part of the spiral arm of one of a huge number of galaxies, 
extending away from us in all directions. Nowhere do we see human value or 
human meaning. 

But there are compensations. Precisely at the most abstract level, furthest 
removed from human experience, we find harmony and order. The enormous fir- 
mament of galaxies is in a state of uniform expansion. Calculations reveal that the 
rate of this expansion is not very different from the "escape velocity " which would 
just barely allow the expansion to continue forever. Furthermore, there seems to be 
a frame of reference in which the expansion is spherically symmetric, and we find 
that this cosmic frame is rotating at less than one second of arc per century. 

The order we find in astronomy on the largest scale is only a small part of a 
much grander intellectual picture, in which all the systematic features of nature 
revealed by experiment flow deductively from a few simple general laws. The 
search for these laws forces us to turn away from the ordinary world of human 
perception, and this may seem to the outsider to be a needless specialization and 
dehumanization of experience, but it is nature that dictates the direction of our 
search. 

When Galileo measured the frequencies of pendulums of varying lengths, 
Simplicio might have objected that this was a purely artificial phenomenon in- 
vented by Galileo himself, less worthy of attention than the natural bodies falling 
freely through the open air that had been discussed by Aristotle. However, Galileo 
perceived the existence of laws of motion which could more easily be approached 
through the nearly frictionless motion of a pendulum than through the study of 
bodies subject to the resistance of the air. Indeed, Galileo's great contribution to 
mechanics was precisely this perception, rather than the discovery of any particular 

law of motion. 

In the same way, when we spend millions today to study the behavior of par- 
ticles that exist nowhere in the universe except in our accelerators, we do so not out 



207 



of a perverse desire to escape ordinary life, but because this is the best way we 
know right now to approach the underlying laws of nature. It is fashionable these 
days to emphasize the social and political influences upon scientific research, but 
my reading of history and my own experience in physics convince me that society 
provides only the opportunity for scientific research, and that the direction of this 
research is what it is to an overwhelming degree because the universe is the way it 
is. 

We have, of course, a long way to go in understanding the laws of nature." 
However, as far as we can now see, these laws are utterly cold, impersonal, and 
value free. By this, I don't at all mean that they are without beauty, or that there 
are no consolations in science. What I mean is that there does not seem to be 
anything in the laws of nature which expresses any concern for human affairs, of 
the sort which we, in our warm-blooded furry mammalian way, have happily 
learned to feel for one another. 

Having committed ourselves to the scientific standard of truth, we have thus 
been forced, not by our own choosing, away from the rhapsodic sensibility. We can 
follow Roszak s lead only by abandoning our commitment. To do so would be to 
lose all of science, and break off our search for its ultimate laws. 

3. If science cannot he reformed, it should he abandoned. 

One must doubt that the world would be happier if we could forget all about the 
laws of nature. The prescientific mind peopled the world not only with nymphs and 
dryads, but also with monsters and devils; at least in one historian's view, it was only 
the triumph of science that put an end to the burning of witches." But suppose for 
the sake of argument that the case could be made that we would be happier if 
science were driven into some obscure utilitarian corner of our consciousness. Should 
we let this happen? 

In the end, the choice is a moral, or even a religious, one. Having once com- 
mitted ourselves to look at nature on its own terms, it is something like a point of 
honor not to flinch at what we see. For me, and perhaps for others, the helplessness 
of man in the face of pain and death also gives a certain bitter satisfaction to the 
attempt to master the objective world, if only in the mind. Roszak and Laing point 
out what they see as the moral dangers of objectivity, fearing that it is likely to 
leave the scientist himself as cold and value free as an adding machine. I do not see 
this happening to my colleagues in science. But, in gurus and flower-children, I do 
see the danger of subjectivity, that the rejection of an external standard of truth 
can leave a person as solipsistic and self-satisfied as a baby. 

Finally, I must emphasize again that the "coldness " I have referred to above 
only characterizes the discovered content of science, and has nothing to do with the 
wonderfully satisfying process of scientific research. In the last section I tried to 
show how scientists are joined together in a world society, fairer and more open 
than most. On an individual level, although we accept a discipline in testing our 
ideas against experiment, the generation of scientific premises is left to the scien- 
tist's imagination, guided but not governed by his previous experience. As Gerald 
Hoi ton recently reminded us in citing Einstein's letter to Solovine, the method of 
scientific discovery often involves a logically discontinous leap upward from the 
plane of experience to premises." For some scientists, in our time notably Einstein 
and Dirac, the aesthetic appeal of the mathematical formalism itself often suggested 



208 



Reflections of a Working Scientist 

the direction for this leap. And even though scientific research may not fill us with 
the rapture suggested by a Van Gogh, the mood of science has its own beauty— clear, 
austere, and reflective, like the art of Vermeer. Or to use a different simile: if you 
accept the cliche that hearing a Bach fugue is like working out a mathematical 
theorem, then you ought also to realize that working out a mathematical theorem is 
like hearing a Bach fugue. 

In the Science Museum in Kensington there is an old picture of the Octa- 
gon Room of the Greenwich Observatory, which seems to me beautifully to ex- 
press the mood of science at its best: the room laid out in a cool, uncluttered, early 
eighteenth-century style, the few scientific instruments standing ready for use, 
clocks of various sorts ticking on the walls, and, from the many windows, filling the 
room, the clear light of day. 

Refehences 

1. L. Meitner, F. Strassmann, and O. Hahn, Zeitschrift fllr Physik. 109 (1938), p 538; O Hahn and F 
Strassmann, NaturuHssenschaften, 26 (1938), p 756 

2. W G. Hoskins, The Making of the English Landscape (London: Hodder and Stoughton, 1955). 

3. J. Schwinger, in Nature of Matter— Purposes of High Energy Physics, ed L. C. L. Yuan (Upton, 
N.Y.: Brookhaven National Laboratory, 1965), p 23 

4 The following remarks are based on my own observations, but the general conclusion, that the scien- 
tific communication system operates in a fair and open manner, is supported by detailed statistical 
studies See H. Zuckerman and R. K. Merton, Minerva, 9 (1971), p 66 and Physics Today (July 1971), 
p 28. For comments on the reward system in science, see S. Cole and J R Cole, American Sociology 
Review. 32 (1967), p, 377 

5 G t Hooft, Nuclear Physics, B33 (1971), p. 173 

6. H. D. Politzer, Physical Review Letters, 30 (1973), p. 1346. 
7 F. J Hasert et ai. Physical Review Letters, 46B (1973), p 121. 

8. The original papers on this subject are conveniently assembled in The Development of Weak 
Interaction Theory, ed. P. K. Kabir (New York: Gordon and Breach, 1963) 

9. The history of these problems is reviewed by S. Weinberg, Gravitation and Cosmology (New York: 
John Wiley, 1972), Sec. 12. Also see E Whittaker, A History of the Theories of Aether and Elec- 
tricity (Edinburgh: Thomas Nelson, 1953), 2, Ch. 5. 

10 For a bibliography and useful comments, see C. Frankel, Science, 180 (1973), p 927. 

11. T Roszak, Where the Wasteland Ends (Garden City, NY.: Doubleday Anchor Books, 1973), p 375 

12. T. Roszak, unpublished comment on an earher version of the present article. 

13. Roszak, Where the Wasteland Ends, pp. 374-375. 

14. 1 have attempted to describe how far along we are now in coming to an understanding of this deduc- 
tive order, in Science, 180 (1973), p. 276. 

15. H. R. Trevor-Roper, The European Witch-Crazes of the Sixteenth and Seventeenth Centuries 
(Hammondsworth, England: Penguin Books, 1969), Ch. 5. 

16. G. Holton, address at the Copernicus Celebration, National Academy of Sciences, Smithsonian 
Institution. April, 1973. 

For help in the preparation of this article, I wish to thank M. Katz, E. Skolnikoff, L. Weinberg, and 
V. F. Weiskopf. 



209 



This chapter from a biography of Albert A. Michelson, the 
first American to win the Nobel Prize, recounts some 
interesting events from his life as a young man. 



1 6 Strzeino to the Golden West 

Dorothy Michelson Livingston 

A chapter from The Master of Light, 1973 



SUNLIGHT filled the village square of Strzeino, Poland, 
I dressed in garlands and bunting for a celebration, and 
shone upon the faces of the men and women standing 
near the town hall and on the many children lined up in or- 
derly rows. They had gathered on that July day in 1963 to hear 
the speeches of the Mayor, the local Commissar, and the Dean 
of Science of Copernicus University in Torun at the dedication 
of a plaque to the memory of a man born in their village on 
December 19, 1852, who had won the Nobel Prize. 

"Strzeino is proud of her son," said the Mayor, "And al- 
though his life was spent far away from us, we will remember 
that his genius came into being here among our people. It is 
a great moment in Polish science. He has put us into history." 

The leader of a small band of musicians had made a special 
eflFort to procure the music for the United States national an- 
them, not readily available in Iron Curtain countries. As the 
band struck up the unfamiliar strains of "The Star Spangled 
Banner," the Mayor unveiled a tablet marking the birthplace 
of Albert Abraham Michelson. When the speeches were over, 
a procession formed and moved down the road to Ulica 
Michelsona (Michelson Street), followed by the band and all 
the children. 

Albert's mother was born Rosalie Przylubska, the second 
of three daughters of Abraham Przylubski, a Polish business- 
man from Inowroclaw near Strzeino. The family name and a 
picture of her mother suggest that she came from typical Po- 
lish peasant stock. Her older sister Auguste married a doctor. 



210 



Strzeino to the Golden West 



and perhaps it was at their wedding that Rosalie first met 
Samuel Michelson, a young merchant of Jewish descent, who 
had come to live in Inowroclaw. He had little in the way of 
financial security to recommend him as a husband; he had no 
store of his own and probably sold his wares from a pushcart. 
Since Rosalie certainly did not marry him for money or posi- 
tion, he must have had a generous amount of personal charm. 
He was twenty-five and Rosalie just a year younger when they 
married and moved to Strzeino, and there Samuel opened a 
shop of his own. No doubt he had some help and plenty of 
advice from his father-in-law, the distance between the vil- 
lages being 30 kilometers, less than a day's ride on horseback. 
Albert was their first baby, born on December 19, 1852. 
He was a healthy boy and much loved. Two little girls, Pauline 
and Johanna, followed shortly. Pauline lived to a ripe old age, 
but poor Johanna seems to have been ill-starred from the be- 
ginning. Her birth was registered under the wrong name and 
Samuel had to have the entry in the register corrected several 
months later. After that, there is no further mention of her. 
Probably she died in infancy. Her brother never spoke of her. 
The Michelson family seems to have left Strzeino late in 
1855. (The last date related to their affairs in the local register 
is August 21, of that year.) Their decision to emigrate was 
probably influenced by the political situation in the Prussian- 
dominated section of Poland. The abortive "revolution of 
1848" had left conditions very unsettled. Anti-Semitism was 
rife, and purges of Jews were frequent in the towns and vil- 
lages around Strzeino. Curfews were enforced and the ghettos 
became intolerable. 

After working their way across northern Europe, Samuel 
and Rosalie and their children embarked on a steamer sailing 
between a Baltic seaport, probably Hamburg, and New York. 
For emigrants, the crossing in steerage was a mixture of joy 
and terror. There was triumph in having extricated them- 
selves from a hopeless past, regret at leaving their relatives and 
the familiar way of life, and fear of the vast ocean tossing their 
ship on its waves. Rosalie, pregnant again, had need of all her 
courage to withstand the discomfort of the crowded vessel and 
to gather her forces against the unknown life ahead. 

The crossing took almost three weeks. Upon landing in 
New York, the Michelsons went to the house of Rosalie's rela- 
tives, the Friedenburgs, on the lower East Side, where they 



211 



stayed to refresh themselves from the long sea voyage. Here 
they heard talk of the wild adventures and the sudden fortunes 
made overnight in the growing rush for California gold. 
Among the "forty-niners" were Samuel's sister Belle and her 
husband, Oscar Meyer, who had made a quick success at Mur- 
phy's Camp in Calaveras County. This news spurred the Mi- 
chelsons to follow. 

There were three routes by which they might continue 
their journey to San Francisco, all dangerous and expensive: by 
covered wagon across the continent; by ship around Cape 
Horn; or by a combination of ship and mule wagon to Panama, 
across the Isthmus, and up the West Coast. The last was the 
route they finally chose. 

Samuel booked passage on a small ship to Porto Bello, on 
the Isthmus, where a vessel might be warped beside the pier. 
The alternative was to risk disembarking in the shark-infested 
waters of a shallower harbor such as Chagres. Porto Bello 
hardly lived up to its name. It was a tropical slum known as the 
"grave of Europeans." Many inhabitants, black, white, and 
Indian, lived there in squalor; many were ill with "brain fe- 
ver," malaria, or smallpox. Apathy lay upon the town like a 
shroud. Money was useless even to those who had it to spend. 
Thieves and robbers looted the dead, the sick, and the un- 
armed passengers. There were no police. 

The Michelsons escaped the perils of Porto Bello and set 
forth on their journey across the Isthmus, traveling in canoes 
paddled by natives, through swamps and lakes. Gaudy parrots 
sitting in the mango trees protested the intrusion, while flocks 
of herons and cranes rose from the river bank as they pro- 
gressed. Changing to muleback on the higher land, they 
passed Indian villages perched on the crests of low, rounded 
mountains. 

The next stage of their journey was probably made on the 
pioneer railroad completed in 1855 between Aspinwall (now 
Colon) and Panama City, a distance of less than fifty miles. 
Here fresh discomforts awaited them. Drinking water was 
available only at exorbitant prices, because it had to be carted 
several miles in barrels. Raw sewage flowed down steep and 
narrow streets lined with saloons, gambling halls, and brothels. 
Violence was common and sensible people armed themselves 
to the teeth, looking like brigands to avoid being taken by 
them. 



212 



Strzeino to the Golden West 



In this tropical hell, Samuel and his family waited for pas- 
sage to San Francisco. Although Albert was not yet four years 
old, the horrors of this trip across the Isthmus, often retold by 
his parents, remained in his memory as long as he lived. Sev- 
eral weeks passed before cabin space was obtained on a ship 
of the Aspinwall Line. After sixty days at sea, the Michelsons 
reached the Golden Gate. 

Clipper ships lying at anchor crowded San Francisco har- 
bor. Many of these stately square-rigged vessels were deserted; 
their crews had gone to the "diggings" seeking gold. Samuel, 
however, did not have the prospecting fever. He felt safer in 
his own familiar trade and so bought supplies that would be 
needed by the miners. As soon as he was able to get accommo- 
dations, he and his family climbed into a stagecoach for the last 
lap of their journey to Murphy's Camp in the foothills of the 
Sierra Nevada, some 150 miles east of San Francisco. 

Murphy's Camp, or Murphy's Diggings as it was first 
known, had been founded in 1848 as a trading post with the 
Indians. John Murphy and his brother Daniel were among the 
first to begin panning for gold in the stream. They hired some 
Indians for this work, and in one year, it is said, they took out 
two million dollars in gold, simultaneously creating a land 
boom in the area of Calaveras. 

By 1856, when the Michelsons arrived. Murphy's had 
grown into a flourishing mining town, fairly well settled. Here 
they were greeted by Samuel's sister and her husband. Oscar 
Meyer was engaged in a mining operation. With his help, Sam- 
uel set up a little store, stocked with picks and shovels, pans for 
gold-panning, pot-bellied stoves, heavy boots and jackets, blan- 
kets, bedding, and canvas tents. 

The rough life of the camp and town made a vivid impres- 
sion on Albert. He acquired here some of the tenacity and 
toughness of mind that he brought to his mature life as a 
scientist. The atmosphere was exciting. For a few lucky ones 
money was rolling in — the claims at Murphy's were the richest 
of any in Calaveras County. Five million dollars was taken 
from just one four-acre placer area. An ounce of gold dust to 
the pan was rather common, four or five ounces was not 
unusual, and many claims paid sixteen ounces to the pan. In a 
period of ten years, during the 1850s and 1860s Wells, Fargo 
and Company shipped fifteen million dollars' worth of gold 
dust from Murphy's. Individual claims were restricted to 80 



213 



square feet. Arguments were usually settled with fists, knives, 
or bullets, and the women and children were safer behind 
locked doors after sundown because the men of the town then 
became gun-happy from gambling and whisky. 

