{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_70678/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_70678","id":"gutenberg_70678","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/70678","summary":null,"tags":["Category: Biographies","Category: Philosophy & Ethics","Category: Science - Physics","Einstein, Albert, 1879-1955","Relativity (Physics)"],"text":"EINSTEIN\n                      THE SEARCHER\n\n               HIS WORK EXPLAINED FROM\n               DIALOGUES WITH EINSTEIN\n\n\n\n\n                           BY\n\n                  ALEXANDER MOSZKOWSKI\n\n\n\n\n                     TRANSLATED BY\n\n                    HENRY L. BROSE\n\n\n\n\n                  METHUEN & CO. LTD.\n                 36 ESSEX STREET W.C.\n                        LONDON\n\n\n\n\nEXTRACT FROM THE AUTHOR'S\nPREFACE\n\n\nTHE book which is herewith presented to the public has few\ncontemporaries of a like nature; it deserves special attention inasmuch\nas it is illuminated by the name _Albert Einstein_, and deals with a\npersonality whose achievements mark a turning-point in the development\nof science.\n\nEvery investigator, who enlarges our vision by some permanent discovery,\nbecomes a milestone on the road to knowledge, and great would be the\narray of those who have defined the stages of the long avenue of\nresearch. One might endeavour, then, to decide to whom mankind owes the\ngreater debt, to Euclid or to Archimedes, to Plato or to Aristotle, to\nDescartes or to Pascal, to Lagrange or to Gauss, to Kepler or to\nCopernicus. One would have to investigate--as far as this is\npossible--in how far each outstanding personality was in advance of his\ntime, whether some contemporary might not have had the equal good\nfortune to stumble on the same discovery, and whether, indeed, the time\nhad not come when it must inevitably have been revealed. If we then\nfurther selected only those who saw far beyond their own age into the\ninimitable future of knowledge, this great number of celebrities would\nbe considerably diminished. We should glance away from the milestones,\nand fix our gaze on the larger signs that denote the lines of\ndemarcation of the sciences, and among them we should find the name of\nAlbert Einstein. We may find it necessary to proceed to a still more\nrigorous classification; Science, herself, may rearrange her\nchronological table later, and reckon the time at which Einstein's\ndoctrine first appeared as the beginning of an important era.\n\nThis would in itself justify--nay, render imperative--the writing of\na book _about_ Einstein. But this need has already been satisfied on\nseveral occasions, and there is even now a considerable amount of\nliterature about him. At the end of this generation we shall possess a\nvoluminous library composed entirely of books about Einstein. The\npresent book will differ from most of these, in that Einstein here\noccurs not only objectively but also subjectively. We shall, of course,\nspeak of him here too, but we shall also hear him speak himself, and\nthere can be no doubt that all who are devoted to the world thought can\nbut gain by listening to him.\n\nThe title agrees with the circumstance to which this book owes its\nbirth. And in undertaking to address itself to the circle of readers as\nto an audience, it promises much eloquence that came from Einstein's own\nlips, during hours of social intercourse, far removed from academic\npurposes and not based on any definite scheme intended for instruction.\nIt will, therefore, be neither a course of lectures nor anything similar\naiming at a systematic order and development. Nor is it a mere\nphonographic record, for this is made impossible if for no other reason\nthan that whoever has the good fortune to converse with this man, finds\nevery minute far too precious to waste it in snatching moments to take\nshorthand notes. What he has heard and discussed crystallizes itself in\nsubsequent notes, and to some extent he relies on his memory, which\nwould have to be extraordinarily lax if it managed to forget the\nessentials of such conversations.\n\nBut these essentials could not be attained by clinging closely to the\nexact terms of utterance. This would be a gain neither for the scheme of\nthe book nor for the reader who wishes to follow a great thinker in all\nthe ramifications of his ideas. It must be reiterated that this book is\nintended neither as a textbook nor as a guide leading to a complete\nsystem of thought; nor, above all, is it in any way due to Einstein, nor\ndesired by him. Any value and attraction of the book is rather to be\nsought in its kaleidoscopic nature, its loose connexion, which expresses\na general meaning without being narrowed to pedantic limits by a\nrestriction to literal repetition. It is just this absence of the method\nthat is rightly demanded of a textbook, which may enable these\nconversations to pass on to the world a little of the pleasure which\nthey originally gave me. Perhaps they will even be sufficient to furnish\nthe reader with a picture of the eminent scientist, sufficient to give\nhim a glimpse of his personality, without demanding a detailed study to\nsecure this end. Even here I should like to state that the range of\nEinstein's genius extends much further than is generally surmised by\nthose who have busied themselves only with the actual physical theory.\nIt sends out rays in all directions, and brings into view wonderful\ncosmic features under his stimulus--features which are, of course,\nembedded in the very refractory mathematical shell of his physics which\nembraces the whole world. But only minds of the distant future, perhaps,\nwill be in a position to realize that _all_ our mental knowledge is\nilluminated by the light of his doctrine.\n\nEinstein's mission is that of a king who is pursuing building operations\non a large scale; carters and workmen, each in their own line, receive\nemployment for decades ahead. But apart from the technical work, there\nmay still be room for non-technical account, which, without following a\ndefinite programme, yet pursues a definite object, to offer Einsteiniana\nin an easily intelligible and ever-changing form, to represent him, as\nit were, wandering over fields and meadows, and every now and then\nstooping to pluck some problem in the guise of a flower. Seeing that he\ngranted me the pleasure of accompanying him on these excursions, it was\nnot within my sphere to expect in addition that he would direct his\nsteps according to a preconceived plan. Often enough the goal vanished,\nand there remained nothing but the pleasure of the rambles themselves\nwith the consciousness of their purpose. As Schopenhauer remarks, one\nwho walks for leisure can never be said to be making detours; and this\nholds true independently of the nature of the country that happens to be\ntraversed at the moment. If I just now mentioned walks on meadowy\nslopes, this is not to be understood literally. In Einstein's company\none encounters from moment to moment quite suddenly some adventure which\ndestroys our comparison with idyllic rambles. Abysmal depths appear, and\none has to pass along dangerous pathways. It is at these moments that\nunexpected views present themselves, and many strips of landscape that,\naccording to our previous estimate, appeared to be situated on higher\nslopes, are now discovered reposing far below. We are familiar with the\n\"Wanderer Fantasie\" of Schubert; its tonal disposition is realistic,\nconforming to Nature, yet its general expression is transcendental: so\nis a ramble with Einstein; he remains firmly implanted in reality, but\nthe distant views that he points out stretch into transcendental\nregions. He seems to me to be essentially as much an artist as a\ndiscoverer, and if some sense of this heaven-sent combination of gifts\nshould be inspired by this book, it alone would justify the publication\nof these talks.\n\n\n\n\nTRANSLATOR'S NOTE\n\n\nIT is scarcely necessary to enlarge on the scope and design of the\npresent book, which manifest themselves at a glance.\n\nThe author merits our thanks for making accessible to us material about\nEinstein which, in the ordinary course of events, would ever remain\nunknown. An account of Einstein's work would be incomplete without a\nsketch of his personality. Mr. Moszkowski invites us to ramble with\nEinstein into realms not confined to pure physics. Many subjects that\nhave a peculiar interest at the present critical stage of the world's\nhistory receive illuminating attention. It is hoped that the appearance\nof the book in English will stimulate further interest in the\nthought-world of a great scientist.\n\nWarm thanks are due to Mr. Raymond Kershaw, B.A., and to my sister, Miss\nHilda Brose, for help in reading the manuscript and the proofs.\n\n                             HENRY L. BROSE\n\nOXFORD, 1921\n\n\n\n\nCONTENTS\n\nCHAPTER\n\nI. Phenomena in the Heavens\n\nII. Beyond our Power\n\nIII. Valhalla\n\nIV. Education\n\nV. The Discoverer\n\nVI. Of Different Worlds\n\nVII. Problems\n\nVIII. Highways and By-ways\n\nIX. An Experimental Analogy\n\nX. Disconnected Suggestions\n\nXI. Einstein's Life and Personality\n\nINDEX\n\n\n\n\nEINSTEIN THE SEARCHER\n\n\n\n\nCHAPTER I\n\nPHENOMENA IN THE HEAVENS\n\n\nProclamation of the New Mechanics.--Verification of Theoretical\nResults.--Parallels with Leverrier.--Neptune and Mercury.--Testing the\nTheory of Relativity.--The Solar Eclipse of 1919.--The Programme of an\nExpedition.