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EINSTEIN THE SEARCHER 
 
EINSTEIN 
 THE SEARCHER 
 
 HIS WORK EXPLAINED FROM 
 DIALOGUES WITH EINSTEIN 
 
 BY '••.:;:; 
 
 ALEXANDER MOSZKOWSkt 
 
 TRANSLATED BY 
 
 HENRY L. BROSE 
 
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 NEW YORK 
 P. BUTTON AND COMPANY 
 PUBLISHERS 
 
 ^''525 Market St \\ 
 
 \ Garfield 19 
 
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• • *. • • • 
 
 MU 
 
 Library 
 
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 ■rr 
 
EXTRACT FROM THE AUTHOR'S 
 PREFACE 
 
 THE book which is herewith presented to the public 
 has few contemporaries of a Uke 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 EucHd 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 personaUty 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 
 iUimitable 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 classifica- 
 
 68^232 
 
vi EINSTEIN THE SEARCHER 
 
 tion ; 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 hterature about him. At the end of 
 this generation we shall possess a voluminous library com- 
 posed 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 him- 
 self, 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 sub- 
 sequent 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 cHnging 
 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 
 
EXTRACT FROM THE AUTHOR'S PREFACE vii 
 
 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 con- 
 nexion, which expresses a general meaning without being 
 narrowed to pedantic hmits by a restriction to Hteral re- 
 petition. It is just this absence of the method that is rightly 
 demanded of a textbook, which may enable these conversa- 
 tions to pass on to the world a httle 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 ghmpse of his personaUty, without 
 demanding a detailed study to secure this end. Even here 
 I should Uke 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 build- 
 ing 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 accompany- 
 ing him on these excursions, it was not within my sphere to 
 expect in addition that he would direct his steps according to 
 
viii EINSTEIN THE SEARCHER 
 
 a preconceived plan. Often enough the goal vanished, and 
 there remained nothing but the pleasure of the rambles them- 
 selves with the consciousness of their purpose. As Schopen- 
 hauer 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 idylUc 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, accord- 
 ing 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 reahstic, 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 personaHty. 
 Mr. Moszkowski invites us to ramble with Einstein into realms 
 not confined to pure physics. Many subjects that have a 
 pecuHar interest at the present critical stage of the world's 
 history receive illuminating attention. It is hoped that the 
 appearance of the book in Enghsh 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 
 
V 
 
 CONTENTS 
 
 CHAP. 
 
 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 .... 
 
 FAGB 
 
 I 
 
 20 
 38 
 62 
 
 88 
 115 
 143 
 172 
 192 
 200 
 220 
 245 
 
2 EINSTEIN THE SEARCHER 
 
 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 werig 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 Poincar^ 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 Ups. 
 
 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 Hotel 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 
 
PHENOMENA IN THE HEAVENS 
 
 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 im- 
 restrained 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 delect ando pari- 
 terque monendo." It was certainly most deHghtful. 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 be- 
 ginning 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 Poincar^ had in the mean- 
 time 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 apprecia- 
 tion by his contemporaries were only a fuller instriunentation 
 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 deahng 
 with Einstein's Reports for the Academy, and had preserved 
 the cuttings in his pocket-book. He considered this a fitting 
 opportunity for enhghtenment. 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- 
 
4 EINSTEIN THE SEARCHER 
 
 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 cafe 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 gravita- 
 tion in its widest sense, and hence also the physical constitu- 
 tion 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 calhng 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 undis- 
 turbed 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 confficts. 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 
 
PHENOMENA IN THE HEAVENS 5 
 
 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 con- 
 vinced 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 he 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 Uttle 
 excitement, but the whole world generally, so much the more. 
 By way of illustration we shall Hnk them up with the result of 
 a forerunner who, Hke 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 cus- 
 tomary to quote the achievement of the French astronomer 
 Leverrier who, pen in hand, estabhshed 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 beUeve 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 BerUn Observatory about 
 seventy-five years ago, as it was at that time in possession of 
 
6 EINSTEIN THE SEARCHER 
 
 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 certadnly 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 appHed them with the mind of genius. Any- 
 one 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 con- 
 sisted in bringing those doctrines in which truth had been 
 proclaimed in its essential features, but not exhaustively, by 
 the genius of Copernicus, GaHlei, 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 
 
PHENOMENA IN THE HEAVENS 7 
 
 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 imaccountable 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 Hkewise been dis- 
 covered 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 un- 
 explored 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 1 9 10 Poincar^ had touched upon this embarrassing 
 question, mentioning that here was a possibility of testing 
 the new mechanics. 
 
 He decHned the suggestion of some astronomers that this 
 was again a Leverrier problem and that there must exist another 
 undiscovered planet still nearer the sim 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. Poincar^ divined that the 
 new mechanics could supply the key to the enigma, but, 
 obviously to be quite conscientious, he expressed his presenti- 
 ment 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 i8th Nov- 
 ember 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 
 
8 EINSTEIN THE SEARCHER 
 
 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 
 possibiUty, would be about equivalent to wishing to learn the 
 history of the world by reading several quarto pages of manu- 
 script 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 intelhgible, 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 occur- 
 rences. These are symbolical representations expressed as 
 formulae 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, 
 
PHENOMENA IN THE HEAVENS 9 
 
 if the distance is trebled, the force becomes one-ninth as 
 greaX. 
 
 According to the Theory of Relativity this fimdamental 
 law is not wrong or invahd, 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 Ught, and the new geometry which operates with 
 " world-lines " in space which, amalgamated with the dimen- 
 sion 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, where- 
 as 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 deHcate pinnacle. For the mathe- 
 matician this pinnacle is given as a combination of signs, 
 representing a so-called " EUiptic Interval." Such an in- 
 terval is a very weird construction, and the man who will 
 make it apprehended by the general reader is yet to be bom. 
 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 inteUigibihty, 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 crystalhzed out ! 
 
 But now the explanation had arrived and could be evalu- 
 ated, if only approximately. Before we give the result, let 
 us just describe at least one technical term, namely, " Peri- 
 heUon." It is that point of a planetory orbit which hes 
 nearest the sun. This orbit is an elUpse, that is, an elongated 
 curved Hne in the interior of which one distinguishes a major 
 axis in the direction of elongation, and a minor axis perpen- 
 dicular to the former at its middle point. The periheUon 
 
10 EINSTEIN THE SEARCHER 
 
 of a planetory orbit is at one of the end points of the major 
 axis. 
 
 In time the perihehon alters its position in space, ad- 
 vancing in the same sense as the orbit is traversed. Ic 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 lie 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 accord- 
 ing to his theory shows that for the planet Mercury the peri- 
 hehon 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 dazzHng that it alone would 
 have sufi&ced 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 apphed 
 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 Ught-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 possibihty 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 fight 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. 
 
PHENOMENA IN THE HEAVENS 11 
 
 Once again current thought encountered a sharp comer, 
 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 Hues, that is, the shortest 
 Hues, 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 sim, 
 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 imder a greater 
 visual angle than if the rays were straight, and interprets this 
 angle as denoting a greater distance between the sources of 
 hght, 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 
 dehcacy 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 i^ 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 rmthinkably small measure. 
 
12 EINSTEIN THE SEARCHER 
 
 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 intelHgible 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 indis- 
 pensable — 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 echpse — 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 
 
PHENOMENA IN THE HEAVENS 13 
 
 Star, so men directed their attention to the constellation of 
 Einstein, which was not yet depicted in stellar maps, but, from 
 which something imcomprehended, 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 Ught on the plate did 
 not answer immediately with Yes or No, but only after 
 mechanical devices of extreme deUcacy had been carefully 
 appUed. 
 
 At the end of September they proclaimed their message. 
 It was in the affirmative, and this Yes out of far-distant tran- 
 scendental regions called forth a resounding echo in the world 
 of everyday hfe. Genuinely and truly the i^ 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 hght and gravitation were seized by this wave and carried 
 on high, immersed in the wish for knowledge although in- 
 capable 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 con- 
 verse of educated people circled about this pole, could not 
 escape from it, continually reverted to the same theme when 
 
14 EINSTEIN THE SEARCHER 
 
 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 comers 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- 
 dimensionaUty. 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 mis- 
 guided idealists. 
 
 And whilst leaders of the people, statesmen, and ministers 
 made vain efforts to steer in the fog, to arrive at results service- 
 able to the nation, the multitude found what was expedient for 
 it, what was upHfting, what sounded like the distant hammer- 
 ing 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 rehgion, lay outside 
 political or material interests. 
 
 The mere thought that a Hving 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 beauti- 
 
PHENOMENA IN THE HEAVENS 15 
 
 fully coloured pictures intended to give the reader an idea of 
 the paths pursued by the rays from the stars during the total 
 echpse 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 op- 
 posite 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 
 Une 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 joumaUstic homage was not immixed 
 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 imbroken ovations 
 became discomfiting, and his feeUngs took up arms against 
 what seemed to be developing into a star-artist cult. It was 
 Uke a breath of fresh air when some column of a chance news- 
 paper 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 I " And these words were uttered in the most 
 natural manner possible. One must know him personally if 
 one is to imderstand these excesses of toleration. So did 
 Socrates defend his opponents. 
 
 In our conversation we retmned to the original question, 
 and I asked whether there was no means of making the deflec- 
 tion of the ray intelhgible 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 explana- 
 tion 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 fives a physicist who makes observations and 
 draws inferences from them. In the course of time he per- 
 ceives, what is famifiar to all of us, that every body not sup- 
 ported and left to itself, for example, a stone that is released, 
 drops to the floor with uniform acceleration, that is, with a 
 
16 EINSTEIN THE SEARCHER 
 
 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 falHng of the stone would suggest 
 nothing unusual ; it would be quite self-evident to every 
 occupant, and quite expHcable 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 pro- 
 perty 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 separted 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 
 faUing " 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 falUng 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 deter- 
 mining 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 vaUd, 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, 
 
PHENOMENA IN THE HEAVENS 17 
 
 connected to one another by relativity ; a fundamental reason 
 for preferring one interpretation to the other cannot be 
 furnished, since the phenomenon of faUing is represented 
 unchanged whether he assumes the stone to be falhng and the 
 box to be at rest, or vice versa. This may be generahzed 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 ob- 
 serve 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 equiv^ence or the identity of inertial and gravitational 
 mass. If we famiharize 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 quaHty 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 sim,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 ceiUng, four waUs, 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 Une parallel to 
 the floor and to the ceihng. But, as we have seen, all events 
 
18 EINSTEIN THE SEARCHER 
 
 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 rectihnear. 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 Hght which 
 is emitted by a source outside in a horizontal direction and 
 which traverses the space between the walls (supposed trans- 
 parent). 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 pro- 
 vided sufficiently delicate means of measurement are applied, 
 it should still be possible to prove the existence of an in- 
 finitesimal deflection from the rectihnear horizontal path, 
 an insignificant concavity towards the floor. 
 
 Consequently this curvature of the hght-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 per- 
 ception to be bent in towards the sun, and the order of this 
 deflection can be determined if sufficiently deHcate instru- 
 ments be used. As above remarked, it is a question of detect- 
 ing a difference of 17 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 " spht- 
 ting 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 
 
PHENOMENA IN THE HEAVENS 19 
 
 a millimetre in linear measure on the plate corresponds to a 
 minute of arc. This means that the sim'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 ihr 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 
 sUghtest 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 naivete. 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 Sim 
 Myth, unperceived by the individual, but as an expression of 
 the universal consciousness, just as when Copernicus con- 
 verted the geocentric picture of the imiverse into a helio- 
 centric one, the Sun Myth again sprang into Hfe ; the sym- 
 boHzation of faith in the Hght -giving and heat -giving star. 
 This time it has arisen, purified of all dross, scarcely perceptible 
 to our senses, hke an aureole spun about the sun by far-distant 
 sources of Hght, 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. — Un- 
 obtainable Calories. — Economics of Coal. — Hopes and Fears. — Dissociated 
 Atoms. 
 
 29/A 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 corre- 
 sponding 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 outHne, colour, 
 tone, pressure, impact, temperature, motion, chemical be- 
 haviour, whereas the thing in itself is the sum-total of its 
 
 energy, in which there is an enormous predominance of those 
 
 20 
 
BEYOND OUR POWER 21 
 
 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 sig- 
 nificance, may be calculated. The fact that it is possible to 
 calculate it takes its origin, hke many other things which had 
 in no wise been suspected, in Einstein's Theory of Relativity. 
 
 Quite objectively and without betraying in the sHghtest 
 degree that an astonishing world-problem was being dis- 
 cussed, Einstein expressed himself thus : 
 
 " According to the Theory of Relativity there is a calcul- 
 able relation between mass, energy, and the velocity of Ught. 
 The velocity of hght (denoted by c, as usual) is equal to 
 3*io^° cm. per second. Accordingly the square of c is equal 
 to 9 times lo^^ cm. per second, or, in round numbers, lo^^ cm. 
 per second. This c^ plays an essential part if we introduce into 
 the calculation the mechanical equivalent of heat, that is, 
 the ratio of a certain amount of energy to the heat theoretically 
 derivable from it ; we get for each gramme 20*10^2^ that is, 
 20 bilHon calories." 
 
 We shall have to explain the meaning of this brief physical 
 statement in its bearing on our practical Uves. It operates 
 with only a small array of symbols, and yet encloses a whole 
 universe, widening our perspective to a world-wide range ! 
 
 To simpUfy the reasoning and make it more evident we 
 shall not think of the conception of substance as an iUimitable 
 whole, but shall fix our ideas on a definite substance, say coal. 
 
 There seems Uttle 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 
 Ufe. I endeavoured to do this during the above conversa- 
 tion, and was grateful to Einstein for agreeing to simpUfy 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 
 
22 EINSTEIN THE SEARCHER 
 
 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 sufQcient 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 eUminated. 
 
 Such effective heat is usually expressed in calories. A calorie 
 is the amount of heat that is necessary to raise the tempera- 
 ture of a gramme of water by one degree centigrade. Now 
 the theorem of the Mechanical Equivalent, which is founded 
 on the investigations of Camot, 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 milHon feet, theoretically, 
 or, what comes to the same approximately, to hft 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 dumb- 
 founded if the new calculation were to be a matter of millions, 
 but actually we are to imagine a magnification to the extent 
 of bilHons. This sounds almost hke a fable when expressed 
 in words. But a milHon is related to a bilHon 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 miUion 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 
 
BEYOND OUR POWER 23 
 
 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 Hght 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 pre- 
 serves 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 pheno- 
 mena," 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 
 imf)elled 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 HeracHtus assumed as a fundamental truth in 
 his assertion fanta 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. Never- 
 theless, there is an absolute despot, who preserves his identity 
 inflexibly among all phenomena — ^the velocity of hght, c, of 
 incalculable influence in practice and yet capable of measure- 
 ment. Its nature has been characterized in one of the main 
 propositions of Einstein stated in 1905 : '* Every ray of hght 
 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, con- 
 nectivity, and invincibiUty of Einstein's world system. 
 
 In our example of the coal, from which we started, c occurs 
 as a square, and it is as a result of multiplying 300,000 by itself 
 (that is, forming c^) that we arrive at the thousands of miUiards 
 of energy imits which we associated above with such a com- 
 
24 EINSTEIN THE SEARCHER 
 
 paratively 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 horse- 
 power 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 justi- 
 iymg 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 
 dazzUng 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 sd^ymg : "At present there is 
 not the slightest indication of when this energy will be ob- 
 tainable, or w^^ether 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 con- 
 tinual explosive decomposition of its atom.. ^-Nevertheless, we 
 can only establish the presence of this proems, but cannot pro- 
 duce it ; Science in its present state majkes it appear almost 
 impossible that we shall ever succeed in BQt^oing." 
 
 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 
 
BEYOND OUR POWER 26 
 
 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 
 multipUed by the square of the velocity of Hght," 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 impos- 
 sible what was later discovered to be within the reach of tech- 
 nical 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 estabUsh their inventions in the face of the 
 general reproach of craziness hurled at them. The eminent 
 physicist Babinet appUed his mathematical artillery to 
 demoHsh the ideas of the advocates of a telegraphic cable 
 between Europe and America. Phihpp Reis, the forerunner 
 of the telephone, failed only as a result of the " impossible " of 
 the learned physicist Poggendorff ; and even when the prac- 
 tical 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 illustra- 
 tions is to be added Robert Mayer's mechanical equivalent of 
 heat, a determining factor in our above calculations of billions ; 
 it Hkewise 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 earUer and also their transformation into 
 useful forces. He would have expressed it in another way and 
 
26 EINSTEIN THE SEARCHER 
 
 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 prim- 
 ordial logic that it was not possible and never would be possible 
 to derive from the piece of wood something which sends out 
 warmth Uke the sun. 
 
 I believe now, indeed, that we have grounds for consider- 
 ing ourselves able to mark off the limits of possibiUty more 
 clearly than the present position of science would seem to 
 warrant. There is the same relation between such possibiHties 
 and absolute impossibihties as there is between Leibniz's 
 veriUs de fait and the verites eternelles. The fact that we shall 
 never succeed in constructing a plane isosceles triangle with 
 unequal base angles is a verite eternelle. On the other hand, 
 it is only a verite de fait that science is precluded from giving 
 mortal man eternal Hfe. 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 
 
 —TT* 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 disbehef, hut I cannot contradict him 
 absolutely.** 
 
 Einstein himself once pointed out to me such very remote 
 possibiHties ; it was in connexion with the following cir- 
 cumstance. It is quite impossible for a moving body ever 
 
BEYOND OUR POWER 27 
 
 to attain a velocity greater than that of light, because it is 
 scientifically inconceivable. On the other hand, it is con- 
 ceivable, and therefore within the range of possibiUty, 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 biUions 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 possibihties of the future. I imagine that this dis- 
 sertation 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 
 vaHdity 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 industriaUsm, 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 
 
28 EINSTEIN THE SEARCHER 
 
 instance a coal-currency. Gold as money is now concen- 
 trated 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 administra- 
 tion of coal. Or, as it has been expressed in other words else- 
 where : " 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' hue 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 vahd, 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 
 
BEYOND OUR POWER 29 
 
 oxygen to counteract it ; this will confer a great benefit on 
 humanity ! 
 
 * 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." 
 
 As if built on soUd 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 milUons 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 be- 
 ginning was the Sun. The energy sent out by the sun to the 
 earth for mankind is the only necessary and inevitable con- 
 dition for deeds. Deeds mean work, and work necessitates 
 fife. 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 possibiUty 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, 
 
 ♦ The parts included between * ... * axe 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, particu- 
 larly 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. 
 
80 EINSTEIN THE SEARCHER 
 
 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 mitiga- 
 tion 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 deaUng 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 in- 
 forms 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 milHards of marks in value (taken 
 at the nominal rate, that is, £100,000,000,000). Never- 
 theless, geologists and mining experts tell us that our whole 
 supply will not last longer than 2000 years, in the case of 
 
BEYOND OUR POWER 81 
 
 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 possibiHty 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 imiverse, 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 imtenable. 
 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 sim'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 hved 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 in- 
 dependent of coal, we may present some figmres. Let us 
 consider a tiny water canal, a mere nothing in the watery 
 network of the earth, fhe Rhine-falls at Schaffliausen, that 
 may appear mighty to the beholder, but only because he 
 appHes 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, equi- 
 valent to 50,000 kilowatts. This cascade alone would suffice 
 to keep illuminated to their full intensity 1,000,000 glow- 
 lamps, each of 50 candle-power, and according to our present 
 tariff we should have to pay at least 70,000 marks (;£35oo 
 
82 EINSTEIN THE SEARCHER 
 
 nominally) per hour. The coal-worshipper will be more im- 
 pressed by a different calculation. The Rhine-falls at Schaff- 
 hausen 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 multi- 
 plied 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 milHonth of a cubic mile, and perhaps if we sum 
 up everything that men and machinery have moved since 
 the time of the Flood till now, a cubic mile would not yet have 
 been completed. In contrast with this, the earth in its tidal 
 motion moves 200 cubic miles of water from one quadrant of 
 the earth's circumference to another in every quarter of a day. 
 From this we see at once that all the coal-mines in the world 
 would mean nothing to us if we could once succeed in making 
 even a fraction of the pulse-beat of the earth available for 
 purposes of industry. 
 
 If, however, we should be compelled to depend on coal, 
 our imaginations cling so much more closely to that enormous 
 quantity given by the expression mc^, which was derived from 
 the theory of relativity. 
 
 The 20 bilUon 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 irre- 
 sistible 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 
 
BEYOND OUR POWER S3 
 
 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 happi- 
 ness 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 Hfe. How 
 alluring is the song of Sirens chanted by our physics with its 
 high " C," the velocity of hght 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 appHed practically, but also brings forward 
 another argument that casts us down to earth again. Sup- 
 posing, 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, unfortimately, we find ourselves obliged to fall in 
 with this view, which is based in the wise old saw fMrjBev dyav, 
 ne quid nimis, nothing in excess. AppHed 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 biUion 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 disin- 
 tegrating the atom, it seems that we should have the biUions 
 of calories rushing unchecked on us, and we should find our- 
 selves unable to cope with them, nay, perhaps even the sohd 
 ground, on which we move, could not withstand them» 
 3 
 
84 EINSTEIN THE SEARCHER 
 
 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 con- 
 ceive 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 Ught 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 
 colUsions 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 mathe- 
 matical physicist Weyl of Ziirich, 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 short- 
 age 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 
 
BEYOND OUR POWER 85 
 
 vice versa, too. Nevertheless, this would not alter the fact 
 that such long-range weapons would probably lead to the 
 destruction of civiHzation. 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 appHcable to all, 
 and with which Kant has dealt imder the term " thinking 
 aloud." What is nowadays a rare and very imperfect tele- 
 pathic " turn " may yet be generaHzed 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 md^- 
 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 symboUc 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 
 nttle 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. Pfliiger, one of the best quahfied 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 differ- 
 ent from that of Einstein, of the possibiHty of making ac- 
 cessible the mc'^. In discussing the practical significance of 
 this eventuaUty, Pfliiger says : "It will be time to talk of 
 this point again a himdred years hence." This seems a 
 short time-Hmit, even if none of us will live to be present at 
 the discussion. Einstein smiled at this pause of a hundred 
 
36 EINSTEIN THE SEARCHER 
 
 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 realiza- 
 tion 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 EngUsh physicist Rutherford had, with deliberate 
 intention, actually succeeded in spUtting 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 splint erings. 
 
 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 pro- 
 
BEYOND OUR POWER 87 
 
 portion 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 Uberate several milliard calories, whereas the 
 net practical result in Rutherford's experiment is still im- 
 measurably small. Nevertheless, it is scientifically estabUshed 
 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 auto- 
 matically 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 trans- 
 mutation of lead into gold. The possibiUty of this transforma- 
 tion of elements is subject to the same argmnents as those 
 above about the spUtting 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 question- 
 able whether mankind will finally have cause to offer up hymns 
 of thanksgiving if this fine 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 vahd since the beginning of our civiUza- 
 tion. 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 Hght, 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. — Inherit- 
 ance of Talent. — A Dynasty of Scholars. — Alexander von Humboldt and 
 Goethe. — Leonardo da Vinci. — Helmholtz. — Robert Mayer and Diihring. — 
 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 pro- 
 curable 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 personaHty in a different Hght 
 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 hst 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 any- 
 one wishing to enter could choose from five hundred and forty 
 entrances. 
 
 In reaUty our little excursion was far from taking these 
 dimensions, the chief reason being probably that we had 
 
VALHALLA 39 
 
 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. 
 
 ReaUty, even figuratively, offered a picture which differed 
 considerably from the measm-es 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 httle collection of portraits as of a miniature 
 museum. No, it is certainly not that, for its catalogue num- 
 bers 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, repre- 
 sented in an excellent Enghsh engraving, whose border con- 
 sists of symbohc insignias encircUng 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 quaUty 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 pro- 
 paganda known to them consists in a passionate demmciation 
 of what has been developed historically by gradual and patient 
 effort ; their retrospect consists of immitigated contempt ; 
 they profess to be disciples only of what is most recent, re- 
 maining confined within the narrow circle surrounding their 
 own ego. The horizon of the discoverer has a different radius. 
 He takes over responsibiUty for the future by never ceasing his 
 offerings at the altar of the Past. There is probably no dis- 
 
40 EINSTEIN THE SEARCHER 
 
 coverer 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 Ency- 
 clopaedias, 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. avBpa /xot eweirT) ! 
 
 Once we began with Laplace ; and it seemed almost as if the 
 " Trait e de la m^chanique celeste ** 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 medi- 
 tatively 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 totaUty 
 of which represents the events of our world." 
 
 Interrupting his remarks, I asked : " Can Gahlei's funda- 
 mental 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 ex- 
 perience, and not merely something based on speculation. 
 It might easily suggest itself to one that an elementary law 
 hke that of Galilei or Newton could be derived from our every- 
 day 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 ? " 
 
VALHALLA 41 
 
 "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 abstrac- 
 tion possessed only by a giant of reason to stabihze rectilinear 
 motion as the fundamental form." 
 
 To this may be added that before and even after the time 
 of GaUlei, 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 curviHnear views to explaining world phenomena that 
 could be made clear only after GaUlei's abstraction had been 
 accepted. 
 
 I asked whether the theory of gravitation was already 
 implicitly contained in GaUlei's Laws of FaUing Bodies. Ein- 
 stein'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 feeUngs of 
 antipathy, which takes its origin from Schopenhauer's un- 
 mathematical type of mind. The vast difference between 
 Hooke *s prehminary 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 appl5dng 
 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 hke Columbus : we now hear of 
 " America," and Hkewise '* Newton's Gravitational System " ! 
 
 Schopenhauer has, however, quite forgotten that he him- 
 self, some pages earlier, trumpeted forth Newton's imperishable 
 
42 EINSTEIN THE SEARCHER 
 
 fame with the words : "To form an estimate of tlie great 
 value of the gravitational system which was at least completed 
 and firmly estabhshed 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 anta- 
 gonist Hegel, who was still more vague in these fields, sought to 
 dispense with both Newton and Kepler by calUng to his aid 
 the so-called pure intuition of the curved Hne. In an exposition 
 of truly comical prolixity, such as would have dehghted the 
 hearts of schohasts, he proves that the ellipse must represent 
 the fundamental type of planetary motion, this being quite in- 
 dependent of Newton's laws, Kepler's observations, and result- 
 ing mathematical relationships. And Hegel actually succeeds, 
 with a nebulous verbosity almost stultifying in its unmeaning- 
 ness, in paraphrasing Kepler's second law in his own fashion. 
 It reads Uke 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 brilUantly 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 
 elUptic path with a definite point within the curve (the focus 
 of the ellipse) by means of straight fines, 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 
 
VALHALLA 48 
 
 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 Ught. 
 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, Philosophice naturalis principia mathe- 
 matica. 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 repUed : " 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 " h3rpo theses " was prevalent with 
 scholars in Newton's time than now. Newton's emphatic 
 defence would then appear a shade more inteUigible Or did 
 
44 EINSTEIN THE SEARCHER 
 
 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, sa3dng 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 GaUlei's Law of Inertia. It is certainly con- 
 ceivable that beyond the domain of human experience there 
 may be an undiscoverable universe in which a different funda- 
 mental law holds, and one which, nevertheless, does not contra- 
 dict the principle of sufficient reason. 
 
 The antithesis : SimpHcity — Complexity, led the conversa- 
 tion 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 pro- 
 portionaUty 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 re- 
 pulsion 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 approxi- 
 
VALHALLA 45 
 
 mate 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 
 compUcated 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 foimd to be 
 expressible in simple formulae, not must it be forgotten that 
 even the ultimate discoverable simpHcity 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, 
 WilHam Whewell, succumbed to this misunderstanding. 
 Credit must be given to a more modem 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 
 
46 EINSTEIN THE SEARCHER 
 
 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 
 hmitation ; in the case of human laws, expressed in the civil 
 and penal code, the hmitation affects the will, and possible 
 actions, whereas natural laws signify the Umitations which we, 
 taught by experience, prescribe to our expectations. Never- 
 theless, 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 conform- 
 ing 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 generahzed 
 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 
 dehcate threads that connect his perceptions. The aspect 
 of knowledge which has not yet been laid bare gives the in- 
 vestigator a feeling akin to that experienced by a child who 
 seeks to grasp the masterly way in which elders manipulate 
 things.'* 
 
 This explanation imphed a personal confession. For he 
 had spoken of the childlike longing felt by all, and had inter- 
 preted the subtle intricacies of the scientist's ideas in par- 
 ticular as springing from a rehgious source. Not all have 
 
VALHALLA 47 
 
 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 I'infame,*' 
 j&nally 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 Umited 
 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 functionii^g of the machine. 
 Finally, he slipped from the path of naive faith on to theo- 
 logical 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 
 feeHng that he was smiUng up his sleeve when he was making 
 some of his solemn declarations. He was a master of com- 
 promise, 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 af&rmed : " The 
 Cartesian doctrine has been mainly ii^strumental in persuading 
 many not to recognize a God.'* 
 
 As Einstein had called special attention to the childHke 
 nature of the scientist's root-impulse, I quoted a remark of 
 Newton that seemed to me at the moment to be a confirma- 
 tion of Einstein's attitude : 
 
 " I do not know what I may appear to the world, but 
 to myself I seem to have been only Uke a boy playing on 
 the seashore, and diverting myself in now and then find- 
 ing a smoother pebble or a prettier shell than ordinary, 
 whilst the great ocean of truth lay all undiscovered before 
 me. 
 
48 EINSTEIN THE SEARCHER 
 
 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 Hke-4;o withhold, inasmuch as it gave rise to a noteworthy 
 observation of Einstein about the nature of genius. We were 
 talking about the '*possibiUty 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 
 d5niasty of great minds, that of the ten BernouUis who were 
 descended of a line of mathematicians, and all of them achieved 
 important results, some of them making extraordinary dis- 
 coveries. 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 GaHleis, 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 BernouUis.* 
 ** 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." 
 
 Einstein, however, contradicted this emphatically : "In- 
 herited talent certainly occurs in many cases, where we do not 
 observe it, for genius in itself and the possibiHty 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 Roman family Cosmati (of the thirteenth century) , which gave us 
 seven splendid representatives of architecture andfmosaic work, hardly comes 
 into consideration, since not one of them is regarded in the history of art as 
 a real genius. 
 
VALHALLA 49 
 
 the genius that is latent. At a certain instant, perhaps, only 
 some impulse was wanting for the latent genius to burst fo^h 
 with all clearness and brilhance ; 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 sHght 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 pronoimced 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 dif&cult to get free 
 from the orders of greatness that one has recognized for de- 
 cades. In my youth people spoke of * a Humboldt * just 
 as we speak of ' a Caesar ' 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 imderstand," 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 
 4 
 
50 EINSTEIN THE SEARCHER 
 
 reflections of a playful poetic character . . . one objection 
 being that Goethe's own knowledge of ornithology was ex- 
 ceedingly Hmited. Even when nearly eighty he could not 
 distinguish a lark from a yellow-hammer or a sparrow I 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 com- 
 manded 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 eUcited 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 Hst, 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. 
 
VALHALLA 51 
 
 he is the Ught of all ages, and in the abundance of his dis- 
 coveries he has never been surpassed before or after his own 
 time. 
 
 As this question had arisen once before, I had come 
 equipped with a Httle 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 GaUlei). 
 Laws of FaUing Bodies (before Gahlei). 
 True interpretation of the twinkling of stars (before 
 Kepler, who, moreover, did not succeed in finding 
 the real explanation). 
 Explanation of the reflected Ught 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 PaUssy). 
 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 Hst 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. 
 
52 EINSTEIN THE SEARCHER 
 
 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 consider- 
 able 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 Itahan 
 painter of the fifteenth century was not less great as a scientist. 
 In the history of science his name is famous and his achieve- 
 ments 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 simultane- 
 ously 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 FalUng 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 fore- 
 runners. In the case of these principles, above all, there is 
 always some predecessor, and it is almost impossible to trace 
 the fine of discoveries back to the first source. Just as writers 
 have wished to deprive Gahlei, 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, 
 
VALHALLA 53 
 
 so one reads, was Hipparchus of Nicaea, 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 archaeologists, 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 con- 
 structive 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 role. 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 Hfe-work 
 of each has an aesthetic 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 produjctivity. 
 
 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 
 
54 EINSTEIN THE SEARCHER 
 
 later times is assured ; Helmholtz himself tasted of this im- 
 mortahty 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 Helm- 
 holtz'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 Helm- 
 holtz was present, a colleague of his was greeted with unanimous 
 applause when he toasted him with the words : " L'ophthal- 
 mologie ^tait dans les tenebres, — Dieu parla, que Helmholtz 
 naquit — Et la lumiere etait 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 Diihring, 
 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. Diihring's aim was to dislodge one of the funda- 
 mental 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. 
 
 Diihring, 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 re- 
 gards it as a pathological symptom, and has only a smile of 
 disdain for many of Diihring'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. 
 
VALHALLA 55 
 
 Diihring 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 Diihring (who also calls him 
 " Helmklotz "), has done no more than distort Mayer's funda- 
 mental mechanical idea, and interpret it falsely. By " philo- 
 sophizing " over it, he has completely spoilt it, and rendered 
 it absurd. It was the greatest of all humihations 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 Diihring, particularly as he had used 
 his *' brazen-tongue " to defend the two renowned mathe- 
 maticians. After he, and Clausius too, had been brought to 
 earth, Diihring launched out against the giants of Gottingen. 
 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 EucUd's 
 axioms and theorems, and proceeded to set up the founda- 
 tions 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.*' 
 
 / 
 
56 EINSTEIN THE SEARCHER 
 
 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 
 Diihring is immortalized, for, apart from the charge of arson, 
 he is notable in himself. In his case we found ourselves con- 
 fronted 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 Diihring, 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 Diihring 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 dis- 
 passionately, 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 in variance of the sum of energy 
 during mechanical actions was known even by Huyghens. 
 The Heilbronn doctor performed one act of genius in his Hfe, 
 whereas Helmholtz during his whole Hfe moved asymptotically 
 to the Une of genius without ever reaching it. If my inter- 
 pretation 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 
 
VALHALLA 57 
 
 to be given a seat among the most illustrious of his branch of 
 science. Einstein wishes to preserve a certain hne of demarca- 
 tion 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 HeracHtus uttering the cry : Introite, nam et hie 
 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 feeUng 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 Ufe-forces, and to 
 bring him the reahzation 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 hght-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 difl&cult. . . . But let us fix our gaze on those 
 
58 EINSTEIN THE SEARCHER 
 
 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 sensibiUty 
 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 outhnes that seem created for all eternity. 
 Associated with this negative motive is a positive one, by 
 virtue of which Man seeks to form a simpUfied 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 mathe- 
 matics. 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 beheve 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 vahd for every kind of natural 
 
VALHALLA 59 
 
 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 theor- 
 etical 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 f 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 recog- 
 nized 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 dis- 
 tracted 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 i action, but 
 of a direct need. . . . May his love for Science grace his 
 future course of Ufe, 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 de- 
 
60 EINSTEIN THE SEARCHER 
 
 scription of the excursion into Valhalla with such a valuable 
 supplement. 
 
 The conversation had begun with the brilliant constella- 
 tion 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 magni- 
 tude. 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," repHed 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 personaUty, 
 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 expres- 
 sion : ' 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, nsLmely, 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 
 
VALHALLA 61 
 
 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 Diflficulties. — Necessity as Instructress. 
 
 OUR conversation turned towards a series of paedagogic 
 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 pre- 
 liminary 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 personahty and his own 
 work in the past. His first care is that a young person should 
 get an insight into the relationship underlying natural pheno- 
 mena, 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 Uttle inclined 
 to wax enthusiastic about the so-called humanistic schools. 
 Certain recollections of my own school life sufi&ce to prevent 
 this, and still more, a certain presentiment of the educational 
 problems of the future." — " To speak quite candidly," he 
 
EDUCATION 68 
 
 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 
 personaUty '' ; and to suggest the root of language formation he 
 said it in Latin : " Quot Hnguas 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 repHed : "I doubt whether this aphorism is 
 generally vahd, for I beheve 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 Uke Mithridates, 
 Mezzofanti, and similar persons. The exact opposite, indeed, 
 may be proved, namely, that in the case of the strongest per- 
 sonahties, and of those who have contributed most to pro- 
 gress, 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 super- 
 abundance of acquired Unguistic 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 im- 
 provement and a result of examining the true aims of a school. 
 He continued : " Man must be educated to ' react delicately ' ; 
 
64 EINSTEIN THE SEARCHER 
 
 he is to acquire and develop * intellectual muscles ' ! And 
 the methods of language drill are much less suited to this pur- 
 pose 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 Hfe-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 founda- 
 tion 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, with- 
 out 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 intelHgence who seem to be 
 smitten with absolute stupidity when confronted with mathe- 
 matics, and whose school-hfe becomes poisoned owing to the 
 torment caused by this subject. There are many cases of 
 living surgeons, lawyers, historians, and Utterateurs, 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 hke a 
 
EDUCATION 65 
 
 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 incUned to throw the responsibihty 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 question- 
 ing has for its purpose to discover what the pupil knows or 
 is capable of knowing. Whenever sins of this sort are com- 
 mitted — and they occur in all branches of knowledge — the 
 personahty of the teacher is mostly at fault. The results of 
 the class furnish an index for the quahty of the preceptor. 
 All things being taken into consideration, the average of 
 abiUty in the class moves, with only sHght 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." 
 5 
 
66 EINSTEIN THE SEARCHER 
 
 " 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 hke some fearful monster guarding 
 our exit from school, throwing its shadow far ahead, and 
 compelUng 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 for- 
 gotten within a few months, and what deserves to be for- 
 gotten. 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 uni- 
 versity ? " 
 
 " Every one who has shown himself to be capable not only 
 in a crucial test of an accidental kind, but in his whole be- 
 haviour. The teacher will be the judge of this, and if he does 
 not know who is quaUfied, 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 — ^f our at school and two for home-work ; 
 that should be the maximum. If this should appear too Uttle 
 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 
 
EDUCATION 67 
 
 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 hmits, and 
 should be presented only in broad outUne, without dates having 
 to be crammed. Leave as many gaps as you Mke, especially 
 in ancient history ; they will not make themselves felt in our 
 ordinary existences. In nowise can I regard it as a mis- 
 fortune if the pupil learns nothing of Alexander the Great, and 
 of the dozens of other conquerors whose documentary remains 
 burden his memory hke so much useless baUast. If he is to 
 get a gUmpse of the grey dawn of time, let him be spared from 
 Cyrus, Artaxerxes, and Vercingetorix, but rather tell him 
 something of the pioneers of civiHzation, Archimedes, Ptolemy, 
 Hero, Appolonius, and of inventors and discoverers, so that 
 the course does not resolve into a series ot 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 him- 
 self is deeply interested in all manifestations of pubUc Ufe. 
 He does not favour an elementary pohtical training received 
 at school, presumably above all owing to the fact that in this 
 branch the instruction cannot be removed from official in- 
 fluences, and because pohtical questions require the attention 
 of a mature mind. His picture of how a youth is to meet the 
 requirements of modem hfe 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 intro- 
 duction of compulsory practical work. Every pupil must 
 learn some handicraft. He should be able to choose for him- 
 self 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 dehvered some useful product of his trade." 
 
68 EINSTEIN THE SEARCHER 
 
 " Do you attach greater importance to the technique itself 
 or to the feehng 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 man- 
 kind 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 Meister singer, 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 mis- 
 conception of Hfe to uphold this point of view and to expect 
 its regulative effectiveness in cases in which we are deahng 
 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 
 
EDUCATION 69 
 
 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 sim ; by this means he will grasp the mathe- 
 matical 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 wiU please him to have 
 discovered the height of the tower without having cHmbed it, 
 and this is the first thrill of the pleasure which he feels later 
 when he learns the geometry of similar triangles and the 
 proportionahty 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 formulae 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 
 formulae 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 con- 
 nexion of a means of education that has so far been used only 
 by way of trial in class-teaching, but from an improved appUca- 
 tion 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 
 
70 EINSTEIN THE SEARCHER 
 
 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 know- 
 ledge 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 experi- 
 ments 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 Hving, and this principle will predominate 
 in future reforms of school-teaching." 
 
 University study was only touched on lightly during this 
 talk. It has become known that Einstein is a very strong 
 supporter of the principle of free learning, and that he would 
 prefer to dispense entirely with the regular documents of ad- 
 mission 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, par- 
 ticularly as, in his own experience, he has frequently found 
 the cleverest people and those with the most definite aims to 
 
EDUCATION 71 
 
 be prone to one-sidedness. According to this, even the inter- 
 mediate 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 
 abihty. If he earher spoke in favour of aboHshing the matricu- 
 lation 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 considera- 
 tions is that the pupil is examined as httle 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 facuUas 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 hving 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. Philo- 
 sophers, 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 
 
72 EINSTEIN THE SEARCHER 
 
 formal difl&culties, which can be overcome only by means of 
 symbols and by using a language which has no means of 
 (Msplaying eloquence, being devoid of expression, emotion, 
 and regular periods. Yet here we have a physicist, a mathe- 
 matician, 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 shghtest 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 formulae, hke 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 geniaUty. He never 
 talks as if in a monologue or as if addressing empty space. 
 He always speaks Hke 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 Hberty 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 con- 
 clusion 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 
 
EDUCATION 73 
 
 invitation of this kind, and \\ill 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 hf e 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 — imfortunately — 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 
 Diihring, the noted scholar, who was doomed to remain a 
 lecturer inasmuch as he went under in his quarrels with 
 confreres 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 siupassed, 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 earher times had reason to 
 declare, hke 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 foimd 
 himself deserted, and he himself twas'^ weU^ aware that no 
 magnetic teaching influence emanated from him. There is 
 yet another case in university history of a brilliant personaUty 
 who, from similar flights of ecstasy, was doomed to disappoint- 
 ment. I must mention his name, which, in this connexion, 
 will probably cause great surprise, namely, Schiller ! He had 
 
74 EINSTEIN THE SEARCHER 
 
 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 argu- 
 ments to oppose it. 
 
 Whether Einstein's ideas and proposals concerning educa- 
 tional reform will be capable of reaUzation 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 apportion- 
 ment 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 
 
EDUCATION 75 
 
 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 inherit- 
 ance 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 shme of the traditional humanism of the Greeks 
 
76 EINSTEIN THE SEARCHER 
 
 and Latins. " The whole language evil of our times/' so these 
 leaders say, **is at bottom due to scientists, who, in the opinion- 
 ated guise of a language caste, and without enriching our 
 conceptions in the slightest, seek by tinkhng empty words to 
 give us the illusion of a new and particularly mysterious occult 
 science, an impression which is unfortunately often produced 
 on ignorant minds. . . . However many muddy outlets 
 official' institutions and language associations may purge and 
 block up, ditch-water from ever new quagmires and drains 
 pours unceasingly into the stately stream of our language." 
 
 Thus the attack on the Latin and Greek language founda- 
 tion in schools identifies itself with the struggle against the 
 academic world as a whole, and a scholar who does defend 
 the classical system of education with all his might finds himself 
 unconsciously drifting into the ranks of the brotherhood which 
 in the last instance is seeking his own extermination. 
 
 This danger must not be under-estimated. It is just this 
 peril, so threatening to our civihzation, that moves me to show 
 my colours frankly here. I am not a supporter of bookworm 
 drudgery in schools, but I feel myself impelled to use every 
 effort in speech and writing to combat the anti-humanists 
 whose password, " For our language," at root signifies 
 " Enemies of Science ! " 
 
 We must put no weapons into their hands, and the only 
 means to avoid this is, in my opinion, to state our creed 
 emphatically and openly after the manner of almost all our 
 classical writers. 
 
 This creed, both as regards language and substance, is to 
 be understood as being based on the efiicacy of the old classical 
 languages. It is the luminous centre of the life and work of 
 the men who caused Bulwer to proclaim our country the country 
 of poets and thinkers. The superabundance of these is so 
 excessive that it is scarcely fair to mention only a few names 
 such as Goethe, Lessing, Schiller, Wieland, Kant, and Schopen- 
 hauer. Our Hterature would be of a provincial standard and 
 not a world possession if this creed had not asserted its 
 sway at all times. 
 
 If the question is raised as to where our youth is to find 
 time for learning ancient languages under the present condi- 
 tions of crowded subjects, the answer is to be furnished by 
 
EDUCATION 77 
 
 improved methods of instruction. My personal point of view 
 is that even the older methods were not so bad. Goethe found 
 himself in no wise embarrassed through lack of time in acquiring 
 all sorts of knowledge and mental equipment, although even as 
 a boy of eight years he could write in Latin in a way which, 
 compared with the bungling efforts of the modem sixth-form 
 boy, seems Ciceronian. Montaigne could express himself 
 earUer in Latin than in French, and if he had not had this 
 " Latin poison '* injected into his blood he would never have 
 become Montaigne. 
 
 It seems to me by no means impossible that the cultured 
 world will one day in the distant future return to the once 
 self-evident view of classical languages, and indeed just for 
 reasons of economy of time, unless the universal language so 
 ardently desired by Hebbel — ^not to be confused with the 
 artificial patchwork called Esperanto — should become a reaUty. 
 But even this language, at present Utopian, but one which will 
 help to link together the nations, will disclose the model of the 
 ancient languages in its structure. Scientific language of the 
 present day shows where the route lies ; and this route will be 
 made passable in spite of all the efforts of Teutonic language 
 saints and assassins of humanism to block it. 
 
 The working out of ideas by research scientists leads to 
 enrichment of language. And since, as is quite natural, they 
 draw copiously on antique forms of expression, they are really 
 the trustees of an instruction that makes these expressions 
 intelligible not merely as components of an artificial language 
 like Volapiik but as organic growths. That is how they pro- 
 ceed when they carry on their research, or describe it and 
 lecture on their own subject. But if they are to decide how 
 the school is to map out its course in actual practice, the prob- 
 lem of time again becomes their chief consideration — that is, 
 they feel in duty bound to give preference to what is most 
 important. Hence there results the wish to reduce the hours 
 apportioned to the language subjects as much as possible. 
 
 On this matter we have a detailed essay by the distinguished 
 Ernst Mach mentioned earUer, who exposes the actual dilemma 
 with the greatest clearness. He treats this exceedingly im- 
 portant question in all its phases, and arrives at almost the 
 same conclusion as Einstein. At the outset he certainly chants 
 
78 EINSTEIN THE SEARCHER 
 
 a Latin psalm almost in the manner of Schopenhauer. Its 
 lower tones represent an elegy lamenting that Latin is no 
 longer the universal language among educated people, as it 
 was from the fifteenth to the eighteenth century. Its fitness 
 for this purpose is quite indisputable, for it can be adapted to 
 express every conception however modern or subtle it may be. 
 
 What a profusion of new conceptions was introduced into 
 science by Sir Isaac Newton, to all of which he succeeded in 
 giving correct and precise Latin names ! The natural inference 
 suggests itself to us that young people should learn the ancient 
 classical tongues — and yet a different result is coming about ; 
 the modern child is to be content with understanding words 
 with a world-wide currency, without knowing their philological 
 origin. 
 
 It is not necessary to be a schoolmaster to feel the in- 
 adequacy of this proceeding. It is true that without knowing 
 Arabic we can grasp the sense and meaning of the word 
 ** Algebra," and in the same way we can extract the essence of 
 a number of Greek and Latin expressions without digging at 
 their etymological roots. But these expressions are to be 
 counted in hundreds and thousands, and are increasing daily, 
 so that we are put before the question whether, merely from 
 the point of view of time, it is practicable to learn them as 
 individual foreign terms or as natural products of a root 
 language with which we have once and for all become familiar. 
 
 It is scarcely necessary for me to point out that Einstein 
 himself is not sparing in the use of these technical expressions, 
 even when he is using popular language. He assumes or 
 introduces terms of which the following are a few examples : 
 continuum, co-ordinate system, dimensional, electrodynamics, 
 kinetic theory, transformation, covariant, heuristic, parabola, 
 translation, principle of equivalence, and he is quite justified 
 in assuming that every one is fully acquainted with such 
 generally accepted expressions as : gravitation, spectral 
 analysis, balHstic, phoronomy, infinitesimal, diagonal, com- 
 ponent, periphery, hydrostatics, centrifugal, and numberless 
 others which are diffused through educated popular language 
 in all directions. Taken all together these represent a foreign 
 realm in which the entrant can always succeed in orientating 
 himself when he receives explanations, examples, or transla- 
 
EDUCATION 79 
 
 tions, whereas with a little preliminary knowledge of the 
 ancient languages he immediately feels himself at home with 
 them ; in this we have not even taken into consideration the 
 general cultural value of this training in view of the access it 
 gives to the old Hterature and to Hellenic culture. 
 
