EINSTEIN
                      THE SEARCHER

               HIS WORK EXPLAINED FROM
               DIALOGUES WITH EINSTEIN




                           BY

                  ALEXANDER MOSZKOWSKI




                     TRANSLATED BY

                    HENRY L. BROSE




                  METHUEN & CO. LTD.
                 36 ESSEX STREET W.C.
                        LONDON




EXTRACT FROM THE AUTHOR'S
PREFACE


THE book which is herewith presented to the public has few
contemporaries of a like nature; it deserves special attention inasmuch
as it is illuminated by the name _Albert Einstein_, and deals with a
personality whose achievements mark a turning-point in the development
of science.

Every investigator, who enlarges our vision by some permanent discovery,
becomes a milestone on the road to knowledge, and great would be the
array of those who have defined the stages of the long avenue of
research. One might endeavour, then, to decide to whom mankind owes the
greater debt, to Euclid or to Archimedes, to Plato or to Aristotle, to
Descartes or to Pascal, to Lagrange or to Gauss, to Kepler or to
Copernicus. One would have to investigate--as far as this is
possible--in how far each outstanding personality was in advance of his
time, whether some contemporary might not have had the equal good
fortune to stumble on the same discovery, and whether, indeed, the time
had not come when it must inevitably have been revealed. If we then
further selected only those who saw far beyond their own age into the
inimitable future of knowledge, this great number of celebrities would
be considerably diminished. We should glance away from the milestones,
and fix our gaze on the larger signs that denote the lines of
demarcation of the sciences, and among them we should find the name of
Albert Einstein. We may find it necessary to proceed to a still more
rigorous classification; Science, herself, may rearrange her
chronological table later, and reckon the time at which Einstein's
doctrine first appeared as the beginning of an important era.

This would in itself justify--nay, render imperative--the writing of
a book _about_ Einstein. But this need has already been satisfied on
several occasions, and there is even now a considerable amount of
literature about him. At the end of this generation we shall possess a
voluminous library composed entirely of books about Einstein. The
present book will differ from most of these, in that Einstein here
occurs not only objectively but also subjectively. We shall, of course,
speak of him here too, but we shall also hear him speak himself, and
there can be no doubt that all who are devoted to the world thought can
but gain by listening to him.

The title agrees with the circumstance to which this book owes its
birth. And in undertaking to address itself to the circle of readers as
to an audience, it promises much eloquence that came from Einstein's own
lips, during hours of social intercourse, far removed from academic
purposes and not based on any definite scheme intended for instruction.
It will, therefore, be neither a course of lectures nor anything similar
aiming at a systematic order and development. Nor is it a mere
phonographic record, for this is made impossible if for no other reason
than that whoever has the good fortune to converse with this man, finds
every minute far too precious to waste it in snatching moments to take
shorthand notes. What he has heard and discussed crystallizes itself in
subsequent notes, and to some extent he relies on his memory, which
would have to be extraordinarily lax if it managed to forget the
essentials of such conversations.

But these essentials could not be attained by clinging closely to the
exact terms of utterance. This would be a gain neither for the scheme of
the book nor for the reader who wishes to follow a great thinker in all
the ramifications of his ideas. It must be reiterated that this book is
intended neither as a textbook nor as a guide leading to a complete
system of thought; nor, above all, is it in any way due to Einstein, nor
desired by him. Any value and attraction of the book is rather to be
sought in its kaleidoscopic nature, its loose connexion, which expresses
a general meaning without being narrowed to pedantic limits by a
restriction to literal repetition. It is just this absence of the method
that is rightly demanded of a textbook, which may enable these
conversations to pass on to the world a little of the pleasure which
they originally gave me. Perhaps they will even be sufficient to furnish
the reader with a picture of the eminent scientist, sufficient to give
him a glimpse of his personality, without demanding a detailed study to
secure this end. Even here I should like to state that the range of
Einstein's genius extends much further than is generally surmised by
those who have busied themselves only with the actual physical theory.
It sends out rays in all directions, and brings into view wonderful
cosmic features under his stimulus--features which are, of course,
embedded in the very refractory mathematical shell of his physics which
embraces the whole world. But only minds of the distant future, perhaps,
will be in a position to realize that _all_ our mental knowledge is
illuminated by the light of his doctrine.

Einstein's mission is that of a king who is pursuing building operations
on a large scale; carters and workmen, each in their own line, receive
employment for decades ahead. But apart from the technical work, there
may still be room for non-technical account, which, without following a
definite programme, yet pursues a definite object, to offer Einsteiniana
in an easily intelligible and ever-changing form, to represent him, as
it were, wandering over fields and meadows, and every now and then
stooping to pluck some problem in the guise of a flower. Seeing that he
granted me the pleasure of accompanying him on these excursions, it was
not within my sphere to expect in addition that he would direct his
steps according to a preconceived plan. Often enough the goal vanished,
and there remained nothing but the pleasure of the rambles themselves
with the consciousness of their purpose. As Schopenhauer remarks, one
who walks for leisure can never be said to be making detours; and this
holds true independently of the nature of the country that happens to be
traversed at the moment. If I just now mentioned walks on meadowy
slopes, this is not to be understood literally. In Einstein's company
one encounters from moment to moment quite suddenly some adventure which
destroys our comparison with idyllic rambles. Abysmal depths appear, and
one has to pass along dangerous pathways. It is at these moments that
unexpected views present themselves, and many strips of landscape that,
according to our previous estimate, appeared to be situated on higher
slopes, are now discovered reposing far below. We are familiar with the
"Wanderer Fantasie" of Schubert; its tonal disposition is realistic,
conforming to Nature, yet its general expression is transcendental: so
is a ramble with Einstein; he remains firmly implanted in reality, but
the distant views that he points out stretch into transcendental
regions. He seems to me to be essentially as much an artist as a
discoverer, and if some sense of this heaven-sent combination of gifts
should be inspired by this book, it alone would justify the publication
of these talks.




TRANSLATOR'S NOTE


IT is scarcely necessary to enlarge on the scope and design of the
present book, which manifest themselves at a glance.

The author merits our thanks for making accessible to us material about
Einstein which, in the ordinary course of events, would ever remain
unknown. An account of Einstein's work would be incomplete without a
sketch of his personality. Mr. Moszkowski invites us to ramble with
Einstein into realms not confined to pure physics. Many subjects that
have a peculiar interest at the present critical stage of the world's
history receive illuminating attention. It is hoped that the appearance
of the book in English will stimulate further interest in the
thought-world of a great scientist.

Warm thanks are due to Mr. Raymond Kershaw, B.A., and to my sister, Miss
Hilda Brose, for help in reading the manuscript and the proofs.

                             HENRY L. BROSE

OXFORD, 1921




CONTENTS

CHAPTER

I. Phenomena in the Heavens

II. Beyond our Power

III. Valhalla

IV. Education

V. The Discoverer

VI. Of Different Worlds

VII. Problems

VIII. Highways and By-ways

IX. An Experimental Analogy

X. Disconnected Suggestions

XI. Einstein's Life and Personality

INDEX




EINSTEIN THE SEARCHER




CHAPTER I

PHENOMENA IN THE HEAVENS


Proclamation of the New Mechanics.--Verification of Theoretical
Results.--Parallels with Leverrier.--Neptune and Mercury.--Testing the
Theory of Relativity.--The Solar Eclipse of 1919.--The Programme of an
Expedition.--The Curved Ray of Light.--Refinement of Calculation and
Measurement.--Stellar Photography.--The Principle of Equivalence.--The
Sun Myth.


ON the 13th October 1910 a memorable event took place in the Berlin
Scientific Association: Henri Poincaré, the eminent physicist and
mathematician, had been announced to give a lecture in the rooms of the
institute "Urania"; an audience of rather meagre dimensions assembled. I
still see him before me in my mind's eye, a scholar who was snatched
away in the prime of his creative period, a man whose external
appearance did not suggest the light of genius, and whose carefully
trimmed beard reminded one rather of the type of a practising barrister.
He walked up and down the platform, accompanying his speech with
gestures marked by an easy elegance. There was no sign of an attempt to
force a doctrine. He developed his thesis, in spite of the foreign
language, in fluent and readily intelligible terms.

It was at this lecture that we heard the name Albert Einstein pronounced
for the first time.

Poincaré's address was on the New Mechanics, and was intended to make
us acquainted with the beginning of a tendency which, he himself
confessed, had violently disturbed the equilibrium of his former
fundamental views. He repeatedly broke the usually even flow of his
voice to indicate, with an emphatic gesture, that we had perhaps arrived
at a critical, nay epochal, point marking the commencement of a new era
of thought.

"Perhaps" was a word he never failed to emphasize. He persistently laid
stress on his doubts, differentiated between hardened facts and
hypotheses, still clinging to the hope that the new doctrine he was
expounding would yet admit of an avenue leading back to the older views.
This revolution, so he said, seemed to threaten things in science which
a short while ago were looked upon as absolutely certain, namely,
fundamental theorems of classical mechanics, for which we are indebted
to the genius of Newton. For the present this revolution is of course
only a threatening spectre, for it is quite possible that, sooner or
later, the old established dynamical principles of Newton will emerge
victoriously. Later in the course of his lecture he declared repeatedly
that he felt a diffidence akin to fear at the sight of the accumulating
number of hypotheses, and that it seemed to border on the impossible to
attempt to arrange them into a system.

It is a matter of complete indifference how the revelations of Poincaré
affected us individually; if I may infer from my own case, there is only
one word to express it--staggering! Oblivious of the doubts of the
lecturer, I was swept along under the impetus of this new and mighty
current of thought. This awakened two wishes in me: to become acquainted
with Einstein's researches as far as lay within my power, and, if
possible, to see him once in person. In me the abstract had become
inseparable from the concrete personal element. The presentiment of the
happy moment in the future hovered before my vision, whispering that I
should hear his doctrine from his own lips.

Several years later Einstein was appointed professor of the Academy of
Sciences with the right of lecturing at the University of Berlin. This
brought my personal wish within reach. Trusting to good fortune, I set
about materializing it. In conjunction with a colleague I wrote him a
letter asking him to honour with his presence one of the informal
evenings instituted by our Literary Society at the Hôtel Bristol. Here
he was my neighbour at table, and chatted with me for some hours.
Nowadays his appearance is known to every one through the innumerable
photos which have appeared in the papers. At that time I had never seen
his countenance before, and I became absorbed in studying his features,
which struck me as being those of a kindly, artistically inclined,
being, in nowise suggesting a professor. He seemed vivacious and
unrestrained in conversation, and, in response to our request, willingly
touched upon his own subject as far as the place and occasion allowed,
exemplifying Horace's saying, "Omne tulit punctum, qui miscuit utile
dulci, tironem delectando pariterque monendo." It was certainly most
delightful. Yet at moments I was reminded of a male sphinx, suggested by
his highly expressive enigmatic forehead. Even now, after a warm
acquaintanceship stretching over years, I cannot shake off this
impression. It often overcomes me in the midst of a pleasant
conversation interspersed with jests whilst enjoying a cigar after tea;
I suddenly feel the mysterious sway of a subtle intellect which
captivates and yet baffles the mind.

At that time, early in 1916, only a few members of the Literary Society
divined who it was that was enjoying their hospitality. In the eyes of
Berlin, Einstein's star was beginning its upward course, but was still
too near the horizon to be visible generally. My own vision, sharpened
by the French lecture and by a friend who was a physicist, anticipated
events, and already saw Einstein's star at its zenith, although I was
not even aware at that time that Poincaré had in the meantime overcome
his doubts and had fully recognized the lasting importance of Einstein's
researches. I had the instinctive feeling that I was sitting next to a
Galilei. The fanfares sounded in the following years as a sign of
appreciation by his contemporaries were only a fuller instrumentation of
the music of destiny which had vibrated in my ears ever since that time.

I recollect one little incident: one of these lovers of literature, who
was, however, totally ignorant of natural science, had accidentally seen
several learned articles dealing with Einstein's Reports for the
Academy, and had preserved the cuttings in his pocket-book. He
considered this a fitting opportunity for enlightenment. Surely a brief
question would suffice to guide one through these intricate channels.
"Professor, will you kindly tell me the meaning of potential, invariant,
contravariant, energy-tensor, scalar, relativity-postulate,
hyper-Euclidean, and inertial system? Can you explain them to me in a
few words?"--"Certainly," said Einstein, "those are merely technical
expressions!" That was the end of the little lesson.

Far into the night three of us sat in a café while Einstein gently
lifted the veil from his newest discovery for the benefit of my
journalist friend and myself. We gathered from his remarks that a
Special Theory of Relativity formed a prelude to a general theory which
embraced the problem of gravitation in its widest sense, and hence also
the physical constitution of the world. What interested me apart from
this theme, which was, of course, only touched upon lightly, was the
personal question in its psychological aspect.

"Professor," said I, "such investigations must involve enormous mental
excitement. I imagine that there lurks behind every solved problem ever
and again some new problem with a threatening or a fascinating aspect,
as the case may be, each one calling up a tumult of emotion in its
author. How do you succeed in mastering this difficulty? Are you not
continually tormented by restless thoughts that noisily invade your
dreams? Do you ever succeed at all in enjoying undisturbed slumber?"

The very tone in which the answer was given showed clearly how free he
felt himself of such nervous troubles which usually oppress even the
mediocre thinker. It is fortunate that such affections do not penetrate
to his high level. "I break off whenever I wish," he said, "and banish
all difficulties when the hour for sleep arrives. Thinking during
dreams, as in the case of artists, such as poets and composers, by which
they weave the thread of day on into the night, is quite foreign to me.
Nevertheless, I must confess that at the very beginning, when the
special theory of relativity began to germinate in me, I was visited by
all sorts of nervous conflicts. When young I used to go away for weeks
in a state of confusion, as one who at that time had yet to overcome the
stage of stupefaction in his first encounter with such questions. Things
have changed since then, and I can assure you that there is no need to
worry about my rest."

"Notwithstanding," I answered, "cases may arise in which a certain
result is to be verified by observation and experiment. This might
easily give rise to nerve-racking experiences. If, for instance, a
theory leads to a calculation which does not agree with reality, the
propounder must surely feel considerably oppressed by this mere
possibility. Let us take a particular event. I have heard that you have
made a new calculation of the path of the planet Mercury on the basis of
your doctrine. This must certainly have been a laborious and involved
piece of work. You were firmly convinced of the theory, perhaps you
alone. It had not yet been verified by an actual fact. In such cases
conditions of great psychological tension must surely assert themselves.
What in Heaven's name will happen if the expected result does not
appear? What if it contradicts the theory? The effect on the founder of
the theory cannot even be imagined!"

"Such questions," said Einstein, "did not lie in my path. That result
could not be otherwise than right. I was only concerned in putting the
result into a lucid form. I did not for one second doubt that it would
agree with observation. There was no sense in getting excited about what
was self-evident."

Let us now consider several facts of natural science, apart from this
chat, but suggested by it, which caused Einstein little excitement, but
the whole world generally, so much the more. By way of illustration we
shall link them up with the result of a forerunner who, like Einstein,
fixed on paper what should happen in the heavens.

Formerly, whenever one wished to play a particularly effective trump
card in favour of research work it was customary to quote the
achievement of the French astronomer Leverrier who, pen in hand,
established the material existence of a planet at that time quite
unknown and unnoticed. Certain disturbances in the orbit of the planet
Uranus, which was regarded as being the most distant of the wandering
stars, at that time had caused him to believe in the certainty of the
existence of a still more distant planet, and by using merely the
theoretical methods of celestial mechanics in connexion with the problem
of three bodies he succeeded in revealing what was hidden behind the
visible constellations. He reported the result of his calculations to
the Berlin Observatory about seventy-five years ago, as it was at that
time in possession of the best instruments. It was then that the amazing
event happened: on the very same evening an observer in Berlin,
Gottfried Galle, discovered the predicted new star almost exactly at the
point of the heavens for which it was prophesied, only half the moon's
diameter from it. The new planet Neptune, the farthest outpost of our
solar system, reposed as a prisoner in his telescope; the seemingly
undiscoverable star had capitulated in the face of mental efforts of a
mathematical scholar, who, in reasoning meditation, had sketched his
curves in the quiet atmosphere of his study.

This was certainly bewildering enough, but nevertheless this incredible
result which stirred the imagination so strongly was directly rooted in
reality, lay on the path of research, followed of necessity from the
laws of motion known at that time, and disclosed itself as a new proof
of the doctrines of astronomy which had long been recognized as supreme
and incontestable. Leverrier had not created these, but had found them
ready; he applied them with the mind of genius. Anyone who nowadays is
sufficiently trained to work through the highly complicated calculation
of Leverrier has every reason to marvel at a work which is entirely
mathematical throughout.

Our own times have been marked by an event of still greater
significance.

Irregularities had shown themselves in observation of the heavens that
could not be explained or grasped by the accepted methods of classical
mechanics. To interpret them, ideas of a revolutionary nature were
necessary. Man's view of the plan according to which the universe is
mapped out had to be radically reformed to bring within comprehension
the problems that presented themselves in macroscopic as well as in
microscopic regions, in the courses of the stars as well as in the
motions of the ultimate constituents of the atom of material bodies,
incapable of being directly observed. The goal consisted in bringing
those doctrines in which truth had been proclaimed in its essential
features, but not exhaustively, by the genius of Copernicus, Galilei,
Kepler, and Newton, to their conclusion by penetrating as far as
possible into the mysteries of the structure of the universe. This is
where Einstein comes forward.

Whereas the outermost planet Neptune had bowed to the accepted laws, by
merely disclosing his presence, Mercury, the innermost planet, preserved
an obstinate attitude even in the face of the most refined calculations.
These always led to an unaccountable remainder, a disagreement, which
seemed very small when expressed in numbers and words, and yet enclosed
a deep secret. Wherein did this disagreement consist? In a difference of
arc which had likewise been discovered by Leverrier and which defied
explanation. It was only a matter of about forty-five insignificant
quantities, seconds of arc, which seemed vanishingly small since this
deviation did not occur within a month or a year, but was spread over a
whole century. By just so much, or rather so little, the rotation of
Mercury's orbit differed from what might be termed the allowable
astronomical value. Observation was exact, calculation was exact; why,
then, the discrepancy?

It was thus inferred that there was still some hidden unexplored factor
which had to be taken into account in the fundamental principles of
celestial mechanics. The formerly invisible Neptune confirmed the old
rule by appearing. Mercury, which was visible, opposed the rule.

In 1910 Poincaré had touched upon this embarrassing question,
mentioning that here was a possibility of testing the new mechanics.

He declined the suggestion of some astronomers that this was again a
Leverrier problem and that there must exist another undiscovered planet
still nearer the sun and disturbing Mercury's orbit. He also refused to
accept the assumption that the disturbance might be caused by a ring of
cosmic matter distributed round the sun. Poincaré divined that the new
mechanics could supply the key to the enigma, but, obviously to be quite
conscientious, he expressed his presentiment in very cautious terms. On
that occasion he said that some special cause had yet to be found to
explain the anomaly of Mercury's behaviour; till that was discovered one
could only say that the new doctrine could not be regarded as in
contradiction to astronomical facts. But the true explanation was
gradually drawing near. Five years later, on 18th November 1915, Albert
Einstein presented to the Prussian Academy of Sciences a paper which
solved this riddle which, expressed in seconds, seemed so insignificant
and yet was of such enormous importance in its bearing on fundamental
questions. He proved the problem was solved quite accurately if the
general Theory of Relativity he had founded was accepted as the only
valid basis for the phenomena of cosmic motions.

Many would at this point express a wish to have the essence of the
doctrine of relativity explained in an easily intelligible manner.
Indeed, some would go even further in their desire, and would ask for a
simple description in a few succinct sentences. This, measured in terms
of difficulty and possibility, would be about equivalent to wishing to
learn the history of the world by reading several quarto pages of
manuscript or a novelette. But even if we start at long range and use
elaborate materials for our description, we should have to give up the
idea that this knowledge may be gained with playful ease. For this
doctrine, inasmuch as it discloses the relationship between mathematical
and physical events, emerges out of mathematics, which thus limits the
mode of its representation. Whoever undertakes to present it in a form
in which it is easily intelligible, that is quite unmathematical and yet
complete, is engaged in an impossible venture; he is like one who would
whistle Kepler's Laws on the flute or would elucidate Kant's Critique of
Pure Reason by means of coloured illustrations. In all frankness we must
confess once and for all that whenever popular accounts are attempted
they can be only in the nature of vague suggestions removed from the
domain of mathematics. But even such indications have a fruitful result
if they succeed in focusing the attention of the reader or the hearer so
that the connexions, the Leitmotivs, so to speak, of the doctrine, are
at least suggested.

It must therefore suffice if we place the conception of approximation in
the foreground here as in other parts of this book. Till quite recently
Newton's Equations of Motion were used as a foundation for verifying
astronomical occurrences. These are symbolical representations expressed
as formulæ that contain in an exceedingly simple form the law of mass
attraction. They express the comprehensive principle that the attraction
is directly proportional to the mass and inversely proportional to the
square of the distance; so that the moving force is doubled when the
mass is doubled, whereas if the distance is double, the force is only a
quarter as great, if the distance is trebled, the force becomes
one-ninth as great.

According to the Theory of Relativity this fundamental law is not wrong
or invalid, but no longer holds fully if pursued to its last inferences.
In applying corrections to it, new factors occur, such as the ratio of
given velocities to the velocity of light, and the new geometry which
operates with "world-lines" in space which, amalgamated with the
dimension of time, is regarded as a quadruply extended continuum.
Einstein has actually supplemented these fundamental equations for the
motion of masses so that the original form states the true condition of
affairs only approximately, whereas Einstein's equations give the motion
with very great accuracy.

The above-mentioned essay of Einstein is carried out as if the structure
bequeathed to us by Newton required the addition of a final, very
delicate pinnacle. For the mathematician this pinnacle is given as a
combination of signs, representing a so-called "Elliptic Interval." Such
an interval is a very weird construction, and the man who will make it
apprehended by the general reader is yet to be born. When Lord Byron
said:


   "And Coleridge, too, has lately taken wing.
    But like a hawk encumbered with his hood,--
    Explaining Metaphysics to the nation--
   _I wish he would explain his Explanation_."

                             (_Dedication to "Don Juan._")


he had still a sure footing in intelligibility, compared with the
non-mathematician, who demands an explanation for such a construction.
And what a complex of mathematical dangers must be overcome even before
the question of the meaning of this integral is crystallized out!

But now the explanation had arrived and could be evaluated, if only
approximately. Before we give the result, let us just describe at least
one technical term, namely, "Perihelion." It is that point of a
planetary orbit which lies nearest the sun. This orbit is an ellipse,
that is, an elongated curved fine in the interior of which one
distinguishes a major axis in the direction of elongation, and a minor
axis perpendicular to the former at its middle point. The perihelion of
a planetary orbit is at one of the end points of the major axis.

In time the perihelion alters its position in space, advancing in the
same sense as the orbit is traversed. It would naturally be assumed that
the amount of this advance as measured astronomically would agree with
the calculation resulting from Newton's theory. But this was not the
case. An unaccountable remainder was left over, which astronomers
ascertained to be 45 seconds (of arc) per 100 years, with a possible
fluctuation of plus or minus 5 seconds. Thus, if the new result were
found to be between 40 and 50 seconds, the new theory would henceforth
have to be regarded as the only valid one.

It happened just as Einstein predicted: calculation according to his
theory shows that for the planet Mercury the perihelion should advance
43 seconds per 100 years. This signifies full agreement with observation
and fully removes the former apparent difficulty. Whereas Leverrier in
his time had pointed out a new planet, Einstein brought to view
something far more important: a new truth.

It was a test of accuracy so dazzling that it alone would have sufficed
to prove the correctness of Einstein's Principles. Yet, a second test,
fraught with graver and more far-reaching consequences, presented
itself--a test which could be applied only several years later, and
which developed into a scientific event of the highest importance.

For at the same time that Einstein solved the problem of Mercury, he had
investigated the path of light-rays according to his revolutionary
method, and had arrived at the conclusion that every ray under the
influence of a gravitational field, as, for example, in the
neighbourhood of the sun, must become curved. This daring announcement
gave a new possibility of putting the theory to a practical test during
the total eclipse of the sun on 29th May 1919. For, when the disc of the
sun is obscured, the stars that are closest to it become visible (even
to the naked eye). They may be photographed, and the distances of the
points of light on the negative allow us to detect whether the rays from
the stars in passing the massive body of the sun have actually been
deflected by the amount prophesied by Einstein.

Once again current thought encountered a sharp corner, and "common
sense," which furnishes its own certificate of merit, threatened to
become rebellious. How now? A ray from a star could be curved? Does not
this contradict the elementary conception of the straight lines, that
is, the shortest lines, for which we have no better picture than just
these rays? Did not Leonardo da Vinci define the straight line by means
of the term _linea radiosa_.

But such supposedly self-evident facts have no longer a place in the
space-time world. The point was to test whether a physical anomaly which
had been predicted actually existed. If the deflection of the rays
really happened, it should manifest itself in the distances between the
stars on the photographic plate being greater than one would expect from
their actual position.

For the curvature has its concave side towards the sun, as is easy to
see, once the phenomenon is regarded as possible. It is as if the ray
were directly subject to gravitation. Let us take two stars, one on each
side of the sun. On account of the concavities the eye receives rays
from them under a greater visual angle than if the rays were straight,
and interprets this angle as denoting a greater distance between the
sources of light, that is, it sees the two stars farther apart than in
the case of rectilinear propagation.

By how much farther apart? The preceding calculation and the subsequent
direct observation demanded incredible delicacy of measurement. If we
suppose the whole arc of the heavens divided into easily picturable
units such as degrees, then the apparent width of the moon is about half
a degree. We may still easily imagine the thirtieth part of this,
namely, a minute of arc. But the sixtieth part of the latter, the second
of arc, vanishes almost out of the range of sense-perception. And it was
just this minute measure that came into question, for the theory which
had been developed from pure thought predicted a deflection of seconds
of arc. This corresponds to about a hairbreadth when seen at a distance
of 17 yards, or to the thickness of a match at a distance of over half a
mile.

One of the greatest problems of the most comprehensive science depended
on this unthinkably small measure.

In no sense did Einstein himself entertain a possibility of doubt.

On repeated occasions before May 1919 I had opportunities of questioning
him on this point. There was no shadow of a scruple, no ominous fears
clouded his anticipations. Yet great things were at stake.

Observation was to show "the correctness of Einstein's world system" by
a fact clearly intelligible to the whole world, one depending on a very
sensitive test of less than two seconds of arc.

"But, Professor," said I, on various occasions, "what if it turns out to
be more or less? These things are dependent on apparatus that may be
faulty, or on unforeseen imperfections of observation." A smile was
Einstein's only answer, and this smile expressed his unshakeable faith
in the instruments and the observers to whom this duty was to be
entrusted.

Moreover, it is to be remarked that no great lengths of time were
available for comfortable experimentation in taking this photographic
record. For the greatest possible duration of a total eclipse of the sun
viewed at a definite place amounts to less than eight minutes, so that
there was no room for mishaps in this short space of time, nor must any
intervening cloud appear. The kindly co-operation of the heavens was
indispensable--and was not refused. The sun, in this case the darkened
sun, brought this fact to light.

Two English expeditions had been equipped for the special occasion of
the eclipse--one to proceed to Sobral and the other to the Island of
Principe, off Portuguese Africa; they were sent officially with
equipment provided in the main by the time-honoured Royal Society.
Considering the times, it was regarded as the first symptom of the
revival of international science, a praiseworthy undertaking. A huge
apparatus was set into motion for a purely scientific object with not
the slightest relation to any purpose useful in practical life. It was a
highly technical investigation whose real significance could be grasped
by only very few minds. Yet interest was excited in circles reaching far
beyond that of the professional scientist. As the solar eclipse
approached, the consciousness of amateurs became stirred with indefinite
ideas of cosmic phenomena. And just as the navigator gazes at the Polar
Star, so men directed their attention to the constellation of Einstein,
which was not yet depicted in stellar maps, but, from which something
uncomprehended, but undoubtedly very important, was to blaze forth.

In June it was announced that the star photographs had been successful
in most cases, yet for weeks, nay for months, we had to exercise
patience. For the photographs, although they required little time to be
taken, took much longer to develop and, above all, to be measured; in
view of the order of smallness of the distances to be compared, this was
a difficult and troublesome task, for the points of light on the plate
did not answer immediately with Yes or No, but only after mechanical
devices of extreme delicacy had been carefully applied.

At the end of September they proclaimed their message. It was in the
affirmative, and this Yes out of far-distant transcendental regions
called forth a resounding echo in the world of everyday life. Genuinely
and truly the seconds of arc had come out, correct to the decimal point.
These points representing ciphers, as it were, had chanted of the
harmony of the spheres in their Pythagorean tongue. The transmission of
this message seemed to be accompanied by the echoing words of Goethe's
"Ariel":


   "With a crash the Light draws near!
    Pealing rays and trumpet-blazes,--
    Eye is blinded, ear amazes."


Never before had anything like this happened. A wave of amazement swept
over the continents. Thousands of people who had never in their lives
troubled about vibrations of light and gravitation were seized by this
wave and carried on high, immersed in the wish for knowledge although
incapable of grasping it. This much all understood, that from the quiet
study of a scholar an illuminating gospel for exploring the universe had
been irradiated.

During that time no name was quoted so often as that of this man.
Everything sank away in face of this universal theme which had taken
possession of humanity. The converse of educated people circled about
this pole, could not escape from it, continually reverted to the same
theme when pressed aside by necessity or accident. Newspapers entered on
a chase for contributors who could furnish them with short or long,
technical or non-technical, notices about Einstein's theory. In all
nooks and corners social evenings of instruction sprang up, and
wandering universities appeared with errant professors that led people
out the three-dimensional misery of daily life into the more hospitable
Elysian fields of four-dimensionality. Women lost sight of domestic
worries and discussed co-ordinate systems, the principle of
simultaneity, and negatively-charged electrons. All contemporary
questions had gained a fixed centre from which threads could be spun to
each. Relativity had become the sovereign password. In spite of some
grotesque results that followed on this state of affairs it could not
fail to be recognized that we were watching symptoms of mental hunger
not less imperative in its demands than bodily hunger, and it was no
longer to be appeased by the former books by writers on popular science
and by misguided idealists.

And whilst leaders of the people, statesmen, and ministers made vain
efforts to steer in the fog, to arrive at results serviceable to the
nation, the multitude found what was expedient for it, what was
uplifting, what sounded like the distant hammering of reconstruction.
Here was a man who had stretched his hands towards the stars; to forget
earthly pains one had but to immerse oneself in his doctrine. It was the
first time for ages that a chord vibrated through the world invoking all
eyes towards something which, like music or religion, lay outside
political or material interests.

The mere thought that a living Copernicus was moving in our midst
elevated our feelings. Whoever paid him homage had a sensation of
soaring above Space and Time, and this homage was a happy augury in an
epoch so bare of brightness as the present.

     *     *     *     *     *     *     *     *

As already remarked, there was no lack of rare fruits among the
newspaper articles, and a chronicler would doubtless have been able to
make an attractive album of them. I brought Einstein several foreign
papers with large illustrations which must certainly have cost the
authors and publishers much effort and money. Among others there were
full-page beautifully coloured pictures intended to give the reader an
idea of the paths pursued by the rays from the stars during the total
eclipse of the sun. These afforded Einstein much amusement, namely, _e
contrario_, for from the physical point of view these pages contained
utter nonsense. They showed the exact opposite of the actual course of
the rays inasmuch as the author of the diagrams had turned the convex
side of the deflected ray towards the sun. He had not even a vague idea
of the character of the deflection, for his rays proceeded in a straight
line through the universe until they reached the sun, where they
underwent a sudden change of direction reminiscent of a stork's legs.
The din of journalistic homage was not unmixed with scattered voices of
dissent, even of hostility. Einstein combated these not only without
anger but with a certain satisfaction. For indeed the series of unbroken
ovations became discomfiting, and his feelings took up arms against what
seemed to be developing into a star-artist cult. It was like a breath of
fresh air when some column of a chance newspaper was devoted to a
polemic against his theory, no matter how unfounded or unreasoned it may
have been, merely because a dissonant tone broke the unceasing chorus of
praise. On one occasion he even said of a shrill disputant, "The man is
quite right!" And these words were uttered in the most natural manner
possible. One must know him personally if one is to understand these
excesses of toleration. So did Socrates defend his opponents.

In our conversation we returned to the original question, and I asked
whether there was no means of making the deflection of the ray
intelligible to an average person.

Einstein replied: "In a very superficial manner this is certainly
possible." And with a few strokes on the paper, which I shall here try
to describe in words, he gave his explanation in terms something like
the following:

This square is to denote the cross-section of a closed box which we
imagine to be situated somewhere in the universe. Inside it there lives
a physicist who makes observations and draws inferences from them. In
the course of time he perceives, what is familiar to all of us, that
every body not supported and left to itself, for example, a stone that
is released, drops to the floor with uniform acceleration, that is, with
a steady increase of velocity in going downwards. There are _two_ ways
open to him to explain this phenomenon.

_Firstly_, he might suspect--and this suspicion would be most likely to
occur to him--that his box was resting on some body in the heavens. For
if indeed the box were a cave in some part of the world, the falling of
the stone would suggest nothing unusual; it would be quite self-evident
to every occupant, and quite explicable to the physicist according to
Galilei's (or Newton's) Laws for Falling Bodies. He need not necessarily
restrict himself to the Earth, for if the box happened to be on some
other star, this phenomenon of falling would likewise occur, with
greater or less speed, and the body would certainly fall with uniform
acceleration. Thus the physicist could say: this is an effect of
gravitation, exhibiting the property of weight which I explain to myself
as usual, as due to the attraction of a heavenly body.

_Secondly_, another idea might strike him. For we stipulated nothing
about the position of the box, and assumed only that it was to exist
"somewhere in the universe." The physicist in the box might reason as
follows:

Supposing I am separated by incalculable distances from every attracting
heavenly body, and supposing gravitation existed neither for me nor for
the stone which I release from my hand, then it would still be possible
for me to give a complete explanation of the phenomena I observe. I
should only have to assume that the body is moving with uniform
acceleration "upwards." The motion previously interpreted by me as a
falling "downwards" need not take place at all. The stone, as an _inert_
body, could persist in its position (relative to the box or the
observer), and would, in spite of this, show exactly the same behaviour
when the box moves with acceleration upwards as if it were falling with
increasing velocity downwards.

Now since our physicist has no system which might serve for reference
and orientation, and since in his box which is shut off from the
universe he has no means at his disposal of determining whether he is in
the sphere of influence of an attracting heavenly body or not, both the
above explanations are feasible for him and both are equally valid, and
it is impossible for him to come to a decision in his choice. He can
interpret the acceleration in either way, as being upwards or downwards,
connected to one another by relativity; a fundamental reason for
preferring one interpretation to the other cannot be furnished, since
the phenomenon of falling is represented unchanged whether he assumes
the stone to be falling and the box to be at rest, or vice versa. This
may be generalized in these words:

At every point of the world the observed acceleration of a body left to
itself may be interpreted either as a gravitational _or_ as an inertial
effect--that is, from the point of view of physics we may assert with
equal right that the system (the box, the complex defining the
orientation) from which I observe the event is accelerated, or that the
event takes place in a gravitational field. The equal right to these two
views is called the "Principle of Equivalence" by Einstein. It asserts
the equivalence or the identity of inertial and gravitational mass. If
we familiarize ourselves with this identity, an exceedingly important
road to knowledge is opened up to our consciousness. We arrive at the
inevitable conclusion that every inertial effect that we perceive in
bodies, the most essential quality of it, itself so to speak in its
persistent nature, is to be traced back to the influence to which it is
subjected by other bodies. When this has become clear to us, we feel
impelled to inquire how a ray of light would behave under the influence
of gravitation. Hence we return to our physicist in the box, and we now
know that as a consequence of the Principle of Equivalence we are free
to assume either that an attracting heavenly body, such as the sun, is
situated somewhere below the box, or to refer the phenomena to the box
regarded as being accelerated upwards. In the box we distinguish the
floor, the ceiling, four walls, and among these again, according to the
position we take up, the wall on the left and its opposite one on the
right.

We now imagine a marksman to be outside the box and having no connexion
with us, being poised freely in space, and suppose him to fire out of a
horizontal gun at the box so that the bullet pierces both the wall on
the left and the wall on the right. Now, if everything else were to
remain at rest, the holes in both walls would be equally distant from
the floor, and the bullet would move in a straight line parallel to the
floor and to the ceiling. But, as we have seen, all events happen as if
the box itself moved with constant acceleration. The bullet that
requires time to pass from one wall to the other thus finds that when it
reaches the wall on the right the latter has advanced a little, so that
the resulting hole is a little lower than that on the left wall. This
means that the flight of the bullet, according to our observation in the
interior of the box, is no longer rectilinear. In fact, if we trace the
bullet from point to point, we should find that for us, situated in the
box, it would describe a line bent downwards, with its concave side to
the floor.

Exactly the same thing happens with a ray of light which is emitted by a
source outside in a horizontal direction and which traverses the space
between the walls (supposed transparent). Only the velocity would be
different. In the course of its flight the ray would move like a
projectile that is whizzing along at the rate of 180,000 miles per
second. But provided sufficiently delicate means of measurement are
applied, it should still be possible to prove the existence of an
infinitesimal deflection from the rectilinear horizontal path, an
insignificant concavity towards the floor.

Consequently this curvature of the light-ray (say, from a star) must
also be perceptible in places where it is subject to the influence of a
gravitational field. If we drop our imaginary picture of the box, the
argument is in nowise altered. A ray from a star which passes close by
the sun seems to our perception to be bent in towards the sun, and the
order of this deflection can be determined if sufficiently delicate
instruments be used. As above remarked, it is a question of detecting a
difference of 1.7 seconds of arc, which is to be manifested as a
distance on the photographic plate, and is actually found to be present.

The fact that scientists are able to detect this appears in itself a
marvel of technical precision far in advance of "splitting hairs," for
in comparison a single hair is, in this case, to be removed to a
considerable distance if we are to use it to give an idea of the size of
angle under consideration. Fortunately stellar photography has been
developed so wonderfully that in every single case extraordinarily
accurate results are got even from preliminary measurements.

In ordinary astronomical practice it is usually found that a millimetre
in linear measure on the plate corresponds to a minute of arc. This
means that the sun's disc itself has a diameter of 3 centimetres on the
photograph. The stars appear as tiny dots, which may be sharply
differentiated in an enlargement. Stars of the fourteenth order of
magnitude and beyond it become visible, whereas the naked eye cannot see
those of order higher than the sixth. A grating whose lines are
¹⁄₁₀₀ millimetre wide is copied on to the plate to make the
measurement more accurate, so that the positions of objects can be
ascertained with certainty to within a few tenths of a second of arc.
Thus the problem which was to be solved by the solar eclipse of 1919 lay
within the realm of possibility as regards our means of measurement.

A copy of this photograph had been sent to Einstein from England, and he
told me of it with evident pleasure. He continually reverted to the
delightful little picture of the heavens, quite fascinated by the thing
itself, without the slightest manifestation of a personal interest in
his own success. Indeed, I may go further and am certainly not mistaken
in saying his new mechanics did not even enter his head, nor the
verification of it by the plate; on the contrary, he displayed that
disposition of the mind which in the case of genius as well as in that
of children shows itself as _naïveté_. The prettiness of the
photograph charmed him, and the thought that the heavens had been drawn
up as for parade to be a model for it.

All things are repeated in the history of life. In these happenings,
which mark the 29th May 1919 as a red-letter day in the history of
science, we recognize a revival of the Sun Myth, unperceived by the
individual, but as an expression of the universal consciousness, just as
when Copernicus converted the geocentric picture of the universe into a
heliocentric one, the Sun Myth again sprang into life; the symbolization
of faith in the light-giving and heat-giving star. This time it has
arisen, purified of all dross, scarcely perceptible to our senses, like
an aureole spun about the sun by far-distant sources of light, in honour
of a principle, and even if most of us do not yet know what a "system of
reference" means, yet for many such a system has unconsciously evolved,
a thought-system serving as a reference for the development of their
knowledge when they thought or spoke of Einstein.




CHAPTER II

BEYOND OUR POWER

Useful and Latent Forces.--Connexion between Mass, Energy, and Velocity
of Light.--Deriving Power by Combustion.--One Gramme of Coal.--Unobtainable
Calories.--Economics of Coal.--Hopes and Fears.--Dissociated Atoms.


                             _29th March_ 1920

WE spoke of the forces that are available for man and which he derives
from Nature as being necessary for his existence and for the development
of life. What forces are at our disposal? What hopes have we of
elaborating our supply of these forces?

Einstein first explained the conception of energy, which is intimately
connected with the conception of mass itself. Every amount of substance
(I am paraphrasing his words), the greatest as well as the smallest, may
be regarded as a store of power, indeed, it is essentially identical
with energy. All that appears to our senses and our ordinary
understanding as the visible, tangible mass, as the objective body
corresponding to which we, in virtue of our individual bodies, abstract
the conceptual outlines, and become aware of the existence of a definite
copy is, from the physical point of view, a complex of energies. These
in part act directly, in part exist in a latent form as strains which,
for us, begin to act only when we release them from their state of
strain by some mechanical or chemical process, that is, when we succeed
in converting the potential energy into kinetic energy. It may be said,
indeed, that we have here a physical picture of what Kant called the
"thing in itself." Things as they appear in ordinary experience are
composed of the sum of our direct sensations; each thing acts on us
through its outline, colour, tone, pressure, impact, temperature,
motion, chemical behaviour, whereas the thing in itself is the sum-total
of its energy, in which there is an enormous predominance of those
energies which remain latent and are quite inaccessible in practice.

But this "thing in itself," to which we shall have occasion to refer
often with a certain regard to its metaphysical significance, may be
calculated. The fact that it is possible to calculate it takes its
origin, like many other things which had in no wise been suspected, in
Einstein's Theory of Relativity.

Quite objectively and without betraying in the slightest degree that an
astonishing world-problem was being discussed, Einstein expressed
himself thus:

"According to the Theory of Relativity there is a calculable relation
between mass, energy, and the velocity of light. The velocity of light
(denoted by _c_, as usual) is equal to 3.10^10 cm. per second.
Accordingly the square of _c_ is equal to 9 times 10^20 cm. per second,
or, in round numbers, 10^21 cm. per second. This _c_^2 plays an
essential part if we introduce into the calculation the mechanical
equivalent of heat, that is, the ratio of a certain amount of energy to
the heat theoretically derivable from it; we get for each gramme
20.10^12, that is, 20 billion calories."

We shall have to explain the meaning of this brief physical statement in
its bearing on our practical lifes. It operates with only a small array
of symbols, and yet encloses a whole universe, widening our perspective
to a world-wide range!

To simplify the reasoning and make it more evident we shall not think of
the conception of substance as an illimitable whole, but shall fix our
ideas on a definite substance, say coal.

There seems little that may strike us when we set down the words:

                             "One Gramme of Coal."

We shall soon see what this one gramme of coal conveys when we translate
the above-mentioned numbers into a language to which a meaning may be
attached in ordinary life. I endeavoured to do this during the above
conversation, and was grateful to Einstein for agreeing to simplify his
argument by confining his attention to the most valuable fuel in our
economic life.

Once whilst I was attending a students' meeting, paying homage to
Wilhelm Dove, the celebrated discoverer took us aback with the following
remark: When a man succeeds in climbing the highest mountain of Europe
he performs a task which, judged from his personal point of view,
represents something stupendous. The physicist smiles and says quite
simply, "Two pounds of coal." He means to say that by burning 2 lb. of
coal we gain sufficient energy to lift a man from the sea-level to the
summit of Mont Blanc.

It is assumed, of course, that an ideal machine is used, which converts
the heat of combustion without loss into work. Such a machine does not
exist, but may easily be imagined by supposing the imperfections of
machines made by human hands to be eliminated.

Such effective heat is usually expressed in calories. A calorie is the
amount of heat that is necessary to raise the temperature of a gramme of
water by one degree centigrade. Now the theorem of the Mechanical
Equivalent, which is founded on the investigations of Carnot, Robert
Mayer, and Clausius, states that from one calorie we may obtain
sufficient energy to lift a pound weight about 3 feet. Since 2 lb. of
coal may be made to yield 8 million calories, they will enable us to
lift a pound weight through 24 million feet, theoretically, or, what
comes to the same approximately, to lift a 17-stone man through 100,000
feet, that is, nearly 19 miles: this is nearly seven times the height of
Mont Blanc.

At the time when Dove was lecturing, Einstein had not yet been born, and
when Einstein was working out his Theory of Relativity, Dove had long
passed away, and with him there vanished the idea of the small value of
the energy stored in substance to give way to a very much greater value
of which we can scarce form an estimate. We should feel dumbfounded if
the new calculation were to be a matter of millions, but actually we are
to imagine a magnification to the extent of billions. This sounds almost
like a fable when expressed in words. But a million is related to a
billion in about the same way as a fairly wide city street to the width
of the Atlantic Ocean. Our Mont Blanc sinks to insignificance. In the
above calculation it would have to be replaced by a mountain 50 million
miles high. Since this would lead far out into space, we may say that
the energy contained in a kilogramme of coal is sufficient to project a
man so far that he will never return, converting him into a human comet.
But for the present this is only a theoretical store of energy which
cannot yet be utilized in practice.

Nevertheless, we cannot avoid it in our calculations just as we cannot
avoid that remarkable quantity _c_, the velocity of light that plays its
part in the tiny portion of substance as it does in everything,
asserting itself as a regulative factor in all world phenomena. It is a
natural constant that preserves itself unchanged as 180,000 miles per
second under all conditions, and which truly represents what appeared to
Goethe as "the immovable rock in the surging sea of phenomena," as a
phantasm beyond the reach of investigators.

It is difficult for one who has not been soaked in all the elements of
physical thought to get an idea of what a natural constant means; so
much the more when he feels himself impelled to picture the constant, so
to speak, as the rigid axis of a world constructed on relativity.
Everything, without exception, is to be subjected not only to continual
change (and this was what Heraclitus assumed as a fundamental truth in
his assertion _panta rhei_, everything flows), but every
length-measurement and time-measurement, every motion, every form and
figure are dependent on and change with the position of the observer, so
that the last vestige of the absolute vanishes from whatever comes into
the realm of observation. Nevertheless, there is an absolute despot, who
preserves his identity inflexibly among all phenomena--the velocity of
light, _c_, of incalculable influence in practice and yet capable of
measurement. Its nature has been characterized in one of the main
propositions of Einstein stated in 1905: "Every ray of light is
propagated in a system at rest with a definite, constant velocity
independent of whether the ray is emitted by a body at rest or in
motion." But this constancy of the omnipotent _c_ is not only in
accordance with world relativity: it is actually the main pillar which
supports the whole doctrine; the further one penetrates into the theory,
the more clearly does one feel that it is just this _c_ which is
responsible for the unity, connectivity, and invincibility of Einstein's
world system.

In our example of the coal, from which we started, _c_ occurs as a
square, and it is as a result of multiplying 300,000 by itself (that is,
forming _c_^2) that we arrive at the thousands of milliards of energy
units which we associated above with such a comparatively insignificant
mass. Let us picture this astounding circumstance in another way,
although we shall soon see that Einstein clips the wings of our soaring
imagination. The huge ocean liner _Imperator_, which can develop a
greater horsepower than could the whole of the Prussian cavalry before
the war, used to require for one day's travel the contents of two very
long series of coal-trucks (each series being as long as it takes the
strongest locomotive to pull). We now know that there is enough energy
in two pounds of coal to enable this boat to do the whole trip from
Hamburg to New York at its maximum speed.

I quoted this fact, which, although it sounds so incredibly fantastic,
is quite true, to Einstein with the intention of justifying the opinion
that it contained the key to a development which would initiate a new
epoch in history and would be the panacea of all human woe. I drew an
enthusiastic picture of a dazzling Utopia, an orgy of hopeful dreams,
but immediately noticed that I received no support from Einstein for
these visionary aspirations. To my disappointment, indeed, I perceived
that Einstein did not even show a special interest in this circumstance
which sprang from his own theory, and which promised such bountiful
gifts. And to state the conclusion of the story straight away I must
confess that his objections were strong enough not only to weaken my
rising hopes, but to annihilate them completely.

Einstein commenced by saying: "At present there is not the slightest
indication of when this energy will be obtainable, or whether it will be
obtainable at all. For it would presuppose a disintegration of the atom
effected at will--a shattering of the atom. And up to the present there
is scarcely a sign that this will be possible. We observe atomic
disintegration only where Nature herself presents it, as in the case of
radium, the activity of which depends upon the continual explosive
decomposition of its atom. Nevertheless, we can only establish the
presence of this process, but cannot produce it; Science in its present
state makes it appear almost impossible that we shall ever succeed in so
doing."

The fact that we are able to abstract a certain number of calories from
coal and put them to practical use comes about owing to the circumstance
that combustion is only a molecular process, a change of configuration,
which leaves fully intact the atoms of which the molecules are composed.
When carbon and oxygen combine, the elementary constituent, the atom,
remains quite unimpaired. The above calculation, "mass multiplied by the
square of the velocity of light;" would have a technical significance
only if we were able to attack the interior of the atom; and of this
there seems, as remarked, not the remotest hope.

Out of the history of technical science it might seem possible to draw
on examples contradictory to this first argument which is soon to be
followed by others equally important. As a matter of fact, rigorous
science has often declared to be impossible what was later discovered to
be within the reach of technical attainment--things that seem to us
nowadays to be ordinary and self-evident. Werner Siemens considered it
impossible to fly by means of machines heavier than air, and Helmholtz
proved mathematically that it was impossible. Antecedent to the
discovery of the locomotive the "impossible" of the academicians played
an important part; Stephenson as well as Riggenbach (the inventors of
the locomotive) had no easy task to establish their inventions in the
face of the general reproach of craziness hurled at them. The eminent
physicist Babinet applied his mathematical artillery to demolish the
ideas of the advocates of a telegraphic cable between Europe and
America. Philipp Reis, the forerunner of the telephone, failed only as a
result of the "impossible" of the learned physicist Poggendorff; and
even when the practical telephone of Graham Bell (1876) had been found
to work in Boston, on this side of the Atlantic there was still a hubbub
of "impossible" owing to scientific reasons. To these illustrations is
to be added Robert Mayer's mechanical equivalent of heat, a determining
factor in our above calculations of billions; it likewise had to
overcome very strong opposition on the part of leading scientists.

Let us imagine the state of mankind before the advent of machines and
before coal had been made available as a source of power. Even at that
time a far-seeing investigator would have been able to discover from
theoretical grounds the 8000 calories mentioned earlier and also their
transformation into useful forces. He would have expressed it in another
way and would have got different figures, but he would have arrived at
the conclusion: Here is a virtual possibility which must unfortunately
remain virtual, as we have no machine in which it can be used. And
however far-sighted he may have been, the idea of, say, a modern dynamo
or a turbine-steamer would have been utterly inconceivable to him. He
would not have dreamed such a thing. Nay, we may even imagine a human
being of the misty dawn of prehistoric ages, of the diluvial period, who
had suddenly had a presentiment of the connexion between a log of wood
and the sun's heat, but who was yet unaware of the uses of fire; he
would argue from his primordial logic that it was not possible and never
would be possible to derive from the piece of wood something which sends
out warmth like the sun.

I believe now, indeed, that we have grounds for considering ourselves
able to mark off the limits of possibility more clearly than the present
position of science would seem to warrant. There is the same relation
between such possibilities and absolute impossibilities as there is
between Leibniz's _vérités de fait_ and the _vérités éternelles_.
The fact that we shall never succeed in constructing a plane isosceles
triangle with unequal base angles is a _vérité éternelle_. On the
other hand, it is only a _vérité de fait_ that science is precluded
from giving mortal man eternal life. This is only improbable in the
highest degree, for the fact that, up to the present, all our ancestors
have died is only a finite proof. The well-known Cajus of our logic
books need not die; the chances of his dying are only _n_⁄_n_+1, where
we denote the total of all persons that have passed away up to this
moment by _n_. If I ask a present-day authority in biology or medicine
what evidence there is that it will be possible to preserve an
individual person permanently from death, he would confess: not the
slightest. Nevertheless, Helmholtz declared: "To a person who tells me
that by using certain means the life of a person may be prolonged
indefinitely I can oppose my extreme disbelief, _but I cannot contradict
him absolutely_."

Einstein himself once pointed out to me such very remote possibilities;
it was in connexion with the following circumstance. It is quite
impossible for a moving body ever to attain a velocity greater than that
of light, because it is scientifically inconceivable. On the other hand,
it is conceivable, and therefore within the range of possibility, that
man may yet fly to the most distant constellations.

There is, therefore, no absolute contradiction to the notion of making
available for technical purposes the billions of calories that occurred
in our problem. As soon as we admit it as possible for discussion, we
find ourselves inquiring what the solution of the problem could signify.
In our intercourse we actually arrived at this question, and discovered
the most radical answer in a dissertation which Friedrich Siemens has
written about coal in general without touching in the slightest on these
possibilities of the future. I imagine that this dissertation was a big
trump in my hand, but had soon to learn from the reasoned contradiction
of Einstein that the point at issue was not to be decided in this way.

Nevertheless, it will repay us to consider these arguments for a moment.

Friedrich Siemens starts from two premises which he seemingly bases on
scientific reasoning, thus claiming their validity generally. They are:
Coal is the measure of all things. The price of every product
represents, directly or indirectly, the value of the coal contained in
it.

As all economic values in over-populated countries are the result of
work, and as work presupposes coal, capital is synonymous with coal. The
economic value of each object is the sum-total of the coal that had to
be used to manufacture the object in question. In over-populated states
each wage is the value of the coal that is necessary to make this extra
life possible. If there is a scarcity of coal, the wages go down in
value; if there is no coal, the wages are of no value at all, no matter
how much paper money be issued.

As soon as agriculture requires coal (this occurs when it is practised
intensively and necessitates the use of railways, machines, artificial
manures), coal becomes involved with food-stuffs. Thanks to
industrialism, coal is involved in clothing and housing, too.