--The Curved Ray of Light.--Refinement of Calculation and\nMeasurement.--Stellar Photography.--The Principle of Equivalence.--The\nSun Myth.\n\n\nON the 13th October 1910 a memorable event took place in the Berlin\nScientific Association: Henri Poincar\u00e9, the eminent physicist and\nmathematician, had been announced to give a lecture in the rooms of the\ninstitute \"Urania\"; an audience of rather meagre dimensions assembled. I\nstill see him before me in my mind's eye, a scholar who was snatched\naway in the prime of his creative period, a man whose external\nappearance did not suggest the light of genius, and whose carefully\ntrimmed beard reminded one rather of the type of a practising barrister.\nHe walked up and down the platform, accompanying his speech with\ngestures marked by an easy elegance. There was no sign of an attempt to\nforce a doctrine. He developed his thesis, in spite of the foreign\nlanguage, in fluent and readily intelligible terms.\n\nIt was at this lecture that we heard the name Albert Einstein pronounced\nfor the first time.\n\nPoincar\u00e9's address was on the New Mechanics, and was intended to make\nus acquainted with the beginning of a tendency which, he himself\nconfessed, had violently disturbed the equilibrium of his former\nfundamental views. He repeatedly broke the usually even flow of his\nvoice to indicate, with an emphatic gesture, that we had perhaps arrived\nat a critical, nay epochal, point marking the commencement of a new era\nof thought.\n\n\"Perhaps\" was a word he never failed to emphasize. He persistently laid\nstress on his doubts, differentiated between hardened facts and\nhypotheses, still clinging to the hope that the new doctrine he was\nexpounding would yet admit of an avenue leading back to the older views.\nThis revolution, so he said, seemed to threaten things in science which\na short while ago were looked upon as absolutely certain, namely,\nfundamental theorems of classical mechanics, for which we are indebted\nto the genius of Newton. For the present this revolution is of course\nonly a threatening spectre, for it is quite possible that, sooner or\nlater, the old established dynamical principles of Newton will emerge\nvictoriously. Later in the course of his lecture he declared repeatedly\nthat he felt a diffidence akin to fear at the sight of the accumulating\nnumber of hypotheses, and that it seemed to border on the impossible to\nattempt to arrange them into a system.\n\nIt is a matter of complete indifference how the revelations of Poincar\u00e9\naffected us individually; if I may infer from my own case, there is only\none word to express it--staggering! Oblivious of the doubts of the\nlecturer, I was swept along under the impetus of this new and mighty\ncurrent of thought. This awakened two wishes in me: to become acquainted\nwith Einstein's researches as far as lay within my power, and, if\npossible, to see him once in person. In me the abstract had become\ninseparable from the concrete personal element. The presentiment of the\nhappy moment in the future hovered before my vision, whispering that I\nshould hear his doctrine from his own lips.\n\nSeveral years later Einstein was appointed professor of the Academy of\nSciences with the right of lecturing at the University of Berlin. This\nbrought my personal wish within reach. Trusting to good fortune, I set\nabout materializing it. In conjunction with a colleague I wrote him a\nletter asking him to honour with his presence one of the informal\nevenings instituted by our Literary Society at the H\u00f4tel Bristol. Here\nhe was my neighbour at table, and chatted with me for some hours.\nNowadays his appearance is known to every one through the innumerable\nphotos which have appeared in the papers. At that time I had never seen\nhis countenance before, and I became absorbed in studying his features,\nwhich struck me as being those of a kindly, artistically inclined,\nbeing, in nowise suggesting a professor. He seemed vivacious and\nunrestrained in conversation, and, in response to our request, willingly\ntouched upon his own subject as far as the place and occasion allowed,\nexemplifying Horace's saying, \"Omne tulit punctum, qui miscuit utile\ndulci, tironem delectando pariterque monendo.\" It was certainly most\ndelightful. Yet at moments I was reminded of a male sphinx, suggested by\nhis highly expressive enigmatic forehead. Even now, after a warm\nacquaintanceship stretching over years, I cannot shake off this\nimpression. It often overcomes me in the midst of a pleasant\nconversation interspersed with jests whilst enjoying a cigar after tea;\nI suddenly feel the mysterious sway of a subtle intellect which\ncaptivates and yet baffles the mind.\n\nAt that time, early in 1916, only a few members of the Literary Society\ndivined who it was that was enjoying their hospitality. In the eyes of\nBerlin, Einstein's star was beginning its upward course, but was still\ntoo near the horizon to be visible generally. My own vision, sharpened\nby the French lecture and by a friend who was a physicist, anticipated\nevents, and already saw Einstein's star at its zenith, although I was\nnot even aware at that time that Poincar\u00e9 had in the meantime overcome\nhis doubts and had fully recognized the lasting importance of Einstein's\nresearches. I had the instinctive feeling that I was sitting next to a\nGalilei. The fanfares sounded in the following years as a sign of\nappreciation by his contemporaries were only a fuller instrumentation of\nthe music of destiny which had vibrated in my ears ever since that time.\n\nI recollect one little incident: one of these lovers of literature, who\nwas, however, totally ignorant of natural science, had accidentally seen\nseveral learned articles dealing with Einstein's Reports for the\nAcademy, and had preserved the cuttings in his pocket-book. He\nconsidered this a fitting opportunity for enlightenment. Surely a brief\nquestion would suffice to guide one through these intricate channels.\n\"Professor, will you kindly tell me the meaning of potential, invariant,\ncontravariant, energy-tensor, scalar, relativity-postulate,\nhyper-Euclidean, and inertial system? Can you explain them to me in a\nfew words?\"--\"Certainly,\" said Einstein, \"those are merely technical\nexpressions!\" That was the end of the little lesson.\n\nFar into the night three of us sat in a caf\u00e9 while Einstein gently\nlifted the veil from his newest discovery for the benefit of my\njournalist friend and myself. We gathered from his remarks that a\nSpecial Theory of Relativity formed a prelude to a general theory which\nembraced the problem of gravitation in its widest sense, and hence also\nthe physical constitution of the world. What interested me apart from\nthis theme, which was, of course, only touched upon lightly, was the\npersonal question in its psychological aspect.\n\n\"Professor,\" said I, \"such investigations must involve enormous mental\nexcitement. I imagine that there lurks behind every solved problem ever\nand again some new problem with a threatening or a fascinating aspect,\nas the case may be, each one calling up a tumult of emotion in its\nauthor. How do you succeed in mastering this difficulty? Are you not\ncontinually tormented by restless thoughts that noisily invade your\ndreams? Do you ever succeed at all in enjoying undisturbed slumber?\"\n\nThe very tone in which the answer was given showed clearly how free he\nfelt himself of such nervous troubles which usually oppress even the\nmediocre thinker. It is fortunate that such affections do not penetrate\nto his high level. \"I break off whenever I wish,\" he said, \"and banish\nall difficulties when the hour for sleep arrives. Thinking during\ndreams, as in the case of artists, such as poets and composers, by which\nthey weave the thread of day on into the night, is quite foreign to me.\nNevertheless, I must confess that at the very beginning, when the\nspecial theory of relativity began to germinate in me, I was visited by\nall sorts of nervous conflicts. When young I used to go away for weeks\nin a state of confusion, as one who at that time had yet to overcome the\nstage of stupefaction in his first encounter with such questions. Things\nhave changed since then, and I can assure you that there is no need to\nworry about my rest.\"\n\n\"Notwithstanding,\" I answered, \"cases may arise in which a certain\nresult is to be verified by observation and experiment. This might\neasily give rise to nerve-racking experiences. If, for instance, a\ntheory leads to a calculation which does not agree with reality, the\npropounder must surely feel considerably oppressed by this mere\npossibility. Let us take a particular event. I have heard that you have\nmade a new calculation of the path of the planet Mercury on the basis of\nyour doctrine. This must certainly have been a laborious and involved\npiece of work. You were firmly convinced of the theory, perhaps you\nalone. It had not yet been verified by an actual fact. In such cases\nconditions of great psychological tension must surely assert themselves.\nWhat in Heaven's name will happen if the expected result does not\nappear? What if it contradicts the theory? The effect on the founder of\nthe theory cannot even be imagined!\"\n\n\"Such questions,\" said Einstein, \"did not lie in my path. That result\ncould not be otherwise than right. I was only concerned in putting the\nresult into a lucid form. I did not for one second doubt that it would\nagree with observation. There was no sense in getting excited about what\nwas self-evident.