 Perhaps I am going too far in adopting the attitude of 
 a laudator temporis acti towards Einstein's very advanced 
 opinion. We are here deahng with a question in which nothing 
 can be proved, and in which everything depends on disposition 
 and personal experiences. In my own case this experience 
 includes the fact that at a very early age, in spite of the very 
 discouraging school methods, I enjoyed the study of Latin and 
 Greek, and that I learned Horatian odes by heart, not because 
 I had to, but because they appealed to me, and finally that 
 Homer opened up a new world to me. When Einstein ex- 
 presses his abhorrence of drill, I agree with him ; but these 
 languages need not be taught as if we are on parade. We see 
 thus that it is a question of method and not of the subject 
 involved. Einstein gives the subject its due by recommend- 
 ing a double series of classes. He allows the paths to diverge, 
 giving his special blessing to the group along the one without 
 setting up obstacles to prevent the other pilgrims from attain- 
 ing happiness in their own way. 
 
 We spoke of higher education for women, and Einstein 
 expressed his views which, as was to be expected, were tolerant, 
 and yet did not suggest those of a champion of the cause. It 
 was impossible to overlook the fact that in spite of his approval 
 he had certain reservations of a theoretical nature. 
 
 " As in all other directions," he said, " so in that of science 
 the way should be made easy for women. Yet it must not be 
 taken amiss if I regard the possible results with a certain 
 amoimt of scepticism. I am referring to certain obstacles in 
 woman's organization which we must regard as given by 
 Nature, and which forbid us from applying the same 
 standard of expectation to women as to men." 
 
 " You beheve, then. Professor, that high achievements 
 cannot be accomplished by women ? To keep our attention 
 on science, can one not quote Madame Curie as a proof to the 
 contrary ? " 
 
80 EINSTEIN THE SEARCHER 
 
 " Surely only as one proof of brilliant exceptions, more 
 of which may occur without refuting the statute of sexual 
 organization." 
 
 " Perhaps this will be possible after all if a sufficient time 
 for development be allowed. There may be much fewer 
 geniuses among the other sex, but there has certainly been a 
 concentration of talent. Or, in other words, totally ignorant 
 women have become much rarer. You, Professor, are for- 
 tunate in not being in a position to compare young women 
 of to-day with those of forty or more years ago. This I can 
 do, and just as once I found it natural that there should be 
 swarms of little geese and peacocks, I never recover from my 
 astonishment nowadays at the amount of knowledge acquired 
 by young womanhood. It requires a considerable effort on 
 my part very often to avoid being completely overshadowed 
 by a partner at dinner. The more this stratum of talent 
 increases, the more we have reason to expect a greater number 
 of geniuses from them in the future." 
 
 " You are given to prognostication," said Einstein, " and 
 calculate with probabiUties which sometimes are lacking in 
 foundation. Increased education and even an increase of 
 talents are quantitative assumptions that make an inference 
 regarding higher quaUty reaching to genius appear very bold." 
 — A passing look of ominous portent flashed over his face, and 
 I noticed that he was preparing to launch a sarcastic aphorism. 
 So it was, for the next words were : " It is conceivable that 
 Nature may have created a sex without brains ! " 
 
 I grasped the sense of this grotesque remark, which was in 
 no way to be taken literally. It was intended as an amusing 
 exaggeration of what he had earlier called the reason for his 
 failing expectation : the organic difference which, being 
 rooted in the physical constitution, had somewhere to express 
 itself on the mental plane, too. The soul of woman strong in 
 impulse shows a refinement of feehng of which we men are 
 not susceptible, whereas the greatest achievements of reason 
 probably depend on a preponderance of brain substance. It is 
 this plus beyond the normal amount that gives promise of 
 great discoveries, inventions, and creations. We can just 
 as little imagine a female Galilei, Kepler, and Descartes, as a 
 female Michelangelo or Sebastian Bach. But when we think 
 
EDUCATION 81 
 
 of these extreme cases, let us also recall the balance on the 
 other side : although a woman could not create the differential 
 calculus, it was she that created Leibniz ; similarly she pro- 
 duced Kant if not the Critique of Pure Reason. Woman, as 
 the author of all great minds, has at least a right of access to 
 all means of education and to all advancement that is proffered 
 by universities. And in this connexion Einstein expressed his 
 wish clearly enough. 
 
 One of the most discussed themes in matters touching 
 school education is at the present time : * * the selection of 
 gifted pupils." It has developed into a principle that is 
 generally recognized by the great majority, the only point 
 of disagreement being in respect to the number that is to be 
 selected. 
 
 The idea running through it is that derived from Darwin's 
 theory of selection : man completes the method of selection 
 practised by Nature. He sifts and chooses, and allows those 
 that are more talented to come to the fore more rapidly and 
 more decidedly ; he favours their advancement and makes easy 
 their ascent. 
 
 This principle has really always been in existence. It 
 started with the distribution of prizes in ancient Olympia and 
 reaches to the present-day examinations that are clearly in- 
 tended as a means of selecting talents. A greater discrimina- 
 tion based on a systematic search for talents was reserved for 
 our own day. 
 
 It was scarcely a matter of doubt to me what attitude 
 Einstein would take up towards this matter. I had already 
 heard him say hard words about the system of examinations, 
 and knew his leaning towards allowing each mind to develop 
 its power freely and naturally. 
 
 In effect, Einstein declared to me that he would hear 
 nothing of a breeding of talents in a sort of sporting way. 
 The dangers of the methods of sport would creep in and lead to 
 results that had only the appearance of truth. From the 
 results so far obtained it was impossible to come to a final 
 decision about it. Yet it was conceivable that a selective 
 process conducted along reasonable lines would in general 
 prove of advantage in education, particularly in the respect 
 6 
 
82 EINSTEIN THE SEARCHER 
 
 that many a talent that would ordinarily become stunted 
 owing to its being kept in darkness would now have an oppor- 
 tunity of coming to light. 
 
 This resolved itself into a talk bearing on many questions, 
 and of which I should hke to state the main issue here. It 
 was specially intended to make clear the gambUng method 
 that Einstein repudiates, and the danger of which seems still 
 more threatening to me than to him. 
 
 If certain pedagogues, whose creed is force, were to have 
 their way, the " most gifted " pupils would be able, or would 
 be compelled, to rush through school at hurricane speed, and, 
 at an age at which their fellows were still spending weary 
 hours at their desks, they would have to clamber to the top- 
 most branches of the academic tree. All things are possible, 
 and history even furnishes cases of such forced marches. 
 Luther's friend Melanchthon quaUfied at the age of thirteen 
 to enter the University of Heidelberg, and at the age of seven- 
 teen he became a professor at Tiibingen, where he gave lectures 
 on the most difi&cult problems of philosophy, as well on the 
 Roman and Greek writers of classical antiquity. This single 
 instance need only be generahzed, and we have the new ideal 
 rising up before our astonished gaze : a race of professorial 
 striphngs whose upper Hps are scarcely darkened with the 
 down of youth I It is a mere matter of making an early 
 discovery of the most gifted, and then raising the scaffolding 
 up which the precocious know-aUs can climb as easily as 
 possible. 
 
 [Interposed query : Where are these discoverers of talent, 
 and how do they prove their own talent ? There was a good 
 opportunity for them in a case which I must here mention. 
 Einstein told me in another connexion that, as early as 1907, 
 that is, when he was stiU very young in years, he had not 
 only succeeded in successfully representing the Principle of 
 Equivalence, one of the main supports of the General Principle 
 of Relativity, but had even published it ; yet it made not the 
 shghtest impression on the learned world. No one suspected 
 the far-reaching consequences, and no one pointed out this 
 flaming up of a new talent of the highest order. And just as 
 this was able to remain concealed from the learned Areopagus 
 of the world at that time, so a similar lack of understanding 
 
EDUCATION 88 
 
 may easily be possible on a smaller scale at school. We know 
 actually that among the recognized great men of science, 
 there were many who did only moderately well at school ; 
 as, for example, Humphry Davy, Robert Mayer, Justus 
 Liebig, and many others. Wilhelm Ostwald goes so far as to 
 affirm : '* Boys ordained to be discoverers later in life have, 
 almost without exception, been bad at school I It is just the 
 most gifted young people who have resisted most strongly 
 the form of intellectual development prescribed by the school ! 
 Schools never cease to show themselves to be the bitter, 
 unrelenting enemies of genius I " — ^in spite of all efiorts at 
 selection which have always been in vogue in the guise of 
 advancement into higher forms.] 
 
 But the new mode of selection is intended to prevent 
 mistakes and oversights. Is this possible ? Do not the traces 
 of previous attempts inspire distrust ? There was once a 
 very ideal selection that had to stand the test of one of the 
 most eminent bodies in existence, the French Academy. Its 
 duty was to discover geniuses on an incomparably higher 
 plane. It, however, repudiated or overlooked : Moli^re, 
 Descartes, Pascal, Diderot, the two Rousseaus, Beaumarchais, 
 Balzac, Beranger, the Goncourts, Daudet, Emile Zola, and 
 many other extremely gifted people, whom it should reaUy 
 have been able to find. 
 
 The only true, and at the same time necessary as well as 
 sufficient, breeding is carried out by Nature herself in con- 
 junction with social conventions, which promise the more 
 success the less they assume the character of incubators 
 and breeding estabUshments. If you wish to apply tests to 
 discover pupils of genius in any class, examine as much as 
 you Hke, excite interest and ambition, distribute prizes even, 
 but not for the purpose of separating at short intervals the 
 shrewd and needle-witted heads from the rest ; and do not 
 lose sight of the fact that among those who appear as the 
 sheep as a result of these systematized tests to discover in- 
 genuity there are many who, ten or twenty years later, will 
 take up their positions as men of eminent talent. 
 
 There is no essential difference between the forced promo- 
 tion of such pupils and the breeding of super-men according 
 to Nietzsche's recipe as exemphfied by his Zarathustra. 
 
84 EINSTEIN THE SEARCHER 
 
 Assuming that super-men are justified in existing at all, 
 they will come about of themselves, but cannot simply be 
 manufactured. Workmen, taken as a class, represent super- 
 men more definitely than an individual such as Napoleon 
 or Caesar Borgia. So the " super-scholar " exists perhaps 
 already to-day, not as an individual phenomenon, but as a 
 whole, representing his class. Whoever has had experience 
 in these things will know that nowadays there are difficult 
 subjects in which it is possible to apply to pupils of fifteen 
 years of age tests that are far above the plane of comprehen- 
 sion of pupils of the same age in former times, provided that 
 the average is considered, that no accidental or artificial 
 separation has occurred, that no pretentiously witty questions 
 have had to be answered, and that there has been no systematic 
 and inquisitive search for talent. 
 
 Let us rest satisfied if we find that the sum-total of talent 
 is continually on the increase. On the other hand, it is by 
 no means proved that we are doing civiHzation a service by 
 persisting in the impossible project of abolishing from the 
 world the struggle for existence prescribed by Nature. It is 
 an elementary fact, and one that is easy to understand, that 
 many talents perish unnoticed. On the other hand, observe 
 the long Ust of eminent men who fought their way upwards 
 out of the lowest stages of existence only to recognize that the 
 difficulties that have been overcome are mostly necessary 
 accompaniments of talent, that is, that Nature's way of 
 selection is to oppose obstacles and raise difficulties in order 
 to test their powers. In the case of the poor lens-grinder 
 Spinoza and many others ranging to Beranger, who was a 
 waiter, what a chain of desperate experiences, yet what 
 triumphs ! Herschel, the astronomer, was too poor to buy 
 a refracting telescope, and it was just this dispensation of 
 poverty that made him succeed in constructing a reflecting 
 type composed of a mirror. Faraday, the son of a blacksmith 
 without means, made his way for years as a bookbinder's 
 apprentice. Joule, one of the founders of the mechanical 
 theory of heat, started as a beer-brewer. Kepler, the dis- 
 coverer of the planetary laws, was descended from a poverty- 
 stricken innkeeper. Of the members in Goethe's circle, 
 Jung-Stilling, of whom Nietzsche was so fond, was a tailor's 
 
EDUCATION 85 
 
 apprentice ; Eckermann, (k)ethe's intimate associate, was a 
 swine-herd, and Zelter was a mason. We could add many 
 recent names to this list, and very many more if we continue 
 the line backwards to Euripides, whose father was a publican 
 and whose mother was a vendor of vegetables. This might 
 serve as a basis for many reflections about the *' upward course 
 of the talented," and about its less favourable reverse side. 
 For one might put the apparently paradoxical question whether 
 a soaring career for many or all talents is a necessity for our 
 civilization, or whether it would not be better to have a sub- 
 stratum interspersed with talent, to cultivate a mossy under- 
 growth which is to serve as nourishment for the blooming 
 plants of the upper layer. 
 
 Maximum is not equivalent to optimum, and we learned 
 elsewhere that Einstein is far removed from identifying them. 
 In the previous case it was a question of the problem of popu- 
 lation ; and in the course of the discussion he mentioned that 
 we are subject to an old error of calculation when we regard 
 it as a desirable aim to have a maximum number of himian 
 beings on the earth. It seems, indeed, that this false con- 
 clusion is already in process of being corrected. A beginning 
 is being made with new and very active organizations and 
 unions whose programme is to reduce the number so that an 
 optimum may be attainable by those left. 
 
 If we extend this line of reasoning still further, we arrive 
 at the depressing question whether too much might not be 
 done for talent, not only as regards breeding it, but also in 
 favouring the greatest number. It is quite possible that in 
 doing so, we might overlook, or take insufficient account of 
 the harm that might be done to the lower stratum, in that 
 we should be depriving it of forces which, according to the 
 economy of Nature, should remain and act in concealment. 
 
 This fear, as here expressed, is not shared by Einstein. 
 However brusquely he repudiates breeding, he speaks in 
 favour of smoothing the way for talent. " I believe," he said, 
 ** that a sensible fostering of gifts is of advantage to humanity 
 generally and prevents injustice being done to the individual. 
 In great cities which give such lavish opportunities of educa- 
 tion, this injustice manifests itself less often ; but it occurs 
 so much the more in rural districts, where there are certainly 
 
86 EINSTEIN THE SEARCHER 
 
 many cases of gifted youths who, if recognized as such at the 
 right age, would attain to an important position, but who, 
 together with their gifts, become stunted, nay, go to ruin, if 
 the principle of selection does not penetrate to their circle." 
 
 This brings us to the most difficult and most dangerous 
 point. The spectre of responsibiUty is rapping at the portals 
 of society, and is reminding us insistently that it is our duty 
 to see that no injustice be done to any talent that may be among 
 us. And this duty is but Uttle removed from the demand that 
 it should be disburdened of the worries of daily Ufe, for, so 
 the moral argument runs, talent will ripen the more surely the 
 less it has to combat these ceaseless disturbances of ordinary 
 hfe. 
 
 But this thesis, so evident on moral grounds, will never be 
 proved empirically. On the contrary, we have good reason to 
 suppose that necessity, the mother of invention on the broader 
 scale, will often in the case of the individual talent prove to be 
 the mother of its best results. Goethe required for his develop- 
 ment an unchallenged life of ease, whereas Schiller, who never 
 emerged from his hfe of misery, and who, up to the time when 
 he wrote Don Carlos, had not been able to earn sufficient with 
 his pen to buy a writing-desk, required distress to make his 
 genius burst into flower. Jean Paul recognized this blessing 
 of gloomy circumstances when he glorified poverty in his 
 novels. Hebbel followed him along this path by saying that it 
 is more fruitful to refuse the most talented person the necessities 
 of Ufe than to grant them to the least gifted. For among 
 a hundred who have been chosen by the method of sifting, 
 there will be only one on the average who will receive the 
 certificate of excellence in the test of future generations, for 
 the latter use entirely diflEerent methods of sifting from that 
 practised by a committee of examiners who expect ready 
 answers to prepared questions. 
 
 This projects us on to the horns of a severe dilemma that 
 scarcely allows of escape. The consciousness of duty towards 
 the optimum expresses itself only in a maximum of assistance, 
 and overhears the whispered objection of reason that Nature 
 has also coarser means at her disposal to attain her ends; 
 in her own cruelty of selection she often enough proves 
 the truth of Menander's saying, which, freely translated. 
 
EDUCATION 87 
 
 says: to be tormented is also part of man's education. 
 The fact that Einstein — with certain reservations — favours 
 the giving of help to the selected few, it is for me a proof, 
 among many others, of his love towards his fellow-men, which 
 fills his heart absolutely, all questions of relativity notwith- 
 standing. 
 
CHAPTER V 
 THE DISCOVERER 
 
 Relation of Discovery and Philosophy in History. — ^The Absolute and the 
 Relative. — The Creative Act. — Value of Intuition. — Constructive Activity. — 
 Invention. — The Artist as Discoverer. — Theory and Proof. — Classical Ex- 
 periments. — Physics in Primitive Ages. — Experimentum Cruets. — Spectral 
 Analysis and Periodic System. — The Role of Chance. — Disappointed Expecta- 
 tions. — ^The Michelson-Morley Experiment and the New Conception of Time. 
 
 NEXT time — so one of our talks ended — ^next time, as 
 you insist on it, we shall talk of discovery in general. 
 This was a promise of special import for me, for it 
 meant that I was to draw near to a fountain-head of instruction, 
 and to have an opportunity of hearing the pronouncements 
 of one whose authority could scarcely be transcended. 
 
 We are precluded from questioning GaHlei personally about 
 the foundations of Mechanics, or Columbus about the inner 
 feelings of a navigator who discovers new lands, or Sebastian 
 Bach about the merits of Counterpoint, but a great discoverer 
 lives among our contemporaries who is to give us a clue to the 
 nature of discovery. Was it not natural that I should feel the 
 importance of his acceptance of my proposal ? 
 
 Before meeting him again I was overwhelmed with ideas 
 that arose in me at the sHghtest echo of the word " discovery '* 
 in my mind. Nothing, it seemed to me, could be higher : 
 man's position in the sphere of creation and the sum of his 
 knowledge can be deduced from the sum of his discoveries 
 which find their chmax in the conceptions civilization and 
 philosophy, just as they are partly conditioned by the 
 philosophy of the time. We might be tempted to ask : 
 which of these two precedes, and which follows ? And 
 perhaps the ambiguous nature of this question would furnish 
 us with the key to the answer. For, ultimately, these two 
 elements cannot at all be resolved into the relationship of 
 cause and effect, antecedent and consequent. 
 
THE DISCOVERER 89 
 
 Neither is primary, and neither secondary : they are in- 
 timately interwoven with one another, and are only different 
 aspects of one and the same process. At the root of this process 
 is our axiomatic belief that the world can be comprehended, 
 and the indomitable will of all thinking men, acting as an 
 elementary instinct, to bring the perceptual events in the 
 universe into harmony with the inner processes of thought. 
 This impulse is eternal ; it is only the form of these attempts 
 to make the world fully intelligible that alters and is subject 
 to the change of time. This form finds expression in the 
 current philosophy which brings each discovery to fruition, 
 just as philosophy bears in itself constituents of the ripe 
 discovery. 
 
 It seemed to me that even at this stage of my reflections I 
 was somewhere near interpreting Einstein's intellectual achieve- 
 ment. For his principle of relativity is tantamount to a regu- 
 lative world-principle that has left a mighty mark in the thought 
 of our times. We have lived to see the death of absolutism ; 
 the relativity of the constituents of pohtical power, and their 
 mutabiUty according to view-point and current tendencies, 
 become manifest to us with a clearness unapproached by any 
 experience of earher historical epochs. The world was far 
 enough advanced in its views for a final achievement of thought 
 which would demolish the absolute also from the mathematico- 
 physical aspect. This is how Einstein's discovery appeared 
 as inevitable. 
 
 Yet a shadow of doubt crossed my mind. Einstein's 
 discoveries came to hght in the year 1905 — that is, at a time 
 when hardly a cloud was visible to forewarn us of the storms 
 which were to uproot absolutism in the world. But what if a 
 different kind of necessity had imposed itself on world-history, 
 and hence on the world-view ? Nowadays we know from 
 authentic accounts, which no one doubts, that all that we have 
 experienced during the war and the revolution has hung upon 
 the activities of one frail human being of quite insignificant 
 exterior, a bureaucrat of the Wilhelm-Strasse, a choleric eccen- 
 tric who succeeded in frustrating the Anglo-German alhance 
 which was unceasingly being pressed upon us for six long 
 years after the beginning of the century. 
 
 Amid the noisy progress of universal evolution the secret 
 
90 EINSTEIN THE SEARCHER 
 
 and insignificant nibbling of a mole cannot be regarded as of 
 momentous importance for history, and yet if we eliminate it 
 from the complete picture of events we find as a result that all 
 our experiences have been inverted. Absolutism would not 
 have been thrown overboard, but would probably have kept 
 the helm with greater mastery than ever as the exponent of an 
 Anglo-German hegemony of the world, and a pohtical outlook 
 fundamentally difiPerent in tendency would now have been 
 prevailing on the earth. 
 
 But Einstein's Theory of Relativity would not have taken 
 the slightest heed of this. It would have arisen independently 
 of the current forms of pohtical conceptions, simply because 
 we had reached that point in our intellectual development and 
 because Einstein was living and spinning his webs of thought. 
 And the question whether his theory will also have crushed 
 absolutism for the non-physicist cannot be answered. 
 
 It may indeed be doubted whether its time had already 
 come. In the case of many important events in the history of 
 thought their moment of birth can be fixed to within about 
 ten years, as for example the Theory of Evolution, which had 
 been conceived in several minds at the same time and had of 
 necessity to come to Hfe in one of them, even if it had failed in 
 the case of the others. I venture to say that without Einstein, 
 the Theory of Relativity in its widest sense, that is, including 
 the new doctrine of gravitation, would perhaps have had to 
 wait another two hundred years before being born. 
 
 This contradiction is cleared up if we use sufficiently great 
 time intervals. History does not adapt itself to the time 
 measures of poUtics and of journaHsm, and philosophies are 
 not to be calculated in terms of days. The philosophy of 
 Aristotle held sway right through the Middle Ages, and that 
 of Epicurus will gain its full force only in the coming genera- 
 tion. But if we make our unit a hundred years the connexion 
 between philosophies and great discoveries remains true. 
 
 Whoever undertakes to explore the necessity of this con- 
 nexion cannot evade the fact that the fines of the result had 
 been marked out in the region of pure thought, as can be proved, 
 before even the great discovery or invention was able to present 
 it in a fully intelHgible form. Even the achievement of Coper- 
 nicus would follow this general rule of development : it was 
 
THE DISCOVERER 91 
 
 the last consequence of the behef in the Sun Myth which had 
 never been forsaken by man in spite of the violent efforts of 
 the Church and of man himself to force the geocentric view. 
 Copernicus concentrated what had survived of the wisdom of 
 the earliest priests — which includes also the germ of our modem 
 ideas of energy and electricity — of the teachings of Anaxagoras 
 and the Eleatics which had remained latent in our conscious- 
 ness : his discovery was the transformation of a myth into 
 science. Mankind, whose wandering fancy first feels pre- 
 sentiments, then thinks and wishes to know, is a large edition 
 of the individual thinker. The latter sees further only because 
 he, so to speak, stands on the shoulders of a sum-total of beings 
 with a world-view. 
 
 Let us turn our attention to an example from the most 
 recent history of philosophy and discovery. The absolute 
 continuity of events was one of the generally accepted canons 
 of thought, and is even nowadays taught by serious philo- 
 sophers as an incontrovertible element in our knowledge. The 
 old quotation Natura non facit saltus, popularized by Linne, 
 is one of the formulae of this apparently invincible truth. But 
 deep down in the consciousness of man there has always been 
 an opposition to it, and when the French philosopher Henri 
 Bergson set out to break up this line of continuity by meta- 
 physical means in ascribing to human knowledge an inter- 
 mittent, cinematographic character, he was proclaiming in an 
 audible and eloquent form only what had lain latent in a new 
 but as yet incomplete philosophy. Bergson made no new 
 " discovery," he felt his way intuitively into a new field of 
 knowledge and recognized that the time was ripe for the real 
 discovery. This was actually presented to us in our day by 
 the eminent physicist Max Planck, the winner of the Nobel 
 Prize for Physics in 1919, in the form of his " Quantum Theory." 
 This is not to be taken as meaning that a revolutionary philo- 
 sophy and a triumph of scientific research now become co- 
 incident, but only that a discontinuous, intermittent sequence, 
 an atomistic structure, was proved by means of the weapons 
 of exact science, to be true of energies which, according to 
 current behef, were expected to be radiated regularly and 
 connectedly. This was probably not a case of the accidental 
 coincidence of a new philosophical view with the results of 
 
92 EINSTEIN THE SEARCHER 
 
 reasoning from physical grounds, but a demand of time, exact- 
 ing that the claims of a new principle of thought be recognized. 
 
 As above suggested, it is more difficult to find a fink between 
 Einstein's discoveries and antecedent presentiments of rela- 
 tivity. For a mere reference to the downfall of absolutism 
 in the world of human events will not suffice. In the case of 
 Einstein, we see such a tremendous rush of thought in one 
 being that we almost feel compelled to recognize an analogy 
 with the Quantum Theory and believe in a discontinuity in the 
 course of intellectual history. Yet there are certainly threads 
 that connect Einstein's achievement with a prophetic insight. 
 In this case, however, we must spread out over centuries what 
 in the case of other discoveries extends, in comparison, only 
 over decades. That doubt of Faust, which troubles the spirit 
 of every thinker : ** whether in yonder spheres there is also an 
 Above and a Below,'* and which goes back as far as Pyrrhon 
 and Protagoras, is itself relativistic ; it expresses doubt whether 
 the co-ordinate system passing through our own lives as centres 
 is vahd. It is ultimately a matter of point of view, and the 
 mathematico-physical consequences of the endless series of 
 questions, and the relation, which arises from the couple, 
 Above-Below, probably leads to a new mode of comprehending 
 the constitution of the world, for which Einstein's creative 
 work found the adequate expression in abstract terms. And 
 from this point onwards, in accordance with the principle of 
 reciprocal action, a new stream of knowledge will pour itself 
 into the hazy stretches of philosophy. A fundamental and 
 radical reform of our philosophy seems inevitable, particularly 
 with respect to our conceptions of Space and Time, perhaps, 
 too, even with respect to Infinity and Causahty. Much dross 
 will have to be sifted out of our old categories of thought and 
 out of our world wisdom, which once served as material for fine 
 structures. What will the finer ones look Hke that are to take 
 their places in obedience to the command of physics ? Who 
 would care to take it upon himself to form an estimate ? 
 
 Much will be uprooted, and it is possible that even the 
 defiant '* ignorabimus," the antipole of the search for truth 
 from Pyrrhon to Dubois, will again take up the cudgel. For 
 in the face of despairing uncertainty there is the one certainty : 
 what cannot be comprehended is being encircled more and more 
 
THE DISCOVERER 98 
 
 by the great discoverers ! And even if the absolute point of 
 convergence can never be reached, there is within our reach at 
 least another point which is a haven of rest in the passing 
 stream of philosophies, namely, a moral centre around which 
 eddies of happiness circle. At the heart of this world- view 
 there is the upHfting behef in an advance of knowledge in 
 spite of all, and a behef in the vanishing of age-long problems 
 and difficulties under the flood of discoveries. And even if 
 afterwards and concurrently ever new problems and diffi- 
 culties arise, these do not suppress our feehng of triumph. 
 Every achievement in this field gives us a sense of enfranchise- 
 ment from prejudices, not the least of which is narrowness of 
 national outlook. Not only do discoverers construct bridges 
 of thought that stretch to astronomical distances, but, what is 
 more difficult, they build bridges for our feeUngs, that sur- 
 mount poUtical obstacles. Every thinking being who plays a 
 part in the making of some great discovery and who, with 
 deepened vision, bows before a new achievement of mind, 
 gradually becomes a disciple of the reUgion of universal 
 poUtics, the creed of which is faith in the brotherhood of 
 thought. The nucleus of a philosophy that belongs to the 
 future is the recognition that differing national view must be 
 compounded into a unity, and that every great discovery 
 means a step towards attaining this end. 
 
 Even if we accept Pascal's. wonderful dictum that human 
 knowledge is represented by a sphere which is continually 
 growing and increasing its points of contact with the imknown, 
 we must not interpret it as a sign of despair. It is not the 
 enlargement of the unknown, but only that of knowledge that 
 stirs our feehngs with ethical forces. The positive calls up in 
 us a Uving force by inspiring in us the feehng that the sphere 
 of knowledge is destined to grow, and that there can be no 
 higher duty for all the energies of mind than to obey the call 
 for combined action towards this growth which will bring the 
 world into harmony. 
 
 Full of such reflections I entered the home of the great 
 discoverer, whose activities imceasingly hovered before my 
 vision as ideal examples of creative effort. I discovered him, 
 as almost always, seated before loose sheets of paper which his 
 hand had covered with mathematical symbols, with hiero- 
 
94 EINSTEIN THE SEARCHER 
 
 glyphics of that universal language in which, according to 
 Galilei, the great book of Nature is written. 
 
 What a very different picture many an outsider draws of 
 the manner in which a seeker in the heavens works ! He is 
 imagined like Tycho Brahe to be surrounded by unusual 
 pieces of apparatus, spying through the ocular of a long range 
 refractor into the universe, seeking to unravel its ultimate 
 secrets. The true picture does not correspond to this fancy 
 in the slightest. Nothing in the make-up of the room reminds 
 one of super-earthly sublimity, no abundance of instruments 
 or books is to be seen, and one soon becomes aware that here 
 a thinker reigns whose only requirement for his work, which 
 encompasses the world, is his own mind, plus a sheet of paper 
 and a pencil. All that acts on the observatories outside, that 
 gives rise to great scientific expeditions, that, indeed, ulti- 
 mately regulates the relationship of mankind to the con- 
 stitution of the universe, the revolution in the knowledge of 
 things connecting heaven and earth, all this is here con- 
 centrated in the simple figure of a still youthful scholar, who 
 spins out endless threads from the fabric of his mind : the 
 words of a poet are recalled to our memory, which, addressed 
 to all of us, have been fulfilled to the last degree by one living 
 among us : — 
 
 " Whereso thou roamest in space, thy Zenith and Nadir unite thee — 
 This to the heavenly height, that to the pole of the world, — 
 Whatsoever thou do, let thy will mount up into Heaven — 
 But let the pole of the world still o'er thine actions preside." 
 
 (Schiller : Translation by Merivale.) 
 
 And this one helped to fulfil this aim and I must break oft 
 his thread of thought to put the question : What is Discovery, 
 and what does it signify ? 
 
 It is a purely abstract question that may appear to many 
 to be devoid of content. Such will repeat to themselves, as 
 best they can, the hst of discoveries and think a man makes 
 a discovery when he finds out something important, such as 
 the Laws of Falling Bodies, the formation of Rainbows, or the 
 Origin of Species : a general denomination may be found for 
 it perhaps only by ascribing to Discovery something requiring 
 a powerful mind, a creative genius. 
 
 At first it staggered me to hear Einstein say : " The use of 
 
THE DISCOVERER 95 
 
 the word ' Discovery ' in itself is to be deprecated. For 
 discovery is equivalent to becoming aware of a thing which is 
 already formed ; this links up with proof, which no longer 
 bears the character of * discovery ' but, in the last instance, of 
 the means that leads to discovery." He then stated at first 
 in blimt terms, which he afterwards elaborated by giving de- 
 tailed illustrations : " Discovery is really not a creative act ! " 
 
 Arguments for and against this view flashed through my 
 mind, and I thought involuntarily of a great master of music 
 who, when he was asked : *' What is Genius ? " answered : 
 '* A genius is one to whom ideas occur." This parallel might 
 be carried still further, for I have repeatedly heard Einstein 
 call " ideas " what we would regard as wonderful thoughts. 
 Does not the philosopher Fritz Mauthner speak of the discovery 
 of gravitation as being an " apergu " of Newton ; yes, in the 
 sense of aperfus as appHed in ancient Greek philosophy, and 
 which included almost everything that was left by Pythagoras, 
 HeracHtus, etc., as a token of their genius. On the other hand, 
 we are all possessed of the desire to differentiate clearly 
 between an idea and a creative act of thought, as occurs in 
 Grillparzer's aphorism : ** An idea is not a thought ; a thought 
 knows its bounds, whereas the idea leaps over them and 
 succeeds in accompHshing nothing 1 " 
 
 Here, then, we must revise our view. We know, for ex- 
 ample, how much Einstein's " ideas," felt by him to be such 
 and named so accordingly, accompUshed. Let us hear how 
 he characterizes in a few words his own " idea " which shook 
 the world : 
 
 " The underlying thought of relativity," he said, in con- 
 nexion with this question, " is that there is physically no 
 unique (specially favoured) state of motion. Or, more exactly, 
 among all states of motion there is none that is favom-ed in 
 the sense that, in contradistinction to the others, it may be 
 said to be a state of rest. Rest and Motion are not only by 
 formal definition but also by their intrinsic physical meaning 
 relative conceptions.*' 
 
 " Well, then," I interposed, " surely this was a creative 
 act ! This first flashed across your mind. Professor ; it re- 
 presents your discovery, so that we may well let the word 
 retain the meaning usually associated with it ! " 
 
96 EINSTEIN THE SEARCHER 
 
 " By no means," answered Einstein, *' for it is not true 
 that this fundamental principle occurred to me as the primary 
 thought. If this had been so perhaps it would be justifiable 
 to call it a " discovery." But the suddenness with which 
 you assume it to have occurred to me must be denied. Actu- 
 ally, I was lead to it by steps arising from the individual laws 
 derived from experience." 
 
 Einstein supplemented this by emphasizing the conception 
 " invention," and ascribed a considerable importance to it : 
 " Invention occurs here as a constructive act. This does not, 
 therefore, constitute what is essentially original in the matter, 
 but the creation of a method of thought to arrive at a logically 
 coherent system . . . the really valuable factor is intuition ! " 
 
 I had thought, long and intently, about these theses to 
 discover as nearly as possible what distinguished their content 
 from the usual view. The fundamental differences suggest 
 an abundance of ideas whose importance grows in value as 
 we apply them to various cases as illustrations. And I feel 
 convinced that we shall yet have to occupy ourselves with 
 these words of Einstein, which present themselves as a con- 
 fession, as with the famous " hypotheses non fingo " that 
 Newton set up as the idea underlying his work. 
 
 The latter as well as the former implies something negative : 
 it denies something. In Einstein's words there is apparently 
 a repudiation of the really creative act in discovery ; he lays 
 stress on the gradual, methodical constructive factors, not 
 omitting to emphasize intuition. There is no other course 
 open to us but to seek indirectly a synthesis of these concep- 
 tions, and to eliminate what is apparently contradictory in 
 them. 
 
 I consider this possible if we decide to subdivide the dis- 
 covery into a series of individual acts in which succession 
 takes the place of instantaneous suddenness The creative 
 factor may then remain intact ; indeed, it attains a still higher 
 degree of importance if we imagine to ourselves that a series 
 of creative ideas must be Unked together to make possible a 
 single important discovery. 
 
 The original idea never springs fully equipped and armed 
 like Minerva out of the head of its creator. And it is wise 
 to bear in mind that even Jupiter had to suffer in his head 
 
THE DISCOVERER 97 
 
 a period of pregnancy accompanied with great pain. It is 
 only in the after-picture that Pallas Athene appears with the 
 attribute of suddenness. It is the nature of our myth-building 
 imagination to leap over the actual act of birth so as to give 
 a more brilliant form to the finished creation. 
 
 We feel great satisfaction when we learn that Gauss, the 
 Prince of Mathematicians, declared in one of his valuable 
 flashes of insight : "I have the result, only I do not yet know 
 how to get to it." For in this utterance we see above all 
 that he emphasizes a Ughtning-Uke intuition. He has posses- 
 sion of a thing, which is, however, not yet his own, and which 
 can only become his own when he has found the way to it. 
 Is this contradictory ? From the point of view of elementary 
 logic, certainly ; but methodologically, by no means. Here 
 it is a question of : Erwirb es um es zu hesitzen ! This makes 
 necessary a series of further intuitions along the road of 
 invention, and of construction. 
 
 This is, then, where that phase commences, which Einstein 
 denotes by the word " gradual,'* or "by steps." The first 
 intuition must be present ; its presence as a rule usually 
 guarantees that further intuition will follow in logical sequence 
 
 This does not always happen. In passing, we discussed 
 several special cases from which particular inferences may 
 be drawn. The powerful mathematician Pierre Fermat has 
 presented the world with a theorem of extremely simple form 
 which he discovered, a proof of which is being sought even 
 nowadays, two and a half centuries after he stated it. In 
 easy language, it is this : the sum of two squares may again 
 be a square, for example, 5^-1-122=132, since 25+144=169; 
 but the sum of two cubes can never be a cube, and, more 
 generally, as soon as the exponent, the power index n, is 
 greater than 2, the equation x''-\-y'* = z*' can never be satisfied 
 by whole number values for x, y, and z ; it is impossible to 
 find three whole numbers for x, y, and z, which, when sub- 
 stituted in the equation, give a correct result. 
 
 This is certainly true ; it is an intuitive discovery. But 
 Fermat 's assertion that he possessed a " wonderful proof," 
 is for very good reasons open to contradiction. No one 
 doubts the absolute truth of the theorem. But the later 
 inspiration, the next step after the intuition, has occurred 
 7 
 
98 EINSTEIN THE SEARCHER 
 
 neither to Fermat nor to anyone else. It cannot be established 
 whether his remark about the proof was due to a subjective 
 error, or was baseless. In any case it seems probable that 
 Fermat had arrived at the result per intuitionem without 
 knowing the way to it. His creative act stopped short ; it 
 was only a first flare of a conflagration, and did not fulfil 
 the condition that Einstein associates with the conception 
 of a logically complete method. 
 
 We may, indeed, pursue this case of Fermat still further. 
 He had enunciated another theorem, again per intuitionem, 
 namely, that it was possible to construct prime numbers of 
 any magnitude by a formula he gave. Euler later showed 
 by a definite example that the theorem was false. It was 
 stated in a letter to Pascal written in 1654 in the words : the 
 result of squaring 2 continuously and then adding i must 
 in each case be a prime number, that is, a^^^' + i must always 
 be a prime no matter what value k may have. Fermat added : 
 " This is a property for the truth of which I answer.'* Euler 
 chanced to try ^=5, and found that 2^^+1=4,294,967,297, 
 which may be represented as the product of 641 and 6,700,417, 
 and hence is not a prime. 
 
 It is conceivable that no Euler might have Uved, and that 
 no one else might have discovered this contradiction. What 
 would then have been the position of this " discovery " of 
 Fermat ? 
 
 We should certainly not have disputed its creative character, 
 for we should have said that it corresponds to a fact which 
 is fully formed, but cannot be proved. But now that we 
 know that the fact does not exist at all, the thing assumes a 
 different colour. It was not a discovery at all, but an erroneous 
 conjecture. But one would never be able to arrive at an 
 erroneous conclusion of this sort without being a mathe- 
 matical genius, and having the inspiration of the moment. 
 And from this again it follows that to make a discovery in 
 the full sense of the word the intuition of the moment does 
 not suffice, but must be supported by a series of intuitions, 
 and this is the condition that it become a permanent com- 
 ponent of universal truth. 
 
 The fact that Einstein refers to the action of " inventing " 
 in his explanation, gives support, it seems to me, to the view 
 
THE DISCOVERER 99 
 
 that, strictly speaking, discovering and inventing are never 
 to be regarded as being separable. In discovering, what has 
 to be constructed persists, and in inventing, it is a question 
 of finding the path along which there is the promise of success, 
 be it by a method, a proof, or by some general work. We 
 spoke of works of art, and I was deUghted to see that Einstein 
 was by no means disinchned to claim certain works of pure 
 thought, which are usually placed in the category of scientific 
 discovery, as works of art. In the latter, however, the pure 
 process of invention plays the prominent part, for in them 
 something is represented that did not exist at all before ; 
 this has repeatedly led to the artist's achievement being given 
 the higher rank, as being properly and exclusively creative. 
 The argument runs somewhat along these Hues : the infinites- 
 imal calculus would certainly have been discovered even 
 if there had been no Newton and no Leibniz, but without 
 Beethoven we should never have had a C Minor Symphony, 
 and never in the future would it have appeared, for it was a 
 subjective, absolutely personal, and unique product of its 
 creator. 
 
 I believe this may be admitted, and that we may neverthe- 
 less retain the view that in the work of art, too, the act of 
 discovering is to be found. Let us consider for a moment the 
 elementary substance of the first movement of this fifth 
 symphony, a colossal movement of 500 bars, which expresses 
 itself quite definitely in four notes, of which one is repeated 
 three times. " Thus Destiny thunders at the gates " is 
 Beethoven's motto for this section ; it is expressed tonally 
 in a succession of notes which through all eternity existed 
 among the possible permutative arrangements of these sounds. 
 
 Beethoven, so it is expressed, invented it. But it is just 
 as correct to say — in Einstein's words — " he became aware of 
 what was already formed " — that is, he " discovered " the 
 fundamental theme, and afterwards " proved it " in terms of 
 musical logic unheard-of beauty in a methodical elaboration. 
 We may, indeed, go further still. This motif of four tones was 
 not only extant as an abstractum, as a possible mathematical 
 arrangement, but also as something natural. Czemy, a 
 pupil of Beethoven, to whom the master confided many a 
 remark about the origin of his compositions, reports that a 
 
100 EINSTEIN THE SEARCHER 
 
 bird, the yellow-hammer, had sung this theme to Beethoven 
 in the woods. But neither the bird nor any other living 
 creature had invented it ; rather what could not be created, 
 because it had always been in existence, became objectified 
 in the medium of sound. Beethoven found it ; it was res 
 nullius when he found it and when he discovered simultaneously 
 with the succession of tones that they were appropriate for a 
 powerful musical representation of sombre Destiny. Every 
 theme, be it of Beethoven, Bach, Wagner, or anyone else, may 
 be represented graphically by a curve (in the case of Bach's 
 fugal themes this has, in fact, been done for special purposes), 
 and just as it is certain that every elliptic-arc existed before 
 all geometry, so it may be affirmed with equal certainty that 
 everything musical was in existence before the advent of 
 composition, and was merely waiting for a discoverer whom 
 we designate the inventor, the creative organ. 
 
 But may not some of this glory be reflected on to scientific 
 discovery ? When we are in an ecstasy of admiration, we 
 talk of a creative act as of something divine ; may we not 
 also grant to the scientist this tribute which, owing to a slight 
 confusion of conceptions, we shower on the artists ? And I 
 beUeve that Einstein's definition does not set up an insuperable 
 barrier in this respect to our admiration, which exerts every 
 effort to pass beyond, refuses to come to a standstill before 
 the rigid fact that the discoverer reveals only what is pre- 
 formed ; our emotions prove to be stronger than our minds 
 with their objective valuation. In the last instance, we opine, 
 the scientific discoverer, too, creates something new, namely, a 
 piece of knowledge that was previously not in existence. And 
 we obey the impulse of hero-worship, when we call a definite 
 first discoverer a creator. 
 
 This silences opposition certainly only for a time, without 
 vanquishing it. For this knowledge, too, lay ready before 
 the first discoverer appeared : he did not create it, but merely 
 drew back the veil that enveloped it. So that, ultimately, 
 we get back to '' intuition " in its literal sense, a becoming 
 aware of things, an exact consideration of things, states, and 
 relationships ; and this intensive consideration, full of wonder- 
 ment, has always been a privilege of a very few chosen men. 
 
 It might be asked : Was there any knowledge of Pythagoras' 
 
THE DISCOVERER 101 
 
 Theorems before Pythagoras gave us his proof ? We should 
 have to answer : It was in existence at least in the still dark 
 field of vision of Pythagoras, which became illumined one 
 day when he took such a view of the number-ratios 3 — 4 — 5 
 that an exact intuition could actually come about. It is 
 erroneous to assume that a creative act suddailyt-cait^d' up 
 before his soul as if by magic the figure with the tfire^ squares 
 drawn externally on the sides of a triangle. Eatbej.J he' '*. tbol&Cj 
 his stride " (as we know from Vitruvius) by cohsiHeiing a 
 triangle whose sides were of a definite length ; and the well- 
 known proof, which is linked indissolubly in our minds with 
 his work, is not his at all, but Euclid's. Yet our annals grow 
 musty, centuries pass by, and the credit of being the creator 
 rests with the man who first succeeded in getting a clear 
 picture of such a triangle. 
 
 It seems natural to test discoveries by experiments. The 
 first result of doing this is a very remarkable increase in the 
 rate at which the intuitive process has developed. In ancient 
 times, intuition, it seems, scarcely felt the need of proving 
 things by experiment ; all that was discovered by Archimedes 
 in mechanics, by the Pythagoreans in acoustics, by Euclid in 
 optics, may be reduced practically to the formula " heureka," 
 and it is probably scarcely an exaggeration to say that more 
 and more fruitful experiments are performed in one week 
 nowadays than in the whole of the classical age taken together.* 
 
 * Recently certain precisians in definition have been seeking to establish 
 a fundamental difference between physicists of reality, experimental physicists, 
 and " blackboard-physicists." The last term is given jeeringly to theoretical 
 physicists because they, in the opinion of these critics, wish to found Nature 
 entirely on formulae argued out on the blackboard. The history of science 
 does recognize this distinction, although it is, of course, quite possible for a 
 physicist to arrive at important discoveries without making any experiments. 
 
 One might be more justified in asserting that the great theorist need not 
 necessarily be a great experimenter and vice versa. But I can quote no 
 example of a physicist who confined himself obstinately to blackboard dis- 
 cussion, and on principle disowned all experimental work. 
 
 I must add that Einstein himself is fond of experimenting, and has had 
 much success in experimental work. The amount of advice and encourage- 
 ment that he has given, and still gives, to many workers in this field is very 
 considerable. But he does not practise experimental work regularly, and 
 remarked that he is obliged to appeal to outside help for certain practical tests. 
 There are specific experimental geniuses, whose activity assumes the happiest 
 and most fruitful form when it supplements that of the theorist and fertilizes it. 
 
102 EINSTEIN THE SEARCHER 
 
 Experiments have become, if not the sole, yet the most definite, 
 test of intuition. I need only recall the observations of the 
 solar eclipse of 1919, which were of an experimental character 
 inasmuch as they used apparatus to question Nature. To the 
 world generally, they gave the irrefutable confirmation of 
 Einstein*s Theory of Gravitation, but not to Einstein himself, 
 whose intuition felt itself so certain that the confirmation was 
 a-mere matter of course. 
 
 But this is hot the average case ; in many cases the in- 
 tuition of the discoverer appeals to experiment as a judge of 
 great authority, who is to confirm, reject, or correct. 
 
 Let us take some examples of cases in which the intensity 
 and the value of intuition were measured by the experimental 
 results. Benjamin FrankHn*s Kite Experiment may be taken 
 as a classical instance. Here is a man in whose head the idea 
 takes root that lightning and electricity are one and the same 
 thing. Innumerable persons before and after his time might 
 have hit on the same idea, which is now the common knowledge 
 of children. Yet, a single man had to appear who became 
 aware of this pre-formed fact and who simultaneously thought 
 out a method of putting it to proof. In 1752 he constructed 
 a kite, sent it up into the clouds during a storm, and caught up 
 sparks on the ground by a metalHc contrivance, and, as d'Alem- 
 bert so aptly described it to the French Academy : 
 
 " Eripuit coelo fulmen ..." 
 
 He wrested the lightning from the heavens. Jupiter tonans 
 illuminated a great discovery, a mighty intuition which had 
 entered like a lightning stroke into the brain of a discoverer. 
 
 This case would be classical, were it not that nine-tenths of 
 it is based on legend. Franklin was by no means the first who 
 had this intuition, and his experimental test was so full of 
 faults that it was within an ace of faiUng. Frankhn used a dry 
 thread of hemp, which he thought to be a conductor, but 
 which became a conductor only after it had been made wet by 
 rain. Till that moment the exhibition of sparks on the ground 
 had been poor enough, and httle was wanting for Franklin 
 to give up his attempt and confess that he had been inspired, 
 not with an intuition, but with a hallucination. 
 