During Albert's second year in Murphy's, work began on 
a great suspension flume, an aqueduct across the canyon at the 
lower end of the valley. It connected with a supply of water 
brought from the Stanislaus River some fifteen miles higher up 
in the mountains. The water was brought to the Central Hill 
Mine, on a ridge a mile south of Murphy's, to wash out the 
miners' gravel. The construction of this flume, completed in 
three months' time, was one of the great engineering feats of 
the early miners. The watertight boxes, suspended on wires, 
zigzagged overhead amid a network of struts and stays, carry- 
ing the main force of the stream across the valley. 

Narrow wooden houses with two-story balconies lined 
both sides of Murphy's unpaved street. No one had time to 
paint them. Bret Harte describes a hotel, modeled after the 
one in Murphy's, in "The Luck of Roaring Camp": 

It was designed with an eye to artistic dreariness. It was 
so much too large for the settlement that it appeared to 
be a very slight improvement on outdoors. It was unpleas- 
antly new. There was the forest flavor of dampness about 
it, and a slight spicing of pine. Nature, outraged, but not 
entirely subdued, sometimes broke out afresh in little 
round resinous tears on the doors and windows.^ 

Harte's character, Perthonia, whom he describes as "dirty, 
drabbled and forlorn," told how she had given up little by little 
what she imagined to be the weaknesses of her early educa- 
tion. Now, transplanted to a backwoods society, she was hated 
by the women and called "proud" and "fine." Such epithets 
may well have been thrown at Rosalie Michelson when she 
insisted that her son begin his schooling, mind his manners, 
and even start lessons on the violin at a time when he was 
hardly able to reach out far enough to hold the fiddle or stretch 
his fingers on the strings. Rosalie set a high standard for her 
children. To be sure, there was no lack of gaiety or fun, but it 
was always after the work was done. No child of Rosalie's failed 
to absorb an enormous respect for literature and a love of 
beauty in one form or another. The eflFect on Albert of his 



214 



Strzeino to the Golden West 



mother's values is clear. Her training made him able to resist 
the lure of easy money all his life. 

Across the street from the Michelsons lived the black- 
smith, Dave Baratini, and a few houses farther away the 
apothecary, Dr. William Jones, who did everything from prob- 
ing for bullets, to dispensing pills and arnica to the miners. A 
young girl, Bee Matteson, operated the first telegraph office in 
Murphy's. Her father, T. J. Matteson, was the surveyor who 
had laid out the route of the canal from the Stanislaus River. 
He also operated the pioneer stagecoach line daily from Mur- 
phy's to Angels, a nearby town. 

The stagecoach usually came into town dreadfully over- 
loaded, with fifteen or more people clinging to the top-heavy 
vehicle. When time came for departure, Matteson's drivers 
often had trouble in preventing more men from climbing 
aboard the coach than it could safely hold. 

Murphy's provided more sinister forms of excitement. 
Public hangings took place frequently, in the hope of in- 
timidating outlaws. One of the outlaws, a "handsome, fancy 
dresser," was a Spaniard named Joaquin Murieta, the three- 
fingered bandit whose raids of revenge upon the men who had 
flogged him kept the whole town in terror during the early 
1850s. 

On Sundays, the villagers enjoyed a quieter diversion. 
They could board a coach in front of the Sperry and Perry 
Hotel (next door to the Michelson house) and ride twelve miles 
to the Big Trees in Calaveras Grove. These were the first 
Sequoia gigantea to be discovered, and they attracted people 
from all over the world. Among them were Ulysses S. Grant 
and Mark Twain. 

Albert attended the first public school built in Murphy's. 
It was furnished with handmade desks, built by the local car- 
penter. In 1857, there were fifty-five children enrolled under 
a Mr. Jaquith, the principal, and his assistant, Isaac Ayers. Al- 
bert's first-grade teacher was Mary Anne Conway, an Irish girl 
of only fourteen who had come around the Horn to California 
in 1847 on the Susan Drew, one of the first ocean-going steam- 
ships built in the United States. Mary Anne had been educated 
in Spanish at the Convent of Monterey and had almost forgot- 
ten her English. 

On a Sunday afternoon three years after the Michelsons 
had arrived in Murphy's, the great fire of 1859 demolished the 



215 



town. In forty minutes everything was in ashes except Peter 
Travers' General Store and the sagging walls of the Murphy 
Hotel. Since the residents of Murphy's had no title to their 
property except pre-emption or "squatters' rights," the fire 
caused a good many arguments over boundaries. Albert's 
family luckily escaped personal injury. Along with the others, 
the Michelsons soon began to rebuild, and out of the ashes a 
new town was born, marking a new and more opulent era. The 
crowning feature of the new Murphy's was Putney's Opera 
House, on the site of the old Smith's Saloon and the office of 
Judge Putney, Justice of the Peace. 

Albert was eight when the Civil War broke out. It took 
some months for the news to reach Murphy's, but when they 
heard it, the miners sided unanimously with the Union. Money 
poured out of their coflFers and almost every man who had two 
legs to walk — and some who did not — joined the Calaveras 
Light Guard, as they called themselves. They drilled up and 
down the street, preparing for the conflict. 

Excitement ran riot in the town when a captain with a 
company of 300 men passed through Murphy's in 1862 on his 
way over Ebbett's Pass to the battlefields of the East. Many of 
the miners left their claims to join the Union Army. When 
news finally came that Lee had surrendered and the war was 
over, the whole population became frantic. Bells tolled, guns 
roared, and for days no one, not even Samuel Michelson, was 
sober. But Murphy's was a town of extremes. The residents' 
exuberance in victory was equaled by their despair in mourn- 
ing Lincoln's assassination. Out of love for the late President, 
the Michelsons gave Albert the middle name of Abraham. 

During these lively years, the Michelson family expanded. 
Julie, Benjamin, Bessie, and Miriam were born in Murphy's 
while the gold rush rose to its peak. 

When Albert reached the age of twelve, his parents felt 
that he had exhausted the slender opportunities for education 
at Murphy's. It was time, they thought, to send him to a 
"proper" school in San Francisco. The decision was made 
easier by the departure for that city of Belle and Oscar Meyer, 
with their sons Mark and young Oscar, in 1864. Albert was sent 
along with his cousins and spent the next two years living with 
the Meyers and attending Lincoln Grammar School. 

In September of 1866, Albert transferred to the San Fran- 
cisco Boys' High School (now called Lowell High School). The 
principal, Theodore Bradley, was so much impressed with him 



216 



Strzeino to the Golden West 



that he took him into his own home and gave him the job of 
setting up experiments for the science class and helping with 
the chores. In the evening, when Albert's studying was 
finished, Bradley encouraged him to practice the violin. 

It was Bradley also who taught Albert the "manly art of 
self-defense," instilling in him the knowledge that he need 
never tolerate insults or be afraid to fight with his fists. The boy 
took to boxing with pleasure; his quick coordination compen- 
sated for his shght build. Albert was fortunate in his teacher. 
Bradley believed in developing his promising student into a 
well-rounded man rather than a prodigy. 

After his first year of high school in San Francisco, Albert 
went home to spend the summer of 1867 with his parents at 
Murphy's. The town was in complete decline; empty shacks 
and abandoned mine shafts were everywhere, and it was im- 
possible to earn a living. The center of prospecting had shifted 
to Virginia City, over the mountains in Nevada, where, in 
1859, silver had been found in the Comstock Lode. Though 
still sparsely populated, the former Nevada Territory had been 
declared a state by President Lincoln in October of 1864. 

The difficulty of supporting his large family caused Samuel 
to follow the miners to Nevada. He and Rosalie piled their 
belongings and their six children into a mule wagon and joined 
the procession of wagons and freight teams winding their way 
past Lake Tahoe and Carson City toward their new home in 
the silver-mining town, Virginia, as the city was often called. 
Samuel, profiting from his ten years of experience in supplying 
miners' needs, sank all his resources into a vast stock to be 
shipped once he had settled himself in a suitable spot. 

Virginia, an overcrowded town of 30,000 people, 
sprawled over the side of Mount Davidson. Gold Hill and Sil- 
ver City, originally separate villages, had been absorbed by the 
expanding town. On the outskirts grazed a herd of Bactrian 
camels, remnants of an experiment of 1861 to introduce the 
two-humped beasts from China to carry salt over the moun- 
tains. Although more useful than mules on desert ground, the 
animals were unsteady on precarious mountain trails where 
the rocks cut into their soft feet. Travelers were terrified when 
they first came upon the camels, and horses often broke into 
a stampede at the mere smell of them. Consequently, the poor 
creatures were penned up in the daytime and allowed to graze 
only after dark. 

At the foot of Mount Davidson lay the Chinese section of 



217 



Virginia, the result of another unpopular experiment in trans- 
plantation. The miners both envied and disliked the Chinese 
laborers who toiled sixteen hours a day, successfully reworking 
the discarded mine dumps. The pungent odor of burning 
opium hovered over the entire quarter. 

Higher up, clinging to the steeper slopes, were the squalid 
shacks of the Piute and Washoe Indian tribes, now thoroughly 
subdued. Livery stables and feed stores lined the road along 
the outskirts of Virginia, but in the town itself brick and stone 
houses had replaced the wooden shacks of yesterday's pio- 
neers. At night the streets were lighted by gas, and at cross- 
roads every corner boasted a thriving saloon. In one year a 
million dollars' worth of liquor was consumed in Virginia City, 
and that year was said to have been rather a dry season; in 
bonanza periods three times as much "tangle leg," "sheep- 
herder's delight," or "tarantula juice" went down the miners' 
throats. Men were said to fall asleep in the road crossing from 
one saloon to another. 

The Michelsons settled in a new house at 24 South C 
Street, where Samuel kept his store on the first floor. Some- 
what intimidated by the struggle for survival in this gilded 
jungle, Rosalie watched over her family closely, barring the 
shutters at night against burglars or stray bullets. The chil- 
dren's enjoyment of their life in the mountains was later ex- 
pressed by Albert's sister Miriam, when she became a success- 
ful novelist. 

They all came, mothers or mothers-to-be of those boys 
born to the town trade, to the miner's lot; and of those 
girls who graced the firemen's engines in the Fourth of 
July procession, bare-armed, bare-necked with crimped 
tresses flying, glowing goddesses of red, white and blue 
liberty. . . . 

But if nothing ever came to Virginia City in that 
season, but spring itself, 'twould be enough . . . there 
would be air fit for the hierarchy of heaven to breathe, 
honey-strained through infinite planes of crystal clear sky. 
Air, and a rare, inefi^able odor breathing over the sunned- 
. through purity, exhilarating, intoxicating, of white sage 
perhaps, of Heaven knows what! 

No wonder we believed in the season's intangible, 
incredible, maddening promise. No wonder we lost hold 



218 



Strzeino to the Golden West 



of prosaic possibilities and, betting on the radiant future, 
gambled with life itself." 

Below the road, the track of the Virginia and Truckee 
Railroad, the richest, most picturesque line in the history of the 
American West, was being laid from Carson City up the steep 
grade to Virginia. The ascent was over 1,600 feet in 13y2 miles, 
spanning ravines and tunneling through the mountains. Day 
after day the Michelson children, along with most of the child 
and adult population of Virginia, watched the giant construc- 
tion winding up the valley. When it was finally completed in 
1870, the railroad became a symbol of the spirit of Western 
adventure. 

While the silver mines roared with activity, the Michelson 
family flourished. Albert's brothers and sisters were swept into 
the drama of Western life. They reveled in the exciting gossip 
about fortunes won or lost, the uninhibited feelings displayed, 
and the joyous abandon of everyday life in this boom town. 
Some of this raucous spirit and much of the vitality were to be 
imbibed by Charlie Michelson, born in 1869 in Virginia City. 

But Albert, who graduated from high school the year of 
Charhe's birth, had acquired a diflPerent set of values. He could 
see no prospect of continuing his studies, as he wanted to do. 
A paper he wrote on optics had drawn favorable comment 
from Bradley and he hoped to explore the subject further. A 
possibility opened when Samuel Michelson spotted in the Ter- 
ritorial Enterprise of April 10, 1869, a letter from the Honora- 
ble Thomas Fitch, Nevada Representative in Congress, stating 
that he proposed to appoint a candidate to the Naval Academy 
from the State of Nevada. The appointment, open to all 
Nevada boys from fourteen to eighteen years of age, would be 
subject to the results of an examination judged by a board of 
examiners. If he could win it, Samuel told his son, his family 
would be proud of him. Bradley also encouraged Albert, point- 
ing out that he would have splendid instruction in the natural 
sciences, including physics and chemistry. Albert agreed to 
take the examination. He brought with him a letter of recom- 
mendation from his teacher: 

To whom it may concern: 

This certifies that the bearer, Albert Michelson, has 
been a member of the San Francisco Boys' High School 



219 



during the last three years; that he has graduated with 
honor from the same; that in character as well as scholar- 
ship he is worthy of great commendation; and that he 
exhibits great aptitude for scientific pursuits. 

Very Resp'y> 

Theodore Bradley 
Principal 
San Francisco 
June 1869 

The examination took place on June 10. Albert was one of 
three who tied for first place. His rivals were James Wilson 
Blakely and William GiflFord Cutler. The examining committee 
passed on this information to Congressman Fitch and left it to 
him to decide which of the boys would get the appointment. 
Fitch selected Blakely for three reasons: his parents could not 
aff"ord to give him a good education, he was the son of a man 
who had lost his right arm (some said in the Civil War) and 
"with whom fortune has not always dealt kindly," and his ap- 
pointment was strongly recommended by the Honorable D. R. 
Ashley, Fitch's predecessor in Congress. 

"I hope the numerous friends of the other candidates will 
be satisfied with my settlement of this vexed question, and will 
receive this as a reply to the one hundred and thirteen letters 
and telegrams on this subject I have had the honor to receive 
during the last four days. I return my thanks to the committee 
for what they did and forgive them for what they left undone," 
Fitch wrote to a local paper. 

After this announcement, Fitch no doubt received an- 
other inundation of mail protesting the injustice of his choice. 
If he followed Blakely 's record at the Naval Academy, he 
would have been forced to recognize that his candidate 
proved to be very poor material indeed. His first academic 
tests show him listed well below passing, he was unable to 
retrieve his standing in the following year, and on November 
16, 1871, he was dropped from the Academy. 

Whether from the pricking of his conscience or, more 
likely, because of the threats of a powerful section of his con- 
stituency, Fitch did not abandon Albert. He was prevailed 
upon to write to the recently elected President, Ulysses S. 



220 



Strzeino to the Golden West 



Grant, stating the reasons he hoped young Michelson could be 



given another chance 



Hamilton, White Pine County, Nevada 

June 17th, 1869 
Sir 

I respectfully solicit your personal perusal of, and at- 
tention to, the communication I now have the honor to 
address you. 

Having been notified by the Secretary of the Navy of 
the [sic] a vacancy in the Naval Academy from this State, 
I determined to submit the appointment to competition, 
and did so by public advertisement — a copy of which I 
have annexed hereto. A number of boys competed for the 
prize, and after an examination of unusual length and 
severity, the committee reported three of the candidates 
as equal in scholastic attainments — I annex a copy of the 
committee report. I also annex a copy of the reasons I 
have given for selecting the lad who has received the 
nomination for Midshipman. 

The object of this communication is to solicit from 
you the appointment of Midshipman for one of the three 
who received the Committee's endorsement — Master A 
A Michelson. 

Had I felt at liberty to be governed by considerations 
of political expediency, I should have selected him. His 
father is a prominent and influential merchant of Virginia 
City, and a member of the Israelite persuasion, who by his 
example and influence has largely contributed to the suc- 
cess of our cause, and induced many of his co-religionists 
to do the same. These people are a powerful element in 
our pohtics, the boy who is uncommonly bright and studi- 
ous is a pet among them, and I do most steadfastly believe 
that his appointment at your hands, would do more to 
fasten these people to the Republican cause, than any- 
thing else that could be done. 

I am sure that young Michelson could pass even a 
severer examination than that made at the Naval 
Academy, and that he would be an ornament to the ser- 
vice, and a credit to his nominator, and if you can give him 
the place you will never regret it. 



221 



The Union people of Nevada are proud and grateful 
for the recognition they have received at your hands in 
the manner of appointments and will demonstrate to you 
hereafter, that the "strong box" of the nation will be the 
stronghold of your administration on this coast. I know 
you can greatly please them and strengthen us by making 
this appointment, and I take the liberty of expressing my 
deep solicitude that it may be made. 