\"\n\nLet us now consider several facts of natural science, apart from this\nchat, but suggested by it, which caused Einstein little excitement, but\nthe whole world generally, so much the more. By way of illustration we\nshall link them up with the result of a forerunner who, like Einstein,\nfixed on paper what should happen in the heavens.\n\nFormerly, whenever one wished to play a particularly effective trump\ncard in favour of research work it was customary to quote the\nachievement of the French astronomer Leverrier who, pen in hand,\nestablished the material existence of a planet at that time quite\nunknown and unnoticed. Certain disturbances in the orbit of the planet\nUranus, which was regarded as being the most distant of the wandering\nstars, at that time had caused him to believe in the certainty of the\nexistence of a still more distant planet, and by using merely the\ntheoretical methods of celestial mechanics in connexion with the problem\nof three bodies he succeeded in revealing what was hidden behind the\nvisible constellations. He reported the result of his calculations to\nthe Berlin Observatory about seventy-five years ago, as it was at that\ntime in possession of the best instruments. It was then that the amazing\nevent happened: on the very same evening an observer in Berlin,\nGottfried Galle, discovered the predicted new star almost exactly at the\npoint of the heavens for which it was prophesied, only half the moon's\ndiameter from it. The new planet Neptune, the farthest outpost of our\nsolar system, reposed as a prisoner in his telescope; the seemingly\nundiscoverable star had capitulated in the face of mental efforts of a\nmathematical scholar, who, in reasoning meditation, had sketched his\ncurves in the quiet atmosphere of his study.\n\nThis was certainly bewildering enough, but nevertheless this incredible\nresult which stirred the imagination so strongly was directly rooted in\nreality, lay on the path of research, followed of necessity from the\nlaws of motion known at that time, and disclosed itself as a new proof\nof the doctrines of astronomy which had long been recognized as supreme\nand incontestable. Leverrier had not created these, but had found them\nready; he applied them with the mind of genius. Anyone who nowadays is\nsufficiently trained to work through the highly complicated calculation\nof Leverrier has every reason to marvel at a work which is entirely\nmathematical throughout.\n\nOur own times have been marked by an event of still greater\nsignificance.\n\nIrregularities had shown themselves in observation of the heavens that\ncould not be explained or grasped by the accepted methods of classical\nmechanics. To interpret them, ideas of a revolutionary nature were\nnecessary. Man's view of the plan according to which the universe is\nmapped out had to be radically reformed to bring within comprehension\nthe problems that presented themselves in macroscopic as well as in\nmicroscopic regions, in the courses of the stars as well as in the\nmotions of the ultimate constituents of the atom of material bodies,\nincapable of being directly observed. The goal consisted in bringing\nthose doctrines in which truth had been proclaimed in its essential\nfeatures, but not exhaustively, by the genius of Copernicus, Galilei,\nKepler, and Newton, to their conclusion by penetrating as far as\npossible into the mysteries of the structure of the universe. This is\nwhere Einstein comes forward.\n\nWhereas the outermost planet Neptune had bowed to the accepted laws, by\nmerely disclosing his presence, Mercury, the innermost planet, preserved\nan obstinate attitude even in the face of the most refined calculations.\nThese always led to an unaccountable remainder, a disagreement, which\nseemed very small when expressed in numbers and words, and yet enclosed\na deep secret. Wherein did this disagreement consist? In a difference of\narc which had likewise been discovered by Leverrier and which defied\nexplanation. It was only a matter of about forty-five insignificant\nquantities, seconds of arc, which seemed vanishingly small since this\ndeviation did not occur within a month or a year, but was spread over a\nwhole century. By just so much, or rather so little, the rotation of\nMercury's orbit differed from what might be termed the allowable\nastronomical value. Observation was exact, calculation was exact; why,\nthen, the discrepancy?\n\nIt was thus inferred that there was still some hidden unexplored factor\nwhich had to be taken into account in the fundamental principles of\ncelestial mechanics. The formerly invisible Neptune confirmed the old\nrule by appearing. Mercury, which was visible, opposed the rule.\n\nIn 1910 Poincar\u00e9 had touched upon this embarrassing question,\nmentioning that here was a possibility of testing the new mechanics.\n\nHe declined the suggestion of some astronomers that this was again a\nLeverrier problem and that there must exist another undiscovered planet\nstill nearer the sun and disturbing Mercury's orbit. He also refused to\naccept the assumption that the disturbance might be caused by a ring of\ncosmic matter distributed round the sun. Poincar\u00e9 divined that the new\nmechanics could supply the key to the enigma, but, obviously to be quite\nconscientious, he expressed his presentiment in very cautious terms. On\nthat occasion he said that some special cause had yet to be found to\nexplain the anomaly of Mercury's behaviour; till that was discovered one\ncould only say that the new doctrine could not be regarded as in\ncontradiction to astronomical facts. But the true explanation was\ngradually drawing near. Five years later, on 18th November 1915, Albert\nEinstein presented to the Prussian Academy of Sciences a paper which\nsolved this riddle which, expressed in seconds, seemed so insignificant\nand yet was of such enormous importance in its bearing on fundamental\nquestions. He proved the problem was solved quite accurately if the\ngeneral Theory of Relativity he had founded was accepted as the only\nvalid basis for the phenomena of cosmic motions.\n\nMany would at this point express a wish to have the essence of the\ndoctrine of relativity explained in an easily intelligible manner.\nIndeed, some would go even further in their desire, and would ask for a\nsimple description in a few succinct sentences. This, measured in terms\nof difficulty and possibility, would be about equivalent to wishing to\nlearn the history of the world by reading several quarto pages of\nmanuscript or a novelette. But even if we start at long range and use\nelaborate materials for our description, we should have to give up the\nidea that this knowledge may be gained with playful ease. For this\ndoctrine, inasmuch as it discloses the relationship between mathematical\nand physical events, emerges out of mathematics, which thus limits the\nmode of its representation. Whoever undertakes to present it in a form\nin which it is easily intelligible, that is quite unmathematical and yet\ncomplete, is engaged in an impossible venture; he is like one who would\nwhistle Kepler's Laws on the flute or would elucidate Kant's Critique of\nPure Reason by means of coloured illustrations. In all frankness we must\nconfess once and for all that whenever popular accounts are attempted\nthey can be only in the nature of vague suggestions removed from the\ndomain of mathematics. But even such indications have a fruitful result\nif they succeed in focusing the attention of the reader or the hearer so\nthat the connexions, the Leitmotivs, so to speak, of the doctrine, are\nat least suggested.\n\nIt must therefore suffice if we place the conception of approximation in\nthe foreground here as in other parts of this book. Till quite recently\nNewton's Equations of Motion were used as a foundation for verifying\nastronomical occurrences. These are symbolical representations expressed\nas formul\u00e6 that contain in an exceedingly simple form the law of mass\nattraction. They express the comprehensive principle that the attraction\nis directly proportional to the mass and inversely proportional to the\nsquare of the distance; so that the moving force is doubled when the\nmass is doubled, whereas if the distance is double, the force is only a\nquarter as great, if the distance is trebled, the force becomes\none-ninth as great.\n\nAccording to the Theory of Relativity this fundamental law is not wrong\nor invalid, but no longer holds fully if pursued to its last inferences.\nIn applying corrections to it, new factors occur, such as the ratio of\ngiven velocities to the velocity of light, and the new geometry which\noperates with \"world-lines\" in space which, amalgamated with the\ndimension of time, is regarded as a quadruply extended continuum.\nEinstein has actually supplemented these fundamental equations for the\nmotion of masses so that the original form states the true condition of\naffairs only approximately, whereas Einstein's equations give the motion\nwith very great accuracy.\n\nThe above-mentioned essay of Einstein is carried out as if the structure\nbequeathed to us by Newton required the addition of a final, very\ndelicate pinnacle. For the mathematician this pinnacle is given as a\ncombination of signs, representing a so-called \"Elliptic Interval.