Since money is equivalent to coal, proper administration of finance is
equivalent to a proper administration of coal resources, and our
standard of currency is in the last instance a coal-currency. Gold as
money is now concentrated coal.

The most advanced people is that which derives from one kilogramme of
coal the greatest possibilities conducive to life. Wise statesmanship
must resolve itself into wise administration of coal. Or, as it has been
expressed in other words elsewhere: "We must think in terms of coal."

These fundamental ideas were discussed, and the result was that Einstein
admitted the premises in the main, but failed to see the conclusiveness
of the inferences. He proved to me, step by step, that Siemens' line of
thought followed a vicious circle, and, by begging the question, arrived
at a false conclusion. The essential factor, he said, is man-power, and
so it will remain; it is this that we have to regard as the primary
factor. Just so much can be saved to advantage as there is man-power
available for purposes other than for the production of coal from which
they are now released. If we succeed in getting greater use out of a
kilogramme of coal by better management, then this is measurable in
man-power, with which one may dispense for the mining of coal, and which
may be applied to other purposes.

If the assertion: "Coal is the measure of all things," were generally
valid, it should stand every test. We need only try it in a few
instances to see that the thesis does not apply. For example, said
Einstein: However much coal we may use, and however cleverly we may
dispose of it, it will not produce cotton. Certainly the freightage of
cotton-wool could be reduced in price, but the value-factor represented
by man-power can never disappear from the price of the cotton.

The most that can be admitted is that an increase of the amount of power
obtained from coal would make it possible for more people to exist than
is possible at present, that is, that the margin of over-population
would become extended. But we must not conclude that this would be a
boon to mankind. "A maximum is not an optimum."

He who proclaims the maximum without qualification as the greatest
measure of good is like one who studies the various gases in the
atmosphere to ascertain their good or bad effect on our breathing, and
arrives at the conclusion: the nitrogen in the air is harmful, so we
must double the proportion of oxygen to counteract it; this will confer
a great benefit on humanity!

[1]*Armed with this striking analogy, we can now subject the foundation
of Siemens' theory to a new scrutiny, and we shall then discover that
even the premises contain a trace of the _petitio principii_ that
finally receives expression in the radical and one-sided expression:
"Coal is everything."

[Footnote 1: The parts included between *...* are to be regarded as
supplementary portions intended to elucidate the arguments involved in
the dialogue. In many points they are founded on utterances of Einstein,
but also contain reflections drawn from other sources, as well as
opinions and inferences which fall to the account of the author, as
already remarked in the preface. One will not get far by judging these
statements as right or wrong, for even the debatable view may prove
itself to be expeditious and suggestive in the perspective of these
conversations. Wherever it was possible, without the connexion being
broken, I have called attention to the parts which Einstein corrected or
disapproved of. In other places I refrained from this, particularly when
the subject under discussion demanded an even flow of argument. It would
have disturbed the exposition if I had made mention of every
counter-argument of the opposing side in all such cases while the
explanation was proceeding along broad lines.]

As if built on solid foundations this first statement looms before us:
Coal is solar energy. This is so far indisputable. For all the coal
deposits that are still slumbering in the earth were once stately
plants, dense woods of fern, which, bearing the burden of millions of
years, have saved up for us what they had once extracted as nutrition
from the sun's rays. We may let the parallel idea pass without
contention: In the beginning was not the Word, nor the Deed, but, in the
beginning was the Sun. The energy sent out by the sun to the earth for
mankind is the only necessary and inevitable condition for deeds. Deeds
mean work, and work necessitates life. But we immediately become
involved in an unjustifiable subdivision of the idea, for the propounder
of the theory says next: "... Coal is solar energy, therefore coal is
necessary if we are to work ..." and this has already thrust us from the
paths of logic; the prematurely victorious ergo breaks down. For, apart
from the solar energy converted into coal, the warmth of our mother
planet radiates on us, and furnishes us with the possibility of work.
Siemens' conclusion, from the point of view of logic, is tantamount to;
Graphite is solar energy; hence graphite is necessary, if we are to be
able to work. The true expression of the state of affairs is: Coal is,
for our present conditions of life, the most important, if not the
exclusive, preliminary for human work.

And when we learn from political economy that "in a social state only
the necessary human labour and the demand for power-installations which
require coal, and hence again labour for their production, come into
question," this in no way implies the assertion, as Siemens appears to
assume, that coal can be made out of labour. But it does signify that
work founded on the sun's energy need not necessarily be reducible to
coal. And this probably coincides with Einstein's opinion, which is so
much the more significant, as his own doctrine points to the highest
measure of effect in forces, even if only theoretically.*

Nevertheless, it is a fact that every increase in the quantity of power
derived, when expressed per kilo, denotes a mitigation of life's
burdens; it is only a question of the limits involved.

Firstly, is technical science with its possibilities, as far as they can
be judged at present, still able to guarantee the future for us? Can it
spread out the effective work so far that we may rely peacefully on the
treasures of coal slumbering in the interior of the earth?

Evidently not. For in this case we are dealing with quantities that may
be approximately estimated. And even if we get three times, nay ten
times, as many useful calories as before, there is a parallel
calculation of evil omen that informs us: there will be an end to this
feast of energy.

In spite of all the embarrassments due to the present shortage of coal
we have still always been able to console ourselves with the thought
that there is really a sufficiency, and that it is only a question of
overcoming stoppages. It is a matter of fact that from the time of the
foundation of the German Empire to the beginning of the World War coal
production had been rising steadily, and it was possible to calculate
that in spite of the stupendous quantities that were being removed from
the black caves of Germany, there remained at least 2000 milliards of
marks in value (taken at the nominal rate, that is, £100,000,000,000).
Nevertheless, geologists and mining experts tell us that our whole
supply will not last longer than 2000 years, in the case of England 500
years, and in that of France 200 years. Even if we allow amply for the
opening up of new coal-fields in other continents, we cannot get over
the fact that in the prehistoric fern forests the sun has stored up only
a finite, exhaustible amount of energy, and that within a few hundred
years humanity will be faced with a coal famine.

Now, if coal were really the measure of all things, and if the
possibility of life depended only on the coal supply, then our distant
descendants would not only relapse into barbarity, but they would have
to expect the absolute zero of existence. We should not need to worry at
all about the entropy death of the universe, as our own extinction on
this earthly planet beckons to us from an incomparably nearer point of
time.

At this stage of the discussion Einstein revealed prospects which were
entirely in accordance with his conviction that the whole argument based
on the coal assumption was untenable. He stated that it was by no means
a Utopian idea that technical science will yet discover totally new ways
of setting free forces, such as using the sun's radiation, or water
power, or the movement of the tides, or power reservoirs of Nature,
among which the present coal supply denotes only one branch. Since the
beginning of coal extraction we have lived only on the remains of a
prehistoric capital that has lain in the treasure-chests of the earth.
It is to be conjectured that the interest on the actual capital of force
will be very much in excess of what we can fetch out of the depositories
of former ages.

To form an estimate of this actual capital, entirely independent of
coal, we may present some figures. Let us consider a tiny water canal, a
mere nothing in the watery network of the earth, the Rhine-falls at
Schaffhausen, that may appear mighty to the beholder, but only because
he applies his tourist's measure instead of a planetary one. But even
this bagatelle in the household of Nature represents very considerable
effectual values for us: 200 cubic metres spread over a terrace 20
metres high yield 67,000 horse-power, equivalent to 50,000 kilowatts.
This cascade alone would suffice to keep illuminated to their full
intensity 1,000,000 glowlamps, each of 50 candle-power, and according to
our present tariff we should have to pay at least 70,000 marks (£3500
nominally) per hour. The coal-worshipper will be more impressed by a
different calculation. The Rhine-falls at Schaffhausen is equivalent in
value to a mine that yields every day 145 tons of the finest brown coal.
If we took the Niagara Falls as an illustration, these figures would
have to be multiplied by about 80.

And by what factor would we have to multiply them, if we wished to get
only an approximate estimate of the energy that the breathing earth
rolls about in the form of the tides? The astronomer Bessel and the
philosopher-physicist Fechner once endeavoured to get at some
comparative picture of these events. It required 360,000 men twenty
years to build the greatest Egyptian pyramid, and yet its cubical
contents are only about the millionth of a cubic mile, and perhaps if we
sum up everything that men and machinery have moved since the time of
the Flood till now, a cubic mile would not yet have been completed. In
contrast with this, the earth in its tidal motion moves 200 cubic miles
of water from one quadrant of the earth's circumference to another _in
every quarter of a day_. From this we see at once that all the
coal-mines in the world would mean nothing to us if we could once
succeed in making even a fraction of the pulse-beat of the earth
available for purposes of industry.

If, however, we should be compelled to depend on coal, our imaginations
cling so much more closely to that enormous quantity given by the
expression _mc_^2, which was derived from the theory of relativity.

The 20 billion calories that are contained in each gramme of coal
exercise a fascination on our minds. And although Einstein states that
there is not the slightest indication that we shall get at this supply,
we get carried along by an irresistible impulse to picture what it would
mean if we should actually succeed in tapping it. The transition from
the golden to the iron age, as pictured in Hesiod, Aratus, and Ovid,
takes shape before our eyes, and following our bent of continuing this
cyclically, we take pleasure in fancying ourselves being rescued from
the serfdom of the iron and of the coal age to a new golden age. A
supply, such as is piled up in an average city storing-place, would be
sufficient to supply the whole world with energy for an immeasurable
time. All the troubles and miseries arising from the running of
machines, the mechanical production of wares, house-fires would vanish,
and all the human labour at present occupied in mining coal would become
free to cultivate the land, all railways and boats would run almost
without expense, an inconceivable wave of happiness would sweep over
mankind. It would mean an end of coal-, freight-, and food-shortage! We
should at last be able to escape out of the hardships of the day, which
is broken up by strenuous work, and soar upwards to brighter spheres
where we would be welcomed by the true values of life. How alluring is
the song of Sirens chanted by our physics with its high "C," the
velocity of light to the second power, which we have got to know as a
factor in this secret store of energy.

But these dreams are futile. For Einstein, to whom we owe this formula
so promising of wonders, not only denies that it can be applied
practically, but also brings forward another argument that casts us down
to earth again. Supposing, he explained, it were possible to set free
this enormous store of energy, then we should only arrive at an age,
compared with which the present coal age would have to be called golden.

And, unfortunately, we find ourselves obliged to fall in with this view,
which is based in the wise old saw μηδὲν ἄγαν, _ne quid
nimis_, nothing in excess. Applied to our case, this means that when
such a measure of power is set free, it does not serve a useful purpose,
but leads to destruction. The process of burning, which we used as an
illustration, calls up the picture of an oven in which we can imagine
this wholesale production of energy, and experience tells us that we
should not heat an oven with dynamite.

If technical developments of this kind were to come about, the energy
supply would probably not be capable of regulation at all. It makes no
difference if we say that we only want a part of those 20 billion
calories, and that we should be glad to be able to multiply the 8000
calories required to-day by 100. That is not possible, for if we should
succeed in disintegrating the atom, it seems that we should have the
billions of calories rushing unchecked on us, and we should find
ourselves unable to cope with them, nay, perhaps even the solid ground,
on which we move, could not withstand them.

No discovery remains a monopoly of only a few people. If a very careful
scientist should really succeed in producing a practical heating or
driving effect from the atom, then any untrained person would be able to
blow up a whole town by means of only a minute quantity of substance.
And any suicidal maniac who hated his fellows and wished to pulverize
all habitations within a wide range would only have to conceive the plan
to carry it out at a moment's notice. All the bombardments that have
taken place ever since fire-arms were invented would be mere child's
play compared with the destruction that could be caused by two buckets
of coal.

At intervals we see stars light up in the heavens, and then become
extinguished again; from these we infer that world catastrophes have
occurred. We do not know whether it is due to the explosion of hydrogen
with other gases, or to collisions between two stellar bodies. There is
still room for the assumption that, immeasurably far away in yonder
regions of celestial space, something is happening which a malevolent
inhabitant of our earth, who has discovered the secret of smashing the
atom, might here repeat. And even if our imaginations can be stretched
to paint the blessings of this release of energy, they certainly fail to
conjure up visions of the disastrous effects which would result.

Einstein turned to a page in a learned work of the mathematical
physicist Weyl of Zürich, and pointed out a part that dealt with such
an appalling liberation of energy. It seemed to me to be of the nature
of a fervent prayer that Heaven preserve us from such explosive forces
ever being let loose on mankind!

Subject to present impossibility, it is possible to weave many parallel
instances. It is conceivable that by some yet undiscovered process
alcohol may be prepared as plentifully and as cheaply as ordinary water.
This would end the shortage of alcohol, and would assure delirium
tremens for hundreds of thousands. The evil would far outweigh the good,
although it might be avoidable, for one can, even if with great
difficulty, imagine precautionary measures.

War technique might lead to the use of weapons of great range, which
would enable a small number of adventurers to conquer a Great Power. It
will be objected: this will hold vice versa, too. Nevertheless, this
would not alter the fact that such long-range weapons would probably
lead to the destruction of civilization. Our last hope of an escape
would be in a superior moral outlook of future generations, which the
optimist may imagine to himself as the _force majeure_.

There are apparently only two inventions, in themselves triumphs of
intellect, against which one would have no defence. The first would be
thought-reading made applicable to all, and with which Kant has dealt
under the term "thinking aloud." What is nowadays a rare and very
imperfect telepathic "turn" may yet be generalized and perfected in a
manner which Kant supposed not impossible on some distant planet. The
association and converse of man with his fellows would not stand the
test of this invention, and we should have to be angels to survive it
even for a day.

The second invention would be the solution of this _mc_^2-problem, which
I call a problem only because I fail to discover a proper term, whereas
so far was it from being a problem for Einstein that it was only in my
presence he began to reckon it out in figures from the symbolic formula.
To us average beings a Utopia may disclose itself, a short frenzy of joy
followed by a cold douche: Einstein stands above it as the pure
searcher, who is interested only in the scientific fact, and who, even
at the first knowledge of it, preserves its essentially theoretical
importance from attempts to apply it practically. If, then, another
wishes to hammer out into a fantastic gold-leaf what he has produced as
a little particle of gold in his physical investigations, he offers no
opposition to such thought-experiments, for one of the deepest traits of
his nature is tolerance.

A. Pflüger, one of the best qualified heralds of the new doctrine, has
touched on the above matter in his essay, _The Principle of Relativity_.
Einstein praised this pamphlet; I mentioned that the author took a view
different from that of Einstein, of the possibility of making accessible
the _mc_^2. In discussing the practical significance of this
eventuality, Pflüger says: "It will be time to talk of this point again
a hundred years hence." This seems a short time-limit, even if none of
us will live to be present at the discussion. Einstein smiled at this
pause of a hundred years, and merely repeated, "A very good essay!" It
is not for me to offer contradictions; and, as far as the implied
prognostication is concerned, it will be best for mankind if it should
prove to be false. If the optimum is unattainable, at least we shall be
spared the worst, which is what the realization of this prophecy would
inflict on us.

Some months after the above discussion had first been put to paper, the
world was confronted by a new scientific event. The English physicist
Rutherford had, with deliberate intention, actually succeeded in
splitting up the atom. When I questioned Einstein on the possible
consequences of this experimental achievement, he declared with his
usual frankness, one of the treasures of his character, that he had now
occasion to modify somewhat the opinion he had shortly before expressed.
This is not to mean that he now considered the practical goal of getting
unlimited supply of energy as having been brought within the realm of
possibility. He gave it as his view that we are now entering on a new
stage of development, which may perhaps disclose fresh openings for
technical science. The scientific importance of these new experiments
with the atom was certainly to be considered very great.

In Rutherford's operations the atom is treated as if he were dealing
with a fortress: he subjects it to a bombardment and then seeks to fire
into the breach. The fortress is still certainly far from capitulating,
but signs of disruption have become observable. A hail of bullets caused
holes, tears, and splinterings.

The projectiles hurled by Rutherford are alpha-particles shot out by
radium, and their velocity approaches two-thirds that of light. Owing to
the extreme violence of the impact, they succeeded in doing damage to
certain atoms enclosed in evacuated glass tubes. It was shown that atoms
of nitrogen had been disrupted. It is still unknown what quantities of
energy are released in this process. This splitting up of the atom
carried out with intention can, indeed, be detected only by the most
careful investigations.

As far as practical applications are concerned, then, we have got no
further, although we have renewed grounds for hope. The unit of measure,
as it were, is still out of proportion to the material to be cut. For
the forces which Rutherford had to use to attain this result are
relatively very considerable. He derived them from a gramme of radium,
which is able to liberate several milliard calories, whereas the net
practical result in Rutherford's experiment is still immeasurably small.
Nevertheless, it is scientifically established that it is possible to
split up atoms of one's own free will, and thus the fundamental
objection raised above falls to the ground.

There is also another reason for increased hope. It seems feasible that,
under certain conditions. Nature would automatically continue the
disruption of the atom, after a human being had intentionally started
it, as in the analogous case of a conflagration which extends, although
it may have started from a mere spark.

A by-product of future research might lead to the transmutation of lead
into gold. The possibility of this transformation of elements is subject
to the same arguments as those above about the splitting up of the atom
and the release of great quantities of energy. The path of decay from
radium to lead lies clearly exposed even now, but it is very
questionable whether mankind will finally have cause to offer up hymns
of thanksgiving if this line from lead on to the precious metals should
be continued, for it would cause our conception of the latter to be
shattered. Gold made from lead would not give rise to an increase in the
value of the meaner metal, but to the utter depreciation of gold, and
hence the loss of the standard of value that has been valid since the
beginning of our civilization. No economist would be possessed of a
sufficiently far-sighted vision to be able to measure the consequences
on the world's market of such a revolution in values.

The chief product would, of course, be the gain in energy, and we must
bear this in mind when we give ourselves up to our speculations, however
optimistic or catastrophic they may be. The impenetrable barrier
"impossible" no longer exists. Einstein's wonderful "Open Sesame," mass
times the square of the velocity of light, is thundering at the portals.

And mankind finds a new meaning in the old saw: One should never say
_never_!




CHAPTER III

VALHALLA

Order of Distinction and Characteristics of Great Discoverers.--Galilei
and Newton.--Forerunners and Priority.--Science and Religion.--Inheritance
of Talent.--A Dynasty of Scholars.--Alexander von Humboldt and
Goethe.--Leonardo da Vinci.--Helmholtz.--Robert Mayer and Dühring.--Gauss
and Riemann.--Max Planck.--Maxwell and Faraday.


I HAD made up my mind to question Einstein about a number of famous men,
not concerning mere facts of their lives and works, for these details
were also procurable elsewhere, and, moreover, I was not ignorant of
them, but what attracted me particularly was to try to discover how the
greatness of one might be compared with that of another. This sometimes
helps us to see a personality in a different light and from a new
perspective, which leads us to assign to him a new position in the
series of orders of merit.

I had really sketched out a list for this purpose, including a great
number of glorious names from the annals of physics and regions just
beyond: a table, as it were, from which one might set up a directory for
Valhalla! It seemed to me a pleasing thought to roam through this hall
of celebrities in company with Einstein, and to pause at the pedestal of
the busts of the great, who, in spite of their number, are still too
few, far too few, in comparison with the far too many who populate the
earth like so many factory-produced articles. If we set to work to draw
up a list of this sort, we soon find that there is no end to these
heroes of Valhalla, and we are reminded of the hall of fame of the
Northern Saga, of the mythological Valhalla, whose ceiling was so high
that the gable was invisible, and whose extent was so great that anyone
wishing to enter could choose from five hundred and forty entrances.

In reality our little excursion was far from taking these dimensions,
the chief reason being probably that we had begun at Newton. However
attractive it may be to hear Einstein talk of Newton, a disadvantage
arises in that we find it hard to take leave of his bust situated at the
main portal, and that we continually revert to it even when we call to
mind the remaining paths free for our choice and stretching out of
sight.

Reality, even figuratively, offered a picture which differed
considerably from the measures of greatness apportioned by legendary
accounts. In Einstein's workroom, certainly, a visitor encounters
portraits, not busts, and it would be rash to speak of this little
collection of portraits as of a miniature museum. No, it is certainly
not that, for its catalogue numbers only to three. But here they act as
a trinity with a special significance under the gaze of Einstein, who
looks up to them with reverence. To him their contribution of thought is
immeasurable; Faraday, Maxwell with his rich coils of hair, and between
them, Newton with his flowing wig, represented in an excellent English
engraving, whose border consists of symbolic insignias encircling his
distinguished-looking countenance.

     *     *     *     *     *     *     *     *

According to Schopenhauer, the measure of reverence that one can feel is
a measure of one's own intrinsic value. Tell me how much respect you can
feel, and I shall tell you what is your worth. It is certainly not
necessary to emphasize this quality specially in the case of Einstein,
for there are other points of vantage from which we may form an estimate
of his excellence. Nevertheless, I make special mention of the
circumstance to give an indication of the difference between a
revolutionary discoverer and revolutionary pioneers in other fields. It
is particularly noticeable that inborn respect is seldom found in
modernists of Art. The only means of propaganda known to them consists
in a passionate denunciation of what has been developed historically by
gradual and patient effort; their retrospect consists of unmitigated
contempt; they profess to be disciples only of what is most recent,
remaining confined within the narrow circle surrounding their own ego.
The horizon of the discoverer has a different radius. He takes over
responsibility for the future by never ceasing his offerings at the
altar of the Past. There is probably no discoverer who is devoid of this
characteristic, but I should like to emphasize that, among all the
scientists with whom I am acquainted, no one recognizes the merit of
others so warmly as Einstein. He becomes carried away with enthusiasm
when he talks of great men, or of such as appear great to him. His
Valhalla is not, of course, the same as that favoured by Encyclopædias,
and many a one whom we rank as a Sirius among men is to be found lower
than the sixth order of magnitude in Einstein's list. Nevertheless, the
number of selection of constellations is no mean one, and the reverence
that was originally inspired by reasoned thought has become infused in
his temperament and become a part of his emotional self.

One need only mention the name of Newton--and even this is scarcely
necessary, for Newton seems always near at hand; if I happen to start
with Descartes or Pascal, it does not take long before we arrive at
Newton, ἄνδρα μοῐ ἔννεπη!

Once we began with Laplace; and it seemed almost as if the "Traité de
la méchanique céleste" was to become the subject of discussion. But
Einstein left his seat, and, taking up a position in front of his series
of portraits on the wall, he meditatively passed his hand through his
hair, and declared:

"In my opinion the greatest creative geniuses are Galilei and Newton,
whom I regard in a certain sense as forming a unity. And in this unity
Newton is he who has achieved the most imposing feat in the realm of
science. These two were the first to create a system of mechanics
founded on a few laws and giving a general theory of motions, the
totality of which represents the events of our world."

Interrupting his remarks, I asked: "Can Galilei's fundamental law of
inertia (Newton's First Law of Motion) be said to be a law deduced from
experience? My reason for asking is that the whole of natural science is
a science of experience, and not merely something based on speculation.
It might easily suggest itself to one that an elementary law like that
of Galilei or Newton could be derived from our everyday experience. But,
if this is the case, how is it that science had to wait so long before
this simple fact was discovered? Experience is as old as the hills; why
did the law of inertia not make its appearance at the very beginning,
when Nature was first subjected to inquiry?"

"By no means!" replied Einstein. "The discovery of the law of
rectilinear motion of a body under no external influences is not at all
a result of experience. On the contrary! A circle, too, is a simple line
of motion, and has often been proclaimed as such by predecessors of
Newton, for example, by Aristoteles. It required the enormous power of
abstraction possessed only by a giant of reason to stabilize rectilinear
motion as the fundamental form."

To this may be added that before and even after the time of Galilei, not
only the circle but also other non-rectilinear lines have been regarded
even by serious thinkers as the primary lines given by Nature; these
thinkers even dared to apply their curvilinear views to explaining world
phenomena that could be made clear only after Galilei's abstraction had
been accepted.

I asked whether the theory of gravitation was already implicitly
contained in Galilei's Laws of Falling Bodies. Einstein's answer was in
the negative: the gravitational theory falls entirely to the credit of
Newton, and the greatness of this intellectual achievement remains
unimpaired even if the efforts of certain forerunners are recognized. He
mentioned Robert Hooke, whom, among others, Schopenhauer sets up against
Newton, with absolute injustice and from petty feelings of antipathy,
which takes its origin from Schopenhauer's unmathematical type of mind.
The vast difference between Hooke's preliminary attempts at explaining
gravitation, and Newton's monumental structure, was beyond his power of
discernment.

*Schopenhauer (vol. II. of the _Parerga_) uses two arguments to
discredit Newton. Firstly, he refers to two original works, both of
which he misinterprets; secondly, he undertakes a psychological analysis
of Newton. He uses psychological means, which would be about equally
reasonable as applying the Integral Calculus to proving facts of Ethical
Psychology, and he arrives at the conclusion that priority in
discovering the law of gravitation is due to some one else; Hooke is
pictured as having been treated like Columbus: we now hear of "America,"
and likewise "Newton's Gravitational System"!

Schopenhauer has, however, quite forgotten that he himself, some pages
earlier, trumpeted forth Newton's imperishable fame with the words: "To
form an estimate of the great value of the gravitational system which
was at least completed and firmly established by Newton, we must remind
ourselves how entirely nonplussed about the origin of the motion of
celestial bodies thinkers had previously been for thousands of years."
That bears the ring of truth. Newton's greatness can be grasped only if
thousands of years are used as a measure.

Whereas Schopenhauer argued from grounds drawn from psychology and the
principle of universal knowledge, his antagonist Hegel, who was still
more vague in these fields, sought to dispense with both Newton and
Kepler by calling to his aid the so-called pure intuition of the curved
line. In an exposition of truly comical prolixity, such as would have
delighted the hearts of scholiasts, he proves that the ellipse must
represent the fundamental type of planetary motion, this being quite
independent of Newton's laws, Kepler's observations, and resulting
mathematical relationships. And Hegel actually succeeds, with a nebulous
verbosity almost stultifying in its unmeaningness, in paraphrasing
Kepler's second law in his own fashion. It reads like an extract from
some carnival publication issued by scientists in a bibulous mood to
make fun of themselves.

But these extravagances, too, serve to add lustre to Newton, for his
genius shines out most brilliantly when it is a question of expressing
clearly, and without assumptions, a phenomenon of cosmic motion. Here
there are no forerunners, not even with regard to his own law of
gravitation. Newton showed with truly triumphant logic that Kepler's
second law belongs to those things that are really self-evident.

This law, taken alone, offers considerable difficulties to anyone who
learns of it for the first time. Every planet describes an ellipse; that
is accepted without demur. But the uninitiated will possibly or even
probably deduce from this that the planet will pass over equal lengths
of arc in equal times. By no means, says Kepler; the arcs traversed in
equal times are unequal. But if we connect every point of the elliptic
path with a definite point within the curve (the focus of the ellipse)
by means of straight lines, each of which is called a radius vector, we
get that the areas swept out by the radius vector in equal times (and
not the arcs) are equally great.

Why is this so? This cannot be understood _a priori_. But one might
argue that since the attraction of the sun is the governing force, this
will probably have something to do with Newton's law of gravitation, in
particular with the inverse square of the distance. And one might
further infer that, if a different principle of gravitation existed,
Kepler's law would assume a new form.

A fact amazing in its simplicity here comes to light. Newton states the
proposition: "According to whatever law an accelerating force acts from
a centre on a body moving freely, the radius vector will always sweep
out equal areas in equal lengths of time."

Nothing is assumed except the law of inertia and a little elementary
mathematics, namely, the theorem that triangles on the same base and of
the same altitude are equal in area. The form in which this theorem
occurs in Newton's simple drawing is certainly astonishing. One feels
that there in a few strokes a cosmic problem is solved; the impression
is ineffaceable.

This theorem together with its proof is contained in Newton's chief
work, _Philosophiæ naturalis principia mathematica_. The interfusion of
philosophy and mathematics furnished him with the natural principles of
knowledge.*

Einstein made some illuminating remarks about Newton's famous phrase:
"Hypotheses non fingo." I had said that Newton must have been aware that
it is impossible to build up a science entirely free from hypotheses.
Even geometry itself has arrived at that critical stage at which Gauss
and Riemann discovered its hypothetical foundations.

Einstein replied: "Accentuate the words correctly and the true sense
will reveal itself!" It is the last word that is to be stressed and not
the first. Newton did not want to feel himself free from hypotheses, but
rather from the assumption that he invented them, except when this was
absolutely necessary. Newton, then, wished to express that he did not go
further back in his analysis of causes than was absolutely inevitable.

Perhaps, I allowed myself to interject, a more violent suspicion against
the word "hypotheses" was prevalent with scholars in Newton's time than
now. Newton's emphatic defence would then appear a shade more
intelligible. Or did he cherish the belief that his world-law was the
only possible one in Nature?

Einstein again referred to the universality of Newton's genius, saying
that Newton was doubtless aware of the range within which his law was
valid: this law applies to the realm of observation and experience, but
is not given _a priori_, no more than Galilei's Law of Inertia. It is
certainly conceivable that beyond the domain of human experience there
may be an undiscoverable universe in which a different fundamental law
holds, and one which, nevertheless, does not contradict the principle of
sufficient reason.

The antithesis: Simplicity--Complexity, led the conversation into a
short bypath; it arose out of an example which I quoted and that I shall
repeat here even if it may seem irrelevant.

One might well expect that just as for attraction there must be a
general law for resistance or repulsion. And if attraction occurs
according to the inverse square of the distance, then it would be an
extremely interesting parallel if a similar law were to hold for
repulsion except that the proportionality were direct instead of
inverse. There have actually been physicists who have proclaimed a
direct square law of repulsion; I have heard it in lectures myself. The
action of a resisting medium, as, for example, the resistance of the air
to the flight of a cannon-ball, is stated to be proportional to the
square of the velocity of the projectile.

This theorem is wrong. If it were correct, and verified by experiment,
we should have to regard it as being presumably the only possible and
directly evident form of the law of repulsion or resistance. There
would, at least, be no logical reason for contradicting it.

But here we have a mixed relationship, as Einstein calls it--that is, we
are unable to express an exact connexion between the velocity of a body
in flight and the air resistance.

This fallacious assumption by no means proceeded from illogical
reasoning, and it seemed to rest on a sound physical basis. For, so it
was argued, if the velocity is doubled, there is twice as much air to be
displaced, so that the resistance will be four times as great. But this
was contradicted outright by experimental evidence. One cannot even call
it an approximate law, except for very low speeds. For greater speeds we
find, instead of a quadratic relation, a cubical one, or one of a more
complex nature. Photographs have demonstrated that the resistance
experienced by a projectile in flight is due to the excitation of a
powerful central wave, to the friction between the air and the surface
of the projectile, and to eddies produced behind the projectile--that
is, to various conjoined factors, each of which follows a different law,
and such that the combined effect cannot be expressed by a simple
formula at all. This phenomenon is thus very complicated and offers
almost insuperable difficulties to analysis. A beautiful remark was once
made, which characterizes such events in Nature.

During a conversation with Laplace, Fresnel said that Nature does not
worry about analytical difficulties. There is nothing simpler than
Newton's Law in spite of the complicated nature of planetary motions.
"Nature here despises our analytical difficulties," said Fresnel; "she
applies simple means, and then by combining them produces an almost
inextricable net of confusion. Simplicity lies concealed in this chaos,
and it is only for us to discover it!" But this simplicity when it is
discovered is not always found to be expressible in simple formulae, not
must it be forgotten that even the ultimate discoverable simplicity
points to certain hypothetical assumptions.

"Hypotheses non fingo!" This phrase of Newton's remains true, if we
maintain Einstein's interpretation: "He did not wish to go further back
in his analysis of causes than was absolutely inevitable." It interested
me to pursue this line of thought suggested by Einstein still further,
and I discovered that these words of Newton had actually been falsely
accentuated and hence misinterpreted by many authorities on science.
Even Mill and the great scholar, William Whewell, succumbed to this
misunderstanding. Credit must be given to a more modern scholar,
Professor Vaihinger of Halle, for being sufficiently keen of hearing to
detect the true accentuation; and now that Einstein has corroborated
fully this explanation, doubts as to the true sense of the words are no
longer to be feared.

The trend of our talk brought us to a discussion of the conception, "law
of nature." Einstein recalled Mach's remarks, and indicated that the
point was to determine how much we read out of Nature; and these
observations made at least one thing clear, namely, that every law
signifies some limitation; in the case of human laws, expressed in the
civil and penal code, the limitation affects the will, and possible
actions, whereas natural laws signify the limitations which we, taught
by experience, prescribe to our expectations. Nevertheless, the
conception remains elastic, for the question will always intrude itself:
What does prescription mean? Who prescribes? Kant has assigned to Man
the foremost position inasmuch as it is he who is regarded by Kant as
prescribing laws to Nature. Bacon of Verulam emphasizes the ambiguous
point of view by asserting: "Natura non vincitur nisi parendo," Man
conquers Nature only by obeying her, that is, by conforming to her
immanent norms. Thus the laws exist without us, and we have only to
discover them. When they have been found, Man can react by applying them
to subdue Nature. Man becomes the dictator and dictates to Nature the
laws according to which she for her part has to subjugate mankind.
Whether we adopt the one view or the other, there is a vicious circle,
from which there is no escape. A law is a creation of intellect, and
Mephisto's words remain true: "In the end we depend on the creatures of
our own making!"

In Newton's soul obedience and the wish to obey must have been
pre-eminent traits. Is he not reputed to have been pious and strong of
faith?

Einstein confirmed this, and, raising his voice, he generalized from it,
saying: "In every true searcher of Nature there is a kind of religious
reverence; for he finds it impossible to imagine that he is the first to
have thought out the exceedingly delicate threads that connect his
perceptions. The aspect of knowledge which has not yet been laid bare
gives the investigator a feeling akin to that experienced by a child who
seeks to grasp the masterly way in which elders manipulate things."

This explanation implied a personal confession. For he had spoken of the
childlike longing felt by all, and had interpreted the subtle
intricacies of the scientist's ideas in particular as springing from a
religious source. Not all have confessed this; we know, indeed, that the
convictions of many a one were not so. Let us cling to the fact that the
greatest in the realm of science--Newton, Descartes, Gauss, and
Helmholtz--were pious, although their faith varied in degree. And let us
not forget that the most bitter opponent of this attitude of mind, the
originator of "Ecrasez l'infame," finally had a temple built bearing the
inscription: "Deo erexit Voltaire."

In Newton positivism found its most faithful disciple, and his research
was directly affected by his religious attitude. He, himself, was the
author of that beautiful thought: "A limited measure of knowledge takes
us away from God; an increased measure of knowledge takes us back to
Him." It was he who considered that the world-machine that he had
disclosed was not sufficiently stabilized by his mathematical law, and
so he enlisted the intermittent help of an assistant for the Creator,
Concursus Dei, to attend to the functioning of the machine. Finally, he
slipped from the path of naïve faith on to theological bypaths and
wrote devout essays on apocalyptic matters. On the other hand,
Descartes' piety, which was genuine at root, exhibited suspicious
offshoots, and one cannot shake off the feeling that he was smiling up
his sleeve when he was making some of his solemn declarations. He was a
master of compromise, and gave due expression to its spirit, which F. A.
Lange bluntly stated was merely a veil for "Cowardice towards the
Church." Voltaire, an apostle of Newton's system of natural philosophy,
went so far in his condemnation of Descartes' confession of faith that
he affirmed: "The Cartesian doctrine has been mainly instrumental in
persuading many not to recognize a God."

As Einstein had called special attention to the childlike nature of the
scientist's root-impulse, I quoted a remark of Newton that seemed to me
at the moment to be a confirmation of Einstein's attitude:

"I do not know what I may appear to the world, but to myself I seem to
have been only like a boy playing on the seashore, and diverting myself
in now and then finding a smoother pebble or a prettier shell than
ordinary, whilst the great ocean of truth lay all undiscovered before
me."

Are we not to regard this analogy of Newton's as being intended to
convey a religious meaning?

"There is no objection to this," said Einstein, "although it seems to me
more probable that, in saying this, Newton set down the view only of the
pure investigator. The essential purpose of his remarks was to express
how small is the range of the attainable compared with the infinite
expanse offered for research."

Through some unexpected phrase that was dropped, the conversation took a
new turn at this point, which I should not like to withhold, inasmuch as
it gave rise to a noteworthy observation of Einstein about the nature of
genius. We were talking about the "possibility of genius for science
being inherited" and about the comparative rareness with which it
occurs. There seems to have been only one case of a real dynasty of
great minds, that of the ten Bernoullis who were descended of a line of
mathematicians, and all of them achieved important results, some of them
making extraordinary discoveries. Why is this exception unique? In other
examples we do not get beyond three or four names in the same family,
even if we take Science and Art conjointly. There were two Plinys, two
Galileis, two Herschels, two Humboldts, two Lippis, two Dumas, several
Bachs, Pisanos, Robbias, and Holbeins--the net result is very poor, even
if we count similar names, disregarding the fact of relationship; there
is no recognizable dynasty except in the case of the ten Bernoullis.[2]
"And so," I continued, "the conclusion seems justified that Nature has
nothing to do with a genealogy of talents, and that, if we happen to
notice manifestations of talent in one and the same family, this is a
mere play of chance."

[Footnote 2: The Roman family Cosmati (of the thirteenth century), which
gave us seven splendid representatives of architecture and mosaic work,
hardly comes into consideration, since not one of them is regarded in
the history of art as a real genius.]

Einstein, however, contradicted this emphatically: "Inherited talent
certainly occurs in many cases, where we do not observe it, for genius
in itself and the possibility of genius being apprehended are certainly
far from always appearing in conjunction. There are only insignificant
differences between the genius that expresses itself in remarkable
achievements and the genius that is latent. At a certain instant,
perhaps, only some impulse was wanting for the latent genius to burst
forth with all clearness and brilliance; or, perhaps, it required only
an unusual situation in the development of science to call into action
his special talents, and thus it remained dormant, whereas a very slight
change of circumstances would have caused them to assert themselves in
definite results.

"In passing I should like to remark that you just now mentioned the two
Humboldts; it seems to me that Alexander von Humboldt, at least, is not
to be counted as a genius. It has struck me repeatedly that you
pronounced his name with particular reverence----"

"And I have observed equally often, Professor, that you made a sign of
disapproval. For this reason slight doubts have gradually been rising in
me. But it is difficult to get free from the orders of greatness that
one has recognized for decades. In my youth people spoke of 'a Humboldt'
just as we speak of 'a Cæsar' or 'a Michelangelo,' to denote some
pinnacle of unrivalled height. To me at that time Humboldt's Kosmos was
the Bible of Natural Science, and probably such memories have a certain
after-effect."

"That is easy to understand," said Einstein. "But we must make it clear
to ourselves that for us of the present day Humboldt scarcely comes into
consideration when we direct our gaze on to the great seers. Or, let us
say more clearly, he does not belong to this category. I certainly grant
him his immense knowledge and his admirable faculty of getting into
touch with the unity of Nature, which reminds us of Goethe."

"Yes; this feeling for the uniformity of the cosmos had probably
persuaded me in his favour," I answered, "and I am glad that you draw a
parallel with Goethe in this respect. It reminds me of Heine's story: If
God had created the whole world, except the trees and the birds, and had
said to Goethe: 'My dear Goethe, I leave it to you to complete this
work,' Goethe would have solved the problem correctly and in a god-like
manner--that is, he would have painted the trees green and given the
birds feathers.

"Humboldt could equally well have been entrusted with this task. But
various objections may be raised against such reflections of a playful
poetic character ... one objection being that Goethe's own knowledge of
ornithology was exceedingly limited. Even when nearly eighty he could
not distinguish a lark from a yellow-hammer or a sparrow! Is that a
fact?"

"Fully confirmed: Eckermann gives a detailed report of it in a
conversation which took place in 1827. As I happened to come across the
passage only yesterday, I can quote the exact words if you will allow
me: 'Great and good man,' thought Eckermann, 'who hast explored Nature
as few have ever done, in ornithology thou seemest still a child!'"

For a speculative philosopher, it may here be interposed, this might
well serve as the starting-point of an attractive investigation. Goethe,
on the one hand, cannot recognize a lark, but would have been able to
grasp the Platonic idea of the feathered species, even if there had been
no such things as birds: Humboldt, on the other hand, would perhaps have
been able to create the revolving planets, if Heaven had commanded it;
but he would never have succeeded in becoming the author of what we call
an astronomical achievement, such as that of Copernicus or of Kepler.

And with reference to certain other men I elicited from Einstein
utterances that reduced somewhat my estimate of their importance.

We were speaking of Leonardo da Vinci, omitting all reference to his
significance in the world of Art--that is, only of Leonardo the Scholar
and the Searcher. Einstein is far from disputing his place in the
Valhalla of great minds, but it was clear that he wished to recommend a
re-numbering of my list, so that the Italian master would not occupy a
position in just the first rank.

The problem of Leonardo excited great interest in me, and it deserves
the consideration of every one. The further the examination of his
writings advances, the more does this problem resolve itself into the
question: How much altogether does modern science owe to Leonardo?
Nowadays it is declared in all earnestness that he was a painter and a
sculptor only by the way, that his chief profession was that of an
engineer, and that he was the greatest engineer of all times. This has
in turn given rise to the opinion that, as a scientist, he is the light
of all ages, and in the abundance of his discoveries he has never been
surpassed before or after his own time.

As this question had arisen once before, I had come equipped with a
little table of facts, hastily drawn from special works to which I had
access. According to my scheme, Leonardo was the true discoverer and
author of the following things:

    Law of Conservation of Momentum.

    Law of Virtual Velocities (before Ubaldi and Galilei).

    Wave Theory (before Newton).

    Discovery of the Circulation of the Blood (before
        Harvey).

    Laws of Friction (before Coulomb).

    Law of Pressure for connected Tubes containing
        Fluid (before Pascal).

    Action of Pressure on Fluids (before Stevin and Galilei).

    Laws of Falling Bodies (before Galilei).

    True interpretation of the twinkling of stars (before
        Kepler, who, moreover, did not succeed in finding
        the real explanation).

    Explanation of the reflected light of the moon (before
        Kepler).

    Principle of Least Action (before Galilei).

    Introduction of the plus and the minus signs into
        calculations.

    Definition of kinetic energy from mass and velocity.

    Theory of Combustion (before Bacon).

    Explanation of the motion of the sea (before Maury).

    Explanation of the ascent of fluids in plants (before
        Hales).

    Theory of Fossilization (before Palissy).

Added to these there are a great number of inventions, in particular
those connected with problems of aviation, such as the parachute (before
Lenormand), and so forth.

This fist aroused great distrust in Einstein: he regarded it as the
outcome of an inquisitive search for sources, excusable historically,
but leading to misrepresentation. We are falsely led to regard slightly
related beginnings, vague tracks, hazy indications, which are found, as
evidences of a real insight, which disposes us to "elevate one above all
others." Hence a mythological process results, comparable to that which,
in former times, thrust all conceivable feats of strength on to one
Hercules.

I learned that recently a strong reaction has asserted itself in
scientific circles against this one-sided hero-worship; its purpose is
to reduce Leonardo's merits to their proper measure. Einstein made it
quite clear that he was certainly not to be found on the side of the
ultra-Leonardists.

It cannot be denied that the latter have valuable arguments to support
their case, and that these arguments become multiplied in proportion as
the publication of Leonardo's writings (in the _Codex Atlanticus_,
etc.), which are so difficult to decipher, proceeds. The partisans of
Leonardo derive considerable support in many points from recognized
authorities, as in the case of Cantor, the author of the monumental
history of mathematics. We there read: "The greatest Italian painter of
the fifteenth century was not less great as a scientist. In the history
of science his name is famous and his achievements are extolled,
particularly those which give him a claim to be regarded as one of the
founders of Optics." He is placed on a level with Regiomantus as one of
the chief builders of mathematics of that time. Nevertheless, Cantor
raises certain doubts by remarking that the results of investigations
made up to the present do not prove Leonardo to be a great
mathematician. On another page he is proclaimed simultaneously with
Archimedes and Pappus as a pioneer of the doctrines of the centre of
gravity.

With regard to the main points, Leonardo's priority in the case of the
Laws of Falling Bodies, the Theory of Wave-motion, and the other
fundamental principles of physics, Einstein has the conviction that the
partisans of Leonardo are either mistaken in the facts or that they
overlook forerunners. In the case of these principles, above all, there
is always _some_ predecessor, and it is almost impossible to trace the
line of discoveries back to the first source. Just as writers have
wished to deprive Galilei, Kepler, and Newton of their laurels in favour
of Leonardo, so the same might be done with Copernicus.

This has actually been attempted. The real Copernicus, so one reads, was
Hipparchus of Nicæa, and if we go back still further, a hundred years
earlier, two thousand years ago, we find that Aristarchus of Samos
taught that the world rotated about its own axis and revolved round the
sun.

And we need not even stop there, in Einstein's opinion. For it is open
to conjecture that Aristarchus in his turn has drawn on Egyptian
sources. This retrogressive investigation may excite the interest of
archæologists, and in particular cases perhaps lead to the discovery of
a primary claim to authorship, but it cannot fail to excite suspicion
against the conscious intention of conferring all the honours of science
on an individual discoverer. Leonardo's superlative constructive genius
is not attacked in these remarks, and there seems no reason for
objecting if anyone wishes to call him the most ingenious engineer of
all times.

All the pressures and tensions occurring in Nature seemed to be repeated
in him as "inner virtues," an expression borrowed from Helmholtz, who
used it with reference to himself. This analogy might be extended by
saying that, in the works of both, Man himself with his organic
functions and requirements plays an important rôle. For them the
abstract was a means of arriving at what was perceptual, physiologically
useful, and stimulating in its effect on life. Leonardo started out from
Art, and throughout the realm of mechanics and machines he remained an
artist in method. Helmholtz set out from the medical side of physiology
and transferred the valuations of beauty derived from the senses to his
pictures of mechanical relationships. The life-work of each has an
æsthetic colouring, Leonardo's being of a gloomy hue, that of Helmholtz
exhibiting brighter and happier tints. Common to both is an almost
inconceivable versatility and an inexhaustible productivity.

Whenever Einstein talks of Helmholtz he begins in warm terms of
appreciation, which tend to become cooler in the course of the
conversation. I cannot quote his exact words, and as I cannot thus give
a complete account for which full responsibility may be taken, it may be
allowable to offer a few important fragments that I have gathered.

Judged by the average of his accomplishments, Helmholtz is regarded by
Einstein as an imposing figure whose fame in later times is assured;
Helmholtz himself tasted of this immortality while still alive. But when
efforts are made to rank him with great thinkers of the calibre of
Newton, Einstein considers that this estimate cannot be fully borne out.
In spite of all the excellence, subtlety, and effectiveness of
Helmholtz's astoundingly varied inspirations, Einstein seems to fail to
discover in him the source of a really great intellectual achievement.

At a Science Congress held in Paris in 1867, at which Helmholtz was
present, a colleague of his was greeted with unanimous applause when he
toasted him with the words: "L'ophthalmologie était dans les
ténèbres,--Dieu parla, que Helmholtz naquît--Et la lumière était
faite!" It was an almost exact paraphrase of the homage which Pope once
addressed to Newton. At that time the words of the toast were re-echoed
throughout the world; ophthalmology was enlarged to science generally,
and the apotheosis was applied universally. Du Bois-Reymond declared
that no other nation had in its scientific literature a book that could
be compared with Helmholtz's works on Physiological Optics and on
Sensations of Tone. Helmholtz was regarded as a god, and there are not a
few to whom he still appears crowned with this divine halo.

A shrill voice pierced the serene atmosphere, attacking one of his main
achievements. The dissentient was Eugen Dühring, to whose essay on the
Principles of Mechanics a coveted prize was awarded, a fact which seemed
to stamp him as being specially authorized to be a judge of pre-eminent
achievements in this sphere. Dühring's aim was to dislodge one of the
fundamental supports of Helmholtz's reputation by attacking his "Law of
the Conservation of Energy." If this assault proved successful, the god
would lie shattered at his own pedestal.

Dühring, indeed, used every means to bespatter his fair name in
science; and it is hardly necessary to remark that Einstein abhors this
kind of polemic. What is more, he regards it as a pathological symptom,
and has only a smile of disdain for many of Dühring's pithy sayings. He
regards them as documents of unconscious humour to be preserved in the
archives of science as warnings against future repetitions of such
methods.

Dühring belonged also to those who wished to exalt one above all
others. He raised an altar to Robert Mayer, and offered up sanguinary
sacrifices. Accustomed to doing his work thoroughly, he did not stop at
Helmholtz in choosing his victims. No hecatomb seemed to him too great
to do honour to the discoverer of the Mechanical Equivalent of Heat, and
so his next prey was Gauss and Riemann.

Gauss and Riemann! Each was a giant in Einstein's opinion. He knew well
that this raging Ajax had also made an assault against them, but he had
no longer a clear recollection of the detailed circumstances; as the
references were near at hand, he allowed me to repeat a few lines of
this tragi-comedy.

Helmholtz, according to Dühring (who also calls him "Helmklotz"), has
done no more than distort Mayer's fundamental mechanical idea, and
interpret it falsely. By "philosophizing" over it, he has completely
spoilt it, and rendered it absurd. It was the greatest of all
humiliations practised on Mayer that his name had been coupled with that
of one whom he had easily out-distanced, and whose clumsy attempts at
being a physicist were even worse than those by which he sought to
establish himself as a philosopher.

The offences of Gauss and Riemann against Mayer are shrouded in
darkness. But there was another would-be scientist, Justus von Liebig,
who, being opposed to Mayer, aroused the suspicions of Dühring,
particularly as he had used his "brazen-tongue" to defend the two
renowned mathematicians. After he, and Clausius too, had been brought to
earth, Dühring launched out against the giants of Göttingen. In the
chapter on Gauss and "Gauss-worship," we read: "His megalomania rendered
it impossible for him to take exception to any tricks that the deficient
parts of his own brain played on him, particularly in the realm of
geometry. Thus he arrived at a pretentiously mystical denial of Euclid's
axioms and theorems, and proceeded to set up the foundations of an
apocalyptic geometry not only of nonsense but of absolute stupidity....
They are abortive products of the deranged mind of a mathematical
professor, whose mania for greatness proclaims them as new and
superhuman truths!... The mathematical delusions and deranged ideas in
question are the fruits of a veritable _paranoia geometrica_."

After Herostratus had burnt to ashes the consecrated temple, the Ionian
cities issued a proclamation that his name was to be condemned to
perpetual oblivion! The iconoclast Dühring is immortalized, for, apart
from the charge of arson, he is notable in himself. In his case we found
ourselves confronted with unfathomable problems of a scholar's complex
nature, problems which even a searcher like Einstein failed to solve.
The simplest solution would be to turn the tables and to apply the term
"paranoia" as a criticism to the book on Robert Mayer, and thus demolish
it. But this will not do, for if we merely pass over the pages of
distorted thought, we are still left with a considerable quantity of
valuable material.

Does Dühring, after all, himself deserve a place in our Valhalla? The
question seems monstrous, and yet cannot be directly answered in the
negative. The individual is to be judged according to his greatest
achievement, and not according to his aberrations. The works of
Aristotle teem with nonsensical utterances, and Leonardo's _Bestiarius_
is an orgy of abstruse concoctions. If Dühring had written nothing
beyond his studies of personalities ranging from Archimedes to Lagrange,
the portals would yet have been open to him. Even in his eulogy of
Robert Mayer, which is besmirched with unseemly remarks, he displays at
least the courage of his convictions.

The attempt at a comparison between Robert Mayer and Helmholtz is doomed
to failure even when considered dispassionately, inasmuch as the
disturbing factor of priority here intrudes itself. The definite fixing
of the Law of Energy is certainly to the credit of Helmholtz, but
perhaps he would have gained by laying more stress on the discovery of
it five years earlier by the doctor in Heilbronn. And again, this would
not have been final, for the invariance of the sum of energy during
mechanical actions was known even by Huyghens. The Heilbronn doctor
performed one act of genius in his life, whereas Helmholtz during his
whole life moved asymptotically to the fine of genius without ever
reaching it. If my interpretation of Einstein's opinion is correct,
Helmholtz is to be credited with having the splendour of an overpowering
gift for research predominant in his nature, but is not necessarily to
be given a seat among the most illustrious of his branch of science.
Einstein wishes to preserve a certain line of demarcation between this
type and not only the Titans of the past, but also those of the present.
When he speaks of the latter, his tone becomes warmer. He does not need
circuitous expressions, each syllable rings with praise. He has in mind,
above all, Hendrik Antoon Lorentz in Leyden, Max Planck, and Niels Bohr;
we then see that he feels Valhalla about him.

     *     *     *     *     *     *     *     *

The reason that I have tried to maintain the metaphor of a Temple of
Fame is due to an echo of Einstein's own words at a celebration held in
honour of the sixtieth birthday of the physicist Planck in the May of
1918. This speech created the impression of a happy harmony resulting
from a fusion of two melodies, one springing from the intellect, the
other rising from the heart. We were standing as at the Propylons with a
new Heraclitus uttering the cry: Introite, nam et hic dii sunt!

I should like to give the gist of this beautiful address in an extract
uninterrupted by commentaries.

"The Temple of Science"--so Einstein began--"is a complex structure of
many parts. Not only are the inmates diverse in nature, but so also are
the inner forces that they have introduced into the temple. Many a one
among them is engaged in Science with a happy feeling of a superior
mind, and finds Science the sport which is congenial to him, and which
is to give him an outlet for his strong life-forces, and to bring him
the realization of his ambitions. There are, indeed, many, too, who
offer up their sacrifice of brain-matter only in the cause of useful
achievements. If now an angel of heaven were to come and expel all from
the temple who belonged to these two categories, a considerable
reduction would result, but there would still remain within the temple
men of present and former times: among these we count our Planck, and
that is why he has our warm affection.