Very Respy. Yours 

Thomas Fitch 

To the President 

Michelson never saw this letter or knew of its existence, 
because it was mailed to the White House. At the same time, 
he was dispatched to Washington with another letter of intro- 
duction, full of praise but minus the political implications. 

He set oflF alone across the continent, riding one of the first 
trains of the transcontinental railway. Only a month before his 
departure, the Central Pacific had raced the Union Pacific to 
a rendezvous midway, each trying to see which could build the 
farthest and fastest, for a prize of vast government land grants 
and bonds, allotted on a mileage basis. The attention of the 
nation was focused on this meeting at which the last rail was 
laid on a tie of California laurel, fastened with a "golden spike," 
while the two locomotives faced each other on a single track. 

Albert saw the breadth of the country for the first time. 
Crossing the Continental Divide, the train descended from the 
Rocky Mountains, scattering great herds of bufi"alo as it crossed 
the broad plains. Armed guards were posted on every car 
because of the danger of an Indian attack or a holdup by 
bandits. 

When Albert announced himself at the White House, 
President Grant, slumped in his chair, received him and lis- 
tened with kindness and interest to his story. Drinking had 
coarsened Grant's face and rounded his belly so that he no 
longer looked like the pictures Albert had seen of him as a 
general charging into battle. But his voice was gentle as he 
broke the news to Albert that he could not help him, having 
already filled the ten appointments-at-large that were allotted 
the President. 



222 



Strzeino to the Golden West 



Albert concealed his disappointment with difficulty. He 
thanked the President politely, bowed, and left his office with 
one of Grant's naval aides. This officer, admiring the boy's 
determination, advised him to go to Annapolis on the chance 
that a vacancy might occur if one of the President's ten appoin- 
tees failed to pass his examination. 

On his arrival at Annapolis in late June, 1869, Michelson 
went straight to the office of the Commandant of Midshipmen, 
Captain Napoleon B. Harrison. He waited three days before he 
finally was granted an interview, was examined, and then told 
there was no vacancy. Embittered and discouraged, his money 
almost gone, he returned to Washington and boarded a train 
for San Francisco. Just as the train was about to leave, a mes- 
senger from the White House came aboard, calling out his 
name. For the second time, Michelson was taken to see the 
President, who had been persuaded by Vice Admiral David D. 
Porter, Superintendent of the Academy, and one of Michel- 
son's examiners, to make an exception in his case. Brushing 
regulations aside. Grant gave him the nomination for an elev- 
enth appointment-at-large, which he received on June 28. 

Michelson, telling this story in later years, chuckled over 
beginning his naval career by what he thought was "Grant's 
illegal act." But having once exceeded his quota. Grant went 
on to appoint two more midshipmen-at-large, a total of thir- 
teen, in 1869. 



223 



Energy is in the news and may well rennain there prominently 
for the rest of this century. This article surveys the key 
scientific, technological, and social issues related to our use 
of energy. 



• ' Energy and the Environment 

John Fowler 

An article from The Science Teacher. December, 1972 



ENERGY: 

WHERE IT COMES FROM 

AND WHERE IT GOES 



THE WORLD runs on energy, both 
literally and figuratively. It spins 
on its axis and travels in its orbit 
about the sun; the winds blow, waves 
crash on the beaches, volcanoes and 
earthquakes rock their surroundings. 
Without energy it would be a dead 
world. Energy was needed to catalyze 
the beginning of life; energy is needed 
to sustain it. 

For most of life, animal and plant, 
energy means food; and most of life 
turns to the sun as ultimate source. 
The linked-lifc patterns — the ecosys- 
tems — which have been established be- 
tween plants and animals are very 
complex; the paths of energy wind and 



twist and double back, but ultimately 
they all begin at that star that holds 
us in our endless circle. 

When man crossed that threshold of 
consciousness which separated him 
from animals, his uses of energy began 
to diversify. He, too, needed food, but 
poorly furred as he was, he also needed 
warmth. With the discovery of fire he 
was able to warm himself. He also 
found that fire could make his food 
digestible and thus increase its effi- 
ciency as an energy source. After a 
while he began also to use fire to make 
the implements through which he 
slowly started to dominate nature. 

Man's use of energy grew very 
slowly. In the beginning he required 
only the 2,000 or so Calories ' per day 
for food; the convenience of warmth 



' We will consistently deal with Calories (kilo- 
calorics), the amount of heat energy needed to 
raise the temperature of one kilogram of water 
one degree Celsius. 



224 



Energy and the Environment 




ol 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 




























O 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


lO 


<D 


N 


00 


<Ji 


o 




<M 


rO 


t 


in 


(0 


N 


oo 


00 


GO 


oo 


00 


0» 


<J) 


O) 


a> 


o> 


<n 


0> 


g> 



YEAR 



Figure 1. Comparison of energy and population growth. United States. 1850-1960. 



added a few thousand more Calorics 
from easily obtainable wood. The first 
big jump in energy use came about 
four or five thousand years BC when 
man domesticated several animals and 
— at the cost of a little food, much of 
which he gathered himself — was able 
to triple the amount of energy at his 
service. 

The watcrwhecl appeared in the first 
century BC and again multiplied the 
amount of energy available to man. Its 
introduction was perhaps even more 
significant because it was a source of 
inanimate energy. For a long time the 
waterwheel was the most important 
source of energy for the nascent in- 
dustry. It was not until the twelfth 



century, more or less, that the analogy 
between Mowing air and llowing water 
led to the use of windmills. 

The beginning of the modern era of 
industry coincided with the develop- 
ment of the steam engine. Since that 
time the world's use of energy, which 
until then had been very nearly pro- 
portional to the number of people, 
began to grow in the industrial coun- 
tries more rapidly than the population 
increased. This growth, shown in Fig- 
ure 1 for the United Slates, continues. 

The second historical trend which, 
together with the increasing per capita 
use, has brought us to the present state, 
is the constant change in the energy 
mix. Wood was the dominant fuel in 



the 1850s but had lost all but 20 per- 
cent of the market to coal by 1900. 
Coal in turn lost out after 75 years to 
petroleum products, which now ac- 
count for 75 percent of the energy, but 
they in turn will be (and musi be as we 
shall see) replaced by other sources. 
Nuclear energy is the best present 
candidate. - 

Energy as a Conimodiiy 
In the early stages of man's history, 
energy was food, something to be 
found and consumed. But as life be- 
came more complex, and early barter 
systems were followed by a money- 
based economy, energy had to be 
bought. At first it was purchased in- 
directly as food or fuel. With the 
introduction of electricity, energy could 
be piped directly into the house or 
factory. 

Energy is a commodity; it can be 
measured, bought, and sold. But its 
price depends on the form in which it 
is purchased — as food or fuel or elec- 
tricity. Table 1 is an "energy shopping 
list." It is clear that we pay for the 
good taste of energy in the form of 
steak. 

Energy values for some fuels and foods 
(retail prices). 









Cost 




Energy 


Energy 


(per 1000 


Source 


(Cal/kg) 


(kWli/lb) 


kWh) 


Coal 


7,200 


3.86 


$ 5.20 


(stove coal) 








Fuel oil 


10,800 


5.72 


4.30 


Natural gas 


11,000 


5.86 


5.46 


Alcohol 


6,460 


3.42 


10.25 


(denatured) 








Alcohol 


2,580 


1.37 


2,920.00 


(Scotch, 80 proof) 






Bread 


2,660 


1.42 


220.00 


Butter 


7,950 


4.20 


200.00 


Sugar 


4,100 


2.16 


68.00 


Beef steak 


1,840 


.97 


1,640.00 


(sirloin) 








Electricity 


— 


— 


20.00 



Where 1 1 Goes 
The energy crisi.s is not a crisis 
caused by the "using up" or the dis- 
appearance of energy. The First Law 
of Thermodynamics assures us of that. 
Energy is conserved, at least in the 
closed system of the universe. The 
crisis must then be found in the path- 
ways of energy conversion. 

-Sic Conk. I I Ik- I low ol l.ncfi;y in .in Indus- 

Irial Soili-ly." Siii-nlilu Aineniiiii 224 114-144; 
Siptcmbcr 1971. 



225 



We use energy in its kinetic form, as 
mechanical energy, heat, or radiant 
energy. The form in which it is stored 
is potential energy. We know from 
physics that the potential energy of 
a system is increased by sE when we 
operate against a force over a distance 
aA', i.e., 

AE = F-SX 
In the infinite variety of the universe 
we have, so far, discovered only three 
types of forces: gravitational, elec- 
trical, and nuclear (there seem to be 
two nuclear forces corresponding to 
the weak and the strong nuclear inter- 
action). It follows, therefore, that 
there are three primary sources of 
energy: gravitational, electrical (chem- 
ical), and nuclear. On the scale of the 
universe these are the most important. 

Figure 2. Paths of energy conversion. 



and the weak force, gravitational, and 
the strong one, nuclear, give us the 
most visible effects. 

At earth's scale we choose other pri- 
mary sources of energy. Solar energy, 
radiated from the thermonuclear proc- 
esses in the sun, is the most important 
of these. It gives us the kinetic energy 
of water power and wind power, warms 
us, is stored as chemical energy in 
growing things, and was preserved in 
the fossil fuels. 

We store the gravitational energy of 
lifted water in reservoirs, but the only 
true primary source of gravitational 
energy of which we make commercial 
use (in a small way, admittedly) is 
that of the tides. Here we draw on 
the gravitational energy stored in the 
earth-moon system. 

We show these and the other im- 



INTERMEDIATE 



lij 





THERMAL 


MECHANICAL 


. ELECTRICAL 


. CHEMICAL 


SOLAR 


V 






k 




i 




1 






■- 




. ■" 










GRAVITATIONAL 












y 










CHEMICAL 


V 








i 
















NUCLEAR 


V 




1 )" 




) 


















GEOTHERMAL 






■"-^ 
































































THERMAL 
















^-n 


N 1 




MECHANICAL 


f-jj 






/ , , . . 






^^ 








ELECTRICAL 




/ 


, 


J 










V- 




CHEMICAL 
















' 


RADIANT 






-^J 





portant primary sources of energy in 
Figure 2. The chemical energy of 
fossil fuels is at present far and away 
the most important of these, but there 
are two non-solar sources, geothermal 
energy from the earth's heated interior 
(originally heated by gravitational con- 
traction and kept warm by radioac- 
tivity) and the new entrant onto the 
scene, nuclear energy. 

Excepting solar energy, the other 
primary sources are of little direct use 
to us; they must be converted to the 
intermediate forms and often converted 
again to the end uses which are also 
shown schematically in Figure 2. 

The major sources of energy in this 
country are the chemical energy of the 
fossil fuels. From them we get 95.9 
percent of the inanimate energy we use. 
They are fuels; their chemical energy is 
released by burning. Thus the major 
conversion pathway is from primary 
chemical energy to intermediate ther- 
mal energy. In fact, most of the 
conversion pathways go through the 
thermal intermediate form. 

We will look later in detail at the 
distribution of energy among the vari- 
ous end uses. We know in advance, 
however, that the major end uses are 
thermal (space heating, for example) 
and mechanical. Mechanical energy is 
also a major intermediate form and is 
also converted to that most important 
intermediate form, electrical energy. 
The convenience of electrical energy 
shows up in its ready conversion to all 
the important end uses. 

Conversion Efficiency 
The most important conversion path- 
way is thus chemical -^ thermal -^ me- 
chanical; and here we enter into the 
domain of the Second Law of Thermo- 
dynamics. It is this "thermal bottle- 
neck" through which most of our 
energy flows that contributes mightily 
to the various facets of the energy 
crisis. We burn to convert, and this 
causes pollution. We are doomed to 
low efficiencies by the Second Law, 
and the wasted heat causes "thermal 
pollution." Let us consider the effi- 
ciency problem first. 

Efficiency, the ratio of output work 
to input energy, varies greatly from 



226 



Energy and the Environment 



PERCENT 
OF U.S. 
ENERGY 
1970 



3.8 HYDRO - 



95.9 



FOSSIL - 
FUELS - 



.3 (NUCLEAR) 



^ THERMAL 
y\ ENERGY 




100 7. 



Figure 3. The flow of energy in tfie United States. 



conversion to conversion. Generally 
speaking, we can convert back and 
forth from electrical energy to other 
forms with high efficiency, but when 
we convert other forms of energy to 
heat and then try to convert heat to 
mechanical energy we enter the one- 
way street of the Second Law.^ 

The efficiency of a "heat engine" 
(a device for converting heat energy to 
mechanical energy) is governed by the 
equation: 



EfT. 



('-^) 



100 



where T,n and To»t are the tempera- 
tures of intake and exhaust. This 
equation sets an upper limit of effi- 
ciency (it is for a "perfect" Carnot 
cycle). Since we are forbidden 
Tout — 0°K or Tin = 00, we are 
doomed to the intermediate range of 
modest efficiencies. For example, most 
modern power plants use steam at 
1,000°F (811 °K) and exhaust at 
about 2I2°F (373°K) with a resulting 
upper limit of efficiency of 63 percent. 
The actual efficiency is closer to 40 
percent. Nuclear reactors presently 
operate at a T,n of about 600°F 
(623^K) and 7,.,„ of 212'F (373°K) 
for an upper limit of 40 percent. They 



■" See Summers, Claude M. "The Conversion of 
Energy." Scientific American 224: 149-160; Sep- 
tember 1971. 



actually operate at about 30 percent. 
In an automobile the input temperature 
of 5,400°F ( 3,255 °K) and output of 
2,100°F (1,433°K) would allow an 
efficiency of 56 percent. The actual 
efficiency is about 25 percent. 

So far we have talked about the 
efficiency of the major conversion 
process, heat to mechanical work. 
What is more important to an under- 
standing of the entire energy picture, 
however, is the system efficiency; for 
example, the overall efficiency with 
which we use the energy stored in the 
petroleum underground to move us 
down a road in an automobile. Table 2 
shows the system efficiency for trans- 
portation by automobile and the pro- 
duction of electric power. One can 
see that overall there are large leaks in 
the system and that most of the avail- 
able energy is lost along the way. 

"Lost" does not, of course, describe 
precisely what happens to energy. We 
know what happens; it is converted to 
heat. The inexorable Second Law de- 
scribes the one-way street of entropy. 
All energy conversion processes arc 
irreversible; even in the highly efficient 
electrical generator some of the me- 
chanical work goes into unwanted heat. 
The conversion of other forms of 
energy to heat is a highly efficient 
process — ultimately 100 percent. It is 
a downhill run. But the reverse is all 



uphill; heat energy can never be com- 
pletely converted to mechanical work. 
The potential energy available to us, 
whether it be chemical, nuclear, or 
gravitational in form, is slowly being 
converted to the random motion of 
molecules. We cannot reverse this 
process, we can only slow it down. 

Patterns of Consumption 
Ever since President Johnson turned 
off the lights in the White House there 
has been a small (too small) but grow- 
ing effort to save energy. It seems 
reasonable that this country and per- 
haps all countries will, at least for a 
while, have to make a real effort in this 
direction. To produce measurable 
effects, however, these efforts will have 
to be aimed at important sections of 
consumption. 

A gross flow chart of energy in our 
economy is shown in Figure 3. One 
sees the thermal bottleneck. Heat is 
the desired end product from about 
half of our energy. We do use that 
amount of energy efficiently. Of the 
half that goes to provide mechanical 
work, however, large amounts are lost 
in the production of electrical energy 
and transportation. The net result is 
that overall (and one must remember 
here that we are dealing with refined 
fuels delivered to the converters) our 
system is about 50 percent efficient. 

Table 2. Energy system efficiencies. 







Efficiency 






Including 


EFFICItNCY 


All Pre- 


OF Each 


ceding 




Step 


Steps 




Percent 


Percent 


A moinohile 






Production of 






crude petroleum 


96 


96 


Refining of petroleum 


87 


83.5 


Transportation of 






gasoline 


97 


81 


Thermal efficiency 






of engine 


29 


23.5 


Mechanical efficiency 






of engine 


71 


16.7 


Rolling efficiency 


30 


5 


Electric Power Generation 




Production of coal 


96 


96 


Chemical energy of 






fuel -» boiler heat 


88 


84.5 


Boiler heat -^ 






mechanical energy 


50 


42.3 


Mechanical energy -^ 






electrical energy 


99 


42 


Transmission efficienc 


y 80 


33.5 



227 



ENVIRONMENTAL 

EFFECTS 
OF ENERGY USE 



Patterns of Consumption 
The intimate connections between 
energy, our way of life, and the natural 
environment occur at many places. The 
most important points are, of course, 
in the production of energy — in the 
mines and wells, refineries and gener- 
ating plants — and at the points of con- 
sumption. Figure 3 gave a crude pic- 
ture of consumption; we need to look 
at it in more detail. 