 But to whom then is the glory of this discovery due ? This 
 
THE DISCOVERER 103 
 
 is a difl&cult point to decide. As early as 1746, that is, six years 
 
 before Franklin's kite made its ascent in Philadelphia, Professor 
 
 Winkler of Leipzig had asserted in a dissertation that the two 
 
 phenomena were identical, and had proved this theoretically ; 
 
 and three years earlier still Abbe Nollet had declared the 
 
 storm clouds to be the conductors of an electrical induction 
 
 machine. Almost simultaneously with Frankhn, DaUbard, 
 
 Delor, Buffon, Le Monnier, Canton, Bevis, and Wilson made 
 
 experiments on an elaborate scale, which far exceeded that of 
 
 Frankhn in their results. To this must be added that the 
 
 experiment was conducted with evident success only in 1753, 
 
 when de Romas of Nerac in South France wove a real conductor 
 
 of thin annealed wire into the kite-string, and succeeded in 
 
 bringing down a regular thunderstorm with flashes of hghtning 
 
 ten feet long, accompanied by a deafening uproar. It was only 
 
 then that the track of the inspiration was traced back through 
 
 time to the Roman Kings, Numa PompiUus and Tullus Hosti- 
 
 hus, as the first experimenters with hghtning. And then the 
 
 physicist Lichtenberg sought to furnish a proof that the old 
 
 Hebrew ark of the Covenant, together with the tabernacle, were 
 
 nothing other than great pieces of electrical apparatus highly 
 
 charged with electricity derived from the air ; thus the first 
 
 intuition, and the priority of discovery, would have to be 
 
 ascribed to Moses or Aaron ! And connected with this was 
 
 the fact, supported by substantial proof, that the Temple of 
 
 Solomon was protected by Ughtning-conductors. 
 
 I must not omit to mention that Einstein regards this 
 whole chain of proofs stretching back to early times as by no 
 means estabUshed, although besides Lichtenberg, other im- 
 portant scholars, such as Bendavid in Berhn and Michaelis in 
 Gottingen, have vouched for their truth. And as it is a matter 
 of electrical relationships, Einstein's doubts cannot be passed 
 over. As far as I recollect, they were not directed against 
 the rough facts in themselves, but against the sense that is 
 construed into them — ^that is to say, in the case of both the 
 ancient Roman and the Bibhcal data, the conception of dis- 
 covery must be excluded, and must be awarded rather to those 
 intellectual efforts which have led to the creation of a method 
 of thought. None the less, we may uphold our statement that 
 in this case, presumed to be classical, neither Franklin nor any- 
 
104 EINSTEIN THE SEARCHER 
 
 one else is to be claimed as the discoverer or as the central 
 figure in a creative act. 
 
 The experimental case of spectral analysis is incomparably 
 simpler and less open to dispute. It is without doubt a dis- 
 covery of fundamental importance bearing all the character- 
 istics of originality, for no predecessors are discernible. I have 
 always felt a Uttle dissatisfied with the fact that it required 
 two men to think it out, that a duo of minds was necessary for 
 one act of thought which appears quite uniform, elementary 
 and inseparable from the intuition of a single mind. But it 
 seems possible that tradition has not handed the facts down to 
 us faithfully, and that the two men, with a unanimity arising 
 from their partnership in work, combined their results, which 
 were not, at the beginning, of a dual character. This possibility 
 became clear to me from a remark of Einstein which made it 
 plain to me that the conjunction Kirchhoff and Bunsen is to 
 be taken as denoting Kirchhoff and then, after a pause, Bunsen 
 in the next breath ! But if we discard this question of unity 
 or duahty, we are left with the fact that the idea of a spectral 
 analysis occurred to some one (as a result of preceding optical 
 experiments with Fraunhofer lines), and was fully confirmed 
 by later experiments. Only fully confirmed ? No, the classic 
 rank of this case manifested itself in a much more triumphant 
 manner, for it is impossible that the intuition of Kirchhoff 
 and Bunsen could have grasped the whole significance and 
 range of their discovery even after they had made it their 
 own. 
 
 Every discovery encloses a germ of hope. However great 
 this may have been in the case of Kirchhoff, it could not by any 
 stretch of imagination approach the degree of its fulfilment. 
 The fundamental theoretical idea that " a vapour absorbs from 
 the ray-complex of white light only those wave-lengths which 
 it can emit *' gave rise to a process, the ingenuity, delicacy, 
 and certainty of which is almost inconceivable. When rays 
 of light emitted by incandescent vapour were separated by a 
 prism, there were discovered fine coloured fines that betrayed 
 some unknown mystery. The spectroscopic experiments 
 proved, in a succession of results, that the author of the above 
 idea had made not only one discovery, but a whole host of them. 
 For example, it was observed that, in burning minute residues 
 
THE DISCOVERER 105 
 
 obtained by evaporating certain mineral waters, a red line and 
 a blue line that had never been seen before appeared in the 
 spectrum. One knew immediately that an element, hitherto 
 undiscovered, was proclaiming its presence. In this way in 
 quick succession the element Caesium was discovered, then 
 Rubidium, ThaUium, Indium, Argon, Hehum, Neon, Krypton, 
 Xenon — certainly things that were already pre-formed in 
 Nature, just as the idea of a bridge from Optics to Chemistry 
 lay all ready in the heart of Nature ; but no blame can be 
 given to the astonished contemporaries who regarded this 
 fundamental discovery of spectroscopic analysis as a creative 
 achievement of the intellect. 
 
 This ray of hope gave a gHmpse of the degree of accuracy 
 attainable. In this connexion the experiment confirmed 
 infinitely more than the boldest imagination could ever have 
 dreamed. A yellow fine was detected in the spectrum of 
 sodium. And it was found experimentally that the three- 
 miUionth part of a thousandth of a gramme of a sodium salt 
 is sufficient to produce this sodium fine in the spectrum of a 
 Bunsen burner. There commenced a dizzying passage in the 
 Calculus of ProbabiHties for, since it was found that in the 
 sun's atmosphere hydrogen, carbon, iron, aluminium, calcium, 
 sodium, nickel, chromium, zinc, and copper were present, the 
 question arose as to how great was the possibihty of an error 
 in this observation. Kirchhoff calculated it as a chance of a 
 trilHon to one that these substances are actually present in 
 the sun ! 
 
 Never before had an experiment verified to such an extreme 
 degree a discoverer's idea. It seems appropriate at this stage 
 to deal with a doctrine which seeks to shed fight into the deepest 
 recesses of the connexion between experiment and discovery. 
 It teaches that an experimentum cruets, an experiment that 
 verifies absolutely, is impossible in physics. That is to say, 
 every idea of a discoverer involves a hypothesis, and, how- 
 ever the experiment that follows may turn out, there still 
 remains the possibihty that this hypothesis was false, and may 
 later have to make way for another essentially contradictory 
 hypothesis which will be vafid again only for a hmited time. 
 
 The chief exponent of this theory is the eminent scholar, 
 Pierre Duhem, Membre de I'lnstitut. He draws a parallel 
 
106 EINSTEIN THE SEARCHER 
 
 between experiment and mathematical proof, particularly with 
 the indirect, apagogic form which has been so successfully 
 appHed in EucUdean geometry. In this method it is assumed 
 that a certain statement is erroneous ; it is then shown that 
 it leads to an obvious contradiction ; consequently the state- 
 ment was correct provided that a certain doubt be excluded. 
 Thus in the domain of mathematics we have a real experi- 
 mentum cruets. 
 
 In accordance with this, Duhem tests the vahdity of two 
 physical theories, both of which were put forward and claimed 
 as discoveries. Newton had discovered the nature of Hght to 
 consist in " emission " ; to him, as well as to Laplace and Biot, 
 light consists of projectiles that are emitted with very great 
 velocity. The discovery of Huyghens, supported by Young 
 and Fresnel, substitutes wave-motion in place of corpuscular 
 emission. Hence, according to Duhem, we have, or we had, 
 here two hypotheses which appear to be the only ones possible. 
 Experiment was to pronounce a judgment, and at first it 
 decided irrefutably in favour of the wave-theory. Therefore, 
 the discovery of Huyghens is alone true, and that of Newton 
 is shown to be an error ; there is no third outlet, and so we 
 have quite certainly an experimentum cruets before us. 
 
 The term itself originates in Bacon's Novum Organum, 
 Contrary to Duhem*s assumption, it does not refer to a signpost 
 at cross-roads giving various routes, nor is it connected with 
 croix ou pile, heads or tails. Experimentum cruets denotes 
 rather a divine judgment at the cross, that is a test that is 
 absolutely decisive and beyond further appeal. But no ! adds 
 Duhem, there is no room for a third judgment in the case of 
 two contradictory statements in geometry, but there is between 
 two contradictory statements in physics. And, in fact, this 
 third possibiHty has manifested itself in the discovery of 
 Maxwell, who has shown that the nature of hght is founded 
 on a process of periodic electromagnetic disturbances. Hence, 
 so concludes Duhem, experiment can never decide whether a 
 certain theory is alone valid. The physicist is never certain 
 that he has exhausted all conceivable possibilities of thought. 
 The truth of a physical statement, the vahdity of a discovery, 
 cannot be confirmed by any experimentum crucis. 
 
 According to this argument, therefore, it is also possible 
 
THE DISCOVERER 107 
 
 that the scientific grounds of spectral analysis do not conform 
 to truth. A contradictory hypothesis may, indeed, be set 
 up, with the result that the same experiments that had led 
 Kirchhoff 's discovery from one triumph to another would have 
 to be interpreted in a totally different sense. 
 
 I must frankly confess that I cannot subscribe to such an 
 extreme eventuahty, since, in my opinion, Duhem's analogy 
 with mathematics excludes this possibiUty. For if a certain 
 probability is expressed by a trilUon to one, then I venture to 
 state that even in the case of mathematical truths certainty 
 reaches no higher degree of probabihty. From the history of 
 mathematics we know of theorems which were enunciated 
 and provided with complete proofs, and yet did not succeed 
 in estabhshing themselves ; hence we see that, however evident 
 a mathematical theorem may be, it is still only a matter of 
 very great probabihty. 
 
 If, following our usual habits of thought, we take this for 
 absolute certainty, then we may also consider the sum-total 
 of experiments in the realm of spectral analysis to be a great 
 experimentum crucis for the correctness of the theory itself. 
 
 Far removed from it, and yet connected with it, there is 
 the " Periodic System of the Elements," the discovery of 
 Mendelejew and Lothar Meyer. It, too, offered prophetic 
 glances into the future, foretold the unknown, hinted at things 
 that were present only in imagination in a scheme of thought 
 that assigned definite places of existence to undiscovered things. 
 The Periodic System is represented by a table containing 
 vertical and horizontal rows, in the squares of which the 
 elements are entered according to certain rules depending on 
 their atomic weights. The discovery consisted theoretically 
 in stating that the physical and chemical properties of each 
 element is the arithmetic mean between the properties of its 
 horizontal and vertical neighbours. This gave rise to pre- 
 dictions concerning the unoccupied squares. These gaps, 
 these blank spaces in the table, seem to say prophetically : 
 There are elements missing here that must be discoverable. 
 The neighbours will betray them, and the empty space itself 
 shows by what means they are to be found. With the shrewd- 
 ness of a detective, Mendelejew was able to say : There must 
 be elements of the atomic weights 44, 70, and 72 ; we do not 
 
108 EINSTEIN THE SEARCHER 
 
 know them yet, but we are in a position to determine the 
 properties of these foundlings of the future, and, what is more, 
 the properties of their compounds with other elements. Later 
 researches, which led to the discovery of the elements. 
 Scandium, Gallium, and Germanium, liave actually confirmed 
 all these predicted properties. 
 
 The metal GalUum was discovered in 1875 by spectroscopic 
 means. Its properties are the mean of those of Aluminium 
 and Indium, and this places it in a position which had already 
 been assigned to it in the periodic table before its discovery ; for, 
 owing to a gap in the system, Mendelejew had asserted its 
 existence five years previously, although he then knew nothing 
 of its characteristic spectral signs, namely, two beautiful violet 
 lines. Radium, too, which was discovered in 1900 and was 
 found to have the atomic weight 226, completely satisfied this 
 test and fitted exactly into the place which this number 
 reserved for it in the table. Thus prediction and confirmatory 
 discovery were fully congruent in this case ; the experiment 
 followed on the visionary insight just as a EucHdean proof 
 follows on a mathematical assertion, and we have every reason 
 to say that the system of Mendelejew and Lothar Meyer has 
 stood the crucial test. Future hypotheses will perhaps sup- 
 plement the system or enlarge our knowledge of it, but will 
 certainly not reduce it ad absurdum. 
 
 Apart from these cases, there are achievements by men 
 who may be called lucky discoverers, although they displayed 
 no genius for finding nor for creating. The philosopher- 
 physicist, Ernst Mach, has devoted a lecture to such intellects, 
 which seems to me very valuable, if only for the reason that he 
 traces back the conceptions of discovery and invention to one 
 common root of knowledge, and explains their difference as 
 being due only to a difference in the appHcation of this 
 discovery. 
 
 But when Ernst Mach in this lecture, " On the Influence 
 of Accidental Circumstances on the Development of Inventions 
 and Discoveries,*' extends the influence of chance to include 
 accidental circumstances that can only enter when the dis- 
 coverer is closely attentive, it seems to me that certain limita- 
 tions are advisable. Otherwise, if we pursue Mach's fine of 
 
THE DISCOVERER 109 
 
 thought to its extreme, we could declare every discovery to 
 be due to chance, and this would be the end of the intuitive- 
 creative idea. This assertion would ultimately mean that 
 genius owes its achievements to the accidental arrangement 
 of the molecules in the brain-cells of its associated body. This 
 would be just as wrong as saying that chess is a game of chance 
 because we lose a game when, by chance, we come up against a 
 better player. 
 
 Huyghens, the great discoverer and inventor, says, in his 
 Dtoptrica, that he would have to consider anyone who invented 
 the telescope without the favourable intervention of chance 
 to be a superhuman genius. Why should he choose just the 
 telescope ? To many the invention of the Differential Calculus 
 will appear grander and due to a higher degree of ingenuity. 
 And since it was produced quite methodically, and since chance 
 was excluded, we may follow Huyghens and with good reason 
 proclcdm its authors superhuman geniuses. 
 
 Many a true inspiration is dependent on some impulse from 
 without. Who discovered Elect romagnetism ? The world- 
 echo answers, " Oersted," with the same confidence that it 
 couples together the names America smd Columbus. This 
 shows how enormously important was the achievement. 
 Next to steam-power nothing has exerted such a revolutionary 
 influence in all branches as electromagnetism. Without it, 
 the world of to-day would present a totally different aspect. 
 Without it, we should have no dynamos, no electric trams, no 
 telegraphy, no electric-power stations, all of which are due to 
 the work of Arago, Gay-Lussac, Ampere, Faraday, Gramme, 
 and Siemens. Without it, there would be none of the abundance 
 of brilHant discoveries that are associated with the names of 
 Maxwell, Hertz, and Einstein. The fact that physics used to be 
 divided into three parts — Mechanics, Optics, Electrodynamics 
 — and that, since then, the coherent unity of the physical 
 picture of the world has been developed, shows us a picture in 
 the background of which we see the illuminating figure of Hans 
 Christian Oersted. It must not be overlooked, however, that 
 in the case of his great discovery, too, chance played a definite 
 part. It occurred one day when Oersted was holding a lecture 
 in the winter of 1819-20 ; a magnetic needle situated near 
 
110 EINSTEIN THE SEARCHER 
 
 his Volta-battery began to vibrate irregularly. This appar- 
 ently unimportant trembUng of the metal points contained the 
 key to a fact, the whole consequences of which could in no 
 conceivable way have entered the mind of this observer of a 
 hundred years ago, in spite of the genius of the Danish scientist, 
 which is documented in the classical and far-famed dissertation, 
 *' Experiment a circa effectum conflictus electrici in Acum 
 magneticam," which appeared in July 1820. It cleared the 
 way for intuitions that were equally as fruitful for theory as for 
 practice. Thirteen years after this initial discovery the world 
 saw the first very important consequence in Gauss' and Weber's 
 electric telegraph, and a Uttle later the eminent discoverer 
 Fechner, in Leipzig, proclaimed it as his conviction that, 
 within two years, electromagnetism would entirely reform the 
 world of machines, and would entirely supersede steam- and 
 water-power. Of course, his time estimate fell far short of the 
 mark. It has been reserved for the present generation to 
 reaHze that we live in an electromagnetic world, and that we 
 have, theoretically and practically, to spend our hfe electro- 
 magnetically. The first indication of this knowledge hung 
 upon the quivering point of a magnetic needle, and from it 
 there evolved the electromagnetic ideas that we are so fond of 
 picturing as our handmaids, but which, in reality, are sovereign 
 over us all. 
 
 A great deal of the history of discovery must be revised 
 and corrected. The Spiral of Archimedes is not due to 
 Archimedes, nor Marriotte's Law to Marriotte, nor Cardan's 
 formula to Cardan, nor Crookes' Tube to Crookes, and Galvan- 
 ism is only related to Galvani by the following anecdote. It 
 arose from an accidental experience of Madame Galvani in 
 the kitchen : a half-skinned frog that was to be fried for the 
 evening meal happened to rest between a scalpel and a tin plate, 
 which brought it into metalHc contact with an accidental 
 discharge of electricity ; the frog twitched ; the head of the 
 house gave a very naive interpretation to the phenomenon ; 
 and it was under such auspices that Galvanism made its entry 
 into the world. It would be a futile task to endeavour to trace 
 the connexion between experiment and the underlying idea, 
 which, in this case, first came to life in Alexander Volta, What 
 
THE DISCOVERER 111 
 
 would have remained a mere frog-dance if left to Galvani now 
 acquired the rank of a discovery through the work of a thinking 
 physicist, who set up a " Voltaic series " ; this discovery then 
 assumed power and dignity in the hands of Nicholson, Davy, 
 Thomson, Helmholtz, and Nernst. The words Galvanic Elec- 
 tricity should be made to give way entirely to Voltaic 
 Electricity,* as in the case of many another expression for 
 which chance and insufficient thought have stood sponsor. 
 
 It often happens that experiment acts as a corrective of 
 the underlpng idea, neither confirming nor contradicting, but 
 nursing it, as it were, strengthening, and purging it of errors. 
 Such experiments, partly in conjimction with chance, play 
 an important, sometimes a decisive, role in the works of 
 Dufay, Bradley, Foucault, Fresnel, Fraunhofer, and Rontgen. 
 Faraday, who was incapable of observing otherwise than 
 intensively, found himself compelled, whilst stud5dng induction 
 phenomena, to alter his initial view, and it is just this correction 
 by experiment that constitutes Faraday's real discovery. In 
 many cases the initial idea is corrected, nay surpassed, by te 
 result. Columbus worked methodically when he set out to 
 reach the East Indies by travelling westwards ; but what he 
 discovered was not a confirmation of his nautical idea only, but 
 something much greater, which certainly did not He in his 
 calculation. Thus he became the archetype of all searchers, 
 who had thought out and anticipated essentially different 
 conditions from those that were afterwards discovered to be 
 prevalent. Among these are to be counted Priestley and 
 Cavendish, who clung to the erroneous notion of phlogiston, 
 even when they had the evidence to the contrary in the ele- 
 ments they had themselves discovered, namely, oxygen and 
 hydrogen. Graham Bell, the inventor, was seeking something 
 quite different from what he later hit on : as a teacher of the 
 deaf and dumb he was trying to give a visual picture of sounds, 
 in order to make clear the formation of soimds to his pupils ; 
 this led him to construct an electrical apparatus, which finally 
 led to the discovery of the telephone. 
 
 The truest and sharpest contrast with the experimentum 
 cruets is furnished by experiment when it shows the exact 
 
 * The usual term in England is Voltaic Electricity, or, simply, Current 
 Electricity.— H. L. B. 
 
112 EINSTEIN THE SEARCHER 
 
 opposite of what the explorer was expecting. But since an 
 absolute No entails a very decisive Yes — ^namely, in this case, 
 the affirmation of a relationship that was previously held to 
 be impossible — a negative experiment of this kind, when it 
 occurs, will be followed by momentous consequences ; these 
 will be the more important in proportion as the question, the 
 affirmation of which was expected by the physicist, is of a 
 fundamental character. 
 
 The experiments of Michelson and Morley, directed at 
 proving the existence of the ether, are to be regarded as the true 
 classical instances of these experiments answering with an 
 overwhelming negative. Their first effect was to produce a 
 sense of helplessness, a check to thought, a void in the chamber 
 of ideas. And to fill this void there arose new views of the 
 world in which we nowadays recognize the true thought - 
 pictures of the universe. The great names — Lorentz, Min- 
 kowski, Albert Einstein — shone out ! 
 
 As there are forerunners for almost every important event, 
 so also in the case of the experimentum cruets of Michelson 
 and Morley. Henri Poincar^, the famous mathematician, 
 whilst still a student of the ficole Polytechnique, had initiated 
 experiments with his fellow-student Fav6, which followed 
 the same object. The Michelson-Morley experiment was at 
 least a hundred times more accurate. In each case the con- 
 clusion was that the laws of optics are not disturbed by a 
 motion of translation, such as that of the earth through space 
 this is, however, contrary to what the old physical ideas lead 
 us to expect. 
 
 If we assume the existence of a space-filling ether, the 
 earth, owing to its own velocity of nineteen miles per second, 
 would have to pass through a hurricane just as in the case of 
 travellers sitting in an open train rushing along at very great 
 speed. If we send out Hght rays in all directions simultane- 
 ously from any point on the earth's surface, some will travel 
 in the teeth of the ether-storm, others will experience only a 
 part of the storm's power ; so that of two hght -rays travelling 
 in exactly opposite directions the retardation of the one should 
 be equal to the acceleration of the other ; and yet they are not 
 quite equal, for a simple calculation shows that in every case 
 the retardation is slightly more than the acceleration. 
 
THE DISCOVERER 118 
 
 This may be made clear by means of a model of easy con- 
 struction, or, better still, by considering a ship that is subject 
 to a constant current and, simultaneously, to a pressure of the 
 wind. The time taken by the boat in making a trip up and 
 down stream can never be the same for the cases when the 
 wind is in the direction of the current, and vice versa. 
 
 In the case of the ray of light, which is sent backwards and 
 forwards by means of a contrivance of mirrors, this fact should 
 be clearly demonstrated by means of the interference-fringes, 
 which are able to show much smaller effects than the experi- 
 ment demands. The experimental oracle was to speak, but 
 it remained silent. This portentous silence signified : no 
 interference-effect, no action of the ether-current, no influence 
 due to translation — ^nothing ! 
 
 This " nothing " compelled a decision of a very startling 
 kind, for the result of this experiment was in direct contradic- 
 tion to another famous experiment. Fizeau had proved that 
 the ether is practically rigid and remains fixed in interstellar 
 space. A decision had to be taken in favour of Fizeau or 
 Michelson and Morley. Yet this was impossible, for both had 
 operated with unsurpassable accuracy. It was impossible 
 to reconcile both views as they were diametrically opposed. 
 This contradiction remains, even if we assume a different 
 hypothesis, not involving the ether, for Fizeau's experiment. 
 A solution was impossible without undertaking revolutionary 
 changes in the whole of physical thought. 
 
 This radical change was effected by Einstein ; and this 
 mysterious contradiction disappeared in the resulting revolu- 
 tion of thought. Einstein supplanted the absolute time- 
 conception by a new relative conception, and thus the perplex- 
 ing problem disappeared. Two great principles arose as 
 regulative factors in thought, and wherever these were apphed, 
 they achieved wonders : one was the new conception of time 
 that deprived the earth of her unique position as the sovereign 
 of time by the introduction of the principle that the rate at 
 which time elapses is different in media moving at different 
 speeds ; the other is the principle of the constancy of the 
 velocity of light. One feels a temptation to apply a mythical 
 allegory : just as the world, according to the Biblical story, 
 originated from nothing, so there arose from the " nothing " 
 8 
 
114 EINSTEIN THE SEARCHER 
 
 of the Michelson-Morley experiment a new world, a world of 
 knowledge, a cosmos of thought, in which perfect harmony 
 reigns. 
 
 Its truth was contained in itself before the experimental 
 proof was furnished. And this reaUzation of truth has become 
 a fact in the experimentum cruets for which the sun and stars 
 formed the material. This will be discussed in another part 
 of the book. 
 
 " The really important factor is ultimately intuition," 
 Einstein had said to me. It made me think of Huyghens' 
 remark about the genius who would have been able to create 
 the telescope without the help of chance. Was not this in- 
 tellect, imagined by Huyghens, sitting opposite me at that 
 moment ? An inner voice answered in the affirmative, for 
 Einstein's thought -complex seemed to me at that moment a 
 kind of telescope for the human mind, a telescope that had 
 arisen out of pure intuition, and whose range stretched to the 
 limits of the universe 
 
CHAPTER VI 
 OF DIFFERENT WORLDS 
 
 Imaginary Experiment with *' Lumen." — Impossibilities. — A Destroyed 
 Illusion. — Is the World Infinite ? — Surface Creatures and Shadow Rambles. 
 — What is the Beyond ? — Action at a Distance. — Ideas of Multi-dimensional 
 Regions. — Hypnotism. — Recollections of Zollner. — Science and Dogma. — The 
 Trial of Galilei. 
 
 A CONVERSATION held during April 1920 destroyed 
 an illusion which had become dear to me. 
 It concerned the fantastic figure, ** Lumen/' con- 
 ceived as an actual human being, imagined as endowed with 
 an extraordinary power of motion and keenness of sight. Mr. 
 Lumen is supposed to be the invention of the astronomer 
 Flammarion, who produced him in the retort of fancy, as Faust 
 produced Homunculus, to use him to prove the possibihty of 
 very remarkable happenings, in particular, the reversal of 
 Time. 
 
 Einstein declared outright : " Firstly, Lumen is not due 
 to Flammarion, who has derived him from other sources ; and 
 secondly, Lumen can in no way be used as a means of proving 
 things." 
 
 MoszKOWSKi : ** It is at least very interesting to operate 
 with him. Lumen is supposed to have a velocity greater than 
 that of light. Let us assume this as given, then the rest follows 
 quite logically. If, for example, he leaves the earth on the day 
 
 of a great event, such as the battle of Waterloo, and May 
 
 I trace out this example, at the risk of tiring you ? " 
 
 Einstein : Do repeat it, and act as if you were telling some- 
 thing entirely new. It is clear that the Lumen-story gives 
 you great amusement, so please talk quite freely. But I can- 
 not forgo the privilege of showing later how the whole adven- 
 ture and its consequences must be demolished. 
 
 M. : Well then, the person. Lumen, sets off at the end of 
 the battle of Waterloo to make an excursion into space with a 
 
 115 
 
116 EINSTEIN THE SEARCHER 
 
 speed of 250,000 miles per second. He thus catches up all the 
 light -rays that left the field of battle and moved in his direction. 
 After an hour he will already have attained a lead of about 
 twenty minutes. This lead will be gradually increased, so that 
 at the end of the second day he will no longer be seeing the 
 end of the battle, but the beginning. What has Lumen been 
 seeing in the meantime ? Clearly he has been observing events 
 happening in the reverse direction, as in the case of a cinemato- 
 graph which is exhibiting pictures backwards. He saw the pro- 
 jectiles leaving the objects they had struck, and returning into 
 the mouths of the cannon. He saw the dead come to Hfe, arise, 
 and arrange themselves into battahon order. He would thus 
 arrive at an exactly opposite view of the passing of time, for 
 what he observes is as much his experience as what we observe 
 is ours. If he had seen all the battles of history and, in fact, 
 all events happening in the reverse order, then in his mind 
 " before " and " after " would be interchanged. That is, he 
 would experience time backwards ; what are causes to us 
 would be effects to him, and our effects would be his causes ; 
 antecedents and consequents would change places, and he 
 would arrive at a causality diametrically opposite to our 
 own. He would be quite as justified in adopting his view of 
 the happening of things, according to his experiences, and of 
 the causal nexus as it appears to him, as we are justified in 
 adopting ours. 
 
 Einstein : And the whole story is mere humbug, absurd, 
 and based on false premises, leading to entirely false con- 
 clusions. 
 
 M. : But it is only to be taken as an imaginary experiment 
 that plays with fantastic impossibilities to direct our ideas on 
 to the relativity of time by a striking illustration. Did not 
 Henri Poincar6 adduce this extreme example to discuss the 
 " reversal " of time ? 
 
 Einstein : You may rest assured that Poincar^, even if he 
 used this example as an entertaining digression in his lectures, 
 took the same view of Lumen as I do. It is not an imaginary 
 experiment : it is a farce, or, to express it more bluntly, it is 
 a mere swindle ! These experiences and topsy-turvy per- 
 ceptions have just as little to do with the relativity of time, 
 such as it is taught by the new machanics, as have the personal 
 
OF DIFFERENT WORLDS 117 
 
 sensations of a man, to whom time seems long or short accord- 
 ing as he experiences pain or pleasure, amusement or boredom. 
 For, in this case, at least the subjective sensation is a reahty, 
 whereas Lumen cannot have reality because his existence is 
 based on nonsense. Lumen is to have a speed greater than 
 that of light. This is not only an impossible, but a fooHsh 
 assumption, because the theory of relativity has shown that 
 the velocity of Ught cannot be exceeded. However great the 
 accelerating force may be, and for however long it may act, it 
 cannot cause this Hmit to be transcended. Lumen is supposed 
 to be equipped with the organ of sight, that is, he is supposed 
 to have a corporal existence. But the mass of a body be- 
 comes infinitely great when it reaches the velocity of hght, so 
 that it is quite absurd to go beyond this stage. It is admissible 
 to operate with impossibiUties in imagination, that is, with 
 things that contradict our practical experience, but not with 
 absolute nonsense. That is why the other adventure of Lumen, 
 in which he jumps to the moon, is also an absurdity. In this, 
 he is supposed to leap with a speed greater than Ught, and, 
 when he reaches the moon, to turn round instantaneously, 
 with the result that he sees himself jumping from the moon to 
 the earth backwards ! This jump is logically meaningless ; 
 and if we try to make deductions of an optical nature from 
 such a nonsensical assumption, we deceive ourselves. 
 
 M. : Nevertheless, I should claim extenuating circum- 
 stances for this case on the ground that I am enUsting the 
 help of the conception of impossibiUty. A journey even at 
 a speed of only looo miles per second is impossible for a man 
 or a homuncT^lus. 
 
 Einstein : Yes, according to our experience, if we measure 
 it against facts. We cannot state definitely that a journey 
 into the imiverse at an enormous yet Hmited velocity is abso- 
 lutely impossible. Within the indicated bounds every play of 
 thought that is argued correctly is allowable. 
 
 M. : Now, suppose that I strip Lumen of all bodily organs 
 and take him as being a pure creature of thought, entirely 
 without substance. A velocity greater than that of light 
 can be imagined, even if it cannot be reahzed physically. If, 
 for example, we think of a Ught house with a revolving Ught, 
 and consider a beam of Ught about 600 miles long, which rotates 
 
118 EINSTEIN THE SEARCHER 
 
 200 times per second. Then we could represent to ourselves 
 that the light at the circumference of this beam travels with a 
 speed of nearly 760,000 miles per second. 
 
 Einstein : As for that, I can give you a much better ex- 
 ample of the same thing. We need only imagine that the 
 earth is poised in space, motionless, and non-rotating. This 
 is physically admissible. Then the most distant stars, as 
 judged by us, would describe their paths with almost un- 
 limited velocities. But this projects us right out of the 
 world of reahty into a pure fiction of thought, which, if 
 followed to its conclusion, leads to the most degenerate form 
 of imagination, namely, to pathological individuahsm. It is 
 in these realms of thought that such perversities as the 
 reversal of time and causality occur. 
 
 M. : Dreams, too, are confined to the individual. Reality 
 constrains all human beings to exist in one and the same world, 
 whereas, in dreams, each one has his own world with a different 
 kind of causahty. Nevertheless, dreams are a positive experi- 
 ence, and signify a reahty for the dreamer. Even for waking 
 reality it would be easy to construct cases in which the causal re- 
 lationship is shattered. Suppose a person who has grown up in 
 a confined retreat, such as Kaspar Hauser, looks in a mirror for 
 the first time in his life. As he knows nothing of the pheno- 
 mena of optical reflexion, he sees in it a new, objective world 
 that gives a shock to, or even subverts, his own idea of causality 
 in so far as it may have become developed in him. Lumen sees 
 himself jump backwards, whereas Kaspar Hauser sees himself 
 performing gestures on the wrong side of his body ; should it 
 not be possible to draw a reasonable parallel between these two 
 cases ? 
 
 Einstein : Quite impossible. However you set about it, 
 your Lumen will inevitably come to grief on the conception of 
 time. Time, denoted in physical expressions by the symbol 
 " t," may, indeed, be given a negative value in these equations, 
 so that an event may be calculated in the reverse direction. 
 ^ But then we are dealing with pure matters of calculation, and 
 in this case we must not allow ourselves to be drawn into 
 the erroneous belief that time itself may travel negatively, 
 that is, retrogressively. This is the root of the misapprehension : 
 that what is allowable and indeed necessary in calculations 
 
OF DIFFERENT WORLDS 119 
 
 is confused with what may be thought possible in Reality.* 
 Whoever seeks to derive new knowledge from the excursions 
 of a creature Uke Lumen into space, confuses the time of an 
 experience with the time of the objective event ; but the 
 former can have a definite meaning only if it is founded on 
 a proper causal relation of space and time. In the above 
 imaginary experiment the order of the experiences in time is 
 the reverse of that of the events. And as far as causality is 
 concerned, it is a scientific conception that relates only to 
 events ordered in space and time, and not to experiences. In 
 brief, the experiments with Lumen are swindles. 
 
 M. : I must resign myself to giving up these illusions. I 
 must frankly confess that I do so with a certain sadness, for 
 such bold flights of constructive fancy exert a powerful attrac- 
 tion on me. At one time I was near outdoing Lumen by 
 assuming a Super-Lumen, who was to traverse aU worlds at 
 once with infinite velocity. He would then be in a position to 
 take a survey of the whole of universal history at a single 
 glance. From the nearest star, Alpha Centauri, he would 
 see the earth as it was four years ago ; from the Pole Star, as 
 it was forty years ago ; and from the boundary of the Milky 
 Way, as it was four thousand years ago. At the same moment 
 he could choose a point of observation that would enable him 
 to see the First Crusade, the Siege of Troy, the Flood, and 
 also the events of the present day simultaneously. 
 
 Einstein : And this flight of thought, which, by the way, 
 has been indulged in repeatedly by others too, has much more 
 sense in it than the former one, because you may make an 
 abstraction which disregards speed cdtogether. It is only a 
 limiting case of reflection. 
 
 M. : I should Hke to touch on other Hmiting cases, in 
 particular two that I find it impossible to interpret. Lotze 
 mentions them in his Logic. The first concerns the infinitely 
 long lever whose fulcrum, or turning-point, is at the confines 
 of the universe. According to the Laws of Levers, a mass of 
 
 * Perhaps an analogy will serve to make this clear. Suppose that a certain 
 quantity of some foodstuff is consumed by ^(^ head of population. The 
 false inference would be that a population is possible which has ^ heads ! 
 In the same way the statistics may be quite correct in arriving at the figure | 
 suicides, but if we leave the realms of calculation, then the ^ suicide loses its 
 meaning entirely. 
 
120 EINSTEIN THE SEARCHER 
 
 magnitude zero will suffice to keep in equilibrium at the end 
 of the other lever-arm any weight, no matter whether it is 
 a million times heavier than the earth. Our imaginations 
 cannot even picture this. Yet I cannot feel satisfied with the 
 mere explanation that it is an exceptional case, an extension 
 of a general law to a case in which it is no longer appUcable. 
 The second example is still more perplexing because it does 
 not require a journey into other worlds, but leads us into in- 
 conceivable consequences even if we remain on the earth. 
 Lotze considers this second limiting case easier ; to me it 
 seems more difi&cult. It is this : The force that a wedge exerts 
 is inversely proportional to its thickness. If it is infinitely 
 thin, this formula gives an infinitely great result, whereas, 
 actually, the force exerted is nil. This very thin wedge, trans- 
 formed finally into a geometrical plane, should be able to split 
 in twain any wooden or even steel block. And now, consider 
 a special arrangement of this wedge in which it is resting with 
 its extremely sharp edge vertically downwards, whereas at the 
 top it broadens to a Httle ledge which supports a weight. We 
 then get the incredible result that this wedge, which can be 
 imagined concretely, should be able to cut through the whole 
 earth with its extremely fine edge, if placed on some base. 
 Where is the fallacy in this case ? 
 
 Einstein : The mechanical facts have not been taken 
 suJB&ciently into consideration. — He illustrated his further 
 remarks by drawing a few strokes with his pen, and proved 
 from his diagram that a wedge of this sort would be able to 
 perform what I assumed, only if the base on which it is placed 
 is composed of separate laminae. Otherwise the assumption 
 that the force is infinitely great would be erroneous. 
 
 After this digression to a limiting case on the earth we 
 returned to more general problems, and the question of the 
 finitude or infinitude of the universe. Shortly before, Einstein 
 had given an address to the BerHn Academy on this point, 
 involving difficult calculations, and I hoped to hear from him 
 an easy explanation at least in general terms. 
 
 It is one of the ultimate problems. Whoever talks of the 
 limits of the world endeavours also to mark off the bounds 
 of the understanding. The average person, at first sight, 
 
OF DIFFERENT WORLDS 121 
 
 almost always decides in favour of an infinite universe, on the 
 ground that a finite world is inconceivable. He argues that, if 
 it were considered finite, we should immediately be confronted 
 with the question : What lies beyond the finite boundary ? 
 Something must be present, even if it is only empty space. 
 This brings us into an inevitable conflict with the first of Kant's 
 *' antinomies," with the thesis and antithesis, from which there 
 is no escape. What is the meaning of the fact that the appre- 
 hensive understanding seeks refuge in ** Infinity " ? It signifies 
 that he gets entangled in the folds of a negative conception, 
 that furnishes him with no explanation at all, and expresses 
 merely that his first assumption of finitude cannot be thought 
 out to its conclusion. 
 
 Besides this, a second disturbing question arises. Is there 
 a finite or infinite number of stellar bodies ? If this question 
 refers to an assumed infinite space, even if such space is in- 
 conceivable, then there are two possible answers. For it 
 would be possible to imagine a finite number of stars even if 
 ' no hmit could be found for space. 
 
 Whereas the general question of space in the universe 
 belongs exclusively to speculative philosophy, the star>question 
 is not purely metaphysical, but is physical, too, and has accord- 
 ingly been treated by physicists. The great astronomer 
 Herschel imagined he could solve it by means of optical prin- 
 .ciples, and he arrived at the conclusion that the number of 
 heavenly bodies must be finite, as otherwise the aspect of 
 the starry firmament, from the point of view of illumination, 
 would be entirely different. But this proof did not estabUsh 
 itself among scientists, for the number of stars of the type of 
 the sun might be finite, whilst there was an infinite number 
 of dark stars. 
 
 A further question presented itself : Would it be possible 
 for a definite part of the heavens (say, that north of the ecUptic) 
 to contain an infinite number of stars, whilst other parts con- 
 tained only a finite number ? At first this sounds very extra- 
 ordinary, but it is by no means unreasonable, as a concrete 
 example will show : If, on a scale of temperature, we count the 
 degrees of heat from a certain point, then they stretch ap- 
 parently to infinity in one direction, whereas they extend 
 only to — 273° (Centigrade) in the other direction, that is, to the 
 
122 EINSTEIN THE SEARCHER 
 
 absolute zero. Thus we can imagine an arrangement which 
 stretches to infinity only in one direction. 
 
 To get an insight into the discussion by Einstein which is 
 about to follow, we must first dispose of a certain arbitrariness 
 of language, lying in the customary indiscriminate use of the 
 terms, infinite, immeasurable, and unbounded. Suppose we 
 have a globe about one foot in diameter, the surface of which 
 is inhabited by extremely small, ultramicroscopic creatures 
 that can move about freely and can think. The surface of the 
 sphere constitutes the world of the micro-men, and he has a 
 very good reason for considering it infinite, for, however far 
 and in whatever direction he may move, he never encounters 
 a boundary. But we, who live in our space, look on to this 
 spherical surface, and recognize that his judgment is erroneous. 
 To us his spherical world seems decidedly finite and quite 
 measurable, although it has no determinable beginning and no 
 end, and thus must appear unbounded to the micro-man. In 
 fact, we ourselves may regard it as boundless, if we can succeed 
 in forming an abstraction that leaves out of account its limita- 
 tions in our own space. 
 
 Now, it might occur to a particularly inteUigent micro- 
 being to undertake a voyage for the purpose of making measure- 
 ments. He carefully marks his point of departure, walks 
 straight ahead in a certain direction, describing a circle on his 
 sphere — a circle which he will necessarily regard as a straight 
 line. He continues ever onwards in the firm conviction that 
 he is getting farther and farther away from his starting-point. 
 Suddenly, he discovers that he has reached it again. He dis- 
 covers, by the mark he made, that he has not been describing 
 a straight line, but a line that merges into itself. 
 
 The micro-professor would be compelled to declare : Our 
 world, the only one known to me, is not infinite, although in a 
 certain sense boundless. Moreover, it is not immeasurable, 
 since it can be measured in at least one direction by the number 
 of steps I have walked. From this we may infer that our former 
 geometrical view was either wrong or incomplete, and that, in 
 order to understand our world properly, we must build up a 
 new geometry. 
 
 We may assume that the majority of the remaining micro- 
 inhabitants would at first protest strongly against this decision. 
 
OF DIFFERENT WORLDS 128 
 
 The idea that a hne, which appears to them to be pointing 
 always in the same direction, is curved, seems to them in- 
 conceivable and absurd. They would only gradually overcome 
 their scruples of thought by getting an insight into a newly 
 developed geometry that makes clear to them for the first time 
 the conception of a sphere. 
 
 In our world of space, which includes all stars, we are the 
 micro-inhabitants. We have been bom with, or have in- 
 herited, the idea of a straight and ever-advancing path in 
 space, and we become filled with the utmost astonishment if 
 some one asks us to beheve that if we undertake a voyage in 
 one direction out into the universe, beyond Sirius and a million 
 times farther, we should finally arrive at our starting-point 
 again, although we had not changed our direction. But the 
 macro-being, who belongs to a universe of higher dimensions 
 and who looks on our world as we looked on the above spherical 
 world one foot in diameter, sees the narrowness of our view. 
 We, too, are in a position to rise above this narrow view by 
 means of a theory founded on our experience, which will lead 
 us to an extended world-geometry, just as the micro-professor 
 used his experience to extend his theory of the circle to include 
 the conception of a sphere. 
 
 After these preliminary remarks we shall endeavour to get 
 an insight into Einstein's reasoning, not in the form in which 
 it was originally presented (in the Report of the Proceedings of 
 the Berhn Academy of Science of 8th February 1917), but in a 
 very easy description which was given to me during a conversa- 
 tion. Here, too, I shall try to preserve the sense of Einstein's 
 remarks without binding myself strictly to his words. For 
 although I am indebted to him for his efforts to avoid difi&cult 
 points, yet the aim of this book is, if possible, to make the 
 explanation still easier. Any lack of accuracy arising from 
 this last simpUfication is to be debited to me. The new form 
 of representing the argument, which is as important as it is 
 fascinating, is, of course, due to Einstein. 
 
 The final result stated by Einstein was : The universe, both 
 as regards extent and mass, has finite limits and can be 
 measured. If anyone asks whether this can be pictured, I shaD 
 not deprive him of the hope. All that is required is a power 
 of imagination that is great enough to follow a pictorial de- 
 
124 EINSTEIN THE SEARCHER 
 
 scription and that can take up the right attitude towards a sort 
 of figurative representation. 
 
 Let us again imagine a sphere of modest dimensions with 
 its two-dimensional surface. We are concerned only with 
 the latter, and not with the cubical content. The sphere is to 
 be considered as resting on an absolutely plane white table of 
 unlimited extent in all directions. The sphere touches the 
 table at a single point which we shall call its South Pole ; 
 on the top side directly opposite, we have the North Pole. 
 To simplify matters we may make a sketch on paper of a 
 vertical section through the centre of the sphere. This profile- 
 picture will show us the sphere as a circle, and the white 
 table as a straight line ; the line joining the two poles is the 
 axis of the globe, and the sectional circle is a meridian. 
 
 Let us further suppose a creature (resembhng, say, a lady- 
 bird in shape) having length and breadth, but no thickness, to 
 crawl along this meridian. Although it has no thickness, we 
 shall imagine it to have one property of a solid body, that of 
 being opaque, so that it can throw a shadow if properly illu- 
 minated. We assume the globe itself to be transparent. 
 At the North Pole we suppose a very strong point-source of 
 light, a little electric lamp, that sends out rays freely in all 
 directions. 
 
 The insect begins its journey at the South Pole and sets 
 out along the meridian to reach the North Pole. It is illu- 
 minated by the lamp all the way, so that it continually throws 
 a shadow on the white table. The shadow moves along the 
 table farther and farther from the South Pole, in proportion 
 as the insect moves up the meridian, with the difference that 
 while the insect is describing an arc of a circle, its shadow 
 moves along a straight line. The position of the shadow can 
 be determined at any moment by drawing the straight line 
 connecting the lamp to the insect, and producing it to meet 
 the white surface of the table ; the point of intersection is the 
 projection of the insect on the plane. 
 
 At the beginning of the excursion the shadow is exactly as 
 large as the flat insect itself, if we assume that its dimensions 
 are negligible compared with the surface of the sphere, for 
 it will then coincide with its own shadow. But when the insect 
 crawls upwards, its shadow will increase, because of the 
 
OF DIFFERENT WORLDS 125 
 
 shortened distance between the insect and the lamp, and because 
 the points of projection on the table separate more and more 
 as their distances from their corresponding points on the sphere 
 become greater. There is thus a twofold increase. The 
 shadows move away more and more rapidly, and at the same 
 time increase in size. 
 
 When the insect gets very near the North Pole, its shadow, 
 now of enormous dimensions, has moved to a very great dis- 
 tance ; and when finally it reaches the Pole, its shadow 
 becomes infinitely great and thus stretches to infinity. 
 
 But let the insect wander on along the meridian, past the 
 North Pole, down towards the South. At the moment when it 
 passes the upper Pole its shadow jumps from the right side to 
 the left. Its shadow now emerges from an infinite distance to 
 the left, and, instead of being infinite size, again becomes finite 
 in dimensions as it approaches. It contracts as it approaches, 
 and, in short, the same process as occurred during the first 
 half of the journey now occurs in the reverse order. 
 
 [If we fix on the critical moment of the jump from the right 
 to the left, that is, from plus infinity to minus infinity, we may 
 encounter difiiculties. For the surface-creature pursues its 
 way without interruption and continuously, and we experience 
 a wish to ascribe to it a shadow-path that is also unbroken and 
 continuous. This is possible only if we assume the two points 
 at infinity to be connected, that is, if we consider them identi- 
 cal. This assumption will seem more natural if we reason as 
 follows. In the profile-picture the table is represented as a 
 straight line, and it is along this fine that the shadow travels. 
 We may regard this line as an infinitely great circle, for an 
 infinitely great circle has zero curvature, just as the straight 
 line, from which it is therefore indistinguishable. The in- 
 finitely great circle has, however, only one point situated at an 
 infinite distance, that is, it associates together the two apparent 
 points at infinity of the straight fine with which we identify 
 it. Accordingly, we preserve the continuity of the shadow- 
 journey, too. Einstein considers it allowable to say that the 
 right and the left portion each represent a half of the infinite 
 projection, which becomes complete only when the two ends 
 are joined.] 
 
 Now we must be prepared for an effort of thought which 
 
126 EINSTEIN THE SEARCHER 
 
 will need considerable help from our imaginations. Firstly, 
 instead of one surface-creature, we shall suppose several crawl- 
 ing about on different meridians, so that a series of shadows 
 will be moving about along straight Hues radiating from the 
 South Pole. Next, let us imagine the whole picture to have 
 its dimensions increased by one, that is, we transform the 
 plane-picture into a space model. The phenomena are to 
 remain the same, except that they are to be strengthened by 
 one dimension, surface conditions becoming space conditions, 
 and surfaces becoming solids. 
 