"I know full well that, in doing this, we have light-heartedly caused
many to be driven out who contributed much to the building of the
temple; in many cases our angel would find a decision difficult.... But
let us fix our gaze on those who find full favour with him! Most of them
are peculiar, reserved, and lonely men, who, in spite of what they have
in common, are really less alike than those who have been expelled. What
led them into the temple?... In the first place, I agree with
Schopenhauer that one of the most powerful motives that attract people
to Science and Art is the longing to escape from everyday life with its
painful coarseness and unconsoling barrenness, and to break the fetters
of their own ever-changing desires. It drives those of keener
sensibility out of their personal existence into the world of objective
perception and understanding. This motive force is similar to the
longing which makes the city-dweller leave his noisy, confused
surroundings and draws him with irresistible force to restful Alpine
heights, where his gaze covers the wide expanse lying peacefully before
him on all sides, and softly passes over the motionless outlines that
seem created for all eternity. Associated with this negative motive is a
positive one, by virtue of which Man seeks to form a simplified
synoptical view of the world in a manner conformable to his own nature,
in order to overcome the world of experience by replacing it, to a
certain degree, by this picture. This is what the painter does, as also
the poet, the speculative philosopher, and the research scientist, each
in his own way. He transfers the centre of his emotional existence into
this picture, in order to find a sure haven of peace, one such as is not
offered in the narrow limits of turbulent personal experience.

"What position does the world-picture of the theoretical physicist
occupy among all those that are possible? He demands the greatest rigour
and accuracy in his representation, such as can be gained only by using
the language of mathematics. But for this very reason the physicist has
to be more modest than others in his choice of material, and must
confine himself to the simplest events of the empirical world, since all
the more complex events cannot be traced by the human mind with that
refined exactness and logical sequence which the physicist demands....
Is the result of such a restricted effort worthy of the proud name
'world-picture'?

"I believe this distinction is well deserved, for the most general laws
on which the system of ideas set up by theoretical physics is founded
claim to be valid for every kind of natural phenomenon. From them it
should be possible by means of pure deduction to find the picture, that
is, the theory, of every natural process, including those of living
organism, provided that this process of deduction does not exceed the
powers of human thought. Thus there is no fundamental reason why the
physical picture of the world should fall short of perfection....

"Evolution has shown that among all conceivable theoretical
constructions there is at each period one which shows itself to be
superior to all others, and that the world of perception determines in
practice the theoretical system, although there is no logical road from
perception to the axioms of the theory, but rather that we are led
towards the latter by our intuition, which establishes contact with
experience....

"The longing to discover the _pre-established harmony_ recognized by
Leibniz is the source of the inexhaustible patience with which we see
Planck devoting himself to the general problems of our science, refusing
to allow himself to be distracted by more grateful and more easily
attainable objects.... The emotional condition which fits him for his
task is akin to that of a devotee or a lover; his daily striving is not
the result of a definite purpose or a programme of action, but of a
direct need.... May his love for Science grace his future course of
life, and lead him to a solution of that all-important problem of the
day which he himself propounded, and to an understanding of which he has
contributed so much! May he succeed in combining the Quantum Theory with
Electrodynamics and Mechanics in a logically complete system!"

     *     *     *     *     *     *     *     *

"What grips me most in your address," I said, "is that it simultaneously
surveys the whole horizon of science in every direction, and traces back
the longing for knowledge to its root in emotion. When your speech was
concluded, I regretted only one thing--that it had ended so soon.
Fortunate is he who may study the text."

"Do you attach any importance to it?" asked Einstein; "then accept this
manuscript." It is due to this act of generosity that I have been able
to adorn the foregoing description of the excursion into Valhalla with
such a valuable supplement.

     *     *     *     *     *     *     *     *

The conversation had begun with the brilliant constellation
Galilei-Newton, and near the end inclined again towards the
consideration of a double-star: the names of Faraday and Maxwell
presented themselves.

"Both pairs," Einstein declared, "are of the same magnitude. I regard
them as fundamentally equal in their services in the onward march of
knowledge."

"Should we not have to add Heinrich Hertz as a third in this bond? This
assistant of Helmholtz is surely regarded as one of the founders of the
Electromagnetic Theory of Light, and we often hear their names coupled,
as in the case of the Maxwell-Hertz equations."

"Doubtless," replied Einstein, "Hertz, who is often mentioned together
with Maxwell, has an important rank and must be placed very high in the
world of experimental physics, yet, as regards the influence of his
scientific personality, he cannot be classed with the others we have
named. Let us, then, confine ourselves to the twin geniuses Faraday and
Maxwell, whose intellectual achievement may be summarized in a few
words. Classical mechanics referred all phenomena, electrical as well as
mechanical, to the direct action of particles on one another,
irrespective of their distances from one another. The simplest law of
this kind is Newton's expression: 'Attraction equals Mass times Mass
divided by the square of the distance.' In contradistinction to this,
Faraday and Maxwell have introduced an entirely new kind of physical
realities, namely, _fields of force_. The introduction of these new
realities gives us the enormous advantage that, in the first place, the
conception of action at a distance, which is contrary to our everyday
experience, is made unnecessary, inasmuch as the fields are superimposed
in space from point to point without a break; in the second place, the
laws for the field, especially in the case of electricity, assume a much
simpler form than if no field be assumed, and only masses and motions be
regarded as realities."

He enlarged still further on the subject of fields, and while he was
describing the technical details, I saw him metaphorically enveloped in
a magnetic field of force. Here, too, an influence, transmitted through
space from point to point, made itself felt, and there could be no
question of action "at a distance" inasmuch as the effective source was
so near at hand. His gaze, as if drawn magnetically, passed along the
wall of the room and fixed affectionately on Maxwell and Faraday.




CHAPTER IV

EDUCATION

School Curricula and Reform of Teaching.--Value of Language Study.--Economy
of Time.--Practice in Manual Work.--Picturesque Illustrations.--Art
of Lecturing.--Selection of Talents by Means of Examinations.--Women
Students.--Social Difficulties.--Necessity as Instructress.


OUR conversation turned towards a series of pædagogic questions, in
which Einstein is deeply interested. For he himself is actively engaged
in teaching, and never disguises the pleasure which he derives from
imparting instruction. Without doubt he has a gift of making his spoken
words react on wide circles anxious to be instructed, composed not only
of University students, but of many others quite outside this category.
When, recently, popular lectures on a large scale were instituted, he
was one of the first to offer his services in this sound undertaking. He
lectured to people of the working class, who could not be assumed to
have any preliminary information on the subject, and he succeeded in
presenting his lectures so that even the less trained minds could easily
follow his argument.

His attitude towards general questions of school education is, of
course, conditioned by his own personality and his own work in the past.
His first care is that a young person should get an insight into the
relationship underlying natural phenomena, that is, that the curricula
should be mapped out so that a knowledge of facts is the predominating
aim.

"My wish," Einstein declared to me, "is far removed from the desire to
eliminate altogether the fundamental features of the old grammar
schools, with their preference for Latin, by making over-hasty reforms,
but I am just as little inclined to wax enthusiastic about the so-called
humanistic schools. Certain recollections of my own school life suffice
to prevent this, and still more, a certain presentiment of the
educational problems of the future."--"To speak quite candidly," he
said, "in my opinion the educative value of languages is, in general,
much over-estimated."

I took the liberty of quoting a saying that is still regarded as
irrefutable by certain scholars. It was Charles V who said: "Each
additional acquired language represents an additional personality"; and
to suggest the root of language formation he said it in Latin: "Quot
linguas quis callet, tot homines valet." This saying has been handed
down through the ages in German in the form: "Soviel Sprachen, soviel
Sinnen" (An added language means an added sense).

Einstein replied: "I doubt whether this aphorism is generally valid, for
I believe that it would at no time have stood a real test. All
experience contradicts it. Otherwise we should be compelled to assign
the highest positions among intellectual beings to linguistic athletes
like Mithridates, Mezzofanti, and similar persons. The exact opposite,
indeed, may be proved, namely, that in the case of the strongest
personalities, and of those who have contributed most to progress, the
multiplicity of their senses in no wise depended on a comprehensive
knowledge of languages, but rather that they avoided burdening their
minds with things that made excessive claims on their memories."

"Certainly," said I, "it may be admitted that this gives rise to
exaggeration in some cases, and that the linguistic sort of sport
practised by many a scholar degenerates to a mere display of knowledge.
An intellectual achievement of lasting merit has very rarely or never
been the result of a superabundance of acquired linguistic knowledge. An
instance occurs to me at this moment. Nietzsche became a philosopher of
far-reaching influence only after he had passed the stage of the
philologist. As far as our present discussion is concerned, the question
is narrowed down considerably: it reduces itself to inquiring whether we
do sufficient, too little, or too much Greek and Latin. I must remark at
the very outset that, formerly, school requirements went much further in
this respect than nowadays, when we scarcely meet with a scholar even in
the upper classes who knows Latin and Greek perfectly."

It is just this fact that Einstein regards as a sign of improvement and
a result of examining the true aims of a school. He continued: "Man must
be educated to 'react delicately'; he is to acquire and develop
'intellectual muscles'! And the methods of language drill are much less
suited to this purpose than those of a more general training that gives
greatest weight to a sharpening of one's own powers of reflection.
Naturally, the inclination of the pupil for a particular profession must
not be neglected, especially in view of the circumstance that such
inclination usually asserts itself at an early age, being occasioned by
personal gifts, by examples of other members of the family, and by
various circumstances that affect the choice of his future life-work.
That is why I support the introduction into schools, particularly
schools devoted to classics, of a division into two branches at, say,
the fourth form, so that at this stage the young pupil has to decide in
favour of one or other of the courses. The elementary foundation to the
fourth form may be made uniform for all, as they are concerned with
factors on education that are scarcely open to the danger of being
exaggerated in any one direction. If the pupil finds that he has a
special interest in what are called _humaniora_ by the educationist, let
him by all means continue along the road of Latin and Greek, and,
indeed, without being burdened by tasks that, owing to his disposition,
oppress or alarm him."

"You are referring," I interposed, "to the distress which pupils feel in
the time allotted to mathematics. There are actually people of
considerable intelligence who seem to be smitten with absolute stupidity
when confronted with mathematics, and whose school-life becomes poisoned
owing to the torment caused by this subject. There are many cases of
living surgeons, lawyers, historians, and litterateurs, who, till late
in life, are visited by dreams of their earlier mathematical ordeals.
Their horror has a very real foundation, for, whereas the pupil who is
bad at Latin yet manages to get an idea of the language, and he who is
weak in history has at least a notion of what is being discussed, the
one who is unmathematical by nature has to worry his way through
numberless lessons in a subject which is entirely incomprehensible to
him, as if belonging to another world and being presented to him in a
totally strange tongue. He is expected to answer questions, the sense of
which he cannot even guess, and to solve problems, every word and every
figure of which glares at him like a sphinx of evil omen. Sitting on
each side of him are pupils to whom this is merely play, and some of
whom could complete the whole of school mathematics within a few months
at express rate. This leads to a contrast between the pupils, which may
press with tragical force on the unfortunate member throughout his whole
school existence. That is why a reform is to be welcomed that sifts out
in time those who should be separated from the rest, and which adapts
the school curriculum as closely as possible to individual talents."

Einstein called my attention to the fact that this division had already
been made in many schools in foreign countries, as in France and in
Denmark, although not so exclusively as suggested by him. "Moreover," he
added, "I am by no means decided whether the torments that you mentioned
are founded primarily on absence of talent in the pupil. I feel much
more inclined to throw the responsibility in most cases on the absence
of talent in the teacher. Most teachers waste their time by asking
questions which are intended to discover what a pupil does _not_ know,
whereas the true art of questioning has for its purpose to discover what
the pupil knows or is capable of knowing. Whenever sins of this sort are
committed--and they occur in all branches of knowledge--the personality
of the teacher is mostly at fault. The results of the class furnish an
index for the quality of the preceptor. All things being taken into
consideration, the average of ability in the class moves, with only
slight fluctuations, about mean values, with which tolerably
satisfactory results may be obtained. If the progress of the class is
not up to this standard, we must not speak of a bad year but rather of
an inefficient instructor. It may be assumed that, as a rule, the
teacher understands the subject with which he is entrusted, and has
mastered its content, but not that he knows how to impart his
information in an interesting manner. This is almost always the source
of the trouble. If the teacher generates an atmosphere of boredom, the
progress is stunted in the suffocating surroundings. To know how to
teach is to be able to make the subject of instruction interesting, to
present it, even if it happens to be abstract, so that the soul of the
pupil resonates in sympathy with that of his instructor, and so that the
curiosity of the pupil is never allowed to wane."

"That is in itself an ideal postulate. If we assume it to be fulfilled,
how do you wish to see the subjects distributed in the curriculum?"

"We must leave the detailed discussion of this question for another
occasion. One of the main points would be the economy of time; all that
is superfluous, vexatious, and only intended as a drill must be
dropped. At present the aim of the whole course is the leaving
certificate. This test must be given up!"

"Is that serious. Professor? Do you wish to do away with the examination
for matriculation?"

"Exactly. For it is like some fearful monster guarding our exit from
school, throwing its shadow far ahead, and compelling teacher and pupil
to work incessantly towards an artificial show of knowledge. This
examination has been elevated by forcible means to a level which the
violently drilled candidates can keep only for a few hours, and is then
lost to sight for ever. If it is eliminated, it will carry away with it
this painful drilling of the memory; it will no longer be necessary to
hammer in for years what will be entirely forgotten within a few months,
and what deserves to be forgotten. Let us return to Nature, which
upholds the principle of getting the maximum amount of effect from the
minimum of effort, whereas the matriculation test does exactly the
opposite."

"Yes, but who is then to be allowed to enter the university?"

"Every one who has shown himself to be capable not only in a crucial
test of an accidental kind, but in his whole behaviour. The teacher will
be the judge of this, and if he does not know who is qualified, he again
is to be blamed. He will find it so much the easier to decide who is
sufficiently advanced to obtain a leaving certificate, in proportion as
the curriculum has weighed less on the minds of the young people. Six
hours a day should be ample--four at school and two for home-work; that
should be the maximum. If this should appear too little to you, I must
ask you to bear in mind that a young mind is being subjected to strain
even in leisure hours, as it has to receive a whole world of
perceptions. And if you ask how the steadily increasing curriculum is to
be covered in this very moderate number of hours, my answer is: Throw
all that is unnecessary overboard! I count as unnecessary the major part
of the subject that is called 'Universal History,' and which is, as a
rule, nothing more than a blurred mass of history compressed into dry
tables of names and dates. This subject should be brought within the
narrowest possible limits, and should be presented only in broad
outline, without dates having to be crammed. Leave as many gaps as you
like, especially in ancient history; they will not make themselves felt
in our ordinary existences. In nowise can I regard it as a misfortune if
the pupil learns nothing of Alexander the Great, and of the dozens of
other conquerors whose documentary remains burden his memory like so
much useless ballast. If he is to get a glimpse of the grey dawn of
time, let him be spared from Cyrus, Artaxerxes, and Vercingetorix, but
rather tell him something of the pioneers of civilization, Archimedes,
Ptolemy, Hero, Appolonius, and of inventors and discoverers, so that the
course does not resolve into a series of adventures and massacres."

"Would it not be expedient," I interrupted, "to take some of the history
time to branch off into an elementary treatment of the real evolution of
the state, including sociology and the legal code?"

Einstein does not consider this desirable, although he himself is deeply
interested in all manifestations of public life. He does not favour an
elementary political training received at school, presumably above all
owing to the fact that in this branch the instruction cannot be removed
from official influences, and because political questions require the
attention of a mature mind. His picture of how a youth is to meet the
requirements of modern life is something quite different, far removed
from all theories. His whole efforts are directed at finding a means of
counteracting the tendency to overburden one side of the youthful mind.
"I should demand the introduction of compulsory practical work. Every
pupil must learn some _handicraft_. He should be able to choose for
himself which it is to be, but I should allow no one to grow up without
having gained some technique, either as a joiner, bookbinder, locksmith,
or member of any other trade, and without having delivered some useful
product of his trade."

"Do you attach greater importance to the technique itself or to the
feeling of social relationship with the broad masses of the people which
it engenders?"

"Both factors are equally important to me," said Einstein, "and others
become added to these which help to justify my wish in this respect. The
handiwork need not be used as a means of earning money by the pupil of
the secondary school, but it will enlarge and make more solid the
foundation on which he will rest as an ethical being. In the first
place, the school is not to produce future officials, scholars,
lecturers, barristers, and authors, but human beings, not merely mental
machines. Prometheus did not begin his education of mankind with
astronomy, but by teaching the properties of fire and its practical
uses...."

"This brings to my mind another analogy," I continued, "namely, that of
the old _Meistersinger_, who were, all of them, expert smiths, tinkers,
or shoemakers, and yet succeeded in building a bridge to the arts. And
at bottom, the sciences, too, belong to the category of free arts. Yet,
a difficulty seems to me to arise. In demanding a compulsory handicraft,
you lay stress on practical use, whereas in your other remarks you
declared science in itself as being utterly independent of practice."

"I do this," replied Einstein, "only when I speak of the ultimate aims
of pure research, that is, of aims that are visible to only a vanishing
minority. It would be a complete misconception of life to uphold this
point of view and to expect its regulative effectiveness in cases in
which we are dealing only with the preliminaries of science. On the
contrary, I maintain that science can be taught much more practically at
schools than it is at present when bookwork has the upper hand. For
example, to return to the question of mathematical teaching: it seems to
me to be almost universally at fault, if only for the reason that it is
not built up on what is _practically_ interesting, what appeals directly
to the senses, and what can be seized intuitively. Child-minds are fed
with definitions instead of being presented with what they can grasp,
and they are expected to be able to understand purely conceptual things,
although they have had no opportunity given them of arriving at the
abstract by way of concrete things. It is very easy to do the latter.
The first beginnings should not be taught in the schoolroom at all, but
in open Nature. A boy should be shown how a meadow is measured and
compared with another. His attention must be directed to the height of a
tower, to the length of his shadow at various times, to the
corresponding altitude of the sun; by this means he will grasp the
mathematical relationships much more rapidly, more surely, and with
greater zeal, than if words and chalk-marks are used to instil into him
the conceptions of dimensions, of angles, or perchance of some
trigonometrical function. What is the actual origin of such branches of
science? They are derived from practice, as, for example, when Thales
first measured the height of the pyramids with the help of a short rod,
which he set up at the ultimate point of the pyramid's shadow. Place a
stick in the boy's hand and lead him on to make experiments with it by
way of a game, and if he is not quite devoid of sense, he will discover
the thing for himself. It will please him to have discovered the height
of the tower without having climbed it, and this is the first thrill of
the pleasure which he feels later when he learns the geometry of similar
triangles and the proportionality of their sides."

"In the matter of physics," pursued Einstein, "the first lessons should
contain nothing but what is experimental and interesting to see. A
pretty experiment is in itself often more valuable than twenty formulæ
extracted from our minds; it is particularly important that a young mind
that has yet to find its way about in the world of phenomena should be
spared from formulæ altogether. In his physics they play exactly the
same weird and fearful part as the figures of dates in Universal
History. If the experimenter is ingenious and expert, this subject may
be begun as early as in the middle forms, and one may then count on a
responsiveness that is rarely observable during the hours of exercise in
Latin grammar."

"This leads me," said Einstein, "to speak in this connexion of a means
of education that has so far been used only by way of trial in
class-teaching, but from an improved application of which I expect
fruitful results later. I mean the school cinema. The triumphal march of
the cinematograph will be continued into pedagogic regions, and here it
will have a chance to make good its wrongs in thousands of picture shows
in showing absurd, immoral, and melodramatic subjects. By means of the
school-film, supplemented by a simple apparatus for projection, it would
be possible firstly to infuse into certain subjects, such as geography,
which is at present wound off organ-like in the form of dead
descriptions, the pulsating life of a metropolis. And the lines on a map
will gain an entirely new complexion in the eyes of the pupil, if he
learns, as if during a voyage, what they actually include, and what is
to be read between them. An abundance of information is imparted by the
film, too, if it gives an accelerated or retarded view of such things as
a plant growing, an animal's heart beating, or the wing of an insect
moving. The cinema seems to me to have a still more important function
in giving pupils an insight into the most important branches of
technical industry, a knowledge of which should become common property.
Very few hours would suffice to impress permanently on the schoolboy's
mind how a power-station, a locomotive, a newspaper, a book, or a
coloured illustration is produced, or what takes place in an electrical
plant, a glass factory, or a gasworks. And, to return to natural
science, many of the rather difficult experiments that cannot be shown
by means of school apparatus may be shown with almost as great clearness
on a film. Taken all in all, the redeeming word in school-teaching is,
for me: an increased appeal to the senses. Wherever it is possible,
learning must become living, and this principle will predominate in
future reforms of school-teaching."

     *     *     *     *     *     *     *     *

University study was only touched on lightly during this talk. It has
become known that Einstein is a very strong supporter of the principle
of free learning, and that he would prefer to dispense entirely with the
regular documents of admission which qualify holders to attend lecture
courses. This is to be interpreted as meaning that as soon as anyone
desirous of furthering his studies has demonstrated his fitness to
follow the lecturer's reasoning by showing his ability in class
exercises or in the laboratory, he should be admitted immediately.
Einstein would not demand the usual certificate of "general education,"
but only of fitness for the special subject, particularly as, in his own
experience, he has frequently found the cleverest people and those with
the most definite aims to be prone to one-sidedness. According to this,
even the intermediate schools should be authorized to bestow a
certificate of fitness to enter on a course in a single definite subject
as soon as the pupil has proved himself to have the necessary ability.
If he earlier spoke in favour of abolishing the matriculation
examination, this is only an indication of his effort to burst open the
portals of higher education for every one. Nevertheless, I remarked
that, in the course of university work itself, he is not in favour of
giving up all regulation concerning the ability of the student--at
least, not in the case of those who intend to devote themselves to
instruction later. He does not desire an intermediate examination (in
the nature of the _tentamen physicum_ of doctors), but he considers it
profitable for the future schoolmaster to have an opportunity early in
his course to prove his fitness for teaching. In this matter, too,
Einstein reveals his affectionate interest in the younger generation,
whose development is threatened by nothing so much as by incapable
teachers: the sum of these considerations is that the pupil is examined
as little as possible, but the teacher so much the more closely. A
candidate for the teaching profession, who in the early stages of his
academic career fails to show his fitness, his individual _facultas
docendi_, should be removed from the university.

There can be no doubt but that Einstein has a claim to be heard as an
authority on these questions. There are few in the realm of the learned
in whose faces it is so clearly manifest that they are called to excite
a desire for knowledge by means of the living word, and to satisfy this
desire. If great audiences assemble around him, if so many foreign
academies open their arms to him to make him their own, these are not
only signs of a magnetic influence that emanates from the famous
discoverer, but they are indications that he is far famed as a teacher
with a captivating personality. Let us consider what this signifies in
his profession. Philosophers, historians, lawyers, doctors, and
theologians have at their disposal innumerable words which they merely
need to pronounce to get into immediate contact with their audiences. In
Einstein's profession, theoretical physics, man disappears; it leaves no
scope for the play of emotion; its implement mathematics--and what an
instrument it is!--bristles with formal difficulties, which can be
overcome only by means of symbols and by using a language which has no
means of displaying eloquence, being devoid of expression, emotion, and
regular periods. Yet here we have a physicist, a mathematician, whose
first word throws a charm over a great crowd of people, and who extracts
from their minds, so to speak, what, in reality, he alone works out
before them. He does not adhere closely to written pages, nor to a
scheme which has been prepared beforehand in all its details; he
develops his subject freely, without the slightest attempt at rhetoric,
but with an effect which comes of itself when the audience feels itself
swept along by the current. He does not need to deliver his words
passionately, as his passion for teaching is so manifest. Even in
regions of thought in which usually only formulæ, like glaciers, give
an indication of the height, he discovers similes and illustrations with
a human appeal, by the aid of which he helps many a one to conquer the
mountain sickness of mathematics. His lectures betray two factors that
are rarely found present in investigators of abstract subjects; they are
temperament and geniality. He never talks as if in a monologue or as if
addressing empty space. He always speaks like one who is weaving threads
of some idea, and these become spun out in a fascinating way that robs
the audience of the sense of time. We all know that no iron curtain
marks the close of Einstein's lecture; anyone who is tormented by some
difficulty or doubt, or who desires illumination on some point, or has
missed some part of the argument, is at liberty to question him.
Moreover, Einstein stands firm through the storm of all questions. On
the very day on which the above conversation took place he had come
straight from a lecture on four-dimensional space, at the conclusion of
which a tempest of questions had raged about him. He spoke of it not as
of an ordeal that he had survived, but as of a refreshing shower. And
such delights abound in his teaching career.

     *     *     *     *     *     *     *     *

It was the last lecture before his departure for Leyden (in May 1920),
where the famous faculty of science, under the auspices of the great
physicist Lorentz, had invited him to accept an honorary professorship.
This was not the first invitation of this kind, and will not be the
last, for distinctions are being showered on him from all parts of the
world. It is true that the universities who confer a degree on him
_honoris causa_ are conferring a distinction on themselves, but Einstein
frankly acknowledges the value of these honours, which he regards as
referring only to the question in hand, and not the person. It gives him
pleasure on account of the principle involved being recognized, and he
regards himself essentially only as one whom fate has ordained as the
personal exponent of these principles.

What this life of hustle and bustle about a scientist signifies is
perhaps more apparent to me, who have a modest share in these
conversations, than to Einstein himself, for I am an old man
who--unfortunately--have to think back a long way to my student days,
and can set up comparisons which are out of reach of Einstein. Formerly,
many years ago, but in my own time, there was an _auditorium maximum_
which only one man could manage to fill with an audience, namely, Eugen
Dühring, the noted scholar, who was doomed to remain a lecturer
inasmuch as he went under in his quarrels with confrères of a higher
rank. But before he made his onslaught against Helmholtz, he was
regarded as a man of unrivalled magnetic power, for his philosophical
and economical lectures gathered together over three hundred hearers, a
record number in those times. Nowadays, in the case of Einstein, four
times this number has been surpassed, a fact which has brought into
circulation the playful saying: One can never miss his auditorium;
whither all are hastening, that is the goal! To make just comparisons,
we must take account of the faithfulness of the assembled crowd, as well
as its number. Many an eminent scholar has in earlier times had reason
to declare, like Faust: "I had the power to attract you, yet had no
power to hold you." Helmholtz began regularly every term with a crowded
lecture-hall, but in a short time he found himself deserted, and he
himself was well aware that no magnetic teaching influence emanated from
him. There is yet another case in university history of a brilliant
personality who, from similar flights of ecstasy, was doomed to
disappointment. I must mention his name, which, in this connexion, will
probably cause great surprise, namely, Schiller! He had fixed his first
lecture in history at Jena, to which he was appointed, and had prepared
for an audience of about a hundred students. But crowd upon crowd
hustled along, and Schiller, who saw the oncoming stream from his
window, was overcome with the impression that there was no end to it.
The whole street took alarm, for at first it was imagined that a fire
had broken out, and at the palace the watch was called out--yet, a
little later in the course, there was a depressing ebb of the tide,
after the first curiosity had been appeased; the audience gradually
vanished into thin air, a proof of the fact that the nimbus of a name
does not suffice to maintain the interest between the lecturer's desk
and the audience.

I mentioned this example at the time when Einstein's gift for teaching
had gradually increased the number of his hearers to the record figure
of 1200, yet I did not on this occasion detect any inordinate joy in him
about his success. I gained the impression that he had strained his
voice in the vast hall. His mood betrayed in consequence a slight
undercurrent of irritation. In an access of scepticism he murmured the
words, "A mere matter of fashion." I cannot imagine that he was entirely
in earnest. It goes without saying that I protested against the
expression. But, even if there were a particle of truth in it, we might
well be pleased to find such a fashion in intellectual matters, one that
persists so long and promises to last. The world would recover its
normal healthy state if fashions of this kind were to come into full
swing. It is, of course, easy to understand on psychological grounds
that Einstein himself takes up a sort of defensive position against his
own renown, and that he occasionally tries to attack it by means of
sarcasm, seeing that he cannot find serious arguments to oppose it.

     *     *     *     *     *     *     *     *

Whether Einstein's ideas and proposals concerning educational reform
will be capable of realization throughout is a question that time alone
can answer. We must make it clear to ourselves that, if carried out
along free-thinking lines, they will demand certain sacrifices, and it
depends on the apportionment of these sacrifices as to what the next, or
the following, generation will have to exhibit in the way of mental
training.

An appreciable restriction will have to be imposed on the time given to
languages. It is a matter of deciding how far this will affect the
foundations that, under the collective term _humaniora_, have supported
the whole system of classical schools for centuries. The fundamental
ideas of reform, which, owing to the redivision of school-hours and the
economy of work, no longer claim precedence for languages, indicate that
not much will be left of the original Latin and Greek basis.

We have noticed above that Einstein, although he does not, in principle,
oppose the old classicism, no longer expects much good of it. But
nowadays the state of affairs is such that it is hardly a question of
supporting or opposing its retention in fragmentary form. Whoever does
not support it with all his power strengthens indirectly the mighty
chorus of those who are radically antagonistic to it. And it is a
remarkable fact that this chorus includes many would-be authorities on
languages who have influence among us because they are champions of the
cause of retaining languages.

They do not wish to rescue languages as such, but only the German
tongue; they point to the _humaniora_ of classical schools, or to
_Humanisterei_, as they call it, as the enemy and corrupter of their
language. In what sense they mean this is obvious from their articles of
faith, of which I should like to cite a few in the original words of one
of their party-leaders:

"Up to the time of the hazardous enterprise of Thomasius (who first
announced lectures in the German language in 1687) German scholars as a
body were the worst enemies of their own tongue.--Luther did not take
his models for writing German from the humanistic mimics who aped the
old Latins. In the case of many, including Lessing and Goethe, we
observe them making a definite attempt to shake themselves free from the
chaos of humanistic influences in Germany--The inheritance of
pseudo-learned concoctions of words stretches back to pretentious
humanism as do most of essential vices of learned styles.--The
far-reaching and lasting corruption of the German language by this
poisonous Latin has its beginnings in the humanism of the sixteenth
century."

And, quite logically, these heralds extend their attacks along the whole
academic front. For, according to their point of view, the whole army of
professors is deeply immersed in the language slime of the traditional
humanism of the Greeks and Latins. "The whole language evil of our
times," so these leaders say, "is at bottom due to scientists, who, in
the opinionated guise of a language caste, and without enriching our
conceptions in the slightest, seek by tinkling empty words to give us
the illusion of a new and particularly mysterious occult science, an
impression which is unfortunately often produced on ignorant minds....
However many muddy outlets official institutions and language
associations may purge and block up, ditch-water from ever new quagmires
and drains pours unceasingly into the stately stream of our language."

Thus the attack on the Latin and Greek language foundation in schools
identifies itself with the struggle against the academic world as a
whole, and a scholar who does defend the classical system of education
with all his might finds himself unconsciously drifting into the ranks
of the brotherhood which in the last instance is seeking his own
extermination.

This danger must not be under-estimated. It is just this peril, so
threatening to our civilization, that moves me to show my colours
frankly here. I am not a supporter of bookworm drudgery in schools, but
I feel myself impelled to use every effort in speech and writing to
combat the anti-humanists whose password, "For _our_ language," at root
signifies "Enemies of Science!"

We must put no weapons into their hands, and the only means to avoid
this is, in my opinion, to state our creed emphatically and openly after
the manner of almost all our classical writers.

This creed, both as regards language and substance, is to be understood
as being based on the efficacy of the old classical languages. It is the
luminous centre of the life and work of the men who caused Bulwer to
proclaim our country the country of poets and thinkers. The
superabundance of these is so excessive that it is scarcely fair to
mention only a few names such as Goethe, Lessing, Schiller, Wieland,
Kant, and Schopenhauer. Our literature would be of a provincial standard
and not a world possession if this creed had not asserted its sway at
all times.

If the question is raised as to where our youth is to find time for
learning ancient languages under the present conditions of crowded
subjects, the answer is to be furnished by improved methods of
instruction. My personal point of view is that even the older methods
were not so bad. Goethe found himself in no wise embarrassed through
lack of time in acquiring all sorts of knowledge and mental equipment,
although even as a boy of eight years he could write in Latin in a way
which, compared with the bungling efforts of the modern sixth-form boy,
seems Ciceronian. Montaigne could express himself earlier in Latin than
in French, and if he had not had this "Latin poison" injected into his
blood he would never have become Montaigne.

It seems to me by no means impossible that the cultured world will one
day in the distant future return to the once self-evident view of
classical languages, and indeed just for reasons of economy of time,
unless the universal language so ardently desired by Hebbel--not to be
confused with the artificial patchwork called Esperanto--should become a
reality. But even this language, at present Utopian, but one which will
help to link together the nations, will disclose the model of the
ancient languages in its structure. Scientific language of the present
day shows where the route lies; and this route will be made passable in
spite of all the efforts of Teutonic language saints and assassins of
humanism to block it.

The working out of ideas by research scientists leads to enrichment of
language. And since, as is quite natural, they draw copiously on antique
forms of expression, they are really the trustees of an instruction that
makes these expressions intelligible not merely as components of an
artificial language like Volapük but as organic growths. That is how
they proceed when they carry on their research, or describe it and
lecture on their own subject. But if they are to decide how the school
is to map out its course in actual practice, the problem of time again
becomes their chief consideration--that is, they feel in duty bound to
give preference to what is most important. Hence there results the wish
to reduce the hours apportioned to the language subjects as much as
possible.

On this matter we have a detailed essay by the distinguished Ernst Mach
mentioned earlier, who exposes the actual dilemma with the greatest
clearness. He treats this exceedingly important question in all its
phases, and arrives at almost the same conclusion as Einstein. At the
outset he certainly chants a Latin psalm almost in the manner of
Schopenhauer. Its lower tones represent an elegy lamenting that Latin is
no longer the universal language among educated people, as it was from
the fifteenth to the eighteenth century. Its fitness for this purpose is
quite indisputable, for it can be adapted to express every conception
however modern or subtle it may be.

What a profusion of new conceptions was introduced into science by Sir
Isaac Newton, to all of which he succeeded in giving correct and precise
Latin names! The natural inference suggests itself to us that young
people should learn the ancient classical tongues--and yet a different
result is coming about; the modern child is to be content with
understanding words with a world-wide currency, without knowing their
philological origin.

It is not necessary to be a schoolmaster to feel the inadequacy of this
proceeding. It is true that without knowing Arabic we can grasp the
sense and meaning of the word "Algebra," and in the same way we can
extract the essence of a number of Greek and Latin expressions without
digging at their etymological roots. But these expressions are to be
counted in hundreds and thousands, and are increasing daily, so that we
are put before the question whether, merely from the point of view of
time, it is practicable to learn them as individual foreign terms or as
natural products of a root language with which we have once and for all
become familiar.

It is scarcely necessary for me to point out that Einstein himself is
not sparing in the use of these technical expressions, even when he is
using popular language. He assumes or introduces terms of which the
following are a few examples: continuum, co-ordinate system,
dimensional, electrodynamics, kinetic theory, transformation, covariant,
heuristic, parabola, translation, principle of equivalence, and he is
quite justified in assuming that every one is fully acquainted with such
generally accepted expressions as: gravitation, spectral analysis,
ballistic, phoronomy, infinitesimal, diagonal, component, periphery,
hydrostatics, centrifugal, and numberless others which are diffused
through educated popular language in all directions. Taken all together
these represent a foreign realm in which the entrant can always succeed
in orientating himself when he receives explanations, examples, or
translations, whereas with a little preliminary knowledge of the ancient
languages he immediately feels himself at home with them; in this we
have not even taken into consideration the general cultural value of
this training in view of the access it gives to the old literature and
to Hellenic culture.

Perhaps I am going too far in adopting the attitude of a _laudator
temporis acti_ towards Einstein's very advanced opinion. We are here
dealing with a question in which nothing can be proved, and in which
everything depends on disposition and personal experiences. In my own
case this experience includes the fact that at a very early age, in
spite of the very discouraging school methods, I enjoyed the study of
Latin and Greek, and that I learned Horatian odes by heart, not because
I had to, but because they appealed to me, and finally that Homer opened
up a new world to me. When Einstein expresses his abhorrence of drill, I
agree with him; but these languages need not be taught as if we are on
parade. We see thus that it is a question of method and not of the
subject involved. Einstein gives the subject its due by recommending a
double series of classes. He allows the paths to diverge, giving his
special blessing to the group along the one without setting up obstacles
to prevent the other pilgrims from attaining happiness in their own way.

     *     *     *     *     *     *     *     *

We spoke of higher education for women, and Einstein expressed his views
which, as was to be expected, were tolerant, and yet did not suggest
those of a champion of the cause. It was impossible to overlook the fact
that in spite of his approval he had certain reservations of a
theoretical nature.

"As in all other directions," he said, "so in that of science the way
should be made easy for women. Yet it must not be taken amiss if I
regard the possible results with a certain amount of scepticism. I am
referring to certain obstacles in woman's organization which we must
regard as given by Nature, and which forbid us from applying the same
standard of expectation to women as to men."

"You believe, then, Professor, that high achievements cannot be
accomplished by women? To keep our attention on science, can one not
quote Madame Curie as a proof to the contrary?"

"Surely only as one proof of brilliant exceptions, more of which may
occur without refuting the statute of sexual organization."

"Perhaps this will be possible after all if a sufficient time for
development be allowed. There may be much fewer geniuses among the other
sex, but there has certainly been a concentration of talent. Or, in
other words, totally ignorant women have become much rarer. You,
Professor, are fortunate in not being in a position to compare young
women of to-day with those of forty or more years ago. This I can do,
and just as once I found it natural that there should be swarms of
little geese and peacocks, I never recover from my astonishment nowadays
at the amount of knowledge acquired by young womanhood. It requires a
considerable effort on my part very often to avoid being completely
overshadowed by a partner at dinner. The more this stratum of talent
increases, the more we have reason to expect a greater number of
geniuses from them in the future."

"You are given to prognostication," said Einstein, "and calculate with
probabilities which sometimes are lacking in foundation. Increased
education and even an increase of talents are quantitative assumptions
that make an inference regarding higher quality reaching to genius
appear very bold."--A passing look of ominous portent flashed over his
face, and I noticed that he was preparing to launch a sarcastic
aphorism. So it was, for the next words were: "It is conceivable that
Nature may have created a sex without brains!"

I grasped the sense of this grotesque remark, which was in no way to be
taken literally. It was intended as an amusing exaggeration of what he
had earlier called the reason for his failing expectation: the organic
difference which, being rooted in the physical constitution, had
somewhere to express itself on the mental plane, too. The soul of woman
strong in impulse shows a refinement of feeling of which we men are not
susceptible, whereas the greatest achievements of reason probably depend
on a preponderance of brain substance. It is this plus beyond the normal
amount that gives promise of great discoveries, inventions, and
creations. We can just as little imagine a female Galilei, Kepler, and
Descartes, as a female Michelangelo or Sebastian Bach. But when we think
of these extreme cases, let us also recall the balance on the other
side: although a woman could not create the differential calculus, it
was she that created Leibniz; similarly she produced Kant if not the
Critique of Pure Reason. Woman, as the author of all great minds, has at
least a right of access to all means of education and to all advancement
that is proffered by universities. And in this connexion Einstein
expressed his wish clearly enough.

     *     *     *     *     *     *     *     *

One of the most discussed themes in matters touching school education is
at the present time: "the selection of gifted pupils." It has developed
into a principle that is generally recognized by the great majority, the
only point of disagreement being in respect to the number that is to be
selected.

The idea running through it is that derived from Darwin's theory of
selection: man completes the method of selection practised by Nature. He
sifts and chooses, and allows those that are more talented to come to
the fore more rapidly and more decidedly; he favours their advancement
and makes easy their ascent.

This principle has really always been in existence. It started with the
distribution of prizes in ancient Olympia and reaches to the present-day
examinations that are clearly intended as a means of selecting talents.
A greater discrimination based on a systematic search for talents was
reserved for our own day.

It was scarcely a matter of doubt to me what attitude Einstein would
take up towards this matter. I had already heard him say hard words
about the system of examinations, and knew his leaning towards allowing
each mind to develop its power freely and naturally.

In effect, Einstein declared to me that he would hear nothing of a
breeding of talents in a sort of sporting way. The dangers of the
methods of sport would creep in and lead to results that had only the
appearance of truth. From the results so far obtained it was impossible
to come to a final decision about it. Yet it was conceivable that a
selective process conducted along reasonable lines would in general
prove of advantage in education, particularly in the respect that many a
talent that would ordinarily become stunted owing to its being kept in
darkness would now have an opportunity of coming to light.

This resolved itself into a talk bearing on many questions, and of which
I should like to state the main issue here. It was specially intended to
make clear the gambling method that Einstein repudiates, and the danger
of which seems still more threatening to me than to him.

If certain pedagogues, whose creed is force, were to have their way, the
"most gifted" pupils would be able, or would be compelled, to rush
through school at hurricane speed, and, at an age at which their fellows
were still spending weary hours at their desks, they would have to
clamber to the topmost branches of the academic tree. All things are
possible, and history even furnishes cases of such forced marches.
Luther's friend Melanchthon qualified at the age of thirteen to enter
the University of Heidelberg, and at the age of seventeen he became a
professor at Tübingen, where he gave lectures on the most difficult
problems of philosophy, as well on the Roman and Greek writers of
classical antiquity. This single instance need only be generalized, and
we have the new ideal rising up before our astonished gaze: a race of
professorial striplings whose upper lips are scarcely darkened with the
down of youth! It is a mere matter of making an early discovery of the
most gifted, and then raising the scaffolding up which the precocious
know-alls can climb as easily as possible.

[Interposed query: Where are these discoverers of talent, and how do
they prove their own talent? There was a good opportunity for them in a
case which I must here mention. Einstein told me in another connexion
that, as early as 1907, that is, when he was still very young in years,
he had not only succeeded in successfully representing the Principle of
Equivalence, one of the main supports of the General Principle of
Relativity, but had even published it; yet it made not the slightest
impression on the learned world. No one suspected the far-reaching
consequences, and no one pointed out this flaming up of a new talent of
the highest order. And just as this was able to remain concealed from
the learned Areopagus of the world at that time, so a similar lack of
understanding may easily be possible on a smaller scale at school. We
know actually that among the recognized great men of science, there were
many who did only moderately well at school; as, for example, Humphry
Davy, Robert Mayer, Justus Liebig, and many others. Wilhelm Ostwald goes
so far as to affirm: "Boys ordained to be discoverers later in life
have, almost without exception, been bad at school! It is just the most
gifted young people who have resisted most strongly the form of
intellectual development prescribed by the school! Schools never cease
to show themselves to be the bitter, unrelenting enemies of genius!"--in
spite of all efforts at selection which have always been in vogue in the
guise of advancement into higher forms.]

But the new mode of selection is intended to prevent mistakes and
oversights. Is this possible? Do not the traces of previous attempts
inspire distrust? There was once a very ideal selection that had to
stand the test of one of the most eminent bodies in existence, the
French Academy. Its duty was to discover geniuses on an incomparably
higher plane. It, however, repudiated or overlooked: Molière,
Descartes, Pascal, Diderot, the two Rousseaus, Beaumarchais, Balzac,
Béranger, the Goncourts, Daudet, Emile Zola, and many other extremely
gifted people, whom it should really have been able to find.

The only true, and at the same time necessary as well as sufficient,
breeding is carried out by Nature herself in conjunction with social
conventions, which promise the more success the less they assume the
character of incubators and breeding establishments. If you wish to
apply tests to discover pupils of genius in any class, examine as much
as you like, excite interest and ambition, distribute prizes even, but
not for the purpose of separating at short intervals the shrewd and
needle-witted heads from the rest; and do not lose sight of the fact
that among those who appear as the sheep as a result of these
systematized tests to discover ingenuity there are many who, ten or
twenty years later, will take up their positions as men of eminent
talent.

There is no essential difference between the forced promotion of such
pupils and the breeding of super-men according to Nietzsche's recipe as
exemplified by his Zarathustra.

Assuming that super-men are justified in existing at all, they will come
about of themselves, but cannot simply be manufactured. Workmen, taken
as a class, represent super-men more definitely than an individual such
as Napoleon or Cæsar Borgia. So the "super-scholar" exists perhaps
already to-day, not as an individual phenomenon, but as a whole,
representing his class. Whoever has had experience in these things will
know that nowadays there are difficult subjects in which it is possible
to apply to pupils of fifteen years of age tests that are far above the
plane of comprehension of pupils of the same age in former times,
provided that the average is considered, that no accidental or
artificial separation has occurred, that no pretentiously witty
questions have had to be answered, and that there has been no systematic
and inquisitive search for talent.

Let us rest satisfied if we find that the sum-total of talent is
continually on the increase. On the other hand, it is by no means proved
that we are doing civilization a service by persisting in the impossible
project of abolishing from the world the struggle for existence
prescribed by Nature. It is an elementary fact, and one that is easy to
understand, that many talents perish unnoticed. On the other hand,
observe the long list of eminent men who fought their way upwards out of
the lowest stages of existence only to recognize that the difficulties
that have been overcome are mostly necessary accompaniments of talent,
that is, that Nature's way of selection is to oppose obstacles and raise
difficulties in order to test their powers. In the case of the poor
lens-grinder Spinoza and many others ranging to Béranger, who was a
waiter, what a chain of desperate experiences, yet what triumphs!
Herschel, the astronomer, was too poor to buy a refracting telescope,
and it was just this dispensation of poverty that made him succeed in
constructing a reflecting type composed of a mirror. Faraday, the son of
a blacksmith without means, made his way for years as a bookbinder's
apprentice. Joule, one of the founders of the mechanical theory of heat,
started as a beer-brewer. Kepler, the discoverer of the planetary laws,
was descended from a poverty-stricken innkeeper. Of the members in
Goethe's circle, Jung-Stilling, of whom Nietzsche was so fond, was a
tailor's apprentice; Eckermann, Goethe's intimate associate, was a
swine-herd, and Zelter was a mason. We could add many recent names to
this list, and very many more if we continue the line backwards to
Euripides, whose father was a publican and whose mother was a vendor of
vegetables. This might serve as a basis for many reflections about the
"upward course of the talented," and about its less favourable reverse
side. For one might put the apparently paradoxical question whether a
soaring career for many or all talents is a necessity for our
civilization, or whether it would not be better to have a substratum
interspersed with talent, to cultivate a mossy undergrowth which is to
serve as nourishment for the blooming plants of the upper layer.

Maximum is not equivalent to optimum, and we learned elsewhere that
Einstein is far removed from identifying them. In the previous case it
was a question of the problem of population; and in the course of the
discussion he mentioned that we are subject to an old error of
calculation when we regard it as a desirable aim to have a maximum
number of human beings on the earth. It seems, indeed, that this false
conclusion is already in process of being corrected. A beginning is
being made with new and very active organizations and unions whose
programme is to reduce the number so that an optimum may be attainable
by those left.

If we extend this line of reasoning still further, we arrive at the
depressing question whether too much might not be done for talent, not
only as regards breeding it, but also in favouring the greatest number.
It is quite possible that in doing so, we might overlook, or take
insufficient account of the harm that might be done to the lower
stratum, in that we should be depriving it of forces which, according to
the economy of Nature, should remain and act in concealment.

This fear, as here expressed, is not shared by Einstein. However
brusquely he repudiates breeding, he speaks in favour of smoothing the
way for talent. "I believe," he said, "that a sensible fostering of
gifts is of advantage to humanity generally and prevents injustice being
done to the individual. In great cities which give such lavish
opportunities of education, this injustice manifests itself less often;
but it occurs so much the more in rural districts, where there are
certainly many cases of gifted youths who, if recognized as such at the
right age, would attain to an important position, but who, together with
their gifts, become stunted, nay, go to ruin, if the principle of
selection does not penetrate to their circle."

This brings us to the most difficult and most dangerous point. The
spectre of responsibility is rapping at the portals of society, and is
reminding us insistently that it is our duty to see that no injustice be
done to any talent that may be among us. And this duty is but little
removed from the demand that it should be disburdened of the worries of
daily life, for, so the moral argument runs, talent will ripen the more
surely the less it has to combat these ceaseless disturbances of
ordinary life.

But this thesis, so evident on moral grounds, will never be proved
empirically. On the contrary, we have good reason to suppose that
necessity, the mother of invention on the broader scale, will often in
the case of the individual talent prove to be the mother of its best
results. Goethe required for his development an unchallenged life of
ease, whereas Schiller, who never emerged from his life of misery, and
who, up to the time when he wrote _Don Carlos_, had not been able to
earn sufficient with his pen to buy a writing-desk, required distress to
make his genius burst into flower. Jean Paul recognized this blessing of
gloomy circumstances when he glorified poverty in his novels. Hebbel
followed him along this path by saying that it is more fruitful to
refuse the most talented person the necessities of life than to grant
them to the least gifted. For among a hundred who have been chosen by
the method of sifting, there will be only one on the average who will
receive the certificate of excellence in the test of future generations,
for the latter use entirely different methods of sifting from that
practised by a committee of examiners who expect ready answers to
prepared questions.

This projects us on to the horns of a severe dilemma that scarcely
allows of escape. The consciousness of duty towards the optimum
expresses itself only in a maximum of assistance, and overhears the
whispered objection of reason that Nature has also coarser means at her
disposal to attain her ends; in her own cruelty of selection she often
enough proves the truth of Menander's saying, which, freely translated,
says: to be tormented is also part of man's education. The fact that
Einstein--with certain reservations--favours the giving of help to the
selected few, it is for me a proof, among many others, of his love
towards his fellow-men, which fills his heart absolutely, all questions
of relativity notwithstanding.




CHAPTER V

THE DISCOVERER

Relation of Discovery and Philosophy in History.--The Absolute and the
Relative.--The Creative Act.--Value of Intuition.--Constructive
Activity.--Invention.--The Artist as Discoverer.--Theory and
Proof.--Classical Experiments.--Physics in Primitive Ages.--_Experimentum
Crucis_.--Spectral Analysis and Periodic System.--The Rôle of
Chance.--Disappointed Expectations.--The Michelson-Morley Experiment
and the New Conception of Time.


NEXT time--so one of our talks ended--next time, as you insist on it, we
shall talk of discovery in general. This, was a promise of special
import for me, for it meant that I was to draw near to a fountain-head
of instruction, and to have an opportunity of hearing the pronouncements
of one whose authority could scarcely be transcended.

We are precluded from questioning Galilei personally about the
foundations of Mechanics, or Columbus about the inner feelings of a
navigator who discovers new lands, or Sebastian Bach about the merits of
Counterpoint, but a great discoverer lives among our contemporaries who
is to give us a clue to the nature of discovery. Was it not natural that
I should feel the importance of his acceptance of my proposal?

Before meeting him again I was overwhelmed with ideas that arose in me
at the slightest echo of the word "discovery" in my mind. Nothing, it
seemed to me, could be higher: man's position in the sphere of creation
and the sum of his knowledge can be deduced from the sum of his
discoveries which find their climax in the conceptions civilization and
philosophy, just as they are partly conditioned by the philosophy of the
time. We might be tempted to ask: which of these two precedes, and which
follows? And perhaps the ambiguous nature of this question would furnish
us with the key to the answer. For, ultimately, these two elements
cannot at all be resolved into the relationship of cause and effect,
antecedent and consequent.

Neither is primary, and neither secondary: they are intimately
interwoven with one another, and are only different aspects of one and
the same process. At the root of this process is our axiomatic belief
that the world can be comprehended, and the indomitable will of all
thinking men, acting as an elementary instinct, to bring the perceptual
events in the universe into harmony with the inner processes of thought.
This impulse is eternal; it is only the form of these attempts to make
the world fully intelligible that alters and is subject to the change of
time. This form finds expression in the current philosophy which brings
each discovery to fruition, just as philosophy bears in itself
constituents of the ripe discovery.

It seemed to me that even at this stage of my reflections I was
somewhere near interpreting Einstein's intellectual achievement. For his
principle of relativity is tantamount to a regulative world-principle
that has left a mighty mark in the thought of our times. We have lived
to see the death of absolutism; the relativity of the constituents of
political power, and their mutability according to view-point and
current tendencies, become manifest to us with a clearness unapproached
by any experience of earlier historical epochs. The world was far enough
advanced in its views for a final achievement of thought which would
demolish the absolute also from the mathematico-physical aspect. This is
how Einstein's discovery appeared as inevitable.

Yet a shadow of doubt crossed my mind. Einstein's discoveries came to
light in the year 1905--that is, at a time when hardly a cloud was
visible to forewarn us of the storms which were to uproot absolutism in
the world. But what if a different kind of necessity had imposed itself
on world-history, and hence on the world-view? Nowadays we know from
authentic accounts, which no one doubts, that all that we have
experienced during the war and the revolution has hung upon the
activities of one frail human being of quite insignificant exterior, a
bureaucrat of the Wilhelm-Strasse, a choleric eccentric who succeeded in
frustrating the Anglo-German alliance which was unceasingly being
pressed upon us for six long years after the beginning of the century.

Amid the noisy progress of universal evolution the secret and
insignificant nibbling of a mole cannot be regarded as of momentous
importance for history, and yet if we eliminate it from the complete
picture of events we find as a result that all our experiences have been
inverted. Absolutism would not have been thrown overboard, but would
probably have kept the helm with greater mastery than ever as the
exponent of an Anglo-German hegemony of the world, and a political
outlook fundamentally different in tendency would now have been
prevailing on the earth.

But Einstein's Theory of Relativity would not have taken the slightest
heed of this. It would have arisen independently of the current forms of
political conceptions, simply because we had reached that point in our
intellectual development and because Einstein was living and spinning
his webs of thought. And the question whether his theory will also have
crushed absolutism for the non-physicist cannot be answered.

It may indeed be doubted whether its time had already come. In the case
of many important events in the history of thought their moment of birth
can be fixed to within about ten years, as for example the Theory of
Evolution, which had been conceived in several minds at the same time
and had of necessity to come to life in one of them, even if it had
failed in the case of the others. I venture to say that without
Einstein, the Theory of Relativity in its widest sense, that is,
including the new doctrine of gravitation, would perhaps have had to
wait another two hundred years before being born.

This contradiction is cleared up if we use sufficiently great time
intervals. History does not adapt itself to the time measures of
politics and of journalism, and philosophies are not to be calculated in
terms of days. The philosophy of Aristotle held sway right through the
Middle Ages, and that of Epicurus will gain its full force only in the
coming generation. But if we make our unit a hundred years the connexion
between philosophies and great discoveries remains true.