Figure 4 gives both a crude break- 
down and details of the 60,526 trillion 
BTUs of energy in each category. One 
sees that industry and transportation 
use the lion's share. The importance of 
space and water heating also shows up 
strongly. Predictions are that trans- 
portation and commercial use will be 
the fastest growing sectors.^ 

Electrical Energy — 
The People's Choice 

What doesn't show up in this presen- 
tation is the special case of electrical 
energy. It is there, contributing heavily 
to all categories except transportation, 
and it shares with transportation most 
of the blame for energy's role in envi- 
ronmental degradation. 

The growth rate of electrical energy 
consumption, shown in Figure 5, is the 
highest of all the various forms of 
energy. In discussing growth a most 
useful concept is "doubling time." The 
energy curve of Figure I shows several 
different periods of growth and, there- 
fore, several different doubling times. 
In the late 1800s the doubling time was 
about 30 years; by the early 1900s this 
had been cut in half to about 16 years. 
The doubling time during the growth 

• In liJVI ihe U.S. C'onsunipilon was 75.561 trillion 
BTU's. 

' I.andsberg, H. H., and S. H. Schiirr. Energy 
in the United States: Sottrcex, Uses anti roliry 
Issues. Random House. New York. 1960. P. 76. 



period from 1950 to 1960 was 25 
years, and for the period 1960 to 1970 
dropped to 18 years. 

Electrical energy can be said to have 
arrived commercially with the start-up 
of the Pearl Street Station by Thomas 
Edison in 1882. (The energy curve in 
Figure 1 breaks away from the "peo- 
ple" curve by about 1890.) The 
doubling time for per capita electrical 
energy consumption of Figure 5 was 
only TVz years during the start-up 
period of 1910 to 1920, was about 14 
years in the 1950s and 60s and has 
decreased to about 10 years now. This 
means that in the period 1970 to 1980 
the per capita use of electrical energy 
will be expected to double. 

The impact of electrical energy can 
be better understood from the plot of 



total electrical energy consumption also 
shown in Figure 5. This curve has been 
doubling every 10 years since 1950. 
This means that in each of those 10- 
year periods the United States used as 
much electrical energy as in its entire 
previous history. 

The reasons for the rapid increase 
in demand for electrical energy are 
several. It is in many ways the most 
convenient of the forms of energy. It 
can be transported by wire to the point 
of consumption and then turned into 
mechanical work, heat, radiant energy, 
or other forms. 

It cannot be very effectively stored, 
and this has also contributed to its 
increasing use. Generating facilities 
have to be designed for peak use. In 
the late 50s and early 60s this peak 



Figure 4. U.S. energy consumption 1Q68 (total 60.5 x 10^^ BTUs). 









% 


^-— — n 


^____^^ 


^ SPACE HTG 


II.O 


^,^^*'-'^^'^ 


^^"^"^"'•n^^^^^ ^_____— -"^ 


WATER HTG 
--^^COOKING 


2.9 

I.I 


y"^^^-^ 


^^^\5r\^ 


/^y^ 


^\^^c^^ 


/^LOTHS DRYING 


.3 


/ /^ 


\X^ 


-^^REFRIGERATION 


I.I 


___-—-/' / TRANSPORTATION 
24.9 FUEL // 25.2% 


RESIDENTIAL V^ 
19.2 % \ 


;;^AIR COND. 
^- — -OTHER 


.7 
2.1 


.3 RAW MTRS. / / 


^^.--^ 


\ 


% 


^V — 


^ COMMERCIAL 
\^^ 14.4 % 


'^ SPACE HTG 

!~f— -WATER HTG. 


6.9 

I.I 




\ \ 


^V L 


3^C00KING 


.2 


''* ^^\\ INDUSTRIAL 

7.5 OTHER ''''^ \\ 41.2% 

3.6 FEED STOCKS -""N^y 
11.4 DIRECT HEAT -— ___\J\. 


-^ 


/^REFRIGERATION 
V^^AIR COND. 
^^FEED STOCKS 
^ OTHERS 


I.I 
1.8 
1.6 
1.7 


% ///^ 


/"^^ 






1.2 ELECTROLYTIC PROC. / y 


/ 






.8 ELECTRIC DRIVE ' / 








16.7 PROCESS STEAM ^ 









228 



Energy and the Environment 



10" 



10 



TOTAL U.S. CONSUMPTION OF 
ELECTRICAL ENERGY. ( USE 
RIGHT VERTICAL SCALE). 



10 




10 



U. S. PER CAPITA USE OF 
ELECTRICAL ENERGY. (USE 
LEFT VERTICAL SCALE). " 



1910 



20 



30 



60 



70 



40 50 

YEARS 
Figure 5. Growth of electrical energy consumption in the United States since 1910 



10 
1980 



came in the winter, when nights were 
longer and more lighting and heating 
were needed. It was economically 
sound to heavily promote off-peak use, 
such as summer use of air conditioners. 



Figure 6. Labor productivity in 
the period 1947-1968. 



I I r ! I I I I I I I I I I I I I I I I I 
VALUE ADDED PER UNIT OF LABOR 




This promotion was so effective that 
the summer is now the peak time, and 
the sales effort seems to be going into 
selling ali-clcctric heating for off-peak 
winter use. 

The rate structure has also con- 
tributed to increasing use of electrical 
energy. Rate reductions arc offered to 
attract bulk consumers. Hindsight sug- 
gests that there has been an imbalance 
between research and promotion. The 
figures bear this out. Senator Lee Met- 
calf has reported that the utilities in 
1969 spent $323.8 million on sales and 
advertising and $41 million for re- 
search and development. 



Perhaps the most important clue to 
the great increase in the use of elec- 
trical energy was suggested by Barry 
Commoner in an address to the Amer- 
ican Association for the Advancement 
of Science."' Commoner looked at the 
important economic parameter "pro- 
ductivity," which is defined as the 
ratio of value added to a product/man- 
hours to produce it. The strength of 
the economy is built on increasing pro- 
ductivity. The data Commoner pre- 
sents, for the period 1947 to 1968 
(Figure 6) show that labor produc- 
tivity has been steadily increasing. He 
and his colleagues then looked at the 
history of electric power productivity. 
These two quantities, man-hours and 
kilowatt-hours, do play similar roles 
in industry — electricity amplifies the 
existing muscle power in many cases. 
This analysis of electric power pro- 
ductivity showed the very different re- 
sults of Figure 7. The ratio of value 
added to kilowatt-hours/electric power 
productivity, declined sharply from 
1947 to 1958 and has flattened out 
since then. This suggests the impor- 
tant conclusion (which merits much 
more careful study) that the increase 
in labor productivity has been bought, 
at least partially, at the expense of a 
decrease in power productivity. Since 
labor is more expensive than electric 
power, the effects on the economy have 
been beneficial. But what about effects 
on the environment? 

linvironiiiental Effects: Air Pollution 
There are two major areas of pollu- 
tion, air and thermal, which are almost 
completely attributable to energy con- 
sumption. Air pollution is unhappily 
well known to all of us through smog — 



■'Commoner. Barry. "Power Consumpdon and 
Human Welfare." Paper prepared for delivery al 
Ihe annual meelini; of ihe American As"iociation 
for Ihe Advancement of Science. December 29. 1971. 



Figure 7. Electric power productivity in 
the period 1947-1968. 



I I I I I I I I I I I I I I I I I I I 

VALUE ADDED PER UNIT OF ELECTRICITY . 



_I L_l 1_J L_l L. 



229 



that collection of irritating hydrocar- 
bons and oxides of sulfur and nitro- 
gen which is becoming a fixture of 
urban living. Table 3 gives a break- 
down of the contributions to pollution 
of the various categories of polluters. 
One sees that the generation of electric 
power is the major source of sulfur 
oxides, while the automobile leads for 
three other pollutants. 

It is of course not possible to deduce 
the importance of these pollutants from 
their gross weight because they have 
very different effects. Some, like car- 
bon monoxide, affect health in even 
minute concentrations, others, like the 
particulates, largely add to cleaning 
bills. This article is not the place for 
a detailed discussion of the effects of 
air pollution." We will simply sum- 
marize the costs, which come from 
effects on the health, damage to crops 
and exposed materials, and property 
values, by quoting the Second Annual 
Report of the Council on Environ- 
mental Quality, August 1971. 

The annual toll of air pollution on health, 
vegetation and property values has been 
estimated by EPA at more than 16 billion 
dollars annually — over $80 for each person 
in the United States.' 

The dependence of our society on 
the automobile for transportation pre- 
sents us with a complex mix of prob- 
lems; in addition to polluting the air, 
it uses one quarter of our energy total 
in a very inefficient way, leads to the 
covering of our countryside with con- 
crete, contributes to many aspects of 
the problems of our cities, and takes a 
high toll of human life. The discussion 
of these problems and suggestions for 
solutions arc fascinating and important, 
but cannot be undertaken here. 

The generation of electric power at 



present depends almost entirely on the 
burning of the fossil fuels. The sulfur 
oxides come from the sulfur impuri- 
ties in these fuels. The burning of 
these fuels also converts large amounts 
of carbon to carbon dioxide. This 
familiar gas is not a pollutant in the 
ordinary sense, but its steady increase 
in the atmosphere is a cause for con- 
cern. Carbon dioxide is largely trans- 
parent to the incoming short-wave 
solar radiation, but reflects the longer- 
wave radiation by which the earth's 
heat is radiated outward, producing the 
so-called "greenhouse effect." Pres- 
ently about six billion tons of COo are 
being added to the earth's atmosphere 
per year, increasing its CO^ content by 
0.5 percent/year. By the year 2000 
the increase could be as much as 25 
percent. Our understanding of the 
atmosphere is not sufficient to predict 
the everttual effects on climate which 
might be produced by this increase and 
by a related increase in water vapor 
and dust, but small changes in the 
average temperature could have cata- 
strophic effects. 

Nuclear Reactors — Clean Power? 

There are strong forces in this coun- 
try pushing the nuclear reactor as an 
answer to our need for clean power 
sources. The reactor gains its energy 
from the fission of U-^"' or Pu-''^. The 
energetic by-products of this fissioning 
are stopped in the fuel rods, heating 
them, and this heat is transferred by 
some heat exchanger to a conventional 
steam-powered electric generator. 

The fission products are radioactive, 
dangerously so. They have many dif- 
ferent half-lives, but the whole mess 
averages a half-life of perhaps 100 to 
150 years. The switch to nuclear 



energy for the generation of electricity 
will be accompanied by a growing 
problem of disposal for this radio- 
active waste. Snow ** has estimated 
that the 16 tons of radioactive fission 
products from reactors accumulated in 
1970 will have grown to 388 tons by 
1980 and will be more than 5,000 tons 
by the year 2000. 

Nuclear reactors are carefully de- 
signed against the release of these 
products which are collected and 
stored for safety. But the storage prob- 
lem itself is a far from negligible one, 
with no generally agreed-on solution 
in sight. It has been proposed that the 
most dangerous wastes be dried and 
stored in salt mines in Kansas. There 
are now indications that above-ground 
storage will be the approved means. 

So far the radioactivity associated 
with nuclear reactors seems to have 
been handled with exemplary safety. 
Any exposure to the general popula- 
tion from this source is in the range 
of present exposure from past nuclear 
testing. It is in all likelihood causing 
damage, but so do all the other forms 
of power generation.^ What really 
must concern us when we consider 
substituting the fissioning of uranium 
for the burning of fuel is the possibility 
of accident. 

When discussing accidents, we are 
not talking about a real nuclear explo- 



•^ Air Pollution, a Scientists' Inslilu".. for Public 
Information Workbook. SIPI, 30 East 68th Street. 
New York. 

' En\ ironnienial Quality, the second annual report 
of the Council on Environmental Quality. August 
1971. U.S. Government Printing Office, Washington, 
DC. P. 107. 

~ Snow. J. •Radioactive Waste from Reactors; 
The Problem that Won't Go Away." Science and 
Citizen (Environment Magazine) 9: 89-95; May 
rt67. 

' This is treated more fully in The Environ- 
mental Ciifi of Electric Power Production. A SIPI 
Workbook. SIPI, .^0 East 68th St., New York. 



Table 3. Estimated emissions of air pollutants by weight nationwide, 1969; total 281.2 million tons ' (in millions of tons year). 





Carhon 






Sulfur 






Nitrogen 






MONOXIDI 


Particulates 


Oxides 


Hydrocarbons 


Oxides 


Total 


Source 


Amount 


Percent 


Amount 


Percent 


Amount 


Percent 


Amount 


Percent 


Amount 


Percent 


Amount 


Automobile 


111.5 


74 


0.8 


■} 


1.1 


3 


19.8 


53 


11.2 


46 


144.4 


Power plants 


1.8 


1 


7.2 


21 


24.4 


73 


.9 


-> 


10.0 


42 


44.3 


Industrial 


12.0 


« 


14.4 


41 


7.5 


22 


s s 


15 


-> 


1 


39.6 


Refuse burning 


7.9 


5 


1.4 


4 


.2 


1 


2.0 


5 


.4 


-) 


11.9 


Miscellaneous 


18.2 


12 


11.4 


32 


-> 


1 


9.2 


~>^ 


2.0 


9 


41.0 


Total 


151.4 


— 


35.2 


— 


33.4 




37.4 


— 


23.8 


— 


281.2 



• Council on Environmcnlal Qualily. Et 



ciiiitl Qualiix . P. 2i:. (See also footnote 7.) 



230 



Energy and the Environment 



sion in which a "critical mass" of fis- 
sionable material accumulates and goes 
off. The low enrichment densities pre- 
clude that. But since the reactor core 
is a witches' caldron of radioactive 
waste products, any accident which 
opens that up and spreads it over the 
countryside is catastrophic. The acci- 
dent that designers fear is cooling sys- 
tem failure. If the cooling-water were 
somehow denied the fuel rods, in only 
a matter of seconds they would begin 
to melt, leaving the reactor core an un- 
controllable blob of melting metal, 
heated internally so that it continues to 
melt. The resulting steam pressure 
explosions then could release the radio- 
activity to the environment. It is this 
small but troublesome chance of acci- 
dent that keeps reactors away from the 
cities where their products, electricity 
and heat, are needed. 

Heal as a Pollutant 
As we have earlier stressed, energy 
conversion is largely a one-way street: 
All work eventually produces heat. The 
"heat engines," because of their ineffi- 
ciency, however, are particularly trou- 
blesome. A steam power plant, which 
is only 30 percent efficient, dumps two 
units of heat energy for every one it 
converts to electricity. As our appetite 
for electricity grows in its apparently 
unbounded way, so also grows the 
problem of heat discharged to the 
environment. 

In the steam power plant the waste 
heat problem is associated with the 
necessity to lower the temperature of 
the exhaust steam (so that the piston 
will not have to work against an appre- 
ciable back pressure). The most in- 
expensive and convenient way to ac- 



complish this is to divert water from 
a stream or river. Nuclear reactors, 
since their working parts are steam 
engines, have the same problems. In 
fact, the nuclear reactor, because of its 
lower efficiency, presents a more seri- 
ous cooling problem. Because of the 
difference in power plant efficiencies 
(30 percent versus 40 percent) and in 
fuel efficiency, and because the fossil- 
fuel plant discharges about 10 percent 
to the atmosphere through its stack, the 
reactor dumps about twice as much 
heat per kilowatt hour of energy pro- 
duced as does the fossil-fuel plant. 

We do not need to look ahead very 
far to see that this heating up of the 
environment cannot go on. There are 
two different sorts of projections that 
make this point. 

The first of these concerns the cool- 
ing-water needs. If the growth of Fig- 
ure 5 continues, we will need one-sixth 
of the total fresh-water run-off of this 
country to cool our generating plants 
by 1990 and one-third by the year 
2000.'" Long before we reach that 
point we will have to make some hard 
decisions about stream and river use 
and plant siting if we are to preserve 
inland aquatic life. 

The second projection is even more 
indicative of the problem. If we ex- 
press our consumption of electricity in 
terms of energy released per square 
foot of U.S. land area, we obtain for 
1970, .017 watts/ft2. At our present 
doubling time of 10 years for electric 
power consumption, in 100 years we 
will have gone through 10 doubling 
periods, and the energy release will 
be 1 7 watts/ft- — almost the same as 
the 18 or 19 watts/ft- of incoming 
solar energy (averaged over 24 hours). 