\" Such\nan interval is a very weird construction, and the man who will make it\napprehended by the general reader is yet to be born. When Lord Byron\nsaid:\n\n\n   \"And Coleridge, too, has lately taken wing.\n    But like a hawk encumbered with his hood,--\n    Explaining Metaphysics to the nation--\n   _I wish he would explain his Explanation_.\"\n\n                             (_Dedication to \"Don Juan._\")\n\n\nhe had still a sure footing in intelligibility, compared with the\nnon-mathematician, who demands an explanation for such a construction.\nAnd what a complex of mathematical dangers must be overcome even before\nthe question of the meaning of this integral is crystallized out!\n\nBut now the explanation had arrived and could be evaluated, if only\napproximately. Before we give the result, let us just describe at least\none technical term, namely, \"Perihelion.\" It is that point of a\nplanetary orbit which lies nearest the sun. This orbit is an ellipse,\nthat is, an elongated curved fine in the interior of which one\ndistinguishes a major axis in the direction of elongation, and a minor\naxis perpendicular to the former at its middle point. The perihelion of\na planetary orbit is at one of the end points of the major axis.\n\nIn time the perihelion alters its position in space, advancing in the\nsame sense as the orbit is traversed. It would naturally be assumed that\nthe amount of this advance as measured astronomically would agree with\nthe calculation resulting from Newton's theory. But this was not the\ncase. An unaccountable remainder was left over, which astronomers\nascertained to be 45 seconds (of arc) per 100 years, with a possible\nfluctuation of plus or minus 5 seconds. Thus, if the new result were\nfound to be between 40 and 50 seconds, the new theory would henceforth\nhave to be regarded as the only valid one.\n\nIt happened just as Einstein predicted: calculation according to his\ntheory shows that for the planet Mercury the perihelion should advance\n43 seconds per 100 years. This signifies full agreement with observation\nand fully removes the former apparent difficulty. Whereas Leverrier in\nhis time had pointed out a new planet, Einstein brought to view\nsomething far more important: a new truth.\n\nIt was a test of accuracy so dazzling that it alone would have sufficed\nto prove the correctness of Einstein's Principles. Yet, a second test,\nfraught with graver and more far-reaching consequences, presented\nitself--a test which could be applied only several years later, and\nwhich developed into a scientific event of the highest importance.\n\nFor at the same time that Einstein solved the problem of Mercury, he had\ninvestigated the path of light-rays according to his revolutionary\nmethod, and had arrived at the conclusion that every ray under the\ninfluence of a gravitational field, as, for example, in the\nneighbourhood of the sun, must become curved. This daring announcement\ngave a new possibility of putting the theory to a practical test during\nthe total eclipse of the sun on 29th May 1919. For, when the disc of the\nsun is obscured, the stars that are closest to it become visible (even\nto the naked eye). They may be photographed, and the distances of the\npoints of light on the negative allow us to detect whether the rays from\nthe stars in passing the massive body of the sun have actually been\ndeflected by the amount prophesied by Einstein.\n\nOnce again current thought encountered a sharp corner, and \"common\nsense,\" which furnishes its own certificate of merit, threatened to\nbecome rebellious. How now? A ray from a star could be curved? Does not\nthis contradict the elementary conception of the straight lines, that\nis, the shortest lines, for which we have no better picture than just\nthese rays? Did not Leonardo da Vinci define the straight line by means\nof the term _linea radiosa_.\n\nBut such supposedly self-evident facts have no longer a place in the\nspace-time world. The point was to test whether a physical anomaly which\nhad been predicted actually existed. If the deflection of the rays\nreally happened, it should manifest itself in the distances between the\nstars on the photographic plate being greater than one would expect from\ntheir actual position.\n\nFor the curvature has its concave side towards the sun, as is easy to\nsee, once the phenomenon is regarded as possible. It is as if the ray\nwere directly subject to gravitation. Let us take two stars, one on each\nside of the sun. On account of the concavities the eye receives rays\nfrom them under a greater visual angle than if the rays were straight,\nand interprets this angle as denoting a greater distance between the\nsources of light, that is, it sees the two stars farther apart than in\nthe case of rectilinear propagation.\n\nBy how much farther apart? The preceding calculation and the subsequent\ndirect observation demanded incredible delicacy of measurement. If we\nsuppose the whole arc of the heavens divided into easily picturable\nunits such as degrees, then the apparent width of the moon is about half\na degree. We may still easily imagine the thirtieth part of this,\nnamely, a minute of arc. But the sixtieth part of the latter, the second\nof arc, vanishes almost out of the range of sense-perception. And it was\njust this minute measure that came into question, for the theory which\nhad been developed from pure thought predicted a deflection of seconds\nof arc. This corresponds to about a hairbreadth when seen at a distance\nof 17 yards, or to the thickness of a match at a distance of over half a\nmile.\n\nOne of the greatest problems of the most comprehensive science depended\non this unthinkably small measure.\n\nIn no sense did Einstein himself entertain a possibility of doubt.\n\nOn repeated occasions before May 1919 I had opportunities of questioning\nhim on this point. There was no shadow of a scruple, no ominous fears\nclouded his anticipations. Yet great things were at stake.\n\nObservation was to show \"the correctness of Einstein's world system\" by\na fact clearly intelligible to the whole world, one depending on a very\nsensitive test of less than two seconds of arc.\n\n\"But, Professor,\" said I, on various occasions, \"what if it turns out to\nbe more or less? These things are dependent on apparatus that may be\nfaulty, or on unforeseen imperfections of observation.\" A smile was\nEinstein's only answer, and this smile expressed his unshakeable faith\nin the instruments and the observers to whom this duty was to be\nentrusted.\n\nMoreover, it is to be remarked that no great lengths of time were\navailable for comfortable experimentation in taking this photographic\nrecord. For the greatest possible duration of a total eclipse of the sun\nviewed at a definite place amounts to less than eight minutes, so that\nthere was no room for mishaps in this short space of time, nor must any\nintervening cloud appear. The kindly co-operation of the heavens was\nindispensable--and was not refused. The sun, in this case the darkened\nsun, brought this fact to light.\n\nTwo English expeditions had been equipped for the special occasion of\nthe eclipse--one to proceed to Sobral and the other to the Island of\nPrincipe, off Portuguese Africa; they were sent officially with\nequipment provided in the main by the time-honoured Royal Society.\nConsidering the times, it was regarded as the first symptom of the\nrevival of international science, a praiseworthy undertaking. A huge\napparatus was set into motion for a purely scientific object with not\nthe slightest relation to any purpose useful in practical life. It was a\nhighly technical investigation whose real significance could be grasped\nby only very few minds. Yet interest was excited in circles reaching far\nbeyond that of the professional scientist. As the solar eclipse\napproached, the consciousness of amateurs became stirred with indefinite\nideas of cosmic phenomena. And just as the navigator gazes at the Polar\nStar, so men directed their attention to the constellation of Einstein,\nwhich was not yet depicted in stellar maps, but, from which something\nuncomprehended, but undoubtedly very important, was to blaze forth.\n\nIn June it was announced that the star photographs had been successful\nin most cases, yet for weeks, nay for months, we had to exercise\npatience. For the photographs, although they required little time to be\ntaken, took much longer to develop and, above all, to be measured; in\nview of the order of smallness of the distances to be compared, this was\na difficult and troublesome task, for the points of light on the plate\ndid not answer immediately with Yes or No, but only after mechanical\ndevices of extreme delicacy had been carefully applied.\n\nAt the end of September they proclaimed their message. It was in the\naffirmative, and this Yes out of far-distant transcendental regions\ncalled forth a resounding echo in the world of everyday life. Genuinely\nand truly the seconds of arc had come out, correct to the decimal point.\nThese points representing ciphers, as it were, had chanted of the\nharmony of the spheres in their Pythagorean tongue. The transmission of\nthis message seemed to be accompanied by the echoing words of Goethe's\n\"Ariel\":\n\n\n   \"With a crash the Light draws near!\n    Pealing rays and trumpet-blazes,--\n    Eye is blinded, ear amazes.