Whoever undertakes to explore the necessity of this connexion cannot
evade the fact that the lines of the result had been marked out in the
region of pure thought, as can be proved, before even the great
discovery or invention was able to present it in a fully intelligible
form. Even the achievement of Copernicus would follow this general rule
of development: it was the last consequence of the belief in the Sun
Myth which had never been forsaken by man in spite of the violent
efforts of the Church and of man himself to force the geocentric view.
Copernicus concentrated what had survived of the wisdom of the earliest
priests--which includes also the germ of our modern ideas of energy and
electricity--of the teachings of Anaxagoras and the Eleatics which had
remained latent in our consciousness: his discovery was the
transformation of a myth into science. Mankind, whose wandering fancy
first feels presentiments, then thinks and wishes to know, is a large
edition of the individual thinker. The latter sees further only because
he, so to speak, stands on the shoulders of a sum-total of beings with a
world-view.

Let us turn our attention to an example from the most recent history of
philosophy and discovery. The absolute continuity of events was one of
the generally accepted canons of thought, and is even nowadays taught by
serious philosophers as an incontrovertible element in our knowledge.
The old quotation _Natura non facit saltus_, popularized by Linné, is
one of the formulae of this apparently invincible truth. But deep down
in the consciousness of man there has always been an opposition to it,
and when the French philosopher Henri Bergson set out to break up this
line of continuity by metaphysical means in ascribing to human knowledge
an intermittent, cinematographic character, he was proclaiming in an
audible and eloquent form only what had lain latent in a new but as yet
incomplete philosophy. Bergson made no new "discovery," he felt his way
intuitively into a new field of knowledge and recognized that the time
was ripe for the real discovery. This was actually presented to us in
our day by the eminent physicist Max Planck, the winner of the Nobel
Prize for Physics in 1919, in the form of his "Quantum Theory." This is
not to be taken as meaning that a revolutionary philosophy and a triumph
of scientific research now become coincident, but only that a
discontinuous, intermittent sequence, an atomistic structure, was proved
by means of the weapons of exact science, to be true of energies which,
according to current belief, were expected to be radiated regularly and
connectedly. This was probably not a case of the accidental coincidence
of a new philosophical view with the results of reasoning from physical
grounds, but a demand of time, exacting that the claims of a new
principle of thought be recognized.

As above suggested, it is more difficult to find a link between
Einstein's discoveries and antecedent presentiments of relativity. For a
mere reference to the downfall of absolutism in the world of human
events will not suffice. In the case of Einstein, we see such a
tremendous rush of thought in one being that we almost feel compelled to
recognize an analogy with the Quantum Theory and believe in a
discontinuity in the course of intellectual history. Yet there are
certainly threads that connect Einstein's achievement with a prophetic
insight. In this case, however, we must spread out over centuries what
in the case of other discoveries extends, in comparison, only over
decades. That doubt of Faust, which troubles the spirit of every
thinker: "whether in yonder spheres there is also an Above and a Below,"
and which goes back as far as Pyrrhon and Protagoras, is itself
relativistic; it expresses doubt whether the co-ordinate system passing
through our own lifes as centres is valid. It is ultimately a matter of
point of view, and the mathematico-physical consequences of the endless
series of questions, and the relation, which arises from the couple,
Above-Below, probably leads to a new mode of comprehending the
constitution of the world, for which Einstein's creative work found the
adequate expression in abstract terms. And from this point onwards, in
accordance with the principle of reciprocal action, a new stream of
knowledge will pour itself into the hazy stretches of philosophy. A
fundamental and radical reform of our philosophy seems inevitable,
particularly with respect to our conceptions of Space and Time, perhaps,
too, even with respect to Infinity and Causality. Much dross will have
to be sifted out of our old categories of thought and out of our world
wisdom, which once served as material for fine structures. What will the
finer ones look like that are to take their places in obedience to the
command of physics? Who would care to take it upon himself to form an
estimate?

Much will be uprooted, and it is possible that even the defiant
"ignorabimus," the antipole of the search for truth from Pyrrhon to
Dubois, will again take up the cudgel. For in the face of despairing
uncertainty there is the one certainty: what cannot be comprehended is
being encircled more and more by the great discoverers! And even if the
absolute point of convergence can never be reached, there is within our
reach at least another point which is a haven of rest in the passing
stream of philosophies, namely, a moral centre around which eddies of
happiness circle. At the heart of this world-view there is the uplifting
belief in an advance of knowledge in spite of all, and a belief in the
vanishing of age-long problems and difficulties under the flood of
discoveries. And even if afterwards and concurrently ever new problems
and difficulties arise, these do not suppress our feeling of triumph.
Every achievement in this field gives us a sense of enfranchisement from
prejudices, not the least of which is narrowness of national outlook.
Not only do discoverers construct bridges of thought that stretch to
astronomical distances, but, what is more difficult, they build bridges
for our feelings, that surmount political obstacles. Every thinking
being who plays a part in the making of some great discovery and who,
with deepened vision, bows before a new achievement of mind, gradually
becomes a disciple of the religion of universal politics, the creed of
which is faith in the brotherhood of thought. The nucleus of a
philosophy that belongs to the future is the recognition that differing
national view must be compounded into a unity, and that every great
discovery means a step towards attaining this end.

Even if we accept Pascal's wonderful dictum that human knowledge is
represented by a sphere which is continually growing and increasing its
points of contact with the unknown, we must not interpret it as a sign
of despair. It is not the enlargement of the unknown, but only that of
knowledge that stirs our feelings with ethical forces. The positive
calls up in us a living force by inspiring in us the feeling that the
sphere of knowledge is destined to grow, and that there can be no higher
duty for all the energies of mind than to obey the call for combined
action towards this growth which will bring the world into harmony.

Full of such reflections I entered the home of the great discoverer,
whose activities unceasingly hovered before my vision as ideal examples
of creative effort. I discovered him, as almost always, seated before
loose sheets of paper which his hand had covered with mathematical
symbols, with hieroglyphics of that universal language in which,
according to Galilei, the great book of Nature is written.

What a very different picture many an outsider draws of the manner in
which a seeker in the heavens works! He is imagined like Tycho Brahe to
be surrounded by unusual pieces of apparatus, spying through the ocular
of a long range refractor into the universe, seeking to unravel its
ultimate secrets. The true picture does not correspond to this fancy in
the slightest. Nothing in the make-up of the room reminds one of
super-earthly sublimity, no abundance of instruments or books is to be
seen, and one soon becomes aware that here a thinker reigns whose only
requirement for his work, which encompasses the world, is his own mind,
plus a sheet of paper and a pencil. All that acts on the observatories
outside, that gives rise to great scientific expeditions, that, indeed,
ultimately regulates the relationship of mankind to the constitution of
the universe, the revolution in the knowledge of things connecting
heaven and earth, all this is here concentrated in the simple figure of
a still youthful scholar, who spins out endless threads from the fabric
of his mind: the words of a poet are recalled to our memory, which,
addressed to all of us, have been fulfilled to the last degree by one
living among us:--


   "Whereso thou roamest in space, thy Zenith and Nadir unite thee--
    This to the heavenly height, that to the pole of the world,--
    Whatsoever thou do, let thy will mount up into Heaven--
    But let the pole of the world still o'er thine actions preside."

                            (Schiller: _Translation by Merivale_.)


And this one helped to fulfil this aim and I must break off his thread
of thought to put the question: What is Discovery, and what does it
signify?

It is a purely abstract question that may appear to many to be devoid of
content. Such will repeat to themselves, as best they can, the list of
discoveries and think a man makes a discovery when he finds out
something important, such as the Laws of Falling Bodies, the formation
of Rainbows, or the Origin of Species: a general denomination may be
found for it perhaps only by ascribing to Discovery something requiring
a powerful mind, a creative genius.

At first it staggered me to hear Einstein say: "The use of the word
'Discovery' in itself is to be deprecated. For discovery is equivalent
to becoming aware of a thing which is already formed; this links up with
proof, which no longer bears the character of 'discovery' but, in the
last instance, of the means that leads to discovery." He then stated at
first in blunt terms, which he afterwards elaborated by giving detailed
illustrations: "Discovery is really not a creative act!"

Arguments for and against this view flashed through my mind, and I
thought involuntarily of a great master of music who, when he was asked:
"What is Genius?" answered: "A genius is one to whom ideas occur." This
parallel might be carried still further, for I have repeatedly heard
Einstein call "ideas" what we would regard as wonderful thoughts. Does
not the philosopher Fritz Mauthner speak of the discovery of gravitation
as being an "aperçu" of Newton; yes, in the sense of _aperçus_ as
applied in ancient Greek philosophy, and which included almost
everything that was left by Pythagoras, Heraclitus, etc., as a token of
their genius. On the other hand, we are all possessed of the desire to
differentiate clearly between an idea and a creative act of thought, as
occurs in Grillparzer's aphorism: "An idea is not a thought; a thought
knows its bounds, whereas the idea leaps over them and succeeds in
accomplishing nothing!"

Here, then, we must revise our view. We know, for example, how much
Einstein's "ideas," felt by him to be such and named so accordingly,
accomplished. Let us hear how he characterizes in a few words his own
"idea" which shook the world:

"The underlying thought of relativity," he said, in connexion with this
question, "is that there is physically no unique (specially favoured)
state of motion. Or, more exactly, among all states of motion there is
none that is favoured in the sense that, in contradistinction to the
others, it may be said to be a state of rest. Rest and Motion are not
only by formal definition but also by their intrinsic physical meaning
_relative conceptions_."

"Well, then," I interposed, "surely this was a creative act! This first
flashed across _your_ mind, Professor; it represents your discovery, so
that we may well let the word retain the meaning usually associated with
it!"

"By no means," answered Einstein, "for it is not true that this
fundamental principle occurred to me as the primary thought. If this had
been so perhaps it would be justifiable to call it a "discovery." But
the suddenness with which you assume it to have occurred to me must be
denied. Actually, I was lead to it by _steps_ arising from the
_individual_ laws derived from experience."

Einstein supplemented this by emphasizing the conception "invention,"
and ascribed a considerable importance to it: "Invention occurs here as
a constructive act. This does not, therefore, constitute what is
essentially original in the matter, but the creation of a method of
thought to arrive at a logically coherent system ... the really valuable
factor is _intuition_!"

I had thought, long and intently, about these theses to discover as
nearly as possible what distinguished their content from the usual view.
The fundamental differences suggest an abundance of ideas whose
importance grows in value as we apply them to various cases as
illustrations. And I feel convinced that we shall yet have to occupy
ourselves with these words of Einstein, which present themselves as a
confession, as with the famous "hypotheses non fingo" that Newton set up
as the idea underlying his work.

The latter as well as the former implies something negative: it denies
something. In Einstein's words there is apparently a repudiation of the
really creative act in discovery; he lays stress on the gradual,
methodical constructive factors, not omitting to emphasize intuition.
There is no other course open to us but to seek indirectly a synthesis
of these conceptions, and to eliminate what is apparently contradictory
in them.

I consider this possible if we decide to subdivide the discovery into a
series of individual acts in which succession takes the place of
instantaneous suddenness The creative factor may then remain intact;
indeed, it attains a still higher degree of importance if we imagine to
ourselves that a series of creative ideas must be finked together to
make possible a single important discovery.

The original idea never springs fully equipped and armed like Minerva
out of the head of its creator. And it is wise to bear in mind that even
Jupiter had to suffer in his head a period of pregnancy accompanied with
great pain. It is only in the after-picture that Pallas Athene appears
with the attribute of suddenness. It is the nature of our myth-building
imagination to leap over the actual act of birth so as to give a more
brilliant form to the finished creation.

We feel great satisfaction when we learn that Gauss, the Prince of
Mathematicians, declared in one of his valuable flashes of insight: "I
have the result, only I do not yet know how to get to it." For in this
utterance we see above all that he emphasizes a lightning-like
intuition. He has possession of a thing, which is, however, not yet his
own, and which can only become his own when he has found the way to it.
Is this contradictory? From the point of view of elementary logic,
certainly; but methodologically, by no means. Here it is a question of:
_Erwirb es um es zu besitzen_! This makes necessary a series of further
intuitions along the road of invention, and of construction.

This is, then, where that phase commences, which Einstein denotes by the
word "gradual," or "by steps." The first intuition must be present; its
presence as a rule usually guarantees that further intuition will follow
in logical sequence.

This does not always happen. In passing, we discussed several special
cases from which particular inferences may be drawn. The powerful
mathematician Pierre Fermat has presented the world with a theorem of
extremely simple form which he discovered, a proof of which is being
sought even nowadays, two and a half centuries after he stated it. In
easy language, it is this: the sum of two squares may again be a square,
for example, 5^2 + 12^2 = 13^2, since 25 + 144 = 169; but the sum of two
cubes can _never_ be a cube, and, more generally, as soon as the exponent,
the power index _n_, is greater than 2, the equation _x_^_n_ + _y_^_n_ =
_z_^_n_ can never be satisfied by whole number values for _x_, _y_, and
_z_; it is impossible to find three whole numbers for _x_, _y_, and _z_,
which, when substituted in the equation, give a correct result.

This is certainly true; it is an intuitive discovery. But Fermat's
assertion that he possessed a "wonderful proof," is for very good
reasons open to contradiction. No one doubts the absolute truth of the
theorem. But the later inspiration, the next step after the intuition,
has occurred neither to Fermat nor to anyone else. It cannot be
established whether his remark about the proof was due to a subjective
error, or was baseless. In any case it seems probable that Fermat had
arrived at the result _per intuitionem_ without knowing the way to it.
His creative act stopped short; it was only a first flare of a
conflagration, and did not fulfil the condition that Einstein associates
with the conception of a logically complete method.

We may, indeed, pursue this case of Fermat still further. He had
enunciated another theorem, again _per intuitionem_, namely, that it was
possible to construct prime numbers of any magnitude by a formula he
gave. Euler later showed by a definite example that the theorem was
false. It was stated in a letter to Pascal written in 1654 in the words:
the result of squaring 2 continuously and then adding 1 must in each
case be a prime number, that is, 2^(2^_k_) + 1 must always be a prime no
matter what value _k_ may have. Fermat added: "This is a property for
the truth of which I answer." Euler chanced to try _k_ = 5, and found
that 2^32 + 1 = 4,294,967,297, which may be represented as the product
of 641 and 6,700,417, and hence is not a prime.

It is conceivable that no Euler might have lived, and that no one else
might have discovered this contradiction. What would then have been the
position of this "discovery" of Fermat?

We should certainly not have disputed its creative character, for we
should have said that it corresponds to a fact which is fully formed,
but cannot be proved. But now that we know that the fact does not exist
at all, the tiling assumes a different colour. It was not a discovery at
all, but an erroneous conjecture. But one would never be able to arrive
at an erroneous conclusion of this sort without being a mathematical
genius, and having the inspiration of the moment. And from this again it
follows that to make a discovery in the full sense of the word the
intuition of the moment does not suffice, but must be supported by a
series of intuitions, and this is the condition that it become a
permanent component of universal truth.

The fact that Einstein refers to the action of "inventing" in his
explanation, gives support, it seems to me, to the view that, strictly
speaking, discovering and inventing are never to be regarded as being
separable. In discovering, what has to be constructed persists, and in
inventing, it is a question of finding the path along which there is the
promise of success, be it by a method, a proof, or by some general work.
We spoke of works of art, and I was delighted to see that Einstein was
by no means disinclined to claim certain works of pure thought, which
are usually placed in the category of scientific discovery, as works of
art. In the latter, however, the pure process of invention plays the
prominent part, for in them something is represented that did not exist
at all before; this has repeatedly led to the artist's achievement being
given the higher rank, as being properly and exclusively creative. The
argument runs somewhat along these lines: the infinitesimal calculus
would certainly have been discovered even if there had been no Newton
and no Leibniz, but without Beethoven we should never have had a C Minor
Symphony, and never in the future would it have appeared, for it was a
subjective, absolutely personal, and unique product of its creator.

I believe this may be admitted, and that we may nevertheless retain the
view that in the work of art, too, the act of discovering is to be
found. Let us consider for a moment the elementary substance of the
first movement of this fifth symphony, a colossal movement of 500 bars,
which expresses itself quite definitely in four notes, of which one is
repeated three times. "Thus Destiny thunders at the gates" is
Beethoven's motto for this section; it is expressed tonally in a
succession of notes which through all eternity existed among the
possible permutative arrangements of these sounds.

Beethoven, so it is expressed, invented it. But it is just as correct to
say--in Einstein's words--"he became aware of what was already
formed"--that is, he "discovered" the fundamental theme, and afterwards
"proved it" in terms of musical logic unheard-of beauty in a methodical
elaboration. We may, indeed, go further still. This _motif_ of four
tones was not only extant as an abstractum, as a possible mathematical
arrangement, but also as something natural. Czerny, a pupil of
Beethoven, to whom the master confided many a remark about the origin of
his compositions, reports that a bird, the yellow-hammer, had sung this
theme to Beethoven in the woods. But neither the bird nor any other
living creature had invented it; rather what could not be created,
because it had always been in existence, became objectified in the
medium of sound. Beethoven found it; it was _res nullius_ when he found
it and when he discovered simultaneously with the succession of tones
that they were appropriate for a powerful musical representation of
sombre Destiny. Every theme, be it of Beethoven, Bach, Wagner, or anyone
else, may be represented graphically by a curve (in the case of Bach's
fugal themes this has, in fact, been done for special purposes), and
just as it is certain that every elliptic-arc existed before all
geometry, so it may be affirmed with equal certainty that everything
musical was in existence before the advent of composition, and was
merely waiting for a discoverer whom we designate the inventor, the
creative organ.

But may not some of this glory be reflected on to scientific discovery?
When we are in an ecstasy of admiration, we talk of a creative act as of
something divine; may we not also grant to the scientist this tribute
which, owing to a slight confusion of conceptions, we shower on the
artists? And I believe that Einstein's definition does not set up an
insuperable barrier in this respect to our admiration, which exerts
every effort to pass beyond, refuses to come to a standstill before the
rigid fact that the discoverer reveals only what is preformed; our
emotions prove to be stronger than our minds with their objective
valuation. In the last instance, we opine, the scientific discoverer,
too, creates something new, namely, a piece of knowledge that was
previously not in existence. And we obey the impulse of hero-worship,
when we call a definite first discoverer a creator.

This silences opposition certainly only for a time, without vanquishing
it. For this knowledge, too, lay ready before the first discoverer
appeared: he did not create it, but merely drew back the veil that
enveloped it. So that, ultimately, we get back to "intuition" in its
literal sense, a becoming aware of things, an exact consideration of
things, states, and relationships; and this intensive consideration,
full of wonderment, has always been a privilege of a very few chosen
men.

It might be asked: Was there any knowledge of Pythagoras' Theorems
before Pythagoras gave us his proof? We should have to answer: It was in
existence at least in the still dark field of vision of Pythagoras,
which became illumined one day when he took such a view of the
number-ratios 3--4--5 that an exact intuition could actually come about.
It is erroneous to assume that a creative act suddenly called up before
his soul as if by magic the figure with the three squares drawn
externally on the sides of a triangle. Rather, he "took his stride" (as
we know from Vitruvius) by considering a triangle whose sides were of a
definite length; and the well-known proof, which is linked indissolubly
in our minds with his work, is not his at all, but Euclid's. Yet our
annals grow musty, centuries pass by, and the credit of being the
creator rests with the man who first succeeded in getting a clear
picture of such a triangle.

It seems natural to test discoveries by experiments. The first result of
doing this is a very remarkable increase in the rate at which the
intuitive process has developed. In ancient times, intuition, it seems,
scarcely felt the need of proving things by experiment; all that was
discovered by Archimedes in mechanics, by the Pythagoreans in acoustics,
by Euclid in optics, may be reduced practically to the formula
"heureka," and it is probably scarcely an exaggeration to say that more
and more fruitful experiments are performed in one week nowadays than in
the whole of the classical age taken together.[3]

[Footnote 3: Recently certain precisians in definition have been seeking
to establish a fundamental difference between physicists of reality,
experimental physicists, and "blackboard-physicists." The last term is
given jeeringly to theoretical physicists because they, in the opinion
of these critics, wish to found Nature entirely on formulæ argued out
on the blackboard. The history of science does recognize this
distinction, although it is, of course, quite possible for a physicist
to arrive at important discoveries without making any experiments.

One might be more justified in asserting that the great theorist need
not necessarily be a great experimenter and vice versa. But I can quote
no example of a physicist who confined himself obstinately to blackboard
discussion, and on principle disowned all experimental work.

I must add that Einstein himself is fond of experimenting, and has had
much success in experimental work. The amount of advice and
encouragement that he has given, and still gives, to many workers in
this field is very considerable. But he does not practise experimental
work regularly, and remarked that he is obliged to appeal to outside
help for certain practical tests. There are specific experimental
geniuses, whose activity assumes the happiest and most fruitful form
when it supplements that of the theorist and fertilizes it.]

Experiments have become, if not the sole, yet the most definite, test of
intuition. I need only recall the observations of the solar eclipse of
1919, which were of an experimental character inasmuch as they used
apparatus to question Nature. To the world generally, they gave the
irrefutable confirmation of Einstein's Theory of Gravitation, but not to
Einstein himself, whose intuition felt itself so certain that the
confirmation was a mere matter of course.

But this is not the average case; in many cases the intuition of the
discoverer appeals to experiment as a judge of great authority, who is
to confirm, reject, or correct.

Let us take some examples of cases in which the intensity and the value
of intuition were measured by the experimental results. Benjamin
Franklin's Kite Experiment may be taken as a classical instance. Here is
a man in whose head the idea takes root that lightning and electricity
are one and the same thing. Innumerable persons before and after his
time might have hit on the same idea, which is now the common knowledge
of children. Yet, a single man had to appear who became aware of this
pre-formed fact and who simultaneously thought out a method of putting
it to proof. In 1752 he constructed a kite, sent it up into the clouds
during a storm, and caught up sparks on the ground by a metallic
contrivance, and, as d'Alembert so aptly described it to the French
Academy:


    "Eripuit coelo fulmen ..."


He wrested the lightning from the heavens. Jupiter Tonans illuminated a
great discovery, a mighty intuition which had entered like a lightning
stroke into the brain of a discoverer.

This case would be classical, were it not that nine-tenths of it is
based on legend. Franklin was by no means the first who had this
intuition, and his experimental test was so full of faults that it was
within an ace of failing. Franklin used a dry thread of hemp, which he
thought to be a conductor, but which became a conductor only after it
had been made wet by rain. Till that moment the exhibition of sparks on
the ground had been poor enough, and little was wanting for Franklin to
give up his attempt and confess that he had been inspired, not with an
intuition, but with a hallucination.

But to whom then is the glory of this discovery due? This is a difficult
point to decide. As early as 1746, that is, six years before Franklin's
kite made its ascent in Philadelphia, Professor Winkler of Leipzig had
asserted in a dissertation that the two phenomena were identical, and
had proved this theoretically; and three years earlier still Abbé
Nollet had declared the storm clouds to be the conductors of an
electrical induction machine. Almost simultaneously with Franklin,
Dalibard, Delor, Buffon, Le Monnier, Canton, Bevis, and Wilson made
experiments on an elaborate scale, which far exceeded that of Franklin
in their results. To this must be added that the experiment was
conducted with evident success only in 1753, when de Romas of Nerac in
South France wove a real conductor of thin annealed wire into the
kite-string, and succeeded in bringing down a regular thunderstorm with
flashes of lightning ten feet long, accompanied by a deafening uproar.
It was only then that the track of the inspiration was traced back
through time to the Roman Kings, Numa Pompilius and Tullus Hostilius, as
the first experimenters with lightning. And then the physicist
Lichtenberg sought to furnish a proof that the old Hebrew ark of the
Covenant, together with the tabernacle, were nothing other than great
pieces of electrical apparatus highly charged with electricity derived
from the air; thus the first intuition, and the priority of discovery,
would have to be ascribed to Moses or Aaron! And connected with this was
the fact, supported by substantial proof, that the Temple of Solomon was
protected by lightning-conductors.

I must not omit to mention that Einstein regards this whole chain of
proofs stretching back to early times as by no means established,
although besides Lichtenberg, other important scholars, such as Bendavid
in Berlin and Michaelis in Göttingen, have vouched for their truth. And
as it is a matter of electrical relationships, Einstein's doubts cannot
be passed over. As far as I recollect, they were not directed against
the rough facts in themselves, but against the sense that is construed
into them--that is to say, in the case of both the ancient Roman and the
Biblical data, the conception of discovery must be excluded, and must be
awarded rather to those intellectual efforts which have led to the
creation of a method of thought. None the less, we may uphold our
statement that in this case, presumed to be classical, neither Franklin
nor anyone else is to be claimed as the discoverer or as the central
figure in a creative act.

The experimental case of spectral analysis is incomparably simpler and
less open to dispute. It is without doubt a discovery of fundamental
importance bearing all the characteristics of originality, for no
predecessors are discernible. I have always felt a little dissatisfied
with the fact that it required two men to think it out, that a duo of
minds was necessary for one act of thought which appears quite uniform,
elementary and inseparable from the intuition of a single mind. But it
seems possible that tradition has not handed the facts down to us
faithfully, and that the two men, with a unanimity arising from their
partnership in work, combined their results, which were not, at the
beginning, of a dual character. This possibility became clear to me from
a remark of Einstein which made it plain to me that the conjunction
Kirchhoff and Bunsen is to be taken as denoting Kirchhoff and then,
after a pause, Bunsen in the next breath! But if we discard this
question of unity or duality, we are left with the fact that the idea of
a spectral analysis occurred to some one (as a result of preceding
optical experiments with Fraunhofer lines), and was fully confirmed by
later experiments. Only fully confirmed? No, the classic rank of this
case manifested itself in a much more triumphant manner, for it is
impossible that the intuition of Kirchhoff and Bunsen could have grasped
the whole significance and range of their discovery even after they had
made it their own.

Every discovery encloses a germ of hope. However great this may have
been in the case of Kirchhoff, it could not by any stretch of
imagination approach the degree of its fulfilment. The fundamental
theoretical idea that "a vapour absorbs from the ray-complex of white
light only those wave-lengths which it can emit" gave rise to a process,
the ingenuity, delicacy, and certainty of which is almost inconceivable.
When rays of light emitted by incandescent vapour were separated by a
prism, there were discovered fine coloured lines that betrayed some
unknown mystery. The spectroscopic experiments proved, in a succession
of results, that the author of the above idea had made not only one
discovery, but a whole host of them. For example, it was observed that,
in burning minute residues obtained by evaporating certain mineral
waters, a red line and a blue line that had never been seen before
appeared in the spectrum. One knew immediately that an element, hitherto
undiscovered, was proclaiming its presence. In this way in quick
succession the element Cæsium was discovered, then Rubidium, Thallium,
Indium, Argon, Helium, Neon, Krypton, Xenon--certainly things that were
already pre-formed in Nature, just as the idea of a bridge from Optics
to Chemistry lay all ready in the heart of Nature; but no blame can be
given to the astonished contemporaries who regarded this fundamental
discovery of spectroscopic analysis as a creative achievement of the
intellect.

This ray of hope gave a glimpse of the degree of accuracy attainable. In
this connexion the experiment confirmed infinitely more than the boldest
imagination could ever have dreamed. A yellow line was detected in the
spectrum of sodium. And it was found experimentally that the
three-millionth part of a thousandth of a gramme of a sodium salt is
sufficient to produce this sodium line in the spectrum of a Bunsen
burner. There commenced a dizzying passage in the Calculus of
Probabilities for, since it was found that in the sun's atmosphere
hydrogen, carbon, iron, aluminium, calcium, sodium, nickel, chromium,
zinc, and copper were present, the question arose as to how great was
the possibility of an error in this observation. Kirchhoff calculated it
as a chance of a trillion to one that these substances are actually
present in the sun!

Never before had an experiment verified to such an extreme degree a
discoverer's idea. It seems appropriate at this stage to deal with a
doctrine which seeks to shed light into the deepest recesses of the
connexion between experiment and discovery. It teaches that an
_experimentum crucis_, an experiment that verifies absolutely, is
_impossible_ in physics. That is to say, every idea of a discoverer
involves a hypothesis, and, however the experiment that follows may turn
out, there still remains the possibility that this hypothesis was false,
and may later have to make way for another essentially contradictory
hypothesis which will be valid again only for a limited time.

The chief exponent of this theory is the eminent scholar, Pierre Duhem,
Membre de l'Institut. He draws a parallel between experiment and
mathematical proof, particularly with the indirect, apagogic form which
has been so successfully applied in Euclidean geometry. In this method
it is assumed that a certain statement is erroneous; it is then shown
that it leads to an obvious contradiction; consequently the statement
was correct provided that a certain doubt be excluded. Thus in the
domain of mathematics we have a real _experimentum crucis_.

In accordance with this, Duhem tests the validity of two physical
theories, both of which were put forward and claimed as discoveries.
Newton had discovered the nature of light to consist in "emission"; to
him, as well as to Laplace and Biot, light consists of projectiles that
are emitted with very great velocity. The discovery of Huyghens,
supported by Young and Fresnel, substitutes wave-motion in place of
corpuscular emission. Hence, according to Duhem, we have, or we had,
here two hypotheses which appear to be the only ones possible.
Experiment was to pronounce a judgment, and at first it decided
irrefutably in favour of the wave-theory. Therefore, the discovery of
Huyghens is alone true, and that of Newton is shown to be an error;
there is no third outlet, and so we have quite certainly an
_experimentum_ crucis before us.

The term itself originates in Bacon's _Novum Organum_. Contrary to
Duhem's assumption, it does not refer to a signpost at cross-roads
giving various routes, nor is it connected with _croix ou pile_, heads
or tails. _Experimentum crucis_ denotes rather a divine judgment at the
cross, that is a test that is absolutely decisive and beyond further
appeal. But no! adds Duhem, there is no room for a third judgment in the
case of two contradictory statements in geometry, but there is between
two contradictory statements in physics. And, in fact, this third
possibility has manifested itself in the discovery of Maxwell, who has
shown that the nature of light is founded on a process of periodic
electromagnetic disturbances. Hence, so concludes Duhem, experiment can
never decide whether a certain theory is alone valid. The physicist is
never certain that he has exhausted all conceivable possibilities, of
thought. The truth of a physical statement, the validity of a discovery,
cannot be confirmed by any _experimentum crucis_.

According to this argument, therefore, it is also possible that the
scientific grounds of spectral analysis do not conform to truth. A
contradictory hypothesis may, indeed, be set up, with the result that
the same experiments that had led Kirchhoff's discovery from one triumph
to another would have to be interpreted in a totally different sense.

I must frankly confess that I cannot subscribe to such an extreme
eventuality, since, in my opinion, Duhem's analogy with mathematics
excludes this possibility. For if a certain probability is expressed by
a trillion to one, then I venture to state that even in the case of
mathematical truths certainty reaches no higher degree of probability.
From the history of mathematics we know of theorems which were
enunciated and provided with complete proofs, and yet did not succeed in
establishing themselves; hence we see that, however evident a
mathematical theorem may be, it is still only a matter of very great
probability.

If, following our usual habits of thought, we take this for absolute
certainty, then we may also consider the sum-total of experiments in the
realm of spectral analysis to be a great _experimentum crucis_ for the
correctness of the theory itself.

Far removed from it, and yet connected with it, there is the "Periodic
System of the Elements," the discovery of Mendelejew and Lothar Meyer.
It, too, offered prophetic glances into the future, foretold the
unknown, hinted at things that were present only in imagination in a
scheme of thought that assigned definite places of existence to
undiscovered things. The Periodic System is represented by a table
containing vertical and horizontal rows, in the squares of which the
elements are entered according to certain rules depending on their
atomic weights. The discovery consisted theoretically in stating that
the physical and chemical properties of each element is the arithmetic
mean between the properties of its horizontal and vertical neighbours.
This gave rise to predictions concerning the unoccupied squares. These
gaps, these blank spaces in the table, seem to say prophetically: There
are elements missing here that must be discoverable. The neighbours will
betray them, and the empty space itself shows by what means they are to
be found. With the shrewdness of a detective, Mendelejew was able to
say: There must be elements of the atomic weights 44, 70, and 72; we do
not know them yet, but we are in a position to determine the properties
of these foundlings of the future, and, what is more, the properties of
their compounds with other elements. Later researches, which led to the
discovery of the elements. Scandium, Gallium, and Germanium, have
actually confirmed all these predicted properties.

The metal Gallium was discovered in 1875 by spectroscopic means. Its
properties are the mean of those of Aluminium and Indium, and this
places it in a position which had already been assigned to it in the
periodic table before its discovery; for, owing to a gap in the system,
Mendelejew had asserted its existence five years previously, although he
then knew nothing of its characteristic spectral signs, namely, two
beautiful violet lines. Radium, too, which was discovered in 1900 and
was found to have the atomic weight 226, completely satisfied this test
and fitted exactly into the place which this number reserved for it in
the table. Thus prediction and confirmatory discovery were fully
congruent in this case; the experiment followed on the visionary insight
just as a Euclidean proof follows on a mathematical assertion, and we
have every reason to say that the system of Mendelejew and Lothar Meyer
has stood the crucial test. Future hypotheses will perhaps supplement
the system or enlarge our knowledge of it, but will certainly not reduce
it _ad absurdum_.

     *     *     *     *     *     *     *     *

Apart from these cases, there are achievements by men who may be called
_lucky_ discoverers, although they displayed no genius for finding nor
for creating. The philosopher-physicist, Ernst Mach, has devoted a
lecture to such intellects, which seems to me very valuable, if only for
the reason that he traces back the conceptions of discovery and
invention to one common root of knowledge, and explains their difference
as being due only to a difference in the application of this discovery.

But when Ernst Mach in this lecture, "On the Influence of Accidental
Circumstances on the Development of Inventions and Discoveries," extends
the influence of chance to include accidental circumstances that can
only enter when the discoverer is closely attentive, it seems to me that
certain limitations are advisable. Otherwise, if we pursue Mach's line
of thought to its extreme, we could declare every discovery to be due to
chance, and this would be the end of the intuitive-creative idea. This
assertion would ultimately mean that genius owes its achievements to the
accidental arrangement of the molecules in the brain-cells of its
associated body. This would be just as wrong as saying that chess is a
game of chance because we lose a game when, by chance, we come up
against a better player.

Huyghens, the great discoverer and inventor, says, in his _Dioptrica_,
that he would have to consider anyone who invented the telescope without
the favourable intervention of chance to be a superhuman genius. Why
should he choose just the telescope? To many the invention of the
Differential Calculus will appear grander and due to a higher degree of
ingenuity. And since it was produced quite methodically, and since
chance was excluded, we may follow Huyghens and with good reason
proclaim its authors superhuman geniuses.

     *     *     *     *     *     *     *     *

Many a true inspiration is dependent on some impulse from without. Who
discovered Electromagnetism? The world-echo answers, "Oersted," with the
same confidence that it couples together the names America and Columbus.
This shows how enormously important was the achievement. Next to
steam-power nothing has exerted such a revolutionary influence in all
branches as electromagnetism. Without it, the world of to-day would
present a totally different aspect. Without it, we should have no
dynamos, no electric trams, no telegraphy, no electric-power stations,
all of which are due to the work of Arago, Gay-Lussac, Ampère, Faraday,
Gramme, and Siemens. Without it, there would be none of the abundance of
brilliant discoveries that are associated with the names of Maxwell,
Hertz, and Einstein. The fact that physics used to be divided into three
parts--Mechanics, Optics, Electrodynamics--and that, since then, the
coherent unity of the physical picture of the world has been developed,
shows us a picture in the background of which we see the illuminating
figure of Hans Christian Oersted. It must not be overlooked, however,
that in the case of his great discovery, too, chance played a definite
part. It occurred one day when Oersted was holding a lecture in the
winter of 1819-20; a magnetic needle situated near his Volta-battery
began to vibrate irregularly. This apparently unimportant trembling of
the metal points contained the key to a fact, the whole consequences of
which could in no conceivable way have entered the mind of this observer
of a hundred years ago, in spite of the genius of the Danish scientist,
which is documented in the classical and far-famed dissertation,
"Experimenta circa effectum conflictus electrici in Acum magneticam,"
which appeared in July 1820. It cleared the way for intuitions that were
equally as fruitful for theory as for practice. Thirteen years after
this initial discovery the world saw the first very important
consequence in Gauss' and Weber's electric telegraph, and a little later
the eminent discoverer Fechner, in Leipzig, proclaimed it as his
conviction that, within two years, electromagnetism would entirely
reform the world of machines, and would entirely supersede steam- and
water-power. Of course, his time estimate fell far short of the mark. It
has been reserved for the present generation to realize that we live in
an electromagnetic world, and that we have, theoretically and
practically, to spend our life electromagnetically. The first indication
of this knowledge hung upon the quivering point of a magnetic needle,
and from it there evolved the electromagnetic ideas that we are so fond
of picturing as our handmaids, but which, in reality, are sovereign over
us all.

     *     *     *     *     *     *     *     *

A great deal of the history of discovery must be revised and corrected.
The Spiral of Archimedes is not due to Archimedes, nor Marriotte's Law
to Marriotte, nor Cardan's formula to Cardan, nor Crookes' Tube to
Crookes, and Galvanism is only related to Galvani by the following
anecdote. It arose from an accidental experience of Madame Galvani in
the kitchen: a half-skinned frog that was to be fried for the evening
meal happened to rest between a scalpel and a tin plate, which brought
it into metallic contact with an accidental discharge of electricity;
the frog twitched; the head of the house gave a very naïve
interpretation to the phenomenon; and it was under such auspices that
Galvanism made its entry into the world. It would be a futile task to
endeavour to trace the connexion between experiment and the underlying
idea, which, in this case, first came to life in Alexander Volta. What
would have remained a mere frog-dance if left to Galvani now acquired
the rank of a discovery through the work of a thinking physicist, who
set up a "Voltaic series"; this discovery then assumed power and dignity
in the hands of Nicholson, Davy, Thomson, Helmholtz, and Nernst. The
words Galvanic Electricity should be made to give way entirely to
Voltaic Electricity,[4] as in the case of many another expression for
which chance and insufficient thought have stood sponsor.

[Footnote 4: The usual term in England is Voltaic Electricity, or,
simply, Current Electricity.--H. L. B.]

It often happens that experiment acts as a corrective of the underlying
idea, neither confirming nor contradicting, but nursing it, as it were,
strengthening, and purging it of errors. Such experiments, partly in
conjunction with chance, play an important, sometimes a decisive, rôle
in the works of Dufay, Bradley, Foucault, Fresnel, Fraunhofer, and
Röntgen. Faraday, who was incapable of observing otherwise than
intensively, found himself compelled, whilst studying induction
phenomena, to alter his initial view, and it is just this correction by
experiment that constitutes Faraday's real discovery. In many cases the
initial idea is corrected, nay surpassed, by the result. Columbus worked
methodically when he set out to reach the East Indies by travelling
westwards; but what he discovered was not a confirmation of his nautical
idea only, but something much greater, which certainly did not lie in
his calculation. Thus he became the archetype of all searchers, who had
thought out and anticipated essentially different conditions from those
that were afterwards discovered to be prevalent. Among these are to be
counted Priestley and Cavendish, who clung to the erroneous notion of
phlogiston, even when they had the evidence to the contrary in the
elements they had themselves discovered, namely, oxygen and hydrogen.
Graham Bell, the inventor, was seeking something quite different from
what he later hit on: as a teacher of the deaf and dumb he was trying to
give a visual picture of sounds, in order to make clear the formation of
sounds to his pupils; this led him to construct an electrical apparatus,
which finally led to the discovery of the telephone.

The truest and sharpest contrast with the _experimentum crucis_ is
furnished by experiment when it shows the exact opposite of what the
explorer was expecting. But since an absolute No entails a very decisive
Yes--namely, in this case, the affirmation of a relationship that was
previously held to be impossible--a negative experiment of this kind,
when it occurs, will be followed by momentous consequences; these will
be the more important in proportion as the question, the affirmation of
which was expected by the physicist, is of a fundamental character.

The experiments of Michelson and Morley, directed at proving the
existence of the ether, are to be regarded as the true classical
instances of these experiments answering with an overwhelming negative.
Their first effect was to produce a sense of helplessness, a check to
thought, a void in the chamber of ideas. And to fill this void there
arose new views of the world in which we nowadays recognize the true
thought-pictures of the universe. The great names--Lorentz, Minkowski,
Albert Einstein--shone out!

As there are forerunners for almost every Important event, so also in
the case of the _experimentum crucis_ of Michelson and Morley. Henri
Poincaré, the famous mathematician, whilst still a student of the
École Polytechnique, had initiated experiments with his fellow-student
Favé, which followed the same object. The Michelson-Morley experiment
was at least a hundred times more accurate. In each case the conclusion
was that the laws of optics are not disturbed by a motion of
translation, such as that of the earth through space this is, however,
contrary to what the old physical ideas lead us to expect.

If we assume the existence of a space-filling ether, the earth, owing to
its own velocity of nineteen miles per second, would have to pass
through a hurricane just as in the case of travellers sitting in an open
train rushing along at very great speed. If we send out light rays in
all directions simultaneously from any point on the earth's surface,
some will travel in the teeth of the ether-storm, others will experience
only a part of the storm's power; so that of two light-rays travelling
in exactly opposite directions the retardation of the one should be
equal to the acceleration of the other; and yet they are not quite
equal, for a simple calculation shows that in every case the retardation
is slightly more than the acceleration.

This may be made clear by means of a model of easy construction, or,
better still, by considering a ship that is subject to a constant
current and, simultaneously, to a pressure of the wind. The time taken
by the boat in making a trip up and down stream can never be the same
for the cases when the wind is in the direction of the current, and vice
versa.

In the case of the ray of light, which is sent backwards and forwards by
means of a contrivance of mirrors, this fact should be clearly
demonstrated by means of the interference-fringes, which are able to
show much smaller effects than the experiment demands. The experimental
oracle was to speak, but it remained silent. This portentous silence
signified: no interference-effect, no action of the ether-current, no
influence due to translation--nothing!

This "nothing" compelled a decision of a very startling kind, for the
result of this experiment was in direct contradiction to another famous
experiment. Fizeau had proved that the ether is practically rigid and
remains fixed in interstellar space. A decision had to be taken in
favour of Fizeau or Michelson and Morley. Yet this was impossible, for
both had operated with unsurpassable accuracy. It was impossible to
reconcile both views as they were diametrically opposed. This
contradiction remains, even if we assume a different hypothesis, not
involving the ether, for Fizeau's experiment. A solution was impossible
without undertaking revolutionary changes in the whole of physical
thought.

This radical change was effected by Einstein; and this mysterious
contradiction disappeared in the resulting revolution of thought.
Einstein supplanted the absolute time-conception by a new relative
conception, and thus the perplexing problem disappeared. Two great
principles arose as regulative factors in thought, and wherever these
were applied, they achieved wonders: one was the new conception of time
that deprived the earth of her unique position as the sovereign of time
by the introduction of the principle that the rate at which time elapses
is different in media moving at different speeds; the other is the
principle of the constancy of the velocity of light. One feels a
temptation to apply a mythical allegory: just as the world, according to
the Biblical story, originated from nothing, so there arose from the
"nothing" of the Michelson-Morley experiment a new world, a world of
knowledge, a cosmos of thought, in which perfect harmony reigns.

Its truth was contained in itself before the experimental proof was
furnished. And this realization of truth has become a fact in the
_experimentum crucis_ for which the sun and stars formed the material.
This will be discussed in another part of the book.

"The really important factor is ultimately intuition," Einstein had said
to me. It made me think of Huyghens' remark about the genius who would
have been able to create the telescope without the help of chance. Was
not this intellect, imagined by Huyghens, sitting opposite me at that
moment? An inner voice answered in the affirmative, for Einstein's
thought-complex seemed to me at that moment a kind of telescope for the
human mind, a telescope that had arisen out of pure intuition, and whose
range stretched to the limits of the universe.




CHAPTER VI

OF DIFFERENT WORLDS

Imaginary Experiment with "Lumen."--Impossibilities.--A Destroyed
Illusion.--Is the World Infinite?--Surface Creatures and Shadow
Rambles.--What is the Beyond?--Action at a Distance.--Ideas of
Multi-dimensional Regions.--Hypnotism.--Recollections of Zöllner.--Science
and Dogma.--The Trial of Galilei.


CONVERSATION held during April 1920 destroyed an illusion which had
become dear to me.

It concerned the fantastic figure, "Lumen," conceived as an actual
human being, imagined as endowed with an extraordinary power of motion
and keenness of sight. Mr. Lumen is supposed to be the invention of the
astronomer Flammarion, who produced him in the retort of fancy, as Faust
produced Homunculus, to use him to prove the possibility of very
remarkable happenings, in particular, the reversal of Time.

Einstein declared outright: "Firstly, Lumen is not due to Flammarion,
who has derived him from other sources; and secondly. Lumen can in no
way be used as a means of proving things."

MOSZKOWSKI: "It is at least very interesting to operate with him. Lumen
is supposed to have a velocity greater than that of light. Let us assume
this as given, then the rest follows quite logically. If, for example,
he leaves the earth on the day of a great event, such as the battle of
Waterloo, and---- May I trace out this example, at the risk of tiring
you?"

EINSTEIN: Do repeat it, and act as if you were telling something
entirely new. It is clear that the Lumen-story gives you great
amusement, so please talk quite freely. But I cannot forgo the privilege
of showing later how the whole adventure and its consequences must be
demolished.

M.: Well then, the person, Lumen, sets off at the end of the battle of
Waterloo to make an excursion into space with a speed of 250,000 miles
per second. He thus catches up all the light-rays that left the field of
battle and moved in his direction. After an hour he will already have
attained a lead of about twenty minutes. This lead will be gradually
increased, so that at the end of the second day he will no longer be
seeing the end of the battle, but the beginning. What has Lumen been
seeing in the meantime? Clearly he has been observing events happening
in the reverse direction, as in the case of a cinematograph which is
exhibiting pictures backwards. He saw the projectiles leaving the
objects they had struck, and returning into the mouths of the cannon. He
saw the dead come to life, arise, and arrange themselves into battalion
order. He would thus arrive at an exactly opposite view of the passing
of time, for what he observes is as much his experience as what we
observe is ours. If he had seen all the battles of history and, in fact,
all events happening in the reverse order, then in his mind "before" and
"after" would be interchanged. That is, he would experience time
backwards; what are causes to us would be effects to him, and our
effects would be his causes; antecedents and consequents would change
places, and he would arrive at a causality diametrically opposite to our
own. He would be quite as justified in adopting his view of the
happening of things, according to his experiences, and of the causal
nexus as it appears to him, as we are justified in adopting ours.

EINSTEIN: And the whole story is mere humbug, absurd, and based on false
premises, leading to entirely false conclusions.

M.: But it is only to be taken as an imaginary experiment that plays
with fantastic impossibilities to direct our ideas on to the relativity
of time by a striking illustration. Did not Henri Poincaré adduce this
extreme example to discuss the "reversal" of time?

EINSTEIN: You may rest assured that Poincaré, even if he used this
example as an entertaining digression in his lectures, took the same
view of Lumen as I do. It is not an imaginary experiment: it is a farce,
or, to express it more bluntly, it is a mere swindle! These experiences
and topsy-turvy perceptions have just as little to do with the
relativity of time, such as it is taught by the new mechanics, as have
the personal sensations of a man, to whom time seems long or short
according as he experiences pain or pleasure, amusement or boredom. For,
in this case, at least the subjective sensation is a reality, whereas
Lumen cannot have reality because his existence is based on nonsense.
Lumen is to have a speed greater than that of light. This is not only an
impossible, but a foolish assumption, because the theory of relativity
has shown that the velocity of light cannot be exceeded. However great
the accelerating force may be, and for however long it may act, it
cannot cause this limit to be transcended. Lumen is supposed to be
equipped with the organ of sight, that is, he is supposed to have a
corporal existence. But the mass of a body becomes infinitely great when
it reaches the velocity of light, so that it is quite absurd to go
beyond this stage. It is admissible to operate with impossibilities in
imagination, that is, with things that contradict our practical
experience, but not with absolute nonsense. That is why the other
adventure of Lumen, in which he jumps to the moon, is also an absurdity.
In this, he is supposed to leap with a speed greater than light, and,
when he reaches the moon, to turn round instantaneously, with the result
that he sees himself jumping from the moon to the earth backwards! This
jump is logically meaningless; and if we try to make deductions of an
optical nature from such a nonsensical assumption, we deceive ourselves.

M.: Nevertheless, I should claim extenuating circumstances for this case
on the ground that I am enlisting the help of the conception of
impossibility. A journey even at a speed of only 1000 miles per second
is impossible for a man or a homunculus.

EINSTEIN: Yes, according to our experience, if we measure it against
facts. We cannot state definitely that a journey into the universe at an
enormous yet limited velocity is absolutely impossible. Within the
indicated bounds every play of thought that is argued correctly is
allowable.

M.: Now, suppose that I strip Lumen of all bodily organs and take him as
being a pure creature of thought, entirely without substance. A velocity
greater than that of light can be imagined, even if it cannot be
realized physically. If, for example, we think of a lighthouse with a
revolving light, and consider a beam of light about 600 miles long,
which rotates 200 times per second. Then we could represent to ourselves
that the light at the circumference of this beam travels with a speed of
nearly 760,000 miles per second.

EINSTEIN: As for that, I can give you a much better example of the same
thing. We need only imagine that the earth is poised in space,
motionless, and non-rotating. This is physically admissible. Then the
most distant stars, as judged by us, would describe their paths with
almost unlimited velocities. But this projects us right out of the world
of reality into a pure fiction of thought, which, if followed to its
conclusion, leads to the most degenerate form of imagination, namely, to
pathological individualism. It is in these realms of thought that such
perversities as the reversal of time and causality occur.

M.: Dreams, too, are confined to the individual. Reality constrains all
human beings to exist in one and the same world, whereas, in dreams,
each one has his own world with a different kind of causality.
Nevertheless, dreams are a positive experience, and signify a reality
for the dreamer. Even for waking reality it would be easy to construct
cases in which the causal relationship is shattered. Suppose a person
who has grown up in a confined retreat, such as Kaspar Hauser, looks in
a mirror for the first time in his life. As he knows nothing of the
phenomena of optical reflexion, he sees in it a new, objective world
that gives a shock to, or even subverts, his own idea of causality in so
far as it may have become developed in him. Lumen sees himself jump
backwards, whereas Kaspar Hauser sees himself performing gestures on the
wrong side of his body; should it not be possible to draw a reasonable
parallel between these two cases?

EINSTEIN: Quite impossible. However you set about it, your Lumen will
inevitably come to grief on the conception of time. Time, denoted in
physical expressions by the symbol "t," may, indeed, be given a negative
value in these equations, so that an event may be calculated in the
reverse direction. But then we are dealing with pure matters of
calculation, and in this case we must not allow ourselves to be drawn
into the erroneous belief that time itself may travel negatively, that
is, retrogressively. This is the root of the misapprehension: that what
is allowable and indeed necessary in calculations is confused with what
may be thought possible in Reality.[5] Whoever seeks to derive new
knowledge from the excursions of a creature like Lumen into space,
confuses the time of an experience with the time of the objective event;
but the former can have a definite meaning only if it is founded on a
proper causal relation of space and time. In the above imaginary
experiment the order of the experiences in time is the reverse of that
of the events. And as far as causality is concerned, it is a scientific
conception that relates only to events ordered in space and time, and
not to experiences. In brief, the experiments with Lumen are swindles.

[Footnote 5: Perhaps an analogy will serve to make this clear. Suppose
that a certain quantity of some foodstuff is consumed by ⅒ head of
population. The false inference would be that a population is possible
which has ⅒ heads! In the same way the statistics may be quite correct
in arriving at the figure ⅕ suicides, but if we leave the realms of
calculation, then the £ suicide loses its meaning entirely.]

M.: I must resign myself to giving up these illusions. I must frankly
confess that I do so with a certain sadness, for such bold flights of
constructive fancy exert a powerful attraction on me. At one time I was
near outdoing Lumen by assuming a Super-Lumen, who was to traverse all
worlds at once with infinite velocity. He would then be in a position to
take a survey of the whole of universal history at a single glance. From
the nearest star, Alpha Centauri, he would see the earth as it was four
years ago; from the Pole Star, as it was forty years ago; and from the
boundary of the Milky Way, as it was four thousand years ago. At the
same moment he could choose a point of observation that would enable him
to see the First Crusade, the Siege of Troy, the Flood, and also the
events of the present day simultaneously.

EINSTEIN: And this flight of thought, which, by the way, has been
indulged in repeatedly by others too, has much more sense in it than the
former one, because you may make an abstraction which disregards speed
altogether. It is only a limiting case of reflection.

M.: I should like to touch on other limiting cases, in particular two
that I find it impossible to interpret. Lotze mentions them in his
Logic. The first concerns the infinitely long lever whose fulcrum, or
turning-point, is at the confines of the universe. According to the Laws
of Levers, a mass of magnitude zero will suffice to keep in equilibrium
at the end of the other lever-arm any weight, no matter whether it is a
million times heavier than the earth. Our imaginations cannot even
picture this. Yet I cannot feel satisfied with the mere explanation that
it is an exceptional case, an extension of a general law to a case in
which it is no longer applicable. The second example is still more
perplexing because it does not require a journey into other worlds, but
leads us into inconceivable consequences even if we remain on the earth.
Lotze considers this second limiting case easier; to me it seems more
difficult. It is this: The force that a wedge exerts is inversely
proportional to its thickness. If it is infinitely thin, this formula
gives an infinitely great result, whereas, actually, the force exerted
is nil. This very thin wedge, transformed finally into a geometrical
plane, should be able to split in twain any wooden or even steel block.
And now, consider a special arrangement of this wedge in which it is
resting with its extremely sharp edge vertically downwards, whereas at
the top it broadens to a little ledge which supports a weight. We then
get the incredible result that this wedge, which can be imagined
concretely, should be able to cut through the whole earth with its
extremely fine edge, if placed on some base. Where is the fallacy in
this case?