Long before we reach such a level, 
something will have to be changed. 

These two projections only serve to 
emphasize what should by now be ob- 
vious: Energy use, particularly electric 
power, cannot be allowed to continue 
to grow as it has. There are other data 
that reinforce this conclusion. Elec- 
tricity means power plants and trans- 
mission lines; doubling consumption 
means doubling these. There are now 
about 300,000 miles of H.V. transmis- 
sion lines occupying four million acres 
of countryside in the United States. 
By 1990 this is projected to be 500,000 
miles of lines occupying seven million 
acres." 

All this serves to make the point 
that exponential growth cannot con- 
tinue. But we could have learned that 
from nature. Exponential growth is 
unnatural; it occurs only for temporary 
periods when there is an uncoupling 
from the constraints of supply and of 
control. For instance, it will be demon- 
strated for a while by the growth of a 
bacterial population with plenty of 
food, but will eventually be turned 
over either by exhaustion of the food 
supply or by control from environ- 
mental processes which resist the pop- 
ulation growth. We have examined 
some of the areas of environmental 
damage which may cause us to resist 
continued growth of energy production 
and consumption. What about our 
energy sources; are they likely to be 
the controlling factor? 



'■• Federal Power Commission Staff Sludy. "Selected 
Materials on Environmental Effects of Producing 
Electric Power." Joint Committee on Atomic 
Energy. August 1969. P. .123, 

" Energy Policy Staff. 'Electric Power and the 
Environment." Office of Science and Technology, 
August 1970. U,S. Government Printing Office. 
Washington. DC. 



RESOURCES AND NEW SOURCES 



Before we ask for a statement of the 
lavish deposits nature has made to our 
energy account, we must shed our 
parochial view and briefly look at 
energy consumption as the world prob- 
lem it is. 



Energy and the GNP 
It can and will be argued that man 
can live happily and productively at 
rather low levels of energy consump- 
tion. The fact remains, however, that 
today per capita energy consumption 



is an indicator of national wealth and 
influence — of the relative state of civi- 
lization as we have defined it. That 
this is so is seen most clearly by plot- 
ting that talisman of success, the (per 
capita) gross national product (GNP) 



231 



against the (per capita) energy con- 
sumption shown in Figure 8. There 
appears a rough proportionality be- 
tween per capita GNP and per capita 
energy consumption with the United 
States at the top, and countries Hke 
Portugal and India near the bottom. 
To the right of the "band of propor- 
tionality" lie the countries which man- 
age a relatively large GNP with a 



relatively small energy expenditure. 
Perhaps they are worthy of study. 

There are two lines of interest which 
lead out from this kind of data and 
bear on future uses of energy. One 
is to look at the time dependence of 
GNP/energy data. Data for the United 
States show two interesting effects. 

We find a long period, 1920 to 1965, 
during which the country was progres- 



sively more efficient in its energy use 
or at least managed to increase its 
per capita GNP more rapidly than its 
per capita energy expenditure. This 
was apparently largely due to increased 
efficiency of conversion and end-use 
techniques. This trend reversed, how- 
ever, around 1965, and we now are 
in a period during which this ratio is 
rising steadily. Reasons for this seem 



Figure 8. Per capita consumption of energy and gross national product tor some countries of the world. From Cook, Earl. "The Flow 
of Energy in an Industrial Society." Scientific American 224:142; September 1971. 



175 



150 



125 



U.S. 



CANADA • 



U.K.* 



Q 100 



BELGIUM AN 5 LUXEMBOURG* 



• AUSTRALIA 
GERMANY 



• SWEDE^ 



75 



POLAND 



SOUTH AFRICA • 



U.S.S.R. • 
• HUNGARY 



• DIINMARK 
NORWAY 



NETHERLANDS 



• FRANCE 



50 - 



IRE .AND* 



• NEW ZEALAND 



25 



BULGARIA • 
ROMANIA* 
ARGENTINA* 



• FINLAND 



• JAPAN 

• ITALY 



— MEXICO* SPAIN 
• • CCH 
YUGOSLAVIA .urjsuay 
COLOMBIA* • GREECE 
BRAZ?L« PORTUGAL 
• INDIA .GHANA 



500 



1 ,000 1 .500 2,000 

GROSS NATIONAL PRODUCT (DOLLARS PER CAPITA) 



2,500 



3,000 



232 



Energy and the Environment 



to be in part at least due to a rise in 
non-GNP connected energy uses, such 
as heating and air conditioning. Since 
these uses are on the increase and 
since we are near ultimate efficiency in 
most of our major conversion and end- 
use techniques, this rise in energy con- 
sumed per dollar of GNP is expected 
to continue for a while and must be 
built into energy use projections. 

The second line of inquiry concerns 
ultimate world use. The United States, 
with 6 percent of the world's popula- 
tion, uses 35 percent of the world's 
energy. If we look at comparative rates 
of growth, we see that the U.S. per 
capita energy consumption is much 
larger (a factor of about 30) than that 
of India, for instance, and is growing 
more rapidly. The world figure is some 
five times smaller but is growing a bit 
more rapidly than is the U.S. figure. 

Even if the United States were to 
stabilize at the present per capita figure 
of 250 kWh/day, it would take about 
120 years for the world per capita 
average to equal it and hundreds of 
years for India at its present rate of 
growth to catch up.'^ If some sort 
of equalization of world energy use is 
what we are aiming at, with the present 



U.S. figure as target, then we are talk- 
ing about increasing world consump- 
tion by a factor of about 100. And 
this brings us to energy resources. 

How Long Will They Last? 

As someone said, "Prophecy is very 
difficult, especially when it deals with 
the future." Predicting the lifetime of 
energy resources is doubly difficult. 
Energy use curves must be projected 
and then unknown resource potentials 
guessed at. It is difficult to hope for 
much accuracy in cither of these 
processes. 

The estimation of resources is based 
on general knowledge of the kind of 
geological conditions associated with 
the resource and on detailed knowledge 
of the distribution and extent of a re- 
source within a favorable geological 
area. Coal is the easiest to work with, 
for it seems almost always to appear 
where it is predicted. Oil and natural 
gas on the other hand are erratic in 
distribution within favorable areas and 
are found only by exploration. In addi- 
tion to coal, oil, and natural gas, there 
are two other sources of organic car- 
bon compounds which are potential 
fuel sources, the so-called tar sands and 



Figure 9. Remaining recoverable energy resources by region. From Williams, R. H. and 
K. Fenton. "World Energy Resources: Distribution, Utilization, and Long-Term 
Availability." (See footnote 13.) 



OIL SHALE 
COAL AND LIGNITE 
NATURAL GAS 
PETROLEUM 
TAR SANDS 



oil shale. In the tar sands, which 
so far have been found in appreciable 
amounts only in Canada, a heavy 
petroleum compound (tar) binds the 
sands together. A Canadian refinery is 
currently producing oil products from 
this material. Oil shale is shale rock 
containing considerable amounts of a 
solid organic carbon compound (kero- 
gan). Oil can be extracted by heating 
the rocks, but this process has not yet 
been demonstrated to have commercial 
viability. 

In Figure 9 we show the estimates 
of world fossil fuel resources of vari- 
ous types and the global distribution of 
these resources. '■• The unit used to 
measure these resources is the Q, 10"* 
BTUs. As a crude reference to the size 
of a Q, it would take about that much 
energy to boil Lake Michigan. Perhaps 
more useful is the fact that U.S. total 
energy consumption in 1970 was about 
0.07 0, and world consumption about 
0.2 Q. 

One sees from these data that most 
of the remaining fossil-fuel resources, 
for the United States and for the world, 
are in the form of coal. 

Presenting data on resources does 
not by itself answer the question "How 
long will they last?" To answer that 
question one has to look at data on the 
rate at which the resources are being 
used. A simplified but very graphic 
way of displaying this has been 
adopted by M. King Hubbert of the 
U.S. Geological Survey.'^ Since sup- 
plies of fossil fuels are finite, the curve 
which traces their production rate will 
be pulse-like, that is, it will rise ex- 
ponentially in the beginning, turn over 
when the resources come into short 
supply, and then decay exponentially 
as the resources become harder and 
harder to find. Such data for U.S. oil 
and U.S. coal are displayed in Figures 
10 and 11. 



USSR. 


EUROPE 


MIDDLE 


LATIN 


AFRICA 


ASIA CANADA 


OCEANIA 


CHINA, 




EAST 


AMERICA 




(EXCEPT 




MONGOLIA 










CHINA. 
MONGOLIA) 





"These points are discussed in more detail in 
Siarr, C. "Energy and Power." and Cook. E. 
"The Flow of Energy in an Industrial Society." 
.Scicnii/k American 224: 37-49 and 1.14-144, re- 
spectively; September 1971. 

"Williams, R. H., and K. Fenton. "World 
Energy Resources: Distribution. Utilization, and 
Long-Term Availability." Paper delivered at the 
annual meeting of the American Association for 
the Advancement of Science, December 29. 1971. 

" Hubbert. M. K. Chapter 8, "Energy Resources." 
in Resources and Man. W, H. Freeman, San 
Francisco, CA. 1969. 



233 











1 — 


2/ 

a' 








1 bbIs 1 

S\\\\\\\\$: 












2 

1 


/ 

; 




Q„=165 


xlO'bbIs 










1 




7 

RCENT (65 y 










r 














> 


/ 


m^ 


\. 1 














Y 








1^ 










- [ 1 1 11 1. 


«^??^^. 


Mi 


L 


...,. 


[1 

bbIs 
1 


1 

29 X 

1 


S 

lO'bbIs ""r^ 

1 ^-~ 





Figure 10. Use rate tor U.S. oil resources. From Hubbert, M. K. Resources and Man. 
P. 183. (See tootnote 14.) 



The curve for U.S. oil is of particu- 
lar interest. It shows that the actual 
rate of production from 1880 to the 
present does have roughly the pre- 
dicted shape. If Hubbert's choice of 
total resources, 165 X 10" billion bar- 
rels, is correct, it also shows that the 
United States is probably now past the 
peak of oil production. The most im- 
portant feature of a curve like this is 
its width, for that tells us how long a 
resource might be expected to last. We 
see that for oil, these data suggest that 
the total amount of oil to be produced 
by the United States is 165 X 10'' 
billion barrels and that 80 percent of 
that will be produced in the 65-year 
period from 1934 to 1999. Thus, 
within our lifetime we can expect to 
sec a radical change in the fuel mix, 
with petroleum losing its dominant po- 
sition. The cflects of this on automo- 
bile transportation will be of major 
importance in our automobile-centered 
economy. 

Figure 10 for coal is consistent with 
the previous Figure 9. We have a great 
amount of coal and arc just started up 
the slope to the peak in production. 
The time scale is much larger, the time 
to produce 80 percent of the U.S. coal 
is on the order of 300 to 400 years. 

In combination. Figures 9, 10, and 
1 I give a representative view of the 
state of U.S. and world fossil-fuel 
resources. They give a qualified answer 
to, "How long will they last?" The 



answer: "Not very long," if we are 
talking about crude oil and natural 
gas; "long enough for us to find other 
sources," if we are talking about coal. 
The answer might also have been: 
"Long enough for us to wreck our en- 
vironment." Without much improve- 
ment in the protection we give our 
environment about two more doubling 
periods of energy consumption may be 
all it can take. Each doubling not only 
reduces the resources but, for instance, 
doubles the generating capacity (more 
plants), doubles (almost) the amount 
of transmission lines, doubles the coal- 
mining activity, doubles (unless rigid 
controls are implemented) the sulfur 
oxides and fly ash in the atmosphere, 
and so on. 

Figure 11. Use rate for U.S. coal resources. 
P. 200. (See footnote 14.) 



Are There Clean Continuous 
Energy Sources? 

While coal may provide for our 
energy needs for 300 to 400 years, it 
won't last forever; on the scale we hope 
is still appropriate to mankind, the 
period of fossil-fuel dependency will be 
a short blip on the sweep of time. If 
we are to see a world in which all 
people have "energy slaves" in num- 
bers which approach the U.S. standard, 
we must find some source of energy 
which can last for at least a few tens 
of thousands of years. 

In Part I we cataloged the primary 
energy sources. Let's look at them 
again. The primary sources with their 
important components are shown in 
Table 4. 

From Table 4 it is easy to see the 
necessary shape of our long-range fu- 
ture. Of the continuous sources only 
solar energy can provide energy at the 
level of expectation. And for solar 
energy, the three converters we now 
use — photosynthesis, hydro power, and 
wind power — even at maximum utiliza- 
tion, could just barely suffice. 

If we look to the depletable sources 
and spend no more time discussing the 
fossil fuels, we see some interesting 
things. In the first place, we are struck 
by the fact that the ordinary nuclear re- 
actor is not a long-term answer. If we 
successfully convert to the controver- 
sial breeder reactor, we see our first 
big number, and we increase our poten- 
tial by a factor of 100. Finally, look- 
ing somewhat further into the future. 

From Hubbert, M. K. Resources and Man. 






1/ 




%, 









%. 



<°\. 



^"'-Jtf*, 



$100x10'^ 
J METRIC N 

:; TONS N 

\ ^ 



tfoj ""^^^'i^^^f;^ 



1800 1900 



2000 2100 2200 



2300 
Years 



234 



Energy and the Envrionment 



determinedly rosy-hued, successful ap- 
plication of the D-D reaction in a 
fusion reactor could, due to the vast 
amounts of deuterium in the ocean, 
give us an essentially infinite source. 

Let us now take off the rose-colored 
glasses and look somewhat more 
sceptically at the most important of 
these estimates. We refer the interested 
reader to the suggested general reading 
for more detailed reviews of these vari- 
ous topics. 

Table 4. Primary energy sources with 
maximum power available.'" 





Maximum 




Power — 


Continuous Sources 


World 




(Units 10" 




watts) 


Solar 


28,000 


Photosynthesis fuel 


13 


Hydro power 


3 


Wind power 


0.1 


Gravitational (tidal) 


1.0 


Geothermal 


0.06 


World cumulative demand 




1960-2000 


-500 


World annual demand by 




year 2000 


~ 15 


Depletable sources 




Chemical (fossil fuels) 


~ 1000 


Nuclear 




■c:-- / ordinary reactor 

P'^^'°" (breeder reactor 


-3000 


- 300,000 


Fusion 


> 5 X 10' 



■ Adopted from Starr, C. "Energy and Power." 
Scientific American 224: 43; September 1971. 

Solar Energy 

Even at the great distance of earth 
from sun, our share of the solar output 
is impressive. Solar energy, which fuels 
life, pours onto the earth in prodigal 
amount. But to harness it for the mas- 
sive needs of industry is something else. 
Solar energy has several disadvantages. 
It is dilute: approximately ~18 watts/ 
ft- averaged over 24 hours. It is 
erratic: not only is there a familiar 
cycle of light and darkness but less 
regular cloud obscuration. This latter 
is a serious problem since neither heat 
nor electricity — the most likely forms 
to which solar energy will be converted 
— can be readily stored. 

There are ambitious schemes being 
proposed to capture and convert sig- 
nificant amounts of solar energy, and 
the budget for solar energy research 
is climbing from the present "hobby" 
level of about $50,000/year to several 
million. We are beginning to make a 
real effort to use this clean free energy 



more massively, but it will take decades 
to see results.''' 

Nuclear Energy — Fission 
We have discussed in Part II some 
of the dangers of the ordinary nuclear 
reactor. This country has embarked on 
a program to develop the fast-breeder 
reactor, which uses some of the neu- 
trons from the fissioning fuel to convert 
U-^~^ to the reactor fuel Pu^^^ifi The 
energy arguments for this are easily 
seen from Table 4. What is not seen 
are the problems this will bring. The 
breeder reactor poses several. It is a 
new and difficult technology, running 
at higher temperatures (more efficient 
but more susceptible to cooling-water 
accidents), it will probably use a liquid 
metal heat exchanger. Most serious, 
however, are the dangers associated 
with plutonium. Creating this material 
in large quantities means that the half- 
life of waste (in which there will be 
some plutonium) will go from about 
150 years to > 20,000 years. Can we 
guarantee safe storage for that long? 
It also means that the material for 
"atomic bombs" will now be created in 
ton lots and shipped across country 
and maybe across oceans. The political 
implications are obvious. 