 What we now see are actual insects with round bodies (if 
 we retain our original type of creatures), or, since there is no 
 restriction as to their size — the shadows have assumed all 
 possible sizes — we may assume any solid bodies whatsoever, 
 stars or even star-systems. Their motions take place in ex- 
 actly the same way as those of the shadows previously thrown 
 by the flat bodies. 
 
 This means that, if a stellar body moves, its size increases 
 until it reaches the spherical boundary of space, where it 
 becomes infinitely great, and, at the same moment, passes 
 from plus infinity to minus infinity, that is, it enters the uni- 
 verse from the opposite direction ; then, if it continues moving 
 in its original direction (as it has been doing all along), it 
 gradually becomes smaller in size until, finally, it reaches its 
 original position and its original size. If we suppose the body 
 to be endowed with the power of sensation, it would not be 
 able to observe its own changes of size, since all its scale- 
 measures would be altered in the same proportion. This 
 whole complex of phenomena would still be taking place in an 
 infinite world of space, but, according to the General Theory 
 of Relativity, the geometry that is vaUd in this world would 
 no longer be that of EucHd ; it is replaced by a system of 
 laws that arise from physics as a geometric necessity. In this 
 new geometry, a circle described with unit radius is a little 
 smaller than it would be in Euclidean geometry, with the 
 result that the greatest conceivable circle in this world cannot 
 assume an infinite size. 
 
 Thus we have to imagine that our soHd bodies, say stars, 
 arrive at a point in their travels which we may term only 
 "enormously distant." If we call the directions right and 
 
OF DIFFERENT WORLDS 127 
 
 left instead of positive and negative, then the process reduces 
 itself to this : the moving body reaches the point, which is 
 enormously distant on the right, and which is identical with 
 the point enormously distant on the left ; this means that 
 the body never moves out of the space continuum of this 
 world, but returns to its initial point of departure even when 
 it moves ever onward in what is apparently a straight line. 
 It moves in a " warped " space. 
 
 Einstein has succeeded in finding an approximate value 
 for this non-infinite universe, from the fact that there is a 
 determinable gravitational constant. In the constitution of 
 the universe it denotes the same for the mass-relationships of 
 the earth as the gravitational constant of the earth denotes for 
 us, namely, the quantity from which we can calculate the final 
 velocity attained by a freely falUng body during a unit of 
 time. He also assumes a probable average for the density of 
 distribution of matter in the universe, by supposing that it is 
 about the same as that of the Milky Way. On this basis 
 Einstein has arrived at the following result by calculation : 
 
 The whole universe has a diameter of loo million Hght- 
 years, in round numbers. That amounts to about 700 triUion 
 miles. 
 
 M. : Does this follow from the discussion you entered on 
 just now ? 
 
 Einstein : It follows from the mathematical calcula- 
 tions which I presented in " Cosmological Considerations arising 
 from the General Theory of Relativity," in which the figure I 
 have just quoted is not given. The exact figure is a minor 
 question. What is important is to recognize that the imi verse 
 may be regarded as a closed continuum as far as distance- 
 measurements are concerned. Another point, too, must not 
 be forgotten. If, in deference to your wish, I used an easy 
 illustration, this must not be regarded otherwise than as an 
 improvised bridge to assist the imagination. 
 
 M. : Nevertheless, it will be very welcome to many, who 
 are unable to grasp the difficult Cosmological Considerations. 
 The number that you mention is overwhelming in the extreme. 
 Indeed, it seems to me that a diameter of 100 milUon fight - 
 years suggests an infinitely great distance more than the word 
 " infinity " itself, mentioned per definitionem, which conveys 
 
128 EINSTEIN THE SEARCHER 
 
 nothing to the ordinary mind. It calls up a regular carnival 
 of numbers, particularly in those to whom the immense number 
 alone gives a certain pleasure. But you were going to give me 
 the number expressing the mass, too ? " 
 
 And then I learned that the weight of the whole universe, 
 expressed in grammes, was lo multiplied by itself 54 times, 
 that is 10^* (453 grammes = I lb., roughly). This seems 
 rather disappointing at first, but assumes a different aspect 
 when we represent to ourselves what this figure signifies. It 
 means that the weight of the universe in kilogrammes is high 
 in the octillions. The earth itself weighs six quadrilUon kilo- 
 grammes, hence the weight of the Einstein universe bears 
 the same relation to the weight of the whole earth as the latter 
 bears to a kilogramme. Again, the earth's weight to that of 
 the sun is as i is to 324,000. Hence we should have to take at 
 least a trillion, that is, a milliard times a milliard, suns to get 
 the weight of the universe. And as far as the linear extent is 
 concerned, let us consider the most distant stars of the Milky 
 Way, which are at an inconceivable distance, expressible only 
 in light-years. If we place 10,000 such Milky Ways end to 
 end we shall arrive at this diameter of the universe, which, 
 accordingly, will have a cubical content a thousand milliard 
 times greater than the region accessible to astronomical 
 observation. 
 
 Thus we have a very spacious universe. Yet it is not 
 spacious enough to satisfy all the demands that a mathe- 
 matician interested in permutations and combinations might 
 make. One of such combinations is exemplified in the so- 
 called Universal Book, that originated in an imaginary 
 experiment of Leibniz. If we picture to ourselves the sum- 
 total of all books that can be printed by making all possible 
 arrangements and successions of our letters, each book differ- 
 ing from any other even if only in one symbol, then, together, 
 they must contain all that can be expressed in sense and non- 
 sense, and everything that is ever reahzable actually or in 
 dreams. Hence, among other things, they would include all 
 world-history, all literature, and all science, even from the 
 beginning of the world to the end. If we agree to the con- 
 vention of operating with 100 different printed signs (letters, 
 figures, stops, spacings, etc.), and of allowing each such book a 
 
OF DIFFERENT WORLDS 129 
 
 million paces for signs, so that each book will still be of a handy 
 size, then the number of these books would amount to exactly 
 10 to the two-miUionth power, or, in figures, i.e. zo^'^^'^^. 
 
 This fully exhaustive universal library containing all 
 wisdom would consist of so many volumes that it could not be 
 contained in a case of the size of the entire stellar universe. 
 And, unhappily, it must be added that the closed universe, 
 just described by Einstein and having a diameter of a hundred 
 million light-years would be much too small to contain this 
 library. 
 
 " Nevertheless," said I, " your universe pictures something 
 inconceivably great ; one might call it an infinity expressed 
 in figures. For in your world there still remains one property 
 of infinity, namely, that it imposes no limitations on motion of 
 any kind. On the other hand, the figures proclaim a Umited 
 measure in the mathematical sense, however great this measure 
 may be. This calls up the old restlessness of mind, due to 
 the persistent question : What Hes beyond ? The absolute 
 Nothing ? Or is it a something which yet does not occupy 
 space ? Descartes and many other great thinkers have never 
 overcome this difficulty, and have always afiirmed that a 
 closed world is impossible. How, then, is the average person 
 to reconcile himself with the dimensions you have estab- 
 Hshed ? " 
 
 Einstein gave an answer which, it seemed to me, offered a 
 last escape to apprehensive minds. "It is possible," so he 
 said, " that other universes exist independently of our own." 
 
 That is to say, it will never be possible to trace a connexion 
 between them. Even after an eternity of observation, calcula- 
 tion, and theoretical investigation, no glimpse or knowledge 
 of any of these ultra-worlds will ever enter our consciousness. 
 " Imagine human creatures to be two-dimensional surface- 
 creatures," he added, '* and that they Uve on a plane of in- 
 definite extent. Suppose that they have organs, instruments, 
 and mental attitude adapted strictly to this two-dimensional 
 existence. Then, at most, they would be able to find out all 
 the phenomena and relationships that objectify themselves in 
 this plane. They would then have an absolutely perfect science 
 of two dimensions, the fullest knowledge of their cosmos. 
 Independent of this, there might be another cosmic plane with 
 9 
 
130 EINSTEIN THE SEARCHER 
 
 other phenomena and relationships, that is, a second analogous 
 universe. There would then be no means of constructing a 
 connexion between these two worlds, or even of suspecting 
 such a connexion. We are in just the same position as these 
 plane-inhabitants except that we have one dimension more. 
 It is possible, in fact, to a certain degree probable, that we 
 shall by means of astronomy discover new worlds far beyond 
 the limits of the region so far investigated, but no discovery 
 can ever lead us beyond the continuum described above, just 
 as little as a discoverer of the plane-world would ever succeed 
 in making discoveries beyond his own world. Thus we must 
 reckon with the finitude of our universe, and the question of 
 regions beyond it can be discussed no further, for it leads 
 only to imaginary possibilities for which science has not the 
 slightest use." 
 
 Einstein left me for a while to the tumult of ideas that he 
 had roused up in me. After I had overcome the first shock, I 
 sought to gain a haven in the idea that arose out of the first 
 shadow-argument, in which the spherical bodies occurred that 
 seek to escape towards infinity on the right but reappear, in- 
 stead, at enormous distances on the left. Has anyone ever had 
 presentiments of this kind of world ? Perhaps something of 
 the sort is to be found in earUer books of science ? If so, they 
 have escaped my notice. Yet, a passage of a poet occurs to 
 me. It is to be found in a volume by Heinrich von Kleist ; 
 it is a volume dealing only with earthly matter and bare of 
 astronomical ideas. Imagine a book the subject of which 
 is a puppet-show, containing, in the middle of it, a section 
 foreshadowing Einstein's universe ! Quite by chance Kleist 
 comes to speak of " the intersection of two lines which, after 
 passing through infinity, suddenly appear on the other side, 
 like a picture in a concave mirror, which moves away to infinity 
 and suddenly returns again and is quite close," and, quite in 
 accordance with our new cosmology, he declares : " Paradise 
 is locked and barred, and the cherub is behind us ; we must 
 make a voyage round the world, and see whether we cannot 
 discover an exit elsewhere at the other end perhaps." 
 
 Perhaps poets of the future will busy themselves with this 
 universei not lyrical poets, but descendants of Hesiod^ Lucretius, 
 
OF DIFFERENT WORLDS 131 
 
 or Rtickert. They will express in verse that Einstein's world 
 offers a source of consolation to tormented spirits which have 
 sickened of Kant's antinomies. For in this still almost im- 
 measurable world the fateful conception ** infinite " has been 
 made bearable for the first time. In a certain way it reHeves 
 us from what is quite inconceivable, yet into which we are 
 usually driven, and forms a bridge between the thesis " finite " 
 and the antithesis infinite. We are brought to a common 
 stream, in which both conceptions peacefully flow together. 
 There was no mention of this in our talk, and I had good reason 
 for being cautious about following out the theme along these 
 lines. I must not allow any doubts to arise on this point : 
 Einstein, himself, clings with unerring logic to the strict 
 mathematically defined conception of infinity, and allows 
 no compromise with the non-infinite. 
 
 When I, on some previous occasion, sought to lead him on 
 to a compromise, involving a transition-boundary, it availed 
 me nothing that I quoted Helmholtz to support the possibility 
 of such an operation : my effort came to an abrupt end. 
 
 In pursuing these considerations about the universe, we 
 arrived at things which, in ordinary language, are usually called 
 " occult." In connexion with this, these remarks ensued : 
 " I am, of course, far from trying to trace out a connexion 
 between the four-dimensionality that you estabUsh, Professor, 
 and the four-dimensionality of certain spiritistic pseudo- 
 philosophers, yet it suggests itself to me that in such occult 
 circles efforts will be made to derive advantage from the fact 
 that the same word is used in both cases. This is more than a 
 conjecture, indeed, for there are no misgivings among the 
 ignorant, and so we actually find the name Einstein quoted in 
 connexion with mediumistic experiments that are flavoured 
 with four-dimensionality." 
 
 " It will not be expected of me," said Einstein, " to enter 
 into discussion with ignoramuses and misinterpreters. Dis- 
 carding them, then, let us confine ourselves to a brief con- 
 sideration of the conception ' occult,' as this has played a part 
 in serious science. The chief example of this in history is 
 gravitation. Huyghens and Leibniz refused to accept gravita- 
 tion, for, so they said, according to Newton's view,^it is an 
 
132 EINSTEIN THE SEARCHER 
 
 action at a distance and hence belongs to the realm of the 
 occult. Like everything occult, it contradicts the causal 
 order in Nature. We must not regard Huyghens' and Leib- 
 niz's contradiction as being due to lack of perspicacity ; rather, 
 they objected on grounds which, as investigators, they had 
 every right to uphold. For, as far as our everyday experience 
 is concerned, every mutual influence of things in Nature occurs 
 only by direct contact, as by pressure or impact, or by chemical 
 action, as when a flame is lit. The fact that sound and Hght 
 apparently form exceptions is not usually felt as a contradiction 
 to the postulate of contact. The case of a magnet appears 
 much more striking because its effect asserts itself as a direct 
 manifestation of force. I must mention that when I, as a child, 
 made my first acquaintance with a compass — and this was 
 before I had ever seen a magnet — it created a sensation in me, 
 which I consider to have been a dominant factor in my hfe up 
 to the very present. There is, indeed, a fundamental difference 
 between pressure and impact on the one hand, and what we 
 hear and see on the other, even in everyday experience. In 
 the case of Hght and sound, something must be ' happening ' 
 continually, if the effect is to occur and continue. . , ." 
 
 " Yet another difference seems to enter here,'' I interposed. 
 " Is it possible to give a full explanation of gravitation by using 
 only the conceptions pressure and impact ? Perhaps * pressure 
 at a distance ' would not have seemed to contemporaries of 
 Newton as unintelligible as a 'tension or pull at a distance.' 
 It seems to me that it is particularly difficult to imagine a pull 
 or an attraction towards a distant object." 
 
 Einstein does not consider this difference considerable, and 
 regards it as possible to overcome it even in a manner which 
 can be directly pictured. " If the force is exerted by a corpus- 
 cular transmission," he explained, " we may imagine a ' force- 
 shadow ' into which the bombarding corpuscles cannot pene- 
 trate. Thus if an obstacle, which produces such a shadow, 
 becomes interposed between a body A and a body B, then there 
 will be a lesser pressure on the side of B facing A, and hence 
 B will experience a greater corpuscular pressure on the other 
 side, with the result that B will be forced in the direction of A, 
 and the observer would gain the impression of a pull from B 
 to A. Nowadays, when the theory of * fields of force ' domin- 
 
OF DIFFERENT WORLDS 183 
 
 ates our physical views, we need trouble just as little about 
 using corpuscular pressures and impacts as about the vortices 
 which Descartes once considered as the ultimate causes of the 
 motions of the heavenly bodies. The efforts of certain 
 reformers to reintroduce these vortices and whirlpools as 
 explanations must be regarded as futile.** 
 
 " Nevertheless," I answered, *' it seems admissible to say 
 that, ultimately, there is always an occult element in every 
 physical explanation, an absolutely final and elementary 
 something which we recognize as a principle, without conceaUng 
 from ourselves that we have reached the Umit of explanation, 
 and our knowledge avails no further. This brings me to 
 another question the discussion of which, as I clearly perceive, 
 leads us on to dangerous ground.'* 
 
 Einstein : Don't hesitate to say what is troubling you. 
 I cannot yet see what you are aiming at. 
 
 M. : I am referring to certain phenomena which are also 
 called *' occult " — with the object of discrediting them. They 
 may at times degenerate to hocus-pocus and fall into the cate- 
 gory of dubious arts. It seems to me, however, that scientists 
 have not always drawn the line with sufficient care, and that 
 they have been disposed to reject as humbug, without examina- 
 tion, everything inexplicable that dares to present itself in the 
 form of open display. 
 
 Einstein : In general, they will be in the right, for investi- 
 gators cannot be expected to occupy themselves with things 
 bolstered up by advertisement, and which are supposed to be 
 connected with some fabulous, occult regions. 
 
 M. : Nevertheless, in my opinion even among such displays 
 there sometimes occur phenomena which scientists should not 
 pass over with contempt. I, myself, have experienced such 
 cases, and have said to myself : There are stranger happenings 
 here 
 
 Einstein : — than are dreamt of in your philosophy, you 
 were about to say ? 
 
 M. : Exactly. These are things that in the guise of sensa- 
 tionalism often hide a physical truth well worthy of study. 
 
 Einstein : But you must not overlook the fact that in such 
 cases you have mostly played the part of an onlooker, and hence 
 were exposed to all possible manner of deception. You are 
 
134 EINSTEIN THE SEARCHER 
 
 baffled on all sides by undiscoverable tricks and by other 
 persons, whose collusion you do not suspect. This renders 
 an objective criticism impossible. 
 
 M. : This presumes that the performing artist is not entirely 
 isolated. It is possible to bring about conditions that posi- 
 tively eliminate all tricks from the very outset. 
 
 Einstein : If you have experienced any such cases, relate 
 them by all means. 
 
 M. : I shall be brief, and shall state only facts. . . . 
 
 Einstein : Or, expressed more accurately, only things 
 which seem to have been facts as far as you can trust to memory. 
 Well then, you think that you have grounds for saying that 
 you caught a glimpse of a mysterious world at that time. 
 
 M. : It is certainly long ago, more than thirty years. 
 Hansen, the freak, one of the most eminent of his profession, 
 was showing hypnotic and telepathic experiments that were 
 partly identical with experiments that the celebrated scientist 
 Charcot at Paris was performing for purposes of pathology. 
 
 Einstein : Well, then, why did you hesitate before ? These 
 experiments come under the head of science, and require no 
 occult veil to appear in the open. 
 
 M. : This touches the main issue. Hansen did not work 
 in the interests of science, but wished, above all, to earn money. 
 Nevertheless he had in his own way produced marvellous 
 results that were used later for scientific work. Unfortun- 
 ately in his case, owing to the fact that he cloaked it in occultism 
 at the outset, he was brusquely repudiated by scientists. The 
 result was that Hansen was condemned to a long period of 
 imprisonment in Dresden, thanks to the recommendation of 
 scientists who declared that the experiments were only possible 
 if deception was practised, and hence that Hansen was an 
 impostor who should be made harmless by being incarcerated. 
 
 Einstein : And how did you yourself seek to discover 
 whether his experiments were genuine ? 
 
 M. : Very easily and with absolute certainty. One of my 
 acquaintances, the wealthy race-horse owner, von Oelschlager, 
 had induced him by means of a high fee to experiment at his 
 country house, at some distance from BerUn, in the presence 
 of persons, not one of whom Hansen knew, and in the case of 
 whom there could be no question of secret collaboration. I can 
 
OF DIFFERENT WORLDS 185 
 
 assure you that everything succeeded without exception. A 
 single second was sufficient for him to communicate his will 
 to each subject of experiment. He operated Hke a super- 
 natural being on those present. 
 
 Einstein : I should hke to hear examples. 
 
 M. : Herx von Oelschlager introduced four jockeys, and 
 suggested a race in the great salon. Hansen placed them 
 astride over chairs, hypnotized them on the spot, described 
 the shape of the course, giving distances in kilometres, curves, 
 and even the value of the prizes. He then gave the signal 
 for starting. The jockeys immediately began treating their 
 chairs as race-horses, exhibiting all the signs of extreme 
 strain which accompany the actual ride. 
 
 Einstein : This is not yet a positive proof. The subjects 
 of experiment may have become cognizant of the fact that 
 they were to serve some eccentric display. Their acquiescence 
 in a prescribed part need by no means signify that they were 
 subjectively convinced of the genuineness of the affair. 
 
 M. : There could be not the shghtest doubt on this point. 
 After a few seconds perspiration was streaming over their 
 faces as a result of the exertion, a symptom that exhibits 
 itself only when the participants are convinced of the absolute 
 earnestness of their undertaking. All that gazed on this 
 baffling ride made the acquaintance of a grotesque reahty, 
 and were looking into a strange world of dreams, which trans- 
 formed wooden chairs into hving thoroughbreds. In the 
 course of his following experiments in the transference of his 
 will-power, Hansen experimented with an actress who was 
 famous at that time, and with whom he had no more acquaint- 
 ance than with the others. He again produced deep hypnosis, 
 and gave the order : I shall ask you various questions, all of 
 which you will be able to answer correctly, with one exception : 
 you will have forgotten your name. And so it happened. 
 In her trance the actress gave correct answers, until, when 
 the question, " What is your name ? " was asked, her own 
 name, Helene Odilon, had vanished from her memory. And 
 immediately afterwards, she told me herself that, in spite of 
 her state of coma, she had retained full consciousness, had 
 understood everything, and had been possessed of her memory 
 until it came to the critical moment when, in spite of extreme 
 
136 EINSTEIN THE SEARCHER 
 
 efforts, she could not recollect the words Helene Odilon. 
 But Hansen did not stop at dictating his thoughts to others, 
 he also transformed corporate things. By a single motion 
 of his hand he converted a stable-boy into a rigid block, 
 devoid of sensation. Never would I have thought such an 
 intense state of cramp possible. He placed the boy with 
 his feet and head alone resting on two supports, so that the 
 body itself was poised in space. He then stood on the body 
 with his whole weight, without the rigid body of the boy 
 bending even an inch. 
 
 Einstein : How did he, in all these cases, restore the 
 normal state ? 
 
 M. : Always by a single gesture, which, like everything 
 that he did, worked at lightning speed. I must admit that 
 his display became a little monotonous after a while, and 
 that his programme did not seem capable of much variation. 
 Things were different, however, in the case of a man who, 
 some years previously, had toured the world as an exponent 
 of occult phenomena, and to whom scientists will some time 
 in the future look back with regret. When he appeared, 
 most academicians took only sufficient notice of him to reject 
 him without having given him a trial. It was Henry Slade, 
 the American, who is not to be confused with other Slades 
 who appropriated his name in order to dupe people whose 
 insatiable curiosity was aroused. 
 
 Einstein : One might almost suppose that your genuine 
 Henry Slade served as a model for them. 
 
 M. : For certain reasons I regard this as out of the question, 
 mainly because the true Slade gave " demonstrations " only 
 occasionally, his chief object being to interest scientists. He, 
 himself, repeatedly asserted that he did not understand his 
 own achievements, and he unceasingly requested the super- 
 vision of professional physicists and physiologists, to whom 
 the unusual phases in his nature were to serve as objects of 
 study. The result was that people Hke Dubois-Reymond, 
 Helmholtz, and Virchow refused to see him, not to mention 
 experiment with him. 
 
 Einstein : These men cannot be reproached for acting in 
 this way. Slade was regarded as a representative of a four- 
 dimensional world in the spiritistic sense ; serious scientists 
 
OF DIFFERENT WORLDS 137 
 
 must avoid all humbug of this sort, since even slight interest 
 in it can easily be misinterpreted by the ignorant pubHc. 
 
 M. : Not every one was afraid of compromising himself. 
 After closed doors had greeted Slade in Berhn, he went to 
 Leipzig, where he became an object of study for one important 
 scientist. 
 
 Einstein : You are referring to Friedrich Zollner, who 
 undoubtedly had a reputation as an astrophysicist to preserve. 
 But he would have served his reputation better if he had not 
 entered into this adventure with the American spiritist. 
 
 M. : Perhaps there will some day be cause for a revision 
 of opinion on this point. The documents are extant, even if, 
 half forgotten, they are reposing in various Hbraries. A 
 renewed investigation of Zollner's Scientific Dissertations, 
 dating from 1878 to 1891, might lead to the judgment that 
 his ghostly interpretations are to be regarded as occult in 
 the worst sense, and yet one would marvel that a great scientist, 
 such as he was, should have felt himself at a complete loss 
 with his knowledge, so that he was forced to resort to abstruse 
 methods in order to escape from the mental confusion into 
 which Slade had plunged him. 
 
 Einstein : That merely shows that Slade, as a cunning 
 practician, siupassed him, and that Zollner did not succeed 
 in seeing through his machinations. 
 
 M. : This would lead one to assume that Slade knew more 
 physics than the Leipzig professor. For in a great number of 
 experiments Zollner himself had prescribed the conditions, 
 including all contrivances which made deception so much 
 the more unhkely, since Slade himself could not know what 
 Zollner's intentions were. It was a question of Electricity, 
 Magnetism, Optics including prepared conditions of polariza- 
 tion, involved Mechanics, in short, things that Zollner as 
 a professional physicist imderstood thoroughly, and which, 
 moreover, were controlled by others of his profession. Among 
 the latter was the celebrated professor of Electricity, Wilhelm 
 Weber, who, hke Zollner, found himself faced by phenomena 
 that were utterly incomprehensible to him. It would be a 
 profitable undertaking to bring these dissertations to hght 
 again, and it would easily be recognized that the things de- 
 scribed actually deal with scientific problems and have not 
 
138 EINSTEIN THE SEARCHER 
 
 the remotest connexion with tricks of magic. For example, 
 there is an account of an incredible anatomical feat. On 
 flour which had been placed carefully in a dish beforehand, 
 there suddenly appeared the imprint of a naked human foot, 
 whilst Slade was present at a certain distance, being fully 
 clothed and subject to careful scrutiny. The footprint 
 showed all the surface-details of the skin, as was confirmed by 
 authorities, just as only a left foot could produce them, but 
 not an artificial copy. 
 
 Einstein : And from this Zollner inferred the intervention 
 of supernatural beings ? He would have done better to 
 measure the dimensions of the foot. 
 
 M. : So he did — at once. A difference of four centimetres 
 between the length of Slade's foot and the copy was disclosed. 
 This riddle, like so many others, remained unexplained. I 
 must repeat that I am not in the slightest degree disposed 
 to assert that occult phenomena really occur, but am interested 
 only in seeing that they are investigated carefully by qualified 
 persons. 
 
 Einstein : Your remarks show that Leipzig scientists 
 did so at that time with no better result than that Zollner's 
 mental confusion became still greater. 
 
 M. : The conjecture remains that the Leipzig experiments, 
 abundant as they were, did not suffice. Allow me to ask a 
 direct question, Professor. Supposing another such agent of 
 miracles should appear, would you yourself feel impelled to 
 test him experimentally ? 
 
 Einstein : Your question is misdirected. I explained 
 above that I share the point of view taken up by Dubois- 
 Reymond and his colleagues. 
 
 M. : The following case may be conceived. A certain man, 
 X, might suddenly appear, who has control of a certain 
 natural force that has never before been investigated ; like 
 one who knew how to use electricity at a time when people 
 had never experienced any electrical phenomenon. He 
 would be able to give hundreds of demonstrations, all of which 
 we should relegate to the realm of inexplicable magic. We 
 should, for instance, be much astonished if he were to draw 
 sparks from a living person. Now, suppose two professors 
 express an opinion. Professor A declares the whole thing to 
 
OF DIFFERENT WORLDS 139 
 
 be a farce, and refuses to look into it at all. Professor B is 
 ready to investigate the achievements of X only if the latter 
 subjects himself from the beginning to all the physical condi- 
 tions that are to be determined beforehand. And suppose the 
 professor arranges liis conditions so that they make impossible 
 the occurrence of electrical phenomena. If, now, all scientists 
 were to behave hke A and B, the consequences would be very 
 depressing. For here was an important field of investigation, 
 which is cut off owing to the distrust or obstinacy of scientists, 
 who should have been the first to open it up. It is quite 
 irrelevant whether X had the character of a charlatan or not, 
 for behind his charlatanism there were facts which clamoured 
 for investigation. 
 
 Einstein : The most that I can grant is that your imagined 
 case does not lie outside the scope of possibility. Yet the 
 chance that there is such a ** natural force " hitherto undis- 
 covered by Man, that is, one that is a " secret force *' as far as 
 we are concerned, is so vanishingly small that it may be set 
 down as equal to impossible. I should refuse to take part in 
 any such practices, served up in the form of sensation, for one 
 reason that I should regret the waste of time, as there are 
 better things to do. It is a different matter if the mood takes 
 me to visit a variety entertainment, in order to derive amuse- 
 ment from such mystifications. For example, only yesterday 
 I was in a little theatre, in which, among diverse items, a 
 thought-reading woman was performing. She correctly guessed 
 the numbers 6i and 59 that I had in my mind. But let no 
 one mention this as a case of telepathic actions at a distance 
 or wireless communication between minds, for an intermediate 
 person, the manager, was present, and I had to whisper the 
 numbers to him. The distance to the stage was certainly 
 too great to allow the sound to be conveyed directly to an 
 audible degree. Hence there must have been a different, very 
 cunningly arranged code of signals, which eluded the notice 
 of people in the stalls. The process consists actually in an 
 extraordinary refinement of observation, which does not, 
 however, seem to me any more wonderful than the training 
 of a reckoner who extracts cubic roots mentally, or than the 
 practised muscles of a juggler all working in unison to enable 
 him to perform feats with twelve plates simultaneously. 
 
140 EINSTEIN THE SEARCHER 
 
 M. : It gives me enough satisfaction, Professor, that you 
 conceded me before a certain limited chance of finding a last 
 refuge in occultism. And even if you, yourself, as a representa- 
 tive of the most rigorous research of physical reality, refuse to 
 consider it, yet the fact that many others are drawn irresistibly 
 towards mysterious phenomena cannot be denied. Should 
 one feel shame on this account ? I beUeve that, in this matter, 
 we are touching on inner confessions that are quite independent 
 of the standard of the mind in which they are embedded. 
 Newton considered the key of the universe to be a personal 
 God, whereas Laplace proclaimed : Dieu — -je n'avais pas besoin 
 de cette hypothese : this contrast allows no inference to be drawn 
 as to their relative keenness of mind. And probably the same 
 may be said of the question whether there are other hidden 
 universes besides the one in which we Hve. In any case, those 
 who feel enthusiasm for such questions can quote in their sup- 
 port good names from the learned world. Immanuel Kant 
 occupied himself seriously and intensively with the wonders of 
 Swedenborg, Kepler practised Astrology, in which he had a 
 firm belief, Roger Bacon, Cardanus, Agrippa, Nostradamus, 
 van Helmont, Pascal, and, among the modem, Fechner, 
 Wallace, Crookes, are to be counted among the mystics. No 
 matter whether the views they held were theosophical, occult, 
 four-dimensional in the spiritistic sense, or coloured by any 
 other superstition ; they proclaimed that things that could 
 be rigorously proved were, alone, insufficient for them. Out of 
 presentiment and conjecture they constructed wings with which 
 to fly into regions extra naturam. This is how it happened that, 
 as the common folk could not find a place in science for many 
 extraordinary achievements, they assigned their authors to the 
 realm of magicians, as in the case of Paracelsus, Albertus 
 Magnus, Raimimdus Lullus, Sylvester II, who were regarded 
 as sorcerers. And this coin is still current : to Edison, of 
 our times, the term, " sorcerer of Menlo-Park," has become 
 attached. In the minds of the populace discovery and in- 
 vention, works of genius and supernatural phenomena, become 
 confused and indistinguishable ; it may even happen to you. 
 Professor, that your works will become invested with legend. 
 I should not like to conjure up what your fate would have been 
 if your theory of relativity had originated at the time of the 
 
OF DIFFERENT WORLDS 141 
 
 Inquisition. For the views put forward by Giordano Bruno 
 are mere child's play compared with your theory of the universe 
 as a quasi-spherical closed space of hyper-EucHdean character. 
 The tribunal of the Inquisition would not have imderstood 
 your differential equation, gravitational potentials, tensors, 
 and equivalence theory ; they would abruptly have declared 
 the whole theory to be a magical formula or a manifestation 
 of the devil, and would have honoured it and you with a 
 funeral pyre. 
 
 Einstein : This is clearly a slight exaggeration. Mathe- 
 matico-physical and astronomical works have never been 
 attacked by the Papal courts, but, on the contrary, have been 
 much encouraged by them down to the present day. This is 
 abundantly clear from the fact that we can set up a whole list 
 of Brothers of Orders, particularly Jesuits, who have made 
 eminent discoveries in natural science. From my personal 
 knowledge of you, I foresee that you will one day sketch a 
 fantastic trial, in which the new world-system will have to 
 defend itself against the Sanctum Officium, 
 
 M. : This would be a very grateful task, judged from the 
 literary point of view. What a splendid colouring could be 
 obtained by bringing these two worlds of thought into conflict 
 with one another, the Relative against the Absolute, which has 
 been estabUshed in tradition and dogma. But we need not 
 even call the historical fancy into action, for, actually, the 
 theory of the structure of the world is even now still at variance 
 with traditional ideas, that act with dogmatic violence. There 
 is no need to deny the fact that every person of education, who 
 makes the acquaintance of Lorentz's, Minkowski's, Einstein's 
 ideas for the first time, feels excited to offer contradictions, and 
 becomes involved in a tumult of pros and cons, and each one ex- 
 periences in himself the excitement of an inquisitorial tribunal. 
 The triumph of the new theory passes over the corpses of con- 
 ceptions that He at the cross-roads of thought and, long after, 
 retain a ghostly existence. Only very few of us are aware of 
 the further inner revolution that awaits us along the hne of 
 development of Einsteinian ideas ; we have only vague pre- 
 sentiments that whisper to us that the end of forms of thought 
 once considered as irrefragable is drawing nigh. When once 
 the principle of causaHty has been set on a relative base, and all 
 
142 EINSTEIN THE SEARCHER 
 
 " properties " have been resolved into occurrence, and all that 
 is three-dimensional has come to be recognized as an abstraction 
 from the four-dimensional world that is alone valid, then the 
 time will have come to arrange for the death procession of all 
 the philosophies that once served as the main pillars of thought. 
 
 A retrospect of the trials of Giordano Bruno and of Galileo 
 GaUlei offers certain parallels other than those usually discovered 
 by scholars. And if, to-day, we proclaim Einstein as the Galilei 
 of the twentieth century, it must be added that in character he 
 is fortunately a Bruno and not a GaHlei. For it is not true 
 that the latter came out of the persecution as a moral victor 
 with an eppur si muove, rather, in spite of the protection of 
 influential prelates and dignitaries, even of the entourage of 
 the Pope, he lacked courage and bowed his head, betraying 
 his science and denying himself as well as Copernicus. Are 
 we to picture how Einstein would have acted under similar 
 circumstances, even if they cannot recur again ? 
 
 Whoever has even an inkling of his character will entertain 
 no doubts. At that time, three hundred years ago, the materials 
 for a magnificent scene, " one world versus the other,'* lay ready. 
 Only one condition was wanting, the moral courage of the hero. 
 The lack of this one factor spoilt the final act for the history of 
 that time. The fine ethical feelings of later generations have 
 had to be propitiated by improvising a legend iridescent with 
 beautiful colours. 
 
m^^iS^nnt^SMT OF crVTL EN^BIH^SEFIP^ 
 BERKELEY. CALJTORNIA 
 
 CHAPTER VII 
 PROBLEMS 
 
 Questions of the Future. — Problem of Three Bodies. — Conception of 
 Approximation. — Object of Mechanics. — Simplicity of Description. — Limits 
 of Proof. — Reflections about the Circle. — From the History of Errors. — 
 Causalities. — Relativity on a Physiological Basis. — ^Physicists as Philosophers. 
 
 WE Spoke of the objects and problems of science in 
 general, and touched on certain recurrent questions 
 with which reputed men of science are confronted 
 from time to time, so that we may ascertain their opinions about 
 immediate as well as more remote aims, and about worthy 
 objects and those within reach. 
 
 " Such stimuh," said Einstein, " may be quite interesting 
 inasmuch as they sharpen the appetite of the pubhc for the 
 works of investigators, and give the latter the opportunity 
 of making wider circles acquainted with their plans. Yet 
 the value of their suggestions must not be overrated, when 
 they are directed at giving trustworthy information about the 
 future hues of development of science. Every scientist, in 
 working out his own research, gravitates to particular points 
 on the boundary which separates the known from the unknown, 
 and becomes inchned to take his particular perspective from 
 these points. It must not, however, be expected that these 
 individual aspects will form a complete picture, and will indicate 
 the only paths along which science can or will advance.'* 
 
 " May I suggest, Professor," I answered, *' that we select 
 certain answers that have been given to these reciurent 
 questions for discussion ? I have brought along a whole series 
 of them ; it would be of value to know what attitude you take 
 up towards some of the statements that have been made about 
 future possibihties." 
 
 Einstein acquiesced, and so I read out a number of ex- 
 pressions of opinion, given by eminent authorities, particu- 
 larly in natural science and mathematics. They came under 
 
 ua 
 
144 EINSTEIN THE SEARCHER 
 
 the heading, " The Future Revolution of Science.*' At the 
 outset we encountered arguments by Bailhaud, the director 
 of the Paris Observatory ; he dealt with the so-called " Problem 
 of Three Bodies/' and with " The Finitude or Infinitude of the 
 Universe." 
 
 Einstein elucidated these questions as follows. The cele- 
 brated Problem of Three Bodies is a special case of the general 
 problem of Many Bodies, the object of which is to discover the 
 exact paths of the heavenly bodies. If we suppose that the 
 planets and the comets are subject only to the attraction of 
 the central body, the sun, then their paths would be exactly 
 those given by Kepler's Laws — that is, they would move about 
 the central body, or, more precisely, about the common centre 
 of gravity in perfectly elliptical orbits. The same result would 
 happen if we regard the orbit of a moon to depend solely on 
 its parent planet. But this assumption is not in agreement 
 with reahty, since all the bodies of our system are also subject 
 to their mutual attraction depending on their masses and 
 distances. Consequently we have the so-called disturbances, 
 perturbations, and divergences from the ideal paths ; and the 
 problem of ascertaining these disturbances is essentially 
 identical with the Problem of Three Bodies. Regarded from 
 the point of view of pure mechanics, this problem may be 
 considered solved in so far as we are able to write down the 
 equations of motion. But, in addition to this purely 
 mechanical process, there is a mathematical problem which 
 has not been completely solved — ^that is to say, the integral 
 expressions that occur in it can be calculated only approxi- 
 mately. This makes no difference to the practical calculation, 
 since the degree of approximation, according to the present 
 methods, may be carried as far as we wish. The error may 
 be reduced to any desirable extent, so that it is probably wrong 
 to expect new revelations on this point from future upheavals 
 in physics. We read on and discovered that several of the 
 scientists mentioned did not stop at expecting all advances 
 of the future from pure theory. They had visions of an 
 optimum of happiness, to gain which the increase of know- 
 ledge alone did not suffice. Thus the celebrated Swedish astro- 
 physicist Svante Arrhenius had summarized his judgment in 
 a few lines : " After the stupendous progress that has been 
 
PROBLEMS 145 
 
 made in the physical and chemical sciences in recent times, 
 it seems to me that the moment has come for attacking the 
 most important problems of mankind with full success, namely, 
 those of biology, and in particular of the art of healing, with 
 the weapons that are furnished by the arsenal of the exact 
 sciences." And the mathematician, Emile Picard, Membre 
 de I'Academie, expressed himself in still more hopeful terms : 
 " There is no doubt but that the discoveries which the human 
 race is awaiting with impatience are those that are seeking to 
 eliminate sickness and the decrepitude of old age. Injections 
 giving immunity against all diseases, an elixir of life (une 
 eau de Jouvence) for persons of advancing age — these are the 
 discoveries that are longed for by every one. There are also 
 sciences that are to be termed ' moral,' from which we are 
 impatiently expecting that guidance which will diminish the 
 hate which seems to be increasing from day to day among 
 the nations. That would be a splendid discovery." 
 
 " These are, indeed, noble and inspiring words," said I. 
 " It shows how deeply rooted is the demand for ethical values 
 in human nature, when even a mathematician, whose intel- 
 lectual interests are directed primarily towards exact results, 
 ranks the discoveries of ethics above all others." 
 
 Einstein answered : " We must carefully distinguish 
 between what we wish for in general and what we have to 
 investigate as belonging to the world of knowledge. The 
 question under consideration is not one of wishes and feeUngs, 
 but was unmistakably aimed at the advances and revolutions 
 in the realm of science. It does not come within the scope 
 of science at all to make moral discoveries ! Its one aim is 
 rather the Truth. Ethics is a science about moral values, 
 but not a science to discover moral * truths.* Ethics, conceived 
 as a science in the usual way, can therefore serve to discover 
 or to promote truth only indirectly. To illustrate my point 
 of view I shall quote an example taken from a totally different 
 field ; it is merely to serve as an analogy. Let us consider 
 the game of chess. Its value and its meaning is not to be 
 sought in scientific factors, but in something entirely different, 
 in a struggle which takes place according to definite rules. 
 But even chess, inasmuch as it sharpens the intellect, may 
 exhibit an indirect value for promoting truth. It may, for 
 
 lO 
 
146 EINSTEIN THE SEARCHER 
 
 instance, suggest examples in permutations, which may con- 
 tain mathematical, that is, purely scientific, truths. I certainly 
 do not deny that there is an ethical factor in all genuine 
 sciences. For being occupied with things for the sake of 
 truth alone emancipates and ennobles the mind." 
 
 " This ennobhng effect,'* I interposed, " should surely show 
 itself in a moderation of the passions which were mentioned 
 in the above expression of opinion. With Picard we should 
 expect above all things to see a diminution in the feehngs of 
 hate between peoples, the tragic consequences of which we 
 have experienced." 
 
 Einstein smiled, and, with a touch of sarcasm, said, " Hate 
 is presumably a privilege of the * cultured,' who have the time 
 and the energy for it, and who are not the slaves of care." His 
 tone indicated clearly that he used the generic term " cultured " 
 to denote the PhiUstines of culture, its snobbish satellites, but 
 not those whose intensive work aimed at increasing and 
 deepening the fields of culture. In general he maintained his 
 view that it is an illusion to expect " discoveries " in the 
 realm of ethics, since every real discovery belonged alone to 
 the sphere of truth in which the division only into right and 
 wrong, not that into good and evil, holds good. 
 
 This led us to the old question of Pilate : What is Truth ? 
 In seeking an answer to this question Einstein first called 
 special attention to the conception of " approximation," 
 which plays a great part in the actual search for truth, inas- 
 much as every physical truth, expressed in measures and 
 numbers, always leaves some remainder, that marks its 
 distance from the unattainable truth of reality. This con- 
 ception, which manifests itself so prominently in the relation 
 of Einstein's own researches to the older, so-called classical, 
 mechanics, will be developed here according to his Une 
 of thought as far as I can recollect from a number of 
 conversations. 
 
 Let us suppose that we overhear two people arguing about 
 the shape of the earth's surface. The one affirms that it is an 
 unhmited plane, whilst the other maintains that it is a sphere. 
 We should not hesitate a moment to say that the first is in error, 
 and that the second gives the true answer. As long as the 
 question was to be decided in favour of a " Plane or a Sphere," 
 
PROBLEMS 147 
 
 the sphere would represent the absolute truth. Yet it would 
 be only relative, for these two statements are contradictory 
 only between themselves, but will no longer be so if a third 
 assertion is made which opposes a new alternative to 
 " sphere." 
 
 If this alternative objection is actually raised, the third 
 person would be quite justified in saying that the " sphere " 
 explanation is wrong. For the conception '* sphere " re- 
 quires that all diameters be equal, whereas we know that they 
 are not so, since the distance from pole to pole has been proved 
 to be smaller than that between opposite points on the equator. 
 The earth is an elHpsoid of rotation, and this truth is absolute 
 in the face of the errors which are expressed by the terms, 
 plane and sphere. 
 
 It would again have to be added that this absoluteness 
 would stand only as long as this contradiction is regarded as 
 being one between a definite sphere and a definite eUipsoid. 
 If, as in the case of the earth, there are quite different diameters 
 in the equatorial and the diametral planes, then there is 
 complete contradiction between the two statements, and as 
 the supporter of the eUipsoid is right, the one who supported 
 the sphere must now give in, although he previously 
 triumphed over his first opponent. His statement was true 
 compared with the latter, but showed itself to be an error 
 when compared with the statement of the third person. 
 
 This does not run coimter to the laws of elementary logic. 
 One of these, somewhat inadequately called the Law of Con- 
 tradiction, states that two directly contrary statements — e.g. 
 this figure is a circle, and this figure is not a circle — cannot 
 both be true simultaneously. The truth of the one implies 
 necessarily the falseness of the other. As this cannot be dis- 
 puted, it follows in our case that we cannot have been con- 
 fronted with contradictory judgments at all concerning the 
 figure of the earth. 
 
 This is to be understood in a geometrical sense. The 
 sphere does not entirely contradict the eUipsoid, since it is a 
 hmiting case of the latter : and the plane is Ukewise a Hmiting 
 case of the sphere, as weU as of the surface of eUipsoids. 
 
 But we are not concerned with purely geometrical con- 
 siderations, for the earth is a definite body, and not a limiting 
 
148 EINSTEIN THE SEARCHER 
 
 configuration derived from abstraction. We are here dealing 
 with measurable quantities, whose difference can be proved, 
 and hence we must have one of the disputants proclaiming the 
 absolute truth, whilst the other proclaims an absolute error. 
 This, however, again is incompatible with our result that 
 the second person is right in the one case and wrong in the 
 other. 
 
 The logical Law of Contradiction overcomes the dilemma 
 in the simplest way. None of these assertions contains the 
 truth, hence none of these judgments allows the falseness of 
 the others to be deduced. Only this may be said, that there 
 is a fraction of truth in each judgment. The true shape of the 
 earth is given by the plane to a first, the sphere to a second, 
 the ellipsoid of rotation to a third, degree of approximation : 
 we reserve the right of further approximations, each of which 
 in succession approaches a higher degree of correctness, but 
 none attains the absolute truth. 
 
 This reflection on a particular case may be generaUzed, and 
 remcdns when we extend it to our attempts at grasping the 
 states, changes, and occurrences of Nature. Whenever we 
 talk of physical laws, we must bear in mind that we are deaUng 
 with human processes of thought, that are subjected to a 
 succession of judgments, courts of appeal, as it were, excluding, 
 however, a final court beyond which no appeal is possible. 
 Each new experience in the course of natural phenomena may 
 render necessary a new trial before a higher court, whose duty 
 is then to give a more definite or different form to the law 
 formulated by us, so as to attain a still higher degree of 
 approximation to the truth. 
 
 If we call to mind some of the most valuable statements 
 made by modern investigators about the nature of natural 
 laws, we recognize that they are all connected by a single 
 thread of thought, namely, that even in the most certain law 
 there is left a remainder that has not been accounted for, and 
 that obHges us to consider a greater approximation to the truth 
 as possible, even if a final stage is not attainable. 
 
 Mechanics furnishes us with the expression of its laws in 
 equations, whose importance Robert Kirchhoff explained in 
 1874 by a definition that has been considered conclusive by 
 scientists. According to him, it is the object of mechanics to 
 
PROBLEMS 149 
 
 describe completely (and not to explain) in the simplest manner 
 the motions that occur in Nature. 
 
 The postulate of simplicity is derived from the fundamental 
 view of science as an economy of thought. It expresses the 
 will of man's mind to arrive at a maximum of result by using 
 a minimum of effort, and to express the greatest sum of experi- 
 ence by using the smallest number of symbols. Let us con- 
 sider two simple examples quoted by Mach. No human brain 
 is capable of grasping all the possible circumstances of bodies 
 falling freely, and it may well be doubted whether even a 
 supernatural mind like that imagined by Laplace could succeed 
 in doing so. But if we take note of Galilei's Law for Falling 
 Bodies and the value of the acceleration due to gravity, which 
 is quite an easy matter, we are equipped for all cases, and have 
 a compendious formula, accessible to any ordinary mind, that 
 allows us to picture to ourselves all possible motions of falling 
 bodies. In the same way no memory in the world could retain 
 all the different cases of the refraction of hght. Instead of 
 trying to do the impossible task of grasping this infinite abund- 
 ance, we simply take note of the sine law, and the indices of 
 refraction of the two media in question ; this enables us to 
 picture any possible case of refraction, or to complete it, since 
 we are free to reheve our memories entirely by having the 
 constants in a book. Thus we have here natural laws that 
 give us a comprehensive yet abbreviated statement of facts, 
 and satisfy the postulate of simpUcity to a high degree. 
 
 But these facts are built up on experiences, and it is not 
 impossible that some new unexpected experience wiU reveal 
 a new fact, which is not sufiiciently taken into account in the 
 law. This would compel us to correct the expression for the 
 law, and to seek a closer approximation for the enlarged 
 number of facts. 
 
 The Law of Inertia, according to our human standard, 
 seems unsurpassable in simpHcity and completeness ; it seems 
 to us fundamental. But this law, which prescribes uniform 
 rectiUnear motion to a body subject to no external forces, 
 selects only one possibiUty out of an infinite number as being 
 valid for us. It does not seem evident to a child, and it is 
 easy to imagine a good scholar in some branch of knowledge 
 other than physics, to whom it would likewise not seem evident. 
 
