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 3.1010 cm. per second. Accordingly the square of c is equal to 9 times 1020 cm. per second, or, in round numbers, 1021 cm. per second. This c2 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 20.1012, 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 c2) 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."
[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 mc2, 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 mc2-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 mc2. 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."
[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."
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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."