Nuclear Energy — Fusion 
We have dreamed for 20 years of 
tapping the essentially unlimited re- 
sources of deuterium to fuel a D-D 
fusion reaction. But so far it is largely 
a dream. Scientifically we understand 
the theory, but to create a plasma of 
fusionable material at the 100,000,- 
000° F we need and to hold it together 
for long enough to get appreciable 
power out, is presently beyond our 
means. Research in this area is being 
accelerated, and the optimists predict 
scientific feasibility by 1980 and pilot 
demonstration by 2000. The pessimists 
laugh.'' 

Fusion, if it can be tapped, offers 
much; not only essentially unlimited 



1 • For further details see Glaser, P. E. "Solar 
Energy— Prospects for Its Large-Scale Use." The 
Science Teacher 39: 36-39; March 1972. 

'■' Seaborg. G. T.. and J. L. Bloom. "Fast Breeder 
Reactors." Scientific American 223: 13; November 
1970. 

'■For a review of progress toward fusion see: 
Auer P. L., and R. N. Sudan. "Progress in Con- 
trolled Fusion Research." The Science Teacher 
39: 44-50; March 1972. 



fuel, but at least hundredfold reduction 
in the radioactive waste problem. It 
will also be, we expect, free from threat 
of accident. There will still be heat to 
worry about, but the combination of 
cleanliness and safety may allow siting 
to take advantage of this heat. 

Conclusion 

Mankind is in the midst of a crisis 
of energy. It has several dimensions. 
On a short time scale, we are faced 
with a serious shortage of natural gas 
and, in certain places where demand 
has exceeded present capacity, with a 
shortage of electric power. 

On an intermediate time scale, 30 
to 60 years, we are faced with the 
necessity of finding a substitute for the 
petroleum products which now dom- 
inate the energy mix. 

Finally, on a larger scale, 300 to 400 
years, we are faced with the exhaustion 
of fossil fuels. 

What can we do? Some of the 
answers are obvious. We can plan 
more carefully and further ahead. We 
can try to reduce energy expenditures 
and increase research and development 
support. As citizens we must demand 
this. We must also demand a role in 
the decision-making process and de- 
cide, for instance, whether we lean 
heavily on the breeder reactor with its 
dangers or rely on coal and coal prod- 
ucts (gases and liquids). 

The science teachers of this coun- 
try have a vital role to play in the 
next few years. These decisions must 
be based on information, and it is the 
science teacher who must make sure 
that developing citizens have access to 
the necessary information devoid of 
bias and distortion. It is my hope that 
this summary, brief and sketchy as it 
is, can serve as a part of the foundation 
of that necessary effort. D 

Suggested General Reading 

1. Scientific American 224; September 1971. The 
issue is devoted entirely to energy. 

2. "The Energy Crisis." Bulletin of the Atomic 
Scientists 27; September and October 1971. Two 
issues on energy. 

3. The Science Teacher 39; March 1972. Five 
articles on energy. 

4. Romer, R. H. "Energy-Resources. Production 
and Environmental Effects." A Resource Letter 
of the American Association of Physics Teach- 
ers. American Journal of Physics 40: 805; 
June 1972. 

5. "Energy and the Environment." J. M. Fowler. 
McGraw-Hill Book Co., N.Y.. 1974. 



235 



The human eye versus the camera lens as an optical instrument 
in this interesting article. 



18 The Lens, a Most Imperfect Eye 

Norman Goldberg 

An article from Popular Photography, 1970 



Hermann \'on Helmholtz. the 
19th century's foremost author- 
ity on the eye and the nature of 
vision, is credited with observ- 
ing that whoever made the hu- 
man eye had not properly 
learned his craft. In the hun- 
dred years since he reached this 
conclusion, other workers in the 
field have passed similar judg- 
ments, based mainly upon their 
direct comparison between the 
eye and a lens. 

Researchers have removed 
the eye from freshly slaughtered 
animals and examined the im- 
age it formed. Almost every ac- 
count of these experiments 
reaches conclusions that seem 
to prove that Helmholtz's re- 
mark was true. The bulk of 
these observations were made 
prior to the breakthrough in op- 
tical design brought about by 
the development of the modern 
high-speed computer. 

Just think how much further 
today's lenses would have 
tipped the scales had thev been 
available when comparisons be- 
tween the eye and a camera lens 
were first being made. 

Why such comparisons were 
made (and are still being made) 
at all is probablv the result of 
attempts to explain the workings 
of one by referring it to the 
other. Most of you have seen 
primary-level books on how 
cameras function. In most of 
these, there's at least one draw- 



ing showing the parallel between 
the eye and the camera. The 
eyelid is compared to the shut- 
ter, the iris to the diaphragm, 
the lens of the eye to the cam- 
era's lens, and the retina to the 
image-recording film. 

n we were to limit ourselves 
to discussing the eye within this 
framework, we could come up 
with some figures that might be 
useful in seeing how true past 
comparisons were when they 
judged the eye to be an inferior 
optical instrimient. If an aver- 
age of values from a variety of 
sources can be used as at least 
the basis of a "normal" eye lens, 
its specifications would be: 

Focal Icni^rh (modified 
zoom) — a 22.7-mm average: 
speed — //2.8: inininjiiin aper- 
ture (without benefit of mor- 
phine) — // 1 1 : angle of view — 
vertical: 130 degrees, horizon- 
tal : 200 dQ%rQQS>\ resolving power 
— on axis: 70 L/mm, one de- 
gree off-axis: 56 L/mm. five 
degrees oflF-axis: 24 L/mm, 20 
degrees off-axis: 7 L/mm. 50 
degrees off-axis: 1.8 L/mm; 
closest working distance — av.: 
250-mm (varies with age). 

Care and maintenance — self- 
cleaning, shutter fatigues after 
about 16 hours of use: stability 
— varies from hour to hour: 
standard accessories — bu i It-i n 
UV absorption filter, automatic 
diaphragm, automatic focus 
control, automatic tarcet-seek- 



ing control with instant lock-on 
once target is within axial spot. 
optional over-ride on command. 

Now tell me — can you find 
a lens that would justify those 
old cats' putting the eye down? 
And before you pore through 
your lens collection, let me 
sneak one more thought into the 
argument. Most of us have 
two eyes, so let's add a few 
things to our list in view of this: 

Stereoscopic, W\\.h 130-degree 
field; fully automatic conver- 
gence and divergence linked to 
target distance and relative posi- 
tion. Manual override possible; 
shutters may be independently 
operated for special effects such 
as providing a homing signal to 
other units similarly equipped, 
but with certain basic construc- 
tional differences. 

But no one can really be seri- 
ous about the comparison be- 
tween eye and lens. I wouldn't 
trade my eyes for any lens or 
lenses made anywhere, any- 
time — and neither would you! 
The eye can't be talked about 
in lens-alone terms, because it's 
so much more than simply a 
lens. Romantic aspects aside, 
the eye is part of an image .v>'v- 
tein that employs memory, ex- 
perience, and lots more. 

About the closest man-made 
contrivance would be a twin- 
lens, stereo TV camera system, 
with full color response, auto- 
exposure control, auto-focus. 



236 



The Lens, a Most Imperfect Eye 



auto-timing, and all the other features 
listed above for the lowly (according 
to Heimholtz) eye. 

What is curious is the way lens de- 
signers have learned to imitate the 
eye in some details. They've found it 
necessary to use several elements, each 
with a different refractive index to 
overcome certain aberrations. The 
eye's crystalline lens employs this 
same feature, but more gracefully. 

The eye is not made up of a big 
chunk of stuff having one refractive 
index, followed by another with a dif- 
ferent index, followed by more of the 
same. Instead, the eye's lens is made 
up of layers of fibers, each so thin that 
the more than two thousand layers 
(encased in a clear, elastic mem- 
brane) take up no more room than a 
small lima bean. 

Successive layers have slightly dif- 
ferent refractive indexes, so that a 
ray-trace through the whole bean- 
sized lens would curve gradually, in- 
stead of displaying the abrupt changes 
in direction encountered in a ray go- 
ing through a man-made lens. And 
there's considerably more. 

To focus the eye between its far and 
near points of distinct vision requires 
an involuntary act on the part of the 
owner called "accommodation." This 
involves the contraction or relaxation 
of some tiny muscles that cause the 
crystalline lens to change its shape 
from a thin lens with relatively flat 
faces, to a fat, squat, bulging lens. 



The thin shape occurs when the eye 
is relaxed and looking at distant ob- 
jects, while the more bulging shape oc- 
curs when the muscles tighten around 
it for close-up work. The whole 
process of focusing from far to near 
involves a change in lens thickness of 
only 1/2-mm (about 1/50 in.). Take 
a camera lens of the same focal length, 
change its focus from infinity to 10 in., 
and you'll have to move the whole as- 
sembly 2.3-mm. (about 1/10 in.). 

Because of the short focal length, 
the figures involved are small, but no- 
tice that the camera lens has to be 
moved about five times as much as the 
eye. And the eye doesn't even move 
(in relation to the body) — its lens 
merely bulges a bit at the center. It's 
almost as though it were taking a 
deep breath, but it costs the owner 
not even that small effort. 

The cornea, which is the outermost 
(and most highly refractive) element 
of the eye is the one that can be com- 
pared rather closely to a man-made 
lens. It can be likened to a meniscus 
lens whose center is thicker than its 
edges — that is, a positive meniscus. 
By itself, it has a focal length of about 
25-mm, so you can see that in the 
compound structure that is the eye, 
the cornea contributes most of the 
light-bending power. 

In fact, the main function of the 
eye's lens is to change the focus by 
altering its shape, thereby changing 
its focal length. So, now you know 



Many animals are thought to see in monochrome rather than in color, as we do. 




237 



why we can call the eye a zoom (or 
variable focal-length) system. 

Sooner or later I'll have to defend 
my listing of the eye's resolving power, 
so let's have at it now. It is true that 
the eye possesses the characteristic of 
having a central spot (called the fo- 
vea) measuring about 0.3-mm in di- 
ameter, that, alone among all other 
regions of the eye, is capable of dis- 
tinguishing fine detail. The remaining 
regions (away from the foveal area) 
become less and less able to discern 
the information-filled fine detail. 

This is the kind of situation that, if 
noted in a camera lens, would spell 
"no-sale." But in the eye it makes 
perfectly good sense. Because of the 
tiny region in which fine details can 
be distinguished, our minds aren't 
cluttered with stimuli from all over the 
130-degree field we see (in stereo). 
We concentrate on the region of acute 
vision provided by the fovea. 

To see how this works, try to look 
intently at both dots in the brackets 
( : ) . You'll soon discover that only 
one dot at a time can really be scruti- 
nized. Because the eye is continuously 
scanning objects, we're unaware that 
our region of acute vision is so 
tightly restricted. 

What about all the rest of the eye's 
field of view? The image on the retina 
other than the tiny fovea is not going 
to waste. The outlying areas of the 
retina are richly supplied with photo 
sensors called "rods" (which are 
highly sensitive to dim light), while 
the fovea is richly supplied with 
"cones," which are responsible for 
this region's great acuity of vision. 

It is in the outer regions that the 
"automatic target-seeking control" in- 
formation is gathered. City dwellers 
who survive traffic while crossing 
streets instinctively learn not to fix 
their gaze on any one small detail. 

They're better off staring at nothing 
in particular so that their peripheral 
vision is free to warn them of some 
idiot bearing down on them with 300 
horsepower. This kind of vision re- 
quires only that gross form and mo- 
tion can be detected. High resolving 
power isn't necessary. 



When making a close examination 
of something with fine detail, we need 
all available resolving power. How 
about the figure of 70 L/mm for 
the on-axis portion of the eye: is it at 
all comparable to a fine lens? Let's de- 
fine our terms first. When I give the 
figure of 70 L/mm as the resolving 
power for the eye, I'm treating the 
eye as if it were a lens looking at a 
bar-target chart and forming the im- 
age on the retina. 

How good is 70 L / mm? 

The 70 L/mm is what I could theo- 
retically see (with proper magnifica- 
tion) on the surface of -the retina. 
This translates to the eye's ability to 
clearly distinguish a one-millimeter 
space sliced into 14 pieces and placed 
at normal reading distance. 

If we have a 35-mm camera and 
want to be able to enlarge the nega- 
tive it makes to 8x10 in., and on this 
print be able to fully exploit our eye's 
best ability to distinguish fine detail, 
the finished print will have to contain 
details of about 7 L/mm (remember 
that in lens-resolving-power jargon, as 
applied to photos, a "line" is taken to 
mean a line-and-a-space). This boils 
down to the negative's having detail 
of at least 56 lines/mm on it. 

NASA studies reveal that with av- 
erage photo-sensitive materials, a 
lens's resolving power is cut in half. 
So, if we apply this factor in our ex- 
ample, the lens under consideration 
will have to be capable of rendering 
over 100 L/mm at a usable contrast 
level. This is a rather tall order. 

While many lenses have this capa- 
bility, only the very best ones can de- 
liver this kind of performance over 
any sizeable portion of their field. As 
a final crusher to anyone comparing 
eye and camera to the disadvantage of 
the eye, consider what optical instru- 
ment we use when judging the cam- 
era lens's final product. 

We use our eye's marvelous ability 
to detect tonal quality, and rendition 
of fine detail. And, most important, 
(something that only the combination 
of eye, brain, and emotions can do) 
we decide if we like the picture. O 



238 



If you are interested in exploring some of the connections 
between science and hunnanity's other creative activities, 
look through this bibliography. 



T9 Science, Technology, and the Arts: 

A Reference Bibliography for Students 

William Davenport 



I. INTRODUCTION 

■ The following annotated biblio- 
graphy is an abridged and condensed rear- 
rangement of items from "Resource Let- 
ter TLA-1 on Technology, Literature, and 
Art since World War 11" (American Jour- 
nal of Physics 38, No. 4, April 1970) and 
"Resource Letter TLA-2 on Technology, 
Literature, and the Arts, Contemporary" 
(American Journal of Physics, forthcom- 
ing). Selected primarily for students, it 
concentrates on journals and books most 
likely to be generally available to them. 
(Other relevant resource letters include 
"Science and Literature," by Marjorie 
Nicolson in American Journal of Physics 
33, 175, 1965; and "Collateral Reading 
for Physics Courses" by Bork and Arons, 
American Journal of Physics 35, 171, 
1967.) 

■ The items below are suggestions, not 
prescriptions, meant to widen perceptions 
and tempt readers to go further on their 
own. Such exploration might include the 
annual b ibhographies in the journals 
Technology and Culture or Isis, and col- 
lections like Science for Society: A Bibli- 
ography, compiled by John A. Moore. 

■ The rationale for providing this list 
involves the following presumptions: Our 
century has already seen the stereotype of 
the isolated "pure" scientist fade, in 
many instances, before a new image of a 
human being whose work is often, if not 
now inevitably, related to social or pohti- 
cal issues. We are now also beginning to 
see that a complete overview of contem- 
porary science and technology brings in 
the interplay between them and the arts, 



involving matters of values and choices: Is 
"Switched-On Bach" musically sound and 
defensible? Is the sculptor vanishing in a 
mass of electronic gadgets and laser 
beams? To what extent have the Machine 
and the Bomb affected modern litera- 
ture? 

■ This is not to say that specialists and 
specialization are outdated, or that all 
students must be Renaissance men and 
women. But just as it has become appar- 
ent that the first mark of a professional, 
as Lynn White tells us, is knowledge of 
the history of his or her craft, so is it fast 
becoming clear that the complete physi- 
cist, chemist, mathematician, or engineer 
will be a better person and professional 
for realizing, as John Donne said, that 
"no man is an island," that some smaU 
corner of educational progress must in- 
clude such topics as physics and musical 
tone; the humanistic imphcations of bio- 
chemistry; the aesthetics of mathematics; 
and the social responsibility of the en- 
gineer. 

■ Students who examine some of 
the following materials will surely find 
exciting possibilities for projects and 
papers, inspiration for creative work, 
stimulus for personal intellectual activity, 
and enjoyable reading in the bargain. 

II. BIBLIOGRAPHY 

l."Art and the Corporation," David 
Antin. Art News 70, No. 5, 22 
(September, 1971). The author, with 
a book on art and technology forth- 
coming, makes the point that the 



239 



artist views science as trying to under- 
stand reality and technology as trying 
to manipulate it. The need for tech- 
nological art was seen by such archi- 
tects as Charles Ashbee, who stated, 
"Modern civUization rests on ma- 
chinery, and no system for the en- 
dowment, or the encouragement, or 
the teaching of art, can be sound that 
does not recognize this." 