150 EINSTEIN THE SEARCHER 
 
 For it is by no means necessary a priori that a body will move 
 at all when all forces are absent. If the law were self-evident, 
 it would not need to have been discovered by Galilei in 1638. 
 Nevertheless, it appears to us, now, to be absolutely self-evident, 
 and we can scarcely imagine that it can ever be otherwise. 
 This is simply because we are bound to the current set of ideas 
 that cannot extend beyond the sum of sense-data and experi- 
 ences that have been inculcated into us by heredity and en- 
 vironment. At a very distant date in the future the average 
 mind may surpass that of GaHlei to the same extent as GaHlei's 
 surpasses that of a child, or of a Papuan native. And of all 
 the infinite possibilities one may occur to a GaUlei of the distant 
 future, which, when formulated as a law, may serve to describe 
 motions of a body subject to no forces better than the law of 
 inertia, proposed in 1638. 
 
 These reflections are not mere hallucinations, but have to 
 do with scientific occurrences that we have observed in the 
 twentieth century. Newton's equation that gives the Law of 
 Attraction is beyond doubt a model of simplicity, and it would 
 have occurred to no thinking person of even the last generation 
 
 to doubt its accuracy. The easily grasped expression k — ^ 
 
 apparently expresses truth in a law which is valid for all 
 eternity. In this expression, he denotes a gravitational con- 
 stant, that is, a quantity which is invariable in the whole uni- 
 verse ; m and m} are two masses that act attractively on one 
 another ; and r is the distance between them. But Newton 
 has been followed by Einstein, who has proved that this ex- 
 pression represents only an approximate value, that leaves a 
 small remainder as an error that may be detected if the greatest 
 refinement be made in our methods of observation. The 
 equations that have been set up by Einstein represent the 
 approximation that is to be considered final for the present, 
 and that may remain valid for thousands of years. They are 
 certainly very complicated, being included in a system of 
 differential equations of awe-inspiring length, and we may 
 feel tempted to object with the question : how do they agree 
 with Kirchhoff' s postulate that the simplest description of the 
 motions must be sought ? But this objection falls to the 
 ground if we look carefully into the question. For simplicity 
 
PROBLEMS 151 
 
 consists not merely in being brief or in excluding difficulty 
 from a formula, but rather in asserting the simplest relation 
 to the universe as a whole, which is independent of all systems 
 of reference. When this independence is proved — and in 
 Einstein's case it is so — the compUcated aspect of the formula 
 disappears entirely in the Ught of the higher simplicity and 
 unity of the world-system that presents itself — a world-system 
 that is directed in conformity with the one fundamental law of 
 general relativity as well in the motion of the electrons as in 
 motion of the most distant stars. With regard to the other 
 postulate, that of completeness, i.e. absolute accuracy, we 
 have been furnished with proofs that have rightly excited the 
 wonder of the present generation. But are we then to recognize 
 the Principle of Approximation in every direction ? Is there 
 then nothing that can be proved rigorously, nothing that is 
 unconditionally valid in the form of knowledge that corresponds 
 exactly to truth ? 
 
 We are led to think of mathematical theorems, which, 
 when they have once been proved, are evident to the same 
 degree as the axioms from which they have been derived, by 
 virtue of logic which cannot be disputed since a contradiction 
 leads to absurdity. It has been said that mathematics est 
 scientia eorum, qui per se clara sunt, that is, is the science of 
 what is self-evident. 
 
 But here again doubts arise. If we should get to know 
 only a single case, in which the self-evident came to grief, the 
 road to further doubts becomes open. Such a case will now 
 be quoted. 
 
 As we know, a tangent is a straight Une, which makes 
 contact with a curve at two coincident (or infinitely near) 
 points without actually cutting the ciurve. The simplest case 
 of this is the perpendicular at the extremity of a radius of a 
 circle. And it agrees fuUy with what our feehng leads us to 
 expect when it is stated that every curved Hne that is " con- 
 tinuous,*' that is, which discloses no break and no sudden bend, 
 has a tangent at every point. Analysis, which treats plane 
 curves as equations in two variables, gives the direction of the 
 tangent in terms of the differential coefficient, and declares 
 accordingly that every continuous function has a differential 
 coefficient, that is, may be differentiated, at every point. The 
 
152 EINSTEIN THE SEARCHER 
 
 one statement amounts to the same as the other, since there 
 must be an equivalent graphical picture corresponding to every 
 functional expression. 
 
 But this apparently rudimentary theorem involves an 
 error, which was not discovered before the year 1875. The 
 theory of curves has been in existence for centuries, but it 
 occurred to no one to doubt the general vahdity of this theorem 
 of tangents. It was regarded as self-evident, as a mathe- 
 matical intuition. And certainly neither Newton, nor Leibniz, 
 nor Bernoulli, not to mention the mathematicians of olden 
 times, even dreamed that a continuous curve without a tangent, 
 or a continuous function without a differential coefficient, 
 was possible. 
 
 -1: Moreover, a proof of the theorem had been accepted. It 
 appeared in text-books, and was often to be heard in lecture 
 rooms ; nor was a shadow of a doubt suggested. For it was 
 not merely a demonstratio ad oculos, but it appeared directly 
 to our sense of intuition. And we may safely say that up to 
 the present day no one has ever been able to imagine a con- 
 tinuously curved line which has no tangent ; no one has been 
 able to picture even one point of such a curve at which no 
 tangent could be drawn. 
 
 Nevertheless, scientists appeared who began to entertain 
 doubts. In the case of Riemann and Schwarz these doubts 
 assumed a concrete form, in that they proved that certain 
 functions are refractory at certain points. But Weierstrass 
 was the first to make a real breach in the old belief that was so 
 firmly rooted. He set up a function that is continuous at every 
 point, but differentiable at no point. The graphical picture 
 would thus have to be a continuous curve having no tangent 
 at all. 
 
 What is the appearance of such a configuration ? We do 
 not know, nor shall we presumably ever get to know. During 
 a conversation in which this problem of Weierstrass arose, 
 Einstein said that such a curve lay beyond the power of 
 imagination. It must be remarked that, although the mathe- 
 matical expression of the Weierstrass function is not exactly 
 simple, it is not inordinately complex. Moreover, seeing that 
 one such function (or curve) exists, others will soon be added 
 to it (Poincare mentions that Darboux actually gave other 
 
PROBLEMS 153 
 
 examples even in the same year that the first was discovered) ; 
 there will, indeed, be found an infinite number of them. We 
 may go still further, and say that, corresponding to each curve 
 that has tangents, there are an infinite number that have 
 no tangents, so that the former form the exception and not the 
 rule. This is an overwhelming confession that shakes the 
 foundations of our mathematical convictions, yet there is no 
 escape. 
 
 How may we apply the principle of " approximation "to 
 these considerations ? May we say that the theorem that was 
 believed earlier is an approximation to a mathematical truth ? 
 
 This is possible only conditionally, in a certain extremely 
 limited sense, namely, if we picture to ourselves that point 
 in the development of science at which the conception and 
 properties of tangents first began to be investigated. Com- 
 pared with this stage of science, the above theorem denotes a 
 first approximation to the truth, in spite of its incorrectness ; 
 for it makes us acquainted with a great abundance of curves 
 that are very important for us and that exhibit tangents at 
 every point. This knowledge brings us a step nearer to the 
 more approximate truth given by Weierstrass*s example. 
 In the distant future, the earnest student will learn this theorem 
 only as a curious anecdote, just as we hear of certain astro- 
 logical and alchemistic fallacies. He will learn, in addition, 
 other theorems that are looked on as proved by us of the present 
 day, although actually they were proved only approximately. 
 For what does it mean when Gauss, for example, repudiated 
 certain proofs of earlier algebraists as being " not sufficiently 
 rigorous,'* and replaced them by more rigorous proofs ? It 
 signifies no more than that, in mathematics, too, what appears 
 to one investigator as flawless, strict, and evident, is found by 
 another to have gaps and weaknesses. Absolute correctness 
 belongs only to identities, tautologies, that are absolutely true 
 in themselves, but cannot bear fruit. Thus at the foundation 
 of every theorem and of every proof there is an incommensurable 
 element of dogma, and in all of them taken together there 
 is the dogma of infallibility that can never be proved nor 
 disproved. 
 
 It must appear extremely interesting that, at first sight, 
 this example of the tangent has its equivalent in Nature 
 
154 EINSTEIN THE SEARCHER 
 
 herself, namely, in molecular motions the investigation of 
 which is again largely due to Einstein. 
 
 Jean Perrin, the author of the famous book, Atoms, describes, 
 in the introduction, the connexion between this mysterious 
 mathematical fact and results that are visible and may be 
 shown by experiment, to which we have been led by the study 
 of certain milky-looking (colloidal) liquids. 
 
 If, for example, we look at one of those white flakes, which 
 we get by mixing soap solution with common salt, we at first 
 see its surface sharply outUned, but the nearer we approach 
 to it, the more indistinct the outline becomes. The eye 
 gradually finds it impossible to draw a tangent to a point of 
 the surface ; a straight line which, viewed superficially, seems 
 to run tangentially, is found on closer examination to be 
 oblique or even perpendicular to the surface. No microscope 
 succeeds in dispelUng this uncertainty. On the contrary, 
 whenever the magnification is increased, new unevennesses 
 seem to appear, and we never succeed in arriving at a continuous 
 picture. Such a flake furnishes us with a model for the general 
 conception of a function which has no differential coefiicient. 
 When, with the help of the microscope, we observe the so- 
 called Brownian movement, which is molecular by nature, 
 we have a parallel to the curve which has no tangent, and 
 the observer is left only with the idea of a function devoid 
 of a differential coefficient. . . . We find ourselves obliged, 
 ultimately, to give up the hope of discovering homogeneity 
 at all in studying matter. The farther we penetrate into its 
 secrets, the more we see that it, matter, is spongy by nature 
 and infinitely complex ; all indications tend to show that closer 
 examination will reveal only more discontinuities. 
 
 I have not yet had an opportunity of seeing these Brownian 
 movements under the microscope, but I must mention that 
 Einstein has repeatedly spoken to me of them with great 
 enthusiasm, of an objective kind, as it were, for he betrayed 
 neither by word nor by look that he himself has done research 
 leading to definite laws that have a recognized place in the 
 history of molecular theory. 
 
 As soon as we approach the question of molecular ir- 
 regularities we recognize that, when we earlier spoke of the 
 figure of the earth in discussing the principle of " appro xima- 
 
PROBLEMS 155 
 
 tion," we were still very far from the limit that may be 
 imagined. We had set up the three stages : plane — sphere — 
 eUipsoid of revolution, as relative geometrical steps, beyond 
 which there must be still further geometrical approximations. 
 If we imagine all differences of level due to mountains and 
 valleys to be eliminated, for example, and if we suppose the 
 earth's surface to consist entirely of liquid, undisturbed by the 
 shghtest breath of wind, even then, the ellipsoid is by no means 
 the final description. For now the discontinuities from mole- 
 cule to molecule begin, the infinite number of configurations 
 without tangents, the macroscopic parallels of what the white 
 flake soap solution showed as microscopically, and no conceiv- 
 able geometry would ever be adequate to grasp these pheno- 
 mena. We arrive at a never-to-be-completed list of functions 
 which can never be described either in words or in symbolic 
 expressions of analysis. 
 
 But even if the ultimate geometrical truth is hidden behind 
 the veils of Maya,* we are yet left with the consolation that the 
 method of approximation, even when appUed to a relatively 
 modest degree, produces remarkable results in the realm of 
 numbers. Let us consider for a moment in the simple figure 
 of a circle the ratio between the circumference and the radius. 
 
 As we know, this ratio is constant, and is called in honour 
 of the man who first gave a trustworthy value for it, Ludolf's 
 number, namely, tt (pi). Thus it makes no difference whether 
 we consider a circle as small as a wedding-ring, or as large as 
 a circus arena, or even one the radius of which is as great as 
 the distance of Sirius. And it makes just as little difference 
 what happens to the circle whilst it is being measured ; the 
 above ratio must remain constant. 
 
 But here, too, a contradiction makes itself heard, issuing 
 from one section of modem science. It calls to mind the 
 saying of Dove that when professors are not quite sure about 
 a thing they always preface their remarks with the phrase : 
 *4t is well known that" . . . We should be well advised in 
 avoiding this method of expression altogether, for even when 
 we feel quite sure, the ghost of the unknown lurks behind 
 what we fain would call well known. 
 
 The theorem that all circles without exception are subject 
 
 * Maya = appearance. 
 
156 EINSTEIN THE SEARCHER 
 
 to the same measure-relation belongs a priori to the synthetic 
 judgments. But fields of thought have been discovered in 
 which the a priori has lost its power. Mathematics — once 
 a quintessence of synthetic statements a priori — is now 
 regarded as being dependent on physical conditions. Physical 
 conditions, however, are empirical and subject to change. 
 Therefore, since the a priori is not subject to change, we 
 encounter a discrepancy. It leads to the question : Is the 
 Euclidean geometry with which we are familiar the only 
 possible geometry ? Or, in particular : Is it the only possible 
 measure-relation ? 
 
 Einstein replies in the negative. He not only shows how 
 another geometry is possible, but he also discloses what once 
 seemed inconceivable, namely, that if we wish to describe 
 the course of the phenomena of Nature exactly by means of 
 the simplest laws, it is not only impossible to do so with the 
 help of Euclidean geometry alone, but that we have to use a 
 different geometry at every point of the world, dependent 
 on the physical condition at that point. 
 
 From the comparatively simple example of two systems 
 rotating relatively to one another, Einstein shows that the 
 peripheral measurement of a rotating circle, as viewed from 
 the other system, exhibits a peculiarity which does not 
 accompany the radial measurement. Fot, according to the 
 theory of relativity, the length of a measuring rod is to be 
 regarded as being dependent on its orientation. In the case 
 quoted, the rod undergoes a relative contraction only when 
 applied along the circumference, so that we count more steps 
 than when we measure the circumference of the same circle 
 at rest, that is, in non-rotation. Since the radius remains 
 constant in each case, we ^'dt a relatively greater value for tt, 
 which shows that we are no longer using Euclidean geometry. 
 
 Yet, formerly, before such considerations could even 
 be conceived in dreams, this tt was regarded as absolutely 
 established and immutable ; and observers used every possible 
 means of determining its value as accurately as possible. 
 
 In Byzantium there Uved during the eleventh and twelfth 
 centuries a learned scholar, Michael Psellus, whose fame as 
 the " Foremost of Philosophers *' stretched far and wide, 
 and whose mathematical researches were regarded as worthy 
 
PROBLEMS 157 
 
 of great admiration. This grand master had discovered by 
 analytical and synthetical means that a circle is to be regarded 
 as the geometric mean between the circumscribed and the 
 inscribed square, which gives to the above quantity, as may 
 easily be calculated, the value \/8, that is, 2*8284271. . . . 
 In other words, the length of the circumference is not even 
 three times that of the radius. 
 
 We have the choice of regarding the result of Psellus as 
 an approximation, or as mere nonsense. Every schoolboy 
 who, in a spirit of fun, measures a circular object, say a top, 
 with a piece of string, arrives at a better result, but the con- 
 temporaries of Psellus accepted this entirely wrong figure 
 with credulous reverence, and continued to birni incense at 
 the feet of the famous master. It is all very well for us of 
 the present to call him a donkey. We have just as much 
 right in saying that mathematicians differ, not in their natures, 
 but only in the order of their brain functions. If a man hke 
 Psellus missed the mark by so much, it is possible that men 
 Hke Fermat or Lagrange may also have erred occasionally 
 or even consistently. 
 
 No heavenly power wiU give us a definite assurance to 
 the contrary, and all of us may be just as false in our judgment 
 of accepted celebrities as were the Byzantines eight hundred 
 years ago in their estimate of PseUus. 
 
 Whereas the latter had obtained a value " less than 3,'* 
 there are learned documents of about the same date that have 
 been preserved, according to which the value of ir comes out 
 as exactly 4. Compared with this grandiose bunghng, even 
 the observations mentioned in the Old Testament are models 
 of refinement. For, as early as three thousand years ago, 
 it is stated of the mighty basin in the temple of Solomon 
 (First Book of Kings, chapter vii.) : " And he made a molten 
 sea, ten cubits from the one brim to the other : it was round 
 all about, and his height was five cubits ; and a fine of thirty 
 cubits did compass it round about." Thus ir here appears 
 as 3, an approximation which no longer satisfied later genera- 
 tions. The wise men of the Talmud went a step further, 
 in saying 3 plus a little more ; and this agrees roughly with 
 the actual value. 
 
 The view became more and more deeply rooted that this 
 
158 EINSTEIN THE SEARCHER 
 
 TT was |a main pillar of mathematical thought and calculation. 
 The more the problem of the quadrature of the circle seized 
 on men's minds, the greater were the efforts made to find 
 the exact value of this " httle more " of the Talmud. Since 
 1770 we know that this is not possible, for ir is not rational, 
 that is, it can be represented only as an infinite and irregular 
 (that is, non-repeating) decimal expression. It occupies, 
 further, a special rank as a transcendental quantity ; this 
 fact was proved by Lindemann as late as 1882 for the first 
 time. Yet, even nowadays, there are incorrigible devotees 
 of quadrature, who are still hunting a solution because they 
 cannot rid themselves of the hallucination that such a simple 
 figure as the circle must submit ultimately to a constructive 
 process. 
 
 The correct way was to carry out an even more accurate 
 determination of the decimal figures. The above-mentioned 
 Ludolf van Ceulen got as far as the 35th place of decimals ; 
 at the turn of the eighteenth century the looth decimal 
 place was reached. Since 1844, thanks to the lightning 
 calculator Dase, we have its value to the 200th decimal place, 
 and this should satisfy even the most extravagant demands. 
 This number, associated with the circle, is a classical example 
 of how an approximation that is expressible in figures of very 
 small value gives an order of accuracy that can be described 
 only by using fantastic illustrations. 
 
 If we take a circle of the size of the equator, and also 
 multiply the value of the diameter of the earth by tt, we know 
 that the latter result will not be exactly equal to the former, 
 and that there will always be a small remainder. If this 
 discrepancy were less than a metre, the order of exactness 
 would be extraordinarily high, for a metre is practically 
 insignificant compared with a mighty circle of the dimensions 
 of the earth's circumference. 
 
 Let us stipulate still greater accuracy. We demand that 
 the error is to be less than the thickness of the thinnest human 
 hair. We find, then, that we must take for tt at most 15 
 places of decimals. Thus, if we use 7^ = 3*14159265358973, 
 we are applying a means of calculation that reduces the 
 possible error in all measurements of circles on the earth 
 to a degree beyond the Umits of human perception. 
 
PROBLEMS 159 
 
 If we pass beyond the world out into celestial space, and 
 consider circles of the dimensions of a planetary orbit, nay, 
 further, if we pass on to the Milky Way or even to the limit of 
 visible stars, to find space for our circle, and if in this case we 
 still reduce the discrepancy so as to be less than any length 
 that is observable under a microscope, then the last given 
 value of TT still suf&ces. Yet we must not forget the proviso : 
 semper aliquid haeret, something unsolved still chngs to the 
 problem. 
 
 Such numerical approximations, however instructive they 
 may be, nevertheless retain a comparatively playful character, 
 and furnish only a superficial analogy to the most important 
 approximations that are contained in our natural laws them- 
 selves. It is these, above all, that manifest themselves so 
 clearly in Einstein's Ufe-work, and they bear the same relation 
 to the former as truth bears to correctness. Truth comprises 
 the greatest conceivable circle of ideas and passes far beyond 
 the sphere of correctness, which deals only with measure- 
 relations, and not with the things in themselves. If Einstein, 
 as we learn, emphatically declares truth to be the only object 
 of science, he means the strictly objective truth that is to be 
 derived from Nature, the true relationship of phenomena and 
 occurrences, independently of whether restless philosophy 
 assigns a question mark to this ultimate objectivity. A great 
 discoverer in the realm of Nature cannot and dare not proceed 
 otherwise. For him there is behind the veil of Maya not a 
 phantom that finally vanishes, but something knowable, that 
 becomes ever clearer and more real as he detaches each suc- 
 cessive veil in his process of approximation. 
 
 During this conversation, when we were talking of the 
 " Future of the Sciences," Einstein gave his ideas free rein, 
 shooting far ahead of the views and prognostications of the 
 above-mentioned scientists : 
 
 " Hitherto we have regarded physical laws only from the 
 point of view of Causality, inasmuch as we always start from 
 a condition known at a definite cross-section of time, that is, 
 by taking a time-section of phenomena in the universe, as, for 
 example, a section corresponding to the present moment. But, 
 I beheve," he added, with earnest emphasis, " that the laws of 
 Nature, the processes of Nature, exhibit a much higher degree 
 
160 EINSTEIN THE SEARCHER 
 
 of uniformity of connexion than is contained in our time- 
 causality ! This possibiHty suggests itself to me particularly 
 as the result of certain reflections concerning Planck's Quantum 
 Theory. The following may be conceived : What belongs to 
 a definite cross-section of time may in itself be entirely devoid 
 of structure, that is, it might contain everything that is physi- 
 cally conceivable, even such things (so I understood him to say) 
 as, in our ordinary physical thought, we consider impossible 
 of realization, for example, electrons of arbitrary size, and 
 having an arbitrary charge, iron of any specific gravity, etc. 
 By our causality we have adjusted our thought to a lower 
 order of structural Umitations than seems realized in Nature. 
 Real Nature is much more limited than our laws imply. To 
 use an allegory, if we regard Nature as a poem, we are Hke 
 children who discover the rhyme but not the prosody and the 
 rhythm." I interpret this as meaning that children do not 
 suspect the restrictions to which the form of the poem is 
 subject, and just as Uttle do we, with our causality, divine 
 the restrictions which Nature imposes on occurrences and 
 conditions even when we regard them as governed by the 
 natural laws we have found. 
 
 Thus a leading problem of science in the future will be 
 to discover the restrictions of Nature as compared with the 
 apparent causality implied in physical laws. 
 
 We have in this an example of the transcendental per- 
 spectives that are opened up when we accompany Einstein 
 on one of his excursions of thought. In this case it is actually 
 a question of ultimate things, of a region of discovery of 
 which we cannot yet form a conception, and it appears 
 doubtful whether the problems latent in it are to be treated by 
 making investigations into physical nature, or whether they 
 are to be allotted to speculative philosophy. 
 
 In the first place, Einstein's remark seems to aim at nothing 
 less than a revision of the conception of causaUty. However 
 much has been done to purify this conception and to make it 
 clear, we have here, perhaps, a new possibility of refining it 
 by making a synthesis of scientific and abstract philosophical 
 views. We shall just touch very lightly and superficially on 
 the possibility of a synthesis giving us an avenue to truth. 
 Whoever has heard these words of Einstein, feels the need of 
 
PROBLEMS 161 
 
 getting on to firm ground to rescue himself out of the turmoil 
 of ideas into which he has been plunged. 
 
 What is Causality ? A physiological answer may be given 
 by saying that it is the irrepressible animal instinct, rooted 
 in our brain-cells, that compels us to connect together things 
 that we have experienced and imagined. Poets have defined 
 Hunger and Love as the fimdamental elements of our social 
 fives ; we need only add the thirst for causafity to this to 
 complete the fist of primary instincts. For this mental thirst 
 is not less intense than our bodily hunger, and is even greater 
 in that it never forsakes us for a moment. It is easier for the 
 body to check breathing than for the soul to still the question 
 of the why and wherefore, of the cause and effect, of the ante- 
 cedent and consequent. 
 
 This ceaseless search for a connexion between occurrences 
 has become organized into a fixed and immovable form of 
 thought, which remains mysterious even when we imagine 
 that we have efiminated all the mystery from it. The rela- 
 tions that we seek and that we regard as being of an elementary 
 character are totally foreign to Nature herself. David Hume, 
 the first real, and at the same time the most penetrating, 
 explorer into this form of thought, said that, in the whole of 
 Nature not a single case of connexion is disclosed which we 
 are able to grasp. All happenings appear, in reafity, dis- 
 connected and separate. One " follows on " another, but we 
 can never detect a connexion between them. They appear 
 ** co-joined," but never " connected." And since we can form 
 no idea of what has never presented itself to our outer or inner 
 perception, the necessary conclusion seems to be that we have 
 absolutely no idea of causal connexions or causative forces, 
 and that these expressions are quite devoid of meaning, how- 
 ever much they may be used in philosophical discussions or 
 in ordinary fife. This ** Inquiry concerning Human Under- 
 standing," with its atmosphere of resignation, has been ela- 
 borated in manifold ways, particularly by Kant and the 
 Kantians ; for it is impossible to take up a philosophic thread 
 without entering on an examination of the fundamental 
 question concerning the existence of a causafity which fies 
 outside our instinct for causafity. It is also inevitable that, 
 whenever we start out in this direction, we encounter the 
 II 
 
162 EINSTEIN THE SEARCHER 
 
 further question : What is Time ? For causality directs 
 itself to the problem of succession, both of sensations and 
 phenomena, consequently the two questions are not only 
 intimately connected, but are really only different expressions 
 of one and the same question. Time, which according to 
 Descartes and Spinoza is a modus cogitandi, not an affectio 
 rerum, and, according to Kant, is an a priori form of thought, 
 dominates our intelhgence with the same sovereign power, as 
 the imagined course of things : what we perceive in the corre- 
 sponding act of thought is regarded as temporal and causal, 
 and impossible of further analysis. 
 
 Now, the conception of time has been entirely revolu- 
 tionized by Einstein himself; and it may be expected that 
 the conception of causality, too — which, in accordance with 
 custom, we still endow with a separate existence — will also be 
 affected by this revolution. 
 
 We thus approach a relativization of causality, and we 
 may advance a step further in this direction, if we call to mind 
 the differences of time-perception that Nature herself leaves 
 open to us. It must be clearly understood that we are not 
 dealing at present with the theoretical time of physics, in 
 the sense of Einstein's theory, but with something physio- 
 logical that ultimately, however, resolves itself into a rela- 
 tivization of time, and hence also of the causal connexions in 
 time. 
 
 To do this, we have to follow the lines of reasoning de- 
 veloped by the celebrated St. Petersburg academician, K. E. 
 von Baer, and we need extend it only very Httle to get at 
 the heart of causality, if we start from his address of i860 : 
 " Which View of Living Nature is correct ? " For the human 
 brain is a part of living nature, and hence the processes of 
 thought may also be conceived as expressions of life. 
 
 The starting-point is a figment, the fictitious character 
 of which vanishes as soon as we approach its results. The 
 bridge of thought may be destroyed later ; it suffices to carry 
 us temporarily, as long a3 it lands us in safety on the other 
 side. 
 
 The rapidity of perception, of the arbitrary motions, of 
 intellectual life seems in the case of various animals to be 
 proportional approximately to the rapidity of their pulse- 
 
PROBLEMS 163 
 
 beats. Since, for example, the pulse of a rabbit beats four 
 times as quickly as that of a bull, it will, in the same interval 
 of time, also perceive four times as quickly, and will be able 
 to execute four times as many acts of will, and will experience 
 four times as much as the bull. In the same astronomical 
 length of time the inner Hfe and perceptual world, in the case 
 of various animals, including Man, will take place at different 
 specific rates, and it is on these rates that each of these living 
 creatures bases its subjective measure of time. Only when 
 compared with our own measure of time does an organic 
 individual, say, a plant, appear as something permanent in 
 size and shape, at least within a short interval. For we may 
 look at it a hundred times and more in a minute, and yet 
 notice no external change in it. Now, if we suppose the 
 pulse-beat, the rate of perception, the external course of Hfe, 
 and the mental process of Man, very considerably accelerated 
 or retarded, the state of affairs becomes greatly changed, 
 and phenomena then occur, which we, fettered by our 
 physiological structure, should have to reject as being fantastic 
 and supernatural, although, on the supposition of a new 
 structure they would be quite logical and necessary. If we 
 suppose human Hfe from childhood to old age to be compressed 
 into a thousandth part of its present duration, say, into a 
 month, so that the pulse beats a thousand times more quickly 
 than occurs in our own experience, we should be able to follow 
 the course of a discharged bullet very exactly from point to 
 point with our eyes, more easily than we can at present observe 
 the fHght of a butterfly. For now the motion of the bullet 
 in a second will be distributed among at least looo pulse- 
 beats, and wiU induce at least looo perceptions, and accord- 
 ingly, in comparison with our everyday perception, it will 
 appear looo times slower. If the duration of our Hfe were 
 again to be reduced to a thousandth of its first reduced value, 
 that is, shortened to about forty minutes, then our flowers 
 and herbs would seem just as motionless and immutable as 
 rocks and mountains, in which we only infer the changes 
 without having directly observed them. We would in the 
 course of our Hves see little more of the growth and decay of 
 a bud and a flower in full bloom than we at present see of 
 the geological changes in the earth's crust. The acts of 
 
164 EINSTEIN THE SEARCHER 
 
 animals would be much too slow to be seen ; at most, we 
 could infer them as we do the motions of the stars at present. 
 If life were shortened still further in the same way, light 
 would cease to be an optical occurrence to us. Instead of 
 seeing the things on which light falls, we should become 
 aware of them as being audible, and what we at present call 
 tones and noises would long have ceased to have an effect 
 on the ear. 
 
 If, however, we let our fancy roam in the opposite direction, 
 that is, if, instead of compressing the duration of human 
 life, we expand it enormously, what a different picture of 
 the world would present itself ! If, for example, the pulse- 
 beat, and hence the rate of perception, were to be made a 
 thousand times slower, so that the average human life would 
 be spread out over, say, 80,000 years, and that we should 
 experience in one whole year only as much as we now ex- 
 perience in a third of a day, then, in every four hours winter 
 or any other season would pass by, vegetation would spring 
 up and as rapidly die. Many a growth would not be per- 
 ceptible, on account of its relative rapidity compared with 
 the rate of the pulse-beat. For example, a mushroom would 
 suddenly come into existence, like a newly formed spring. 
 Day and night would alternate as a light and a dark minute ; 
 and the sun would appear to fly over the heavens like a fiery 
 projectile. If we were again to make the duration of human 
 life a thousand times longer still, and hence the rate of life 
 a thousand times slower still, we should, during the whole of 
 an ordinary year, be able to have only 190 distinct perceptions, 
 so that the difference between day and night would vanish 
 entirely, and the sun's path woiild be a glowing circular 
 band in the heavens, and all changes of form that seem to us 
 to happen quietly and regularly, and to preserve a certain 
 permanency, would melt together in the wild stream of 
 happening, engulfed in its onward rush. 
 
 Are we justified in opposing to this relative perception 
 of time " our own " time, which is something specific and 
 dependent on our constitution as human beings ? Should 
 we not rather adopt the view that this specific time, adapted 
 to our particular pulse-beat, gives only a very limited picture 
 of the world, which is conditioned and determined by the 
 
PROBLEMS 165 
 
 limitations of our own dej&nite intelligence ? Is it, perhaps, 
 only a distorted picture, a caricature, of actual occurrences ? 
 
 An intelligence infinitely superior to our own would no 
 longer be dependent on the separate sensations such as are 
 presented to us with the rhythm of the pulse. For such a 
 mind there would be no metronomic foundation in the sequence 
 of occurrences, beyond what represents itself as time to our 
 understanding. He would be situated outside of time in what 
 Thomas Aquinas called the nunc stans, in the stationary 
 present, without a retrospect of the past and without ex- 
 pectation of a future. Without the Before and the After, the 
 occurrences of the world would acquire the clearest and 
 simplest meaning, hke that given by an equation of identity. 
 What presents itself to us as a " succession " of events would 
 merge together into one whole, just as a succession of numerical 
 calculations become summarized in a rule of calculation, or 
 as a series of logical operations resolves into a logical self- 
 evident truth. If the mind conceived by Laplace actually 
 existed, it would stand above the necessity of introducing 
 time as a quantity into its world-equations, for time is a 
 purely anthropomorphic quantity, produced by our percep- 
 tion, and regulated by our own characteristic pulses. Accord- 
 ingly, the conception of causality, too, which is indissolubly 
 connected with time, must be regarded as anthropomorphic, 
 as something that we read into, and not out of. Nature. We 
 should at least have to recognize that if there is a causality 
 outside ourselves, then we can learn only a minimum about 
 it, and even this only in a world displaced or distorted by 
 the accidental rate of our pulse-beat. 
 
 Let us now repeat Einstein's assertion " that the laws of 
 Nature, the processes of Nature, exhibit a much higher degree 
 of uniformity of connexion than is contained in our time- 
 causaUty ! It is possible that what belongs to a definite 
 cross-section of time may in itself be entirely devoid of struc- 
 ture, that is, it might contain ever5d:hing that is physically 
 conceivable, even such things as, in our ordinary physical 
 thought, we consider impossible of reaUzation, for example, 
 iron of any arbitrary specific gravity." It seems to me that 
 the non-physicist will, perhaps, gain a clearer insight into these 
 highly significant words of Einstein, now that he has received 
 
,166 EINSTEIN THE SEARCHER 
 
 the assistance of these physiological considerations. It must 
 be granted that the philosophic grounds of Einstein are quite 
 different and lie much deeper than those of von Baer, who 
 starts from organic functions and ends by arriving at a 
 mysterious relativity that is yet consistent in itself. Never- 
 theless, there is one point of contact, inasmuch as in each case 
 possibilities that lie apparently extra naturam are suggested. 
 
 Einstein says : ' * Hitherto we have regarded physical laws 
 only from the point of view of causality, inasmuch as we always 
 start from a condition known at a definite cross-section of 
 time, as, for example, a section corresponding to the present 
 moment.*' At our own risk an easy paraphrase of his words 
 will be attempted : 
 
 The time-section of the present contains for us the sum 
 of all previous experiences, out of which the necessary course 
 of our thought sifts out the category of causaUty. 
 
 What is not present in experience cannot appear in our 
 causality. Let us consider for a moment Hume's example of 
 the Indian who has never known ice. Without being told, 
 and if he is dependent only on his own sensations, he would 
 never learn that water freezes in cold climates. The influence 
 of cold on water is not gradual, corresponding to an increase 
 of cold, and not one that may be anticipated in all its conse- 
 quences, but at the freezing-point water, which a moment 
 before was a very mobile liquid, passes into a very rigid solid. 
 The causality of the Indian cannot account for this. If we 
 tell him of this phenomenon, he has two courses open to him. 
 Either he refuses to believe it — and this would be quite 
 natural, since rigid water is to him as meaningless as is a square 
 circle to us. Or else he beheves the story, and then his Hst 
 of categories incurs a break, passing through the middle of 
 causality. He has then to reconcile himself to the assumption 
 that something that is meaningless to him and that stands out- 
 side the connexion of cause and effect is possible of reaUzation. 
 Up to that moment, in his time-section of the present, there 
 was no room for it in his causaUty. To Torricelli the concep- 
 tion of liquid air, which we have been able to prepare only 
 since 1883, would have appeared impossible and incompatible 
 with his causaUty. 
 
 So there is no room in our causaUty for the idea of iron 
 
PROBLEMS 167 
 
 with the specific gravity of air, or with one several times that of 
 gold. For, reasoning along the lines of our causaUty, we shoiild 
 conclude that a substance that is so light or so heavy may, 
 indeed, exhibit chemical relationship with iron, but it would 
 not itself be sufficiently defined by the term iron. 
 
 Now Einstein also said : " Real Nature is much more 
 limited (or bound) than our laws imply." A sceptic might be 
 disposed to take these statements separately in order to con- 
 strue a contradiction out of them. For, if there are limiting 
 conditions in Nature, which are foreign to the views expressed 
 in our laws, how would it then be possible for phenomena, 
 which cannot be imagined, to become reahzed ? If Nature 
 can do this, surely she must have more Hberty than we seek 
 to impose on her. This apparent contradiction vanishes if 
 we treat the conception of structural design or uniformity as 
 something distinct from the measure of all experience up to 
 the present. This would give us the following interpretation : 
 
 Out of the manifold of occurrences that are possible in 
 mechanical Nature, real Nature selects a very closely defined 
 manifold. Thus the true laws imply a much greater degree of 
 hmitation than those known to us. For example, the laws 
 known to us at present would not be affected if we should dis- 
 cover electrons of arbitrary size or iron of arbitrary specific 
 weight. But Nature reahzes only electrons of a quite definite 
 size and iron of a definite specific weight. 
 
 Let us bear in mind that in aiming at ultimate truths we 
 have no final courts of appeal. Nor are the latter to be 
 assumed even when, in pursuing a theory, we encounter a 
 difficulty, which at first exhibits all the signs of a direct con- 
 ceptual contradiction. It should rather be reahzed that a 
 fiction containing an initial but only provisional contradiction 
 serves as a starting-point for just those investigations that are 
 most subtle and that have far-reaching consequences. We 
 should have no Infinitesimal Calculus, no Algebra, no Atomic 
 Theory, no Theory of Gravitation if, to avoid all initial con- 
 tradictions, we surrender the fiction of differentials, of imaginary 
 quantities, of the atom, of action at a distance. In short, 
 it may, indeed, be said that not only knowledge, but also hfe, 
 the holding together of people by convention, law, and duty, 
 
168 EINSTEIN THE SEARCHER 
 
 would become impossible if we did not accept the fiction 
 of free will, which directly contradicts the determinate char- 
 acter of all happening, including actions and motives, which, 
 physically, alone seems recognizable. 
 
 Fiction (not to be confused with hypothesis) and anthropo- 
 morphism, in spite of their inner inconsistency, are the two 
 poles about which our thoughts and our hves revolve. And 
 no doctrine will ever soar to such heights that it will be able 
 to deny completely its origin from these roots of all thought. 
 The Archimedean thought-centre of the universe, which would 
 enable us to hft the world out of its hinges, is unattainable, 
 because it does not exist at all. 
 
 Is this also to apply to the new physics, whose results are 
 to be regarded as the last word in scientific knowledge ? Many 
 a hypercritical thinker might be led away by the current of 
 the preceding statement, and feel disposed to answer in the 
 afiirmative, were it not that, here too, a contradiction intrudes 
 itself. This is expressed in the fact that not one of the present- 
 day philosophers is in a position to pursue the threads of this 
 theoretical fabric to their hidden ends. 
 
 Thus we arrive at a parting of the ways. Whoever aims 
 at becoming thoroughly famihar with Einstein's new world- 
 system finds that the study of the theory claims so much 
 attention that there is scarcely a possibility left of proceeding 
 to an ultimate philosophical analysis. And whoever is ab- 
 sorbed only by the desire of making philosophic investiga- 
 tions soon enough arrives at border-hnes of thought, at which 
 his conscience warns him to beware of insufiicient scientific 
 knowledge. He will be attacked by doubts as to whether he 
 has properly understood the theory. And he will be con- 
 fronted with the question whether he is justified in drawing 
 ultimate philosophical conclusions before he has mastered all 
 the mathematical details. 
 
 As far as can be judged at present, only one thinker has, 
 so far, had sufiiciently wide knowledge to enable him to corre- 
 late the physical theory methodically with the theory of know- 
 ledge. I mean Professor Moritz Schlick of Rostock, who has 
 set out his ideas systematically in his book Erkenntnislehre, 
 which is extraordinary in itself and in its great scope ; it 
 takes us beyond Kant. In Schhck's opinion Einstein's theory 
 
PROBLEMS 169 
 
 furnishes us with the key to new and unexpected chambers of 
 thought ; it is a wonderful instrument for opening up new 
 avenues, and would appear more wonderful still if we could 
 use this instrument without having recourse to anthropo- 
 morphism. This Hmitation may lead to a Utopia, or may en- 
 tail a circulus vitiosus. But we have one philosophy nowadays 
 which apphes to what cannot be fulfilled ** AS if " it really 
 is capable of fulfilment. Among the disciples of Vaihinger, the 
 founder of the As-If-doctrine of thought, we, however, notice 
 the tendency to follow anthropomorphic and fictitious paths 
 also in his field of thought. 
 
 From numerous utterances of Einstein, I have gathered 
 that he himself does not give his unquaHfied approval to all 
 attempts at unraveUing the ultimate problems by means of 
 philosophy, that is, by using metaphysics alone. He does not 
 deprecate these endeavours, but even expresses admiration 
 for some of the newer works, as for that of Schhck, yet he sees 
 certain obstacles in the purely philosophical methods, that at 
 least restrain him from taking a systematic interest in them. 
 This reluctant acceptance of, and doubt in, the processes of 
 philosophy, that has never forsaken the exact investigator, 
 this suspicious attitude which scents traces of sophistic and 
 scholastic machinations in all metaphysical arguments, also 
 asserts itself in him in a noticeable form. He feels the absence 
 of rigour and of consistency of direction, which is a guarantee 
 of progress in passing from one result to another, in the method 
 of thought of those who are pure philosophers : and he de- 
 plores the spongy and murky appearance of certain ex- 
 pressions of thought, which, it must be admitted, form a poor 
 contrast to the completeness and the crystal clearness of 
 mathematico-physical reasoning. There was an inscription 
 on the portals of the Athenian Academy which stated that 
 entrance was forbidden to all who had had no mathematical 
 training ; we may imagine next to it an academy of pure 
 transcendental philosophy, bearing the inscription : No exact 
 research allowed ! I beUeve that this clear-cut distinction 
 would tally with Einstein's view. 
 
 In the case of the great Ernst Mach, for whom Einstein 
 has intense admiration, we observe a similar attitude, or we 
 may say that, in the language of allegory, he sang openly the 
 
170 EINSTEIN THE SEARCHER v 
 
 same refrain in another key. He never ceased reiterating that 
 he was properly " no philosopher at all, but only an investigator 
 of Nature." At the beginning of the introduction to one of 
 his works we read his confession : " Without in the slightest 
 degree being a philosopher, or even wishing to be one . . ." ; 
 and some lin^es further on he calls himself sarcastically " a 
 mere amateur sportsman " in philosophical regions. Yet, 
 Mach's initial remark is followed by a remarkable result, for 
 the book in question, Knowledge and Error (Erkenntnis und 
 Irrtum), is to be reckoned among the most important works 
 in philosophical literature ; and he himself, the amateur 
 sportsman, who did not even desire to be called a philosopher, 
 accepted in 1895 the post of Professor of Philosophy at Vienna 
 University. It was merely his timidity in the face of the 
 philosophical fraternity that had made him emphasize re- 
 peatedly the distinction between his own work and that of the 
 philosophers, whereas in his heart he had nourished a passion 
 for Philosophy, the first mother of Science. And in my 
 opinion such a moment may arrive for even the most rigorous 
 investigator when he succumbs to the siren strains from 
 the shores of philosophy. 
 
 As far as Einstein himself is concerned, I cannot venture 
 on a prognostication. Even though he belongs to the category 
 and rank of Descartes, Pascal, d'Alembert, and Leibniz, in 
 whom Mathematics and speculative Philosophy are inter- 
 mingled, he is yet characterized by such a pronounced in- 
 dividuality, that it is quite inadmissible to draw conclusions 
 about him from others. He has no need to experience a day 
 of Damascus, for he carries the gospel of salvation in himself, 
 and it radiates from him. One thing seems possible, in my 
 opinion, namely, that Einstein will occasionally roam into the 
 neighbouring realm merely from aesthetic motives. Although 
 the means of philosophy are nebulous and more indefinite 
 than those of exact science, which are almost glaringly distinct, 
 philosophy itself for this reason is the more closely related to 
 Art. And a theory that applies to the whole universe must 
 assuredly contain many germs that may come to life if sub- 
 jected to the methods of Art. The connecting link between 
 Kant and Schiller shows in what sense this is to be understood. 
 Even at present there are indications in Art which tend to 
 
PROBLEMS 171 
 
 show that it is ready to estabhsh points of contact with 
 Knowledge. In France symphonic poems were written on 
 the measure relations of the circle, and on logarithms : these 
 are at present only curiosities, but may in future become 
 models. At a much later date, perhaps, the four-dimensional 
 universe may become ripe for treatment by such methods of 
 Art. On the way to this goal there is the treatment with the 
 symbolic, non-rigorous, and semi-poetic means of expression 
 used by Philosophy. Many will use their efforts to achieve 
 this, and perhaps they will come within closer range of success, 
 if Einstein himself lends a helping hand. It will not be 
 possible to arrive at new physical truths by following this 
 path, but those that are actually known will be traced more 
 readily to the great mainstream of philosophy. To fathom the 
 secrets of the world is the work of a recluse, but to make it 
 comprehensible to a wide circle, a preacher is necessary, who 
 uses the beautiful methods of philosophical rhetoric. GDsmos 
 denotes the World and its Ornamentation ; its creator. 
 Demiurge, is a master who fashions his forms along the Hnes 
 of Art. 
 
 Thus we have learned what Einstein regards as the sole 
 purpose of Science, namely, the search after Truth. For him, 
 the latter is something absolute in itself, and the possibihty 
 of getting nearer to it is as great as the impossibihty of de- 
 riving results of scientific use from, say, ethical discoveries. 
 For ethics is a field which is haunted by the conceptual 
 ghosts, and the manner of treatment, ordine geometrico, that 
 Spinoza wished to apply to it, is reserved for physics. Einstein 
 leaves the inverse philosophical query : "Is not Truth in 
 itself only something that we have constructed in imagina- 
 tion ? " to those who find pleasure in sauntering along paths 
 of thought that are totally unconnected, whereas he himself 
 advances in a straight hne with the consciousness that even 
 if the goal is unattainable, he will at least not lose the right 
 direction ! 
 
CHAPTER VIII 
 HIGHWAYS AND BY-WAYS 
 
 Practical Aims of Science. — Pure Search for Truth. — Retrospective Con- 
 siderations. — The Practical Side of Kepler. — A Saying of Kant. — Mathe- 
 matics as a Criterion of Truth. — Deductive and Inductive Methods. — Con- 
 ceptual and Perceptual Knowledge. — Happiness and the Pleasures of Theory. 
 — Achievements of Science and Works [of Art. — Ethical Results. — Minor 
 Questions. 
 
 I 
 
 AGAIN we chanced to refer to the great subject : Can 
 or should theoretical science also pursue practical 
 aims ? 
 It is impossible to overrate the importance of this question. 
 It haunts us daily and often enough looms up threateningly 
 on the horizon of mankind. Observe what form the discus- 
 sions of educated people take when the finest and most sub- 
 lime achievements of mind are being debated : one talks of 
 the wonders of research in the remotest corners of astronomy 
 where the structures of world-wide star-systems are being 
 investigated ; we hear observations about the theories that 
 aim at tracing the cosmogonic development of universes from 
 the original chaos of countless ages ago. We hear mention 
 of exalted sciences, the Theory of Functions and Numbers, 
 whose founders and representatives are just as remarkable 
 in propounding problems as in solving them, and inevitably 
 the following question obtrudes itself : Of what use is it, 
 ultimately ? What can one do with it ? Can it be admitted 
 that theoretical science has an object of its own, or have we 
 at least the right to maintain the hope that, sooner or later, it 
 will bring us a real " Utility " expressible in practical terms ? 
 And just as the devotees of pure art have framed the 
 expression, " L'art pour I'art," so Einstein proclaims that 
 science is its own object, " Science for its own sake ! " It 
 carries its aims absolutely in itself and must not, through aim- 
 
 172 
 
HIGHWAYS AND BY-WAYS 173 
 
 ing at other purposes, stray from its own highways. "It is 
 my inner conviction," said he, " that the development of 
 science itself seeks in the main to satisfy the longing for pure 
 knowledge, which, psychologically, asserts itself as religious 
 feehng." 
 
 " To yourself. Professor, the practical aspect seems com- 
 paratively insignificant ? " 
 
 " I did not say that, and it was not imphed in the question. 
 We must not lose sight of our premises. As long as I am in- 
 terested in working along Hues of research — this was the 
 assumption — the practical aspect, that is, every practical 
 result that is found simultaneously or arises out of it later, 
 is a matter of complete indifference to me." 
 
 Far be it from me, even in thought, to wish to question this 
 confession of faith, particularly as the fact that it comes from a 
 searcher of the truth gives it the more weight. Yet a certain 
 uneasiness has crept over me because voices have recently 
 made themselves heard that demand for science a totally 
 different tendency. They arise not only from the pubhc at 
 large, but 'also from academic circles. Just a short time ago 
 I read an exposition by a well-known scientist, W. Wien, 
 in which he indulged in a violent polemic against the view 
 that purely scientific objects are alone vaHd. Professor Wien 
 addressed himself particularly to German physicists, reproach- 
 ing them with underestimating technical science, and with 
 regarding it as a " lowering of status " when a physicist enters 
 into practical Hfe. 
 