\"\n\n\nNever before had anything like this happened. A wave of amazement swept\nover the continents. Thousands of people who had never in their lives\ntroubled about vibrations of light and gravitation were seized by this\nwave and carried on high, immersed in the wish for knowledge although\nincapable of grasping it. This much all understood, that from the quiet\nstudy of a scholar an illuminating gospel for exploring the universe had\nbeen irradiated.\n\nDuring that time no name was quoted so often as that of this man.\nEverything sank away in face of this universal theme which had taken\npossession of humanity. The converse of educated people circled about\nthis pole, could not escape from it, continually reverted to the same\ntheme when pressed aside by necessity or accident. Newspapers entered on\na chase for contributors who could furnish them with short or long,\ntechnical or non-technical, notices about Einstein's theory. In all\nnooks and corners social evenings of instruction sprang up, and\nwandering universities appeared with errant professors that led people\nout the three-dimensional misery of daily life into the more hospitable\nElysian fields of four-dimensionality. Women lost sight of domestic\nworries and discussed co-ordinate systems, the principle of\nsimultaneity, and negatively-charged electrons. All contemporary\nquestions had gained a fixed centre from which threads could be spun to\neach. Relativity had become the sovereign password. In spite of some\ngrotesque results that followed on this state of affairs it could not\nfail to be recognized that we were watching symptoms of mental hunger\nnot less imperative in its demands than bodily hunger, and it was no\nlonger to be appeased by the former books by writers on popular science\nand by misguided idealists.\n\nAnd whilst leaders of the people, statesmen, and ministers made vain\nefforts to steer in the fog, to arrive at results serviceable to the\nnation, the multitude found what was expedient for it, what was\nuplifting, what sounded like the distant hammering of reconstruction.\nHere was a man who had stretched his hands towards the stars; to forget\nearthly pains one had but to immerse oneself in his doctrine. It was the\nfirst time for ages that a chord vibrated through the world invoking all\neyes towards something which, like music or religion, lay outside\npolitical or material interests.\n\nThe mere thought that a living Copernicus was moving in our midst\nelevated our feelings. Whoever paid him homage had a sensation of\nsoaring above Space and Time, and this homage was a happy augury in an\nepoch so bare of brightness as the present.\n\n     *     *     *     *     *     *     *     *\n\nAs already remarked, there was no lack of rare fruits among the\nnewspaper articles, and a chronicler would doubtless have been able to\nmake an attractive album of them. I brought Einstein several foreign\npapers with large illustrations which must certainly have cost the\nauthors and publishers much effort and money. Among others there were\nfull-page beautifully coloured pictures intended to give the reader an\nidea of the paths pursued by the rays from the stars during the total\neclipse of the sun. These afforded Einstein much amusement, namely, _e\ncontrario_, for from the physical point of view these pages contained\nutter nonsense. They showed the exact opposite of the actual course of\nthe rays inasmuch as the author of the diagrams had turned the convex\nside of the deflected ray towards the sun. He had not even a vague idea\nof the character of the deflection, for his rays proceeded in a straight\nline through the universe until they reached the sun, where they\nunderwent a sudden change of direction reminiscent of a stork's legs.\nThe din of journalistic homage was not unmixed with scattered voices of\ndissent, even of hostility. Einstein combated these not only without\nanger but with a certain satisfaction. For indeed the series of unbroken\novations became discomfiting, and his feelings took up arms against what\nseemed to be developing into a star-artist cult. It was like a breath of\nfresh air when some column of a chance newspaper was devoted to a\npolemic against his theory, no matter how unfounded or unreasoned it may\nhave been, merely because a dissonant tone broke the unceasing chorus of\npraise. On one occasion he even said of a shrill disputant, \"The man is\nquite right!\" And these words were uttered in the most natural manner\npossible. One must know him personally if one is to understand these\nexcesses of toleration. So did Socrates defend his opponents.\n\nIn our conversation we returned to the original question, and I asked\nwhether there was no means of making the deflection of the ray\nintelligible to an average person.\n\nEinstein replied: \"In a very superficial manner this is certainly\npossible.\" And with a few strokes on the paper, which I shall here try\nto describe in words, he gave his explanation in terms something like\nthe following:\n\nThis square is to denote the cross-section of a closed box which we\nimagine to be situated somewhere in the universe. Inside it there lives\na physicist who makes observations and draws inferences from them. In\nthe course of time he perceives, what is familiar to all of us, that\nevery body not supported and left to itself, for example, a stone that\nis released, drops to the floor with uniform acceleration, that is, with\na steady increase of velocity in going downwards. There are _two_ ways\nopen to him to explain this phenomenon.\n\n_Firstly_, he might suspect--and this suspicion would be most likely to\noccur to him--that his box was resting on some body in the heavens. For\nif indeed the box were a cave in some part of the world, the falling of\nthe stone would suggest nothing unusual; it would be quite self-evident\nto every occupant, and quite explicable to the physicist according to\nGalilei's (or Newton's) Laws for Falling Bodies. He need not necessarily\nrestrict himself to the Earth, for if the box happened to be on some\nother star, this phenomenon of falling would likewise occur, with\ngreater or less speed, and the body would certainly fall with uniform\nacceleration. Thus the physicist could say: this is an effect of\ngravitation, exhibiting the property of weight which I explain to myself\nas usual, as due to the attraction of a heavenly body.\n\n_Secondly_, another idea might strike him. For we stipulated nothing\nabout the position of the box, and assumed only that it was to exist\n\"somewhere in the universe.\" The physicist in the box might reason as\nfollows:\n\nSupposing I am separated by incalculable distances from every attracting\nheavenly body, and supposing gravitation existed neither for me nor for\nthe stone which I release from my hand, then it would still be possible\nfor me to give a complete explanation of the phenomena I observe. I\nshould only have to assume that the body is moving with uniform\nacceleration \"upwards.\" The motion previously interpreted by me as a\nfalling \"downwards\" need not take place at all. The stone, as an _inert_\nbody, could persist in its position (relative to the box or the\nobserver), and would, in spite of this, show exactly the same behaviour\nwhen the box moves with acceleration upwards as if it were falling with\nincreasing velocity downwards.\n\nNow since our physicist has no system which might serve for reference\nand orientation, and since in his box which is shut off from the\nuniverse he has no means at his disposal of determining whether he is in\nthe sphere of influence of an attracting heavenly body or not, both the\nabove explanations are feasible for him and both are equally valid, and\nit is impossible for him to come to a decision in his choice. He can\ninterpret the acceleration in either way, as being upwards or downwards,\nconnected to one another by relativity; a fundamental reason for\npreferring one interpretation to the other cannot be furnished, since\nthe phenomenon of falling is represented unchanged whether he assumes\nthe stone to be falling and the box to be at rest, or vice versa. This\nmay be generalized in these words:\n\nAt every point of the world the observed acceleration of a body left to\nitself may be interpreted either as a gravitational _or_ as an inertial\neffect--that is, from the point of view of physics we may assert with\nequal right that the system (the box, the complex defining the\norientation) from which I observe the event is accelerated, or that the\nevent takes place in a gravitational field. The equal right to these two\nviews is called the \"Principle of Equivalence\" by Einstein. It asserts\nthe equivalence or the identity of inertial and gravitational mass. If\nwe familiarize ourselves with this identity, an exceedingly important\nroad to knowledge is opened up to our consciousness. We arrive at the\ninevitable conclusion that every inertial effect that we perceive in\nbodies, the most essential quality of it, itself so to speak in its\npersistent nature, is to be traced back to the influence to which it is\nsubjected by other bodies. When this has become clear to us, we feel\nimpelled to inquire how a ray of light would behave under the influence\nof gravitation. Hence we return to our physicist in the box, and we now\nknow that as a consequence of the Principle of Equivalence we are free\nto assume either that an attracting heavenly body, such as the sun, is\nsituated somewhere below the box, or to refer the phenomena to the box\nregarded as being accelerated upwards. In the box we distinguish the\nfloor, the ceiling, four walls, and among these again, according to the\nposition we take up, the wall on the left and its opposite one on the\nright.