2. Poetics of Space. Gaston Bachelard. 
(Orion Press, New York, 1964). A 

physicist-philosopher justifies poetry 
as an answer to technology and for- 
mulas. In a provocative discussion of 
the "spaceness" of cellars, attics, and 
closets and of their relative effects on 
us, of which we are generally un- 
aware, the author makes us see the 
familiar in a new light. He offers stim- 
ulating contrasts with common no- 
tions of space in physics and in the 
public mind, as influenced by Apollo 
missions. 

3. Science and Technology in Art To- 
day. Jonathan Benthall. (Praeger, N. 
Y., 1972). In this modestly priced, 
well illustrated paperback, Benthall 
traces the ups and downs of the sci- 
ence-technology-art relationship in 
modern times; his book is a primer of 
sorts. Pointing out that virtually all 
art uses some form of technology, the 
author feels that those who remain 
aloof simply prefer technologies al- 
ready "absorbed into traditional art"; 
not many using the new media have 
advanced significantly - for that mat- 
ter, there isn't much good art in any 
medium in the newer neighborhoods. 

4. "Creativity, Poetic Language, and the 
Computer," Marie Boroff. Yale Re- 
view 60, 481 (June, 1971). With 
grace, humor, sanity, and balance this 
Yale poet and EngUsh professor used 
a grant to tackle the computer, learn- 
ing its language and processes from 
the ground up. Boroff finds computer 
poetry "startlingly and unpredictably 
effective," with good random lines 
and stimulus for "live" working ideas. 
However, she concludes, that to be re- 



ally creative a computer would have 
to initiate, recognize sahency in ver- 
bal expression, make comparative 
judgments among alternative word- 
ings. Admitting technological possi- 
bilities, the author notes that only hu- 
mans can experience life, death, hu- 
mor, fear, anger, sex, etc. — the stuff 
of existence. Even if ultimately a 
machine can experience and artfuUy 
express itself, "the value of that art 
for human beings must be assessed by 
human beings. Such assessment is the 
domain of the humanist." 

5. "Science as a Humanistic Discipline," 
J. Bronowski. Bull. Atomic Scientists 
24, No. 8, 33 (1968). The author of 
Science and Human Values here cov- 
ers the history of humanism, values, 
choice, and the human being as a uni- 
que creature. It is the duty of science 
to transmit this sense of uniqueness, 
to teach the world that people are 
guided by self-created values and thus 
comfort it for loss of absolute pur- 
pose. 

6. Beyond Modern Sculpture: Effects of 
Science & Technology on the Sculp- 
ture of this Century. Jack Burnham. 
(George Braziller Inc., N. Y. 1969). 
"Today's sculpture is preparing man 
for his replacement by information- 
processing energy." Burnham sees an 
argument for a mechanistic tele- 
ological interpretation of life in which 
culture, including art, becomes a vehi- 
cle for qualitative changes in man's 
biological status. [See review by 
Charlotte Willard in Saturday Rev. 52, 
No. 2, 19(1969).] 

7. "The Mythos of the Electronic Revo- 
lution," James W. Carey and John J. 
Quirk. American Scholar 39, No. 2, 
219; No. 3, 395 (1970). A two-part 
article which criticizes literary neo- 
Luddite activity, but also notes that 
"electronics is neither the arrival of 
Apocalypse nor the dispensation of 
grace." Encourages positive promo- 
tion of the values of the arts in place 
of negativistic attitudes toward tech- 
nology. 



240 



A Reference Bibliography 



8. "The Computer and the Poet," Nor- 
man Cousins. Saturday Rev. 49, No. 
30, 42 (23 July 1966). Suggests edi- 
torially (and movingly) that poets and 
programmers should get together to 
"see a larger panorama of possibilities 
than technology alone may inspire," 
and warns against the "tendency to 
mistake data for wisdom." 

9. Engineering: Its Role and Function in 
Human Society. William H. Daven- 
port and Daniel Rosenthal, Eds. 
(Pergamon Press, Inc., New York, 
1967). An anthology with four sec- 
tions on the viewpoint of the human- 
ist, the attitudes of the engineer, hu- 
man and machine, and technology 
and the future. Many of the writers in 
this bibUography are represented in 
an effort to present historical and 
contemporary perspectives on tech- 
nology and society. 

10. "Art and Technology — The New 
Combine," Douglas M. Davis. Art in 
Amer. 56, 28 (Jan.- Feb. 1968). 
Notes a new enthusiasm among many 
modern artists because of the forms, 
effects, and materials made possible 
by the new technology. Envisions full 
partnership between artist and ma- 
chine in the creative process. 

11. "The Artist and the Computer," 
Douglas Davis. Newsweek 78, No. 
11, 78 (Sept. 13, 1971). Theorizes 
that there are now no images which 
people cannot make, especially with a 
reserve store locked away in elec- 
tronic circuits. 

12. 5*0 Human an Animal Rene Dubos, 
(Charles Scribner's & Sons, N. Y., 
1968). Dubos, a prominent microbio- 
logist, won a Pulitzer Prize for his 
work, and it deserves wide reading. 
Motivated by humanistic impulses, 
writing now like a philospher and 
again like a poet, he discusses dehu- 
manization under technological ad- 
vance. People can adjust, Dubos says 
— at a price. But first they must un- 
derstand themselves as creatures of 
heredity and environment and then 



learn the science of Ufe, not merely 
science. 

13. The Theatre of the Absurd. Martin 
Esslin, (Anchor Books — Doubleday 
and Co., Inc., Garden City, N.Y. , 
1961). The drama director for the 
British Broadcasting Company ex- 
plains the work of Beckett, lonesco, 
Albee, and others as a reaction to loss 
of values, reason, and control in an 
age of totalitarianism and of that 
technological development, the 
Bomb. 

14. Engineering and the Liberal Arts. 
Samuel C. Florman. (McGraw-HUl 
Book Co., New York, 1968). The sub- 
title tells the story: A technologist's 
Guide to History, Literature, Philoso- 
phy, Art, and Music. Explores the re- 
lationships between technology and 
the hberal arts — historical, aesthetic, 
functional. Useful reading lists are in- 
cluded. 

15. The Creative Process. Brewster 
Ghiselin, Ed. (University of California 
Press, Berkeley, 1952; Mentor Books, 
The New American Library, Inc., 
New York, paperback, 1961). Mathe- 
maticians, musicians, painters, and 
poets, in a symposium on the per- 
sonal experience of creativity. Of use 
to those interested in the interplay 
between science and art. 

16. The Poet and the Machine. Paul 
Ginestier. Martin B. Friedman, TransL 
(University of North CaroMna Press, 
Chapel Hill, 1961; College and Uni- 
versity Press, New Haven, Conn., 
paperback, 1964). Considers through 
analysis of generous examples from 
modem and contemporary poetry 
the effect of the machine on subject 
matter, form, and attitude. An origi- 
nal approach to the value, meaning, 
and influence, as the author puts it, 
of the poetry of our technology- 
oriented era. 

17. "The Secret War Between Science and 
Poetry," Robert Graves. New Scien- 
tist 52, No. 772, 34 (2 Dec. 1971). 
"The dean of Enghsh poets" finds 



241 



that "technology produces millions of 
identical and spiritually dead objects" 
and that modern science "lacks a uni- 
fied conscience." Fellow English poet 
Roy Fuller, however, ("The Osmotic 
Sap," Times (London) Literary Sup- 
plement, No. 3611, 559, May 14, 
1971) believes that "a blind or neu- 
tral attitude to science tends to insu- 
late the poet from the spirit of the 
age," leading to sentimentalism . 

18. "Automation and Imagination," 
Jacquetta Hawkes, Harper's 231, 92 
(Oct. 1965.) A prominent archaeolo- 
gist fears the loss of human imagina- 
tion under years of technical training. 
While the technological revolution 
sweeps on toward a total efficiency of 
means, she says, we must control the 
ends and not forget the significance 
of the individual. 

19. The Future as Nightmare. Mark R. 
Hillegas. (Oxford University Press, 
New York, 1967). A study that be- 
gins with Wells and ends with recent 
science fiction by Ray Bradbury, 
Kurt Vonnegut, and Walter Miller, Jr. 
The latter three are worried about the 
mindless life of modern humans with 
radio, TV, and high-speed travel; the 
need to learn nothing more than how 
to press buttons; the machine's rob- 
bing us of the pleasure of working 
with our hands, leaving us nothing 
useful to do, and lately making deci- 
sions for us; and, of course, the possi- 
bility of a nuclear holocaust. 

20. "Computer Music," Lejaren A. Hiller, 
Jr. Scientific American 201, No. 6, 
109 (Dec. 1959). Thesis: "Informa- 
tion theory makes possible the pro- 
gramming of a computer to compose 
music. The process by which the 
machine does so throws light on musi- 
cal structure and on the methods of 
human composers." Among discuss- 
able points is the assertion that 
"acoustics reduces the definition of 
musical sound to a plot of waveform 
amplitude versus time." 

2\. Science and Culture. Gerald Holton, 
Ed. (Beacon Press, Boston, 1967). Al- 



most all of the 1 5 essays in this out- 
standing collection appeared, several 
in different form, in the Winter 1965 
issue of the quarterly journal 
Daedalus. Of particular relevance to 
the area of this bibUography are Her- 
bert Marcuse's view of science as ulti- 
mately just technology; Gyorgy 
Kepes' criticism of modern artists for 
missing vital connections with techno- 
logical reality; Rene Dubos' conten- 
tion that technological applications are 
becoming increasingly ahenated from 
human needs; and Oscar Handlin's 
documentation of the ambivalent atti- 
tude of modern society toward tech- 
nology. 

22. Thematic Origins of Scientific 
Thought. Gerald Holton, (Harvard 
University Press, Cambridge, 1973). 
In this fine collection of essays and 
addresses ranging from Kepler to 
Einstein, Chapter 10 ("On Trying 
to Understand Scientific Genius") en- 
gagingly discusses Einstein's playful 
combining of objects of imagination 
which were real to him — an exercise 
which recalls the poet Wallace 
Stevens' assertion that the world of 
the imagination is the true reality — 
and Chapter 15 shows relevance to 
our present theme in its title, "Phys- 
ics and Culture: Criteria for Curricu- 
lum Design." 

23. "The Fiction of Anti-Utopia," Irving 
Howe. New Republic 146, 13 (23 
Apr. 1962). An analysis of the effect 
on modern fiction of the splitting apart 
of technique and values and the ap- 
pearance of technical means to alter 
human nature, both events leading to 
the American dream's becoming a 
nightmare, 

24. The Divine Proportion: A Study in 
Mathematical Beauty. H. E. Huntley. 
(Dover, N. Y., 1970). The section on 
"Surprise, Wonder, Curiosity" is par- 
ticularly pertinent. Discussing ratios 
and sequences: "A pretty result? 
What constitutes the essence of the 
aesthetic appeal of this outcome of 
simple mathematics? It appears to be 



242 



A Reference Bibliography 



compounded of a mixture of archaic 
emotions. There is surprise at the un- 
expected encounter; there is also both 
curiosity and wonder — making three 
of the flavors included in the idea of 
beauty." Elsewhere Hartley says that 
mathematics reads like poetry to a 
mathematician who is aesthetically 
minded. 

25. Literature and Science. Aldous 
Huxley. (Harper & Row, PubUshers, 
New York, 1963). A literary and 
highly literate attempt to show 
bridges between the two cultures. 
Technological know-how tempered 
by human understanding and respect 
for nature will dominate the scene for 
some time to come, but only if men 
and women of letters and scientists 
respect each other's contributions. 

26. The Sciences and the Humanities. W. 
T. Jones. (University of California 
Press, Berkeley, 1965). A professor of 
philosophy discusses conflict and re- 
conciliation between the two cul- 
tures, largely in terms of the nature of 
reality and the need to understand 
each other's language. 

21. New Landscape in Science and Art. 
Gyorgy Kepes. (Paul Theobald, 
Chicago, 1967). Like the earlier Vi- 
sion in Motion by L. Moholy-Nagy 
(Paul Theobald, Chicago, 1947), this 
work will make the reader see more, 
better, and differently. Essays and 
comments by Gabo, Giedion, 
Gropius, Rossi, Wiener, and others 
plus lavish illustration assist Kepes, au- 
thor of the influential Language of 
Vision and head of the program on 
advanced visual design at the Mass- 
achusetts Institute of Technology, to 
discuss morphology in art and sci- 
ence, form in engineering, esthetic 
motivation in science — in short, to 
demonstrate that science and its ap- 
plications belong to the humanities. 

28. The Scientist vs. the Humanist. 
George Levine and Owen Thomas, 
Eds. (W. W. Norton, New York, 
1963). Among the most relevant 
items are I. I. Rabi's "Scientist and 



Humanist"; Oppenheimer's "The Tree 
of Knowledge"; Howard Mumford 
Jones's "The Humanities and the 
Common Reader" (which treats tech- 
nological jargon); and P. W. 
Bridgman's "Quo Vadis." 

29. "The New Poetry," Frank MacShane. 
A mer. Scholar 37, 642 (Autumn, 
1968). Frequently, the modem poet 
writes of confrontation of humanity 
and machine. The poet is both at- 
tracted and repelled by technological 
change, which both benefits and 
blights. 

30. The Machine in the Garden: Tech- 
nology and the Pastoral Ideal in 
America. Leo Marx. (Oxford Univer- 
sity Press, New York, 1964; Galaxy, 
Oxford Univ. Press, New York, paper- 
back, 1967). One of the three most 
significant contemporary works on 
the interplay of Uterature and tech- 
nology [along with Sussman (45) and 
Sypher (47)] , this study concentrates 
on 19th-century American authors 
and their ambivalent reactions to the 
sudden appearance of the machine on 
the landscape. Whitman, Emerson, 
Thoreau, Hawthorne, Melville, and 
others reveal, under Marx's scrutiny, 
the meaning inherent in productivity 
and power. Whitman assimilated the 
machine, Emerson welcomed it but 
disliked ugly mills, Thoreau respected 
tools but hated the noise and smoke, 
Hawthorne and Melville noted hu- 
manity's growing alienation with 
the green fields gone, Henry Adams 
set the theme for the"ancient war be- 
tween the kingdom of love and the 
kingdom of power. . .waged endlessly 
in American writing ever since." The 
domination of the machine has divest- 
ed of meaning the older notions of 
beauty and order, says Marx, leaving 
the American hero dead, alienated, or 
no hero at all. Aptly used quotations, 
chronological order, and clarity of 
perspective and statement (with 
which not all may agree) make this 
a "must" for basic reading in this 
special category. Furthermore, there 
are links to Frost, Hemingway, 
Faulkner, and other modern writers. 



243 



31. "Science and Literature," P. B. Meda- 
war. Encounter 32, No. 1, 15 
(January, 1969). A frequently pub- 
lished British scientist finds holes in 
the Uterary opponent's game plan: a 
suspect claim to deep insight, a use of 
imagination without self-criticism, 
and an emphasis on too-often obscure 
style. 

32. The Science of Art. R. E. Mueller. 
(John Day. N.Y., 1967). A veritable 
textbook on the subject which dis- 
cusses technology as a force in art, 
cybernetics and art, and the meaning 
of art for science, among other topics. 
Sub-topics include new media, mate- 
rials, revelations of nature, devices 
and tools, processes, and knowledge 
of human functioning. 

33. The Myth of the Machine. Lewis 
Mumford. (Harcourt, Brace & World, 
Inc., New York, 1967). Important his- 
torical study of human cultural 
development, that shows a major shift 
of emphasis from human being to 
machine, questions our commitment 
to technical progress, and warns 
against the down-playing of literature 
and fine arts so vital to complete life 
experience. See also his earlier Art and 
Technics (Columbia University Press, 
New York, 1952), and Technics and 
Civilization. 

34. "Design, Technology, and the Pur- 
suit of Ugliness," George Nelson. 

Saturday Review 54, No. 40, 22 (Oct. 
2, 1971). Technology as an extension 
of tools originally brought blessings, 
but now, a blind Moloch under no 
controls, it overrides "all needs of the 
human spirit, all traditions, custom, 
languages, races, ideologies." This dis- 
cussion of design, mostly industrial, 
condemns us for junkpiles, roadside 
strips, billboards - which are our por- 
traits. Technology plus design, a 
bridge between technology and hu- 
manity, can clean up the mess. 