 To this Einstein remarked : " I do not know at whom this 
 reproach is aimed, but I venture to think that my own atti- 
 tude can never have given rise to an attack of this Idnd. For I 
 make no divisions of rank, and recognize no higher and no 
 lower status. I affirm only what is the nature of science 
 herself, and the objects according to which she, objectively, 
 has to direct her gaze. Whatever further orientation in- 
 dividual investigators may seek for themselves depends on 
 the determining conditions of life of each, although these 
 conditions do not serve as a means for deducing the main 
 lines of research. The accusation that I am unwarranted in 
 putting forward this view will, I hope, not be levelled at me, 
 for my connexions with practice are manifold enough, and up 
 
174 EINSTEIN THE SEARCHER 
 
 to the present moment I have often collaborated with practical 
 physicists. ..." 
 
 '* As I have regretfully observed when you were obliged 
 to interrupt a conversation with me to give an audience to 
 impatient persons seeking advice in technical matters ! " 
 
 " My own associations with the world of practice are not, 
 indeed, of recent date. My own parents originally wanted me 
 to become a technical scientist, and I was expected to choose 
 this profession to earn my Hvelihood. I was not, however, 
 sympathetically inclined to it, for even at an early age these 
 practical aims were to me, on the whole, indifferent and de- 
 pressing. My idea of human culture did not coincide with 
 the current view, that cultural development is to be measured 
 in terms of technical progress. Doubts, indeed, arose in me 
 as to whether technical improvements and advances would 
 actually contribute to the well-being of mankind. I must add 
 that, later, when I came into actual touch with technical 
 science, my opinion became somewhat modified, for the reason 
 that, here too, pleasures of theory often visited me." 
 
 The true position is probably that the technical worker 
 who does not merely think out improvements for machines, 
 but occupies himself with inventions on a higher plane, never 
 ceases to feel himself a theorist, since his achievements are 
 dependent for their inspiration on the fruits of theory. The 
 practical results of to-day are rooted in the theoretical results 
 of decades ago, and what is nowadays regarded as an idea of 
 pure research may in later decades acquire practical value. 
 Whether it actually becomes of value, or not, is of httle account 
 in judging the idea. At any rate experience has shown that 
 the beginning of theoretical investigations hardly ever gives 
 us the chance of making prognostications. We spoke of the 
 discoveries of Volta, Ampere, and Faraday. When these 
 were first known, the world might have asked : Why have 
 they been disclosed ? To what can they be applied ? Of what 
 use are they ? Nowadays we know the answers that still 
 lay hidden at that time, and we proudly point to modern 
 dynamos. But does a dynamo really represent the significance 
 of these discoveries ? Would the importance and rank of 
 Volta, Ampere, and Faraday be less if the dynamo had not 
 come into existence ? Only an out-and-out materiaHst would 
 
HIGHWAYS AND BY-WAYS 175 
 
 affirm this, and, strictly speaking, the question should not 
 even be raised. For it is in a sense equivalent to wishing to 
 judge of the importance and significance of the Polar Star 
 from its usefulness to the navigator on the earth's surface in 
 finding his bearings. We may put the question (although only 
 in the spirit of psychological curiosity, and without expect- 
 ing much elucidation) : Would these discoverers have been 
 particularly happy if they had divined the far-reaching conse- 
 quences of their work ? Did they, indeed, in the course of their 
 abstract researches, have a pre-vision of the future dominated 
 by the dynamo ? Einstein refused to answer this in the 
 decisive negative. He left room, if ever so little, for doubts — 
 that is, he considered that, in all probabihty, these three dis- 
 coverers had no presentiment of these consequences, and even 
 if they had in a dream caught a gUmpse of our present electrical 
 age, their zest for discovery, their " pleasure in theory," could 
 scarcely have been increased ; for they were discoverers by 
 nature, who, swept along by their own spirits, did not need to 
 wait to satisfy the desires of practical application. 
 
 In Einstein's opinion, the presentiment that a discovery 
 may have practical appHcations in the future may react on 
 pure research. He quoted bacteriology as a proof of this. 
 In the series of eminent bacteriologists, ranging from Spallan- 
 zani to Schwann and Pasteur, there were certainly some 
 whose desire for knowledge was directed primarily towards 
 discovering purely scientific relationships. Pcisteur himself 
 started from the theoretical question of the creation of life, that 
 is, from the problem of the origin of organic creatures from in- 
 organic matter without the medium of parent organisms. As a 
 pan-spermist he took up a negative attitude, that is, he tried 
 to prove that it is impossible to discover a bridge between 
 organic and inorganic matter. Yet he doubtless knew that 
 his theoretical efforts stretched out into practical regions, and 
 he may easily have foreseen that they would exert a very 
 important influence on Medicine and Hygiene, although he 
 could not measure its full extent. In this case, then, we cannot 
 fail to recognize that a certain connexion between the desire 
 for pure knowledge and the impulse to apply it practically 
 is possible, serviceable, and justified in itself. 
 
 An influence in the opposite direction is also possible, and 
 
176 EINSTEIN THE SEARCHER 
 
 when, during the course of our conversation, we went in search 
 of examples, we came across one of great interest. It shows us 
 that a question may arise out of ordinary practice that may 
 open up an immense field of pure knowledge, nay, it may lead 
 to a science of very wide scope. As this example is not well 
 known, I shall mention it here ; I do so with additional 
 pleasure as the scientist involved is one of those whom Einstein 
 quotes most frequently and for whom he has the greatest 
 admiration, namely, Johannes Kepler. First we have the 
 surprising fact that Kepler, who, even when at the height of 
 his fame, was not free from care, was once the possessor of some 
 money. In the year 1615, his blessed year of fortune, the great 
 astronomer owned a comfortable home in Linz, and even dared 
 to conceive the idea of placing some well-filled casks in his 
 cellar; nay, more, he was in a position to publish a new scientific 
 work at his own expense, and thus appear as his own publisher. 
 This production of Kepler and his casks of wine are directly 
 connected, as we see clearly from the title : Doliometrie, 
 literally, " The Measurement of Casks." But the title of 
 the work gives not the slightest hint of its importance. For 
 these investigations relating to wine-casks actually became 
 the foundation of a science of sovereign power, the In- 
 finitesimal Calculus. 
 
 What was Kepler's aim ? It was something entirely 
 practical, and directed to a definite purpose, quite independent 
 of " pleasures of theory," to repeat Einstein's expression. 
 His problem was a question of economy, of using material 
 sparingly and appropriately, in accordance with the require- 
 ments of the careful head of a house. How must such a 
 cask be constructed from a minimum of wood to give the 
 greatest cubical content ? 
 
 His dehberations began by regarding wine as the precious 
 content enclosed by a figure in space, and then conceiving 
 the cask as representing a particular class of " bodies of 
 revolution," that is, of figures in space that may be regarded 
 as produced by the revolution of a curved Une about an axis. 
 At this point he at first endeavoured to gain a complete 
 survey of the question. He varied the boards along the 
 sides, the staves, and formed successively ninety-two such 
 bodies of revolution, some of which he named after the fruits 
 
HIGHWAYS AND BY-WAYS ITT 
 
 which they resembled in shape, as, for example, apple-shaped, 
 lemon-shaped, olive-shaped bodies. He started out by 
 measuring casks, and the final result was that his work, 
 Doliometrie, became the source of all future cubatures or 
 measurements of volume. 
 
 Now we come to the deciding point. What conditions 
 has the hmiting surface of such a cask-Uke body of revolution 
 to fulfil, if the body is to have a maximum volmne ? An 
 epochal discovery here came to light. The practical head of 
 the house soars up into the subhme realms of the theory of 
 magnitudes. Kepler discovered the conception of changes 
 in functions, and their peculiarities at the maximum point. 
 (He did not, of course, use these modem terms.) By this 
 means, long before Newton and Leibniz, he laid the founda- 
 tions of Infinitesimal Calculus, which later became the heart 
 and soul of mathematics, of astronomy, of theoretical physics, 
 and of technical science, in so far as it is foimded in mechanical 
 relations. 
 
 On the other hand, Einstein who now, three hundred years 
 later, has set up his differential equations, and, with them, a 
 new world-system, stands before us as a pure discoverer, 
 devoid of practical aims. But in these equations there are 
 elements of analysis that once came to fight in a happy idyll. 
 This event did not come out of the grey obscurity of abstrac- 
 tion, but out of a region of earthly happiness, when a ray of 
 light found its way into Kepler's gloomy existence. No poet 
 has yet expressed this curious complex of events in a ballad, 
 teUing how Truth, the only object of Science, was pressed out 
 of the grape, and how Practice, inspired by the inquiry of a 
 cooper, found its way to a Theory that stretches to the confines 
 of the Universe. 
 
 II 
 
 The conversation touched on famous expressions, words 
 carved in stone, in particular a saying of Kant which seeks 
 to fix the foundation and the limits of knowledge. " Every 
 science of Nature," the great philosopher of Konigsberg 
 had said, ** contains just as much Truth as it contains mathe- 
 matics." And since, ultimately. Nature includes everything 
 
 12 
 
178 EINSTEIN THE SEARCHER 
 
 — for a demarcation between physical and mental science no 
 longer seems possible — then, if we follow Kant, we should 
 have to regard mathematics as the sole measure of science. 
 
 It is certainly not yet possible to enter into a discussion 
 on this point with historians, medical or legal practitioners. 
 They would be justified in refusing it, since, in their subjects, 
 *' truth '* is not the sole factor, and because we cannot see at 
 present how the conception of a comprehensive mathematical 
 truth is to find a place in them. But when we question a 
 physicist on this point, who unceasingly uses mathematics 
 as his chief instrument, we should surely expect him to answer 
 with an unconditional affirmative. At least, I should not 
 have been surprised if Einstein had answered in this way, 
 and if he had indeed claimed its validity for every branch of 
 science. 
 
 But Einstein considered this quotation to be true only 
 conditionally, in that he accepted it as a principle, but did not 
 regard it as universal. That is, he does not recognize mathe- 
 matics as the only test of truth. 
 
 " The sovereignty of mathematics,'* said Einstein, *' is 
 based on very simple assumptions ; it is rooted in the con- 
 ception of magnitude itself. Its dominant position is due to 
 the fact that it gives us much more delicate means of dis- 
 tingmshing between infinitely varied possibilities than any 
 other method of thought that expresses itself in language 
 and is restricted to the use of words. The greater the field 
 taken into consideration, the clearer does this become ; but 
 even in such a narrow range as i to loo, an estimate such 
 as 27 is incomparably more exact than can be expressed in 
 words in any other way. If we think of a series of sensations, 
 ranging from pleasure to pain, or from sweet to bitter, we 
 find that words leave us in an uncertain, confused state, 
 and we do not succeed in fixing on a point of the series with 
 the same precision as we above fixed on the 27 out of the 100. 
 But when the theory of magnitude plays a part in the question, 
 as, for example, in a series of tones, whose vibrations exhibit a 
 mathematical sequence, we immediately attain a much higher 
 order of precision by using numbers. ..." 
 
 That is why there is a sort of scientific pleasure in the 
 sequence of tones, so my thoughts ran on. Leibniz remarks 
 
 y 
 
HIGHWAYS AND BY-WAYS 179 
 
 that " Music is the pleasure of the human soul, which arises 
 from counting without knowing that it is counting." Here 
 Pythagoras' *' Number is the essence of all things " is verified. 
 As soon as we arrive at the stage at which we feel the psycho- 
 logical essence of number, we fall into a sort of ecstasy, 
 because, in our subconscious minds, we experience not only 
 the pleasure of sense but also the underiying truth. 
 
 Einstein resumed : " Kant's remark is correct in the 
 sense that it sets up two things in clear contradiction to one 
 another. On the one hand, he has in view the fruits of know- 
 ledge of ordinary life, in which our ordinary perceptions and 
 experiences are intermingled and cannot be disentangled by 
 inductive methods and deductive considerations. Opposed 
 to these, and to be regarded of higher rank, are the properly 
 scientific constructions — that is, such in which we find a neat 
 differentiation of connected thoughts that are based on regular 
 foundations and that form the links of a chain of deduction. 
 Whenever our science succeeds in detaching this logically 
 ordered knowledge from its sense-sources, it has a mathe- 
 matical character, and the amount of truth contained in it 
 will accordingly be determined by Kant's criterion. But Kant 
 demands too much when he asks us to apply this scale to all 
 attainable knowledge of science. It would seem advisable to 
 draw Umitations if his remark is to serve as a regulative 
 measure. A great part of biological science will in future 
 still be obliged to make its way independently of purely mathe- 
 matical considerations." 
 
 " Your reflections. Professor, would then also apply to 
 the saying of Galilei : The book of Nature lies open before 
 us, but is written in letters other than those of our alphabet ; 
 its characters are composed of triangles, quadrilaterals, circles, 
 and spheres." 
 
 " With all due honour to the beauty of this observation, I 
 cannot refrain from doubting its universal validity. If we 
 were to accept it unconditionally we should have to regard 
 the paths of all research as purely mathematical, and this 
 would exclude certain very important possibihties, above all, 
 certain forms of intuition that have shown themselves to be 
 extremely fruitful. Thus, according to GaHlei's interpreta- 
 tion, the book of Nature would have been illegible for Goethe, 
 
180 EINSTEIN THE SEARCHER 
 
 for his spirit was entirely non-mathematical, indeed anti- 
 mathematical. But he possessed a particular form of intuition 
 that expressed itself as a feeling which put him into direct 
 contact with Nature, with the result that he obtained a clearer 
 vision than many an exact investigator." 
 
 " Do you then consider intuitive gifts to be separable at 
 all in form and in kind ? " 
 
 *' It would be pedantic to seek to establish a fundamental 
 difference, even if we may regard the non-mathematical 
 intuition of Goethe as a very striking case. Moreover, as I 
 have often emphasized, all great achievements of science start 
 from intuitive knowledge, namely, in axioms, from which 
 deductions are then made. It is possible to arrive at such 
 axioms only if we gain a true survey of thought -complexes 
 that are not yet logically ordered ; so that, in general, intuition 
 is the necessary condition for the discovery of such axioms. 
 And it cannot be denied that, in the great majority of minds 
 with a mathematical tendency, this intuition exhibits itself as 
 a characteristic of their creative power." 
 
 " From these remarks it would appear that you value 
 deduction considerably higher than induction. Perhaps in 
 using these catchwords I am expressing myself a Httle vaguely ; 
 it seems to me that great things have been achieved, too, by 
 using inductive processes." 
 
 " Let us first define what each of these terms means. 
 Deduction is the derivation of the particular from the general, 
 whereas induction is the process of deriving the general from 
 the particular case. Now, quote any example of a brilliant 
 achievement, which you feel illustrates the power of the 
 inductive method. Of whatever kind your example may be, 
 you will soon become aware of the difference in the significance 
 of the two processes." 
 
 " For me the most perfect example of induction is given by 
 certain reasoning of Euchd. The question was whether there 
 is a finite or an infinite number of primes (that is, numbers 
 that cannot be divided without leaving a remainder except 
 by unity). EucHd found an elegant proof that the total 
 number is infinite by the following strictly inductive reasoning. 
 If the total number were finite there would have to be a 
 greatest prime. Let us call it n, and then form the product 
 
HIGHWAYS AND BY-WAYS 181 
 
 of all primes up to n and including it, finally adding one, 
 thus: 2x3x5x7x11x13 . . . w, plus I. This new number, 
 say Y, is certainly greater than n, and now there are two 
 possibilities, either n is prime or it is not prime. 
 
 " If it is not prime, it must be divisible by some existing 
 prime. But the primes up to and including n cannot divide 
 exactly into Y, as there is always a remainder, namely, i. 
 Hence Y must be divisible by an existing prime X greater 
 than n. This contradicts the assumption that n is the greatest 
 prime, for^X^is shown to be greater than n. 
 
 " Secondly, if Y is a prime, it immediately follows that n 
 cannot be the greatest prime, for Y is greater than n. Hence, 
 however great may be any prime that we may assume, there 
 will always be one that is greater, and even if we do not 
 succeed in expressing it in figures, we see that it must certainly 
 exist. Thus by studying carefuUy a particular case — the 
 prime n, which was assumed to be the greatest possible one — 
 we have arrived at a general theorem which states that there 
 is no Umit to the number of primes. Is not that, too, a triumph 
 of intuition ? " 
 
 ** Certainly," said Einstein. " But you must not overlook 
 the fact that a theorem of this kind cannot be ranked with 
 a theorem of a fimdamentally axiomatic character. The one 
 you havefdiscussed has been derived by a clever process of 
 reasoning, but it does not exhibit the characteristic of a 
 momentous discovery. This theorem of Euclid can be im- 
 agined absent from science without the content of truth in 
 science being essentially effected. Compare with it a theorem 
 of axiomatic significance, such as Gahlei's Law of Inertia, or 
 Newton's Law of Gravitation. Theorems such as the latter 
 are characterized by being starting-points of knowledge that 
 are inexhaustible in the consequences that may be deduced 
 from them. Your question, earher, as to whether I consider 
 the deductive method superior to the inductive, was not 
 formulated in correct terms. To this I answered above that 
 the inductive method as a means of discovering general truths 
 usually appears over-estimated. The proper form of the 
 question is : Which truths are of the higher order, those that 
 are found inductively, or those that lead to further deduction ? 
 There can scarcely be doubt about the answer." 
 
182 EINSTEIN THE SEARCHER 
 
 ** No, that is certainly true. If I understand your meaning 
 rightly, the answer may be expressed by an allegory. In- 
 tuition of the highest order creates treasure-mines, those of 
 lesser degree individual articles of value that are significant 
 in themselves, although they cannot be compared with the 
 inestimable value of the mines. The fact that the highest 
 intuition is found in minds with a mathematical trend makes 
 it appear possible that Kant's remark may gain more and 
 more credence in the future. It already appHes in a measure 
 to subjects to which it seemed inappHcable during Kant's 
 hfetime, for example, in Psychology, in which the relations 
 between stimulus and response have been established mathe- 
 matically only since the Weber-Fechner Law was set up ; 
 and also, since the time of Quetelet, in Moral Science and 
 Sociology, we learn from mathematical methods of statistics 
 and probability that even Man as an active being is subjected 
 to mechanical causaUty. At any rate it seems manifest that 
 Kant's remark, that in every science there is just as much 
 truth as there is mathematics, has received additional support 
 in recent times." 
 
 '* That may be admitted," concluded Einstein, " without 
 recognizing his remark as an axiom. It is still far removed 
 from making possible unassailable deductions, and will never 
 quite succeed in doing so ; yet it may claim equal significance 
 as a beautifully expressed idea with that of Pythagoras, which 
 asserts number to be the nature of all things." 
 
 Ill 
 
 " The lines of demarcation between ' conceptual know- 
 ledge ' (Erkennen) and * perceptual knowledge ' (Kennen) are 
 being drawn more and more closely nowadays. The former 
 is regarded as being the exclusive possession of the highly 
 developed human mind, and the latter as being characteristic 
 of the lower intelhgence of other hving creatures. Is this not 
 a pronounced case of anthropomorphism, and does it not 
 mislead us to form opinions that we should at once disown 
 if we succeed in stepping out of our human frames even^for 
 a moment ? " 
 
HIGHWAYS AND BY-WAYS 188 
 
 " We have to rest satisfied with anthropomorphism once 
 and for all," answered Einstein, ** and there is no sense in 
 wishing to escape from it, for the arguments about anthropo- 
 morphism are necessarily also diffused with it, itself. We are 
 thus moving in a circle if we imagine we can deduce something 
 outside of human knowledge. As soon as we have argued 
 around the circle, we find ourselves again at the starting- 
 point, and so we are compelled to mark clear Unes of division 
 between instinctive knowledge, derived directly by perception, 
 from conceptual knowledge, derived by processes of abstraction 
 and reflection ; in this way we award the palm of supremacy 
 to the human mind." 
 
 " But what if the following contradiction were to assert 
 itself ? Suppose that the logical ' circle * is not a circle at 
 all, but a spiral, so that the final point of the argument hes 
 just a trifle above the initial point. I feel instinctively that 
 such apparently fruitless circuitous arguments might finally 
 lead to a definite piece of knowledge. For example, a certain 
 insect, the ichneumon-fly, although devoid of a knowledge of 
 science in our sense, infaUibly plants its sting in a definite 
 point in the rings of a caterpillar, at just the point that serves 
 its purpose of paralysing the caterpillar without killing it. 
 It acts instinctively, and it is open to me to interpret this 
 occurrence in other words. The fly discloses that it * knows * 
 the anatomy of the foreign creature, although it has no con- 
 ceptual knowledge of it in our sense. But it immediately 
 follows from this analogy that, from the point of view of the 
 fly, its perceptual intelUgence stands higher than our con- 
 ceptual intelligence — that is, by changing the perspective, I 
 am led to declare the anatomical knowledge of the fly to be 
 of higher rank than the analogous knowledge of the most 
 learned anatomist. In the same way I might persuade myself 
 that the mathematics of a bird of passage stands above the 
 cartographic knowledge of any human explorer. The migratory 
 bird that flies from the interior of Africa in a straight Hne to 
 its nest in Mecklenburg must have something in the nature 
 of a co-ordinate system in its organism. The real reason that 
 we assign a higher position to our conceptual knowledge is 
 that we are equally proud of our inteUigence as of our science ; 
 this is perhaps a deception depending on some compromise. 
 
184 EINSTEIN THE SEARCHER 
 
 a sort of illicit deal in which the mind draws bills of exchange 
 on science, and, as a return, science meets its obligations by 
 paying in cheques drawn on the mind ! " 
 
 I must confess that these hazardous suggestions received 
 no welcome from Einstein, and were not even met with the 
 friendly smile with which he usually accompanies his refuta- 
 tions. Nor do I disguise from myself that the question of 
 conceptual or perceptual knowledge can in no way serve as 
 a basis of proof ; we may at most base certain conjectures 
 on the difference of these types of knowledge, conjectures 
 that suggest in words what eludes our clear comprehension. 
 Einstein's refusal to allow this possibility certainly rests on 
 much firmer ground than the somewhat Bergsonian views 
 that I tried to present. Perhaps they are of a hair-spHtting 
 nature, and deal with things lying on different planes ; and 
 are deduced by unjustifiably altering the perspective with a 
 sort of sophistic somersault ; perhaps I may be reproached 
 with seeking, hke Miinchhausen, to reach a higher standpoint 
 without having a support from which to start. Yet how is it 
 that I find it impossible to free myself from this chain of 
 thought ? No reason is forthcoming, for it is a purely meta- 
 physical question, and there has never yet been a clear system 
 of metaphysics free from ambiguities and sophism. 
 
 Let us rather confine ourselves to the conceptual intelli- 
 gence characteristic of human beings, with which, according 
 to Einstein, so many pleasures of theory are available. I 
 asked him whether he would recognize differences of degree 
 in these pleasures, dependent on their intensities. Although 
 I rightly felt that he would answer in the affirmative, his 
 answer took a totally different turn from what I had expected. 
 It was, indeed, a great surprise, for in the matter of happiness 
 of spirit he expressed a view, according to which he — a great 
 discoverer 1 — does not regard Science as the deepest source 
 of happiness ! 
 
 *' Personally," said Einstein, " I experience the greatest 
 degree of pleasure in getting contact with works of Art. They 
 furnish me with happy feelings of an intensity such as I cannot 
 derive from other realms." 
 
 ** This is indeed a remarkable revelation, Professor!" I 
 exclaimed. " Not that I have ever doubted your receptivity 
 
HIGHWAYS AND BY-WAYS 185 
 
 for products of art, for I have often enough observed how you 
 are affected by good music, and with what interest you yourself 
 practise music. But even at such moments when you gave 
 yourself up to the pleasures of the Muses, and were soaring in 
 regions far removed from the earth, I used to say to myself : 
 This is a delightful arabesque in Einstein's existence ; but I 
 should never have surmised that you regard this decorative 
 side-issue as the greatest source of happiness. But your con- 
 fession seems to go further, perhaps even beyond music ? " 
 
 " At the moment I was thinking particularly of hterature." 
 
 ** Do you mean literature in general ? Or had you a 
 definite writer in mind, when you were speaking of the 
 feUcitous effect of works of art ? " 
 
 " I meant it generally, but if you ask in whom I am most 
 interested at present, I must answer : Dostojewski ! " He 
 repeated the name several times with increasing emphasis. 
 And, as if to deal a mortal blow at every conceivable objection, 
 he added : " Dostojewski gives me more than any scientist, 
 more than Gauss ! " 
 
 " If, Professor," said I, after a pause that may easily be 
 accounted for — " if you mention in the same breath the names 
 of two such powerful but essentially different intellects, you 
 open the way to a discussion that cannot be settled by a mere 
 positive assertion. It is possible to admire intensely Dosto- 
 jewski as one who moulds personahties and who analyses the 
 inner struggles of the soul, and yet to deny him perpetual 
 fame. This depends on individual judgment, and, as for my 
 own, I believe that Dostojewski, in spite of his direct artistic 
 appeal, will not have his name perpetuated through the 
 centuries Hke that of many another member of Parnassus. It 
 seems to me to be a more important matter whether a common 
 measure can be found for Art and Discovery at all. Perhaps 
 the test of how far a work can be replaced may be regarded 
 as vaUd for each. When you say that Dostojewski gives you 
 more than Gauss, this probably corresponds with the feeling 
 that without Dostojewski you would have no * Karamasoffs ' 
 and hence would lack a certain life-value that cannot be 
 replaced. But if Gauss had failed to produce one of his funda- 
 mental theorems of Algebra, probably some other Gauss 
 would have appeared, who would have achieved this result. 
 
186 EINSTEIN THE SEARCHER 
 
 According to this, then, our instinct increases the value of a 
 work of art, as we feel that we are dependent on one being 
 alone for its creation." 
 
 ** But this is only to be admitted conditionally,'* said 
 Einstein, " for the best that Gauss has given us was likewise 
 an exclusive production. If he had not created his geometry 
 of surfaces, which served Riemann as a basis, it is scarcely 
 conceivable that anyone else would have discovered it. I 
 do not hesitate to confess that to a certain extent a similar 
 pleasure may be found by absorbing ourselves in questions 
 of pinre geometry." 
 
 " Perhaps we may use a different characteristic as a means 
 of comparison," I suggested, " namely, the permanency of 
 the impression produced on the subject receiving it. For 
 example, a fine piece of music never loses its influence. We can 
 hsten to the first movement of Beethoven's Ninth Symphony 
 a hundred times, and, although we know at every beat what 
 will follow, the state of pleasure continues unweakened ; 
 indeed, it might rather be said that the expectation of pleasure 
 increases from one hearing to the next." 
 
 " This characteristic, too," answered Einstein, " cannot 
 be claimed as the exclusive property of works of art. Its 
 existence cannot be doubted, inasmuch as it belongs to every 
 eminent example of art. Yet we encounter it outside the 
 realm of art, too, in great advances of science, with which we 
 never cease occupying ourselves, and yet the impression con- 
 tinues unweakened." 
 
 " Do you include among them the impressions that a 
 discoverer experiences when he reviews in his mind the progress 
 due to his own efforts ? " 
 
 " Naturally, and these, indeed, quite particularly ; and if 
 this question were put to me directly, I should answer un- 
 hesitatingly that I find pleasure in reflecting on my own 
 discoveries, and never experience feelings of weariness in 
 passing over them again. So that, to return to our original 
 thesis, we must adopt a new basis of value if we wish to 
 account for the fact that the greatest degree of happiness is 
 to be expected of a work of art. It is the moral impression, 
 the feeling of elevation, that takes hold of me when the work 
 of art is presented. And I was thinking of these ethical 
 
HIGHWAYS AND BY-WAYS 187 
 
 factors when I gave preference to Dostojewski's works. There 
 is no need for me to carry out a literary analysis, nor to enter 
 on a search for psychological subtleties, for all investigations 
 of this kind fail to penetrate to the heart of a work such as 
 " The Karamasoffs." This can be grasped only by means of 
 the feeUngs, that find satisfaction in passing through trying 
 and difficult circumstances, and that become intensified to ex- 
 ultation when the author offers the reader ethical satisfaction. 
 Yes, that is the right expression, ' ethical satisfaction ' ! I 
 can find no other words for it.'* 
 
 His whole face lit up, and I was deeply touched by his 
 expression. At that moment it seemed to me that he had 
 drawn the last veil from his soul to allow me to share in his 
 ecstasy. Was that the same physicist who interprets the 
 events of the world in terms of mathematics, and whose 
 equations encompass phenomena from electrons to universes ? 
 If so, it was a different soul ; one which gave utterance, like 
 that of Faust, to the words : 
 
 " And when in the feeling wholly blest thou art. 
 Call it then what thou wilt. 
 Call it Bhss ! Heart ! Love I God I 
 I have no name for it I 
 FeeUng is aU in all ! 
 Name is but sound and reek, 
 A mist round the glow of heaven I " 
 
 And, certainly, the book need not have been one of 
 Dostojewski's to excite this feehng in him. He chose the 
 latter to give expression to a mood that may change according 
 to what he reads, but undergoes no fluctuations in its ethical 
 foundation. From other occasions we know how little ethics, 
 that is conducted along systematic fines, signifies to him, and 
 that he does not even include it in the sciences. But at the 
 same time we see now that his inner fife is dominated entirely by 
 the ethical principle. His deep love of Art is characterized by 
 it, and receives full satisfaction from the source of ethical joy of 
 which Art is the centre. 
 
 IV 
 
 During the autumn of 1918 Einstein was feehng indisposed, 
 and, on the advice of his doctor, did not leave his bed. When 
 
188 EINSTEIN THE SEARCHER 
 
 I entered his room, I saw at once that there was no reason 
 for alarm, for pieces of paper covered with mysterious symbols 
 were l5Hing about, and he was absorbed in making additions 
 to some of them. Nevertheless, I considered it my duty to 
 treat him as a patient under medical care, and did not conceal 
 my intention of leaving him after having inquired about his 
 condition. But he would not accept my visit as a mere call 
 to ascertain his progress towards recovery, and insisted that 
 I should remain with him a while, to converse about amusing 
 little problems as usual. y 
 
 I pointed out to him that there were two objections to 
 this, the first being that he was unwell, and the second that I 
 was intruding on his work. 
 
 " How illogical ! " he answered. " If I interrupt my work 
 to chat with you, I am putting aside exactly what the doctor 
 would deny me if I were to allow him. So, let us make a 
 start. You have probably some conundrum weighing on your 
 mind." 
 
 " That may not be far wrong. I have been troubled by 
 something in connexion with Kepler's second law. It almost 
 robbed me of my night's sleep. My thoughts kept returning 
 to a certain question, and I should like to know whether there 
 is any sense in the question itself at all." 
 
 " Let us hear it ! " 
 
 " The law in question states that every planet in describing 
 its elliptic path, sweeps out with its radius vector equal 
 sectorial areas in equal intervals of time. But this seems 
 only half a law, for the radius vectors are only considered 
 drawn from the one focus of the ellipse, namely, the gravita- 
 tional centre. Now, another focus exists, that may be situated 
 in space somewhere, perhaps far away in totally empty regions, 
 if we assume the orbit to be very eccentric. My question is : 
 What form does this law take if the radius vectors are drawn 
 from this second focus and if the corresponding sectorial areas 
 are considered, instead of these quantities being referred to 
 the first focus exclusively ? " 
 
 '* This question is not devoid of sense, but it serves no 
 useful purpose. It may be solved analytically, but would 
 probably lead to very complicated expressions, that would 
 be of no interest for celestial mechanics. For the second 
 
HIGHWAYS AND BY-WAYS 189 
 
 focus is only a constructive addition, that has nothing 
 real in space corresponding to it. What else is troubUng 
 you ? " 
 
 ** My next difficulty is a Uttle problem that sounds quite 
 simple and yet is sufficiently awkward to make one rack one's 
 brains. It was suggested to me by an engineer who certainly 
 has a keen mind for such things, and yet, as far as I could 
 judge, he did not get a solution for it. It concerns the position 
 of the hands of a clock." 
 
 *' You surely are not referring to the children's puzzle 
 of how often and when both hands coincide in position ? " 
 
 " By no means. As I said just now, it is really quite per- 
 plexing. Let us assume the position of the hands at twelve 
 o'clock, when both hands coincide. If they are now inter- 
 changed, we still have a possible position of the hands, giving 
 an actual time. But, in another case, say, exactly six o'clock, 
 we get a false position of the hands, if we interchange them, 
 for on a normal clock it is impossible for the large hand to 
 be on the six whilst the small hand is on the twelve. The 
 question is now : When and how often are the two hands 
 situated so that when they are interchanged, the new position 
 gives a possible time on the clock ? " 
 
 " There, you see," said Einstein, ** that is just the right 
 kind of distraction for an invalid. It is quite interesting, and 
 not too easy. But I am afraid the pleasure will not be of 
 great duration, for I already see a way to solve it." 
 
 Supporting himself on his elbow, he sketched a diagram 
 on a sheet of paper that gave a clear picture of the conditions 
 of the problem. I can no longer recollect how he arrived at 
 the terms of his equation. At any rate, the result soon came 
 to hand in a time not much longer than I had taken to enunciate 
 the problem to him. It was a so-called indeterminate (Dio- 
 phantic) equation between two unknowns, that was to be 
 satisfied by simple integers only. He showed that the desired 
 position of the hands was possible 143 times in 12 hours, 
 an equal interval separating each successive position ; that 
 is, starting from twelve o'clock, the two hands may be inter- 
 changed every 5 minutes ttu seconds, and yet give a possible 
 time. 
 
190 EINSTEIN THE SEARCHER 
 
 I mention this little episode, which is insignificant in itself, 
 merely to give an example of how a great discoverer, too, 
 finds amusement in such distractions. In Einstein's case this 
 tendency to practise his ingenuity on unimportant trifles is 
 so much the more pronounced from the fact that he requires 
 an outlet for his virtuosity in calculation, and gratefully 
 welcomes every suggestion that helps him to relieve his mental 
 tension. Similar characteristics are reported of the great 
 Euler, as well as of Fermat, whereas many another eminent 
 mathematician feels decidedly unhappy if he drifts within 
 reach of the realm of actual numerical calculation. In my 
 mind's eye I still see Ernst Kummer, the splendid savant 
 (who, in his time, conferred distinction on Berlin University 
 by his very presence), suffering agonies whenever ordinary 
 arithmetical tables threatened to appear in the working-out of 
 his formulae. As a matter of fact, these two things, a mastery 
 over mathematics and a talent for ingenious calculation, are 
 to be considered as quite independent, even if we now and 
 then find them present in the same person. 
 
 In the case of Einstein this tendency is a symptom of an 
 incredible universality of spirit. It moreover presents itself 
 in the pleasant est forms, and a character-sketch of Einstein 
 would be incomplete if this trait were not mentioned. Every 
 problem which is in any way amusing excites in him a willing 
 interest and enthusiasm. I once directed our conversation 
 to the so-called Scherenschnitte. These are made from 
 long strips of paper or canvas, the ends of which are caused 
 to overlap a Httle and then pasted together, but instead of 
 being fixed so that a flat wheel results, which rolls on one side 
 of the strip, the strip is twisted one or more times before the 
 ends are fastened together. If now the strip is cut lengthwise 
 right along its centre, various unexpected results occur, depend- 
 ing on the number of twists that have been made before pasting. 
 
 Some very complex geometrical difliculties are involved in 
 these problems. This is shown by the fact that learned 
 mathematicians have written extensive disquisitions on these 
 curious constructions (for example. Dr. Dingeldey's book, 
 published by Teubner, Leipzig). Einstein had never taken 
 notice of these wonders of the scissors, but when I began to 
 form these strips, to paste them, and to cut them, he immedi- 
 
HIGHWAYS AND BY-WAYS 191 
 
 ately became interested in the underlying problem, and pre- 
 dicted in a flash what puzzUng chain constructions would 
 result in each case, with a certainty that would lead one to 
 imagine that he had spent days at it. On another occasion 
 a space-problem dealing with dress came up for discussion : 
 Can a properly dressed man divest himself of his waistcoat 
 without first taking off his coat ? One would not have dared 
 to confront Copernicus or Laplace with such a problem. 
 Einstein at once attacked it with enthusiasm, as if it were an 
 exercise in mechanics, the body being the object ; he solved it 
 in a trice, practically, with a little energetic manipulation, 
 much to the amazement and joy of the beholder, who asked 
 himself : Is this the same Einstein who developed the work 
 of Copernicus and Newton ? A little later, perhaps, the con- 
 versation centres around some serious point drawn from 
 poUtics, political economy, sociology, or jurisprudence. What- 
 ever it may be, he knows how to spin out the suggested thread, 
 to establish contact with his partner in conversation, to open 
 up his own perspectives without ever insisting on his point 
 of view, always stimulating and showing a ready S5mipathy 
 for the subject of discussion and for all the ideas which it 
 crystaUizes, the prototype of the scientist, in the mouth of 
 whom Terence put the words : " I am a human being ; nothing 
 that is human is alien to me ! " 
 
CHAPTER IX 
 AN EXPERIMENTAL ANALOGY 
 
 Forms of Physical Laws. — Aids to Understanding. — Popular Descriptions. 
 — Optical Signals. — Simultaneity. — Experiments in Similes. 
 
 I WISH to ask you, Professor, to help me over a difficulty 
 and to treat me as the spokesman of a great number 
 who are similarly troubled. In most accounts of your 
 theory of relativity, there is a dearth of definite, concrete, 
 illustrative examples on which we can fix our minds whenever 
 the theorem is to be applied generally without limitation. 
 Let me express this more precisely : Your simplified picture 
 of the structure of the universe is achieved in the theory of 
 relativity by emancipating all observations from fixed co- 
 ordinate systems, and by proclaiming the equivalence of all 
 systems of reference. One of your earliest theorems states 
 that physical laws describing how the states of physical 
 systems alter, remain the same, no matter to which of two 
 co-ordinate systems these states are referred, provided that 
 the co-ordinate systems are moving rectilinearly and uniformly 
 relatively to one another. This theorem entails the following 
 statement . If we — erroneously — adopt a non-relativistic view, 
 we shaU come to the conclusion that physical laws depend on 
 the particular system of reference chosen, and will thus assume 
 a different form for each different system. At this point we 
 experience a desire to hear definite examples. What varying 
 forms may a certain given physical law, known under a definite 
 form, assume, and how can we use this law to show that it 
 must adapt itself to the postulate of relativity ? " 
 
 Einstein explained that such examples cannot be given 
 in special cases, but only in very general terms. If we were 
 to suggest the elliptic orbits of the planets (at which I had 
 
 192 
 
AN EXPERIMENTAL ANALOGY 198 
 
 hinted in my remarks), we should fall into error, for the law 
 of elliptic orbits is no such law. For, from another point of 
 view, the elUptic paths of the planets might be drawn out into 
 wavy lines, or into spirals, and they would remain ellipses 
 only as long as the lines of motion are referred to the central 
 attracting body. But the constancy of the velocity of Ught 
 is such a law, as also is the law of inertia, according to which 
 a body that is left to itself moves uniformly in a straight line. 
 I confessed to him that this limitation to a few very general 
 laws would be a painful matter for many an enthusiast of 
 average attainments, who has great difficulty in distinguishing 
 the laws that are generally valid from those that hold only 
 within circumscribed limits. But if this were not so, we should 
 have to alter our conception of what is conveyed by a popular 
 exposition. For it is called popular, not because it now and 
 then uses the patronizing words " dear reader," but because 
 it anticipates the questions and doubts of the man of average 
 sense, and examines them, proving some to be unjustified 
 and others to be reasonable or unreasonable, as the case may 
 be. " Then there is a further matter that troubles me," I 
 continued. " Let us suppose an ordinary reader of such a 
 popular account to get a first insight into the new conception 
 of Time. He is glad to feel the ideas dawning in him, and, to 
 get a more lasting view of the idea, he repeats the arguments 
 through which he has just threaded his way, and, in doing so, 
 again encounters the phrase ' uniform motion.' At the first 
 reading he imagined that he understood the expression quite 
 well, but the second time he pauses and considers. For now 
 that he knows how much depends on it, he is anxious to find 
 out the exact meaning of a ' uniform motion.' He looks for a 
 definition, and if he cannot find one in the book he is perusing, 
 he endeavours to reason it out for himself. With good luck 
 he arrives at the usual statement : a body moves with * uni- 
 form motion ' if it traverses equal distances in equal intervals 
 of time. But equal intervals of time are clearly those during 
 which a body in uniform motion traverses equal distances. 
 In other words, he explains A by means of B, and B by means 
 of A, so that he has involved himself in a vicious circle from 
 which he cannot escape. This is his hour of need, due to the 
 difficulty of ' time.' 
 13 
 
194 EINSTEIN THE SEARCHER 
 
 '* He hopes that further study will remove this obstacle. 
 He meets with the conception of ' simultaneity/ which is 
 defined for him anew, and is disclosed as being * relative.' 
 He manoeuvres further towards the fundamental theorem that 
 every body of reference has its own particular time. 
 
 ** His popular booklet makes this clear to him by quoting 
 the example of a flying-machine, or, better still, a railway train 
 that is rushing along an embankment at a very great speed, 
 and that carries a passenger. Two strokes of lightning I and II 
 are to take place at two widely distant points on the embank- 
 ment. The question is then : When are these two flashes 
 of lightning to be considered ' simultaneous ' ? What 
 conditions must be fulfilled to ensure this ? It is found — 
 incontrovertibly — ^that the light -rays starting out from the 
 two strokes of lightning must meet at the mid-point of the 
 embankment. 
 
 " It now follows from a short chain of argument that the 
 observer in the train will see flash II earlier than flash I, 
 if they reach the observer, who is at rest, at the same moment. 
 That is, two events that are simultaneous with respect to the 
 embankment are not simultaneous for a moving system (such 
 as a train or a flying-machine) ; the converse is, of course, 
 also true. 
 
 " Here, again, the eager layman encounters difficulty, for 
 he asks himself : Why should the two events be characterized 
 or defined by lightning-flashes in particular ? If acoustic 
 signals were used instead, nothing would be altered in the 
 fundamental determination, for the sound rays (sound-waves) 
 would likewise meet at the mid-point of the line joining the 
 sources of disturbance. What is the reason that the relativity 
 of time arises only when phenomena are regarded optically, 
 and that rays of light play the deciding part in all later develop- 
 ments ? 
 
 *' And this particular query is followed by one which is more 
 general : Why does the popular pamphlet not read this question 
 in my mind ? I know that the author of it is more skilled in 
 these matters than I, but just this superiority should help him 
 to divine what is passing in my mind when I make efforts to 
 follow his reasoning." 
 
 Einstein had listened to me patiently, and then he explained 
 
AN EXPERIMENTAL ANALOGY 195 
 
 to me at considerable length why in this case optical signals 
 cannot be replaced by sound signals : hght is the only mode of 
 motion that shows itself to be entirely independent of the 
 carrier of the motion, of the transmitting medium. Thus the 
 constancy of velocity is assumed in the above argument, and 
 as this constancy is an exclusive property of light, every other 
 method must be discarded as unallowable for investigating 
 the conception " simultaneity." Furthermore, he showed me 
 how, on the basis of relativity, starting from the embankment - 
 experiment, we may arrive at a perfectly consistent representa- 
 tion of the conception of Time. He certainly did this by 
 applying subtle physical arguments that exceed the scope of 
 the present book.* He added, in substance, that it was 
 futile and impossible to discuss in detail all the conceivable 
 objections that might arise in the mind of one reading a popular 
 work of this kind : it was a futile undertaking, because the 
 true purpose was defeated, inasmuch as a clear development 
 of the fundamental thought would be almost impossible under 
 the cross-fire of so many random questions. 
 
 Thus, in this matter, Einstein takes the same stand as 
 Schopenhauer in the preface of his chief work, in which he 
 says : " To understand this work no better way can be advised 
 than to read it twice (at least), inasmuch as the beginning 
 assumes the end, almost as much as the end assumes the 
 beginning ; the smallest part cannot be understood if the 
 whole has not already been understood." Whoever accepts 
 and follows this advice will find that the intermediate objec- 
 tions will gradually balance and cancel one another, and that 
 it is not necessary that they should interrupt the steady and 
 consistent line of development. 
 
 The position would be different if a disciple of the new 
 theory should resolve to dispense with strictly scientific reason- 
 ing altogether, and should wish to meet the wishes of his 
 readers or hearers by discarding accuracy entirely. Such a 
 programme seems quite feasible. 
 
 * In these arguments, arrangements of synchronous clocks occur, which 
 are fixed into the co-ordinate systems, the positions of their hands being 
 compared with one another. The " time " of an event is then defined as 
 the position of the hands of a clock immediately adjacent to the scene of the 
 event. 
 
196 EINSTEIN THE SEARCHER 
 
 " This would be merely following the sketchy method of a 
 magazine," Einstein remarked, " but you do not seriously 
 think that it would lead to anything ? " 
 
 " It would not be a true explanation, which is reserved for 
 technical productions. But I can imagine that it would not 
 be unprofitable to help one who is entirely ignorant on these 
 questions by using makeshifts, in the form of allegories or 
 analogies, which will serve as supports if he should take fright 
 during the course of his earlier studies. These shocks are 
 bound to occur, as, for instance, when he learns that a moving 
 rigid rod undergoes contraction in the direction of motion." 
 
 " But this is proved to him ! " 
 
 " Nevertheless, he does not easily accept it. For the 
 general reader will say to himself : * A superhuman effort is 
 imposed on my mind. A rigid rod is the most constant of all 
 things, and never before has one been compelled to regard 
 something that is constant as variable.' " 
 
 " If he does not grasp it, no analogy will teach him." 
 
 " But perhaps it is possible. The analogy is to show him 
 that the effort is not superhuman, and that thinking Man has 
 already had occasion to become familiar with such trans- 
 formations from constant to variable factors." 
 
 " I am afraid your analogy will prove a failure." 
 
 " From the scientific point of view this is probably true, 
 inasmuch as all comparisons are imperfect, but the analogy 
 may yet be of service as a last resort. For example, I should 
 say to my general reader : ' Picture to yourself a savant of the 
 Middle Ages who reflects on the constitution of animals and 
 plants. One fact seems to him to be irrevocably true, namely, 
 that the species are unchangeable ! A palm tree is a palm 
 tree, a horse is a horse, a worm a worm, and what is once a 
 reptile remains a reptile. A species in itself denotes something 
 absolutely invariant." 
 
 ** The expression is wrong when taken in this connexion ; 
 you mean invariable.'* 
 
 " A Httle inaccuracy more or less does not affect the 
 analogy. For the sake of my picture I should like to retain 
 the conception-couple, variable and invariant. Well, then, 
 the species give our savant the impression of invariance, as 
 in the view that was held by Linn6 and Cuvier. This view 
 
AN EXPERIMENTAL ANALOGY 197 
 
 necessarily has its counterpart in his thought. He argues 
 that every species has its own original root, and that, in this 
 sense, there is very extensive variation. The fundamental 
 roots are extremely manifold ; Nature has produced in- 
 numerable variations in her individual acts of creation. But 
 now the Theory of Descent of Lamarck, Goethe, Oken, Geoff roy 
 St. Hilaire, enters the field and produces a complete inversion 
 of these two elements ; the two parts of the earlier point of 
 view change places. Our savant has to revise his whole world 
 of thought. Now all organisms are to be traced back to a 
 single original root : the latter, which was variable before, 
 becomes an invariable unicellular primitive organism, but the 
 apparently unchangeable species now becomes variable, in the 
 widest possible sense. And even if this savant should ex- 
 claim : * How am I to reconcile myself to this view ? * his 
 descendants later find no difficulty in accepting the idea that 
 the organic roots are uniform, and that it is the species that 
 are subject to all manner of variation as a compensating 
 feature." 
 
 Einstein expressed himself very little pleased with this 
 attempt at an analogy, and found that it was so far fetched 
 that it could not be considered admissible. 
 