\n\nWe now imagine a marksman to be outside the box and having no connexion\nwith us, being poised freely in space, and suppose him to fire out of a\nhorizontal gun at the box so that the bullet pierces both the wall on\nthe left and the wall on the right. Now, if everything else were to\nremain at rest, the holes in both walls would be equally distant from\nthe floor, and the bullet would move in a straight line parallel to the\nfloor and to the ceiling. But, as we have seen, all events happen as if\nthe box itself moved with constant acceleration. The bullet that\nrequires time to pass from one wall to the other thus finds that when it\nreaches the wall on the right the latter has advanced a little, so that\nthe resulting hole is a little lower than that on the left wall. This\nmeans that the flight of the bullet, according to our observation in the\ninterior of the box, is no longer rectilinear. In fact, if we trace the\nbullet from point to point, we should find that for us, situated in the\nbox, it would describe a line bent downwards, with its concave side to\nthe floor.\n\nExactly the same thing happens with a ray of light which is emitted by a\nsource outside in a horizontal direction and which traverses the space\nbetween the walls (supposed transparent). Only the velocity would be\ndifferent. In the course of its flight the ray would move like a\nprojectile that is whizzing along at the rate of 180,000 miles per\nsecond. But provided sufficiently delicate means of measurement are\napplied, it should still be possible to prove the existence of an\ninfinitesimal deflection from the rectilinear horizontal path, an\ninsignificant concavity towards the floor.\n\nConsequently this curvature of the light-ray (say, from a star) must\nalso be perceptible in places where it is subject to the influence of a\ngravitational field. If we drop our imaginary picture of the box, the\nargument is in nowise altered. A ray from a star which passes close by\nthe sun seems to our perception to be bent in towards the sun, and the\norder of this deflection can be determined if sufficiently delicate\ninstruments be used. As above remarked, it is a question of detecting a\ndifference of 1.7 seconds of arc, which is to be manifested as a\ndistance on the photographic plate, and is actually found to be present.\n\nThe fact that scientists are able to detect this appears in itself a\nmarvel of technical precision far in advance of \"splitting hairs,\" for\nin comparison a single hair is, in this case, to be removed to a\nconsiderable distance if we are to use it to give an idea of the size of\nangle under consideration. Fortunately stellar photography has been\ndeveloped so wonderfully that in every single case extraordinarily\naccurate results are got even from preliminary measurements.\n\nIn ordinary astronomical practice it is usually found that a millimetre\nin linear measure on the plate corresponds to a minute of arc. This\nmeans that the sun's disc itself has a diameter of 3 centimetres on the\nphotograph. The stars appear as tiny dots, which may be sharply\ndifferentiated in an enlargement. Stars of the fourteenth order of\nmagnitude and beyond it become visible, whereas the naked eye cannot see\nthose of order higher than the sixth. A grating whose lines are\n\u00b9\u2044\u2081\u2080\u2080 millimetre wide is copied on to the plate to make the\nmeasurement more accurate, so that the positions of objects can be\nascertained with certainty to within a few tenths of a second of arc.\nThus the problem which was to be solved by the solar eclipse of 1919 lay\nwithin the realm of possibility as regards our means of measurement.\n\nA copy of this photograph had been sent to Einstein from England, and he\ntold me of it with evident pleasure. He continually reverted to the\ndelightful little picture of the heavens, quite fascinated by the thing\nitself, without the slightest manifestation of a personal interest in\nhis own success. Indeed, I may go further and am certainly not mistaken\nin saying his new mechanics did not even enter his head, nor the\nverification of it by the plate; on the contrary, he displayed that\ndisposition of the mind which in the case of genius as well as in that\nof children shows itself as _na\u00efvet\u00e9_. The prettiness of the\nphotograph charmed him, and the thought that the heavens had been drawn\nup as for parade to be a model for it.\n\nAll things are repeated in the history of life. In these happenings,\nwhich mark the 29th May 1919 as a red-letter day in the history of\nscience, we recognize a revival of the Sun Myth, unperceived by the\nindividual, but as an expression of the universal consciousness, just as\nwhen Copernicus converted the geocentric picture of the universe into a\nheliocentric one, the Sun Myth again sprang into life; the symbolization\nof faith in the light-giving and heat-giving star. This time it has\narisen, purified of all dross, scarcely perceptible to our senses, like\nan aureole spun about the sun by far-distant sources of light, in honour\nof a principle, and even if most of us do not yet know what a \"system of\nreference\" means, yet for many such a system has unconsciously evolved,\na thought-system serving as a reference for the development of their\nknowledge when they thought or spoke of Einstein.\n\n\n\n\nCHAPTER II\n\nBEYOND OUR POWER\n\nUseful and Latent Forces.--Connexion between Mass, Energy, and Velocity\nof Light.--Deriving Power by Combustion.--One Gramme of Coal.--Unobtainable\nCalories.--Economics of Coal.--Hopes and Fears.--Dissociated Atoms.\n\n\n                             _29th March_ 1920\n\nWE spoke of the forces that are available for man and which he derives\nfrom Nature as being necessary for his existence and for the development\nof life. What forces are at our disposal? What hopes have we of\nelaborating our supply of these forces?\n\nEinstein first explained the conception of energy, which is intimately\nconnected with the conception of mass itself. Every amount of substance\n(I am paraphrasing his words), the greatest as well as the smallest, may\nbe regarded as a store of power, indeed, it is essentially identical\nwith energy. All that appears to our senses and our ordinary\nunderstanding as the visible, tangible mass, as the objective body\ncorresponding to which we, in virtue of our individual bodies, abstract\nthe conceptual outlines, and become aware of the existence of a definite\ncopy is, from the physical point of view, a complex of energies. These\nin part act directly, in part exist in a latent form as strains which,\nfor us, begin to act only when we release them from their state of\nstrain by some mechanical or chemical process, that is, when we succeed\nin converting the potential energy into kinetic energy. It may be said,\nindeed, that we have here a physical picture of what Kant called the\n\"thing in itself.\" Things as they appear in ordinary experience are\ncomposed of the sum of our direct sensations; each thing acts on us\nthrough its outline, colour, tone, pressure, impact, temperature,\nmotion, chemical behaviour, whereas the thing in itself is the sum-total\nof its energy, in which there is an enormous predominance of those\nenergies which remain latent and are quite inaccessible in practice.\n\nBut this \"thing in itself,\" to which we shall have occasion to refer\noften with a certain regard to its metaphysical significance, may be\ncalculated. The fact that it is possible to calculate it takes its\norigin, like many other things which had in no wise been suspected, in\nEinstein's Theory of Relativity.\n\nQuite objectively and without betraying in the slightest degree that an\nastonishing world-problem was being discussed, Einstein expressed\nhimself thus:\n\n\"According to the Theory of Relativity there is a calculable relation\nbetween mass, energy, and the velocity of light. The velocity of light\n(denoted by _c_, as usual) is equal to 3.10^10 cm. per second.\nAccordingly the square of _c_ is equal to 9 times 10^20 cm. per second,\nor, in round numbers, 10^21 cm. per second. This _c_^2 plays an\nessential part if we introduce into the calculation the mechanical\nequivalent of heat, that is, the ratio of a certain amount of energy to\nthe heat theoretically derivable from it; we get for each gramme\n20.10^12, that is, 20 billion calories.\"\n\nWe shall have to explain the meaning of this brief physical statement in\nits bearing on our practical lifes. It operates with only a small array\nof symbols, and yet encloses a whole universe, widening our perspective\nto a world-wide range!\n\nTo simplify the reasoning and make it more evident we shall not think of\nthe conception of substance as an illimitable whole, but shall fix our\nideas on a definite substance, say coal.\n\nThere seems little that may strike us when we set down the words:\n\n                             \"One Gramme of Coal.\"\n\nWe shall soon see what this one gramme of coal conveys when we translate\nthe above-mentioned numbers into a language to which a meaning may be\nattached in ordinary life. I endeavoured to do this during the above\nconversation, and was grateful to Einstein for agreeing to simplify his\nargument by confining his attention to the most valuable fuel in our\neconomic life.