35. "Speculative Equations: Poems, 
Poets, Computer," Howard Nemerov. 
American Scholar 36, No. 3, 394 



(Summer, 1967). Sometime Consul- 
tant in Poetry to the Library of Con- 
gress, Nemerov faces the issue of 
mechanical perfection vs. human, of- 
ten flawed, work. If computer poetry 
eventually receives love and praise, he 
fears that this would mean "obeisance 
to its idol the machine" by the hu- 
man mind, not intrinsic value in the 
poetry. (Compare Boroff [4]). He re- 
calls Hannah Arendt's gloomy prog- 
nostication that the "modern age 
may end in the deadUest, most sterile 
passivity history has ever known." 

36. Aesthetics and Technology in Build- 
ing. Pier Luigi Nervi. (Harvard Univer- 
sity Press, Cambridge, Mass., 1965). 
"Nervi's thesis is that good architec- 
ture is a synthesis of technology and 
art," according to an expert review 
by Carl W. Condit, in Technology and 
Culture 7, No. 3, 432 (Summer, 
1966), which we also recommend. 

37. "Notes on the Future of an Esthetic," 
Carter Ratcliff. Art International 16, 
No. 10, 81 (December, 1972). Feels 
that attempts to "esthetize" bits of 
the world by calling on science and 
technology (as do Gyorgy Kepes and 
other workers in advanced visual de- 
sign) produce results "in pathetic dis- 
proportion to the grandiose fore- 
casts." This occasionally rude attack 
on such enthusiasts as Douglas Davis 
(11) reUes on the thesis that their 
work projects only dream worlds, 
that artists using computers are not 
reaUy doing anything new, and that 
lack of taste makes their creations 
acceptable mostly "to the freaky side 
of the new humanism." Biased, but 
provocative. 

38. "Art and Life," Sir Herbert Read. 
Saturday Evening Post 232, 34 (26 
Sept. 1 959). Modern violence and rest- 
lessness stem in great part from a 
neurosis in humans who have stopped 
making things by hand. Production, 
not grace or beauty, is the guiding 
force of technological civilization. 
Recommends the activity of art to re- 



244 



A Reference Bibliography 



lease creative, rather than destructive, 
forces. 

39. Cybernetic Serendipity: The Com- 
puter and the Arts. Jasia Reichardt, 
ed. (Praeger, N. Y., 1969). A special 
issue of Studio International in book 
form showing how the computer can 
extend creativity; the title is that of 
an exhibition at the Institute of 
Contemporary Arts, London, 1968. 
The volume serves as a useful intro- 
duction to the field, containing 100 
illustrated pages of speciaUst essays 
on computer music, dance, poetry, 
painting, graphics, and film. (See also 
Ms. Reichardt's Cybernetics, Art and 
Ideas, 1972). 

40. "Analysis of Musical Instrument 
Tones," J-C Risset and M. V. 
Mathews. Physics Today 22, No. 2, 
23 (February, 1969). Thesis: "With 
computers we can not only analyze 
the sound of a musical instrument 
but also build up a synthesized copy 
of the sound. Comparison of real and 
synthetic tones tells which are the 
important parameters that lead to re- 
cognition of timbre." 

41. "Art and Science: Analysis and Com- 
munication of Biological Form," 
Philip C. Ritterbush. Science 162, 
1307 (Dec. 13, 1968). In an ex- 
position of the influence of biological 
concepts of form on modern artists, 
the author notes that 'Taul Klee's care- 
ful studies of the architectural prin- 
ciples underlying plant form and his 
interest in analogies between music 
and rhythms of growth played a 
very large role in his artistic develop- 
ment and are reflected in much of his 
work." 

42. "Is Technology Taking Over?" 
Charles E. Silberman. Fortune 73, 
No. 2. 112 (February, 1966). A brisk 
discussion of familiar topics: art as 
defense; technology as an end; de- 
humanization and destruction; mass 
idleness; meaninglessness. Technology 
may not determine our destiny, but it 
surely affects it and, in enlarging 



choice, creates new dangers. As the 
author points out, however, borrow- 
ing from Whitehead, the great ages 
have been the dangerous and dis- 
turbed ones. 

43. "Science as Art." Beatrice Stegman. 
Bulletin of the Atomic Scientists 25, 
No. 4, 27 (April, 1969). Philosophical 
discussion of the aesthetics of 
science, particularly the resemblances 
between acts of creativity in science 
and in art. Suggests analysis of a 
scientific theory be done as one 
would analyze a poem, via elements, 
form, central image, since "the ele- 
ments of a scientific theory are 
human constructions rather than 
physical things." 

44. "A Future Literacy," George Steiner. 
Atlantic 228, No. 2, 41 (Aug. 1971). 
Treats other Uteracies - music, math- 
ematics, biomedical engineering, elec- 
tronics — boosts science, criticizes 
humanists for looking to the past, 
and flatly states that indifference to 
current technological phenomena is 
"to opt out of reason." Steiner finds 
science rich in metaphor, myth, and 
laughter, citing the "deep elegance" 
and "quickness and merriment of the 
spirit" in the Banach-Tarski theorem 
of the sun and a pea, and the Penrose 
theory in cosmology. Points to Musil, 
Nabokov, Valery, Borges and others 
whose writing owes much to science 
training. Challenging and fresh. 

45. Victorians and the Machine: The 
Literary Response to Technology. 
Herbert L. Sussman. (Harvard Uni- 
versity Press, Cambridge, Mass., 
1968). Does for English writers of the 
19th century what Leo Marx (30) did 
for the Americans, with substantially 
similar conclusions. Writers stressed 
are Carlyle, Butler, Dickens, Wells, 
Ruskin, KipUng, and Morris, whose 
thought and art centered on the 
effects of mechanization on the in- 
tellectual and aesthetic life of their 
day. A major study of the machine as 
image, symbol, servant, and god - 



245 



something feared and respected, ugly 
and beautiful, functional and de- 
structive — as seen by the significant 
Victorian Uterary figures, this work 
also helps explain the thrust of much 
contemporary writing, 

46. "The Poet as Anti-SpeciaUst," May 
Swenson. Saturday Review 48, No. 5 
16 (40 Jan. 1965). A poet tells how 
her art can show us how to stay 
human in a technologized age, 
compares and contrasts the languages 
of science and poetry, wonders about 
the denerving and desensualizing of 
astronauts "trained to become a 
piece of equipment." 

^1. Literature and Technology. Wylie 
Sypher. (Random House, Inc., N.Y., 
1968). The best, almost the only, 
general study of its kind, to be re- 
quired reading along with Leo Marx 
[30] and Herbert Sussman [45]. De- 
velops the thesis that technology 
dreads waste and, being concerned 
with economy and precaution, lives 
by an ethic of thrift. The humanities, 
including art, exist on the notion that 
every full life includes waste - of 
virtue, intention, thinking, and work. 
The thesis is illustrated by examples 
from literature and art. Although, 
historically, technology minimizes 
individual participation and resultant 
pleasure, Sypher concedes that lately 
"technology has been touched by the 
joy of finding in its solutions the play 
of intellect that satisfies our need to 
invent." 

48. "The Poet in the Machine Age," Peter 
Viereck. /. History Ideas 10, No. 1, 88 
(Jan., 1949). A classification of anti- 
machine poets, who for esthetic, 
pious, instinctual, or timid reasons 
have backed away, and promachine 
poets, who, as materialists, cultists, or 
adapters, have used the new gadgets 
to advantage. We must try to unite 
the world of machinery and the 
world of the spirit, or "our road to 
hell will be paved with good inven- 
tions." 



49. Behind Appearance. C. H. Wadding- 
ton. (MIT Press, Cambridge, 1970). 
This "study of relations between 
painting and the natural sciences in 
this century" is large, lavishly illus- 
trated, and expensive. Its author, pro- 
fessor of animal genetics in the Uni- 
versity of Edinburgh and author of 
The Scientific Attitude, traces the in- 
fluence of modern scientific concepts 
of space, time, and uncertainty on 
the philosophy of modern art, partic- 
ularly in such movements as Cubism, 
constructivism, Dada, and Surrealism, 
and the specific bearing of mathema- 
tics on the content and form of art 
works by Naum Gabo, Mondrian, and 
Max Bill, Though all will not agree 
with aU of his conclusions (e.g., that 
connections between painting and 
science are stronger than between 
painting and literature), Waddington 
has put together a fascinating and 
stimulating presentation for student 
and teacher alike, 

50, Reflections on Big Science. Alvin 
Weinberg. (The MIT Press, Cam- 
bridge, Mass., 1967). The former 
director of Oak Ridge National 
Laboratory devotes his first chapter, 
"The Promise of Scientific Tech- 
nology; The New Revolutions," to 
nuclear energy, cheap electricity, 
technology of information, the 
Bomb, and dealing with nuclear 
garbage. He calls upon the humanists 
to restore meaning and purpose to 
our lives. 

51. Flesh of Steel: Literature and the 
Machine in American Culture. 
Thomas Reed West. (Vanderbilt Uni- 
versity Press, Nashville, Tenn., 1967). 
A consideration of the writings of 
Sherwood Anderson, Dos Passos, 
Sandburg, Sinclair Lewis, Mumford, 
and Veblen. While conceding that 
most of them are antimachine most 
of the time. West preaches the posi- 
tive virtues of the Machine: law, 
order, energy, discipline, which, at a 
price, produce a city like New York, 



246 



A Reference Bibliography 



where artists and writers may live and 
work on their own terms. 

52. "A Computer Art for the Video 
Picture WaU," John H. Whitney. Art 
International 15, No. 7, 35 (Septem- 
ber, 1971). Praises the power of the 
computer to bring visual enlighten- 
ment to much "that was formerly 
abstruse mathematical data." 
Welcomes the challenge that the com- 
puter "can become the universal 
musical instrument" if we acquire a 
knowledge of psychoacoustics. Draws 
analogies between the effects of 
wonder caused by periodic aspects of 
the world of mathematics and those 
aroused by music. Describes using the 
computer as a kind of piano "to 
generate periodic visual action, with a 
mind to reveal harmonic, juxtaposed 
against enharmonic, phenomena." 
The article is enhanced by color 
illustrations of the art of this well- 
known maker of experimental films. 

III. Postscript 

■ Since most of the foregoing 
material is critical or expository, except 
for quoted illustration, readers may wish 
to make a start with firsthand creative 
literary pieces. Here are some suggestions 
available in various paperback editions or 
standard anthologies. 

Plays 

On the theme of machine replacing 
man, there are two early modern classics 
for background: 

53. R. U.K. KarelCapek. 

54. The Adding Machine. Elmer Rice. 

Three British plays deal directly with 
the Bomb, and the fourth, the only one 
available in paper, alludes to it: 

55. The Tiger and the Horse. Robert 
Bolt, In Three Plays (Mercury 
Books, London, 1963). 

56. The Offshore Island. Marghanita 
Laski. (Cresset Press, London, 1959). 

57. Each His Own Wilderness. Doris 



Lessing. In New English Dramatists, 
E. Martin Browne, Ed. (Penguin 
Plays, London). 

58. Look Back in Anger. John Osborne. 

Two recent plays deaUng with physi- 
cists: 

59. The Physicists. Friedrich Durrenmatt. 

60. In the Matter of J. Robert Oppenhei- 
mer. Heinar Kipphardt. 

Fiction 

A quartet of Utopian or anti-Utopian 
novels: 

61. Brave New World. Aldous Huxley. 

62. Nineteen Eighty-Four, George Orwell. 

63. Walden //. B. F. Skinner. 

64. We. E. Zamiatan. 

A quartet of science fiction: 

65. Fahrenheit 451. Ray Bradbury. 

66. Canticle for Leibowitz. Walter Miller, 
Jr. 

67. Player Piano. Kurt Vonnegut, Jr. 

68. Cat's Cradle. Kurt Vonnegut, Jr. 

A trio of short stories: 

69. "By the Waters of Babylon," Stephen 
V. Benet. 

70. "The Portable Phonograph," Walter 
Van Tilburg Clark. 

7L "The Machine Stops," E. M. Forster. 

Poetry 

See Ginestier above. Also: 

72. The Modern Poets. John M. Brinnin 
and Bill Read, Eds. (McGraw-HiU 
Book Co., New York, 1963). Con- 
tains poems by Hoffman, Lowell, 
Moss, and Nemerov pertaining to the 
Bomb. 

73. Inside Outer Space: Poems. Robert 
vas Dias, Ed. (Doubleday Anchor, 
1970). 

74. Weep Before God. John Wain. (The 
Macmillan Company, London, 1961). 
Sections VI-VII consider the 
Machine. 



247 



Authors 



Jacob Bronowski, creator of and performer in 
the television series "The Ascent of Man", 
received his PhD fronn Cannbridge University in 
1933. At his death he was a Fellow of the Salk 
Institute of Biological Studies in California. 
Previously he had served as Director of General 
Process Development for the National Coal Board 
of England, as the Science Deputy to the British 
Chiefs of Staff, and as head of the Projects 
Division of UNESCO. He wrote extensively on the 
nature of science and its social consequences. 

William H. Davenport, born in Connecticut 
in 1908, has been professor of English at various 
colleges, most recently at the Harvey Mudd 
College in Claremont, California. He studied 
at Dartmouth College, Tufts University, and 
Yale. His concerns for the role of science in 
society are illustrated by his co-authorship in 
1967 of the book "Engineering: Its Role 
in Society". 

Engineering Concepts Curriculum Projects 

developed a course, "The Man-Made World" , 
for study in schools and colleges. The staff 
included numerous well known scientists and 
engineers concerned about the role of engineering 
and technology in the world. 

John M. Fowler was born in Alabama in 1926 
and studied at Earlham College, the University 
of Oklahoma, and the Johns Hopkins University. 
His scientific studies are in nuclear physics. 
In addition, his pedagogical interests have led 
him to be prominent in the instructional pro- 
grams sponsored by the American Association of 
Physics Teachers. He is professor of physics 
at the University of Maryland. 

Werner Heisenberg received the Nobel Prize 
for his pioneering contributions to the develop- 
ment of quantum mechanics. He was born in 
Wurzburg, Germany in 1901 and studied at the 
University of Munich and Gottingen. After a 
professorship at the University of Leipzig, he 
was Director of the Kaiser Wilhelm I nstitute for 
Physics in Berlin, then Director of the Max 
Planck Institute for Physics in Gottingen, and 
later of the Max Planck Institute in Munich. 

Donald F. Holcomb and Philip Morrison are 

professors of physics; Holcomb at Cornell Uni- 
versity and Morrison at the Massachusetts 
Institute of Technology. Holcomb's studies have 
dealt with solid state physics. Morrison is con- 
cerned with the application of physics to 
astronomy and also with the interrelation of 
science and society. 



Dorothy Michelson Livingston, the daughter of 
Albert Michelson, America's first Nobel Prize 
winner, has written a documentary — a biography 
of her father and his many scientific studies. 
The book, entitled The Master of Light is 
the source from which the essay reproduced in 
this Reader was drawn. 

The Physics Survey Committee of the National 
Research Council and the National Academy 

of Science functioned under the leadership of 
the physicist, D. Bromley of Yale University. 
The report reappraises the nature of physics 
and its role in society and in education. 

Vincent J. Schaefer is the discoverer and 
developer of methods of seeding clouds to pro- 
duce rain. Born in Schenectady, New York in 1908, 
Schaefer graduated from Union College and later 
from the Davey College of Tree Surgeons. At the 
General Electric Laboratories he began as an 
assistant to Irving Langmuir. 

Dietrich Schroeer is a physicist at the 
University of North Carolina, Chapel Hill. He 
was born in Berlin in 1938 and studied at Ohio 
State University. His range of interests is 
illustrated by his award of a Humanities fellow- 
ship in 1972-73. 

Walter Sullivan, science writer for the 
New York Times, was born in New York City in 
1918. After graduating from Yale University, 
he joined the staff of the Times and served as 
correspondent in the Far East, in Germany, and 
at the United Nations. For his journalistic 
writing about science he has received numerous 
prizes and awards. 

Masao Watanabe is professor of the history 
of science at the University of Tokyo, Japan. 
He is known for his studies in the history of 
science, and also for his involvement in 
social and educational work. 

Steven Weinberg, born in 1933, is Higgins 
Professor of Physics at Harvard University and 
Senior Scientist at the Smithsonian Astrophysical 
Observatory. He studied at Cornell University, 
the Copenhagen Institute of Theoretical Physics, 
and Princeton University. He has been professor 
of physics at the University of California and 
the Massachusetts Institute of Technology. His 
researches deal with elementary particles and 
cosmology. Also he has served as consultant to 
the U.S. Arms Control and Disarmament Agency. 



248