EINSTEIN: The mechanical facts have not been taken sufficiently into
consideration.--He illustrated his further remarks by drawing a few
strokes with his pen, and proved from his diagram that a wedge of this
sort would be able to perform what I assumed, only if the base on which
it is placed is composed of separate laminae. Otherwise the assumption
that the force is infinitely great would be erroneous.

     *     *     *     *     *     *     *     *

After this digression to a limiting case on the earth we returned to
more general problems, and the question of the finitude or infinitude of
the universe. Shortly before, Einstein had given an address to the
Berlin Academy on this point, involving difficult calculations, and I
hoped to hear from him an easy explanation at least in general terms.

It is one of the ultimate problems. Whoever talks of the limits of the
world endeavours also to mark off the bounds of the understanding. The
average person, at first sight, almost always decides in favour of an
infinite universe, on the ground that a finite world is inconceivable.
He argues that, if it were considered finite, we should immediately be
confronted with the question: What lies _beyond_ the finite boundary?
Something must be present, even if it is only empty space. This brings
us into an inevitable conflict with the first of Kant's "antinomies,"
with the thesis and antithesis, from which there is no escape. What is
the meaning of the fact that the apprehensive understanding seeks refuge
in "Infinity"? It signifies that he gets entangled in the folds of a
negative conception, that furnishes him with no explanation at all, and
expresses merely that his first assumption of finitude cannot be thought
out to its conclusion.

Besides this, a second disturbing question arises. Is there a finite or
infinite number of stellar bodies? If this question refers to an assumed
infinite space, even if such space is inconceivable, then there are two
possible answers. For it would be possible to imagine a finite number of
stars even if no limit could be found for space.

Whereas the general question of space in the universe belongs
exclusively to speculative philosophy, the star-question is not purely
metaphysical, but is physical, too, and has accordingly been treated by
physicists. The great astronomer Herschel imagined he could solve it by
means of optical principles, and he arrived at the conclusion that the
number of heavenly bodies must be finite, as otherwise the aspect of the
starry firmament, from the point of view of illumination, would be
entirely different. But this proof did not establish itself among
scientists, for the number of stars of the type of the sun might be
finite, whilst there was an infinite number of _dark_ stars.

A further question presented itself: Would it be possible for a definite
part of the heavens (say, that north of the ecliptic) to contain an
infinite number of stars, whilst other parts contained only a finite
number? At first this sounds very extraordinary, but it is by no means
unreasonable, as a concrete example will show: If, on a scale of
temperature, we count the degrees of heat from a certain point, then
they stretch apparently to infinity in one direction, whereas they
extend only to -273° (Centigrade) in the other direction, that is, to
the absolute zero. Thus we can imagine an arrangement which stretches to
infinity only in one direction.

To get an insight into the discussion by Einstein which is about to
follow, we must first dispose of a certain arbitrariness of language,
lying in the customary indiscriminate use of the terms, infinite,
immeasurable, and unbounded. Suppose we have a globe about one foot in
diameter, the surface of which is inhabited by extremely small,
ultramicroscopic creatures that can move about freely and can think. The
surface of the sphere constitutes the world of the micro-men, and he has
a very good reason for considering it infinite, for, however far and in
whatever direction he may move, he never encounters a boundary. But we,
who live in our space, look on to this spherical surface, and recognize
that his judgment is erroneous. To us his spherical world seems
decidedly finite and quite measurable, although it has no determinable
beginning and no end, and thus must appear unbounded to the micro-man.
In fact, we ourselves may regard it as boundless, if we can succeed in
forming an abstraction that leaves out of account its limitations in our
own space.

Now, it might occur to a particularly intelligent micro-being to
undertake a voyage for the purpose of making measurements. He carefully
marks his point of departure, walks Straight ahead in a certain
direction, describing a circle on his sphere--a circle which he will
necessarily regard as a straight line. He continues ever onwards in the
firm conviction that he is getting farther and farther away from his
starting-point. Suddenly, he discovers that he has reached it again. He
discovers, by the mark he made, that he has not been describing a
straight line, but a line that merges into itself.

The micro-professor would be compelled to declare: Our world, the only
one known to me, is not infinite, although in a certain sense boundless.
Moreover, it is not immeasurable, since it can be measured in at least
one direction by the number of steps I have walked. From this we may
infer that our former geometrical view was either wrong or incomplete,
and that, in order to understand our world properly, we must build up a
new geometry.

We may assume that the majority of the remaining micro-inhabitants would
at first protest strongly against this decision. The idea that a line,
which appears to them to be pointing always in the same direction, is
curved, seems to them inconceivable and absurd. They would only
gradually overcome their scruples of thought by getting an insight into
a newly developed geometry that makes clear to them for the first time
the conception of a sphere.

In our world of space, which includes all stars, we are the
micro-inhabitants. We have been born with, or have inherited, the idea
of a straight and ever-advancing path in space, and we become filled
with the utmost astonishment if some one asks us to believe that if we
undertake a voyage in one direction out into the universe, beyond Sirius
and a million times farther, we should finally arrive at our
starting-point again, although we had not changed our direction. But the
macro-being, who belongs to a universe of higher dimensions and who
looks on our world as we looked on the above spherical world one foot in
diameter, sees the narrowness of our view. We, too, are in a position to
rise above this narrow view by means of a theory founded on our
experience, which will lead us to an extended world-geometry, just as
the micro-professor used his experience to extend his theory of the
circle to include the conception of a sphere.

After these preliminary remarks we shall endeavour to get an insight
into Einstein's reasoning, not in the form in which it was originally
presented (in the Report of the Proceedings of the Berlin Academy of
Science of 8th February 1917), but in a very easy description which was
given to me during a conversation. Here, too, I shall try to preserve
the sense of Einstein's remarks without binding myself strictly to his
words. For although I am indebted to him for his efforts to avoid
difficult points, yet the aim of this book is, if possible, to make the
explanation still easier. Any lack of accuracy arising from this last
simplification is to be debited to me. The new form of representing the
argument, which is as important as it is fascinating, is, of course, due
to Einstein.

The final result stated by Einstein was: The universe, both as regards
extent and mass, has finite limits and can be measured. If anyone asks
whether this can be pictured, I shall not deprive him of the hope. All
that is required is a power of imagination that is great enough to
follow a pictorial description and that can take up the right attitude
towards a sort of figurative representation.

Let us again imagine a sphere of modest dimensions with its
two-dimensional surface. We are concerned only with the latter, and not
with the cubical content. The sphere is to be considered as resting on
an absolutely plane white table of unlimited extent in all directions.
The sphere touches the table at a single point which we shall call its
South Pole; on the top side directly opposite, we have the North Pole.
To simplify matters we may make a sketch on paper of a vertical section
through the centre of the sphere. This profile-picture will show us the
sphere as a circle, and the white table as a straight line; the line
joining the two poles is the axis of the globe, and the sectional circle
is a meridian.

Let us further suppose a creature (resembling, say, a ladybird in shape)
having length and breadth, but no thickness, to crawl along this
meridian. Although it has no thickness, we shall imagine it to have one
property of a solid body, that of being opaque, so that it can throw a
shadow if properly illuminated. We assume the globe itself to be
transparent. At the North Pole we suppose a very strong point-source of
light, a little electric lamp, that sends out rays freely in all
directions.

The insect begins its journey at the South Pole and sets out along the
meridian to reach the North Pole. It is illuminated by the lamp all the
way, so that it continually throws a shadow on the white table. The
shadow moves along the table farther and farther from the South Pole, in
proportion as the insect moves up the meridian, with the difference that
while the insect is describing an arc of a circle, its shadow moves
along a straight line. The position of the shadow can be determined at
any moment by drawing the straight line connecting the lamp to the
insect, and producing it to meet the white surface of the table; the
point of intersection is the projection of the insect on the plane.

At the beginning of the excursion the shadow is exactly as large as the
flat insect itself, if we assume that its dimensions are negligible
compared with the surface of the sphere, for it will then coincide with
its own shadow. But when the insect crawls upwards, its shadow will
increase, because of the shortened distance between the insect and the
lamp, and because the points of projection on the table separate more
and more as their distances from their corresponding points on the
sphere become greater. There is thus a twofold increase. The shadows
move away more and more rapidly, and at the same time increase in size.

When the insect gets very near the North Pole, its shadow, now of
enormous dimensions, has moved to a very great distance; and when
finally it reaches the Pole, its shadow becomes infinitely great and
thus stretches to infinity.

But let the insect wander on along the meridian, past the North Pole,
down towards the South. At the moment when it passes the upper Pole its
shadow jumps from the right side to the left. Its shadow now emerges
from an infinite distance to the left, and, instead of being infinite
size, again becomes finite in dimensions as it approaches. It contracts
as it approaches, and, in short, the same process as occurred during the
first half of the journey now occurs in the reverse order.

[If we fix on the critical moment of the jump from the right to the
left, that is, from plus infinity to minus infinity, we may encounter
difficulties. For the surface-creature pursues its way without
interruption and continuously, and we experience a wish to ascribe to it
a shadow-path that is also unbroken and continuous. This is possible
only if we assume the two points at infinity to be connected, that is,
if we consider them identical. This assumption will seem more natural if
we reason as follows. In the profile-picture the table is represented as
a straight line, and it is along this line that the shadow travels. We
may regard this line as an infinitely great circle, for an infinitely
great circle has zero curvature, just as the straight line, from which
it is therefore indistinguishable. The infinitely great circle has,
however, only one point situated at an infinite distance, that is, it
associates together the two apparent points at infinity of the straight
line with which we identify it. Accordingly, we preserve the continuity
of the shadow-journey, too. Einstein considers it allowable to say that
the right and the left portion each represent a half of the infinite
projection, which becomes complete only when the two ends are joined.]

Now we must be prepared for an effort of thought which will need
considerable help from our imaginations. Firstly, instead of one
surface-creature, we shall suppose several crawling about on different
meridians, so that a series of shadows will be moving about along
straight lines radiating from the South Pole. Next, let us imagine the
whole picture to have its dimensions increased by one, that is, we
transform the plane-picture into a space model. The phenomena are to
remain the same, except that they are to be strengthened by one
dimension, surface conditions becoming space conditions, and surfaces
becoming solids.

What we now see are actual insects with round bodies (if we retain our
original type of creatures), or, since there is no restriction as to
their size--the shadows have assumed all possible sizes--we may assume
any solid bodies whatsoever, stars or even star-systems. Their motions
take place in exactly the same way as those of the shadows previously
thrown by the flat bodies.

This means that, if a stellar body moves, its size increases until it
reaches the spherical boundary of space, where it becomes infinitely
great, and, at the same moment, passes from plus infinity to minus
infinity, that is, it enters the universe from the opposite direction;
then, if it continues moving in its original direction (as it has been
doing all along), it gradually becomes smaller in size until, finally,
it reaches its original position and its original size. If we suppose
the body to be endowed with the power of sensation, it would not be able
to observe its own changes of size, since all its scale-measures would
be altered in the same proportion. This whole complex of phenomena would
still be taking place in an infinite world of space, but, according to
the General Theory of Relativity, the geometry that is valid in this
world would no longer be that of Euclid; it is replaced by a system of
laws that arise from physics as a geometric necessity. In this new
geometry, a circle described with unit radius is a little smaller than
it would be in Euclidean geometry, with the result that the greatest
conceivable circle in this world cannot assume an infinite size.

Thus we have to imagine that our solid bodies, say stars, arrive at a
point in their travels which we may term only "enormously distant." If
we call the directions right and left instead of positive and negative,
then the process reduces itself to this: the moving body reaches the
point, which is enormously distant on the right, and which is identical
with the point enormously distant on the left; this means that the body
never moves out of the space continuum of this world, but returns to its
initial point of departure even when it moves ever onward in what is
apparently a straight line. It moves in a "warped" space.

Einstein has succeeded in finding an approximate value for this
non-infinite universe, from the fact that there is a determinable
gravitational constant. In the constitution of the universe it denotes
the same for the mass-relationships of the earth as the gravitational
constant of the earth denotes for us, namely, the quantity from which we
can calculate the final velocity attained by a freely falling body
during a unit of time. He also assumes a probable average for the
density of distribution of matter in the universe, by supposing that it
is about the same as that of the Milky Way. On this basis Einstein has
arrived at the following result by calculation:

The whole universe has a diameter of 100 million light-years, in round
numbers. That amounts to about 700 trillion miles.

M.: Does this follow from the discussion you entered on just now?

EINSTEIN: It follows from the mathematical calculations which I
presented in "Cosmological Considerations arising from the General
Theory of Relativity," in which the figure I have just quoted is not
given. The exact figure is a minor question. What is important is to
recognize that the universe may be regarded as a closed continuum as far
as distance-measurements are concerned. Another point, too, must not be
forgotten. If, in deference to your wish, I used an easy illustration,
this must not be regarded otherwise than as an improvised bridge to
assist the imagination.

M.: Nevertheless, it will be very welcome to many, who are unable to
grasp the difficult Cosmological Considerations. The number that you
mention is overwhelming in the extreme. Indeed, it seems to me that a
diameter of 100 million light-years suggests an infinitely great
distance more than the word "infinity" itself, mentioned _per
definitionem_, which conveys nothing to the ordinary mind. It calls up a
regular carnival of numbers, particularly in those to whom the immense
number alone gives a certain pleasure. But you were going to give me the
number expressing the mass, too?

And then I learned that the weight of the whole universe, expressed in
grammes, was 10 multiplied by itself 54 times, that is 10^54 (453
grammes = 1 lb., roughly). This seems rather disappointing at first, but
assumes a different aspect when we represent to ourselves what this
figure signifies. It means that the weight of the universe in
kilogrammes is high in the octillions. The earth itself weighs six
quadrillion kilogrammes, hence the weight of the Einstein universe bears
the same relation to the weight of the whole earth as the latter bears
to a kilogramme. Again, the earth's weight to that of the sun is as 1 is
to 324,000. Hence we should have to take at least a trillion, that is, a
milliard times a milliard, suns to get the weight of the universe. And
as far as the linear extent is concerned, let us consider the most
distant stars of the Milky Way, which are at an inconceivable distance,
expressible only in light-years. If we place 10,000 such Milky Ways end
to end we shall arrive at this diameter of the universe, which,
accordingly, will have a cubical content a thousand milliard times
greater than the region accessible to astronomical observation.

Thus we have a very spacious universe. Yet it is not spacious enough to
satisfy all the demands that a mathematician interested in permutations
and combinations might make. One of such combinations is exemplified in
the so-called _Universal Book_, that originated in an imaginary
experiment of Leibniz. If we picture to ourselves the sum-total of all
books that can be printed by making all possible arrangements and
successions of our letters, each book differing from any other even if
only in one symbol, then, together, they must contain all that can be
expressed in sense and nonsense, and everything that is ever realizable
actually or in dreams. Hence, among other things, they would include all
world-history, all literature, and all science, even from the beginning
of the world to the end. If we agree to the convention of operating with
100 different printed signs (letters, figures, stops, spacings, etc.),
and of allowing each such book a million paces for signs, so that each
book will still be of a handy size, then the number of these books would
amount to exactly 10 to the two-millionth power, or, in figures, _i.e._
10^2,000,000.

This fully exhaustive universal library containing all wisdom would
consist of so many volumes that it could not be contained in a case of
the size of the entire stellar universe. And, unhappily, it must be
added that the closed universe, just described by Einstein and having a
diameter of a hundred million light-years would be much too small to
contain this library.

"Nevertheless," said I, "your universe pictures something inconceivably
great; one might call it an infinity expressed in figures. For in your
world there still remains one property of infinity, namely, that it
imposes no limitations on motion of any kind. On the other hand, the
figures proclaim a limited measure in the mathematical sense, however
great this measure may be. This calls up the old restlessness of mind,
due to the persistent question: What lies beyond? The absolute Nothing?
Or is it a something which yet does not occupy space? Descartes and many
other great thinkers have never overcome this difficulty, and have
always affirmed that a closed world is impossible. How, then, is the
average person to reconcile himself with the dimensions you have
established?"

Einstein gave an answer which, it seemed to me, offered a last escape to
apprehensive minds. "It is possible," so he said, "that other universes
exist independently of our own."

That is to say, it will never be possible to trace a connexion between
them. Even after an eternity of observation, calculation, and
theoretical investigation, no glimpse or knowledge of any of these
ultra-worlds will ever enter our consciousness. "Imagine human creatures
to be two-dimensional surface-creatures," he added, "and that they five
on a plane of indefinite extent. Suppose that they have organs,
instruments, and mental attitude adapted strictly to this
two-dimensional existence. Then, at most, they would be able to find out
all the phenomena and relationships that objectify themselves in this
plane. They would then have an absolutely perfect science of two
dimensions, the fullest knowledge of their cosmos. Independent of this,
there might be another cosmic plane with other phenomena and
relationships, that is, a second analogous universe. There would then be
no means of constructing a connexion between these two worlds, or even
of suspecting such a connexion. We are in just the same position as
these plane-inhabitants except that we have one dimension more. It is
possible, in fact, to a certain degree probable, that we shall by means
of astronomy discover new worlds far beyond the limits of the region so
far investigated, but no discovery can ever lead us beyond the continuum
described above, just as little as a discoverer of the plane-world would
ever succeed in making discoveries beyond his own world. Thus we must
reckon with the finitude of our universe, and the question of regions
beyond it can be discussed no further, for it leads only to imaginary
possibilities for which science has not the slightest use."

     *     *     *     *     *     *     *     *

Einstein left me for a while to the tumult of ideas that he had roused
up in me. After I had overcome the first shock, I sought to gain a haven
in the idea that arose out of the first shadow-argument, in which the
spherical bodies occurred that seek to escape towards infinity on the
right but reappear, instead, at enormous distances on the left. Has
anyone ever had presentiments of this kind of world? Perhaps something
of the sort is to be found in earlier books of science? If so, they have
escaped my notice. Yet, a passage of a poet occurs to me. It is to be
found in a volume by Heinrich von Kleist; it is a volume dealing only
with earthly matter and bare of astronomical ideas. Imagine a book the
subject of which is a puppet-show, containing, in the middle of it, a
section foreshadowing Einstein's universe! Quite by chance Kleist comes
to speak of "the intersection of two lines which, after passing through
infinity, suddenly appear on the other side, like a picture in a concave
mirror, which moves away to infinity and suddenly returns again and is
quite close," and, quite in accordance with our new cosmology, he
declares: "Paradise is locked and barred, and the cherub is behind us;
we must make a voyage round the world, and see whether we cannot
discover an exit elsewhere at the other end perhaps."

Perhaps poets of the future will busy themselves with this universe; not
lyrical poets, but descendants of Hesiod, Lucretius, or Rückert. They
will express in verse that Einstein's world offers a source of
consolation to tormented spirits which have sickened of Kant's
antinomies. For in this still almost immeasurable world the fateful
conception "infinite" has been made bearable for the first time. In a
certain way it relieves us from what is quite inconceivable, yet into
which we are usually driven, and forms a bridge between the thesis
"finite" and the antithesis infinite. We are brought to a common stream,
in which both conceptions peacefully flow together. There was no mention
of this in our talk, and I had good reason for being cautious about
following out the theme along these lines. I must not allow any doubts
to arise on this point: Einstein, himself, clings with unerring logic to
the strict mathematically defined conception of infinity, and allows no
compromise with the non-infinite.

When I, on some previous occasion, sought to lead him on to a
compromise, involving a transition-boundary, it availed me nothing that
I quoted Helmholtz to support the possibility of such an operation: my
effort came to an abrupt end.

     *     *     *     *     *     *     *     *

In pursuing these considerations about the universe, we arrived at
things which, in ordinary language, are usually called "occult." In
connexion with this, these remarks ensued: "I am, of course, far from
trying to trace out a connexion between the four-dimensionality that you
establish, Professor, and the four-dimensionality of certain spiritistic
pseudo-philosophers, yet it suggests itself to me that in such occult
circles efforts will be made to derive advantage from the fact that the
same word is used in both cases. This is more than a conjecture, indeed,
for there are no misgivings among the ignorant, and so we actually find
the name Einstein quoted in connexion with mediumistic experiments that
are flavoured with four-dimensionality."

"It will not be expected of me," said Einstein, "to enter into
discussion with ignoramuses and misinterpreted. Discarding them, then,
let us confine ourselves to a brief consideration of the conception
'occult,' as this has played a part in serious science. The chief
example of this in history is gravitation. Huyghens and Leibniz refused
to accept gravitation, for, so they said, according to Newton's view, it
is an action at a distance and hence belongs to the realm of the occult.
Like everything occult, it contradicts the causal order in Nature. We
must not regard Huyghens' and Leibniz's contradiction as being due to
lack of perspicacity; rather, they objected on grounds which, as
investigators, they had every right to uphold. For, as far as our
everyday experience is concerned, every mutual influence of things in
Nature occurs only by direct contact, as by pressure or impact, or by
chemical action, as when a flame is lit. The fact that sound and light
apparently form exceptions is not usually felt as a contradiction to the
postulate of contact. The case of a magnet appears much more striking
because its effect asserts itself as a direct manifestation of force. I
must mention that when I, as a child, made my first acquaintance with a
compass--and this was before I had ever seen a magnet--it created a
sensation in me, which I consider to have been a dominant factor in my
life up to the very present. There is, indeed, a fundamental difference
between pressure and impact on the one hand, and what we hear and see on
the other, even in everyday experience. In the case of light and sound,
something must be 'happening' continually, if the effect is to occur and
continue...."

"Yet another difference seems to enter here," I interposed. "Is it
possible to give a full explanation of gravitation by using only the
conceptions pressure and impact? Perhaps 'pressure at a distance' would
not have seemed to contemporaries of Newton as unintelligible as a
'tension or pull at a distance.' It seems to me that it is particularly
difficult to imagine a pull or an attraction towards a distant object."

Einstein does not consider this difference considerable, and regards it
as possible to overcome it even in a manner which can be directly
pictured. "If the force is exerted by a corpuscular transmission," he
explained, "we may imagine a 'force-shadow' into which the bombarding
corpuscles cannot penetrate. Thus if an obstacle, which produces such a
shadow, becomes interposed between a body A and a body B, then there
will be a lesser pressure on the side of B facing A, and hence B will
experience a greater corpuscular pressure on the other side, with the
result that B will be forced in the direction of A, and the observer
would gain the impression of a pull from B to A. Nowadays, when the
theory of 'fields of force' dominates our physical views, we need
trouble just as little about using corpuscular pressures and impacts as
about the vortices which Descartes once considered as the ultimate
causes of the motions of the heavenly bodies. The efforts of certain
reformers to reintroduce these vortices and whirlpools as explanations
must be regarded as futile."

"Nevertheless," I answered, "it seems admissible to say that,
ultimately, there is always an occult element in every physical
explanation, an absolutely final and elementary something which we
recognize as a principle, without concealing from ourselves that we have
reached the limit of explanation, and our knowledge avails no further.
This brings me to another question the discussion of which, as I clearly
perceive, leads us on to dangerous ground."

EINSTEIN: Don't hesitate to say what is troubling you. I cannot yet see
what you are aiming at.

M.: I am referring to certain phenomena which are also called
"occult"--with the object of discrediting them. They may at times
degenerate to hocus-pocus and fall into the category of dubious arts. It
seems to me, however, that scientists have not always drawn the line
with sufficient care, and that they have been disposed to reject as
humbug, without examination, everything inexplicable that dares to
present itself in the form of open display.

EINSTEIN: In general, they will be in the right, for investigators
cannot be expected to occupy themselves with things bolstered up by
advertisement, and which are supposed to be connected with some
fabulous, occult regions.

M.: Nevertheless, in my opinion even among such displays there sometimes
occur phenomena which scientists should not pass over with contempt. I,
myself, have experienced such cases, and have said to myself: There are
stranger happenings here----

EINSTEIN:--than are dreamt of in your philosophy, you were about to say?

M.: Exactly. These are things that in the guise of sensationalism often
hide a physical truth well worthy of study.

EINSTEIN: But you must not overlook the fact that in such cases you have
mostly played the part of an onlooker, and hence were exposed to all
possible manner of deception. You are baffled on all sides by
undiscoverable tricks and by other persons, whose collusion you do not
suspect. This renders an objective criticism impossible.

M.: This presumes that the performing artist is not entirely isolated.
It is possible to bring about conditions that positively eliminate all
tricks from the very outset.

EINSTEIN: If you have experienced any such cases, relate them by all
means.

M.: I shall be brief, and shall state only facts....

EINSTEIN: Or, expressed more accurately, only things which seem to have
been facts as far as you can trust to memory. Well then, you think that
you have grounds for saying that you caught a glimpse of a mysterious
world at that time.

M.: It is certainly long ago, more than thirty years. Hansen, the freak,
one of the most eminent of his profession, was showing hypnotic and
telepathic experiments that were partly identical with experiments that
the celebrated scientist Charcot at Paris was performing for purposes of
pathology.

EINSTEIN: Well, then, why did you hesitate before? These experiments
come under the head of science, and require no occult veil to appear in
the open.

M.: This touches the main issue. Hansen did not work in the interests of
science, but wished, above all, to earn money. Nevertheless he had in
his own way produced marvellous results that were used later for
scientific work. Unfortunately in his case, owing to the fact that he
cloaked it in occultism at the outset, he was brusquely repudiated by
scientists. The result was that Hansen was condemned to a long period of
imprisonment in Dresden, thanks to the recommendation of scientists who
declared that the experiments were only possible if deception was
practised, and hence that Hansen was an impostor who should be made
harmless by being incarcerated.

EINSTEIN: And how did you yourself seek to discover whether his
experiments were genuine?

M.: Very easily and with absolute certainty. One of my acquaintances,
the wealthy race-horse owner, von Oelschläger, had induced him by means
of a high fee to experiment at his country house, at some distance from
Berlin, in the presence of persons, not one of whom Hansen knew, and in
the case of whom there could be no question of secret collaboration. I
can assure you that everything succeeded without exception. A single
second was sufficient for him to communicate his will to each subject of
experiment. He operated like a supernatural being on those present.

EINSTEIN: I should like to hear examples.

M.: Herr von Oelschläger introduced four jockeys, and suggested a race
in the great salon. Hansen placed them astride over chairs, hypnotized
them on the spot, described the shape of the course, giving distances in
kilometres, curves, and even the value of the prizes. He then gave the
signal for starting. The jockeys immediately began treating their chairs
as race-horses, exhibiting all the signs of extreme strain which
accompany the actual ride.

EINSTEIN: This is not yet a positive proof. The subjects of experiment
may have become cognizant of the fact that they were to serve some
eccentric display. Their acquiescence in a prescribed part need by no
means signify that they were subjectively convinced of the genuineness
of the affair.

M.: There could be not the slightest doubt on this point. After a few
seconds perspiration was streaming over their faces as a result of the
exertion, a symptom that exhibits itself only when the participants are
convinced of the absolute earnestness of their undertaking. All that
gazed on this baffling ride made the acquaintance of a grotesque
reality, and were looking into a strange world of dreams, which
transformed wooden chairs into living thoroughbreds. In the course of
his following experiments in the transference of his will-power, Hansen
experimented with an actress who was famous at that time, and with whom
he had no more acquaintance than with the others. He again produced deep
hypnosis, and gave the order: I shall ask you various questions, all of
which you will be able to answer correctly, with one exception: you will
have forgotten your name. And so it happened. In her trance the actress
gave correct answers, until, when the question, "What is your name?" was
asked, her own name, Helene Odilon, had vanished from her memory. And
immediately afterwards, she told me herself that, in spite of her state
of coma, she had retained full consciousness, had understood everything,
and had been possessed of her memory until it came to the critical
moment when, in spite of extreme efforts, she could not recollect the
words Helene Odilon. But Hansen did not stop at dictating his thoughts
to others, he also transformed corporate things. By a single motion of
his hand he converted a stable-boy into a rigid block, devoid of
sensation. Never would I have thought such an intense state of cramp
possible. He placed the boy with his feet and head alone resting on two
supports, so that the body itself was poised in space. He then stood on
the body with his whole weight, without the rigid body of the boy
bending even an inch.

EINSTEIN: How did he, in all these cases, restore the normal state?

M.: Always by a single gesture, which, like everything that he did,
worked at lightning speed. I must admit that his display became a little
monotonous after a while, and that his programme did not seem capable of
much variation. Things were different, however, in the case of a man
who, some years previously, had toured the world as an exponent of
occult phenomena, and to whom scientists will some time in the future
look back with regret. When he appeared, most academicians took only
sufficient notice of him to reject him without having given him a trial.
It was Henry Slade, the American, who is not to be confused with other
Slades who appropriated his name in order to dupe people whose
insatiable curiosity was aroused.

EINSTEIN: One might almost suppose that your genuine Henry Slade served
as a model for them.

M.: For certain reasons I regard this as out of the question, mainly
because the true Slade gave "demonstrations" only occasionally, his
chief object being to interest scientists. He, himself, repeatedly
asserted that he did not understand his own achievements, and he
unceasingly requested the supervision of professional physicists and
physiologists, to whom the unusual phases in his nature were to serve as
objects of study. The result was that people like Dubois-Reymond,
Helmholtz, and Virchow refused to see him, not to mention experiment
with him.

EINSTEIN: These men cannot be reproached for acting in this way. Slade
was regarded as a representative of a four-dimensional world in the
spiritistic sense; serious scientists must avoid all humbug of this
sort, since even slight interest in it can easily be misinterpreted by
the ignorant public.

M.: Not every one was afraid of compromising himself. After closed doors
had greeted Slade in Berlin, he went to Leipzig, where he became an
object of study for one important scientist.

EINSTEIN: You are referring to Friedrich Zöllner, who undoubtedly had a
reputation as an astrophysicist to preserve. But he would have served
his reputation better if he had not entered into this adventure with the
American spiritist.

M.: Perhaps there will some day be cause for a revision of opinion on
this point. The documents are extant, even if, half forgotten, they are
reposing in various libraries. A renewed investigation of Zöllners
_Scientific Dissertations_, dating from 1878 to 1891, might lead to the
judgment that his ghostly interpretations are to be regarded as occult
in the worst sense, and yet one would marvel that a great scientist,
such as he was, should have felt himself at a complete loss with his
knowledge, so that he was forced to resort to abstruse methods in order
to escape from the mental confusion into which Slade had plunged him.

EINSTEIN: That merely shows that Slade, as a cunning practician,
surpassed him, and that Zöllner did not succeed in seeing through his
machinations.

M.: This would lead one to assume that Slade knew more physics than the
Leipzig professor. For in a great number of experiments Zöllner himself
had prescribed the conditions, including all contrivances which made
deception so much the more unlikely, since Slade himself could not know
what Zöllner's intentions were. It was a question of Electricity,
Magnetism, Optics including prepared conditions of polarization,
involved Mechanics, in short, things that Zöllner as a professional
physicist understood thoroughly, and which, moreover, were controlled by
others of his profession. Among the latter was the celebrated professor
of Electricity, Wilhelm Weber, who, like Zöllner, found himself faced
by phenomena that were utterly incomprehensible to him. It would be a
profitable undertaking to bring these dissertations to light again, and
it would easily be recognized that the things described actually deal
with scientific problems and have not the remotest connexion with tricks
of magic. For example, there is an account of an incredible anatomical
feat. On flour which had been placed carefully in a dish beforehand,
there suddenly appeared the imprint of a naked human foot, whilst Slade
was present at a certain distance, being fully clothed and subject to
careful scrutiny. The footprint showed all the surface-details of the
skin, as was confirmed by authorities, just as only a left foot could
produce them, but not an artificial copy.

EINSTEIN: And from this Zöllner inferred the intervention of
supernatural beings? He would have done better to measure the dimensions
of the foot.

M.: So he did--at once. A difference of four centimetres between the
length of Slade's foot and the copy was disclosed. This riddle, like so
many others, remained unexplained. I must repeat that I am not in the
slightest degree disposed to assert that occult phenomena really occur,
but am interested only in seeing that they are investigated carefully by
qualified persons.

EINSTEIN: Your remarks show that Leipzig scientists did so at that time
with no better result than that Zöllners mental confusion became still
greater.

M.: The conjecture remains that the Leipzig experiments, abundant as
they were, did not suffice. Allow me to ask a direct question,
Professor. Supposing another such agent of miracles should appear, would
you yourself feel impelled to test him experimentally?

EINSTEIN: Your question is misdirected. I explained above that I share
the point of view taken up by Dubois-Reymond and his colleagues.

M.: The following case may be conceived. A certain man, X, might
suddenly appear, who has control of a certain natural force that has
never before been investigated; like one who knew how to use electricity
at a time when people had never experienced any electrical phenomenon.
He would be able to give hundreds of demonstrations, all of which we
should relegate to the realm of inexplicable magic. We should, for
instance, be much astonished if he were to draw sparks from a living
person. Now, suppose two professors express an opinion. Professor A
declares the whole thing to be a farce, and refuses to look into it at
all. Professor B is ready to investigate the achievements of X only if
the latter subjects himself from the beginning to all the physical
conditions that are to be determined beforehand. And suppose the
professor arranges his conditions so that they make impossible the
occurrence of electrical phenomena. If, now, all scientists were to
behave like A and B, the consequences would be very depressing. For here
was an important field of investigation, which is cut off owing to the
distrust or obstinacy of scientists, who should have been the first to
open it up. It is quite irrelevant whether X had the character of a
charlatan or not, for behind his charlatanism there were facts which
clamoured for investigation.

EINSTEIN: The most that I can grant is that your imagined case does not
lie outside the scope of possibility. Yet the chance that there is such
a "natural force" hitherto undiscovered by Man, that is, one that is a
"secret force" as far as we are concerned, is so vanishingly small that
it may be set down as equal to impossible. I should refuse to take part
in any such practices, served up in the form of sensation, for one
reason that I should regret the waste of time, as there are better
things to do. It is a different matter if the mood takes me to visit a
variety entertainment, in order to derive amusement from such
mystifications. For example, only yesterday I was in a little theatre,
in which, among diverse items, a thought-reading woman was performing.
She correctly guessed the numbers 61 and 59 that I had in my mind. But
let no one mention this as a case of telepathic actions at a distance or
wireless communication between minds, for an intermediate person, the
manager, was present, and I had to whisper the numbers to him. The
distance to the stage was certainly too great to allow the sound to be
conveyed directly to an audible degree. Hence there must have been a
different, very cunningly arranged code of signals, which eluded the
notice of people in the stalls. The process consists actually in an
extraordinary refinement of observation, which does not, however, seem
to me any more wonderful than the training of a reckoner who extracts
cubic roots mentally, or than the practised muscles of a juggler all
working in unison to enable him to perform feats with twelve plates
simultaneously.

M.: It gives me enough satisfaction, Professor, that you conceded me
before a certain limited chance of finding a last refuge in occultism.
And even if you, yourself, as a representative of the most rigorous
research of physical reality, refuse to consider it, yet the fact that
many others are drawn irresistibly towards mysterious phenomena cannot
be denied. Should one feel shame on this account? I believe that, in
this matter, we are touching on inner confessions that are quite
independent of the standard of the mind in which they are embedded.
Newton considered the key of the universe to be a personal God, whereas
Laplace proclaimed: _Dieu--je n'avais pas besoin de cette hypothèse_:
this contrast allows no inference to be drawn as to their relative
keenness of mind. And probably the same may be said of the question
whether there are other hidden universes besides the one in which we
live. In any case, those who feel enthusiasm for such questions can
quote in their support good names from the learned world. Immanuel Kant
occupied himself seriously and intensively with the wonders of
Swedenborg, Kepler practised Astrology, in which he had a firm belief,
Roger Bacon, Cardanus, Agrippa, Nostradamus, van Helmont, Pascal, and,
among the modern, Fechner, Wallace, Crookes, are to be counted among the
mystics. No matter whether the views they held were theosophical,
occult, four-dimensional in the spiritistic sense, or coloured by any
other superstition; they proclaimed that things that could be rigorously
proved were, alone, insufficient for them. Out of presentiment and
conjecture they constructed wings with which to fly into regions _extra
naturam_. This is how it happened that, as the common folk could not
find a place in science for many extraordinary achievements, they
assigned their authors to the realm of magicians, as in the case of
Paracelsus, Albertus Magnus, Raimundus Lullus, Sylvester II, who were
regarded as sorcerers. And this coin is still current: to Edison, of our
times, the term, "sorcerer of Menlo-Park," has become attached. In the
minds of the populace discovery and invention, works of genius and
supernatural phenomena, become confused and indistinguishable; it may
even happen to you. Professor, that your works will become invested with
legend. I should not like to conjure up what your fate would have been
if your theory of relativity had originated at the time of the
Inquisition. For the views put forward by Giordano Bruno are mere
child's play compared with your theory of the universe as a
quasi-spherical closed space of hyper-Euclidean character. The tribunal
of the Inquisition would not have understood your differential equation,
gravitational potentials, tensors, and equivalence theory; they would
abruptly have declared the whole theory to be a magical formula or a
manifestation of the devil, and would have honoured it and you with a
funeral pyre.

EINSTEIN: This is clearly a slight exaggeration. Mathematico-physical
and astronomical works have never been attacked by the Papal courts,
but, on the contrary, have been much encouraged by them down to the
present day. This is abundantly clear from the fact that we can set up a
whole list of Brothers of Orders, particularly Jesuits, who have made
eminent discoveries in natural science. From my personal knowledge of
you, I foresee that you will one day sketch a fantastic trial, in which
the new world-system will have to defend itself against the _Sanctum
Officium_.

M.: This would be a very grateful task, judged from the literary point
of view. What a splendid colouring could be obtained by bringing these
two worlds of thought into conflict with one another, the Relative
against the Absolute, which has been established in tradition and dogma.
But we need not even call the historical fancy into action, for,
actually, the theory of the structure of the world is even now still at
variance with traditional ideas, that act with dogmatic violence. There
is no need to deny the fact that every person of education, who makes
the acquaintance of Lorentz's, Minkowski's, Einstein's ideas for the
first time, feels excited to offer contradictions, and becomes involved
in a tumult of pros and cons, and each one experiences in himself the
excitement of an inquisitorial tribunal. The triumph of the new theory
passes over the corpses of conceptions that lie at the cross-roads of
thought and, long after, retain a ghostly existence. Only very few of us
are aware of the further inner revolution that awaits us along the line
of development of Einsteinian ideas; we have only vague presentiments
that whisper to us that the end of forms of thought once considered as
irrefragable is drawing nigh. When once the principle of causality has
been set on a relative base, and all "properties" have been resolved
into occurrence, and all that is three-dimensional has come to be
recognized as an abstraction from the four-dimensional world that is
alone valid, then the time will have come to arrange for, the death
procession of all the philosophies that once served as the main pillars
of thought.

A retrospect of the trials of Giordano Bruno and of Galileo Galilei
offers certain parallels other than those usually discovered by
scholars. And if, to-day, we proclaim Einstein as the Galilei of the
twentieth century, it must be added that in character he is fortunately
a Bruno and not a Galilei. For it is not true that the latter came out
of the persecution as a moral victor with an _eppur si muove_, rather,
in spite of the protection of influential prelates and dignitaries, even
of the entourage of the Pope, he lacked courage and bowed his head,
betraying his science and denying himself as well as Copernicus. Are we
to picture how Einstein would have acted under similar circumstances,
even if they cannot recur again?

Whoever has even an inkling of his character will entertain no doubts.
At that time, three hundred years ago, the materials for a magnificent
scene, "one world _versus_ the other," lay ready. Only one condition was
wanting, the moral courage of the hero. The lack of this one factor
spoilt the final act for the history of that time. The fine ethical
feelings of later generations have had to be propitiated by improvising
a legend iridescent with beautiful colours.




CHAPTER VII

PROBLEMS

Questions of the Future.--Problem of Three Bodies.--Conception of
Approximation.--Object of Mechanics.--Simplicity of Description.--Limits
of Proof.--Reflections about the Circle.--From the History of
Errors.--Causalities.--Relativity on a Physiological Basis.--Physicists
as Philosophers.


WE spoke of the objects and problems of science in general, and touched
on certain recurrent questions with which reputed men of science are
confronted from time to time, so that we may ascertain their opinions
about immediate as well as more remote aims, and about worthy objects
and those within reach.

"Such stimuli," said Einstein, "may be quite interesting inasmuch as
they sharpen the appetite of the public for the works of investigators,
and give the latter the opportunity of making wider circles acquainted
with their plans. Yet the value of their suggestions must not be
overrated, when they are directed at giving trustworthy information
about the future lines of development of science. Every scientist, in
working out his own research, gravitates to particular points on the
boundary which separates the known from the unknown, and becomes
inclined to take his particular perspective from these points. It must
not, however, be expected that these individual aspects will form a
complete picture, and will indicate the only paths along which science
can or will advance."

"May I suggest, Professor," I answered, "that we select certain answers
that have been given to these recurrent questions for discussion? I have
brought along a whole series of them; it would be of value to know what
attitude you take up towards some of the statements that have been made
about future possibilities."

Einstein acquiesced, and so I read out a number of expressions of
opinion, given by eminent authorities, particularly in natural science
and mathematics. They came under the heading, "The Future Revolution of
Science." At the outset we encountered arguments by Bailhaud, the
director of the Paris Observatory; he dealt with the so-called "Problem
of Three Bodies," and with "The Finitude or Infinitude of the Universe."

Einstein elucidated these questions as follows. The celebrated Problem
of Three Bodies is a special case of the general problem of Many Bodies,
the object of which is to discover the exact paths of the heavenly
bodies. If we suppose that the planets and the comets are subject only
to the attraction of the central body, the sun, then their paths would
be exactly those given by Kepler's Laws--that is, they would move about
the central body, or, more precisely, about the common centre of gravity
in perfectly elliptical orbits. The same result would happen if we
regard the orbit of a moon to depend solely on its parent planet. But
this assumption is not in agreement with reality, since all the bodies
of our system are also subject to their mutual attraction depending on
their masses and distances. Consequently we have the so-called
disturbances, perturbations, and divergences from the ideal paths; and
the problem of ascertaining these disturbances is essentially identical
with the Problem of Three Bodies. Regarded from the point of view of
pure mechanics, this problem may be considered solved in so far as we
are able to write down the equations of motion. But, in addition to this
purely mechanical process, there is a mathematical problem which has not
been completely solved--that is to say, the integral expressions that
occur in it can be calculated only approximately. This makes no
difference to the practical calculation, since the degree of
approximation, according to the present methods, may be carried as far
as we wish. The error may be reduced to any desirable extent, so that it
is probably wrong to expect new revelations on this point from future
upheavals in physics. We read on and discovered that several of the
scientists mentioned did not stop at expecting all advances of the
future from pure theory. They had visions of an optimum of happiness, to
gain which the increase of knowledge alone did not suffice. Thus the
celebrated Swedish astrophysicist Svante Arrhenius had summarized his
judgment in a few lines: "After the stupendous progress that has been
made in the physical and chemical sciences in recent times, it seems to
me that the moment has come for attacking the most important problems of
mankind with full success, namely, those of biology, and in particular
of the art of healing, with the weapons that are furnished by the
arsenal of the exact sciences." And the mathematician, Emile Picard,
Membre de l'Académie, expressed himself in still more hopeful terms:
"There is no doubt but that the discoveries which the human race is
awaiting with impatience are those that are seeking to eliminate
sickness and the decrepitude of old age. Injections giving immunity
against all diseases, an elixir of life (_une eau de Jouvence_) for
persons of advancing age--these are the discoveries that are longed for
by every one. There are also sciences that are to be termed 'moral,'
from which we are impatiently expecting that guidance which will
diminish the hate which seems to be increasing from day to day among the
nations. That would be a splendid discovery."

"These are, indeed, noble and inspiring words," said I. "It shows how
deeply rooted is the demand for ethical values in human nature, when
even a mathematician, whose intellectual interests are directed
primarily towards exact results, ranks the discoveries of ethics above
all others."

Einstein answered: "We must carefully distinguish between what we wish
for in general and what we have to investigate as belonging to the world
of knowledge. The question under consideration is not one of wishes and
feelings, but was unmistakably aimed at the advances and revolutions in
the realm of science. It does not come within the scope of science at
all to make moral discoveries! Its one aim is rather the Truth. Ethics
is a science about moral values, but not a science to discover moral
'truths.' Ethics, conceived as a science in the usual way, can therefore
serve to discover or to promote truth only indirectly. To illustrate my
point of view I shall quote an example taken from a totally different
field; it is merely to serve as an analogy. Let us consider the game of
chess. Its value and its meaning is not to be sought in scientific
factors, but in something entirely different, in a struggle which takes
place according to definite rules. But even chess, inasmuch as it
sharpens the intellect, may exhibit an indirect value for promoting
truth. It may, for instance, suggest examples in permutations, which may
contain mathematical, that is, purely scientific, truths. I certainly
do not deny that there is an ethical factor in all genuine sciences. For
being occupied with things for the sake of truth alone emancipates and
ennobles the mind."

"This ennobling effect," I interposed, "should surely show itself in a
moderation of the passions which were mentioned in the above expression
of opinion. With Picard we should expect above all things to see a
diminution in the feelings of hate between peoples, the tragic
consequences of which we have experienced."

Einstein smiled, and, with a touch of sarcasm, said, "Hate is presumably
a privilege of the 'cultured,' who have the time and the energy for it,
and who are not the slaves of care." His tone indicated clearly that he
used the generic term "cultured" to denote the Philistines of culture,
its snobbish satellites, but not those whose intensive work aimed at
increasing and deepening the fields of culture. In general he maintained
his view that it is an illusion to expect "discoveries" in the realm of
ethics, since every real discovery belonged alone to the sphere of truth
in which the division only into right and wrong, not that into good and
evil, holds good.

This led us to the old question of Pilate: What is Truth? In seeking an
answer to this question Einstein first called special attention to the
conception of "approximation," which plays a great part in the actual
search for truth, inasmuch as every physical truth, expressed in
measures and numbers, always leaves some remainder, that marks its
distance from the unattainable truth of reality. This conception, which
manifests itself so prominently in the relation of Einstein's own
researches to the older, so-called classical, mechanics, will be
developed here according to his line of thought as far as I can
recollect from a number of conversations.

Let us suppose that we overhear two people arguing about the shape of
the earth's surface. The one affirms that it is an unlimited plane,
whilst the other maintains that it is a sphere. We should not hesitate a
moment to say that the first is in error, and that the second gives the
true answer. As long as the question was to be decided in favour of a
"Plane or a Sphere," the sphere would represent the absolute truth. Yet
it would be only relative, for these two statements are contradictory
only between themselves, but will no longer be so if a third assertion
is made which opposes a new alternative to "sphere."

If this alternative objection is actually raised, the third person would
be quite justified in saying that the "sphere" explanation is wrong. For
the conception "sphere" requires that all diameters be equal, whereas we
know that they are not so, since the distance from pole to pole has been
proved to be smaller than that between opposite points on the equator.
The earth is an ellipsoid of rotation, and this truth is absolute in the
face of the errors which are expressed by the terms, plane and sphere.

It would again have to be added that this absoluteness would stand only
as long as this contradiction is regarded as being one between a
definite sphere and a definite ellipsoid. If, as in the case of the
earth, there are quite different diameters in the equatorial and the
diametral planes, then there is complete contradiction between the two
statements, and as the supporter of the ellipsoid is right, the one who
supported the sphere must now give in, although he previously triumphed
over his first opponent. His statement was true compared with the
latter, but showed itself to be an error when compared with the
statement of the third person.

This does not run counter to the laws of elementary logic. One of these,
somewhat inadequately called the Law of Contradiction, states that two
directly contrary statements--_e.g._ this figure is a circle, and this
figure is not a circle--cannot both be true simultaneously. The truth of
the one implies necessarily the falseness of the other. As this cannot
be disputed, it follows in our case that we cannot have been confronted
with contradictory judgments at all concerning the figure of the earth.

This is to be understood in a geometrical sense. The sphere does not
entirely contradict the ellipsoid, since it is a limiting case of the
latter: and the plane is likewise a limiting case of the sphere, as well
as of the surface of ellipsoids.

But we are not concerned with purely geometrical considerations, for the
earth is a definite body, and not a limiting configuration derived from
abstraction. We are here dealing with measurable quantities, whose
difference can be proved, and hence we must have one of the disputants
proclaiming the absolute truth, whilst the other proclaims an absolute
error. This, however, again is incompatible with our result that the
second person is right in the one case and wrong in the other.

The logical Law of Contradiction overcomes the dilemma in the simplest
way. None of these assertions contains the truth, hence none of these
judgments allows the falseness of the others to be deduced. Only this
may be said, that there is a fraction of truth in each judgment. The
true shape of the earth is given by the plane to a first, the sphere to
a second, the ellipsoid of rotation to a third, degree of approximation:
we reserve the right of further approximations, each of which in
succession approaches a higher degree of correctness, but none attains
the absolute truth.

This reflection on a particular case may be generalized, and remains
when we extend it to our attempts at grasping the states, changes, and
occurrences of Nature. Whenever we talk of physical laws, we must bear
in mind that we are dealing with human processes of thought, that are
subjected to a succession of judgments, courts of appeal, as it were,
excluding, however, a final court beyond which no appeal is possible.
Each new experience in the course of natural phenomena may render
necessary a new trial before a higher court, whose duty is then to give
a more definite or different form to the law formulated by us, so as to
attain a still higher degree of approximation to the truth.

If we call to mind some of the most valuable statements made by modern
investigators about the nature of natural laws, we recognize that they
are all connected by a single thread of thought, namely, that even in
the most certain law there is left a remainder that has not been
accounted for, and that obliges us to consider a greater approximation
to the truth as possible, even if a final stage is not attainable.

Mechanics furnishes us with the expression of its laws in equations,
whose importance Robert Kirchhoff explained in 1874 by a definition that
has been considered conclusive by scientists. According to him, it is
the object of mechanics to describe completely (and not to explain) in
the simplest manner the motions that occur in Nature.

The postulate of simplicity is derived from the fundamental view of
science as an economy of thought. It expresses the will of man's mind to
arrive at a maximum of result by using a minimum of effort, and to
express the greatest sum of experience by using the smallest number of
symbols. Let us consider two simple examples quoted by Mach. No human
brain is capable of grasping all the possible circumstances of bodies
falling freely, and it may well be doubted whether even a supernatural
mind like that imagined by Laplace could succeed in doing so. But if we
take note of Galilei's Law for Falling Bodies and the value of the
acceleration due to gravity, which is quite an easy matter, we are
equipped for all cases, and have a compendious formula, accessible to
any ordinary mind, that allows us to picture to ourselves all possible
motions of falling bodies. In the same way no memory in the world could
retain all the different cases of the refraction of light. Instead of
trying to do the impossible task of grasping this infinite abundance, we
simply take note of the sine law, and the indices of refraction of the
two media in question; this enables us to picture any possible case of
refraction, or to complete it, since we are free to relieve our memories
entirely by having the constants in a book. Thus we have here natural
laws that give us a comprehensive yet abbreviated statement of facts,
and satisfy the postulate of simplicity to a high degree.

But these facts are built up on experiences, and it is not impossible
that some new unexpected experience will reveal a new fact, which is not
sufficiently taken into account in the law. This would compel us to
correct the expression for the law, and to seek a closer approximation
for the enlarged number of facts.

The Law of Inertia, according to our human standard, seems unsurpassable
in simplicity and completeness; it seems to us fundamental. But this
law, which prescribes uniform rectilinear motion to a body subject to no
external forces, selects only one possibility out of an infinite number
as being valid for us. It does not seem evident to a child, and it is
easy to imagine a good scholar in some branch of knowledge other than
physics, to whom it would likewise not seem evident. For it is by no
means necessary a priori that a body will move at all when all forces
are absent. If the law were self-evident, it would not need to have been
discovered by Galilei in 1638. Nevertheless, it appears to us, now, to
be absolutely self-evident, and we can scarcely imagine that it can ever
be otherwise. This is simply because we are bound to the current set of
ideas that cannot extend beyond the sum of sense-data and experiences
that have been inculcated into us by heredity and environment. At a very
distant date in the future the average mind may surpass that of Galilei
to the same extent as Galilei's surpasses that of a child, or of a
Papuan native. And of all the infinite possibilities one may occur to a
Galilei of the distant future, which, when formulated as a law, may
serve to describe motions of a body subject to no forces better than the
law of inertia, proposed in 1638.

These reflections are not mere hallucinations, but have to do with
scientific occurrences that we have observed in the twentieth century.
Newton's equation that gives the Law of Attraction is beyond doubt a
model of simplicity, and it would have occurred to no thinking person of
even the last generation to doubt its accuracy. The easily grasped
expression k (m.m^1⁄r^2) apparently expresses truth in a law which is
valid for all eternity. In this expression, he denotes a gravitational
constant, that is, a quantity which is invariable in the whole universe;
_m_ and _m_^1 are two masses that act attractively on one another; and
_r_ is the distance between them. But Newton has been followed by
Einstein, who has proved that this expression represents only an
approximate value, that leaves a small remainder as an error that may be
detected if the greatest refinement be made in our methods of
observation. The equations that have been set up by Einstein represent
the approximation that is to be considered final for the present, and
that may remain valid for thousands of years. They are certainly very
complicated, being included in a system of differential equations of
awe-inspiring length, and we may feel tempted to object with the
question: how do they agree with Kirchhoff's postulate that the simplest
description of the motions must be sought? But this objection falls to
the ground if we look carefully into the question. For simplicity
consists not merely in being brief or in excluding difficulty from a
formula, but rather in asserting the simplest relation to the universe
as a whole, which is independent of all systems of reference. When this
independence is proved--and in Einstein's case it is so--the complicated
aspect of the formula disappears entirely in the light of the higher
simplicity and unity of the world-system that presents itself--a
world-system that is directed in conformity with the one fundamental law
of general relativity as well in the motion of the electrons as in
motion of the most distant stars. With regard to the other postulate,
that of completeness, _i.e._ absolute accuracy, we have been furnished
with proofs that have rightly excited the wonder of the present
generation. But are we then to recognize the Principle of Approximation
in every direction? Is there then nothing that can be proved rigorously,
nothing that is unconditionally valid in the form of knowledge that
corresponds exactly to truth?