\n\nOnce whilst I was attending a students' meeting, paying homage to\nWilhelm Dove, the celebrated discoverer took us aback with the following\nremark: When a man succeeds in climbing the highest mountain of Europe\nhe performs a task which, judged from his personal point of view,\nrepresents something stupendous. The physicist smiles and says quite\nsimply, \"Two pounds of coal.\" He means to say that by burning 2 lb. of\ncoal we gain sufficient energy to lift a man from the sea-level to the\nsummit of Mont Blanc.\n\nIt is assumed, of course, that an ideal machine is used, which converts\nthe heat of combustion without loss into work. Such a machine does not\nexist, but may easily be imagined by supposing the imperfections of\nmachines made by human hands to be eliminated.\n\nSuch effective heat is usually expressed in calories. A calorie is the\namount of heat that is necessary to raise the temperature of a gramme of\nwater by one degree centigrade. Now the theorem of the Mechanical\nEquivalent, which is founded on the investigations of Carnot, Robert\nMayer, and Clausius, states that from one calorie we may obtain\nsufficient energy to lift a pound weight about 3 feet. Since 2 lb. of\ncoal may be made to yield 8 million calories, they will enable us to\nlift a pound weight through 24 million feet, theoretically, or, what\ncomes to the same approximately, to lift a 17-stone man through 100,000\nfeet, that is, nearly 19 miles: this is nearly seven times the height of\nMont Blanc.\n\nAt the time when Dove was lecturing, Einstein had not yet been born, and\nwhen Einstein was working out his Theory of Relativity, Dove had long\npassed away, and with him there vanished the idea of the small value of\nthe energy stored in substance to give way to a very much greater value\nof which we can scarce form an estimate. We should feel dumbfounded if\nthe new calculation were to be a matter of millions, but actually we are\nto imagine a magnification to the extent of billions. This sounds almost\nlike a fable when expressed in words. But a million is related to a\nbillion in about the same way as a fairly wide city street to the width\nof the Atlantic Ocean. Our Mont Blanc sinks to insignificance. In the\nabove calculation it would have to be replaced by a mountain 50 million\nmiles high. Since this would lead far out into space, we may say that\nthe energy contained in a kilogramme of coal is sufficient to project a\nman so far that he will never return, converting him into a human comet.\nBut for the present this is only a theoretical store of energy which\ncannot yet be utilized in practice.\n\nNevertheless, we cannot avoid it in our calculations just as we cannot\navoid that remarkable quantity _c_, the velocity of light that plays its\npart in the tiny portion of substance as it does in everything,\nasserting itself as a regulative factor in all world phenomena. It is a\nnatural constant that preserves itself unchanged as 180,000 miles per\nsecond under all conditions, and which truly represents what appeared to\nGoethe as \"the immovable rock in the surging sea of phenomena,\" as a\nphantasm beyond the reach of investigators.\n\nIt is difficult for one who has not been soaked in all the elements of\nphysical thought to get an idea of what a natural constant means; so\nmuch the more when he feels himself impelled to picture the constant, so\nto speak, as the rigid axis of a world constructed on relativity.\nEverything, without exception, is to be subjected not only to continual\nchange (and this was what Heraclitus assumed as a fundamental truth in\nhis assertion _panta rhei_, everything flows), but every\nlength-measurement and time-measurement, every motion, every form and\nfigure are dependent on and change with the position of the observer, so\nthat the last vestige of the absolute vanishes from whatever comes into\nthe realm of observation. Nevertheless, there is an absolute despot, who\npreserves his identity inflexibly among all phenomena--the velocity of\nlight, _c_, of incalculable influence in practice and yet capable of\nmeasurement. Its nature has been characterized in one of the main\npropositions of Einstein stated in 1905: \"Every ray of light is\npropagated in a system at rest with a definite, constant velocity\nindependent of whether the ray is emitted by a body at rest or in\nmotion.\" But this constancy of the omnipotent _c_ is not only in\naccordance with world relativity: it is actually the main pillar which\nsupports the whole doctrine; the further one penetrates into the theory,\nthe more clearly does one feel that it is just this _c_ which is\nresponsible for the unity, connectivity, and invincibility of Einstein's\nworld system.\n\nIn our example of the coal, from which we started, _c_ occurs as a\nsquare, and it is as a result of multiplying 300,000 by itself (that is,\nforming _c_^2) that we arrive at the thousands of milliards of energy\nunits which we associated above with such a comparatively insignificant\nmass. Let us picture this astounding circumstance in another way,\nalthough we shall soon see that Einstein clips the wings of our soaring\nimagination. The huge ocean liner _Imperator_, which can develop a\ngreater horsepower than could the whole of the Prussian cavalry before\nthe war, used to require for one day's travel the contents of two very\nlong series of coal-trucks (each series being as long as it takes the\nstrongest locomotive to pull). We now know that there is enough energy\nin two pounds of coal to enable this boat to do the whole trip from\nHamburg to New York at its maximum speed.\n\nI quoted this fact, which, although it sounds so incredibly fantastic,\nis quite true, to Einstein with the intention of justifying the opinion\nthat it contained the key to a development which would initiate a new\nepoch in history and would be the panacea of all human woe. I drew an\nenthusiastic picture of a dazzling Utopia, an orgy of hopeful dreams,\nbut immediately noticed that I received no support from Einstein for\nthese visionary aspirations. To my disappointment, indeed, I perceived\nthat Einstein did not even show a special interest in this circumstance\nwhich sprang from his own theory, and which promised such bountiful\ngifts. And to state the conclusion of the story straight away I must\nconfess that his objections were strong enough not only to weaken my\nrising hopes, but to annihilate them completely.\n\nEinstein commenced by saying: \"At present there is not the slightest\nindication of when this energy will be obtainable, or whether it will be\nobtainable at all. For it would presuppose a disintegration of the atom\neffected at will--a shattering of the atom. And up to the present there\nis scarcely a sign that this will be possible. We observe atomic\ndisintegration only where Nature herself presents it, as in the case of\nradium, the activity of which depends upon the continual explosive\ndecomposition of its atom. Nevertheless, we can only establish the\npresence of this process, but cannot produce it; Science in its present\nstate makes it appear almost impossible that we shall ever succeed in so\ndoing.\"\n\nThe fact that we are able to abstract a certain number of calories from\ncoal and put them to practical use comes about owing to the circumstance\nthat combustion is only a molecular process, a change of configuration,\nwhich leaves fully intact the atoms of which the molecules are composed.\nWhen carbon and oxygen combine, the elementary constituent, the atom,\nremains quite unimpaired. The above calculation, \"mass multiplied by the\nsquare of the velocity of light;\" would have a technical significance\nonly if we were able to attack the interior of the atom; and of this\nthere seems, as remarked, not the remotest hope.\n\nOut of the history of technical science it might seem possible to draw\non examples contradictory to this first argument which is soon to be\nfollowed by others equally important. As a matter of fact, rigorous\nscience has often declared to be impossible what was later discovered to\nbe within the reach of technical attainment--things that seem to us\nnowadays to be ordinary and self-evident. Werner Siemens considered it\nimpossible to fly by means of machines heavier than air, and Helmholtz\nproved mathematically that it was impossible. Antecedent to the\ndiscovery of the locomotive the \"impossible\" of the academicians played\nan important part; Stephenson as well as Riggenbach (the inventors of\nthe locomotive) had no easy task to establish their inventions in the\nface of the general reproach of craziness hurled at them. The eminent\nphysicist Babinet applied his mathematical artillery to demolish the\nideas of the advocates of a telegraphic cable between Europe and\nAmerica. Philipp Reis, the forerunner of the telephone, failed only as a\nresult of the \"impossible\" of the learned physicist Poggendorff; and\neven when the practical telephone of Graham Bell (1876) had been found\nto work in Boston, on this side of the Atlantic there was still a hubbub\nof \"impossible\" owing to scientific reasons. To these illustrations is\nto be added Robert Mayer's mechanical equivalent of heat, a determining\nfactor in our above calculations of billions; it likewise had to\novercome very strong opposition on the part of leading scientists.