 " Then I must ask your permission to continue my at- 
 tempt ; perhaps something useful may yet result from it. 
 I now picture to myself a human being who lived in classical 
 times and who, following Ovid and the great majority of his 
 contemporaries, regards the earth as a disc. On this disc, 
 each inhabitant of the earth has his own particular position, 
 for the disc has a centre with reference to which the position 
 of a person can be specified if his distance and his angular 
 displacement from a given initial radius is specified. Thus, 
 there is a variation of position if various persons are considered. 
 On the other hand, the Above and the Below is absolutely 
 invariable for all persons, for the Hues running between Above 
 and Below are all parallel for them, since they all have uni- 
 formly the same disc under their feet and the same heaven 
 above their heads. Ovid would therefore have refused to 
 entertain for a moment the suggestion that Above-Below is a 
 variable. But his distant descendants accepted the view that 
 the earth is spherical and that there are antipodes as self- 
 
198 EINSTEIN THE SEARCHER 
 
 evident, and they found not the slightest difficulty in 
 considering the line Above-Below to vary with their own 
 position, making all possible angles with an initial line extend- 
 ing to direct oppositeness. Referred to the centre of the sphere, 
 all people have now an * invariant ' position, whereas, in 
 compensation, the Above-Below is subject to every conceivable 
 variation. And now I again address myself to the average 
 reader, and say that the meaning of these analogies is that 
 every doctrine that leads to a great uniformity converts what 
 was formerly invariant into a variable quantity, and vice 
 versa. The theory of relativity makes all considerations about 
 the physical world independent of all co-ordinate systems ; 
 it establishes completely invariable uniformity, removed from 
 all changes due to varying points of view. Hence what was 
 previously invariable — such as a rigid measuring-rod — will 
 now become variable. It is not surprising that this requires 
 a new method of thought, a revision of our mode of reasoning, 
 for the above analogies show that these radical adjustments 
 are characteristically necessary in the case of comprehensive 
 theories, and that such theories are able to overcome appar- 
 ently firmly established ideas. The parallels that I drew 
 above will at least inspire the average reader with a certain 
 confidence, for they show him how results of reasoning that 
 were once considered incredible were regarded as self-evident 
 by later generations." 
 
 I have already emphasized sufficiently that Einstein 
 regards as inadequate these auxiliary pictures that have 
 presented themselves to me. Yet in the course of the conversa- 
 tion I gained the impression that his judgment grew somewhat 
 milder, and that, with certain reservations, he was disposed 
 to let them pass as tolerably useful helps — and they are not 
 intended to be more than this. I think, therefore, that I 
 am not acting counter to his wishes in citing these allegorical 
 examples here, particularly as they arose in the course of our 
 talks. 
 
 Since then, I have had many opportunities of testing these 
 examples on certain persons, and may mention that they 
 proved quite useful. Analogies of this kind may offer a 
 friendly help in moments when the uninitiated feel themselves 
 in peril, and encounter a difficulty which they imagine to be 
 
AN EXPERIMENTAL ANALOGY 199 
 
 insurmountable. They do not remove the difficulty, but they 
 impart a certain power of expansion to the intellect and 
 encourage a continuation of effort, which would probably 
 otherwise be relaxed at the first sign of something which is 
 imagined to be inconceivable. There is thus no room in 
 textbooks for such helps, but they may justifiably find a 
 place in a book that departs from the methodical route, and 
 hopes to discover in by-wa}^ things that are suggestive and 
 instructive. 
 
CHAPTER X 
 DISCONNECTED SUGGESTIONS 
 
 Conditionality and Unconditionality of Physical Laws. — Conception of 
 Temperature. — Grain of Sand and Universe. — Are Laws unalterable ? — 
 Paradoxes of Science. — Rejuvenation by Motion. — Gain of a Second. — 
 Deformed Worlds. — Atomic Model, — Researches of Rutherford and Niels 
 Bohr. — Microcosmos and Macrocosmos. — Brief Statement of the Principle 
 of Relativity. — Science with reduced Sense-Organs. — Eternal Repetition. — 
 Higher Types of Culture. 
 
 IN all branches of reasoning, no word and no conception 
 has played a more important part than that of law. 
 Phj^ical laws denote the barrier that separates strictly 
 chance and arbitrariness from necessity, and it seems to us 
 that the region of the latter must ever extend so that finally 
 nothing will be left of the former, which will have become 
 amalgamated with necessity. We shall be constrained to 
 beheve more and more in a supreme law that will be a com- 
 plete expression of all the partial laws which science presents 
 to us as more or less permanent results of individual researches. 
 
 Our conversation was centred about these individual laws, 
 such as those that are taught in the theory of gases, optics, 
 etc., and that are associated with the names, Boyle, Gay- 
 Lussac, Dalton, Mariotte, Huyghens, Fresnel, Kirchhoff, 
 Boltzmann, and others. In connexion with these I asked 
 Einstein whether he regarded the laws as things unconditioned 
 in themselves, and capable of proof under every set of circum- 
 stances ; and whether absolutely valid laws existed or could 
 exist. 
 
 Einstein's answer was essentially in the negative. ** A 
 law cannot be final, if only for the reason that the conceptions, 
 which we use to formulate it, show themselves to be imperfect 
 or insufficient as science progresses. Let us consider, for 
 
 200 
 
DISCONNECTED SUGGESTIONS 201 
 
 example, an elementary law such as Newton's Law of Force. 
 From our more recent point of view we find the conception 
 of direct action at a distance to be inexact in Nature. For 
 it has been shown that action at a distance is not an ultimate 
 factor, but must be resolved into a multiplicity of actions 
 between immediately neighbouring points (The Theory of 
 Action by Contact or Contiguous Action). Another example 
 is provided by the conception Temperature. This conception 
 becomes meaningless if we endeavour to apply it to molecules : 
 it leads to no result if we try to impose it on the smallest parts 
 of matter as such. The reason is that the state, the velocity, 
 and the inner energy of the individual molecules fluctuates 
 between very wide limits. The conception * temperature ' 
 is applicable only to a configuration composed of many mole- 
 cules, and even then it is not appUcable quite generally. For 
 let us picture to ourselves an extremely rarefied gas contained 
 in a closed receiver. Two opposite walls are to be at different 
 temperatures, the one being cold and the other being hot 
 In a gas at such very low pressure the molecules come into 
 colHsion so seldom that, practically, we have to take into 
 account only the collisions of the molecules with the confining 
 walls. The molecules that rebound from the hot wall have 
 greater velocities than those coming from the colder wall, and 
 hence the conception of temperature becomes untenable for 
 this gas." 
 
 ** Would the temperature-scale on the thermometer then 
 denote nothing ? " I asked. ** The greater or lesser degree of 
 warmth of a body, in this case of the mass of gas, depends on 
 the more rapid or less rapid motion of its smallest parts. The 
 motions are in any case present, so what would a thermometer 
 indicate ? " 
 
 " It would betray only that it had nothing to indicate. 
 If a thermometer that is blackened on one side were inserted 
 into the vessel containing the gas, then different temperatures 
 would be recorded if the thermometer were gradually turned 
 about its own axis ; and this signifies that the conception of 
 temperature has become meaningless for this configuration 
 of molecules. And passing beyond the quoted examples, I 
 should maintain that all our conceptions, however subtly they 
 may have been thought out, are shown in the course of pro- 
 
202 EINSTEIN THE SEARCHER 
 
 gressive knowledge to be too rough hewn, that is, too little 
 differentiated/' 
 
 We spoke of the " Properties of Things," and of the degree 
 to which these properties could be investigated. As an 
 extreme thought, the following question was proposed : 
 
 Supposing it were possible to discover all the properties 
 of a grain of sand, would we then have gained a complete 
 knowledge of the whole universe ? Would there then remain 
 no unsolved component of our comprehension of the universe ? 
 
 Einstein declared that this question was to be answered 
 with an unconditional affirmative. " For if we had completely 
 and in a scientific sense learned the processes in the grain of 
 sand, this would have been possible only on the basis of an 
 exact knowledge of the laws of mechanical events in time and 
 space. These laws, differential equations, would be the most 
 general laws of the universe, from which the quintessence of all 
 other events would have to be deducible." 
 
 [This thought may be spun out in yet another direction. 
 Every piece of research, however specialized it may appear 
 and of whatever minor importance it may be, retains a relation- 
 ship with researches into the universe, and may prove to be 
 valuable for this latter task. If we accept the view that 
 science is capable of realizing perfection, then every con- 
 tribution to knowledge, even the most insignificant, is essenti- 
 ally indispensable for attaining this goal.] 
 
 Can a physical law alter with time ? In more precise 
 language, can time, as such, enter explicitly into laws, so that, 
 for example, an experiment that is carried out at different 
 times leads to different results ? This question has been 
 treated several times, among others, by Poincar6, who answered 
 it with an emphatic " No ! " but also by others to whom the 
 invariability of physical laws did not seem to hold for all 
 eternity. If my memory does not play me false, Helmholtz 
 once expressed faint doubts about the constancy of laws. 
 
 Einstein answered this question with a decided negative. 
 ** For a law of physical nature is, by definition, a rule to which 
 events conform wherever and whenever they take place. 
 Thus, if we were to be compelled as a result of experience to 
 
DISCONNECTED SUGGESTIONS 208 
 
 make a law dependent on time, it would be a necessary step 
 to seek a law independent of time, which would include in 
 itself the law dependent on the time as a special case. The 
 latter would be excluded from the category of physical laws, 
 and would henceforward play the part only of a result deduced 
 from the law which is independent of the time/* 
 
 What attitude should we adopt if, in studying a scientific 
 doctrine, we encounter paradoxical results even though the 
 inferences have been drawn correctly — ^that is, if we meet 
 with a deduction to which our reasoning powers object, 
 although no fallacy is discoverable in the argument ? 
 
 Before we deal with cases which seem to me, personally, 
 to be interesting, let us hear what is Einstein's attitude in 
 general. " As soon as a paradox presents itself, we may, as a 
 rule, infer that inaccurate reasoning is the cause, and should 
 thus examine in each particular case whether an^^errorlof 
 logic is discoverable, or whether the paradoxical result denotes 
 only a violent contrast with our present views.*' 
 
 Let us first take examples from an entirely modem science, 
 from the Theory of Aggregates founded by Georg Cantor of 
 Halle. We shall follow the argument by the only possible 
 method for this book, namely, by rough indications that will 
 serve our purpose and do not claim to be accurate in expression 
 or in sense. 
 
 If we take an aggregate of three objects, for example, an 
 apple, a pear, and a plum, we may, by definition, form six 
 partial aggregates, namely : 
 
 the apple 
 the peax 
 the plum 
 
 UlC piUIU 
 
 the apple and the pear 
 the apple and the plum 
 the pear and the plum. 
 
 The aggregate of the partial aggregates, which contains 
 six elements, is thus greater than (actually twice as great 
 as) the original aggregate, in which only three elements 
 occur. 
 
 If the original aggregate contains an additional element, 
 
204 EINSTEIN THE SEARCHER 
 
 for example, a nut, the following partial aggregates may be 
 formed : 
 
 the apple 
 
 the peax 
 
 the plum 
 
 the nut 
 
 the apple and the pear 
 
 the apple and the plum 
 
 the apple and the nut 
 
 the pear and the plum 
 
 the pear and the nut 
 
 the plum and the nut 
 
 the apple, the pear, and the plum 
 
 the apple, the pear, and the nut 
 
 the apple, the plum, and the nut 
 
 the pear, the plum, and the nut. 
 
 Thus, in this case, the aggregate of the partial aggregates is 
 already considerably greater than the original aggregate. This 
 numerical excess increases rapidly with each successive increase 
 in the original aggregate, so that if we apply the same reason- 
 ing to an infinite aggregate, the aggregate of partial aggregates 
 becomes an infinity of a higher order. This is expressed by 
 sa5dng that the infinite aggregate of partial aggregates has a 
 greater potentiality than the infinity of the elements of the 
 original aggregate. 
 
 So we see that the one infinity is, in popular language, 
 much more comprehensive, more powerful than the other. 
 Our minds do not find it impossible to grasp this. But in a 
 definite imaginary experiment it is found that this theorem 
 of progression not only fails in its application, but leads to 
 flagrant contradiction. 
 
 For if we start from the primary aggregate of " all con- 
 ceivable things,'* its infinity can certainly not be transcended 
 by any other infinity. But according to the above theorem 
 the " aggregate of all partial aggregates " would have a greater 
 potentiality, although it itself cannot extend further than 
 to the conception of the maximum of all conceivable things. 
 We thus arrive at an insoluble paradox, a typical example of 
 how, in the system of conceptions involved, something is 
 insufficient or not in conformity with logical thought. And 
 this sceptical view receives support from various remarks of 
 Descartes, Locke, Leibniz, and particularly Gauss, who, long 
 
DISCONNECTED SUGGESTIONS 205 
 
 before the advent of the Theory of Aggregates, raised a protest 
 against inexact definitions of infinity. 
 
 In another case, however, the same theory seems to arise 
 by perfectly logical processes, although it again leads to a 
 statement that does not seem correct to " common sense." 
 For it shows by a very subtle and ingenious method that all 
 the surface-points of a surface infinitely extended in all direc- 
 tions may be brought to correspond in a reversible single 
 manner to the linear points of a Une, however small ; so that 
 to every point of the unhmited plane there corresponds a 
 definite point of the fine, and vice versa. The same theorem 
 may be extended to three-dimensional space, with the result 
 that we have to reconcile ourselves with the incredible fact 
 that, expressed in popular language, a straight line of however 
 small length exhibits the same potentiality with regard to the 
 number of its points, as all the points in the universe. 
 
 For my own part, I must confess that no means suggests 
 itself to me to make this paradox intelligible. But the sacri- 
 ficium intellectus comes within dangerous proximity. Einstein, 
 who values and marvels at the theory of aggregates as a science, 
 or perhaps more as a work of art built up from the materials of 
 science, gives whole-hearted support to the proof. He refuses 
 to accept the notion of a paradox — ^that is, he recognizes a 
 contradiction not in our process of reasoning, but only in a 
 habit of thought that is open to correction. I should give 
 much to discover the means of correction ! 
 
 A third example arises out of the special theory of rela- 
 tivity. It has a mysterious paradoxical character that 
 vanishes when a clear view of the relationships involved has 
 been obtained. 
 
 According to this theory the rate at which events happen 
 alters according to the state of motion of the system under 
 consideration. Let us now consider two twins A and B, 
 that, although born at one place on the earth, are immediately 
 separated, B remaining at rest, whilst A rushes out into space 
 at an enormous rate, describing what, viewed from the earth, 
 is an inconceivably great circle. In this way the rate of 
 happening of all events is reduced very considerably for A 
 in a manner that may be calculated. If A then returns to 
 
206 EINSTEIN THE SEARCHER 
 
 B, it may happen that the twin who stayed at home is now 
 sixty years old, whereas the wanderer is only fifteen years of 
 age, or is perhaps only an infant still. 
 
 The first introduction to this flight of imagination naturally 
 causes profound perplexity. Nevertheless, we are dealing not 
 with a realm of miracles, but with something that is within 
 the range of comprehension. 
 
 " In the case of these two twins," Einstein declared, " we 
 have merely a paradox of feeling. It would be a paradox of 
 thought only if no sufficient ground could be suggested for the 
 behaviour of these two creatures . This ground, which accounts 
 for the comparative youth of A, is given, from the point of 
 view of the special theory of relativity, by the fact that the 
 creature in question, and only this creature, has been subject 
 to accelerations. A proper grasp of the reason is furnished 
 only when we adopt the general theory of relativity, which 
 tell us that, from the point of view of A, a centrifugal field 
 exists, whereas it is absent from the point of view of B. This 
 field exerts an influence on the relative rate of happening of 
 the events of life.*' 
 
 It certainly requires a prodigious mechanism to allow 
 the moving twin to gain even only one second of time. If he 
 were to spend a year in a merry-go-round whose circumference 
 were about 19 milliard miles in length, he would have to 
 travel in it at the rate of over 600 miles per second if he is to 
 gain a second on his brother. 
 
 This inevitable result that is immediately apparent to a 
 trained scientific mind throws light on the nature of " common 
 sense,'' the validity of which, as an ultimate criterion, Kant 
 too has refused to recognize, in so far as this " common sense " 
 is incapable of passing beyond the examples offered in its own 
 experience. It circulates, as Einstein says, in the " realms 
 of feeling and analogy.'' It finds no analogy for a phenomenon 
 like that described above, and since it can apply rules only 
 concretely, many things appear to it paradoxical that, in the 
 light of intensified abstraction, appear logical and necessary. 
 
 Let us speculate on the following question. If all things 
 in the universe should increase or decrease enormously in 
 dimensions, and if, at the same time, in a manner totally 
 
DISCONNECTED SUGGESTIONS 207 
 
 concealed from us, certain physical conditions should become 
 changed, we should lack all means of discovering the difference 
 between things before and after the change. For since all 
 measuring-rods, including those furnished by our senses, would 
 have become changed in the same proportion, the two condi- 
 tions could not be differentiated from one another. It may 
 easily be shown that this would necessarily occur, if an extra- 
 mundane power were non-uniformly to displace, deform, 
 compress, or bend all things in the universe, provided that our 
 instruments and senses participated in this transformation. 
 Accordingly it is permissible also to regard the universe known 
 to us as one that is deformed, and one that is derived from 
 another, the original form of which will ever remain a secret 
 to us. 
 
 Is there any connexion between this grotesque speculation 
 and the theory of relativity ? 
 
 We can establish only one that is negative and that arises 
 e contrario, " These deformations," said Einstein, " are in 
 themselves abstractions that are physically meaningless. Only 
 relations between bodies have a physical meaning, for example, 
 the relation between measuring-rods and the objects they 
 measure. Therefore, it is reasonable to talk of deformations 
 only when we are dealing with the deformations of two or 
 more bodies with respect to one another, whereas the con- 
 ception of deformation has no sense, unless a real object is 
 specified, to which it is referred. The philosophical merit of 
 the general theory of relativity, as compared with previous 
 views of physics, consists in the fact that the former avoids 
 entirely these meaningless abstractions with respect to space 
 and time." 
 
 [According to this, it is not purposeless to enter on these 
 grotesque trains of thought, even if they are untenable physi- 
 cally. For since the new physics teaches us to avoid these 
 false tracks, it seems of value to know what it is that is to be 
 avoided. Just as we must study scholastic thought if we 
 wish to grasp thoroughly the philosophy which sprang up after 
 the scholastic fetters were burst. Moreover, these reflections 
 on concealed universes are not without a certain attraction, 
 reminiscent of the sorcerer's wand, if they pursued any other 
 goal than that of making universes distorted. It is true that 
 
208 EINSTEIN THE SEARCHER 
 
 they hold out latent temptations that may in some cases lead 
 us on to dangerous ground, in encouraging us to venture on 
 analogies beyond the scope of geometry and physics. Would 
 it be possible to enter suddenly into a world that is distorted 
 and deformed with respect to its ethics, its culture, and its 
 reasoning intellects, without our observing the difference ? 
 Are we ourselves perhaps living under such deranged conditions, 
 of which we cannot become aware, because our perceptual 
 organs have likewise become deformed ? I must frankly 
 confess that I do not regard it as quite inconceivable that 
 this argument of deformation may be spun out in this direction, 
 but I must add that Einstein rejects absolutely all such exten- 
 sions, since, as he emphasizes, they lead to regions that are 
 merely fields for the exhibition of " verbal gymnastics/*] 
 
 The question whether Nature makes leaps or not is very 
 old. In the theory of descent it forms the foundation of the 
 difference between revolutionists and the evolutionists, who 
 uphold the axiom natura non facit saltus, with all its conse- 
 quences. Recently attempts have been made, particularly by 
 psychologists, to propound and justify a natural principle of 
 discontinuity. They assert that our own perceptions and 
 sensations are discontinuous in themselves, and that the 
 mechanism of every perception is akin to that of a cinemato- 
 graph with its extremely rapid interruptions. If this should 
 actually be the case, we should scarcely have a means of solving 
 definitely the question whether continuity reigns, or not, in 
 Nature. 
 
 Einstein does not recognize the possibility of this alternative 
 for a moment. If a doubt had ever arisen, the researches of 
 Maxwell would in themselves have been sufficient to dispel it. 
 Our universe that is to be described in terms of differential 
 equations is absolutely continuous. 
 
 " But," I interjected, " does not modern physics offer a 
 certain support to the assumption of a discontinuity ? Does 
 not the Quantum Theory point to an atomistic structure of 
 energy, and hence also of events that are to be imagined as 
 happening in jerks and as involving relations expressible in 
 whole numbers ? *' 
 
 Einstein gave an answer of epigrammatic brevity and 
 
DISCONNECTED SUGGESTIONS 209 
 
 flavour. " The fact that these phenomena are expressible in 
 whole numbers must not be construed into an argument 
 against continuous happening. Just imagine to yourself for 
 a moment that beer is sold only in whole litres ; would you 
 then infer that beer, as such, is discontinuous ? " 
 
 What achievements are to be expected of astronomy in the 
 present era ? 
 
 This question would have a special meaning if it were 
 assumed that the astronomer who works in observatories is 
 surrounded by solved problems, and can no longer hope to 
 solve problems having the universal significance of those of 
 Coperniciis or Kepler. This assumption, however, would not 
 be in agreement with the actual state of affairs. 
 
 Einstein indicated to me a number of fundamental prob- 
 lems that present themselves to modem astronomy, and the 
 solution of which he expected of future times. 
 
 Above all, the geometrical and physical constitution of the 
 stellar systems will, in the main, become revealed. 
 
 At present we do not yet know whether Newton's Law of 
 Attraction holds, at least approximately, for configurations of 
 the type of the Milky Way and of the spherical clusters of 
 stars — ^that is, in extents of space in which the influence of 
 space-curvature would become appreciable. The rapid pro- 
 gress of recent astronomy justifies our great hopes that the 
 solution of this universal problem will be found within the 
 coming decades. 
 
 In distant connexion with this we also touched on the 
 question of the habit ability of other worlds. This theme of 
 Fontenelle, " la pluralite des mondes habits," which has 
 again become a centre of public interest, owing to investigations 
 of Mars, has evoked a storm of discussion. We hear the noisy 
 war-cries of geocentric scientists who wish to regain for the 
 earth her shattered supremacy in astronomy, and who claim 
 the existence of organic forms as the sole prerogative of our 
 planet. It is scarcely necessary to mention that Einstein 
 rejects the motives of these human and all-too-human in- 
 dividuals as small-minded and short-sighted. Creatures in 
 distant worlds are derived from, and are subject to, conditions 
 of organic nature, of which we can form no idea by deductions 
 14 
 
210 EINSTEIN THE SEARCHER 
 
 from the world which we inhabit. But to deny their existence 
 on numberless constellations, or to demand an ocular proof 
 of their presence, is no better than to assume the point of view 
 of an infusoria to whom there is no life other than that in a 
 dirty drop of ditch-water. 
 
 The idea of the atom as the ultimate structural element 
 involves a philological as well as a conceptual contradiction. 
 For atomos signifies the indivisible, the no-further-divisible, 
 whereas the idea of a body, however small, an element of 
 structure differing from zero, demands, at least geometrically, 
 further divisibility. Even the original founders of the theory 
 of atoms, Leukippus, Epicurus, and Democritus, assigned 
 definite forms to the ultimate components, and we may read 
 in the splendid work of Lucretius how he infers from the 
 nature of substance that the ultimate particles are smooth, 
 round, or rough, or have the shapes of hooks and eyes. The 
 further analysis pressed forward, the more the simplicity of the 
 original idea vanished. Microcosms came to be regarded as 
 copies of macrocosms, and the atoms of present-day science 
 actually exact from us that we should regard them as worlds 
 in themselves. 
 
 Einstein acceded to my request that he might give a sketch 
 of the latest achievements of science sufficient to provide an 
 approximate idea of the atomic model. According to the 
 researches of Rutherford and Niels Bohr, we are to picture it 
 as a planetary system. 
 
 The central body of this system is represented by a positively 
 charged nucleus, which constitutes almost the whole mass of 
 the atom, surrounded by a certain number of electrons, negative 
 charges, that move in uniform circular or elliptic orbits about 
 the nucleus. There is thus a certain analogy that allows us 
 to regard the nucleus as the sun, and the electrons as the 
 planets of this system. 
 
 The number of these electrons varies between the limits 
 T and 92, according to the chemical constitution of the element. 
 The smallest number occurs in the case of helium (in which 
 there are two), and of the hydrogen atom, in which only one 
 electron-planet describes its circular path about the nucleus. 
 In other atoms there are probably more comphcated orbits, 
 
DISCONNECTED SUGGESTIONS 211 
 
 although they are more or less approximately circular. Ac- 
 cording to this still very new theory, which is supported by 
 very convincing facts, the electrons are to be imagined as 
 arranged in concentric sheUs (like the layers of an onion), 
 among which the innermost shell plays a distinctive part 
 inasmuch as the number of the electrons arranged in it decides 
 the chemical character of the atom in question. It sometimes 
 occurs that electrons spring, under external influence, from one 
 orbit to another ; when the electron jumps back to the original 
 orbit, Ught is emitted. An essential fact is to be noted : 
 Whereas any arbitrary orbits of any arbitrary radius may 
 occur in a planetary system of the celestial regions, the mani- 
 fold of these orbits in the case of the electrons is restricted, 
 in that only certain orbits are possible, namely, those that are 
 determined mathematically by the quantum condition. 
 
 *' Perhaps,'* I interrupted, " the whole analogy may be 
 inverted. If the atom is considered analogous to a planetary 
 system in the model, it should be admissible to regard our 
 true planetary system as a cosmic atom. And then, long after 
 we have become accustomed to regard our earth as playing the 
 part of a grain of sand, the sovereignty of the sun, too, would 
 be past. The whole majesty of the solar system as far as the 
 orbit of Neptune would then shrink to a configuration com- 
 pared with which the world of a grain of sand would be 
 infinitely complex." 
 
 " This fantastic inversion is permissible up to a certain 
 extent," said Einstein, " but we must not lose sight of the 
 fact that there is a cardinal difference. If we disregard the 
 enormous disparity in dimensions, the analogy is far from 
 exact owing to the circumstance that the atom is only an 
 element of structure, whereas the true planetary system is an 
 extraordinarily complex structure in itself. Thus the differ- 
 ence between a simple thing and one that is very highly 
 complex still remains." 
 
 ** But, Professor, may not a similar complexity yet be 
 discovered in the atom ? It may be merely a difference of 
 philosophical view from the primary idea to that of regarding 
 the electrons as circulating Hke planets. May we not con- 
 jecture that in each successive step we are merely carrying out 
 a true regressus in infinitum ? " 
 
212 EINSTEIN THE SEARCHER 
 
 " That seems highly improbable," he replied, " although, 
 of course, structural investigations can never cease. At first 
 they are directed at the more remote object of finding out why 
 certain atoms are radioactive, that is, exhibit a tendency to 
 disintegrate. It has already been established that this ten- 
 dency is a property of the positive nucleus, of which Uttle is as 
 yet known. This means that the nucleus is not simple, yet 
 it does not open up the possibility of an unending regression. 
 Our aim must be to get a clear insight into the constitution 
 of the nucleus, as regards the positive and negative charges, 
 and it is my opinion," he concluded, " that beyond this there 
 will be no further subdivision of matter." 
 
 When Goethe writes of the immovable pole in the flux of 
 phenomena, we recognize that his beautiful remark pronounces 
 an elegy to the possibility of attaining ultimate simplicity. 
 Einstein's utterance, if I understand him aright, converts this 
 elegy into a song of hope. If the subdivision of matter 
 actually has an end somewhere, then we are now on the 
 threshold of ultimate things, we are near the immovable pole, 
 which we are capable of reaching. 
 
 " Every new truth of science must be such that, in ordinary 
 writing, it may be communicated completely within the space 
 of a quarto leaf." Kirchhoff made this remark, and gave a 
 sufficient, if not literal, demonstration of its truth. When 
 Bunsen and he published the first notice about spectral 
 analysis, they compressed their publication into the small 
 space of three printed pages. 
 
 But what is to happen if the new truth should be built 
 up of very comprehensive materials, when it requires many 
 links, of which none can be omitted if the truth is to be 
 made intelligible ? Would Kirchhoff *s quarto page still be 
 sufficient ? 
 
 " Certainly," said Einstein, '* provided, of course, that it is 
 addressed to a reader who has already mastered what went 
 before — ^that is, to one who is so far acquainted with the older 
 facts that he has to learn only the really new part of the new 
 truth." 
 
 *' That sounds very hopeful," I remarked, ** for then it 
 
DISCONNECTED SUGGESTIONS 213 
 
 should also be possible to describe very briefly the theory of 
 relativity/* 
 
 " Let us rather say its essentials — ^the heart of the matter. 
 Well, then, get your Kirchhoff page ready. We shall see 
 whether we can set out on it the special theory of relativity." 
 
 The totaUty of our experience compels us to assume that 
 Ught travels with a constant velocity in empty space. like- 
 wise, our whole experience in optics compels us to recognize 
 that all inertial systems are equivalent ; these are systems 
 that are produced from an allowable one by means of a uniform 
 translation. An allowable system is one in which GaUlei's 
 and Newton's Law of Inertia holds. (This law states that a 
 moving body that is left to itself retains its direction and 
 velocity permanently.) 
 
 Now, the law of the constancy of light propagation seems 
 to conflict with the classical principle of relativity, according 
 to which the velocity of a ray of Ught assumes different values 
 in the moving system according to the direction of the ray. 
 
 This apparent incompatibiHty arises from the following 
 unproved assumptions : 
 
 (a) If two events are simultaneous with regard to one 
 inertial system, they are also simultaneous with regard to 
 any other inertial system. 
 
 (b) The length of a measuring-rod, the shape smd size of a 
 rigid body, and the rate of a clock are independent of their 
 motion with respect to the system of reference used, provided 
 this motion is rectilinear and non-rotational. 
 
 These assumptions must be discarded if this disagreement 
 is to be ehminated. If we substitute for them the assumption 
 that all inertial systems are equivalent and that the velocity 
 of light in vacuo is constant, we ^et : 
 
 (i) That the dimensions of bodies and the rate of clocks 
 have a functional relation to the motion. 
 
 (2) That the equations of motion of Newton require to 
 be modified ; this modification leads to results that, for rapid 
 motions, differ appreciably from those of Newton. 
 
 This is, in a very compressed form, the meaning of the 
 special theory of relativity. 
 
 As there is still some space left on our quarto page, we 
 
214 EINSTEIN THE SEARCHER 
 
 may add k remark that, it is hoped, will make a little clearer 
 the above-mentioned discrepancy. 
 
 Let us choose as our system of reference an express train 
 i8 miles long. There are two passengers — Mr. Front, right at 
 the front of the train, and Mr. Back, at the extreme end of the 
 train, so that a rigid distance of i8 miles separates the two 
 passengers. The carriages are transparent, so that the two 
 passengers can signal to one another. They are, moreover, 
 furnished with ideal clocks that run at exactly the same rate. 
 
 First, suppose that the train is at rest . Back is just opposite 
 milestone lOO, whilst Front is opposite milestone ii8. By 
 means of a flash, Back signals to Front his time, exactly 
 12 o'clock. It takes light very nearly ytt.^otj- second to 
 traverse the length of the train — 18 miles ; hence the flash will 
 reach Front at 12 o'clock tt^.^tht second. Exactly the same 
 result would have come about if Front had signalled his time 
 to Back. Light makes no difference in travelling forwards 
 and backwards. If the train moves at a great speed, the two 
 travellers can conduct the same experiment as when the train 
 was at rest. They will then set the time that light takes to 
 travel from Back to Front equal to the time that it takes to 
 traverse the same way in the reverse direction. But this 
 phenomenon will assume a different aspect if viewed from the 
 railway embankment. An observer on the latter would 
 aihrm that Hght does not take the same time in travelHng the 
 length of the train in one direction as it does when travelling 
 in the opposite direction. 
 
 For the ray of light moving in the forward direction has 
 to traverse not only the distance between Back and Front, 
 but also the very short distance that Front has moved forward 
 during the interval that the light has been moving ; whereas, 
 inversely, the flash sent out by Front to Back will traverse 
 a distance that is correspondingly less than that between the 
 passengers, since Back is moving towards the signal. 
 
 Thus the duration of the two phenomena of light propaga- 
 tion is the same or different, respectively, according as it is 
 judged from the train or from the embankment. In other 
 words, the judgment of the length of time depends on the state of 
 motion of the observer. 
 
 All further pronouncements of the special theory of rela- 
 
DISCONNECTED SUGGESTIONS 215 
 
 tivity are based on the preceding arguments of the relativity 
 of time. 
 
 Would Man be able to construct a Science if he possessed 
 one sense less than at present — ^for example, if he were deprived 
 of sight ? Let us apply this to a definite case. In the new 
 physics the velocity of light plays a decisive part as a world- 
 constant. At first sight it would appear impossible for us 
 to determine it and recognize its importance, if we had not at 
 our disposal some organ which enabled us to become aware of 
 optical phenomena. 
 
 But, as Einstein explained to me, even under such difiicult 
 circumstances, it would be possible to build up a science, for 
 the reason that phenomena, as far as they are perceptible, 
 may be transformed so that they become manifest to other 
 senses if one sense should be absent. For example, the 
 electrical conductivity of selenium is strongly influenced by the 
 amount of illumination that falls on it. Thus Ught acts on a 
 selenium cell, causing changes of current intensity, which in 
 their turn may be perceived by feeling, or by chemical action 
 on the mucous fluid of the tongue. Ultimately we are con- 
 cerned only with a differentiation that enables us to refer 
 identical experiences to identical events. We should certainly 
 encounter enormous difiiculties in endeavouring to form a 
 physical picture of our surrounding world if the number of our 
 senses should become less than the organs with which we actu- 
 ally operate. Yet, in principle, we should be able to overcome 
 all difficulties by means of much lengthened and complicated 
 lines of research, even if we should have only a single sense 
 left, or if we had only one at the very outset . The construction 
 of a Science would then be possible, and would give the same 
 results, although it might be propounded only after a delay of 
 perhaps millions of years. 
 
 [It is naturally assumed that the intellect is retained, as 
 this is the necessary condition for all scientific research. Since 
 the degree of understanding depends on the senses — nihil est 
 in intellectu, quod non priusfuerit in sensu — ^we may conjecture 
 that a human being with only one sense organ would work 
 with a minimum degree of understanding, which would be 
 insufficient for the acquirement of any knowledge whatsoever. 
 
216 EINSTEIN THE SEARCHER 
 
 This transcendental question, which lies almost beyond the 
 bounds of discussion, was not touched on in our conversation, 
 as the subject was restricted so that it should not drift into 
 metaphysical regions. 
 
 Nevertheless, I should like to mention that a speculation 
 of this kind is recorded in the history of science. Condillac, 
 in a study teeming with ideas, investigates the behaviour of 
 a " Statue," that he represents as a human being, with the 
 assumption that there is at first no idea in the soul of this 
 statue-person. This living creature is enclosed in a marble 
 envelope, the sole exterior organ of which is at first the organ 
 of smell. He then shows that by means of this single sense 
 all manner of sensations and expressions of will may develop 
 in his " statue." Condillac does not, however, undertake to 
 give a convincing proof that this creature, restricted to the 
 organ of smell, would be able to discover physically the relation- 
 ships that hold in physical nature, and thus to build up a 
 scientific sj^tem. Thus Einstein, in his discussion, goes 
 considerably further than the author of this statue.] 
 
 Has the " eternal repetition," as outlined by Nietzsche, 
 any meaning ? 
 
 The sage of Sils -Maria tells us that this revelation came 
 to him midway between tears and ecstasy, as a fantasy 
 with a real meaning. The crux of his idea is a finite world 
 built up of a finite number of atoms. From the fact that the 
 present state emerges out of the immediately preceding one, 
 the latter from the one just before, and so on, he concludes 
 that the present state exhibits repetition both forwards and 
 backwards. All becoming recurs and moves in a multiple 
 cycle of absolutely identical states. 
 
 Let us discard for the moment all philosophical objections, 
 above all this, that the recurrence of the same disposition 
 of atoms may not necessarily entail the recurrence of the 
 same psychical states. Furthermore, let us suppress the 
 C5mical thought that in the return to the same state the world 
 would have reason to enjoy extreme happiness only for 
 moments, but to lament for aeons. Then we are left with the 
 comparatively simple question : Is this repetition, from the 
 point of view of physics, conceivable and possible ? 
 
DISCONNECTED SUGGESTIONS 217 
 
 It would be the death-knell of Nietzsche's idea if the answer 
 of a great physical research scientist were entirely in the 
 negative. But Einstein still allows it a small measure of life. 
 ** Eternal repetition," so he expressed himself, " cannot be 
 denied by science with absolute certainty." The disciples of 
 Nietzsche will have to rest satisfied with this very small con- 
 cession. For what, in Nietzsche's eyes, is a logical necessity 
 becomes transformed by Einstein's supplementary remark 
 into a vague assumption, the product of fantasy. From 
 the point of view of physics the recurrence of the same con- 
 dition is to be regarded as "enormously improbable." This 
 statement is founded chiefly on the famous second Law of 
 Thermodynamics, according to which the processes of Nature 
 are in the main irreversible, so that a one-sided tendency is 
 expressed in natural phenomena. The fact that the course 
 of phenomena is in only one sense or direction speaks in 
 favour of the view that the events of the world are to be re- 
 garded as occurring only once. 
 
 So that when Nietzsche, in contradistinction to this, 
 vigorously supported the doctrine of repetition, he contra- 
 dicted at least one important recognized theorem of physics. 
 The fact that he did not become conscious of this contradiction, 
 but that, on the contrary, he regarded his idea as the most 
 important event in the development of his intellect, may be 
 regarded as an example of a docta ignorantia. But it is 
 allowable, too, that philosophic fantasies that complete the 
 poetical picture of the universe should be given expression. 
 And Nietzsche would presumably have been deprived of a 
 degree of pleasure if he had been aware of this second law. 
 
 " Truth is the most expedient error " ; this statement may 
 be traced back to a sequence of thought developed by Nietzsche. 
 But the Eternal Repetition is shattered by just this remark, 
 for judged by its consequences it would be a very inexpedient 
 error. 
 
 Supposing we should succeed in exchanging thoughts with 
 the inhabitants of distant worlds and should, through them, 
 acquire the elements of a civilization superior to our own, 
 would this knowledge prove a blessing to us or the reverse ? 
 
 The word " superior " must, of course, be treated circum- 
 
218 EINSTEIN THE SEARCHER 
 
 spectly. It is to denote only that, relatively, this distant 
 civilization bears somewhat the same relation to our civiliza- 
 tion of to-day as our own bears to that of an Australasian 
 negro or an anthropoid ape. There are fanatics of progress 
 whose wishes plunge headlong and without restraint into the 
 future, and to whom nothing could be more desirable than the 
 sudden appearance of a civilization that, as they opine, would 
 at one stroke carry us *' forward " many thousands of years. 
 
 But the view of these magicians with their seven-league 
 boots is untenable. Let me cite a mere outhne of the many 
 opposing arguments in a few words of Einstein. " Every 
 sudden change in the conditions of existence, even if it occurred 
 in the form of a higher development, would come upon us 
 like a doom, and would probably annihilate us, just as the 
 Indians succumb to the civilization that has outstripped 
 them. The tragedy of our own highly civilized times is that 
 we cannot create the social organizations that have become 
 necessary as a consequence of the technical advances of the 
 last century. This has given rise to the crises, impasses, and 
 senseless competition between nations, and to the impoverish- 
 ment of defenceless individuals. These deplorable conditions 
 would become inconceivably accentuated if we were to be 
 invaded by extra-mundane technical sciences of a higher 
 order." 
 
 Nevertheless, there is still a possibility that the " superior 
 civilization " might contain indications of the organizations 
 which we lack. Instead of entering on the question of this 
 Utopia, we confined ourselves to comparing past conditions 
 in our world with present ones. Did we not have the most 
 promising preliminaries for an organization that was devoid of 
 friction and tended to reduce the competition between nations 
 in the numerous international institutions that drew together 
 a great section of the intellectual world to work in co-operation ? 
 Are there hopes that this international coalition will be 
 resumed ? 
 
 Einstein expressed himself optimistically, not to do homage 
 to an organization artificially formed, but to extol the world- 
 wide mastery of intellect. " Even if international congresses 
 were to be swept away," he said, " international co-operation 
 
DISCONNECTED SUGGESTIONS 219 
 
 would not be abolished, as it effects itself automatically." I 
 should venture to assert that if all these congresses were to 
 cease, we should not even have cause to fear that there would 
 be an appreciable diminution in the combined effort of research. 
 If certain developments are hindered by poUtical conditions, 
 it is only due to the resulting economic hardships affecting 
 individuals in their work and robbing them of their intellectual 
 freedom. The real friends of Truth have alwa-ys clung to- 
 gether, and do so actually now ; indeed, many feel the tie to 
 be closer than that connecting them to their own country. 
 In spite of all obstacles and boundaries they will never cease 
 to find contact with one another ! 
 
CHAPTER XI 
 EINSTEIN'S LIFE AND PERSONALITY 
 
 WE know from the biographies of great thinkers that 
 they seldom personify the character of a dramatic 
 ideal. They are not heroes of fiction who pass 
 through complex experiences and struggle with mysterious 
 problems of existence that may unduly excite the imagina- 
 tion of observers. Whoever follows their development re- 
 marks in the majority of cases the predominance of the inner 
 life, the course of which is discoverable only by study of their 
 works, no clue being given in the confusion of ordinary exterior 
 manifestations. An eminent man of thought, whose energies 
 are concentrated on mental effort, rarely finds time to present 
 in addition an interesting figure in the epic sense. The poet 
 who moulds his forms from life finds little scope in him as a 
 model, and only in exceptional cases has he succeeded in 
 idealizing the savant in a work of art. 
 
 It would be a fruitless undertaking to treat Einstein's life 
 as one of these exceptional cases. It is possible to trace the 
 various phases of his development, yet neither the writer nor 
 the reader must disguise from himself the fact that such 
 outlines give only the external picture of the man and chrono- 
 logical events of importance. Nevertheless, a book of which 
 he forms the theme cannot pass over the task of giving his 
 curriculum vitcB. And if it should partly appear aphoristic 
 and disjointed, it must be borne in mind that this account 
 originated from conversations and scraps of conversation 
 that touched on various episodes of his Hfe, according as they 
 had a bearing on the subject under discussion. 
 
 The story of Einstein's life begins at Ulm, the town which 
 possesses the highest building in Germany. Gladly would I 
 stand on the belfry of the Ulm Cathedral in order to obtain a 
 
EINSTEIN'S LIFE AND PERSONALITY 221 
 
 general survey of Einstein's youth. But the view discloses 
 nothing beyond the bare fact that he was born there in March 
 1879. The detail which has already been mentioned above, 
 namely, that it was something physical that first arrested the 
 child's attention, remains to be noted. His father once showed 
 the infant, as he lay in his cot, a compass, simply with the idea 
 of amusing him — and in the five-year-old boy the swinging 
 metal needle awakened for the first time the greatest wonder- 
 ment about unknown cohesive forces, a wonderment that was 
 an index of the research spirit that was still lying dormant in 
 his consciousness. The remembrance of this psychical event 
 has a significant meaning for the Einstein of to-day. In him 
 all the impressions of early childhood seem to be still vivid, the 
 more so as all other physical occurrences, such as the falling 
 of an unsupported body, left no impression on him. His 
 attention was fixed on the compass, and the compass alone. 
 This instrument addressed him in oracular language, indicating 
 to him an electromagnetic field that was in later years to 
 serve him as a domain for fruitful research. 
 
 His father, who had a sunny, optimistic temperament, and 
 was inclined towards a somewhat aimless existence, at this 
 time moved the seat of the family from Ulm to Munich. They 
 here Hved in a modest house in an idyllic situation and sur- 
 rounded by a garden. The pure joy of Nature entered into 
 the heart of the boy, a feeling that is usually foreign to the 
 youthful inhabitants of cities of dead stone. Nature whis- 
 pered song to him, and at the coming of the spring-tide infused 
 his being with joy, to which he resigned himself in happy 
 contemplation. A religious imdercurrent of feeling made 
 itself manifest in him, and it was strengthened by the ele- 
 mentary stimulus of the scented air, of buds and bushes, to 
 which was added the educational influence of home and 
 school. This was not because ritualistic habits reigned in the 
 family. But it had so happened that he learned simultaneously 
 the teachings of the Jewish as well as the Catholic Church ; 
 and he had extracted from them that which was common 
 and conducive to a strengthening of faith, and not what 
 conflicted. 
 
 Youthful impetuosity, which in boys of a similar age 
 usually expresses itself in rash enterprises and loose tricks, did 
 
222 EINSTEIN THE SEARCHER 
 
 not appear in him. His spirit was adjusted to contemplation, 
 and an inborn fatalism, diffused with a super-sensuous element 
 appertaining to dreams, restrained him from responding to 
 external impulses. He reacted slowly and hesitatingly, and 
 he interpreted what his senses offered him and all the Httle 
 experiences of early days in terms of a reverence reflected from 
 within. Words did not easily rise from his lips, and measured 
 by the ordinary scale of rapidity of learning and readiness in 
 answering questions, he would scarcely have been judged to 
 possess unusual gifts. As an infant he had started to talk 
 so late that his parents had been in some alarm about the 
 possibility of an abnormality in their child. At the age of 
 eight or nine years he presented the picture of a shy, hesitating, 
 unsociable boy, who passed on his way alone, dreaming to 
 himself, and going to and from school without feeling the need 
 of a comrade. He was nicknamed " Biedermaier," because he 
 was looked on as having a pathological love for truth and 
 justice. What at that time seemed to be pathological, to-day 
 appears as a deeply rooted and irrepressible natural instinct. 
 Whoever has got to know Einstein as a man and as a scientist 
 knows that this failing of his boyhood was but the forerunner 
 of a very healthy outlook. 
 
 Signs of his love for music showed themselves very early. 
 He thought out little songs in praise of God, and used to sing 
 them to himself in the pious seclusion that he preserved even 
 with respect to his parents. Music, Nature, and God became 
 intermingled in him in a complex of feeling, a moral unity, 
 the traces of which never vanished, although later the religious 
 factor became extended to a general ethical outlook on the 
 world. At first he clung to a faith free from all doubt, as had 
 been infused into him by the private Jewish instruction at 
 home and the Catholic instruction at school. He read his 
 Bible without feeUng the need of examining it critically ; he 
 accepted it as a simple moral teaching and found himself little 
 inclined to confirm it by rational arguments inasmuch as his 
 reading extended very little beyond its circle. 
 
 Painful inner conflicts were not wanting. Jewish children 
 formed a small minority in the school, and it was here that the 
 boy Albert felt the first ripples of the anti-semitic wave that, 
 sweeping on from without, was threatening to overwhelm 
 
EINSTEIN'S LIFE AND PERSONALITY 223 
 
 master and pupil alike. For the first time he felt himself 
 oppressed by something that was not in harmony with his simple 
 temperament. His modesty made him a prey to injustice, 
 and in defending himself his originally gentle and restrained 
 nature gained a certain independence and individuahty. 
 
 If one may speak of achievements at all in a preparatory 
 school, those of Albert were of the average modest level. He 
 was careful as a pupil, generally satisfied requirements, but in 
 no way betrayed special talents : indeed, so much the less, as 
 he showed himself to be possessed of a very uncertain memory 
 for words. The methodic plan of the elementary school that 
 he attended to his tenth year was, however, not other than 
 the usual scheme mapped out by drill-masters ; it made up 
 for what was lacking in an understanding of the pupils by 
 applying drastic strictness. The beautiful sentence of Jean 
 Paul : " Memory is the only paradise from which we cannot 
 be banished," finds no echo in Einstein's school memories, 
 of which he has often spoken to me without a shadow of regret 
 for a lost paradise. He told me with bitter sarcasm that his 
 teachers had the character of sergeants — ^those later in the 
 gymnasium (secondary school) were of the nature of lieutenants. 
 Both terms are used in the pre-armistice sense, and his words 
 were directed against the self-opinionated tone and customs 
 of these garrison-schools of earher days. 
 