We are led to think of mathematical theorems, which, when they have once
been proved, are evident to the same degree as the axioms from which
they have been derived, by virtue of logic which cannot be disputed
since a contradiction leads to absurdity. It has been said that
mathematics _est scientia eorum_, _qui per se clara sunt_, that is, is
the science of what is self-evident.

But here again doubts arise. If we should get to know only a single
case, in which the self-evident came to grief, the road to further
doubts becomes open. Such a case will now be quoted.

As we know, a tangent is a straight line, which makes contact with a
curve at two coincident (or infinitely near) points without actually
cutting the curve. The simplest case of this is the perpendicular at the
extremity of a radius of a circle. And it agrees fully with what our
feeling leads us to expect when it is stated that every curved line that
is "continuous," that is, which discloses no break and no sudden bend,
has a tangent at every point. Analysis, which treats plane curves as
equations in two variables, gives the direction of the tangent in terms
of the differential coefficient, and declares accordingly that every
continuous function has a differential coefficient, that is, may be
differentiated, at every point. The one statement amounts to the same as
the other, since there must be an equivalent graphical picture
corresponding to every functional expression.

But this apparently rudimentary theorem involves an error, which was not
discovered before the year 1875. The theory of curves has been in
existence for centuries, but it occurred to no one to doubt the general
validity of this theorem of tangents. It was regarded as self-evident,
as a mathematical intuition. And certainly neither Newton, nor Leibniz,
nor Bernoulli, not to mention the mathematicians of olden times, even
dreamed that a continuous curve without a tangent, or a continuous
function without a differential coefficient, was possible.

Moreover, a proof of the theorem had been accepted. It appeared in
text-books, and was often to be heard in lecture rooms; nor was a shadow
of a doubt suggested. For it was not merely a _demonstratio ad oculos_,
but it appeared directly to our sense of intuition. And we may safely
say that up to the present day no one has ever been able to _imagine_ a
continuously curved line which has no tangent; no one has been able to
picture even one point of such a curve at which no tangent could be
drawn.

Nevertheless, scientists appeared who began to entertain doubts. In the
case of Riemann and Schwarz these doubts assumed a concrete form, in
that they proved that certain functions are refractory at certain
points. But Weierstrass was the first to make a real breach in the old
belief that was so firmly rooted. He set up a function that is
continuous at every point, but differentiable at no point. The graphical
picture would thus have to be a continuous curve having no tangent at
all.

What is the appearance of such a configuration? We do not know, nor
shall we presumably ever get to know. During a conversation in which
this problem of Weierstrass arose, Einstein said that such a curve lay
beyond the power of imagination. It must be remarked that, although the
mathematical expression of the Weierstrass function is not exactly
simple, it is not inordinately complex. Moreover, seeing that one such
function (or curve) exists, others will soon be added to it (Poincaré
mentions that Darboux actually gave other examples even in the same year
that the first was discovered); there will, indeed, be found an infinite
number of them. We may go still further, and say that, corresponding to
each curve that has tangents, there are an infinite number that have no
tangents, so that the former form the exception and not the rule. This
is an overwhelming confession that shakes the foundations of our
mathematical convictions, yet there is no escape.

How may we apply the principle of "approximation" to these
considerations? May we say that the theorem that was believed earlier is
an approximation to a mathematical truth?

This is possible only conditionally, in a certain extremely limited
sense, namely, if we picture to ourselves that point in the development
of science at which the conception and properties of tangents first
began to be investigated. Compared with this stage of science, the above
theorem denotes a first approximation to the truth, in spite of its
incorrectness; for it makes us acquainted with a great abundance of
curves that are very important for us and that exhibit tangents at every
point. This knowledge brings us a step nearer to the more approximate
truth given by Weierstrass's example. In the distant future, the earnest
student will learn this theorem only as a curious anecdote, just as we
hear of certain astrological and alchemistic fallacies. He will learn,
in addition, other theorems that are looked on as proved by us of the
present day, although actually they were proved only approximately. For
what does it mean when Gauss, for example, repudiated certain proofs of
earlier algebraists as being "not sufficiently rigorous," and replaced
them by more rigorous proofs? It signifies no more than that, in
mathematics, too, what appears to one investigator as flawless, strict,
and evident, is found by another to have gaps and weaknesses. Absolute
correctness belongs only to identities, tautologies, that are absolutely
true in themselves, but cannot bear fruit. Thus at the foundation of
every theorem and of every proof there is an incommensurable element of
dogma, and in all of them taken together there is the dogma of
infallibility that can never be proved nor disproved.

It must appear extremely interesting that, at first sight, this example
of the tangent has its equivalent in Nature herself, namely, in
molecular motions the investigation of which is again largely due to
Einstein.

Jean Perrin, the author of the famous book, _Atoms_, describes, in the
introduction, the connexion between this mysterious mathematical fact
and results that are visible and may be shown by experiment, to which we
have been led by the study of certain milky-looking (colloidal) liquids.

If, for example, we look at one of those white flakes, which we get by
mixing soap solution with common salt, we at first see its surface
sharply outlined, but the nearer we approach to it, the more indistinct
the outline becomes. The eye gradually finds it impossible to draw a
tangent to a point of the surface; a straight line which, viewed
superficially, seems to run tangentially, is found on closer examination
to be oblique or even perpendicular to the surface. No microscope
succeeds in dispelling this uncertainty. On the contrary, whenever the
magnification is increased, new unevennesses seem to appear, and we
never succeed in arriving at a continuous picture. Such a flake
furnishes us with a model for the general conception of a function which
has no differential coefficient. When, with the help of the microscope,
we observe the so-called Brownian movement, which is molecular by
nature, we have a parallel to the curve which has no tangent, and the
observer is left only with the idea of a function devoid of a
differential coefficient.... We find ourselves obliged, ultimately, to
give up the hope of discovering homogeneity at all in studying matter.
The farther we penetrate into its secrets, the more we see that it,
matter, is spongy by nature and infinitely complex; all indications tend
to show that closer examination will reveal only more discontinuities.

I have not yet had an opportunity of seeing these Brownian movements
under the microscope, but I must mention that Einstein has repeatedly
spoken to me of them with great enthusiasm, of an objective kind, as it
were, for he betrayed neither by word nor by look that he himself has
done research leading to definite laws that have a recognized place in
the history of molecular theory.

As soon as we approach the question of molecular irregularities we
recognize that, when we earlier spoke of the figure of the earth in
discussing the principle of "approximation," we were still very far from
the limit that may be imagined. We had set up the three stages:
plane--sphere--ellipsoid of revolution, as relative geometrical steps,
beyond which there must be still further geometrical approximations. If
we imagine all differences of level due to mountains and valleys to be
eliminated, for example, and if we suppose the earth's surface to
consist entirely of liquid, undisturbed by the slightest breath of wind,
even then, the ellipsoid is by no means the final description. For now
the discontinuities from molecule to molecule begin, the infinite number
of configurations without tangents, the macroscopic parallels of what
the white flake soap solution showed as microscopically, and no
conceivable geometry would ever be adequate to grasp these phenomena. We
arrive at a never-to-be-completed list of functions which can never be
described either in words or in symbolic expressions of analysis.

But even if the ultimate geometrical truth is hidden behind the veils of
Maya,[6] we are yet left with the consolation that the method of
approximation, even when applied to a relatively modest degree, produces
remarkable results in the realm of numbers. Let us consider for a moment
in the simple figure of a circle the ratio between the circumference and
the radius.

[Footnote 6: Maya = appearance.]

As we know, this ratio is constant, and is called in honour of the man
who first gave a trustworthy value for it, Ludolf's number, namely, π
(pi). Thus it makes no difference whether we consider a circle as small
as a wedding-ring, or as large as a circus arena, or even one the radius
of which is as great as the distance of Sirius. And it makes just as
little difference what happens to the circle whilst it is being
measured; the above ratio must remain constant.

But here, too, a contradiction makes itself heard, issuing from one
section of modern science. It calls to mind the saying of Dove that when
professors are not quite sure about a thing they always preface their
remarks with the phrase: "it is well known that" ... We should be well
advised in avoiding this method of expression altogether, for even when
we feel quite sure, the ghost of the unknown lurks behind what we fain
would call well known.

The theorem that all circles without exception are subject to the same
measure-relation belongs _a priori_ to the synthetic judgments. But
fields of thought have been discovered in which the _a priori_ has lost
its power. Mathematics--once a quintessence of synthetic statements _a
priori_--is now regarded as being dependent on physical conditions.
Physical conditions, however, are empirical and subject to change.
Therefore, since the _a priori_ is not subject to change, we encounter a
discrepancy. It leads to the question: Is the Euclidean geometry with
which we are familiar the only possible geometry? Or, in particular: Is
π the only possible measure-relation?

Einstein replies in the negative. He not only shows how another geometry
is possible, but he also discloses what once seemed inconceivable,
namely, that if we wish to describe the course of the phenomena of
Nature exactly by means of the simplest laws, it is not only impossible
to do so with the help of Euclidean geometry alone, but that we have to
use a different geometry at every point of the world, dependent on the
physical condition at that point.

From the comparatively simple example of two systems rotating relatively
to one another, Einstein shows that the peripheral measurement of a
rotating circle, as viewed from the other system, exhibits a peculiarity
which does not accompany the radial measurement. For, according to the
theory of relativity, the length of a measuring rod is to be regarded as
being dependent on its orientation. In the case quoted, the rod
undergoes a relative contraction only when applied along the
circumference, so that we count more steps than when we measure the
circumference of the same circle at rest, that is, in non-rotation.
Since the radius remains constant in each case, we get a relatively
greater value for π, which shows that we are no longer using Euclidean
geometry.

Yet, formerly, before such considerations could even be conceived in
dreams, this π was regarded as absolutely established and immutable;
and observers used every possible means of determining its value as
accurately as possible.

In Byzantium there lived during the eleventh and twelfth centuries a
learned scholar, Michael Psellus, whose fame as the "Foremost of
Philosophers" stretched far and wide, and whose mathematical researches
were regarded as worthy of great admiration. This grand master had
discovered by analytical and synthetical means that a circle is to be
regarded as the geometric mean between the circumscribed and the
inscribed square, which gives to the above quantity, as may easily be
calculated, the value √8, that is, 2.8284271.... In other words, the
length of the circumference is not even three times that of the radius.

We have the choice of regarding the result of Psellus as an
approximation, or as mere nonsense. Every schoolboy who, in a spirit of
fun, measures a circular object, say a top, with a piece of string,
arrives at a better result, but the contemporaries of Psellus accepted
this entirely wrong figure with credulous reverence, and continued to
burn incense at the feet of the famous master. It is all very well for
us of the present to call him a donkey. We have just as much right in
saying that mathematicians differ, not in their natures, but only in the
order of their brain functions. If a man like Psellus missed the mark by
so much, it is possible that men like Fermat or Lagrange may also have
erred occasionally or even consistently.

No heavenly power will give us a definite assurance to the contrary, and
all of us may be just as false in our judgment of accepted celebrities
as were the Byzantines eight hundred years ago in their estimate of
Psellus.

Whereas the latter had obtained a value "less than 3," there are learned
documents of about the same date that have been preserved, according to
which the value of π comes out as exactly 4. Compared with this
grandiose bungling, even the observations mentioned in the Old Testament
are models of refinement. For, as early as three thousand years ago, it
is stated of the mighty basin in the temple of Solomon (First Book of
Kings, chapter VII.): "And he made a molten sea, ten cubits from the one
brim to the other: it was round all about, and his height was five
cubits; and a line of thirty cubits did compass it round about." Thus π
here appears as 3, an approximation which no longer satisfied later
generations. The wise men of the Talmud went a step further, in saying 3
plus a little more; and this agrees roughly with the actual value.

The view became more and more deeply rooted that this π was a main
pillar of mathematical thought and calculation. The more the problem of
the quadrature of the circle seized on men's minds, the greater were the
efforts made to find the exact value of this "little more" of the
Talmud. Since 1770 we know that this is not possible, for π is not
rational, that is, it can be represented only as an infinite and
irregular (that is, non-repeating) decimal expression. It occupies,
further, a special rank as a transcendental quantity; this fact was
proved by Lindemann as late as 1882 for the first time. Yet, even
nowadays, there are incorrigible devotees of quadrature, who are still
hunting a solution because they cannot rid themselves of the
hallucination that such a simple figure as the circle must submit
ultimately to a constructive process.

The correct way was to carry out an even more accurate determination of
the decimal figures. The above-mentioned Ludolf van Ceulen got as far as
the 35th place of decimals; at the turn of the eighteenth century the
100th decimal place was reached. Since 1844, thanks to the lightning
calculator Dase, we have its value to the 200th decimal place, and this
should satisfy even the most extravagant demands. This number,
associated with the circle, is a classical example of how an
approximation that is expressible in figures of very small value gives
an order of accuracy that can be described only by using fantastic
illustrations.

If we take a circle of the size of the equator, and also multiply the
value of the diameter of the earth by π, we know that the latter result
will not be exactly equal to the former, and that there will always be a
small remainder. If this discrepancy were less than a metre, the order
of exactness would be extraordinarily high, for a metre is practically
insignificant compared with a mighty circle of the dimensions of the
earth's circumference.

Let us stipulate still greater accuracy. We demand that the error is to
be less than the thickness of the thinnest human hair. We find, then,
that we must take for π at most 15 places of decimals. Thus, if we use
π = 3.14159265358973, we are applying a means of calculation that
reduces the possible error in all measurements of circles on the earth
to a degree beyond the limits of human perception.

If we pass beyond the world out into celestial space, and consider
circles of the dimensions of a planetary orbit, nay, further, if we pass
on to the Milky Way or even to the limit of visible stars, to find space
for our circle, and if in this case we still reduce the discrepancy so
as to be less than any length that is observable under a microscope,
then the last given value of π still suffices. Yet we must not forget
the proviso: _semper aliquid haeret_, something unsolved still clings to
the problem.

Such numerical approximations, however instructive they may be,
nevertheless retain a comparatively playful character, and furnish only
a superficial analogy to the most important approximations that are
contained in our natural laws themselves. It is these, above all, that
manifest themselves so clearly in Einstein's life-work, and they bear
the same relation to the former as truth bears to correctness. Truth
comprises the greatest conceivable circle of ideas and passes far beyond
the sphere of correctness, which deals only with measure-relations, and
not with the things in themselves. If Einstein, as we learn,
emphatically declares truth to be the only object of science, he means
the strictly objective truth that is to be derived from Nature, the true
relationship of phenomena and occurrences, independently of whether
restless philosophy assigns a question mark to this ultimate
objectivity. A great discoverer in the realm of Nature cannot and dare
not proceed otherwise. For him there is behind the veil of Maya not a
phantom that finally vanishes, but something knowable, that becomes ever
clearer and more real as he detaches each successive veil in his process
of approximation.

During this conversation, when we were talking of the "Future of the
Sciences," Einstein gave his ideas free rein, shooting far ahead of the
views and prognostications of the above-mentioned scientists:

"Hitherto we have regarded physical laws only from the point of view of
_Causality_, inasmuch as we always start from a condition known at a
definite cross-section of time, that is, by taking a time-section of
phenomena in the universe, as, for example, a section corresponding to
the present moment. But, I believe," he added, with earnest emphasis,
"that the laws of Nature, the processes of Nature, exhibit a much higher
degree of uniformity of connexion than is contained in our
time-causality! This possibility suggests itself to me particularly as
the result of certain reflections concerning Planck's Quantum Theory.
The following may be conceived: What belongs to a definite cross-section
of time may in itself be entirely devoid of structure, that is, it might
contain everything that is physically conceivable, even such things (so
I understood him to say) as, in our ordinary physical thought, we
consider impossible of realization, for example, electrons of arbitrary
size, and having an arbitrary charge, iron of any specific gravity, etc.
By our causality we have adjusted our thought to a lower order of
structural limitations than seems realized in Nature. Real Nature is
much more limited than our laws imply. To use an allegory, if we regard
Nature as a poem, we are like children who discover the rhyme but not
the prosody and the rhythm." I interpret this as meaning that children
do not suspect the restrictions to which the form of the poem is
subject, and just as little do we, with our causality, divine the
restrictions which Nature imposes on occurrences and conditions even
when we regard them as governed by the natural laws we have found.

Thus a leading problem of science in the future will be to discover the
restrictions of Nature as compared with the apparent causality implied
in physical laws.

We have in this an example of the transcendental perspectives that are
opened up when we accompany Einstein on one of his excursions of
thought. In this case it is actually a question of ultimate things, of a
region of discovery of which we cannot yet form a conception, and it
appears doubtful whether the problems latent in it are to be treated by
making investigations into physical nature, or whether they are to be
allotted to speculative philosophy.

In the first place, Einstein's remark seems to aim at nothing less than
a revision of the conception of causality. However much has been done to
purify this conception and to make it clear, we have here, perhaps, a
new possibility of refining it by making a synthesis of scientific and
abstract philosophical views. We shall just touch very lightly and
superficially on the possibility of a synthesis giving us an avenue to
truth. Whoever has heard these words of Einstein, feels the need of
getting on to firm ground to rescue himself out of the turmoil of ideas
into which he has been plunged.

What is Causality? A physiological answer may be given by saying that it
is the irrepressible animal instinct, rooted in our brain-cells, that
compels us to connect together things that we have experienced and
imagined. Poets have defined Hunger and Love as the fundamental elements
of our social lifes; we need only add the thirst for causality to this
to complete the list of primary instincts. For this mental thirst is not
less intense than our bodily hunger, and is even greater in that it
never forsakes us for a moment. It is easier for the body to check
breathing than for the soul to still the question of the why and
wherefore, of the cause and effect, of the antecedent and consequent.

This ceaseless search for a connexion between occurrences has become
organized into a fixed and immovable form of thought, which remains
mysterious even when we imagine that we have eliminated all the mystery
from it. The relations that we seek and that we regard as being of an
elementary character are totally foreign to Nature herself. David Hume,
the first real, and at the same time the most penetrating, explorer into
this form of thought, said that, in the whole of Nature not a single
case of connexion is disclosed which we are able to grasp. All
happenings appear, in reality, disconnected and separate. One "follows
on" another, but we can never detect a connexion between them. They
appear "co-joined," but never "connected." And since we can form no idea
of what has never presented itself to our outer or inner perception, the
necessary conclusion seems to be that we have absolutely no idea of
causal connexions or causative forces, and that these expressions are
quite devoid of meaning, however much they may be used in philosophical
discussions or in ordinary life. This "Inquiry concerning Human
Understanding," with its atmosphere of resignation, has been elaborated
in manifold ways, particularly by Kant and the Kantians; for it is
impossible to take up a philosophic thread without entering on an
examination of the fundamental question concerning the existence of a
causality which lies outside our instinct for causality. It is also
inevitable that, whenever we start out in this direction, we encounter
the further question: What is Time? For causality directs itself to the
problem of succession, both of sensations and phenomena, consequently
the two questions are not only intimately connected, but are really only
different expressions of one and the same question. Time, which
according to Descartes and Spinoza is a _modus cogitandi_, not an
_affectio rerum_, and, according to Kant, is an _a priori_ form of
thought, dominates our intelligence with the same sovereign power, as
the imagined course of things: what we perceive in the corresponding act
of thought is regarded as temporal and causal, and impossible of further
analysis.

Now, the conception of time has been entirely revolutionized by Einstein
himself; and it may be expected that the conception of causality,
too--which, in accordance with custom, we still endow with a separate
existence--will also be affected by this revolution.

We thus approach a relativization of causality, and we may advance a
step further in this direction, if we call to mind the differences of
time-perception that Nature herself leaves open to us. It must be
clearly understood that we are not dealing at present with the
theoretical time of physics, in the sense of Einstein's theory, but with
something physiological that ultimately, however, resolves itself into a
relativization of time, and hence also of the causal connexions in time.

To do this, we have to follow the lines of reasoning developed by the
celebrated St. Petersburg academician, K. E. von Baer, and we need
extend it only very little to get at the heart of causality, if we start
from his address of 1860: "Which View of Living Nature is correct?" For
the human brain is a part of living nature, and hence the processes of
thought may also be conceived as expressions of life.

The starting-point is a figment, the fictitious character of which
vanishes as soon as we approach its results. The bridge of thought may
be destroyed later; it suffices to carry us temporarily, as long as it
lands us in safety on the other side.

The rapidity of perception, of the arbitrary motions, of intellectual
life seems in the case of various animals to be proportional
approximately to the rapidity of their pulse-beats. Since, for example,
the pulse of a rabbit beats four times as quickly as that of a bull, it
will, in the same interval of time, also perceive four times as quickly,
and will be able to execute four times as many acts of will, and will
experience four times as much as the bull. In the same astronomical
length of time the inner life and perceptual world, in the case of
various animals, including Man, will take place at different specific
rates, and it is on these rates that each of these living creatures
bases its subjective measure of time. Only when compared with our own
measure of time does an organic individual, say, a plant, appear as
something permanent in size and shape, at least within a short interval.
For we may look at it a hundred times and more in a minute, and yet
notice no external change in it. Now, if we suppose the pulse-beat, the
rate of perception, the external course of life, and the mental process
of Man, very considerably accelerated or retarded, the state of affairs
becomes greatly changed, and phenomena then occur, which we, fettered by
our physiological structure, should have to reject as being fantastic
and supernatural, although, on the supposition of a new structure they
would be quite logical and necessary. If we suppose human life from
childhood to old age to be compressed into a thousandth part of its
present duration, say, into a month, so that the pulse beats a thousand
times more quickly than occurs in our own experience, we should be able
to follow the course of a discharged bullet very exactly from point to
point with our eyes, more easily than we can at present observe the
flight of a butterfly. For now the motion of the bullet in a second will
be distributed among at least 1000 pulse-beats, and will induce at least
1000 perceptions, and accordingly, in comparison with our everyday
perception, it will appear 1000 times slower. If the duration of our
life were again to be reduced to a thousandth of its first reduced
value, that is, shortened to about forty minutes, then our flowers and
herbs would seem just as motionless and immutable as rocks and
mountains, in which we only infer the changes without having directly
observed them. We would in the course of our lifes see little more of
the growth and decay of a bud and a flower in full bloom than we at
present see of the geological changes in the earth's crust. The acts of
animals would be much too slow to be seen; at most, we could infer them
as we do the motions of the stars at present. If life were shortened
still further in the same way, light would cease to be an optical
occurrence to us. Instead of seeing the things on which light falls, we
should become aware of them as being audible, and what we at present
call tones and noises would long have ceased to have an effect on the
ear.

If, however, we let our fancy roam in the opposite direction, that is,
if, instead of compressing the duration of human life, we expand it
enormously, what a different picture of the world would present itself!
If, for example, the pulse-beat, and hence the rate of perception, were
to be made a thousand times slower, so that the average human life would
be spread out over, say, 80,000 years, and that we should experience in
one whole year only as much as we now experience in a third of a day,
then, in every four hours winter or any other season would pass by,
vegetation would spring up and as rapidly die. Many a growth would not
be perceptible, on account of its relative rapidity compared with the
rate of the pulse-beat. For example, a mushroom would suddenly come into
existence, like a newly formed spring. Day and night would alternate as
a light and a dark minute; and the sun would appear to fly over the
heavens like a fiery projectile. If we were again to make the duration
of human life a thousand times longer still, and hence the rate of life
a thousand times slower still, we should, during the whole of an
ordinary year, be able to have only 190 distinct perceptions, so that
the difference between day and night would vanish entirely, and the
sun's path would be a glowing circular band in the heavens, and all
changes of form that seem to us to happen quietly and regularly, and to
preserve a certain permanency, would melt together in the wild stream of
happening, engulfed in its onward rush.

Are we justified in opposing to this relative perception of time "our
own" time, which is something specific and dependent on our constitution
as human beings? Should we not rather adopt the view that this specific
time, adapted to our particular pulse-beat, gives only a very limited
picture of the world, which is conditioned and determined by the
limitations of our own definite intelligence? Is it, perhaps, only a
distorted picture, a caricature, of actual occurrences?

An intelligence infinitely superior to our own would no longer be
dependent on the separate sensations such as are presented to us with
the rhythm of the pulse. For such a mind there would be no metronomic
foundation in the sequence of occurrences, beyond what represents itself
as time to our understanding. He would be situated outside of time in
what Thomas Aquinas called the _nunc stans_, in the stationary present,
without a retrospect of the past and without expectation of a future.
Without the Before and the After, the occurrences of the world would
acquire the clearest and simplest meaning, like that given by an
equation of identity. What presents itself to us as a "succession" of
events would merge together into one whole, just as a succession of
numerical calculations become summarized in a rule of calculation, or as
a series of logical operations resolves into a logical self-evident
truth. If the mind conceived by Laplace actually existed, it would stand
above the necessity of introducing time as a quantity into its
world-equations, for time is a purely anthropomorphic quantity, produced
by our perception, and regulated by our own characteristic pulses.
Accordingly, the conception of causality, too, which is indissolubly
connected with time, must be regarded as anthropomorphic, as something
that we read into, and not out of Nature. We should at least have to
recognize that if there is a causality outside ourselves, then we can
learn only a minimum about it, and even this only in a world displaced
or distorted by the accidental rate of our pulse-beat.

Let us now repeat Einstein's assertion "that the laws of Nature, the
processes of Nature, exhibit a much higher degree of uniformity of
connexion than is contained in our time-causality! It is possible that
what belongs to a definite cross-section of time may in itself be
entirely devoid of structure, that is, it might contain everything that
is physically conceivable, even such things as, in our ordinary physical
thought, we consider impossible of realization, for example, iron of any
arbitrary specific gravity." It seems to me that the non-physicist will,
perhaps, gain a clearer insight into these highly significant words of
Einstein, now that he has received the assistance of these physiological
considerations. It must be granted that the philosophic grounds of
Einstein are quite different and lie much deeper than those of von Baer,
who starts from organic functions and ends by arriving at a mysterious
relativity that is yet consistent in itself. Nevertheless, there is one
point of contact, inasmuch as in each case possibilities that lie
apparently _extra naturam_ are suggested.

Einstein says: "Hitherto we have regarded physical laws only from the
point of view of _causality_, inasmuch as we always start from a
condition known at a definite cross-section of time, as, for example, a
section corresponding to the present moment." At our own risk an easy
paraphrase of his words will be attempted:

The time-section of the present contains for us the sum of all previous
experiences, out of which the necessary course of our thought sifts out
the category of causality.

What is not present in experience cannot appear in our causality. Let us
consider for a moment Hume's example of the Indian who has never known
ice. Without being told, and if he is dependent only on his own
sensations, he would never learn that water freezes in cold climates.
The influence of cold on water is not gradual, corresponding to an
increase of cold, and not one that may be anticipated in all its
consequences, but at the freezing-point water, which a moment before was
a very mobile liquid, passes into a very rigid solid. The causality of
the Indian cannot account for this. If we tell him of this phenomenon,
he has two courses open to him. Either he refuses to believe it--and
this would be quite natural, since rigid water is to him as meaningless
as is a square circle to us. Or else he believes the story, and then his
list of categories incurs a break, passing through the middle of
causality. He has then to reconcile himself to the assumption that
something that is meaningless to him and that stands outside the
connexion of cause and effect is possible of realization. Up to that
moment, in his time-section of the present, there was no room for it in
his causality. To Torricelli the conception of liquid air, which we have
been able to prepare only since 1883, would have appeared impossible and
incompatible with his causality.

So there is no room in our causality for the idea of iron with the
specific gravity of air, or with one several times that of gold. For,
reasoning along the lines of our causality, we should conclude that a
substance that is so light or so heavy may, indeed, exhibit chemical
relationship with iron, but it would not itself be sufficiently defined
by the term _iron_.

Now Einstein also said: "Real Nature is much more limited (or bound)
than our laws imply." A sceptic might be disposed to take these
statements separately in order to construe a contradiction out of them.
For, if there are limiting conditions in Nature, which are foreign to
the views expressed in our laws, how would it then be possible for
phenomena, which cannot be imagined, to become realized? If Nature can
do this, surely she must have more liberty than we seek to impose on
her. This apparent contradiction vanishes if we treat the conception of
structural design or uniformity as something distinct from the measure
of all experience up to the present. This would give us the following
interpretation:

Out of the manifold of occurrences that are possible in mechanical
Nature, real Nature selects a very closely defined manifold. Thus the
true laws imply a much greater degree of limitation than those known to
us. For example, the laws known to us at present would not be affected
if we should discover electrons of arbitrary size or iron of arbitrary
specific weight. But Nature realizes only electrons of a quite definite
size and iron of a definite specific weight.

     *     *     *     *     *     *     *     *

Let us bear in mind that in aiming at ultimate truths we have no final
courts of appeal. Nor are the latter to be assumed even when, in
pursuing a theory, we encounter a difficulty, which at first exhibits
all the signs of a direct conceptual contradiction. It should rather be
realized that a fiction containing an initial but only provisional
contradiction serves as a starting-point for just those investigations
that are most subtle and that have far-reaching consequences. We should
have no Infinitesimal Calculus, no Algebra, no Atomic Theory, no Theory
of Gravitation if, to avoid all initial contradictions, we surrender the
fiction of differentials, of imaginary quantities, of the atom, of
action at a distance. In short, it may, indeed, be said that not only
knowledge, but also life, the holding together of people by convention,
law, and duty, would become impossible if we did not accept the fiction
of free will, which directly contradicts the determinate character of
all happening, including actions and motives, which, physically, alone
seems recognizable.

Fiction (not to be confused with hypothesis) and anthropomorphism, in
spite of their inner inconsistency, are the two poles about which our
thoughts and our lives revolve. And no doctrine will ever soar to such
heights that it will be able to deny completely its origin from these
roots of all thought. The Archimedean thought-centre of the universe,
which would enable us to lift the world out of its hinges, is
unattainable, because it does not exist at all.

Is this also to apply to the new physics, whose results are to be
regarded as the last word in scientific knowledge? Many a hypercritical
thinker might be led away by the current of the preceding statement, and
feel disposed to answer in the affirmative, were it not that, here too,
a contradiction intrudes itself. This is expressed in the fact that not
one of the present-day philosophers is in a position to pursue the
threads of this theoretical fabric to their hidden ends.

Thus we arrive at a parting of the ways. Whoever aims at becoming
thoroughly familiar with Einstein's new world-system finds that the
study of the theory claims so much attention that there is scarcely a
possibility left of proceeding to an ultimate philosophical analysis.
And whoever is absorbed only by the desire of making philosophic
investigations soon enough arrives at border-lines of thought, at which
his conscience warns him to beware of insufficient scientific knowledge.
He will be attacked by doubts as to whether he has properly understood
the theory. And he will be confronted with the question whether he is
justified in drawing ultimate philosophical conclusions before he has
mastered all the mathematical details.

As far as can be judged at present, only one thinker has, so far, had
sufficiently wide knowledge to enable him to correlate the physical
theory methodically with the theory of knowledge. I mean Professor
Moritz Schlick of Rostock, who has set out his ideas systematically in
his book _Erkenntnislehre_, which is extraordinary in itself and in its
great scope; it takes us beyond Kant. In Schlick's opinion Einstein's
theory furnishes us with the key to new and unexpected chambers of
thought; it is a wonderful instrument for opening up new avenues, and
would appear more wonderful still if we could use this instrument
without having recourse to anthropomorphism. This limitation may lead to
a Utopia, or may entail a _circulus vitiosus_. But we have one
philosophy nowadays which applies to what cannot be fulfilled "AS IF" it
really is capable of fulfilment. Among the disciples of Vaihinger, the
founder of the As-If-doctrine of thought, we, however, notice the
tendency to follow anthropomorphic and fictitious paths also in his
field of thought.

From numerous utterances of Einstein, I have gathered that he himself
does hot give his unqualified approval to all attempts at unravelling
the ultimate problems by means of philosophy, that is, by using
metaphysics alone. He does not deprecate these endeavours, but even
expresses admiration for some of the newer works, as for that of
Schlick, yet he sees certain obstacles in the purely philosophical
methods, that at least restrain him from taking a systematic interest in
them. This reluctant acceptance of, and doubt in, the processes of
philosophy, that has never forsaken the exact investigator, this
suspicious attitude which scents traces of sophistic and scholastic
machinations in all metaphysical arguments, also asserts itself in him
in a noticeable form. He feels the absence of rigour and of consistency
of direction, which is a guarantee of progress in passing from one
result to another, in the method of thought of those who are pure
philosophers: and he deplores the spongy and murky appearance of certain
expressions of thought, which, it must be admitted, form a poor contrast
to the completeness and the crystal clearness of mathematico-physical
reasoning. There was an inscription on the portals of the Athenian
Academy which stated that entrance was forbidden to all who had had no
mathematical training; we may imagine next to it an academy of pure
transcendental philosophy, bearing the inscription: No exact research
allowed! I believe that this clear-cut distinction would tally with
Einstein's view.

In the case of the great Ernst Mach, for whom Einstein has intense
admiration, we observe a similar attitude, or we may say that, in the
language of allegory, he sang openly the same refrain in another key. He
never ceased reiterating that he was properly "no philosopher at all,
but only an investigator of Nature." At the beginning of the
introduction to one of his works we read his confession: "Without in the
slightest degree being a philosopher, or even wishing to be one ...";
and some lines further on he calls himself sarcastically "a mere amateur
sportsman" in philosophical regions. Yet, Mach's initial remark is
followed by a remarkable result, for the book in question, _Knowledge
and Error_ (Erkenntnis und Irrtum), is to be reckoned among the most
important works in philosophical literature; and he himself, the amateur
sportsman, who did not even desire to be called a philosopher, accepted
in 1895 the post of Professor of Philosophy at Vienna University. It was
merely his timidity in the face of the philosophical fraternity that had
made him emphasize repeatedly the distinction between his own work and
that of the philosophers, whereas in his heart he had nourished a
passion for Philosophy, the first mother of Science. And in my opinion
such a moment may arrive for even the most rigorous investigator when he
succumbs to the siren strains from the shores of philosophy.

As far as Einstein himself is concerned, I cannot venture on a
prognostication. Even though he belongs to the category and rank of
Descartes, Pascal, d'Alembert, and Leibniz, in whom Mathematics and
speculative Philosophy are intermingled, he is yet characterized by such
a pronounced individuality, that it is quite inadmissible to draw
conclusions about him from others. He has no need to experience a day of
Damascus, for he carries the gospel of salvation in himself, and it
radiates from him. One thing seems possible, in my opinion, namely, that
Einstein will occasionally roam into the neighbouring realm merely from
æsthetic motives. Although the means of philosophy are nebulous and
more indefinite than those of exact science, which are almost glaringly
distinct, philosophy itself for this reason is the more closely related
to Art. And a theory that applies to the whole universe must assuredly
contain many germs that may come to life if subjected to the methods of
Art. The connecting link between Kant and Schiller shows in what sense
this is to be understood. Even at present there are indications in Art
which tend to show that it is ready to establish points of contact with
Knowledge. In France symphonic poems were written on the measure
relations of the circle, and on logarithms: these are at present only
curiosities, but may in future become models. At a much later date,
perhaps, the four-dimensional universe may become ripe for treatment by
such methods of Art. On the way to this goal there is the treatment with
the symbolic, non-rigorous, and semi-poetic means of expression used by
Philosophy. Many will use their efforts to achieve this, and perhaps
they will come within closer range of success, if Einstein himself lends
a helping hand. It will not be possible to arrive at new physical truths
by following this path, but those that are actually known will be traced
more readily to the great mainstream of philosophy. To fathom the
secrets of the world is the work of a recluse, but to make it
comprehensible to a wide circle, a preacher is necessary, who uses the
beautiful methods of philosophical rhetoric. Cosmos denotes the World
and its Ornamentation; its creator, Demiurge, is a master who fashions
his forms along the lines of Art.

Thus we have learned what Einstein regards as the sole purpose of
Science, namely, the search after Truth. For him, the latter is
something absolute in itself, and the possibility of getting nearer to
it is as great as the impossibility of deriving results of scientific
use from, say, ethical discoveries. For ethics is a field which is
haunted by the conceptual ghosts, and the manner of treatment, _ordine
geometrico_, that Spinoza wished to apply to it, is reserved for
physics. Einstein leaves the inverse philosophical query: "Is not Truth
in itself only something that we have constructed in imagination?" to
those who find pleasure in sauntering along paths of thought that are
totally unconnected, whereas he himself advances in a straight line with
the consciousness that even if the goal is unattainable, he will at
least not lose the right direction!




CHAPTER VIII

HIGHWAYS AND BY-WAYS

Practical Aims of Science.--Pure Search for Truth.--Retrospective
Considerations.--The Practical Side of Kepler.--A Saying of
Kant.--Mathematics as a Criterion of Truth.--Deductive and Inductive
Methods.--Conceptual and Perceptual Knowledge.--Happiness and the
Pleasures of Theory.--Achievements of Science and Works of Art.--Ethical
Results.--Minor Questions.


AGAIN we chanced to refer to the great subject: Can or should
theoretical science also pursue practical aims?

It is impossible to overrate the importance of this question. It haunts
us daily and often enough looms up threateningly on the horizon of
mankind. Observe what form the discussions of educated people take when
the finest and most sublime achievements of mind are being debated: one
talks of the wonders of research in the remotest corners of astronomy
where the structures of world-wide star-systems are being investigated;
we hear observations about the theories that aim at tracing the
cosmogonic development of universes from the original chaos of countless
ages ago. We hear mention of exalted sciences, the Theory of Functions
and Numbers, whose founders and representatives are just as remarkable
in propounding problems as in solving them, and inevitably the following
question obtrudes itself: Of what use is it, ultimately? What can one do
with it? Can it be admitted that theoretical science has an object of
its own, or have we at least the right to maintain the hope that, sooner
or later, it will bring us a real "Utility" expressible in practical
terms?

And just as the devotees of pure art have framed the expression, "L'art
pour l'art," so Einstein proclaims that science is its own object,
"Science for its own sake!" It carries its aims absolutely in itself and
must not, through aiming at other purposes, stray from its own highways.
"It is my inner conviction," said he, "that the development of science
itself seeks in the main to satisfy the longing for pure knowledge,
which, psychologically, asserts itself as religious feeling."

"To yourself, Professor, the practical aspect seems comparatively
insignificant?"

"I did not say that, and it was not implied in the question. We must not
lose sight of our premises. As long as I am interested in working along
lines of research--this was the assumption--the practical aspect, that
is, every practical result that is found simultaneously or arises out of
it later, is a matter of complete indifference to me."

Far be it from me, even in thought, to wish to question this confession
of faith, particularly as the fact that it comes from a searcher of the
truth gives it the more weight. Yet a certain uneasiness has crept over
me because voices have recently made themselves heard that demand for
science a totally different tendency. They arise not only from the
public at large, but also from academic circles. Just a short time ago
I read an exposition by a well-known scientist, W. Wien, in which he
indulged in a violent polemic against the view that purely scientific
objects are alone valid. Professor Wien addressed himself particularly
to German physicists, reproaching them with underestimating technical
science, and with regarding it as a "lowering of status" when a
physicist enters into practical life.

To this Einstein remarked: "I do not know at whom this reproach is
aimed, but I venture to think that my own attitude can never have given
rise to an attack of this kind. For I make no divisions of rank, and
recognize no higher and no lower status. I affirm only what is the
nature of science herself, and the objects according to which she,
objectively, has to direct her gaze. Whatever further orientation
individual investigators may seek for themselves depends on the
determining conditions of life of each, although these conditions do not
serve as a means for deducing the main lines of research. The accusation
that I am unwarranted in putting forward this view will, I hope, not be
levelled at me, for my connexions with practice are manifold enough, and
up to the present moment I have often collaborated with practical
physicists...."

"As I have regretfully observed when you were obliged to interrupt a
conversation with me to give an audience to impatient persons seeking
advice in technical matters!"

"My own associations with the world of practice are not, indeed, of
recent date. My own parents originally wanted me to become a technical
scientist, and I was expected to choose this profession to earn my
livelihood. I was not, however, sympathetically inclined to it, for even
at an early age these practical aims were to me, on the whole,
indifferent and depressing. My idea of human culture did not coincide
with the current view, that cultural development is to be measured in
terms of technical progress. Doubts, indeed, arose in me as to whether
technical improvements and advances would actually contribute to the
well-being of mankind. I must add that, later, when I came into actual
touch with technical science, my opinion became somewhat modified, for
the reason that, here too, pleasures of theory often visited me."

The true position is probably that the technical worker who does not
merely think out improvements for machines, but occupies himself with
inventions on a higher plane, never ceases to feel himself a theorist,
since his achievements are dependent for their inspiration on the fruits
of theory. The practical results of to-day are rooted in the theoretical
results of decades ago, and what is nowadays regarded as an idea of pure
research may in later decades acquire practical value. Whether it
actually becomes of value, or not, is of little account in judging the
idea. At any rate experience has shown that the beginning of theoretical
investigations hardly ever gives us the chance of making
prognostications. We spoke of the discoveries of Volta, Ampère, and
Faraday. When these were first known, the world might have asked: Why
have they been disclosed? To what can they be applied? Of what use are
they? Nowadays we know the answers that still lay hidden at that time,
and we proudly point to modern dynamos. But does a dynamo really
represent the significance of these discoveries? Would the importance
and rank of Volta, Ampère, and Faraday be less if the dynamo had not
come into existence? Only an out-and-out materialist would affirm this,
and, strictly speaking, the question should not even be raised. For it
is in a sense equivalent to wishing to judge of the importance and
significance of the Polar Star from its usefulness to the navigator on
the earth's surface in finding his bearings. We may put the question
(although only in the spirit of psychological curiosity, and without
expecting much elucidation): Would these discoverers have been
particularly happy if they had divined the far-reaching consequences of
their work? Did they, indeed, in the course of their abstract
researches, have a pre-vision of the future dominated by the dynamo?
Einstein refused to answer this in the decisive negative. He left room,
if ever so little, for doubts--that is, he considered that, in all
probability, these three discoverers had no presentiment of these
consequences, and even if they had in a dream caught a glimpse of our
present electrical age, their zest for discovery, their "pleasure in
theory," could scarcely have been increased; for they were discoverers
by nature, who, swept along by their own spirits, did not need to wait
to satisfy the desires of practical application.

In Einstein's opinion, the presentiment that a discovery may have
practical applications in the future may react on pure research. He
quoted bacteriology as a proof of this. In the series of eminent
bacteriologists, ranging from Spallanzani to Schwann and Pasteur, there
were certainly some whose desire for knowledge was directed primarily
towards discovering purely scientific relationships. Pasteur himself
started from the theoretical question of the creation of life, that is,
from the problem of the origin of organic creatures from inorganic
matter without the medium of parent organisms. As a pan-spermist he took
up a negative attitude, that is, he tried to prove that it is impossible
to discover a bridge between organic and inorganic matter. Yet he
doubtless knew that his theoretical efforts stretched out into practical
regions, and he may easily have foreseen that they would exert a very
important influence on Medicine and Hygiene, although he could not
measure its full extent. In this case, then, we cannot fail to recognize
that a certain connexion between the desire for pure knowledge and the
impulse to apply it practically is possible, serviceable, and justified
in itself.

An influence in the opposite direction is also possible, and when,
during the course of our conversation, we went in search of examples, we
came across one of great interest. It shows us that a question may arise
out of ordinary practice that may open up an immense field of pure
knowledge, nay, it may lead to a science of very wide scope. As this
example is not well known, I shall mention it here; I do so with
additional pleasure as the scientist involved is one of those whom
Einstein quotes most frequently and for whom he has the greatest
admiration, namely, Johannes Kepler. First we have the surprising fact
that Kepler, who, even when at the height of his fame, was not free from
care, was once the possessor of some money. In the year 1615, his
blessed year of fortune, the great astronomer owned a comfortable home
in Linz, and even dared to conceive the idea of placing some well-filled
casks in his cellar; nay, more, he was in a position to publish a new
scientific work at his own expense, and thus appear as his own
publisher.

This production of Kepler and his casks of wine are directly connected,
as we see clearly from the title: _Doliometrie_, literally, "The
Measurement of Casks." But the title of the work gives not the slightest
hint of its importance. For these investigations relating to wine-casks
actually became the foundation of a science of sovereign power, the
_Infinitesimal Calculus_.

What was Kepler's aim? It was something entirely practical, and directed
to a definite purpose, quite independent of "pleasures of theory," to
repeat Einstein's expression. His problem was a question of economy, of
using material sparingly and appropriately, in accordance with the
requirements of the careful head of a house. How must such a cask be
constructed from a minimum of wood to give the greatest cubical content?

His deliberations began by regarding wine as the precious content
enclosed by a figure in space, and then conceiving the cask as
representing a particular class of "bodies of revolution," that is, of
figures in space that may be regarded as produced by the revolution of a
curved line about an axis. At this point he at first endeavoured to gain
a complete survey of the question. He varied the boards along the sides,
the staves, and formed successively ninety-two such bodies of
revolution, some of which he named after the fruits which they resembled
in shape, as, for example, apple-shaped, lemon-shaped, olive-shaped
bodies. He started out by measuring casks, and the final result was that
his work, _Doliometrie_, became the source of all future cubatures or
measurements of volume.

Now we come to the deciding point. What conditions has the limiting
surface of such a cask-like body of revolution to fulfil, if the body is
to have a maximum volume? An epochal discovery here came to light. The
practical head of the house soars up into the sublime realms of the
theory of magnitudes. Kepler discovered the conception of changes in
functions, and their peculiarities at the maximum point. (He did not, of
course, use these modern terms.) By this means, long before Newton and
Leibniz, he laid the foundations of Infinitesimal Calculus, which later
became the heart and soul of mathematics, of astronomy, of theoretical
physics, and of technical science, in so far as it is founded in
mechanical relations.

On the other hand, Einstein who now, three hundred years later, has set
up his differential equations, and, with them, a new world-system,
stands before us as a pure discoverer, devoid of practical aims. But in
these equations there are elements of analysis that once came to light
in a happy idyll. This event did not come out of the grey obscurity of
abstraction, but out of a region of earthly happiness, when a ray of
light found its way into Kepler's gloomy existence. No poet has yet
expressed this curious complex of events in a ballad, telling how Truth,
the only object of Science, was pressed out of the grape, and how
Practice, inspired by the inquiry of a cooper, found its way to a Theory
that stretches to the confines of the Universe.




II


The conversation touched on famous expressions, words carved in stone,
in particular a saying of Kant which seeks to fix the foundation and the
limits of knowledge. "Every science of Nature," the great philosopher of
Königsberg had said, "contains just as much Truth as it contains
mathematics." And since, ultimately. Nature includes everything--for a
demarcation between physical and mental science no longer seems
possible--then, if we follow Kant, we should have to regard mathematics
as the sole measure of science.

It is certainly not yet possible to enter into a discussion on this
point with historians, medical or legal practitioners. They would be
justified in refusing it, since, in their subjects, "truth" is not the
sole factor, and because we cannot see at present how the conception of
a comprehensive mathematical truth is to find a place in them. But when
we question a physicist on this point, who unceasingly uses mathematics
as his chief instrument, we should surely expect him to answer with an
unconditional affirmative. At least, I should not have been surprised if
Einstein had answered in this way, and if he had indeed claimed its
validity for every branch of science.

But Einstein considered this quotation to be true only conditionally, in
that he accepted it as a principle, but did not regard it as universal.
That is, he does not recognize mathematics as the only test of truth.

"The sovereignty of mathematics," said Einstein, "is based on very
simple assumptions; it is rooted in the conception of magnitude itself.
Its dominant position is due to the fact that it gives us much more
delicate means of distinguishing between infinitely varied possibilities
than any other method of thought that expresses itself in language and
is restricted to the use of words. The greater the field taken into
consideration, the clearer does this become; but even in such a narrow
range as 1 to 100, an estimate such as 27 is incomparably more exact
than can be expressed in words in any other way. If we think of a series
of sensations, ranging from pleasure to pain, or from sweet to bitter,
we find that words leave us in an uncertain, confused state, and we do
not succeed in fixing on a point of the series with the same precision
as we above fixed on the 27 out of the 100. But when the theory of
magnitude plays a part in the question, as, for example, in a series of
tones, whose vibrations exhibit a mathematical sequence, we immediately
attain a much higher order of precision by using numbers...."

That is why there is a sort of scientific pleasure in the sequence of
tones, so my thoughts ran on. Leibniz remarks that "Music is the
pleasure of the human soul, which arises from counting without knowing
that it is counting." Here Pythagoras' "Number is the essence of all
things" is verified. As soon as we arrive at the stage at which we feel
the psychological essence of number, we fall into a sort of ecstasy,
because, in our subconscious minds, we experience not only the pleasure
of sense but also the underlying truth.

Einstein resumed: "Kant's remark is correct in the sense that it sets up
two things in clear contradiction to one another. On the one hand, he
has in view the fruits of knowledge of ordinary life, in which our
ordinary perceptions and experiences are intermingled and cannot be
disentangled by inductive methods and deductive considerations. Opposed
to these, and to be regarded of higher rank, are the properly scientific
constructions—that is, such in which we find a neat differentiation of
connected thoughts that are based on regular foundations and that form
the links of a chain of deduction. Whenever our science succeeds in
detaching this logically ordered knowledge from its sense-sources, it
has a mathematical character, and the amount of truth contained in it
will accordingly be determined by Kant's criterion. But Kant demands too
much when he asks us to apply this scale to all attainable knowledge of
science. It would seem advisable to draw limitations if his remark is to
serve as a regulative measure. A great part of biological science will
in future still be obliged to make its way independently of purely
mathematical considerations."

"Your reflections, Professor, would then also apply to the saying of
Galilei: The book of Nature lies open before us, but is written in
letters other than those of our alphabet; its characters are composed of
triangles, quadrilaterals, circles, and spheres."

"With all due honour to the beauty of this observation, I cannot refrain
from doubting its universal validity. If we were to accept it
unconditionally we should have to regard the paths of all research as
purely mathematical, and this would exclude certain very important
possibilities, above all, certain forms of intuition that have shown
themselves to be extremely fruitful. Thus, according to Galilei's
interpretation, the book of Nature would have been illegible for Goethe,
for his spirit was entirely non-mathematical, indeed anti-mathematical.
But he possessed a particular form of intuition that expressed itself as
a feeling which put him into direct contact with Nature, with the result
that he obtained a clearer vision than many an exact investigator."

"Do you then consider intuitive gifts to be separable at all in form and
in kind?"

"It would be pedantic to seek to establish a fundamental difference,
even if we may regard the non-mathematical intuition of Goethe as a very
striking case. Moreover, as I have often emphasized, all great
achievements of science start from intuitive knowledge, namely, in
axioms, from which deductions are then made. It is possible to arrive at
such axioms only if we gain a true survey of thought-complexes that are
not yet logically ordered; so that, in general, intuition is the
necessary condition for the discovery of such axioms. And it cannot be
denied that, in the great majority of minds with a mathematical
tendency, this intuition exhibits itself as a characteristic of their
creative power."

"From these remarks it would appear that you value deduction
considerably higher than induction. Perhaps in using these catchwords I
am expressing myself a little vaguely; it seems to me that great things
have been achieved, too, by using inductive processes."

"Let us first define what each of these terms means. Deduction is the
derivation of the particular from the general, whereas induction is the
process of deriving the general from the particular case. Now, quote any
example of a brilliant achievement, which you feel illustrates the power
of the inductive method. Of whatever kind your example may be, you will
soon become aware of the difference in the significance of the two
processes."

"For me the most perfect example of induction is given by certain
reasoning of Euclid. The question was whether there is a finite or an
infinite number of primes (that is, numbers that cannot be divided
without leaving a remainder except by unity). Euclid found an elegant
proof that the total number is infinite by the following strictly
inductive reasoning. If the total number were finite there would have to
be a _greatest_ prime. Let us call it _n_, and then form the product of
all primes up to _n_ and including it, finally adding one, thus:
2 x 3 x 5 x 7 x 11 x 13 ... _n_, plus 1. This new number, say Y, is
certainly greater than _n_, and now there are two possibilities, either
_n_ is prime or it is not prime.

"If it is not prime, it must be divisible by some existing prime. But
the primes up to and including _n_ cannot divide exactly into Y, as
there is always a remainder, namely, 1. Hence Y must be divisible by an
existing prime X greater than _n_. This contradicts the assumption that
_n_ is the greatest prime, for X is shown to be greater than _n_.

"Secondly, if Y _is_ a prime, it immediately follows that _n_ cannot be
the greatest prime, for Y is greater than _n_. Hence, however great may
be any prime that we may assume, there will always be one that is
greater, and even if we do not succeed in expressing it in figures, we
see that it must certainly exist. Thus by studying carefully a
particular case--the prime _n_, which was assumed to be the greatest
possible one--we have arrived at a general theorem which states that
there is no limit to the number of primes. Is not that, too, a triumph
of intuition?"

"Certainly," said Einstein. "But you must not overlook the fact that a
theorem of this kind cannot be ranked with a theorem of a fundamentally
axiomatic character. The one you have discussed has been derived by a
clever process of reasoning, but it does not exhibit the characteristic
of a momentous discovery. This theorem of Euclid can be imagined absent
from science without the content of truth in science being essentially
effected. Compare with it a theorem of axiomatic significance, such as
Galilei's Law of Inertia, or Newton's Law of Gravitation. Theorems such
as the latter are characterized by being starting-points of knowledge
that are inexhaustible in the consequences that may be deduced from
them. Your question, earlier, as to whether I consider the deductive
method superior to the inductive, was not formulated in correct terms.
To this I answered above that the inductive method as a means of
discovering general truths usually appears over-estimated. The proper
form of the question is: Which truths are of the higher order, those
that are found inductively, or those that lead to further deduction?
There can scarcely be doubt about the answer."

"No, that is certainly true. If I understand your meaning rightly, the
answer may be expressed by an allegory. Intuition of the highest order
creates treasure-mines, those of lesser degree individual articles of
value that are significant in themselves, although they cannot be
compared with the inestimable value of the mines. The fact that the
highest intuition is found in minds with a mathematical trend makes it
appear possible that Kant's remark may gain more and more credence in
the future. It already applies in a measure to subjects to which it
seemed inapplicable during Kant's lifetime, for example, in Psychology,
in which the relations between stimulus and response have been
established mathematically only since the Weber-Fechner Law was set up;
and also, since the time of Quetelet, in Moral Science and Sociology, we
learn from mathematical methods of statistics and probability that even
Man as an active being is subjected to mechanical causality. At any rate
it seems manifest that Kant's remark, that in every science there is
just as much truth as there is mathematics, has received additional
support in recent times."

"That may be admitted," concluded Einstein, "without recognizing his
remark as an axiom. It is still far removed from making possible
unassailable deductions, and will never quite succeed in doing so; yet
it may claim equal significance as a beautifully expressed idea with
that of Pythagoras, which asserts number to be the nature of all
things."




III


"The lines of demarcation between 'conceptual knowledge' (_Erkennen_)
and 'perceptual knowledge' (_Kennen_) are being drawn more and more
closely nowadays. The former is regarded as being the exclusive
possession of the highly developed human mind, and the latter as being
characteristic of the lower intelligence of other living creatures. Is
this not a pronounced case of anthropomorphism, and does it not mislead
us to form opinions that we should at once disown if we succeed in
stepping out of our human frames even for a moment?"

"We have to rest satisfied with anthropomorphism once and for all,"
answered Einstein, "and there is no sense in wishing to escape from it,
for the arguments about anthropomorphism are necessarily also diffused
with it, itself. We are thus moving in a circle if we imagine we can
deduce something outside of human knowledge. As soon as we have argued
around the circle, we find ourselves again at the starting-point, and so
we are compelled to mark clear lines of division between instinctive
knowledge, derived directly by perception, from conceptual knowledge,
derived by processes of abstraction and reflection; in this way we award
the palm of supremacy to the human mind."

"But what if the following contradiction were to assert itself? Suppose
that the logical 'circle' is not a circle at all, but a spiral, so that
the final point of the argument lies just a trifle above the initial
point. I feel instinctively that such apparently fruitless circuitous
arguments might finally lead to a definite piece of knowledge. For
example, a certain insect, the ichneumon-fly, although devoid of a
knowledge of science in our sense, infallibly plants its sting in a
definite point in the rings of a caterpillar, at just the point that
serves its purpose of paralysing the caterpillar without killing it. It
acts instinctively, and it is open to me to interpret this occurrence in
other words. The fly discloses that it 'knows' the anatomy of the
foreign creature, although it has no conceptual knowledge of it in our
sense. But it immediately follows from this analogy that, from the point
of view of the fly, its _perceptual_ intelligence stands higher than our
_conceptual_ intelligence--that is, by changing the perspective, I am
led to declare the anatomical knowledge of the fly to be of higher rank
than the analogous knowledge of the most learned anatomist. In the same
way I might persuade myself that the mathematics of a bird of passage
stands above the cartographic knowledge of any human explorer. The
migratory bird that flies from the interior of Africa in a straight fine
to its nest in Mecklenburg must have something in the nature of a
co-ordinate system in its organism. The real reason that we assign a
higher position to our conceptual knowledge is that we are equally proud
of our intelligence as of our science; this is perhaps a deception
depending on some compromise, a sort of illicit deal in which the mind
draws bills of exchange on science, and, as a return, science meets its
obligations by paying in cheques drawn on the mind!"

I must confess that these hazardous suggestions received no welcome from
Einstein, and were not even met with the friendly smile with which he
usually accompanies his refutations. Nor do I disguise from myself that
the question of conceptual or perceptual knowledge can in no way serve
as a basis of proof; we may at most base certain conjectures on the
difference of these types of knowledge, conjectures that suggest in
words what eludes our clear comprehension. Einstein's refusal to allow
this possibility certainly rests on much firmer ground than the somewhat
Bergsonian views that I tried to present. Perhaps they are of a
hair-splitting nature, and deal with things lying on different planes;
and are deduced by unjustifiably altering the perspective with a sort of
sophistic somersault; perhaps I may be reproached with seeking, like
Münchhausen, to reach a higher standpoint without having a support from
which to start. Yet how is it that I find it impossible to free myself
from this chain of thought? No reason is forthcoming, for it is a purely
metaphysical question, and there has never yet been a clear system of
metaphysics free from ambiguities and sophism.

Let us rather confine ourselves to the conceptual intelligence
characteristic of human beings, with which, according to Einstein, so
many pleasures of theory are available. I asked him whether he would
recognize differences of degree in these pleasures, dependent on their
intensities. Although I rightly felt that he would answer in the
affirmative, his answer took a totally different turn from what I had
expected. It was, indeed, a great surprise, for in the matter of
happiness of spirit he expressed a view, according to which he--a great
discoverer!--does not regard Science as the deepest source of happiness!

"Personally," said Einstein, "I experience the greatest degree of
pleasure in getting contact with works of Art. They furnish me with
happy feelings of an intensity such as I cannot derive from other
realms."

"This is indeed a remarkable revelation, Professor!" I exclaimed. "Not
that I have ever doubted your receptivity for products of art, for I
have often enough observed how you are affected by good music, and with
what interest you yourself practise music. But even at such moments when
you gave yourself up to the pleasures of the Muses, and were soaring in
regions far removed from the earth, I used to say to myself: This is a
delightful arabesque in Einstein's existence; but I should never have
surmised that you regard this decorative side-issue as the greatest
source of happiness. But your confession seems to go further, perhaps
even beyond music?"

"At the moment I was thinking particularly of literature."

"Do you mean literature in general? Or had you a definite writer in
mind, when you were speaking of the felicitous effect of works of art?"

"I meant it generally, but if you ask in whom I am most interested at
present, I must answer: Dostojewski!" He repeated the name several times
with increasing emphasis. And, as if to deal a mortal blow at every
conceivable objection, he added: "Dostojewski gives me more than any
scientist, more than Gauss!"

"If, Professor," said I, after a pause that may easily be accounted
for--"if you mention in the same breath the names of two such powerful
but essentially different intellects, you open the way to a discussion
that cannot be settled by a mere positive assertion. It is possible to
admire intensely Dostojewski as one who moulds personalities and who
analyses the inner struggles of the soul, and yet to deny him perpetual
fame. This depends on individual judgment, and, as for my own, I believe
that Dostojewski, in spite of his direct artistic appeal, will not have
his name perpetuated through the centuries like that of many another
member of Parnassus. It seems to me to be a more important matter
whether a common measure can be found for Art and Discovery at all.
Perhaps the test of how far a work can be replaced may be regarded as
valid for each. When you say that Dostojewski gives you more than Gauss,
this probably corresponds with the feeling that without Dostojewski you
would have no 'Karamasoffs' and hence would lack a certain life-value
that cannot be replaced. But if Gauss had failed to produce one of his
fundamental theorems of Algebra, probably some other Gauss would have
appeared, who would have achieved this result. According to this, then,
our instinct increases the value of a work of art, as we feel that we
are dependent on one being alone for its creation."

"But this is only to be admitted conditionally," said Einstein, "for the
best that Gauss has given us was likewise an exclusive production. If he
had not created his geometry of surfaces, which served Riemann as a
basis, it is scarcely conceivable that anyone else would have discovered
it. I do not hesitate to confess that to a certain extent a similar
pleasure may be found by absorbing ourselves in questions of pure
geometry."

"Perhaps we may use a different characteristic as a means of
comparison," I suggested, "namely, the permanency of the impression
produced on the subject receiving it. For example, a fine piece of music
never loses its influence. We can listen to the first movement of
Beethoven's Ninth Symphony a hundred times, and, although we know at
every beat what will follow, the state of pleasure continues unweakened;
indeed, it might rather be said that the expectation of pleasure
increases from one hearing to the next."

"This characteristic, too," answered Einstein, "cannot be claimed as the
exclusive property of works of art. Its existence cannot be doubted,
inasmuch as it belongs to every eminent example of art. Yet we encounter
it outside the realm of art, too, in great advances of science, with
which we never cease occupying ourselves, and yet the impression
continues unweakened."

"Do you include among them the impressions that a discoverer experiences
when he reviews in his mind the progress due to his own efforts?"

"Naturally, and these, indeed, quite particularly; and if this question
were put to me directly, I should answer unhesitatingly that I find
pleasure in reflecting on my own discoveries, and never experience
feelings of weariness in passing over them again. So that, to return to
our original thesis, we must adopt a new basis of value if we wish to
account for the fact that the greatest degree of happiness is to be
expected of a work of art. It is the moral impression, the feeling of
elevation, that takes hold of me when the work of art is presented. And
I was thinking of these ethical factors when I gave preference to
Dostojewskis works. There is no need for me to carry out a literary
analysis, nor to enter on a search for psychological subtleties, for all
investigations of this kind fail to penetrate to the heart of a work
such as "The Karamasoffs." This can be grasped only by means of the
feelings, that find satisfaction in passing through trying and difficult
circumstances, and that become intensified to exultation when the author
offers the reader ethical satisfaction. Yes, that is the right
expression, 'ethical satisfaction'! I can find no other words for it."

His whole face lit up, and I was deeply touched by his expression. At
that moment it seemed to me that he had drawn the last veil from his
soul to allow me to share in his ecstasy. Was that the same physicist
who interprets the events of the world in terms of mathematics, and
whose equations encompass phenomena from electrons to universes? If so,
it was a different soul; one which gave utterance, like that of Faust,
to the words:


   "And when in the feeling wholly blest thou art,
    Call it then what thou wilt.
    Call it Bliss! Heart! Love! God!
    I have no name for it!
    Feeling is all in all!
    Name is but sound and reek,
    A mist round the glow of heaven!"


And, certainly, the book need not have been one of Dostojewski's to
excite this feeling in him. He chose the latter to give expression to a
mood that may change according to what he reads, but undergoes no
fluctuations in its ethical foundation. From other occasions we know how
little ethics, that is conducted along systematic lines, signifies to
him, and that he does not even include it in the sciences. But at the
same time we see now that his inner life is dominated entirely by the
ethical principle. His deep love of Art is characterized by it, and
receives full satisfaction from the source of ethical joy of which Art
is the centre.




IV


During the autumn of 1918 Einstein was feeling indisposed, and, on the
advice of his doctor, did not leave his bed. When I entered his room, I
saw at once that there was no reason for alarm, for pieces of paper
covered with mysterious symbols were lying about, and he was absorbed in
making additions to some of them. Nevertheless, I considered it my duty
to treat him as a patient under medical care, and did not conceal my
intention of leaving him after having inquired about his condition. But
he would not accept my visit as a mere call to ascertain his progress
towards recovery, and insisted that I should remain with him a while, to
converse about amusing little problems as usual.

I pointed out to him that there were two objections to this, the first
being that he was unwell, and the second that I was intruding on his
work.

"How illogical!" he answered. "If I interrupt my work to chat with you,
I am putting aside exactly what the doctor would deny me if I were to
allow him. So, let us make a start. You have probably some conundrum
weighing on your mind."

"That may not be far wrong. I have been troubled by something in
connexion with Kepler's second law. It almost robbed me of my night's
sleep. My thoughts kept returning to a certain question, and I should
like to know whether there is any sense in the question itself at all."

"Let us hear it!"

"The law in question states that every planet in describing its elliptic
path, sweeps out with its radius vector equal sectorial areas in equal
intervals of time. But this seems only half a law, for the radius
vectors are only considered drawn from the one focus of the ellipse,
namely, the gravitational centre. Now, another focus exists, that may be
situated in space somewhere, perhaps far away in totally empty regions,
if we assume the orbit to be very eccentric. My question is: What form
does this law take if the radius vectors are drawn from this second
focus and if the corresponding sectorial areas are considered, instead
of these quantities being referred to the first focus exclusively?"

"This question is not devoid of sense, but it serves no useful purpose.
It may be solved analytically, but would probably lead to very
complicated expressions, that would be of no interest for celestial
mechanics. For the second focus is only a constructive addition, that
has nothing real in space corresponding to it. What else is troubling
you?"

"My next difficulty is a little problem that sounds quite simple and yet
is sufficiently awkward to make one rack one's brains. It was suggested
to me by an engineer who certainly has a keen mind for such things, and
yet, as far as I could judge, he did not get a solution for it. It
concerns the position of the hands of a clock."

"You surely are not referring to the children's puzzle of how often and
when both hands coincide in position?"

"By no means. As I said just now, it is really quite perplexing. Let us
assume the position of the hands at twelve o'clock, when both hands
coincide. If they are now interchanged, we still have a possible
position of the hands, giving an actual time. But, in another case, say,
exactly six o'clock, we get a false position of the hands, if we
interchange them, for on a normal clock it is impossible for the large
hand to be on the six whilst the small hand is on the twelve. The
question is now: When and how often are the two hands situated so that
when they are interchanged, the new position gives a possible time on
the clock?"

"There, you see," said Einstein, "that is just the right kind of
distraction for an invalid. It is quite interesting, and not too easy.
But I am afraid the pleasure will not be of great duration, for I
already see a way to solve it."

Supporting himself on his elbow, he sketched a diagram on a sheet of
paper that gave a clear picture of the conditions of the problem. I can
no longer recollect how he arrived at the terms of his equation. At any
rate, the result soon came to hand in a time not much longer than I had
taken to enunciate the problem to him. It was a so-called indeterminate
(Diophantic) equation between two unknowns, that was to be satisfied by
simple integers only. He showed that the desired position of the hands
was possible 143 times in 12 hours, an equal interval separating each
successive position; that is, starting from twelve o'clock, the two
hands may be interchanged every 5 minutes ²⁄₁₄₃ seconds, and yet give a
possible time.

     *     *     *     *     *     *     *     *

I mention this little episode, which is insignificant in itself, merely
to give an example of how a great discoverer, too, finds amusement in
such distractions. In Einstein's case this tendency to practise his
ingenuity on unimportant trifles is so much the more pronounced from the
fact that he requires an outlet for his virtuosity in calculation, and
gratefully welcomes every suggestion that helps him to relieve his
mental tension. Similar characteristics are reported of the great Euler,
as well as of Fermat, whereas many another eminent mathematician feels
decidedly unhappy if he drifts within reach of the realm of actual
numerical calculation. In my mind's eye I still see Ernst Kummer, the
splendid savant (who, in his time, conferred distinction on Berlin
University by his very presence), suffering agonies whenever ordinary
arithmetical tables threatened to appear in the working-out of his
formulae. As a matter of fact, these two things, a mastery over
mathematics and a talent for ingenious calculation, are to be considered
as quite independent, even if we now and then find them present in the
same person.

In the case of Einstein this tendency is a symptom of an incredible
universality of spirit. It moreover presents itself in the pleasantest
forms, and a character-sketch of Einstein would be incomplete if this
trait were not mentioned. Every problem which is in any way amusing
excites in him a willing interest and enthusiasm. I once directed our
conversation to the so-called _Scherenschnitte_. These are made from
long strips of paper or canvas, the ends of which are caused to overlap
a little and then pasted together, but instead of being fixed so that a
flat wheel results, which rolls on one side of the strip, the strip is
twisted one or more times before the ends are fastened together. If now
the strip is cut lengthwise right along its centre, various unexpected
results occur, depending on the number of twists that have been made
before pasting.

Some very complex geometrical difficulties are involved in these
problems. This is shown by the fact that learned mathematicians have
written extensive disquisitions on these curious constructions (for
example, Dr. Dingeldey's book, published by Teubner, Leipzig). Einstein
had never taken notice of these wonders of the scissors, but when I
began to form these strips, to paste them, and to cut them, he
immediately became interested in the underlying problem, and predicted
in a flash what puzzling chain constructions would result in each case,
with a certainty that would lead one to imagine that he had spent days
at it. On another occasion a space-problem dealing with dress came up
for discussion: Can a properly dressed man divest himself of his
waistcoat without first taking off his coat? One would not have dared to
confront Copernicus or Laplace with such a problem. Einstein at once
attacked it with enthusiasm, as if it were an exercise in mechanics, the
body being the object; he solved it in a trice, practically, with a
little energetic manipulation, much to the amazement and joy of the
beholder, who asked himself: Is this the same Einstein who developed the
work of Copernicus and Newton? A little later, perhaps, the conversation
centres around some serious point drawn from politics, political
economy, sociology, or jurisprudence. Whatever it may be, he knows how
to spin out the suggested thread, to establish contact with his partner
in conversation, to open up his own perspectives without ever insisting
on his point of view, always stimulating and showing a ready sympathy
for the subject of discussion and for all the ideas which it
crystallizes, the prototype of the scientist, in the mouth of whom
Terence put the words: "I am a human being; nothing that is human is
alien to me!"




CHAPTER IX

AN EXPERIMENTAL ANALOGY

Forms of Physical Laws.--Aids to Understanding.--Popular
Descriptions.--Optical Signals.--Simultaneity.--Experiments in Similes.


"I WISH to ask you. Professor, to help me over a difficulty and to treat
me as the spokesman of a great number who are similarly troubled. In
most accounts of your theory of relativity, there is a dearth of
definite, concrete, illustrative examples on which we can fix our minds
whenever the theorem is to be applied generally without limitation. Let
me express this more precisely: Your simplified picture of the structure
of the universe is achieved in the theory of relativity by emancipating
all observations from fixed co-ordinate systems, and by proclaiming the
equivalence of all systems of reference. One of your earliest theorems
states that physical laws describing how the states of physical systems
alter, remain the same, no matter to which of two co-ordinate systems
these states are referred, provided that the co-ordinate systems are
moving rectilinearly and uniformly relatively to one another. This
theorem entails the following statement. If we--erroneously--adopt a
non-relativistic view, we shall come to the conclusion that physical
laws depend on the particular system of reference chosen, and will thus
assume a different form for each different system. At this point we
experience a desire to hear definite examples. What varying forms may a
certain given physical law, known under a definite form, assume, and how
can we use this law to show that it must adapt itself to the postulate
of relativity?"

Einstein explained that such examples cannot be given in special cases,
but only in very general terms. If we were to suggest the elliptic
orbits of the planets (at which I had hinted in my remarks), we should
fall into error, for the law of elliptic orbits is no such law. For,
from another point of view, the elliptic paths of the planets might be
drawn out into wavy lines, or into spirals, and they would remain
ellipses only as long as the lines of motion are referred to the central
attracting body. But the constancy of the velocity of light is such a
law, as also is the law of inertia, according to which a body that is
left to itself moves uniformly in a straight line.

I confessed to him that this limitation to a few very general laws would
be a painful matter for many an enthusiast of average attainments, who
has great difficulty in distinguishing the laws that are _generally_
valid from those that hold only within circumscribed limits. But if this
were not so, we should have to alter our conception of what is conveyed
by a popular exposition. For it is called _popular_, not because it now
and then uses the patronizing words "dear reader," but because it
anticipates the questions and doubts of the man of average sense, and
examines them, proving some to be unjustified and others to be
reasonable or unreasonable, as the case may be. "Then there is a further
matter that troubles me," I continued. "Let us suppose an ordinary
reader of such a popular account to get a first insight into the new
conception of Time. He is glad to feel the ideas dawning in him, and, to
get a more lasting view of the idea, he repeats the arguments through
which he has just threaded his way, and, in doing so, again encounters
the phrase 'uniform motion.' At the first reading he imagined that he
understood the expression quite well, but the second time he pauses and
considers. For now that he knows how much depends on it, he is anxious
to find out the exact meaning of a 'uniform motion.' He looks for a
definition, and if he cannot find one in the book he is perusing, he
endeavours to reason it out for himself. With good luck he arrives at
the usual statement: a body moves with 'uniform motion' if it traverses
equal distances in equal intervals of time. But equal intervals of time
are clearly those during which a body in uniform motion traverses equal
distances. In other words, he explains A by means of B, and B by means
of A, so that he has involved himself in a vicious circle from which he
cannot escape. This is his hour of need, due to the difficulty of
'time.'

"He hopes that further study will remove this obstacle. He meets with
the conception of 'simultaneity,' which is defined for him anew, and is
disclosed as being 'relative.' He manœuvres further towards the
fundamental theorem that every body of reference has its own particular
time.

"His popular booklet makes this clear to him by quoting the example of a
flying-machine, or, better still, a railway train that is rushing along
an embankment at a very great speed, and that carries a passenger. Two
strokes of lightning I and II are to take place at two widely distant
points on the embankment. The question is then: When are these two
flashes of lightning to be considered 'simultaneous'? What conditions
must be fulfilled to ensure this? It is found--incontrovertibly--that
the light-rays starting out from the two strokes of lightning must meet
at the mid-point of the embankment.

"It now follows from a short chain of argument that the observer in the
train will see flash II earlier than flash I, if they reach the
observer, who is at rest, at the same moment. That is, two events that
are simultaneous with respect to the embankment are not simultaneous for
a moving system (such as a train or a flying-machine); the converse is,
of course, also true.

"Here, again, the eager layman encounters difficulty, for he asks
himself: Why should the two events be characterized or defined by
lightning-flashes in particular? If acoustic signals were used instead,
nothing would be altered in the fundamental determination, for the sound
rays (sound-waves) would likewise meet at the mid-point of the line
joining the sources of disturbance. What is the reason that the
relativity of time arises only when phenomena are regarded optically,
and that rays of light play the deciding part in all later developments?

"And this particular query is followed by one which is more general: Why
does the popular pamphlet not read this question in my mind? I know that
the author of it is more skilled in these matters than I, but just this
superiority should help him to divine what is passing in my mind when I
make efforts to follow his reasoning."

Einstein had listened to me patiently, and then he explained to me at
considerable length why in this case optical signals cannot be replaced
by sound signals: light is the only mode of motion that shows itself to
be entirely independent of the carrier of the motion, of the
transmitting medium. Thus the constancy of velocity is assumed in the
above argument, and as this constancy is an exclusive property of light,
every other method must be discarded as unallowable for investigating
the conception "simultaneity." Furthermore, he showed me how, on the
basis of relativity, starting from the embankment-experiment, we may
arrive at a perfectly consistent representation of the conception of
Time. He certainly did this by applying subtle physical arguments that
exceed the scope of the present book.[7] He added, in substance, that it
was futile and impossible to discuss in detail all the conceivable
objections that might arise in the mind of one reading a popular work of
this kind: it was a futile undertaking, because the true purpose was
defeated, inasmuch as a clear development of the fundamental thought
would be almost impossible under the cross-fire of so many random
questions.

[Footnote 7: In these arguments, arrangements of synchronous clocks
occur, which are fixed into the co-ordinate systems, the positions of
their hands being compared with one another. The "time" of an event is
then defined as the position of the hands of a clock immediately
adjacent to the scene of the event.]

Thus, in this matter, Einstein takes the same stand as Schopenhauer in
the preface of his chief work, in which he says: "To understand this
work no better way can be advised than to read it twice (at least),
inasmuch as the beginning assumes the end, almost as much as the end
assumes the beginning; the smallest part cannot be understood if the
whole has not already been understood." Whoever accepts and follows this
advice will find that the intermediate objections will gradually balance
and cancel one another, and that it is not necessary that they should
interrupt the steady and consistent line of development.

The position would be different if a disciple of the new theory should
resolve to dispense with strictly scientific reasoning altogether, and
should wish to meet the wishes of his readers or hearers by discarding
accuracy entirely. Such a programme seems quite feasible.

"This would be merely following the sketchy method of a magazine,"
Einstein remarked, "but you do not seriously think that it would lead to
anything?"

"It would not be a true explanation, which is reserved for technical
productions. But I can imagine that it would not be unprofitable to help
one who is entirely ignorant on these questions by using makeshifts, in
the form of allegories or analogies, which will serve as supports if he
should take fright during the course of his earlier studies. These
shocks are bound to occur, as, for instance, when he learns that a
moving rigid rod undergoes contraction in the direction of motion."

"But this is _proved_ to him!"

"Nevertheless, he does not easily accept it. For the general reader will
say to himself: 'A superhuman effort is imposed on my mind. A rigid rod
is the most constant of all things, and never before has one been
compelled to regard something that is constant as variable.'"

"If he does not grasp it, no analogy will teach him."

"But perhaps it is possible. The analogy is to show him that the effort
is not _superhuman_, and that thinking Man has already had occasion to
become familiar with such transformations from constant to variable
factors."

"I am afraid your analogy will prove a failure."

"From the scientific point of view this is probably true, inasmuch as
all comparisons are imperfect, but the analogy may yet be of service as
a last resort. For example, I should say to my general reader: 'Picture
to yourself a savant of the Middle Ages who reflects on the constitution
of animals and plants. One fact seems to him to be irrevocably true,
namely, that the species are unchangeable! A palm tree is a palm tree, a
horse is a horse, a worm a worm, and what is once a reptile remains a
reptile. A species in itself denotes something absolutely _invariant_.'"

"The expression is wrong when taken in this connexion; you mean
_invariable_."

"A little inaccuracy more or less does not affect the analogy. For the
sake of my picture I should like to retain the conception-couple,
_variable_ and _invariant_. Well, then, the species give our savant the
impression of invariance, as in the view that was held by Linné and
Cuvier. This view necessarily has its counterpart in his thought. He
argues that every species has its own original root, and that, in this
sense, there is very extensive variation. The fundamental roots are
extremely manifold; Nature has produced innumerable variations in her
individual acts of creation. But now the _Theory of Descent_ of Lamarck,
Goethe, Oken, Geoffroy St. Hilaire, enters the field and produces a
complete inversion of these two elements; the two parts of the earlier
point of view change places. Our savant has to revise his whole world of
thought. Now all organisms are to be traced back to a single original
root: the latter, which was variable before, becomes an invariable
unicellular primitive organism, but the apparently unchangeable species
now becomes variable, in the widest possible sense. And even if this
savant should exclaim: 'How am I to reconcile myself to this view?' his
descendants later find no difficulty in accepting the idea that the
organic roots are uniform, and that it is the species that are subject
to all manner of variation as a compensating feature."

Einstein expressed himself very little pleased with this attempt at an
analogy, and found that it was so far fetched that it could not be
considered admissible.

"Then I must ask your permission to continue my attempt; perhaps
something useful may yet result from it. I now picture to myself a human
being who lived in classical times and who, following Ovid and the great
majority of his contemporaries, regards the earth as a disc. On this
disc, each inhabitant of the earth has his own particular position, for
the disc has a centre with reference to which the position of a person
can be specified if his distance and his angular displacement from a
given initial radius is specified. Thus, there is a variation of
position if various persons are considered. On the other hand, the
_Above_ and the _Below_ is absolutely invariable for all persons, for
the lines running between _Above_ and _Below_ are all parallel for them,
since they all have uniformly the same disc under their feet and the
same heaven above their heads. Ovid would therefore have refused to
entertain for a moment the suggestion that _Above-Below_ is a variable.
But his distant descendants accepted the view that the earth is
spherical and that there are antipodes as self-evident, and they found
not the slightest difficulty in considering the line _Above-Below_ to
vary with their own position, making all possible angles with an initial
line extending to direct oppositeness. Referred to the centre of the
sphere, all people have now an 'invariant' position, whereas, in
compensation, the _Above-Below_ is subject to every conceivable
variation. And now I again address myself to the average reader, and say
that the meaning of these analogies is that every doctrine that leads to
a great _uniformity_ converts what was formerly invariant into a
variable quantity, and vice versa. The theory of relativity makes all
considerations about the physical world independent of all co-ordinate
systems; it establishes completely invariable uniformity, removed from
all changes due to varying points of view. Hence what was previously
invariable--such as a rigid measuring-rod--will now become variable. It
is not surprising that this requires a new method of thought, a revision
of our mode of reasoning, for the above analogies show that these
radical adjustments are characteristically necessary in the case of
comprehensive theories, and that such theories are able to overcome
apparently firmly established ideas. The parallels that I drew above
will at least inspire the average reader with a certain confidence, for
they show him how results of reasoning that were once considered
incredible were regarded as self-evident by later generations."

I have already emphasized sufficiently that Einstein regards as
inadequate these auxiliary pictures that have presented themselves to
me. Yet in the course of the conversation I gained the impression that
his judgment grew somewhat milder, and that, with certain reservations,
he was disposed to let them pass as tolerably useful helps--and they are
not intended to be more than this. I think, therefore, that I am not
acting counter to his wishes in citing these allegorical examples here,
particularly as they arose in the course of our talks.

Since then, I have had many opportunities of testing these examples on
certain persons, and may mention that they proved quite useful.
Analogies of this kind may offer a friendly help in moments when the
uninitiated feel themselves in peril, and encounter a difficulty which
they imagine to be insurmountable. They do not remove the difficulty,
but they impart a certain power of expansion to the intellect and
encourage a continuation of effort, which would probably otherwise be
relaxed at the first sign of something which is imagined to be
inconceivable. There is thus no room in textbooks for such helps, but
they may justifiably find a place in a book that departs from the
methodical route, and hopes to discover in by-ways things that are
suggestive and instructive.




CHAPTER X

DISCONNECTED SUGGESTIONS

Conditionality and Unconditionality of Physical Laws.--Conception of
Temperature.--Grain of Sand and Universe.--Are Laws
unalterable?--Paradoxes of Science.--Rejuvenation by Motion.--Gain of a
Second.--Deformed Worlds.--Atomic Model.--Researches of Rutherford and
Niels Bohr.--Microcosmos and Macrocosmos.--Brief Statement of the Principle
of Relativity.--Science with reduced Sense-Organs.--Eternal
Repetition.--Higher Types of Culture.


IN all branches of reasoning, no word and no conception has played a
more important part than that of _law_. Physical laws denote the barrier
that separates strictly chance and arbitrariness from necessity, and it
seems to us that the region of the latter must ever extend so that
finally nothing will be left of the former, which will have become
amalgamated with necessity. We shall be constrained to believe more and
more in a supreme law that will be a complete expression of all the
partial laws which science presents to us as more or less permanent
results of individual researches.

Our conversation was centred about these individual laws, such as those
that are taught in the theory of gases, optics, etc., and that are
associated with the names, Boyle, Gay-Lussac, Dalton, Marriotte,
Huyghens, Fresnel, Kirchhoff, Boltzmann, and others. In connexion with
these I asked Einstein whether he regarded the laws as things
unconditioned in themselves, and capable of proof under every set of
circumstances; and whether absolutely valid laws existed or could exist.

Einstein's answer was essentially in the negative. "A law cannot be
final, if only for the reason that the conceptions, which we use to
formulate it, show themselves to be imperfect or insufficient as science
progresses. Let us consider, for example, an elementary law such as
Newton's Law of Force. From our more recent point of view we find the
conception of direct action at a distance to be inexact in Nature. For
it has been shown that action at a distance is not an ultimate factor,
but must be resolved into a multiplicity of actions between immediately
neighbouring points (The Theory of Action by Contact or Contiguous
Action). Another example is provided by the conception _Temperature_.
This conception becomes meaningless if we endeavour to apply it to
molecules: it leads to no result if we try to impose it on the smallest
parts of matter as such. The reason is that the state, the velocity, and
the inner energy of the individual molecules fluctuates between very
wide limits. The conception 'temperature' is applicable only to a
configuration composed of many molecules, and even then it is not
applicable quite generally. For let us picture to ourselves an extremely
rarefied gas contained in a closed receiver. Two opposite walls are to
be at different temperatures, the one being cold and the other being hot
In a gas at such very low pressure the molecules come into collision so
seldom that, practically, we have to take into account only the
collisions of the molecules with the confining walls. The molecules that
rebound from the hot wall have greater velocities than those coming from
the colder wall, and hence the conception of temperature becomes
untenable for this gas."

"Would the temperature-scale on the thermometer then denote nothing?" I
asked. "The greater or lesser degree of warmth of a body, in this case
of the mass of gas, depends on the more rapid or less rapid motion of
its smallest parts. The motions are in any case present, so what would a
thermometer indicate?"

"It would betray only that it had nothing to indicate. If a thermometer
that is blackened on one side were inserted into the vessel containing
the gas, then _different_ temperatures would be recorded if the
thermometer were gradually turned about its own axis; and this signifies
that the conception of temperature has become meaningless for this
configuration of molecules. And passing beyond the quoted examples, I
should maintain that all our conceptions, however subtly they may have
been thought out, are shown in the course of progressive knowledge to be
too rough hewn, that is, too little differentiated."

     *     *     *     *     *     *     *     *

We spoke of the "Properties of Things," and of the degree to which these
properties could be investigated. As an extreme thought, the following
question was proposed:

Supposing it were possible to discover _all_ the properties of a _grain
of sand_, would we then have gained a complete knowledge of the _whole
universe_? Would there then remain no unsolved component of our
comprehension of the universe?

Einstein declared that this question was to be answered with an
unconditional affirmative. "For if we had completely and in a scientific
sense learned the processes in the grain of sand, this would have been
possible only on the basis of an exact knowledge of the laws of
mechanical events in time and space. These laws, differential equations,
would be the most general laws of the universe, from which the
quintessence of all other events would have to be deducible."

[This thought may be spun out in yet another direction. Every piece of
research, however specialized it may appear and of whatever minor
importance it may be, retains a relationship with researches into the
universe, and may prove to be valuable for this latter task. If we
accept the view that science is capable of realizing perfection, then
every contribution to knowledge, even the most insignificant, is
essentially indispensable for attaining this goal.]

     *     *     *     *     *     *     *     *

Can a physical law alter with time? In more precise language, can time,
as such, enter explicitly into laws, so that, for example, an experiment
that is carried out at different times leads to different results? This
question has been treated several times, among others, by Poincaré, who
answered it with an emphatic "No!" but also by others to whom the
invariability of physical laws did not seem to hold for all eternity. If
my memory does not play me false, Helmholtz once expressed faint doubts
about the constancy of laws.

Einstein answered this question with a decided negative. "For a law of
physical nature is, by definition, a rule to which events conform
wherever and whenever they take place. Thus, if we were to be compelled
as a result of experience to make a law dependent on time, it would be a
necessary step to seek a law independent of time, which would include in
itself the law dependent on the time as a special case. The latter would
be excluded from the category of physical laws, and would henceforward
play the part only of a result deduced from the law which is independent
of the time."

     *     *     *     *     *     *     *     *

What attitude should we adopt if, in studying a scientific doctrine, we
encounter paradoxical results even though the inferences have been drawn
correctly--that is, if we meet with a deduction to which our reasoning
powers object, although no fallacy is discoverable in the argument?

Before we deal with cases which seem to me, personally, to be
interesting, let us hear what is Einstein's attitude in general. "As
soon as a paradox presents itself, we may, as a rule, infer that
inaccurate reasoning is the cause, and should thus examine in each
particular case whether an error of logic is discoverable, or whether
the paradoxical result denotes only a violent contrast with our present
views."

Let us first take examples from an entirely modern science, from the
_Theory of Aggregates_ founded by Georg Cantor of Halle. We shall follow
the argument by the only possible method for this book, namely, by rough
indications that will serve our purpose and do not claim to be accurate
in expression or in sense.

If we take an aggregate of three objects, for example, an apple, a pear,
and a plum, we may, by definition, form six partial aggregates, namely:

    the apple
    the pear
    the plum
    the apple and the pear
    the apple and the plum
    the pear and the plum.

The aggregate of the partial aggregates, which contains six elements, is
thus greater than (actually twice as great as) the original aggregate,
in which only three elements occur.

If the original aggregate contains an additional element, for example, a
nut, the following partial aggregates may be formed:

    the apple
    the pear
    the plum
    the nut
    the apple and the pear
    the apple and the plum
    the apple and the nut
    the pear and the plum
    the pear and the nut
    the plum and the nut
    the apple, the pear, and the plum
    the apple, the pear, and the nut
    the apple, the plum, and the nut
    the pear, the plum, and the nut.

Thus, in this case, the aggregate of the partial aggregates is already
considerably greater than the original aggregate. This numerical excess
increases rapidly with each successive increase in the original
aggregate, so that if we apply the same reasoning to an infinite
aggregate, the aggregate of partial aggregates becomes an infinity of a
_higher order_. This is expressed by saying that the infinite aggregate
of partial aggregates has a greater _potentiality_ than the infinity of
the elements of the original aggregate.

So we see that the one infinity is, in popular language, much more
comprehensive, more powerful than the other. Our minds do not find it
impossible to grasp this. But in a definite imaginary experiment it is
found that this theorem of progression not only fails in its
application, but leads to flagrant contradiction.

For if we start from the primary aggregate of "all conceivable things,"
its infinity can certainly not be transcended by any other infinity. But
according to the above theorem the "aggregate of all partial aggregates"
would have a greater potentiality, although it itself cannot extend
further than to the conception of the maximum of all conceivable things.
We thus arrive at an insoluble paradox, a typical example of how, in the
system of conceptions involved, something is insufficient or not in
conformity with logical thought. And this sceptical view receives
support from various remarks of Descartes, Locke, Leibniz, and
particularly Gauss, who, long before the advent of the Theory of
Aggregates, raised a protest against inexact definitions of infinity.

In another case, however, the same theory seems to arise by perfectly
logical processes, although it again leads to a statement that does not
seem correct to "common sense." For it shows by a very subtle and
ingenious method that all the surface-points of a surface infinitely
extended in all directions may be brought to correspond in a reversible
single manner to the linear points of a line, however small; so that to
every point of the unlimited plane there corresponds a definite point of
the line, and vice versa. The same theorem may be extended to
three-dimensional space, with the result that we have to reconcile
ourselves with the incredible fact that, expressed in popular language,
a straight line of however small length exhibits the same potentiality
with regard to the number of its points, as all the points in the
universe.

For my own part, I must confess that no means suggests itself to me to
make this paradox intelligible. But the _sacrificium intellectus_ comes
within dangerous proximity. Einstein, who values and marvels at the
theory of aggregates as a science, or perhaps more as a work of art
built up from the materials of science, gives whole-hearted support to
the proof. He refuses to accept the notion of a paradox--that is, he
recognizes a contradiction not in our process of reasoning, but only in
a habit of thought that is open to correction. I should give much to
discover the means of correction!

     *     *     *     *     *     *     *     *

A third example arises out of the special theory of relativity. It has a
mysterious paradoxical character that vanishes when a clear view of the
relationships involved has been obtained.

According to this theory the rate at which events happen alters
according to the state of motion of the system under consideration. Let
us now consider two twins A and B, that, although born at one place on
the earth, are immediately separated, B remaining at rest, whilst A
rushes out into space at an enormous rate, describing what, viewed from
the earth, is an inconceivably great circle. In this way the rate of
happening of all events is reduced very considerably for A in a manner
that may be calculated. If A then returns to B, it may happen that the
twin who stayed at home is now sixty years old, whereas the wanderer is
only fifteen years of age, or is perhaps only an infant still.

The first introduction to this flight of imagination naturally causes
profound perplexity. Nevertheless, we are dealing not with a realm of
miracles, but with something that is within the range of comprehension.

"In the case of these two twins," Einstein declared, "we have merely a
paradox of _feeling_. It would be a paradox of thought only if no
sufficient ground could be suggested for the behaviour of these two
creatures. This ground, which accounts for the comparative youth of A,
is given, from the point of view of the special theory of relativity, by
the fact that the creature in question, and only this creature, has been
subject to accelerations. A proper grasp of the reason is furnished only
when we adopt the _general_ theory of relativity, which tell us that,
from the point of view of A, a centrifugal field exists, whereas it is
absent from the point of view of B. This field exerts an influence on
the relative rate of happening of the events of life."

It certainly requires a prodigious mechanism to allow the moving twin to
gain even only one second of time. If he were to spend a year in a
merry-go-round whose circumference were about 19 milliard miles in
length, he would have to travel in it at the rate of over 600 miles per
second if he is to gain a second on his brother.

This inevitable result that is immediately apparent to a trained
scientific mind throws light on the nature of "common sense," the
validity of which, as an ultimate criterion, Kant too has refused to
recognize, in so far as this "common sense" is incapable of passing
beyond the examples offered in its own experience. It circulates, as
Einstein says, in the "realms of feeling and analogy." It finds no
analogy for a phenomenon like that described above, and since it can
apply rules only concretely, many things appear to it paradoxical that,
in the light of intensified abstraction, appear logical and necessary.

     *     *     *     *     *     *     *     *

Let us speculate on the following question. If all things in the
universe should increase or decrease enormously in dimensions, and if,
at the same time, in a manner totally concealed from us, certain
physical conditions should become changed, we should lack all means of
discovering the difference between things before and after the change.
For since all measuring-rods, including those furnished by our senses,
would have become changed in the same proportion, the two conditions
could not be differentiated from one another. It may easily be shown
that this would necessarily occur, if an extramundane power were
non-uniformly to displace, deform, compress, or bend all things in the
universe, provided that our instruments and senses participated in this
transformation. Accordingly it is permissible also to regard the
universe known to us as one that is deformed, and one that is derived
from another, the original form of which will ever remain a secret to
us.

Is there any connexion between this grotesque speculation and the theory
of relativity?

We can establish only one that is negative and that arises _e
contrario_. "These deformations," said Einstein, "are in themselves
abstractions that are physically meaningless. Only _relations between
bodies_ have a physical meaning, for example, the relation between
measuring-rods and the objects they measure. Therefore, it is reasonable
to talk of deformations only when we are dealing with the deformations
of two or more bodies with respect to one another, whereas the
conception of deformation has no sense, unless a real object is
specified, to which it is referred. The philosophical merit of the
general theory of relativity, as compared with previous views of
physics, consists in the fact that the former avoids entirely these
meaningless abstractions with respect to space and time."

[According to this, it is not purposeless to enter on these grotesque
trains of thought, even if they are untenable physically. For since the
new physics teaches us to avoid these false tracks, it seems of value to
know what it is that is to be avoided. Just as we must study scholastic
thought if we wish to grasp thoroughly the philosophy which sprang up
after the scholastic fetters were burst. Moreover, these reflections on
concealed universes are not without a certain attraction, reminiscent of
the sorcerer's wand, if they pursued any other goal than that of making
universes distorted. It is true that they hold out latent temptations
that may in some cases lead us on to dangerous ground, in encouraging us
to venture on analogies beyond the scope of geometry and physics. Would
it be possible to enter suddenly into a world that is distorted and
deformed with respect to its ethics, its culture, and its reasoning
intellects, without our observing the difference? Are we ourselves
perhaps living under such deranged conditions, of which we cannot become
aware, because our perceptual organs have likewise become deformed? I
must frankly confess that I do not regard it as quite inconceivable that
this argument of deformation may be spun out in this direction, but I
must add that Einstein rejects absolutely all such extensions, since,
as he emphasizes, they lead to regions that are merely fields for the
exhibition of "verbal gymnastics."]

     *     *     *     *     *     *     *     *

The question whether Nature makes leaps or not is very old. In the
theory of descent it forms the foundation of the difference between
revolutionists and the evolutionists, who uphold the axiom _natura non
facit saltus_, with all its consequences. Recently attempts have been
made, particularly by psychologists, to propound and justify a natural
principle of discontinuity. They assert that our own perceptions and
sensations are discontinuous in themselves, and that the mechanism of
every perception is akin to that of a cinematograph with its extremely
rapid interruptions. If this should actually be the case, we should
scarcely have a means of solving definitely the question whether
continuity reigns, or not, in Nature.

Einstein does not recognize the possibility of this alternative for a
moment. If a doubt had ever arisen, the researches of Maxwell would in
themselves have been sufficient to dispel it. Our universe that is to be
described in terms of differential equations is absolutely continuous.

"But," I interjected, "does not modern physics offer a certain support
to the assumption of a discontinuity? Does not the Quantum Theory point
to an atomistic structure of energy, and hence also of events that are
to be imagined as happening in jerks and as involving relations
expressible in whole numbers?"

Einstein gave an answer of epigrammatic brevity and flavour. "The fact
that these phenomena are expressible in whole numbers must not be
construed into an argument against continuous happening. Just imagine to
yourself for a moment that beer is sold only in whole litres; would you
then infer that beer, as such, is discontinuous?"

     *     *     *     *     *     *     *     *

What achievements are to be expected of astronomy in the present era?

This question would have a special meaning if it were assumed that the
astronomer who works in observatories is surrounded by solved problems,
and can no longer hope to solve problems having the universal
significance of those of Copernicus or Kepler. This assumption, however,
would not be in agreement with the actual state of affairs.

Einstein indicated to me a number of fundamental problems that present
themselves to modern astronomy, and the solution of which he expected of
future times.

Above all, the geometrical and physical constitution of the stellar
systems will, in the main, become revealed.

At present we do not yet know whether Newton's Law of Attraction holds,
at least approximately, for configurations of the type of the Milky Way
and of the spherical clusters of stars--that is, in extents of space in
which the influence of space-curvature would become appreciable. The
rapid progress of recent astronomy justifies our great hopes that the
solution of this universal problem will be found within the coming
decades.

In distant connexion with this we also touched on the question of the
habitability of other worlds. This theme of Fontenelle, "la pluralité
des mondes habités," which has again become a centre of public
interest, owing to investigations of Mars, has evoked a storm of
discussion. We hear the noisy war-cries of geocentric scientists who
wish to regain for the earth her shattered supremacy in astronomy, and
who claim the existence of organic forms as the sole prerogative of our
planet. It is scarcely necessary to mention that Einstein rejects the
motives of these human and all-too-human individuals as small-minded and
short-sighted. Creatures in distant worlds are derived from, and are
subject to, conditions of organic nature, of which we can form no idea
by deductions from the world which we inhabit. But to deny their
existence on numberless constellations, or to demand an ocular proof of
their presence, is no better than to assume the point of view of an
infusoria to whom there is no life other than that in a dirty drop of
ditch-water.

     *     *     *     *     *     *     *     *

The idea of the atom as the ultimate structural element involves a
philological as well as a conceptual contradiction. For _atomos_
signifies the indivisible, the no-further-divisible, whereas the idea of
a body, however small, an element of structure differing from zero,
demands, at least geometrically, further divisibility. Even the original
founders of the theory of atoms, Leukippus, Epicurus, and Democritus,
assigned definite forms to the ultimate components, and we may read in
the splendid work of Lucretius how he infers from the nature of
substance that the ultimate particles are smooth, round, or rough, or
have the shapes of hooks and eyes. The further analysis pressed forward,
the more the simplicity of the original idea vanished. Microcosms came
to be regarded as copies of macrocosms, and the atoms of present-day
science actually exact from us that we should regard them as worlds in
themselves.

Einstein acceded to my request that he might give a sketch of the latest
achievements of science sufficient to provide an approximate idea of the
_atomic model_. According to the researches of Rutherford and Niels
Bohr, we are to picture it as a planetary system.

The central body of this system is represented by a positively charged
nucleus, which constitutes almost the whole mass of the atom, surrounded
by a certain number of electrons, negative charges, that move in uniform
circular or elliptic orbits about the nucleus. There is thus a certain
analogy that allows us to regard the nucleus as the sun, and the
electrons as the planets of this system.

The number of these electrons varies between the limits 1 and 92,
according to the chemical constitution of the element. The smallest
number occurs in the case of helium (in which there are two), and of the
hydrogen atom, in which only one electron-planet describes its circular
path about the nucleus. In other atoms there are probably more
complicated orbits, although they are more or less approximately
circular. According to this still very new theory, which is supported by
very convincing facts, the electrons are to be imagined as arranged in
concentric shells (like the layers of an onion), among which the
innermost shell plays a distinctive part inasmuch as the number of the
electrons arranged in it decides the chemical character of the atom in
question. It sometimes occurs that electrons spring, under external
influence, from one orbit to another; when the electron jumps back to
the original orbit, light is emitted. An essential fact is to be noted:
Whereas any arbitrary orbits of any arbitrary radius may occur in a
planetary system of the celestial regions, the manifold of these orbits
in the case of the electrons is restricted, in that only certain orbits
are possible, namely, those that are determined mathematically by the
quantum condition.

"Perhaps," I interrupted, "the whole analogy may be inverted. If the
atom is considered analogous to a planetary system in the model, it
should be admissible to regard our true planetary system as a cosmic
atom. And then, long after we have become accustomed to regard our earth
as playing the part of a grain of sand, the sovereignty of the sun, too,
would be past. The whole majesty of the solar system as far as the orbit
of Neptune would then shrink to a configuration compared with which the
world of a grain of sand would be infinitely complex."

"This fantastic inversion is permissible up to a certain extent," said
Einstein, "but we must not lose sight of the fact that there is a
cardinal difference. If we disregard the enormous disparity in
dimensions, the analogy is far from exact owing to the circumstance that
the atom is only an element of structure, whereas the true planetary
system is an extraordinarily complex structure in itself. Thus the
difference between a simple thing and one that is very highly complex
still remains."

"But, Professor, may not a similar complexity yet be discovered in the
atom? It may be merely a difference of philosophical view from the
primary idea to that of regarding the electrons as circulating like
planets. May we not conjecture that in each successive step we are
merely carrying out a true _regressus in infinitum_?"

"That seems highly improbable," he replied, "although, of course,
structural investigations can never cease. At first they are directed at
the more remote object of finding out why certain atoms are radioactive,
that is, exhibit a tendency to disintegrate. It has already been
established that this tendency is a property of the positive nucleus, of
which little is as yet known. This means that the nucleus is not simple,
yet it does not open up the possibility of an unending regression. Our
aim must be to get a clear insight into the constitution of the nucleus,
as regards the positive and negative charges, and it is my opinion," he
concluded, "that beyond this there will be no further subdivision of
matter."

When Goethe writes of the immovable pole in the flux of phenomena, we
recognize that his beautiful remark pronounces an elegy to the
possibility of attaining ultimate simplicity. Einstein's utterance, if I
understand him aright, converts this elegy into a song of hope. If the
subdivision of matter actually has an end somewhere, then we are now on
the threshold of ultimate things, we are near the immovable pole, which
we are capable of reaching.

     *     *     *     *     *     *     *     *

"Every new truth of science must be such that, in ordinary writing, it
may be communicated completely within the space of a quarto leaf."
Kirchhoff made this remark, and gave a sufficient, if not literal,
demonstration of its truth. When Bunsen and he published the first
notice about spectral analysis, they compressed their publication into
the small space of three printed pages.

But what is to happen if the new truth should be built up of very
comprehensive materials, when it requires many links, of which none can
be omitted if the truth is to be made intelligible? Would Kirchhoffs
quarto page still be sufficient?

"Certainly," said Einstein, "provided, of course, that it is addressed
to a reader who has already mastered what went before--that is, to one
who is so far acquainted with the older facts that he has to learn only
the really new part of the new truth."

"That sounds very hopeful," I remarked, "for then it should also be
possible to describe very briefly the theory of relativity."

"Let us rather say its essentials--the heart of the matter. Well, then,
get your Kirchhoff page ready. We shall see whether we can set out on it
the special theory of relativity."

The totality of our experience compels us to assume that light travels
with a constant velocity in empty space. Likewise, our whole experience
in optics compels us to recognize that all inertial systems are
equivalent; these are systems that are produced from an allowable one by
means of a uniform translation. An allowable system is one in which
Galilei's and Newton's Law of Inertia holds. (This law states that a
moving body that is left to itself retains its direction and velocity
permanently.)

Now, the law of the constancy of light propagation seems to conflict
with the classical principle of relativity, according to which the
velocity of a ray of light assumes different values in the moving system
according to the direction of the ray.

This apparent incompatibility arises from the following unproved
assumptions:

(_a_) If two events are simultaneous with regard to one inertial system,
they are also simultaneous with regard to any other inertial system.

(_b_) The length of a measuring-rod, the shape and size of a rigid body,
and the rate of a clock are independent of their motion with respect to
the system of reference used, provided this motion is rectilinear and
non-rotational.

These assumptions must be discarded if this disagreement is to be
eliminated. If we substitute for them the assumption that all inertial
systems are equivalent and that the velocity of light _in vacuo_ is
constant, we get:

(1) That the dimensions of bodies and the rate of clocks have a
functional relation to the motion.

(2) That the equations of motion of Newton require to be modified; this
modification leads to results that, for rapid motions, differ
appreciably from those of Newton.

This is, in a very compressed form, the meaning of the special theory of
relativity.


As there is still some space left on our quarto page, we may add a
remark that, it is hoped, will make a little clearer the above-mentioned
discrepancy.

Let us choose as our system of reference an express train 18 miles long.
There are two passengers--Mr. Front, right at the front of the train,
and Mr. Back, at the extreme end of the train, so that a rigid distance
of 18 miles separates the two passengers. The carriages are transparent,
so that the two passengers can signal to one another. They are,
moreover, furnished with ideal clocks that run at exactly the same rate.

First, suppose that the train is at rest. Back is just opposite
milestone 100, whilst Front is opposite milestone 118. By means of a
flash, Back signals to Front his time, exactly 12 o'clock. It takes
light very nearly ¹⁄₁₀₀₀₀ second to traverse the length of
the train--18 miles; hence the flash will reach Front at 12 o'clock
¹⁄₁₀₀₀₀ second. Exactly the same result would have come
about if Front had signalled his time to Back. Light makes no difference
in travelling forwards and backwards. If the train moves at a great
speed, the two travellers can conduct the same experiment as when the
train was at rest. They will then set the time that light takes to
travel from Back to Front equal to the time that it takes to traverse
the same way in the reverse direction. But this phenomenon will assume a
different aspect if viewed from the railway embankment. An observer on
the latter would affirm that light does not take the same time in
travelling the length of the train in one direction as it does when
travelling in the opposite direction.

For the ray of light moving in the forward direction has to traverse not
only the distance between Back and Front, but also the very short
distance that Front has moved forward during the interval that the light
has been moving; whereas, inversely, the flash sent out by Front to Back
will traverse a distance that is correspondingly less than that between
the passengers, since Back is moving towards the signal.

Thus the duration of the two phenomena of light propagation is the same
or different, respectively, according as it is judged from the train or
from the embankment. In other words, _the judgment of the length of time
depends on the state of motion of the observer_.

All further pronouncements of the special theory of relativity are based
on the preceding arguments of the relativity of time.

     *     *     *     *     *     *     *     *

Would Man be able to construct a Science if he possessed one sense less
than at present--for example, if he were deprived of sight? Let us apply
this to a definite case. In the new physics the velocity of light plays
a decisive part as a world-constant. At first sight it would appear
impossible for us to determine it and recognize its importance, if we
had not at our disposal some organ which enabled us to become aware of
optical phenomena.