 The next stage of his development was a course of study 
 at the Luitpold-Gymnasium in Munich, which placed him in 
 the second class. In Einstein's retrospect of these days more 
 friendly recollections present themselves, connected, however, 
 only with particular persons, and not breathing praise in 
 general ; on the contrary, from his account, it is clear that 
 although he conceived affection for individual teachers, he 
 felt the tone of the institute as a whole to be rough. As we 
 know, many things have been changed in these schools since 
 then, following on a revulsion from the convict atmosphere 
 that used to characterize them, and which meant suffering 
 enough for the pupils. The result was that the schoolboy 
 Einstein developed a contempt for human institutions and 
 assigned Uttle value to the subjects of study which he was 
 obhged to absorb in schematic form without the application of 
 his own mentad energy. This gloomy picture is relieved at 
 
224 EINSTEIN THE SEARCHER 
 
 points by the presence of several teachers, above all, one called 
 Ruess, who took pains in exposing the beauty of classical 
 antiquity to the fourteen-year-old boy. We learn elsewhere 
 that Einstein at present admits the humanistic ideal for the 
 school of the future only under very restricted limitations. 
 But when he thinks of this teacher and his influence, a warm 
 appreciation of classical study vibrates in his words, occasion- 
 ally rising, indeed, to an unbounded enthusiasm for the treasures 
 of Greek history and literature. His instruction was not 
 restricted to the acquisition of a perspective of the antique. 
 Under the direction of the same teacher, he was introduced 
 into the poetic world of his native country, and learned the 
 magic of Goethe in his " Hermann and Dorothea *' ; this poem, 
 as he confesses, was explained to him in a really model manner. 
 Thus there were some oases in the desert of schematic teaching : 
 they served as refreshing halts for the spirit of the eager young 
 searcher after knowledge. 
 
 We must go back one or two years to note a weighty ex- 
 perience, which occurred when he made his first acquaintance 
 with elementary mathematics ; this subject presented itself 
 to him with the intensity of a revelation. It did not happen in 
 the ordinary course of school- work, but was due to a sort of 
 wizard-like inquiring inner spirit that plied him with questions 
 and that gave him inward thrills of joy when he found a sharp- 
 witted solution. From the very beginning Albert proved 
 himself to be a good solver of problems, even before he achieved 
 an arithmetical virtuosity, and before he knew the technique 
 of equations. He helped himself by means of little tricks, 
 experimented roundabout inventions, and was happily excited 
 when they led to the goal. One day he asked his uncle, Jacob 
 Einstein, an engineer who lived in Munich, a certain question. He 
 had heard the word " algebra " andsurmisedthat his uncle would 
 be able to explain the term to him. Uncle Jacob answered : 
 '* Algebra is the calculus of indolence. If you do not know a 
 certain quantity, you call it x and treat it as if you do know it, 
 then you put down the relationship given, and determine this 
 X later." That was quite sufficient. The boy received a book 
 containing algebraic problems that he solved all alone in accord- 
 ance with this not exhaustive but expedient direction. On 
 another occasion Uncle Jacob told him the enunciation of 
 
EINSTEIN'S LIFE AND PERSONALITY 225 
 
 Pythagoras' theorem without giving him a proof. His nephew 
 understood the relationship involved, and felt that it had to 
 be founded on some reasoning. Again he set about all alone 
 to furnish what was wanting. This was, however, not a case for 
 the " calculus of indolence " with an x that was to be deter- 
 mined. Here it was a question of developing a facility for 
 geometric argument, such as very few possess at such an early 
 stage of development. The boy plunged himself for three 
 weeks into the task of solving the theorem, using all his power 
 of thought. He came to consider similarity of triangles (by 
 dropping a perpendicular from one vertex of the right-angled 
 triangle on to the hypotenuse), and was thus led to a proof 
 for which he had so ardently longed ! And although it con- 
 cerned only a very old well-known theorem, he experienced 
 the first joy of the discoverer. The proof that he had found 
 proved that the ingenuity of the worrying young mind was 
 awakening. 
 
 A new world was opened for him when he made the acquaint- 
 ance of A. Bernstein's comprehensive popular books on scientific 
 subjects. This work is looked on nowadays as being some- 
 what antiquated and, in the eyes of many a professional 
 scientist, has sunk to the level of a pseudo-scientific " shocker " ; 
 even when Einstein as a boy made explorations in it, there were 
 signs of rust and decay in the work, for it originated in the 
 fifties of the previous century and, in point of subject-matter, 
 had long been transcended. Yet it could be read then — and 
 even now — as a story containing thousands of interspersed 
 phj^ical, astronomical, and chemical wonders, and for the boy 
 Einstein it came to be a true book of Nature, which presented 
 to his mind, greedy for knowledge, as much as it did to his 
 imagination. 
 
 Other vistas were opened up to him by Biichner's Kraft 
 und Stoff [Force and Substance), a book the cheapness of which 
 he could not yet discern, but which called up wonder in him 
 without rousing his criticism. In addition, his attention was 
 chiefly occupied by a handbook of elementary planimetry, 
 containing an abundance of geometrical exercises, which he 
 fearlessly attacked and within a very short time solved almost 
 in their entirety. His delight grew when he ventured into 
 the difficulties of analytical geometry and infinitesimal calculus 
 15 
 
226 EINSTEIN THE SEARCHER 
 
 quite apart from the curriculum of his school-work. Lubsen*s 
 textbook had fallen into his hands, and these directions 
 sufficed for his audacious spirit. Whereas many of his school 
 companions were still standing undecidedly before the pools 
 of theorems of congruence and repeating decimals, he was 
 already disporting himself freely in the ocean of infinitesimals. 
 His work did not remain concealed, and gained appreciation. 
 His mathematical teacher declared that the fifteen-year-old 
 boy was ripe for university study. 
 
 Yet he was not to find a way into the open by matriculating 
 very early, but through an event that unexpectedly threw 
 him into new surroundings of life. In 1894 his parents trans- 
 ferred their abode to Italy. The chronicler has nothing to 
 report of pangs of separation in Albert when he left Bavarian 
 soil. He was glad to get away from the drill academy, Luitpold, 
 and, as an inhabitant of Milan, he enjoyed the change in his 
 existence, and was not encumbered by attacks of home-sick- 
 ness. All in all, he had felt himself in an unhappy position 
 under school compulsion in Munich, in spite of the mathe- 
 matical delights he had provided for himself, and in spite of the 
 rapturous moments that musical revelations had created for 
 him since his twelfth year. Defiance and distrust against out- 
 side influences had remained active in him as forces that did not 
 allow the happy disposition proper to his age to assert itself. 
 But now the fetters had fallen and the pent-up joy of fife 
 burst forth as if through opened sluices. The sun and land- 
 scape of the South, Italian manners of life, art freely displayed 
 in the matket -place and on the street, realized for him dream- 
 pictures that had appeared to him earlier during the hours 
 of oppression. Whatever he saw, felt, and experienced lay 
 outside the ordinary course of his life, awakened his sense for 
 natural and human things, and set his spirit free from all bonds. 
 There was no question of his going to school in the first six 
 months. He enjoyed complete freedom, occupied himself 
 with literature, and undertook extended excursions. Starting 
 from Pa via, he wandered all alone over the Apennine to Genoa. 
 Whilst he was being intoxicated with the sublime Alpine 
 landscape, he came into contact with the lower stratum of 
 the people, who aroused his deepest sympathy. The tour 
 took him over a short stretch of the Italian Riviera, the 
 
EINSTEIN'S LIFE AND PERSONALITY 227 
 
 beauties of which, as depicted by Bocklin, do not seem to 
 have revealed themselves to him. At that time he was 
 probably subject to a feehng of upward striving such as 
 possessed Zarathustra. 
 
 With all their joys and inspirations the experiences in Italy 
 remained but a short episode. Einstein resolved on a new 
 tour, which was not without a professional purpose. He made 
 a pilgrimage to Switzerland with the intention of studying 
 mathematics and physics at the Ziirich Polytechnical Institute. 
 But he was not to be successful in his first effort to gain entrance. 
 The conditions of entry required a standard in descriptive 
 sciences and modern languages that he had not yet reached. 
 So he turned to Aarau, where he was allowed to extend his 
 knowledge with the help of excellent methods at the Canton 
 school. Even at the present day Einstein talks with extreme 
 enthusiasm of the organization of this model school that corre- 
 sponds in rank approximately to a German Realgymnasium 
 (or an EngUsh Grammar School). There was nothing to 
 remind him of the continual manipulation of the sceptre of 
 authority at the Luitpold school barracks ; he easily obtained 
 his leaving certificate, and now the portals of the Ziirich 
 Polytechnicum were open for him. 
 
 He himself was probably not aware that he carried a 
 marshal's baton in his own mathematical equipment. But, 
 in looking back, we come across astounding things. For it 
 is a fact that even in the pupil at Aarau problems had taken 
 root that already lay in the vanguard of research at that 
 time. He was not yet a finder, but what he sought as a 
 sixteen-year-old boy was already stretching into the realms 
 of his later discoveries. We have here simply to register 
 facts, and to abstain from making an anal5^is of his develop- 
 ment, for how are we to trace out the intermediate steps, and 
 to discover the sudden phases of thought that lead a very 
 young Canton pupil to feel his way into a still undiscovered 
 branch of physics ? The problem that occupied him was 
 the optics of moving bodies, or, more exactly, the emission 
 of Hght from bodies that move relatively to the ether. This 
 contains the first flash of the grandiose complex of ideas that 
 was later to lead to a revision of our picture of the world. 
 And if a biographer should state that the first 'jeginnings of 
 
228 EINSTEIN THE SEARCHER 
 
 the doctrine of relativity occurred at that time, he would not 
 be making an objectively false statement. 
 
 The ambitions of the youth by no means reached these 
 flights of imagination, for whereas the latter signified the coming 
 power of his wings, he himself set a modest goal. He wished 
 to become a schoolmaster, and imagined that in choosing this 
 career he was allowing his hopes to run high. This was in 
 conformity with the esteem in which he held the status of 
 teachers. In the Zurich Technical School there is a section 
 equipped as a department for preparing teachers, and in this 
 Einstein studied from the age of seventeen to the age of 
 twenty-one, perfectly satisfied with the thought of sitting, not 
 on the pupil's bench, but at the master's desk, and of exercising 
 a beneficial if limited influence as a preceptor of the young. 
 
 He was still under the sway of the feeling that he was 
 not sufficiently experienced in life and that he dare not 
 venture out into the fight for existence in the great turmoil 
 of the world. He saw in this struggle, which pitted man 
 against man, led to exhibitions of violence, and aroused 
 ambition for glittering unreaHties, cause only for disgust 
 and alienation. The prospect of personal success did not 
 lure him to try force against force. Thus, for the time being, 
 it was his ideal to lead a very modest existence. From various 
 quarters he had been given hopes of a position as assistant to 
 some professor of physics or mathematics. But for unknown 
 reasons he was everywhere refused. These apparently obscure 
 grounds, it must be said with regret, become clearer when we 
 bear in mind his confession of faith. Nor did his hopes of 
 teaching at a gymnasium seem near fulfilment, as certain 
 conditions of birth raised obstacles. In the first place, he was 
 not a Swiss ; in fact, since his stay in Milan he was without a 
 nationality at all in the bureaucratic sense, and then he had 
 no personal connexions, without which, at least at that time, 
 there was no chance of progress even for a talented person. 
 Yet the young student who was entirely without protection 
 of any sort had to overcome the cares and satisfy the needs of 
 daily Ufe. He could not rely on material help from his parents, 
 who themselves lived in restricted circumstances, and thus 
 we find him a little later in Schaffhausen and Bern, where he 
 earned a small pittance as a private tutor. 
 
EINSTEIN'S LIFE AND PERSONALITY 229 
 
 He found consolation in the fact that he preserved a 
 certain independence, which meant the more to him as his 
 instinct for freedom led him to discover the essential things 
 in himself. Thus, earlier, too, during his studies at Ziirich 
 he had carried on his work in theoretical physics at home, 
 almost entirely apart from the lectures at the Polytechnic, 
 plunging himself into the writings of Kirchhoff, Helmholtz, 
 Hertz, Boltzmann, and Drude. Disregarding chronological 
 order, we must here mention that he found a partner in these 
 studies who was working in a similar direction, a Southern 
 Slavonic student, whom he married in the year 1903. This 
 union was dissolved after a number of years. Later he found 
 the ideal of domestic happiness at the side of a woman w^hose 
 grace is matched by her intelligence. Else Einstein, his cousin, 
 whom he married in Berlin. 
 
 In 1 90 1, after living in Switzerland for five years, he 
 acquired the citizenship of Ziirich, and this at last gave him 
 the opportunity of rising above material cares. His Uni- 
 versity friend. Marcel Grossmann, lent him a helping hand by 
 recommending him to the Swiss Patent Office, the director of 
 which was his personal friend. Einstein occupied himseK here 
 from 1902 to 1905 as a technical expert, that is, as an examiner 
 of appHcations for patents, and this position gave him the 
 chance of moving about in absolute freedom in the realms of 
 technical science. Whoever has a strong predilection for 
 discovery will perhaps feel estranged to find Einstein so long 
 in the sphere of " invention," but, as Einstein himself em- 
 phasizes very strongly, both regions make great demands on 
 clearly defined and accurate thought. • He recognizes a definite 
 relationship between the knowledge that he gained at the 
 Patent Office and the theoretical results that appeared at the 
 same time as products of intensive thought. 
 
 In 1905, in the midst of his work, the storm broke loose in 
 him with the suddenness of a hurricane. In quick succession 
 his mind disburdened itself of the abundance of ideas that 
 had stored themselves up in the work of the preceding years, 
 and these ideas signify more to us than a definite stage in the 
 development of an individual. What physicists have come 
 to regard as an elaboration of the heritage of Galilei and 
 Newton had matured in him. We merely record the title 
 
230 EINSTEIN THE SEARCHER 
 
 of dissertations, which appeared in 1905 in the Annalen der 
 Physik : " Concerning a Heuristic Standpoint towards the Pro- 
 duction and Transformation of Light " — " Concerning the 
 Inertia of Energy " — " The Law of Brownian Movement." 
 — Then the most important contribution : '' The Electro- 
 dynamics of Moving Bodies," that contained the revolutionary 
 ideas underlying the special theory of relativity. To these is to 
 be added a dissertation for his doctorate in the same year : 
 " A New Determination of Molecular Dimensions." 
 
 In all, these represent a Ufe-work that belongs to the 
 history of science. It was certainly some considerable time 
 before his work began its triumphal march in the sight of the 
 world, and it may be added that treasures were hidden in these 
 disquisitions that were not understood till long years after- 
 wards. Yet the youthful discoverer was not passed over 
 without signs of friendly appreciation. He received a letter, 
 couched in very warm terms, from the celebrated physicist, 
 Max Planck, who was a complete stranger to him at that 
 time ; it spoke in glowing words of his essay, " The Electro- 
 dynamics of Moving Bodies." This letter was the first 
 diploma, the forerunner of all the honours that later swept over 
 him like a tidal wave. 
 
 It was his intention to obtain a tutorial position at the Uni- 
 versity. An appointment to Bern was at first again hindered 
 by certain obstacles which he would probably have overcome 
 if he had applied himself energetically to attaining his goal. 
 He finally received his appointment, but exercised his duties 
 for only a very short time, as Ziirich now opened her arms to 
 him. In 1909 he accepted the position of Professor extra- 
 ordinarius there for theoretical physics, and soon assembled 
 a grateful audience about himself. Nevertheless, during the 
 earlier stages of his professorship he found it difficult to sup- 
 press a longing for the quiet, unexcited life of his patent -office 
 work, in which he seemed to have had a still greater degree 
 of independence. In 191 1 he accepted a new appointment 
 as Professor ordinarius to Prague, which offered him more 
 favourable emoluments as an inducement. In the autumn of 
 1912 he returned to Zurich as a Professor at the Polytechnic, 
 and in the early part of 1914 he was drawn into the strong 
 magnetic field of the northern capital ; he arrived at the Spree, 
 
EINSTEIN'S LIFE AND PERSONALITY 231 
 
 and has, since then, lived among us. He is now a Swiss by 
 nationality, a world citizen by conviction, and, professionally, 
 a member of the Berlin Academy and attached in a lecturing 
 capacity to the University. Here he perfected his works on 
 relativity, ending in the superlative elaboration of the theory 
 of gravitation, the beginnings of which stretch back to the 
 year 1907. He had spent eight years in a concentrated effort 
 of severe thought to bring it to completion, and perhaps 
 centuries will be necessary before the world will gain a com- 
 plete perspective of all the consequences of his theory. 
 
 For the theory asks us to brush aside habits of thought 
 that have claimed an hereditary position in pre-eminent minds. 
 One of the foremost physicists, Henri Poincare, had confessed 
 as late as'1910 that it caused him the greatest effort to find 
 his way into Einstein's new mechanics. Another whole year 
 passed before he gave up his last doubts. Then he passed 
 with flying colours into Einstein's camp, and recommended 
 Einstein's appointment to the Professorship at Ziirich, in con- 
 junction with the discoverer of radium, Madame Curie, in an 
 exuberant letter which may add its note of appreciation here : 
 
 " Herr Einstein," so wrote the great Poincare, " is one of 
 the most original minds that I have ever met. In spite of his 
 youth he already occupies a very honourable position among 
 the foremost savants of his time. What we marvel at in him, 
 above all, is the ease with which he adjusts himself to new 
 conceptions and draws all possible deductions from them. He 
 does not cling tightly to classical principles, but sees all con- 
 ceivable possibilities when he is confronted with a physical 
 problem. In his mind this becomes transformed into an 
 anticipation of new phenomena that may some day be verified 
 in actual experience. . . . The future will give more and more 
 proofs of the merits of Herr Einstein, and the University that 
 succeeds in attaching him to itself may be certain that it will 
 derive honour from its connexion with the young master." 
 
 We may be tempted to look back and ask whether the 
 criteria that Wilhelm Ostwald once set up as a test of great 
 men are verified in Einstein's case. He has certainly not 
 broken the first and most general rule, the principle of " early 
 maturity." This showed itself clearly when his impulse to- 
 wards mathematical knowledge and discovery asserted itself. 
 
232 EINSTEIN THE SEARCHER 
 
 and when he penetrated far into the future with his optical 
 problems. The history of science and of art may offer more 
 striking examples in this connexion, but at any rate in 
 Einstein's case the indications are sufficient to serve as a con- 
 firmation of the rule. On the other hand, the second test of 
 Ostwald seems to be valid only conditionally when applied to 
 Einstein. For Ostwald takes up arms against a " gradual 
 intensification " of ability, and proclaims it as an almost 
 universal rule that the exceptional achievement is the privilege 
 of quite young persons : " what he achieves later is seldom 
 as impressive as his first brilHant achievement." Thus, in 
 Einstein's case, the exception is evident. For if we fix on 
 only two chief discoveries, passing over many others, there is 
 no doubt that the second (the theory of gravitation) surpasses 
 the first (special relativity) in both range and significance. 
 Indeed, we cannot escape from the idea of a " gradual in- 
 tensification," for the second discovery could come about only 
 as a result of the first. Moreover, it is not yet night, and there 
 is nothing to refute the assumption that there will be a further 
 progression. 
 
 Furthermore, Ostwald takes into consideration the tempo 
 of the intellectual pulse of inspiration to divide the main 
 types of great men into a classical and a romantic category : 
 this classification cannot, however, be appHed to Einstein. 
 He is decidedly classical, in so far as his work seems calculated 
 to serve later generations as a classical foundation for all 
 mechanical investigations of the macrocosm of the heavens 
 and the microcosm of atoms. On the other hand, his ver- 
 satility, the mobility and resource of his highly imaginative 
 mind, stamp him as a romantic spirit. His deUght in teaching 
 would also assign him to this category, for in the case of many 
 classical spirits there is a decided aversion to imparting in- 
 struction. So that, although we might well be able to speak 
 of a synthesis of these two forms, it seems better to estimate 
 Einstein, not in the light of a ready scheme, but rather as a 
 type of which he is the unique representative. 
 
 Just as the external contour of his life is on the whole 
 regular and unbroken, so also his inner life is attuned to 
 simplicity. Nowhere, it might almost be said, do we observe a 
 
EINSTEIN'S LIFE AND PERSONALITY 283 
 
 break, a spasmodic turn, or a sudden intensification. Although 
 he has grasped and suggested so many problems, he himself 
 presents no psychological riddle, and we meet with no 
 singularities in analysing his personality. It has already 
 been remarked several times that Art plaj^ a part in his life. 
 What I learned from him himself about his affection for music 
 coincides exactly with what observation clearly discloses. 
 The expression of his countenance when he is listening to 
 music is a suf&cient indication of the resonances induced in 
 him. He is confessedly a classicist, and a sincere devotee of 
 the revelations of Bach, Haydn, and Mozart. What fascinates 
 and enraptures him above all is that which is directed inwards, 
 which is contemplative and erected on a reUgious basis. The 
 simple masterful flow in musical development and invention 
 is all-important for him. The architectonic structure that we 
 marvel at in Bach, the Gothic tendency towards heavenly 
 heights, perhaps calls up in him sensations that emanate from 
 his hidden wealth of constructive mathematical ideas. It 
 seems to me that this possibiHty is not unworthy of remark. 
 It suggests a reason for the fact that he gives himself up only 
 unwillingly to the nervous strain of drama directed at emo- 
 tional upheaval. He does not gladly overstep the boundary 
 that separates the simple from the psychologically subtle, and 
 whenever his desire to understand art requires him to venture 
 beyond it, his appreciation is not accompanied by genuine 
 pleasure. His subjectivity does not fix this boundary in 
 accordance with the ordinary rules of concert aesthetics, which 
 are actuall}^ not rules at all, but only changeable valuations 
 and crystallizations of the feelings of certain groups of people. 
 He gives himself up quietly and freely to what is presented, 
 but makes no special effort to assimilate experiences to which 
 his being does not spontaneously react. There would be no 
 meaning in seeking to mark off the Hmits of his receptivity in 
 accordance with this, and to tell him that it is too limited, and 
 that it should be enlarged, and that he should not regard as an 
 opinionated exaggeration what appears to others to be a deep 
 and mighty revelation, or seems to be possessed of divine 
 sweetness. He would be able to point out that even in the 
 case of masters of the musical art a change of faith was not 
 a rare occurrence, and that they learned anew, or rejected what 
 
234 EINSTEIN THE SEARCHER 
 
 they once idolized, and very often found no permanent haven 
 in their own faith. Whoever, Uke Einstein, gives himself up 
 to the simply contemplative, and feels no impulse towards 
 sensationalism, is spared the task of learning afresh, and finds 
 still one world left for him even if many other worlds are in- 
 accessible. To mention only the main features, then, neither 
 Beethoven as a composer of symphonies, nor Richard Wagner, 
 denote the pinnacles of music for him ; he could live without 
 the Ninth Symphony, but not without Beethoven's ensemble 
 music. The number of composers and compositions which 
 are not a necessity of Ufe for him is very considerable. It 
 includes the majority of romanticists, the erotically inclined 
 school of Chopin and Schumann, which revels in sensation, 
 and, as already mentioned, the neo-German dramatic com- 
 posers. He has much objective admiration for them, yet he 
 does not conceal the fact that he also feels lively opposition 
 in the gamut of his sensations. He regards the properly 
 modern productions as interesting phenomena, and has 
 various degrees of disapproval for them, extending to complete 
 aversion. It costs him an effort to hear an opera of Wagner, 
 and when he has done so, he returns home bearing with him 
 the leitmotiv of Meister Eckhard : ** The lust of creatures is 
 intermingled with bitterness." In general he seems to take 
 up approximately the point of view of Rossini. Wagner 
 gives him wonderful moments, followed, however, by periods 
 of acute emotional distress. I need hardly add that I myself, 
 who confess to being an ultra-Wagnerite, never strove in my 
 conversations with Einstein to make my opinion prevail 
 against his. For I am deeply convinced that in this matter 
 there is no question of right and wrong, and that every musical 
 valuation represents no more than an accidental judgment 
 dependent on one's own nature, entirely ego-centric and thus 
 objectively of no account. 
 
 Einstein also occupies himself in an active sense with 
 music, and has developed into a very fair viohnist, without 
 claiming higher degrees of achievement. Among other things 
 I once heard him play the vioHn part of a Brahms Sonata, 
 and his performance approached concert standard. He draws 
 a beautiful tone, infuses expression into his rendering, and 
 knows how to overcome the technical difficulties. Among 
 
EINSTEIN'S LIFE AND PERSONALITY 235 
 
 the supreme artists of his instrument who have exerted a 
 personal influence on him, Joachim assumes the first place. 
 Einstein still speaks with great enthusiasm of Joachim's 
 performance of Beethoven's Tenth Sonata and of Bach's 
 Chaconne. He himself plays the latter piece, for which the 
 purity and accuracy of his double and multiple stopping fits 
 him. Whoever chooses the right moment — ^this good fortune 
 has not yet befallen me — may overhear Einstein at his pianistic 
 studies. As he confessed to me, improvisation on the piano is 
 a necessity of his fife. Every journey that takes him away 
 from the instrument for some time excites a home-sickness for 
 his piano, and when he returns he longingly caresses the keys 
 to ease himself of the burden of the tone experiences that have 
 mounted up in him, giving them utterance in improvisations. 
 
 The regular run of concerts in which displays of bravura 
 play an important part finds Uttle favour with him ; above all, 
 he is not a worshipper of the orchestral conductor, whom he 
 regards only as an interpreter and not as a virtuoso on the 
 orchestral instrument . He expressed this idea in unmistakable 
 words : " The conductor should keep himself in the back- 
 ground." I believe that his dearest wish would be to breathe 
 in the tones without a personal or material medium, merely out 
 of the air or out of space. Furthermore, I believe that there 
 is an unfathomable connexion between his musical instinct 
 and his nature as a research scientist. For the ear, as we 
 know from Mach, is the true organ that enables us to experience 
 space, and thus things may occur within the ear of the investi- 
 gator of space that may have a different significance from 
 that of music which is represent able in tones. I strongly 
 doubt whether traces of compositional form occur in Einstein's 
 tone-monologues, but perhaps they contain examples of an 
 art for which the aesthetics of a distant future may find a 
 name. 
 
 With regard to higher literature, and indeed all writings 
 not connected with science, Einstein has Uttle to say. He 
 himself rarely directs conversation on to this topic, and still 
 less rarely does he give vent to an enthusiastic outburst that 
 betrays warm interest. He restricts himself to making short, 
 aphoristic comments, and now and then allows his listener 
 
236 EINSTEIN THE SEARCHER 
 
 to gather that he can easily imagine an existence without 
 literature. The number of accepted novels, tales, and poetic 
 works which he has not read is legion, and all the pretentiously 
 artistic, historical, and critical writings that are added to them 
 have attracted only a very momentary interest from him. 
 
 I have never seen him attracted in any way by the pro- 
 mising aspect of some new book intended for diversion. If 
 such a one happens to get into his hands, he merely places it 
 among the others. At times I was constrained to think of 
 Caliph Omar's words : " If the book contains what is already in 
 the Koran, it is unnecessary ; if it contains something else, it is 
 harmful." It is harmful at least in the sense that it robs us 
 of time that may be better spent in another way. I am 
 purposely exaggerating here to make it quite clear that Einstein 
 finds full satisfaction in a narrow circle of literature, and that 
 he experiences no loss if numerous new works pass by and 
 escape his notice. 
 
 Nevertheless, he speaks with reverence of a series of authors, 
 to whom he owes enrichment : among them are the classical 
 writers, who naturally occupy the highest position, with 
 certain exceptions, which he equally naturally wishes to be 
 taken as a personal opinion and not in the sense of a critical 
 valuation. With him the difference reveals itself in the in- 
 tonation from which we may read a greater or lesser measure 
 of affection. When he says ** Shakespeare," the eternal 
 greatness seems to be inherent in the actual sound of the 
 name. When he says " Goethe," we notice a slight undertone 
 of dissonance, which may be interpreted without difficulty. 
 He admires him with the pathos of distance, but no warmth 
 glows through this pathos. 
 
 I had ventured to deduce from my knowledge of his nature 
 the men and the works which, in my opinion, should awaken 
 strong echoes in him. A fairly clearly defined line leads to 
 the true path. Outside of any systematic series, I may 
 mention Dostojewski, Cervantes, Homer, Strindberg, Gottfried 
 KeUer in the positive sense, Emile Zola and Ibsen in the 
 negative sense. Taken as a whole, this prognostication does 
 not disagree seriously with his own statement, excepting 
 that he lays still greater emphasis on Don Quixote and the 
 Brothers Karamasoff than I had surmised. He expressed 
 
EINSTEIN'S LIFE AND PERSONALITY 237 
 
 himself with reserve about Voltaire. He has no belief in 
 Voltaire's poetic qualities, and sees in him only a subtle- 
 minded and amusing writer. Perhaps if Einstein were to 
 devote himself a little more intensively to Voltaire and Zola, 
 he would assign a higher value to these related spirits. But 
 there is little hope of this occurring, as the wide range of 
 Voltaire's works tends to restrain him. Time, which the 
 physicist Einstein has shown to be relative, has an absolute 
 value for him when measured in hours, and whoever seeks to 
 persuade him to read thick volumes is not Ukely to gain his 
 goodwill. 
 
 Our philosophical Uterature is not received with acclama- 
 tion by him. If some one wished to undertake the task of 
 ascertaining Einstein's attitude towards philosophy, he would 
 be well advised to plunge into Einstein's works rather than to 
 ask him personally. In them the questioner would find ample 
 hints, pointing towards a new theory of knowledge, the first 
 indications of which are already perceptible. A great portion 
 of philosophic doctrine will yet have to pass through the 
 Einstein filter to be purified. He himself, it seems to me, 
 leaves this process of filtering mostly to other thinkers, but we 
 must not lose sight of the fact that these others derive their 
 views of space, time, and causality from Einstein's physics. 
 It is thus immediately evident that he does not find revelations 
 about ultimate things in already extant Uterature, for the 
 simple reason that they are not to be found there. For him 
 famous works represent, in Kant's language, " Prolegomena 
 to every future system of metaphysics which can claim to 
 rank as a science." The accent is to be put on the future 
 that has not yet become the present. He praises many, 
 particularly Locke and Hume, but will grant finality to none, 
 not even to the great Kant, not to mention Hegel, Schelling, 
 and Fichte, whom he barely mentions in this connexion. 
 To Schopenhauer and Nietzsche he assigns a high position as 
 writers, as masters of language and moulders of impressive 
 thoughts. He values them for their Hterary excellence, but 
 denies them philosophic depth. As far as Nietzsche is con- 
 cerned, whom, by the way, he regards as too gUttering, Einstein 
 certainly experiences ethical objections against this prophet of 
 the aristocratic cult whose views are so diametrically opposed 
 
238 EINSTEIN THE SEARCHER 
 
 to Einstein's own opinion of the relations between man and 
 man. 
 
 Earlier when we were talking of classical poetry he had 
 particularly emphasized Sophocles as one who was dear to him. 
 And this name leads us to the innermost source of Einstein as 
 a man. " I am not here to hate with you but to love with 
 you/' is the cry of Sophocles' Antigone, and this cry is the key- 
 note of Einstein's emotional existence. I shall not give way 
 to the temptation to follow those who in the turmoil of the 
 present day refer to Einstein as a political figure. That would 
 lead to a description of policy and party arguments that lie 
 beyond the scope of this book ; so much the less am I incHned 
 to do so as Einstein's convictions may be expressed very clearly 
 without reference to schematic terms of a very elastic nature. 
 An individuality such as his cannot be compressed into a party 
 programme . And if anyone should insist on placing him among 
 the radicals or on assigning him far to the left, I should suggest 
 that it would be better to choose, instead of the classification 
 right and left, that of above and below. I look up towards his 
 idealism, whose altitude may perhaps be reached one day by 
 the raising of our ethical standards. But not by means of 
 paragraphs of laws. I have seldom heard him talk of such 
 schematic recipes, but so much the nftore have I noted utter- 
 ances which bore witness to a very intense and ever-present 
 sympathy with every human creature. His programme, which 
 is written not in ink but in heart 's-blood, proclaims in the 
 simplest manner the categorical imperative : Fulfil your duty 
 to your fellow-being : offer help to every one : ward off every 
 material oppression. " Well, then, he is a socialist," so the cry 
 runs. If it is your pleasure to call him so, he will not deny you 
 it. But to me this term seems to denote too narrow limits for 
 him. I see no contradiction in applying the term, but there is 
 no perfect congruence. If one word is necessary, I should be 
 rather more inclined to say that he is in the widest sense a 
 democrat of liberal trend. 
 
 For him the State is not its own aim, nor does he imagine 
 himself to be the possessor of a panacea. " The attitude of the 
 individual to socialism," he said, " is uncertain owing to the 
 fact that we can never ascertain clearly how much of the iron 
 compulsion and blind working of our economic system may be 
 
EINSTEIN'S LIFE AND PERSONALITY 289 
 
 overcome by appropriate institutions." And I should like to 
 add that such instituj:ions would scarcely have a permanent 
 result, but that more may be expected from the ethical example 
 of those who have the power of renunciation. Whoever 
 reaUzes the motto of Antigone, " I am here to love with you," 
 brings us nearer the goal. All in all, our longing continually 
 flees from the confusion of poUtical considerations to simple 
 morality. For Einstein this is the primary element, that 
 which is directly evident and not open to misrepresentation. 
 It includes sympathy, and, what is more important, joy in 
 conjunction with others. " The best that hfe has to offer," 
 he once exclaimed, ** is a face glowing with happiness ! " 
 
 This look is expressed on his own face when he discusses 
 his ideals, above all the internationahty of all intellectual 
 workers and the reaUzation of eternal peace among the nations. 
 To him pacifism is a matter of mind as weU as of heart, and he 
 is of the opinion that the course of history so far is but the 
 prelude to its reaUzation. The past, with its bloodstained 
 fingers that reach into the present, does not discourage him 
 He points to the endless city wars of the Middle Ages in Italy, 
 which had finally to cease in answer to the increasing feeling 
 of solidarity. So he believes in the victory of peace, which 
 the unified consciousness of all humanity will one day win over 
 the demonic powers of tyranny and conquest. 
 
 The pacifist ic goal seems to him to be attainable without the 
 peculiarities of the various States being destroyed. National 
 characteristics arising from tradition and hereditary influences 
 do not signify in his eyes a contradiction to the internationalism 
 that embraces the common intellectual factors of civilized 
 peoples. Thus the desire for the preservation and care of 
 particularities directs him to the secondary goal of Zionism. 
 His blood asserts itself when he supports the foundation of a 
 State in Palestine, which seems to him to be the only means of 
 preserving the national individuaUty of his race without the 
 freedom of the individual being affected. 
 
 We had left Art to talk of the State, and then returned to 
 the former theme to touch lightly on the pictorial arts. Paint- 
 ing was allowed to pass with merely a fleeting remark. It 
 plays no considerable part in Einstein's existence, and he 
 would not suffer great grief if it were to vanish from the plane 
 
240 EINSTEIN THE SEARCHER 
 
 of culture, a consummation to which definite signs seems to 
 point. I have described these signs in other writings (as in 
 Kunst in looo Jahren), and maintain the point of view that the 
 latest branches of painting as represented by expressionism and 
 cubistic futurism denote, in essence, the last convulsions of a 
 dying surface art . And even the chief represent ati ves of former 
 flourishing periods are beginning to fade away, and Einstein will 
 not be the only one who will relegate this art, as compared with 
 music, to a lower plane among the inspired arts that bring joy 
 to humanity. He is only more frank than others when he 
 freely confesses that he cannot convince himself that a life 
 without the joys of pictorial art would be hopelessly impover- 
 ished. But he bows his head to sculpture, and, for him, 
 architecture is a goddess. It is again his deeply rooted piety 
 that asserts itself when memory recalls to him the Gothic dome 
 with its pinnacles striving towards heaven. Goethe and 
 Schlegel have called architecture " frozen music," and this 
 picture is present in his mind when he sees Gothic architecture 
 as frozen music of Bach. It is open to anyone to analyse this 
 specific impression in another way by seeking the fundamental 
 elements, in which the essence of the art is to provide support 
 for a weighty structure and to overcome gravitation. For a 
 spirit that works with mechanics and that feels within itself the 
 pressures and tensions occurring in external nature, archi- 
 tecture is a kind of statics and dynamics transformed into a 
 thing of beauty, a ravishing picture of his own science. 
 
 Einstein has told me many a story of his travels, and 
 these reports were characterized by an absence of definite 
 purpose. The conception of something worth seeing in the 
 tourists' sense does not exist for him, and he does not set out in 
 eager pursuit of those things that are marked with two asterisks 
 in Baedeker. The intense romanticism of Swiss scenery, that 
 lay within such easy reach for him, has never enticed him into 
 its magic circle, and he has nothing to do with the abysmal 
 terrors of glaciers and the world of snow-peaks. His en- 
 thusiasm for landscape beauty conforms with the behaviour of 
 the barometer : the greater the altitude, the lower the mercury. 
 In simple contact with Nature he prefers the lesser mountains, 
 the seashore, and extensive plains, whereas brilliant panoramic 
 
EINSTEIN'S LIFE AND PERSONALITY 241 
 
 contours like those of the Vierwaldstetter See do not rouse 
 him into ecstasy. It is unnecessary to remark that he does 
 not arrange his Uving on the standard of the Grand Palace 
 Hotels en route. It is nearer the truth to picture him as a 
 vagrant who tramps along without a sense of time and without 
 a goal, in the fairy atmosphere of a joyous wanderer who has 
 unconsciously adopted the old rule of Philander : Walk with 
 a steady step : make your burden small : start early in the 
 morn, and leave home all care ! 
 
 Am I to record the Hst of pleasures and hobbies that are 
 foreign to him ? The Ust would be very long, and I should 
 arrive at my goal more quickly by setting his sporting tendencies 
 equal to zero. I once suspected him of being given to aquatic 
 sport, as I learned that he had taken part in several yachting 
 excursions. But I was mistaken. He sails in the same way 
 as he walks on his tours, without a set purpose, dreaming, and 
 uninterested in what is regarded by members of sailing clubs 
 as a " feat/* In the negative list of his games we see even 
 chess, that usually exerts a strong attraction on natures with 
 a mathematical tendency. The particular types of combina- 
 tion offered by this game have never tempted him, and the 
 world of chess has remained terra incognita for him. He is 
 just as little interested in every kind of collection, even that of 
 books. I have seldom or never met a savant who attaches so 
 little value to the personal possession of numerous and valuable 
 books. This statement may be extended as far as saying that 
 he experiences no pleasure at all in possession as such : he 
 says so himself, and his whole manner of Ufe proves it. There 
 seems to me to be an element of resignation in his amiable 
 hedonism, a kind of monkish asceticism. He never rids him- 
 self of the feeling that he is only paying a visit in this world. 
 
 I do not know whether Einstein considers that his life- 
 work can be completed within the span of this visit. At 
 any rate he makes no attempt to extract more out of the day 
 by following a rigid programme of work than the day volun- 
 tarily offers. He does not compel himself to cover a definitely 
 circumscribed piece of ground with chronological exactitude. 
 There are brain-workers, especially artists, who actually never 
 shake off the fetters of the twenty-four hours day of work 
 inasmuch as they spin on the threads of daily effort into the 
 i6 
 
242 EINSTEIN THE SEARCHER 
 
 nightly fabric of dreams. Einstein can make a pause, inter- 
 rupt liis work, or divert himself into side-channels at leisure 
 and according to the demands of the hour, but dreams offer 
 him no inspiration and do not waylay him with problems. 
 
 On the other hand, however, he is waylaid so much the 
 more during the day by things and persons that make an 
 assault on him. This starts as soon as the first post arrives, 
 to see through which requires a special bureau. In addition 
 to the communications of a professional or official nature 
 there appear innumerable letters from everywhere and any- 
 where asking him to grant a little of his time. Whatever 
 each individual writer has thought about the principle of 
 relativity, all his thoughts and doubts, additions, and, above 
 all, that which he has not been able to understand, all this is 
 to be answered by Einstein. Has he, the child of fame, even a 
 quarter of an hour for himself ? There they wait in the hall, 
 the painter, the photographer, the sculptor, and the inter- 
 viewer ; with whatever powers of persuasion and argumenta- 
 tive subtlety his attentive wife may seek to defend his hours 
 of rest, some of these visitors will yet succeed in gaining the 
 upper hand, and will produce something in oil-colours, in 
 plaster of Paris, in black and white, in water-colours, or in 
 print. Fame, too, demands her sacrifices, and if we talk of a 
 hunt after fame, then Einstein is certainly not the hunter, 
 but the hunted. 
 
 He sighs under the burden of his correspondence, not only 
 as the recipient, but also with the sender, whose letter has to 
 remain unanswered. Yet he is never roused to anger by the 
 intruder on his time. If this were not so, the aphorism of 
 Cyrus that patience is the panacea of all ills would not hold 
 for him, and how would I myself otherwise have dared to 
 claim so many hours of him ? A sense of guilt falls on me ! 
 
 But even Einstein's patience can come to an end, and this 
 is at the point where " society " begins : I mean the con- 
 gregation of persons in a salon, society entertainments to 
 which one is invited to be seen, and so that one may claim 
 to have been there. A solemn representation in which he is 
 to be made the cynosure of all eyes is a torture to him. If in a 
 very exceptional case he is compelled to participate in such a 
 gathering, the joy of his hosts will not be entirely unmixed. 
 
EINSTEIN'S LIFE AND PERSONALITY 243 
 
 for it does not require a thought -reader to recognize the longing 
 for solitude imprinted on his countenance : " Could I but 
 escape ! " 
 
 So much the happier does he feel himself in the narrow 
 circle of his friends, who offer what means tp him much more 
 than admiration, namely, affection, and an appreciation of 
 his human self. He is what one wishes him to be. He is 
 happy when he can forget the doctor profundus, and can 
 yield himself up to the atmosphere of stimulating and un- 
 constrained converse. He is a master in the art of Hstening, 
 and is not averse to contradiction ; when possible, he even 
 emphasizes the arguments of his opponent. Audiatur et 
 altera pars ! This is a further manifestation of his altruistic 
 personality, which rejoices when he extracts the true kernel 
 from the husk of the opposing opinion. Here he also displays 
 a characteristic which one does not usually expect to find among 
 abstract thinkers, a sense of humour that runs through the 
 whole gamut from a gentle smile to hearty laughter, and that 
 is the happy source of many a striking sally. It may happen 
 that the subject of conversation excites his anger, especially 
 in political debates when he calls to mind militaristic or feudal 
 misgovernment. He then becomes roused, and, as a cynical 
 philosopher, sarcastically attacks personaHties and points out 
 the primary source of perennial hate, immediately afterwards 
 soaring up to happy speculations of the future. 
 
 It is a matter for regret that the subjects that he has 
 discoursed on lightly have not been fixed phonographically. 
 Such records would form an interesting supplement to the 
 conversations outhned in this book. It would never occur 
 to him to set down in permanent literary form the inspiration 
 of the moment. What he writes emanates from other regions, 
 and is, to use his own expression, a precipitate of ** thick ink.'* 
 This is obvious, for what he has to proclaim as a scientist 
 cannot be presented in a " thin " form. But many a so-called 
 writer would have reason to congratulate himself, if so much 
 thinly flowing matter occurred to him in writing as to Einstein 
 in speaking. 
 
 The record of these conversations was began in the summer of 1919, and 
 completed in the autumn of 1920. 
 
INDEX 
 
 Aristoteles, 41 
 Arrhenius, 144 
 
 Babinet, 25 
 Bach, 88, 235 
 Bacon, 46 
 
 Baer, K. E. von, 162 
 Bailhaud, 144 
 Beethoven, 99, 234, 235 
 Bell, Graham, 25, iii 
 Beranger, 84 
 Bergson, 91 
 Bernoulli, 48 
 Bernstein, 225 
 Bessel, 32 
 
 Bohr, Niels, 57, 210 
 Brahe, Tycho, 94 
 Bruno, Giordano, 141 
 Biichner, 225 
 Bulwer, 76 
 Bunsen, 164 
 Byron, 9 
 
 Cantor, 52, 203 
 Cavendish, iii 
 Ceulen, Ludolf van, 158 
 Condillac, 216 
 Copernicus, 6, 90 
 Cosmati, 48 
 
 Curie, Madame, 79, 231 
 Cuvier, 196 
 
 Darboux, 152 
 Dase, 158 
 
 Descartes, 47, 133, 162 
 Dingeldey, 190 
 Dostojewski, 185, 187 
 Dove, 21, 155 
 Duhem, 105, 106 
 Duhring, 54, 56 
 
 Eckermann, 50, 85 
 Edison, 140 
 Euclid, 180 
 Euler, 98 
 Euripides, 85 
 
 Faraday, 39, 61, 84 
 Fechner, no, 182 
 
 Fermat, 97, 190 
 Fizeau, 113 
 Flammarion, 115 
 Franklin, 102 
 Fresnel, 45 
 
 Galilei, 6, 40, 150, 179, 181 
 
 GaUe, 6 
 
 Galvani, no 
 
 Gauss, 55, 185, 186 
 
 Goethe, 13, 23, 179, 197, 212, 236 
 
 240 
 Grillparzer, 95 
 Grossmann, 229 
 
 Hansen, 134 
 
 Hebbel, 77, 86 
 
 Hegel, 42 
 
 Heine, 49 
 
 Helmholtz, 25, 26, 53, 73 
 
 Heraclitus, 23 
 
 Herschel, 84 
 
 Hertz, 60 
 
 Hooke, 41 
 
 Horace, 3 
 
 Humboldt, 49 
 
 Hume, 161 
 
 Huyghens, 56, 109, 132 
 
 Jean Paul, 86, 223 
 
 Joule, 84 
 
 Jung Stilling, 84 
 
 Kant, 35, 121, 170, 177, 179, 237 
 Kepler, 6, 42, 84, 176, 177 
 Kirchhofif, 104-7, 148, 212 
 Kleist, 130 
 Kummer, 190 
 
 Lamarck, 197 
 
 Lange, 47 
 
 Laplace, 40, 45, 140, 165 
 
 Leibniz, 26, 128 
 
 Leonardo da Vinci, 11, 50-54 
 
 Leverrier, 6, 10 
 
 Liebig, 55 
 
 Lindemann, 158 
 
 Linn6, 196 
 
 Lorentz, 57, 72 
 
 a45 
 
246 
 
 EINSTEIN THE SEARCHER 
 
 Lothar Meyer, 107 
 Lucretius, 210 
 
 Mach, 46, 77, 108, 149, 169 
 Mauthner, 95 
 Maxwell, 39, 60 
 Mayer, Robert, 25, 55, 56 
 Melanchthon, 82 
 Menander, 86 
 Mendelejew, 107 
 Mezzofanti, 63 
 Michelangelo, 49 
 Michelson and Morley, 112 
 Mill, 45 
 
 Mithridates, 63 
 Montaigne, 77 
 Mozart, 233 
 
 Newton, 2, 6, 8, 39, 40, 43, 96 
 Nietzsche, 63, 217, 237 
 NoUet, 103 
 
 Odilon, Helene, 135 
 Oersted, 109 
 Ostwald, 83, 231, 232 
 Ovid, 197 
 
 Pascal, 93, 98 
 
 Pasteur, 175 
 
 Perrin, 154 
 
 Pfliiger, 35 
 
 Philander, 241 
 
 Picard, 144 
 
 Planck, 57, 59, 91, 230 
 
 Poincare, i, 7, 112, 116, 231 
 
 Pope, 54 
 
 Priestley, iii 
 
 Psellus, 156 
 
 Pyxrhon, 92 
 
 Pythagoras, loi, 179 
 
 Quetelet, 182 
 
 Regiomantus, 52 
 Reis, 25 
 Riemann, 186 
 Riggenbach, 25 
 Ruess, 224 
 Rutherford, 36, 210 
 
 Schiller, 74, 94, 170 
 Schlegel, 240 
 Schlick, Moritz, 168 
 Schopenhauer, 41, 237 
 Schwann, 175 
 Shakespeare, 236 
 Siemens, 25, 27-30 
 Slade, 136 
 Sophocles, 238 
 Spinoza, 84, 162 
 Stephenson, 25 
 
 Terence, 191 
 Thomas Aquinas, 165 
 TorriceUi, 166 
 
 Vaihinger, 45, 169 
 Vitruvius, loi 
 Volta, no, III 
 Voltaire, 47, 237 
 
 Wagner, 234 
 Weber, 182 
 Weierstrass, 152 
 Weyl, 34 
 Whewell, 45 
 Wien, 173 
 
 Zelter, 84 
 Zollner, 137 
 
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