But, as Einstein explained to me, even under such difficult
circumstances, it would be possible to build up a science, for the
reason that phenomena, as far as they are perceptible, may be
transformed so that they become manifest to other senses if one sense
should be absent. For example, the electrical conductivity of selenium
is strongly influenced by the amount of illumination that falls on it.
Thus light acts on a selenium cell, causing changes of current
intensity, which in their turn may be perceived by feeling, or by
chemical action on the mucous fluid of the tongue. Ultimately we are
concerned only with a differentiation that enables us to refer identical
experiences to identical events. We should certainly encounter enormous
difficulties in endeavouring to form a physical picture of our
surrounding world if the number of our senses should become less than
the organs with which we actually operate. Yet, in principle, we should
be able to overcome all difficulties by means of much lengthened and
complicated lines of research, even if we should have only a single
sense left, or if we had only one at the very outset. The construction
of a Science would then be possible, and would give the same results,
although it might be propounded only after a delay of perhaps millions
of years.

[It is naturally assumed that the intellect is retained, as this is the
necessary condition for all scientific research. Since the degree of
understanding depends on the senses--_nihil est in intellectu, quod non
prius fuerit in sensu_--we may conjecture that a human being with only
one sense organ would work with a minimum degree of understanding, which
would be insufficient for the acquirement of any knowledge whatsoever.
This transcendental question, which lies almost beyond the bounds of
discussion, was not touched on in our conversation, as the subject was
restricted so that it should not drift into metaphysical regions.

Nevertheless, I should like to mention that a speculation of this kind
is recorded in the history of science. Condillac, in a study teeming
with ideas, investigates the behaviour of a "Statue," that he represents
as a human being, with the assumption that there is at first no idea in
the soul of this statue-person. This living creature is enclosed in a
marble envelope, the sole exterior organ of which is at first the organ
of smell. He then shows that by means of this single sense all manner of
sensations and expressions of will may develop in his "statue."
Condillac does not, however, undertake to give a convincing proof that
this creature, restricted to the organ of smell, would be able to
discover physically the relationships that hold in physical nature, and
thus to build up a scientific system. Thus Einstein, in his discussion,
goes considerably further than the author of this statue.]

     *     *     *     *     *     *     *     *

Has the "eternal repetition," as outlined by Nietzsche, any meaning?

The sage of Sils-Maria tells us that this revelation came to him midway
between tears and ecstasy, as a fantasy with a real meaning. The crux of
his idea is a finite world built up of a finite number of atoms. From
the fact that the present state emerges out of the immediately preceding
one, the latter from the one just before, and so on, he concludes that
the present state exhibits repetition both forwards and backwards. All
becoming recurs and moves in a multiple cycle of absolutely identical
states.

Let us discard for the moment all philosophical objections, above all
this, that the recurrence of the same disposition of atoms may not
necessarily entail the recurrence of the same psychical states.
Furthermore, let us suppress the cynical thought that in the return to
the same state the world would have reason to enjoy extreme happiness
only for moments, but to lament for aeons. Then we are left with the
comparatively simple question: Is this repetition, from the point of
view of physics, conceivable and possible?

It would be the death-knell of Nietzsche's idea if the answer of a great
physical research scientist were entirely in the negative. But Einstein
still allows it a small measure of life. "Eternal repetition," so he
expressed himself, "cannot be denied by science with absolute
certainty." The disciples of Nietzsche will have to rest satisfied with
this very small concession. For what, in Nietzsche's eyes, is a logical
necessity becomes transformed by Einstein's supplementary remark into a
vague assumption, the product of fantasy. From the point of view of
physics the recurrence of the same condition is to be regarded as
"enormously improbable." This statement is founded chiefly on the famous
second Law of Thermodynamics, according to which the processes of Nature
are in the main irreversible, so that a one-sided tendency is expressed
in natural phenomena. The fact that the course of phenomena is in only
one sense or direction speaks in favour of the view that the events of
the world are to be regarded as occurring only once.

So that when Nietzsche, in contradistinction to this, vigorously
supported the doctrine of repetition, he contradicted at least one
important recognized theorem of physics. The fact that he did not become
conscious of this contradiction, but that, on the contrary, he regarded
his idea as the most important event in the development of his
intellect, may be regarded as an example of a _docta ignorantia_. But it
is allowable, too, that philosophic fantasies that complete the poetical
picture of the universe should be given expression. And Nietzsche would
presumably have been deprived of a degree of pleasure if he had been
aware of this second law.

"Truth is the most expedient error"; this statement may be traced back
to a sequence of thought developed by Nietzsche. But the Eternal
Repetition is shattered by just this remark, for judged by its
consequences it would be a very inexpedient error.

     *     *     *     *     *     *     *     *

Supposing we should succeed in exchanging thoughts with the inhabitants
of distant worlds and should, through them, acquire the elements of a
civilization _superior to our own_, would this knowledge prove a
blessing to us or the reverse?

The word "superior" must, of course, be treated circumspectly. It is to
denote only that, relatively, this distant civilization bears somewhat
the same relation to our civilization of to-day as our own bears to that
of an Australasian negro or an anthropoid ape. There are fanatics of
progress whose wishes plunge headlong and without restraint into the
future, and to whom nothing could be more desirable than the sudden
appearance of a civilization that, as they opine, would at one stroke
carry us "forward" many thousands of years.

But the view of these magicians with their seven-league boots is
untenable. Let me cite a mere outline of the many opposing arguments in
a few words of Einstein. "Every sudden change in the conditions of
existence, even if it occurred in the form of a higher development,
would come upon us like a doom, and would probably annihilate us, just
as the Indians succumb to the civilization that has outstripped them.
The tragedy of our own highly civilized times is that we cannot create
the social organizations that have become necessary as a consequence of
the technical advances of the last century. This has given rise to the
crises, impasses, and senseless competition between nations, and to the
impoverishment of defenceless individuals. These deplorable conditions
would become inconceivably accentuated if we were to be invaded by
extra-mundane technical sciences of a higher order."

     *     *     *     *     *     *     *     *

Nevertheless, there is still a possibility that the "superior
civilization" might contain indications of the organizations which we
lack. Instead of entering on the question of this Utopia, we confined
ourselves to comparing past conditions in our world with present ones.
Did we not have the most promising preliminaries for an organization
that was devoid of friction and tended to reduce the competition between
nations in the numerous international institutions that drew together a
great section of the intellectual world to work in co-operation? Are
there hopes that this international coalition will be resumed?

Einstein expressed himself optimistically, not to do homage to an
organization artificially formed, but to extol the world-wide mastery of
intellect. "Even if international congresses were to be swept away," he
said, "international co-operation would not be abolished, as it effects
itself automatically." I should venture to assert that if all these
congresses were to cease, we should not even have cause to fear that
there would be an appreciable diminution in the combined effort of
research. If certain developments are hindered by political conditions,
it is only due to the resulting economic hardships affecting individuals
in their work and robbing them of their intellectual freedom. The real
friends of Truth have always clung together, and do so actually now;
indeed, many feel the tie to be closer than that connecting them to
their own country. In spite of all obstacles and boundaries they will
never cease to find contact with one another!




CHAPTER XI

EINSTEIN'S LIFE AND PERSONALITY


WE know from the biographies of great thinkers that they seldom
personify the character of a dramatic ideal. They are not heroes of
fiction who pass through complex experiences and struggle with
mysterious problems of existence that may unduly excite the imagination
of observers. Whoever follows their development remarks in the majority
of cases the predominance of the inner life, the course of which is
discoverable only by study of their works, no clue being given in the
confusion of ordinary exterior manifestations. An eminent man of
thought, whose energies are concentrated on mental effort, rarely finds
time to present in addition an interesting figure in the epic sense. The
poet who moulds his forms from life finds little scope in him as a
model, and only in exceptional cases has he succeeded in idealizing the
savant in a work of art.

It would be a fruitless undertaking to treat Einstein's life as one of
these exceptional cases. It is possible to trace the various phases of
his development, yet neither the writer nor the reader must disguise
from himself the fact that such outlines give only the external picture
of the man and chronological events of importance. Nevertheless, a book
of which he forms the theme cannot pass over the task of giving his
_curriculum vitæ_. And if it should partly appear aphoristic and
disjointed, it must be borne in mind that this account originated from
conversations and scraps of conversation that touched on various
episodes of his life, according as they had a bearing on the subject
under discussion.

The story of Einstein's life begins at Ulm, the town which possesses the
highest building in Germany. Gladly would I stand on the belfry of the
Ulm Cathedral in order to obtain a general survey of Einstein's youth.
But the view discloses nothing beyond the bare fact that he was born
there in March 1879. The detail which has already been mentioned above,
namely, that it was something physical that first arrested the child's
attention, remains to be noted. His father once showed the infant, as he
lay in his cot, a compass, simply with the idea of amusing him--and in
the five-year-old boy the swinging metal needle awakened for the first
time the greatest wonderment about unknown cohesive forces, a wonderment
that was an index of the research spirit that was still lying dormant in
his consciousness. The remembrance of this psychical event has a
significant meaning for the Einstein of to-day. In him all the
impressions of early childhood seem to be still vivid, the more so as
all other physical occurrences, such as the falling of an unsupported
body, left no impression on him. His attention was fixed on the compass,
and the compass alone. This instrument addressed him in oracular
language, indicating to him an electromagnetic field that was in later
years to serve him as a domain for fruitful research.

His father, who had a sunny, optimistic temperament, and was inclined
towards a somewhat aimless existence, at this time moved the seat of the
family from Ulm to Munich. They here lived in a modest house in an
idyllic situation and surrounded by a garden. The pure joy of Nature
entered into the heart of the boy, a feeling that is usually foreign to
the youthful inhabitants of cities of dead stone. Nature whispered song
to him, and at the coming of the spring-tide infused his being with joy,
to which he resigned himself in happy contemplation. A religious
undercurrent of feeling made itself manifest in him, and it was
strengthened by the elementary stimulus of the scented air, of buds and
bushes, to which was added the educational influence of home and school.
This was not because ritualistic habits reigned in the family. But it
had so happened that he learned simultaneously the teachings of the
Jewish as well as the Catholic Church; and he had extracted from them
that which was common and conducive to a strengthening of faith, and not
what conflicted.

Youthful impetuosity, which in boys of a similar age usually expresses
itself in rash enterprises and loose tricks, did not appear in him. His
spirit was adjusted to contemplation, and an inborn fatalism, diffused
with a super-sensuous element appertaining to dreams, restrained him
from responding to external impulses. He reacted slowly and
hesitatingly, and he interpreted what his senses offered him and all the
little experiences of early days in terms of a reverence reflected from
within. Words did not easily rise from his lips, and measured by the
ordinary scale of rapidity of learning and readiness in answering
questions, he would scarcely have been judged to possess unusual gifts.
As an infant he had started to talk so late that his parents had been in
some alarm about the possibility of an abnormality in their child. At
the age of eight or nine years he presented the picture of a shy,
hesitating, unsociable boy, who passed on his way alone, dreaming to
himself, and going to and from school without feeling the need of a
comrade. He was nicknamed "Biedermaier," because he was looked on as
having a pathological love for truth and justice. What at that time
seemed to be pathological, to-day appears as a deeply rooted and
irrepressible natural instinct. Whoever has got to know Einstein as a
man and as a scientist knows that this failing of his boyhood was but
the forerunner of a very healthy outlook.

Signs of his love for music showed themselves very early. He thought out
little songs in praise of God, and used to sing them to himself in the
pious seclusion that he preserved even with respect to his parents.
Music, Nature, and God became intermingled in him in a complex of
feeling, a moral unity, the traces of which never vanished, although
later the religious factor became extended to a general ethical outlook
on the world. At first he clung to a faith free from all doubt, as had
been infused into him by the private Jewish instruction at home and the
Catholic instruction at school. He read his Bible without feeling the
need of examining it critically; he accepted it as a simple moral
teaching and found himself little inclined to confirm it by rational
arguments inasmuch as his reading extended very little beyond its
circle.

Painful inner conflicts were not wanting. Jewish children formed a small
minority in the school, and it was here that the boy Albert felt the
first ripples of the anti-semitic wave that, sweeping on from without,
was threatening to overwhelm master and pupil alike. For the first time
he felt himself oppressed by something that was not in harmony with his
simple temperament. His modesty made him a prey to injustice, and in
defending himself his originally gentle and restrained nature gained a
certain independence and individuality.

If one may speak of achievements at all in a preparatory school, those
of Albert were of the average modest level. He was careful as a pupil,
generally satisfied requirements, but in no way betrayed special
talents: indeed, so much the less, as he showed himself to be possessed
of a very uncertain memory for words. The methodic plan of the
elementary school that he attended to his tenth year was, however, not
other than the usual scheme mapped out by drill-masters; it made up for
what was lacking in an understanding of the pupils by applying drastic
strictness. The beautiful sentence of Jean Paul: "Memory is the only
paradise from which we cannot be banished," finds no echo in Einstein's
school memories, of which he has often spoken to me without a shadow of
regret for a lost paradise. He told me with bitter sarcasm that his
teachers had the character of sergeants--those later in the _gymnasium_
(secondary school) were of the nature of lieutenants. Both terms are
used in the pre-armistice sense, and his words were directed against the
self-opinionated tone and customs of these garrison-schools of earlier
days.

The next stage of his development was a course of study at the
Luitpold-Gymnasium in Munich, which placed him in the second class. In
Einstein's retrospect of these days more friendly recollections present
themselves, connected, however, only with particular persons, and not
breathing praise in general; on the contrary, from his account, it is
clear that although he conceived affection for individual teachers, he
felt the tone of the institute as a whole to be rough. As we know, many
things have been changed in these schools since then, following on a
revulsion from the convict atmosphere that used to characterize them,
and which meant suffering enough for the pupils. The result was that the
schoolboy Einstein developed a contempt for human institutions and
assigned little value to the subjects of study which he was obliged to
absorb in schematic form without the application of his own mental
energy. This gloomy picture is relieved at points by the presence of
several teachers, above all, one called Ruëss, who took pains in
exposing the beauty of classical antiquity to the fourteen-year-old boy.
We learn elsewhere that Einstein at present admits the humanistic ideal
for the school of the future only under very restricted limitations. But
when he thinks of this teacher and his influence, a warm appreciation of
classical study vibrates in his words, occasionally rising, indeed, to
an unbounded enthusiasm for the treasures of Greek history and
literature. His instruction was not restricted to the acquisition of a
perspective of the antique. Under the direction of the same teacher, he
was introduced into the poetic world of his native country, and learned
the magic of Goethe in his "Hermann and Dorothea"; this poem, as he
confesses, was explained to him in a really model manner. Thus there
were some oases in the desert of schematic teaching: they served as
refreshing halts for the spirit of the eager young searcher after
knowledge.

We must go back one or two years to note a weighty experience, which
occurred when he made his first acquaintance with elementary
mathematics; this subject presented itself to him with the intensity of
a revelation. It did not happen in the ordinary course of school-work,
but was due to a sort of wizard-like inquiring inner spirit that plied
him with questions and that gave him inward thrills of joy when he found
a sharp-witted solution. From the very beginning Albert proved himself
to be a good solver of problems, even before he achieved an arithmetical
virtuosity, and before he knew the technique of equations. He helped
himself by means of little tricks, experimented roundabout inventions,
and was happily excited when they led to the goal. One day he asked his
uncle, Jacob Einstein, an engineer who lived in Munich, a certain
question. He had heard the word "algebra" and surmised that his uncle
would be able to explain the term to him. Uncle Jacob answered: "Algebra
is the calculus of indolence. If you do not know a certain quantity, you
call it _x_ and treat it as if you do know it, then you put down the
relationship given, and determine this _x_ later." That was quite
sufficient. The boy received a book containing algebraic problems that
he solved all alone in accordance with this not exhaustive but expedient
direction. On another occasion Uncle Jacob told him the enunciation of
Pythagoras' theorem without giving him a proof. His nephew understood
the relationship involved, and felt that it had to be founded on some
reasoning. Again he set about all alone to furnish what was wanting.
This was, however, not a case for the "calculus of indolence" with an
_x_ that was to be determined. Here it was a question of developing a
facility for geometric argument, such as very few possess at such an
early stage of development. The boy plunged himself for three weeks into
the task of solving the theorem, using all his power of thought. He came
to consider similarity of triangles (by dropping a perpendicular from
one vertex of the right-angled triangle on to the hypotenuse), and was
thus led to a proof for which he had so ardently longed! And although it
concerned only a very old well-known theorem, he experienced the first
joy of the discoverer. The proof that he had found proved that the
ingenuity of the worrying young mind was awakening.

A new world was opened for him when he made the acquaintance of A.
Bernstein's comprehensive popular books on scientific subjects. This
work is looked on nowadays as being somewhat antiquated and, in the eyes
of many a professional scientist, has sunk to the level of a
pseudo-scientific "shocker"; even when Einstein as a boy made
explorations in it, there were signs of rust and decay in the work, for
it originated in the fifties of the previous century and, in point of
subject-matter, had long been transcended. Yet it could be read
then--and even now--as a story containing thousands of interspersed
physical, astronomical, and chemical wonders, and for the boy Einstein
it came to be a true book of Nature, which presented to his mind, greedy
for knowledge, as much as it did to his imagination.

Other vistas were opened up to him by Büchner's _Kraft und Stoff_
(_Force and Substance_), a book the cheapness of which he could not yet
discern, but which called up wonder in him without rousing his
criticism. In addition, his attention was chiefly occupied by a handbook
of elementary planimetry, containing an abundance of geometrical
exercises, which he fearlessly attacked and within a very short time
solved almost in their entirety. His delight grew when he ventured into
the difficulties of analytical geometry and infinitesimal calculus quite
apart from the curriculum of his school-work. Lübsen's textbook had
fallen into his hands, and these directions sufficed for his audacious
spirit. Whereas many of his school companions were still standing
undecidedly before the pools of theorems of congruence and repeating
decimals, he was already disporting himself freely in the ocean of
infinitesimals. His work did not remain concealed, and gained
appreciation. His mathematical teacher declared that the
fifteen-year-old boy was ripe for university study.

Yet he was not to find a way into the open by matriculating very early,
but through an event that unexpectedly threw him into new surroundings
of life. In 1894 his parents transferred their abode to Italy. The
chronicler has nothing to report of pangs of separation in Albert when
he left Bavarian soil. He was glad to get away from the drill academy,
Luitpold, and, as an inhabitant of Milan, he enjoyed the change in his
existence, and was not encumbered by attacks of home-sickness. All in
all, he had felt himself in an unhappy position under school compulsion
in Munich, in spite of the mathematical delights he had provided for
himself, and in spite of the rapturous moments that musical revelations
had created for him since his twelfth year. Defiance and distrust
against outside influences had remained active in him as forces that did
not allow the happy disposition proper to his age to assert itself. But
now the fetters had fallen and the pent-up joy of life burst forth as if
through opened sluices. The sun and landscape of the South, Italian
manners of life, art freely displayed in the market-place and on the
street, realized for him dream-pictures that had appeared to him earlier
during the hours of oppression. Whatever he saw, felt, and experienced
lay outside the ordinary course of his life, awakened his sense for
natural and human things, and set his spirit free from all bonds. There
was no question of his going to school in the first six months. He
enjoyed complete freedom, occupied himself with literature, and
undertook extended excursions. Starting from Pavia, he wandered all
alone over the Apennine to Genoa. Whilst he was being intoxicated with
the sublime Alpine landscape, he came into contact with the lower
stratum of the people, who aroused his deepest sympathy. The tour took
him over a short stretch of the Italian Riviera, the beauties of
which, as depicted by Böcklin, do not seem to have revealed themselves
to him. At that time he was probably subject to a feeling of upward
striving such as possessed Zarathustra.

With all their joys and inspirations the experiences in Italy remained
but a short episode. Einstein resolved on a new tour, which was not
without a professional purpose. He made a pilgrimage to Switzerland with
the intention of studying mathematics and physics at the Zürich
Polytechnical Institute. But he was not to be successful in his first
effort to gain entrance. The conditions of entry required a standard in
descriptive sciences and modern languages that he had not yet reached.
So he turned to Aarau, where he was allowed to extend his knowledge with
the help of excellent methods at the Canton school. Even it the present
day Einstein talks with extreme enthusiasm of the organization of this
model school that corresponds in rank approximately to a German
Realgymnasium (or an English Grammar School). There was nothing to
remind him of the continual manipulation of the sceptre of authority at
the Luitpold school barracks; he easily obtained his leaving
certificate, and now the portals of the Zürich Polytechnicum were open
for him.

He himself was probably not aware that he carried a marshal's baton in
his own mathematical equipment. But, in looking back, we come across
astounding things. For it is a fact that even in the pupil at Aarau
problems had taken root that already lay in the vanguard of research at
that time. He was not yet a finder, but what he sought as a
sixteen-year-old boy was already stretching into the realms of his later
discoveries. We have here simply to register facts, and to abstain from
making an analysis of his development, for how are we to trace out the
intermediate steps, and to discover the sudden phases of thought that
lead a very young Canton pupil to feel his way into a still undiscovered
branch of physics? The problem that occupied him was the optics of
moving bodies, or, more exactly, the emission of light from bodies that
move relatively to the ether. This contains the first flash of the
grandiose complex of ideas that was later to lead to a revision of our
picture of the world. And if a biographer should state that the first
beginnings of the doctrine of relativity occurred at that time, he would
not be making an objectively false statement.

The ambitions of the youth by no means reached these flights of
imagination, for whereas the latter signified the coming power of his
wings, he himself set a modest goal. He wished to become a schoolmaster,
and imagined that in choosing this career he was allowing his hopes to
run high. This was in conformity with the esteem in which he held the
status of teachers. In the Zürich Technical School there is a section
equipped as a department for preparing teachers, and in this Einstein
studied from the age of seventeen to the age of twenty-one, perfectly
satisfied with the thought of sitting, not on the pupil's bench, but at
the master's desk, and of exercising a beneficial if limited influence
as a preceptor of the young.

He was still under the sway of the feeling that he was not sufficiently
experienced in life and that he dare not venture out into the light for
existence in the great turmoil of the world. He saw in this struggle,
which pitted man against man, led to exhibitions of violence, and
aroused ambition for glittering unrealities, cause only for disgust and
alienation. The prospect of personal success did not lure him to try
force against force. Thus, for the time being, it was his ideal to lead
a very modest existence. From various quarters he had been given hopes
of a position as assistant to some professor of physics or mathematics.
But for unknown reasons he was everywhere refused. These apparently
obscure grounds, it must be said with regret, become clearer when we
bear in mind his confession of faith. Nor did his hopes of teaching at a
gymnasium seem near fulfilment, as certain conditions of birth raised
obstacles. In the first place, he was not a Swiss; in fact, since his
stay in Milan he was without a nationality at all in the bureaucratic
sense, and then he had no personal connexions, without which, at least
at that time, there was no chance of progress even for a talented
person. Yet the young student who was entirely without protection of any
sort had to overcome the cares and satisfy the needs of daily life. He
could not rely on material help from his parents, who themselves lived
in restricted circumstances, and thus we find him a little later in
Schaffhausen and Bern, where he earned a small pittance as a private
tutor.

He found consolation in the fact that he preserved a certain
independence, which meant the more to him as his instinct for freedom
led him to discover the essential things in himself. Thus, earlier, too,
during his studies at Zürich he had carried on his work in theoretical
physics at home, almost entirely apart from the lectures at the
Polytechnic, plunging himself into the writings of Kirchhoff, Helmholtz,
Hertz, Boltzmann, and Drude. Disregarding chronological order, we must
here mention that he found a partner in these studies who was working in
a similar direction, a Southern Slavonic student, whom he married in the
year 1903. This union was dissolved after a number of years. Later he
found the ideal of domestic happiness at the side of a woman whose grace
is matched by her intelligence, Else Einstein, his cousin, whom he
married in Berlin.

In 1901, after living in Switzerland for five years, he acquired the
citizenship of Zürich, and this at last gave him the opportunity of
rising above material cares. His University friend, Marcel Grossmann,
lent him a helping hand by recommending him to the Swiss Patent Office,
the director of which was his personal friend. Einstein occupied himself
here from 1902 to 1905 as a technical expert, that is, as an examiner of
applications for patents, and this position gave him the chance of
moving about in absolute freedom in the realms of technical science.
Whoever has a strong predilection for discovery will perhaps feel
estranged to find Einstein so long in the sphere of "invention," but, as
Einstein himself emphasizes very strongly, both regions make great
demands on clearly defined and accurate thought. He recognizes a
definite relationship between the knowledge that he gained at the Patent
Office and the theoretical results that appeared at the same time as
products of intensive thought.

In 1905, in the midst of his work, the storm broke loose in him with the
suddenness of a hurricane. In quick succession his mind disburdened
itself of the abundance of ideas that had stored themselves up in the
work of the preceding years, and these ideas signify more to us than a
definite stage in the development of an individual. What physicists have
come to regard as an elaboration of the heritage of Galilei and Newton
had matured in him. We merely record the title of dissertations, which
appeared in 1905 in the _Annalen der Physik_: "Concerning a Heuristic
Standpoint towards the Production and Transformation of
Light"--"Concerning the Inertia of Energy"--"The Law of Brownian
Movement."--Then the most important contribution: "The Electrodynamics
of Moving Bodies," that contained the revolutionary ideas underlying the
special theory of relativity. To these is to be added a dissertation for
his doctorate in the same year: "A New Determination of Molecular
Dimensions."

In all, these represent a life-work that belongs to the history of
science. It was certainly some considerable time before his work began
its triumphal march in the sight of the world, and it may be added that
treasures were hidden in these disquisitions that were not understood
till long years afterwards. Yet the youthful discoverer was not passed
over without signs of friendly appreciation. He received a letter,
couched in very warm terms, from the celebrated physicist, Max Planck,
who was a complete stranger to him at that time; it spoke in glowing
words of his essay, "The Electrodynamics of Moving Bodies." This letter
was the first diploma, the forerunner of all the honours that later
swept over him like a tidal wave.

It was his intention to obtain a tutorial position at the University. An
appointment to Bern was at first again hindered by certain obstacles
which he would probably have overcome if he had applied himself
energetically to attaining his goal. He finally received his
appointment, but exercised his duties for only a very short time, as
Zürich now opened her arms to him. In 1909 he accepted the position of
Professor extraordinarius there for theoretical physics, and soon
assembled a grateful audience about himself. Nevertheless, during the
earlier stages of his professorship he found it difficult to suppress a
longing for the quiet, unexcited life of his patent-office work, in
which he seemed to have had a still greater degree of independence. In
1911 he accepted a new appointment as Professor Ordinarius to Prague,
which offered him more favourable emoluments as an inducement. In the
autumn of 1912 he returned to Zürich as a Professor at the Polytechnic,
and in the early part of 1914 he was drawn into the strong magnetic
field of the northern capital; he arrived at the Spree, and has, since
then, lived among us. He is now a Swiss by nationality, a world citizen
by conviction, and, professionally, a member of the Berlin Academy and
attached in a lecturing capacity to the University. Here he perfected
his works on relativity, ending in the superlative elaboration of the
theory of gravitation, the beginnings of which stretch back to the year
1907. He had spent eight years in a concentrated effort of severe
thought to bring it to completion, and perhaps centuries will be
necessary before the world will gain a complete perspective of all the
consequences of his theory.

For the theory asks us to brush aside habits of thought that have
claimed an hereditary position in pre-eminent minds. One of the foremost
physicists, Henri Poincaré, had confessed as late as 1910 that it
caused him the greatest effort to find his way into Einstein's new
mechanics. Another whole year passed before he gave up his last doubts.
Then he passed with flying colours into Einstein's camp, and recommended
Einstein's appointment to the Professorship at Zürich, in conjunction
with the discoverer of radium, Madame Curie, in an exuberant letter
which may add its note of appreciation here:

"Herr Einstein," so wrote the great Poincaré, "is one of the most
original minds that I have ever met. In spite of his youth he already
occupies a very honourable position among the foremost savants of his
time. What we marvel at in him, above all, is the ease with which he
adjusts himself to new conceptions and draws all possible deductions
from them. He does not cling tightly to classical principles, but sees
all conceivable possibilities when he is confronted with a physical
problem. In his mind this becomes transformed into an anticipation of
new phenomena that may some day be verified in actual experience.... The
future will give more and more proofs of the merits of Herr Einstein,
and the University that succeeds in attaching him to itself may be
certain that it will derive honour from its connexion with the young
master."

We may be tempted to look back and ask whether the criteria that Wilhelm
Ostwald once set up as a test of great men are verified in Einstein's
case. He has certainly not broken the first and most general rule, the
principle of "early maturity." This showed itself clearly when his
impulse towards mathematical knowledge and discovery asserted itself,
and when he penetrated far into the future with his optical problems.
The history of science and of art may offer more striking examples in
this connexion, but at any rate in Einstein's case the indications are
sufficient to serve as a confirmation of the rule. On the other hand,
the second test of Ostwald seems to be valid only conditionally when
applied to Einstein. For Ostwald takes up arms against a "gradual
intensification" of ability, and proclaims it as an almost universal
rule that the exceptional achievement is the privilege of quite young
persons: "what he achieves later is seldom as impressive as his first
brilliant achievement." Thus, in Einstein's case, the exception is
evident. For if we fix on only two chief discoveries, passing over many
others, there is no doubt that the second (the theory of gravitation)
surpasses the first (special relativity) in both range and significance.
Indeed, we cannot escape from the idea of a "gradual intensification,"
for the second discovery could come about only as a result of the first.
Moreover, it is not yet night, and there is nothing to refute the
assumption that there will be a further progression.

Furthermore, Ostwald takes into consideration the tempo of the
intellectual pulse of inspiration to divide the main types of great men
into a classical and a romantic category: this classification cannot,
however, be applied to Einstein. He is decidedly classical, in so far as
his work seems calculated to serve later generations as a classical
foundation for all mechanical investigations of the macrocosm of the
heavens and the microcosm of atoms. On the other hand, his versatility,
the mobility and resource of his highly imaginative mind, stamp him as a
romantic spirit. His delight in teaching would also assign him to this
category, for in the case of many classical spirits there is a decided
aversion to imparting instruction. So that, although we might well be
able to speak of a synthesis of these two forms, it seems better to
estimate Einstein, not in the light of a ready scheme, but rather as a
type of which he is the unique representative.

     *     *     *     *     *     *     *     *

Just as the external contour of his life is on the whole regular and
unbroken, so also his inner life is attuned to simplicity. Nowhere, it
might almost be said, do we observe a break, a spasmodic turn, or a
sudden intensification. Although he has grasped and suggested so many
problems, he himself presents no psychological riddle, and we meet with
no singularities in analysing his personality. It has already been
remarked several times that Art plays a part in his life. What I learned
from him himself about his affection for music coincides exactly with
what observation clearly discloses. The expression of his countenance
when he is listening to music is a sufficient indication of the
resonances induced in him. He is confessedly a classicist, and a sincere
devotee of the revelations of Bach, Haydn, and Mozart. What fascinates
and enraptures him above all is that which is directed inwards, which is
contemplative and erected on a religious basis. The simple masterful
flow in musical development and invention is all-important for him. The
architectonic structure that we marvel at in Bach, the Gothic tendency
towards heavenly heights, perhaps calls up in him sensations that
emanate from his hidden wealth of constructive mathematical ideas. It
seems to me that this possibility is not unworthy of remark. It suggests
a reason for the fact that he gives himself up only unwillingly to the
nervous strain of drama directed at emotional upheaval. He does not
gladly overstep the boundary that separates the simple from the
psychologically subtle, and whenever his desire to understand art
requires him to venture beyond it, his appreciation is not accompanied
by genuine pleasure. His subjectivity does not fix this boundary in
accordance with the ordinary rules of concert æsthetics, which are
actually not rules at all, but only changeable valuations and
crystallizations of the feelings of certain groups of people. He gives
himself up quietly and freely to what is presented, but makes no special
effort to assimilate experiences to which his being does not
spontaneously react. There would be no meaning in seeking to mark off
the limits of his receptivity in accordance with this, and to tell him
that it is too limited, and that it should be enlarged, and that he
should not regard as an opinionated exaggeration what appears to others
to be a deep and mighty revelation, or seems to be possessed of divine
sweetness. He would be able to point out that even in the case of
masters of the musical art a change of faith was not a rare occurrence,
and that they learned anew, or rejected what they once idolized, and
very often found no permanent haven in their own faith. Whoever, like
Einstein, gives himself up to the simply contemplative, and feels no
impulse towards sensationalism, is spared the task of learning afresh,
and finds still one world left for him even if many other worlds are
inaccessible. To mention only the main features, then, neither Beethoven
as a composer of symphonies, nor Richard Wagner, denote the pinnacles of
music for him; he could live without the Ninth Symphony, but not without
Beethoven's ensemble music. The number of composers and compositions
which are not a necessity of life for him is very considerable. It
includes the majority of romanticists, the erotically inclined school of
Chopin and Schumann, which revels in sensation, and, as already
mentioned, the neo-German dramatic composers. He has much objective
admiration for them, yet he does not conceal the fact that he also feels
lively opposition in the gamut of his sensations. He regards the
properly modern productions as interesting phenomena, and has various
degrees of disapproval for them, extending to complete aversion. It
costs him an effort to hear an opera of Wagner, and when he has done so,
he returns home bearing with him the _leitmotiv_ of Meister Eckhard:
"The lust of creatures is intermingled with bitterness." In general he
seems to take up approximately the point of view of Rossini. Wagner
gives him wonderful moments, followed, however, by periods of acute
emotional distress. I need hardly add that I myself, who confess to
being an ultra-Wagnerite, never strove in my conversations with Einstein
to make my opinion prevail against his. For I am deeply convinced that
in this matter there is no question of right and wrong, and that every
musical valuation represents no more than an accidental judgment
dependent on one's own nature, entirely egocentric and thus objectively
of no account.

Einstein also occupies himself in an active sense with music, and has
developed into a very fair violinist, without claiming higher degrees of
achievement. Among other things I once heard him play the violin part of
a Brahms Sonata, and his performance approached concert standard. He
draws a beautiful tone, infuses expression into his rendering, and knows
how to overcome the technical difficulties. Among the supreme artists of
his instrument who have exerted a personal influence on him, Joachim
assumes the first place. Einstein still speaks with great enthusiasm of
Joachim's performance of Beethoven's Tenth Sonata and of Bach's
Chaconne. He himself plays the latter piece, for which the purity and
accuracy of his double and multiple stopping fits him. Whoever chooses
the right moment--this good fortune has not yet befallen me--may
overhear Einstein at his pianistic studies. As he confessed to me,
improvisation on the piano is a necessity of his life. Every journey
that takes him away from the instrument for some time excites a
home-sickness for his piano, and when he returns he longingly caresses
the keys to ease himself of the burden of the tone experiences that have
mounted up in him, giving them utterance in improvisations.

The regular run of concerts in which displays of bravura play an
important part finds little favour with him; above all, he is not a
worshipper of the orchestral conductor, whom he regards only as an
interpreter and not as a virtuoso on the orchestral instrument. He
expressed this idea in unmistakable words: "The conductor should keep
himself in the background." I believe that his dearest wish would be to
breathe in the tones without a personal or material medium, merely out
of the air or out of space. Furthermore, I believe that there is an
unfathomable connexion between his musical instinct and his nature as a
research scientist. For the ear, as we know from Mach, is the true organ
that enables us to experience space, and thus things may occur within
the ear of the investigator of space that may have a different
significance from that of music which is representable in tones. I
strongly doubt whether traces of compositional form occur in Einstein's
tone-monologues, but perhaps they contain examples of an art for which
the æsthetics of a distant future may find a name.

     *     *     *     *     *     *     *     *

With regard to higher literature, and indeed all writings not connected
with science, Einstein has little to say. He himself rarely directs
conversation on to this topic, and still less rarely does he give vent
to an enthusiastic outburst that betrays warm interest. He restricts
himself to making short, aphoristic comments, and now and then allows
his listener to gather that he can easily imagine an existence without
literature. The number of accepted novels, tales, and poetic works which
he has not read is legion, and all the pretentiously artistic,
historical, and critical writings that are added to them have attracted
only a very momentary interest from him.

I have never seen him attracted in any way by the promising aspect of
some new book intended for diversion. If such a one happens to get into
his hands, he merely places it among the others. At times I was
constrained to think of Caliph Omar's words: "If the book contains what
is already in the Koran, it is unnecessary; if it contains something
else, it is harmful." It is harmful at least in the sense that it robs
us of time that may be better spent in another way. I am purposely
exaggerating here to make it quite clear that Einstein finds full
satisfaction in a narrow circle of literature, and that he experiences
no loss if numerous new works pass by and escape his notice.

Nevertheless, he speaks with reverence of a series of authors, to whom
he owes enrichment: among them are the classical writers, who naturally
occupy the highest position, with certain exceptions, which he equally
naturally wishes to be taken as a personal opinion and not in the sense
of a critical valuation. With him the difference reveals itself in the
intonation from which we may read a greater or lesser measure of
affection. When he says "Shakespeare," the eternal greatness seems to be
inherent in the actual sound of the name. When he says "Goethe," we
notice a slight undertone of dissonance, which may be interpreted
without difficulty. He admires him with the pathos of distance, but no
warmth glows through this pathos.

I had ventured to deduce from my knowledge of his nature the men and the
works which, in my opinion, should awaken strong echoes in him. A fairly
clearly defined line leads to the true path. Outside of any systematic
series, I may mention Dostojewski, Cervantes, Homer, Strindberg,
Gottfried Keller in the positive sense, Emile Zola and Ibsen in the
negative sense. Taken as a whole, this prognostication does not disagree
seriously with his own statement, excepting that he lays still greater
emphasis on Don Quixote and the Brothers Karamasoff than I had surmised.
He expressed himself with reserve about Voltaire. He has no belief in
Voltaire's poetic qualities, and sees in him only a subtle-minded and
amusing writer. Perhaps if Einstein were to devote himself a little more
intensively to Voltaire and Zola, he would assign a higher value to
these related spirits. But there is little hope of this occurring, as
the wide range of Voltaire's works tends to restrain him. Time, which
the physicist Einstein has shown to be relative, has an absolute value
for him when measured in hours, and whoever seeks to persuade him to
read thick volumes is not likely to gain his goodwill.

Our philosophical literature is not received with acclamation by him. If
some one wished to undertake the task of ascertaining Einstein's
attitude towards philosophy, he would be well advised to plunge into
Einstein's works rather than to ask him personally. In them the
questioner would find ample hints, pointing towards a new theory of
knowledge, the first indications of which are already perceptible. A
great portion of philosophic doctrine will yet have to pass through the
Einstein filter to be purified. He himself, it seems to me, leaves this
process of filtering mostly to other thinkers, but we must not lose
sight of the fact that these others derive their views of space, time,
and causality from Einstein's physics. It is thus immediately evident
that he does not find revelations about ultimate things in already
extant literature, for the simple reason that they are not to be found
there. For him famous works represent, in Kant's language, "Prolegomena
to every future system of metaphysics which can claim to rank as a
science." The accent is to be put on the future that has not yet become
the present. He praises many, particularly Locke and Hume, but will
grant finality to none, not even to the great Kant, not to mention
Hegel, Schelling, and Fichte, whom he barely mentions in this connexion.
To Schopenhauer and Nietzsche he assigns a high position as writers, as
masters of language and moulders of impressive thoughts. He values them
for their literary excellence, but denies them philosophic depth. As far
as Nietzsche is concerned, whom, by the way, he regards as too
glittering, Einstein certainly experiences ethical objections against
this prophet of the aristocratic cult whose views are so diametrically
opposed to Einstein's own opinion of the relations between man and man.

Earlier when we were talking of classical poetry he had particularly
emphasized Sophocles as one who was dear to him. And this name leads us
to the innermost source of Einstein as a man. "I am not here to hate
with you but to love with you," is the cry of Sophocles' Antigone, and
this cry is the keynote of Einstein's emotional existence. I shall not
give way to the temptation to follow those who in the turmoil of the
present day refer to Einstein as a political figure. That would lead to
a description of policy and party arguments that lie beyond the scope of
this book; so much the less am I inclined to do so as Einstein's
convictions may be expressed very clearly without reference to schematic
terms of a very elastic nature. An individuality such as his cannot be
compressed into a party programme. And if anyone should insist on
placing him among the radicals or on assigning him far to the left, I
should suggest that it would be better to choose, instead of the
classification right and left, that of above and below. I look up
towards his idealism, whose altitude may perhaps be reached one day by
the raising of our ethical standards. But not by means of paragraphs of
laws. I have seldom heard him talk of such schematic recipes, but so
much the more have I noted utterances which bore witness to a very
intense and ever-present sympathy with every human creature. His
programme, which is written not in ink but in heart's-blood, proclaims
in the simplest manner the categorical imperative: Fulfil your duty to
your fellow-being: offer help to every one: ward off every material
oppression. "Well, then, he is a socialist," so the cry runs. If it is
your pleasure to call him so, he will not deny you it. But to me this
term seems to denote too narrow limits for him. I see no contradiction
in applying the term, but there is no perfect congruence. If one word is
necessary, I should be rather more inclined to say that he is in the
widest sense a democrat of liberal trend.

For him the State is not its own aim, nor does he imagine himself to be
the possessor of a panacea. "The attitude of the individual to
socialism," he said, "is uncertain owing to the fact that we can never
ascertain clearly how much of the iron compulsion and blind working of
our economic system may be overcome by appropriate institutions." And I
should like to add that such institutions would scarcely have a
permanent result, but that more may be expected from the ethical example
of those who have the power of renunciation. Whoever realizes the motto
of Antigone, "I am here to love with you," brings us nearer the goal.
All in all, our longing continually flees from the confusion of
political considerations to simple morality. For Einstein this is the
primary element, that which is directly evident and not open to
misrepresentation. It includes sympathy, and, what is more important,
joy in conjunction with others. "The best that life has to offer," he
once exclaimed, "is a face glowing with happiness!"

This look is expressed on his own face when he discusses his ideals,
above all the internationality of all intellectual workers and the
realization of eternal peace among the nations. To him pacifism is a
matter of mind as well as of heart, and he is of the opinion that the
course of history so far is but the prelude to its realization. The
past, with its bloodstained fingers that reach into the present, does
not discourage him He points to the endless city wars of the Middle Ages
in Italy, which had finally to cease in answer to the increasing feeling
of solidarity. So he believes in the victory of peace, which the unified
consciousness of all humanity will one day win over the demonic powers
of tyranny and conquest.

The pacifistic goal seems to him to be attainable without the
peculiarities of the various States being destroyed. National
characteristics arising from tradition and hereditary influences do not
signify in his eyes a contradiction to the internationalism that
embraces the common intellectual factors of civilized peoples. Thus the
desire for the preservation and care of particularities directs him to
the secondary goal of Zionism. His blood asserts itself when he supports
the foundation of a State in Palestine, which seems to him to be the
only means of preserving the national individuality of his race without
the freedom of the individual being affected.

We had left Art to talk of the State, and then returned to the former
theme to touch lightly on the pictorial arts. Painting was allowed to
pass with merely a fleeting remark. It plays no considerable part in
Einstein's existence, and he would not suffer great grief if it were to
vanish from the plane of culture, a consummation to which definite signs
seems to point. I have described these signs in other writings (as in
_Kunst in 1000 Jahren_), and maintain the point of view that the latest
branches of painting as represented by expressionism and cubistic
futurism denote, in essence, the last convulsions of a dying surface
art. And even the chief representatives of former flourishing periods
are beginning to fade away, and Einstein will not be the only one who
will relegate this art, as compared with music, to a lower plane among
the inspired arts that bring joy to humanity. He is only more frank than
others when he freely confesses that he cannot convince himself that a
life without the joys of pictorial art would be hopelessly impoverished.
But he bows his head to sculpture, and, for him, architecture is a
goddess. It is again his deeply rooted piety that asserts itself when
memory recalls to him the Gothic dome with its pinnacles striving
towards heaven. Goethe and Schlegel have called architecture "frozen
music," and this picture is present in his mind when he sees Gothic
architecture as frozen music of Bach. It is open to anyone to analyse
this specific impression in another way by seeking the fundamental
elements, in which the essence of the art is to provide support for a
weighty structure and to overcome gravitation. For a spirit that works
with mechanics and that feels within itself the pressures and tensions
occurring in external nature, architecture is a kind of statics and
dynamics transformed into a thing of beauty, a ravishing picture of his
own science.

     *     *     *     *     *     *     *     *

Einstein has told me many a story of his travels, and these reports were
characterized by an absence of definite purpose. The conception of
something worth seeing in the tourists' sense does not exist for him,
and he does not set out in eager pursuit of those things that are marked
with two asterisks in Baedeker. The intense romanticism of Swiss
scenery, that lay within such easy reach for him, has never enticed him
into its magic circle, and he has nothing to do with the abysmal terrors
of glaciers and the world of snow-peaks. His enthusiasm for landscape
beauty conforms with the behaviour of the barometer: the greater the
altitude, the lower the mercury. In simple contact with Nature he
prefers the lesser mountains, the seashore, and extensive plains,
whereas brilliant panoramic contours like those of the Vierwaldstetter
See do not rouse him into ecstasy. It is unnecessary to remark that he
does not arrange his living on the standard of the Grand Palace Hotels
en route. It is nearer the truth to picture him as a vagrant who tramps
along without a sense of time and without a goal, in the fairy
atmosphere of a joyous wanderer who has unconsciously adopted the old
rule of Philander: Walk with a steady step: make your burden small:
start early in the morn, and leave home all care!

Am I to record the list of pleasures and hobbies that are foreign to
him? The list would be very long, and I should arrive at my goal more
quickly by setting his sporting tendencies equal to zero. I once
suspected him of being given to aquatic sport, as I learned that he had
taken part in several yachting excursions. But I was mistaken. He sails
in the same way as he walks on his tours, without a set purpose,
dreaming, and uninterested in what is regarded by members of sailing
clubs as a "feat." In the negative list of his games we see even chess,
that usually exerts a strong attraction on natures with a mathematical
tendency. The particular types of combination offered by this game have
never tempted him, and the world of chess has remained _terra incognita_
for him. He is just as little interested in every kind of collection,
even that of books. I have seldom or never met a savant who attaches so
little value to the personal possession of numerous and valuable books.
This statement may be extended as far as saying that he experiences no
pleasure at all in possession as such: he says so himself, and his whole
manner of life proves it. There seems to me to be an element of
resignation in his amiable hedonism, a kind of monkish asceticism. He
never rids himself of the feeling that he is only paying a visit in this
world.

I do not know whether Einstein considers that his life-work can be
completed within the span of this visit. At any rate he makes no attempt
to extract more out of the day by following a rigid programme of work
than the day voluntarily offers. He does not compel himself to cover a
definitely circumscribed piece of ground with chronological exactitude.
There are brain-workers, especially artists, who actually never shake
off the fetters of the twenty-four hours day of work inasmuch as they
spin on the threads of daily effort into the nightly fabric of dreams.
Einstein can make a pause, interrupt his work, or divert himself into
side-channels at leisure and according to the demands of the hour, but
dreams offer him no inspiration and do not waylay him with problems.

On the other hand, however, he is waylaid so much the more during the
day by things and persons that make an assault on him. This starts as
soon as the first post arrives, to see through which requires a special
bureau. In addition to the communications of a professional or official
nature there appear innumerable letters from everywhere and anywhere
asking him to grant a little of his time. Whatever each individual
writer has thought about the principle of relativity, all his thoughts
and doubts, additions, and, above all, that which he has not been able
to understand, all this is to be answered by Einstein. Has he, the child
of fame, even a quarter of an hour for himself? There they wait in the
hall, the painter, the photographer, the sculptor, and the interviewer;
with whatever powers of persuasion and argumentative subtlety his
attentive wife may seek to defend his hours of rest, some of these
visitors will yet succeed in gaining the upper hand, and will produce
something in oil-colours, in plaster of Paris, in black and white, in
water-colours, or in print. Fame, too, demands her sacrifices, and if we
talk of a hunt after fame, then Einstein is certainly not the hunter,
but the hunted.

He sighs under the burden of his correspondence, not only as the
recipient, but also with the sender, whose letter has to remain
unanswered. Yet he is never roused to anger by the intruder on his time.
If this were not so, the aphorism of Cyrus that patience is the panacea
of all ills would not hold for him, and how would I myself otherwise
have dared to claim so many hours of him? A sense of guilt falls on me!

But even Einstein's patience can come to an end, and this is at the
point where "society" begins: I mean the congregation of persons in a
salon, society entertainments to which one is invited to be seen, and so
that one may claim to have been there. A solemn representation in which
he is to be made the cynosure of all eyes is a torture to him. If in a
very exceptional case he is compelled to participate in such a
gathering, the joy of his hosts will not be entirely unmixed, for it
does not require a thought-reader to recognize the longing for solitude
imprinted on his countenance: "Could I but escape!"

So much the happier does he feel himself in the narrow circle of his
friends, who offer what means to him much more than admiration, namely,
affection, and an appreciation of his human self. He is what one wishes
him to be. He is happy when he can forget the doctor profundus, and can
yield himself up to the atmosphere of stimulating and unconstrained
converse. He is a master in the art of listening, and is not averse to
contradiction; when possible, he even emphasizes the arguments of his
opponent. _Audiatur et altera pars_! This is a further manifestation of
his altruistic personality, which rejoices when he extracts the true
kernel from the husk of the opposing opinion. Here he also displays a
characteristic which one does not usually expect to find among abstract
thinkers, a sense of humour that runs through the whole gamut from a
gentle smile to hearty laughter, and that is the happy source of many a
striking sally. It may happen that the subject of conversation excites
his anger, especially in political debates when he calls to mind
militaristic or feudal misgovernment. He then becomes roused, and, as a
cynical philosopher, sarcastically attacks personalities and points out
the primary source of perennial hate, immediately afterwards soaring up
to happy speculations of the future.

It is a matter for regret that the subjects that he has discoursed on
lightly have not been fixed phonographically. Such records would form an
interesting supplement to the conversations outlined in this book. It
would never occur to him to set down in permanent literary form the
inspiration of the moment. What he writes emanates from other regions,
and is, to use his own expression, a precipitate of "thick ink." This is
obvious, for what he has to proclaim as a scientist cannot be presented
in a "thin" form. But many a so-called writer would have reason to
congratulate himself, if so much thinly flowing matter occurred to him
in writing as to Einstein in speaking.

     *     *     *     *     *     *     *     *

The record of these conversations was begun in the summer of 1919, and
completed in the autumn of 1920.




INDEX

Aristoteles, 41
Arrhenius, 144

Babinet, 25
Bach, 88, 235
Bacon, 46
Baer, K. E. von, 162
Bailhaud, 144
Beethoven, 99, 234, 235
Bell, Graham, 25, 111
Béranger, 84
Bergson, 91
Bernoulli, 48
Bernstein, 225
Bessel, 32
Bohr, Niels, 57, 210
Brahe, Tycho, 94
Bruno, Giordano, 141
Büchner, 225
Bulwer, 76
Bunsen, 164
Byron, 9

Cantor, 52, 203
Cavendish, 111
Ceulen, Ludolf van, 158
Condillac, 216
Copernicus, 6, 90
Cosmati, 48
Curie, Madame, 79, 231
Cuvier, 196

Darboux, 152
Dase, 158
Descartes, 47, 133, 162
Dingeldey, 190
Dostojewski, 185, 187
Dove, 21, 155
Duhem, 105, 106
Dühring, 54, 56

Eckermann, 50, 85
Edison, 140
Euclid, 180
Euler, 98
Euripides, 85

Faraday, 39, 61, 84
Fechner, 110, 182
Fermat, 97, 190
Fizeau, 113
Flammarion, 115
Franklin, 102
Fresnel, 45

Galilei, 6, 40, 150, 179, 181
Galle, 6
Galvani, 110
Gauss, 55, 185, 186
Goethe, 13, 23, 179, 197, 212, 236
  240
Grillparzer, 95
Grossmann, 229

Hansen, 134
Hebbel, 77, 86
Hegel, 42
Heine, 49
Helmholtz, 25, 26, 53, 73
Heraclitus, 23
Herschel, 84
Hertz, 60
Hooke, 41
Horace, 3
Humboldt, 49
Hume, 161
Huyghens, 56, 109, 132

Jean Paul, 86, 223
Joule, 84
Jung Stilling, 84

Kant, 35, 121, 170, 177, 179, 237
Kepler, 6, 42, 84, 176, 177
Kirchhoff, 104-107, 148, 212
Kleist, 130
Kummer, 190

Lamarck, 197
Lange, 47
Laplace, 40, 45, 140, 165
Leibniz, 26, 128
Leonardo da Vinci, 11, 50-54
Leverrier, 6, 10
Liebig, 55
Lindemann, 158
Linné, 196
Lorentz, 57, 72
Lothar Meyer, 107
Lucretius, 210

Mach, 46, 77, 108, 149, 169
Mauthner, 95
Maxwell, 39, 60
Mayer, Robert, 25, 55, 56
Melanchthon, 82
Menander, 86
Mendelejew, 107
Mezzofanti, 63
Michelangelo, 49
Michelson and Morley, 112
Mill, 45

Mithridates, 63
Montaigne, 77
Mozart, 233

Newton, 2, 6, 8, 39, 40, 43, 96
Nietzsche, 63, 217, 237
Nollet, 103

Odilon, Helene, 135
Oersted, 109
Ostwald, 83, 231, 232
Ovid, 197

Pascal, 93, 98
Pasteur, 175
Perrin, 154
Pflüger, 35
Philander, 241
Picard, 144
Planck, 57, 59, 91, 230
Poincaré, 1, 7, 112, 116, 231
Pope, 54
Priestley, 111
Psellus, 156
Pyrrhon, 92
Pythagoras, 101, 179

Quetelet, 182

Regiomantus, 52
Reis, 25
Riemann, 186
Riggenbach, 25
Ruëss, 224
Rutherford, 36, 210

Schiller, 74, 94, 170
Schlegel, 240
Schlick, Moritz, 168
Schopenhauer, 41, 237
Schwann, 175
Shakespeare, 236
Siemens, 25, 27-30
Slade, 136
Sophocles, 238
Spinoza, 84, 162
Stephenson, 25

Terence, 191
Thomas Aquinas, 165
Torricelli, 166

Vaihinger, 43, 169
Vitruvius, 101
Volta, 110, 111
Voltaire, 47, 237

Wagner, 234
Weber, 182
Weierstrass, 152
Weyl, 34
Whewell, 45
Wien, 173

Zelter, 84
Zöllner, 137