\n\nLet us imagine the state of mankind before the advent of machines and\nbefore coal had been made available as a source of power. Even at that\ntime a far-seeing investigator would have been able to discover from\ntheoretical grounds the 8000 calories mentioned earlier and also their\ntransformation into useful forces. He would have expressed it in another\nway and would have got different figures, but he would have arrived at\nthe conclusion: Here is a virtual possibility which must unfortunately\nremain virtual, as we have no machine in which it can be used. And\nhowever far-sighted he may have been, the idea of, say, a modern dynamo\nor a turbine-steamer would have been utterly inconceivable to him. He\nwould not have dreamed such a thing. Nay, we may even imagine a human\nbeing of the misty dawn of prehistoric ages, of the diluvial period, who\nhad suddenly had a presentiment of the connexion between a log of wood\nand the sun's heat, but who was yet unaware of the uses of fire; he\nwould argue from his primordial logic that it was not possible and never\nwould be possible to derive from the piece of wood something which sends\nout warmth like the sun.\n\nI believe now, indeed, that we have grounds for considering ourselves\nable to mark off the limits of possibility more clearly than the present\nposition of science would seem to warrant. There is the same relation\nbetween such possibilities and absolute impossibilities as there is\nbetween Leibniz's _v\u00e9rit\u00e9s de fait_ and the _v\u00e9rit\u00e9s \u00e9ternelles_.\nThe fact that we shall never succeed in constructing a plane isosceles\ntriangle with unequal base angles is a _v\u00e9rit\u00e9 \u00e9ternelle_. On the\nother hand, it is only a _v\u00e9rit\u00e9 de fait_ that science is precluded\nfrom giving mortal man eternal life. This is only improbable in the\nhighest degree, for the fact that, up to the present, all our ancestors\nhave died is only a finite proof. The well-known Cajus of our logic\nbooks need not die; the chances of his dying are only _n_\u2044_n_+1, where\nwe denote the total of all persons that have passed away up to this\nmoment by _n_. If I ask a present-day authority in biology or medicine\nwhat evidence there is that it will be possible to preserve an\nindividual person permanently from death, he would confess: not the\nslightest. Nevertheless, Helmholtz declared: \"To a person who tells me\nthat by using certain means the life of a person may be prolonged\nindefinitely I can oppose my extreme disbelief, _but I cannot contradict\nhim absolutely_.\"\n\nEinstein himself once pointed out to me such very remote possibilities;\nit was in connexion with the following circumstance. It is quite\nimpossible for a moving body ever to attain a velocity greater than that\nof light, because it is scientifically inconceivable. On the other hand,\nit is conceivable, and therefore within the range of possibility, that\nman may yet fly to the most distant constellations.\n\nThere is, therefore, no absolute contradiction to the notion of making\navailable for technical purposes the billions of calories that occurred\nin our problem. As soon as we admit it as possible for discussion, we\nfind ourselves inquiring what the solution of the problem could signify.\nIn our intercourse we actually arrived at this question, and discovered\nthe most radical answer in a dissertation which Friedrich Siemens has\nwritten about coal in general without touching in the slightest on these\npossibilities of the future. I imagine that this dissertation was a big\ntrump in my hand, but had soon to learn from the reasoned contradiction\nof Einstein that the point at issue was not to be decided in this way.\n\nNevertheless, it will repay us to consider these arguments for a moment.\n\nFriedrich Siemens starts from two premises which he seemingly bases on\nscientific reasoning, thus claiming their validity generally. They are:\nCoal is the measure of all things. The price of every product\nrepresents, directly or indirectly, the value of the coal contained in\nit.\n\nAs all economic values in over-populated countries are the result of\nwork, and as work presupposes coal, capital is synonymous with coal. The\neconomic value of each object is the sum-total of the coal that had to\nbe used to manufacture the object in question. In over-populated states\neach wage is the value of the coal that is necessary to make this extra\nlife possible. If there is a scarcity of coal, the wages go down in\nvalue; if there is no coal, the wages are of no value at all, no matter\nhow much paper money be issued.\n\nAs soon as agriculture requires coal (this occurs when it is practised\nintensively and necessitates the use of railways, machines, artificial\nmanures), coal becomes involved with food-stuffs. Thanks to\nindustrialism, coal is involved in clothing and housing, too.\n\nSince money is equivalent to coal, proper administration of finance is\nequivalent to a proper administration of coal resources, and our\nstandard of currency is in the last instance a coal-currency. Gold as\nmoney is now concentrated coal.\n\nThe most advanced people is that which derives from one kilogramme of\ncoal the greatest possibilities conducive to life. Wise statesmanship\nmust resolve itself into wise administration of coal. Or, as it has been\nexpressed in other words elsewhere: \"We must think in terms of coal.\"\n\nThese fundamental ideas were discussed, and the result was that Einstein\nadmitted the premises in the main, but failed to see the conclusiveness\nof the inferences. He proved to me, step by step, that Siemens' line of\nthought followed a vicious circle, and, by begging the question, arrived\nat a false conclusion. The essential factor, he said, is man-power, and\nso it will remain; it is this that we have to regard as the primary\nfactor. Just so much can be saved to advantage as there is man-power\navailable for purposes other than for the production of coal from which\nthey are now released. If we succeed in getting greater use out of a\nkilogramme of coal by better management, then this is measurable in\nman-power, with which one may dispense for the mining of coal, and which\nmay be applied to other purposes.\n\nIf the assertion: \"Coal is the measure of all things,\" were generally\nvalid, it should stand every test. We need only try it in a few\ninstances to see that the thesis does not apply. For example, said\nEinstein: However much coal we may use, and however cleverly we may\ndispose of it, it will not produce cotton. Certainly the freightage of\ncotton-wool could be reduced in price, but the value-factor represented\nby man-power can never disappear from the price of the cotton.\n\nThe most that can be admitted is that an increase of the amount of power\nobtained from coal would make it possible for more people to exist than\nis possible at present, that is, that the margin of over-population\nwould become extended. But we must not conclude that this would be a\nboon to mankind. \"A maximum is not an optimum.\"\n\nHe who proclaims the maximum without qualification as the greatest\nmeasure of good is like one who studies the various gases in the\natmosphere to ascertain their good or bad effect on our breathing, and\narrives at the conclusion: the nitrogen in the air is harmful, so we\nmust double the proportion of oxygen to counteract it; this will confer\na great benefit on humanity!\n\n[1]*Armed with this striking analogy, we can now subject the foundation\nof Siemens' theory to a new scrutiny, and we shall then discover that\neven the premises contain a trace of the _petitio principii_ that\nfinally receives expression in the radical and one-sided expression:\n\"Coal is everything.\"\n\n[Footnote 1: The parts included between *...* are to be regarded as\nsupplementary portions intended to elucidate the arguments involved in\nthe dialogue. In many points they are founded on utterances of Einstein,\nbut also contain reflections drawn from other sources, as well as\nopinions and inferences which fall to the account of the author, as\nalready remarked in the preface. One will not get far by judging these\nstatements as right or wrong, for even the debatable view may prove\nitself to be expeditious and suggestive in the perspective of these\nconversations. Wherever it was possible, without the connexion being\nbroken, I have called attention to the parts which Einstein corrected or\ndisapproved of. In other places I refrained from this, particularly when\nthe subject under discussion demanded an even flow of argument. It would\nhave disturbed the exposition if I had made mention of every\ncounter-argument of the opposing side in all such cases while the\nexplanation was proceeding along broad lines.]\n\nAs if built on solid foundations this first statement looms before us:\nCoal is solar energy. This is so far indisputable. For all the coal\ndeposits that are still slumbering in the earth were once stately\nplants, dense woods of fern, which, bearing the burden of millions of\nyears, have saved up for us what they had once extracted as nutrition\nfrom the sun's rays. We may let the parallel idea pass without\ncontention: In the beginning was not the Word, nor the Deed, but, in the\nbeginning was the Sun. The energy sent out by the sun to the earth for\nmankind is the only necessary and inevitable condition for deeds. Deeds\nmean work, and work necessitates life. But we immediately become\ninvolved in an unjustifiable subdivision of the idea, for the propounder\nof the theory says next: \"... Coal is solar energy, therefore coal is\nnecessary if we are to work ...\" and this has already thrust us from the\npaths of logic; the prematurely victorious ergo breaks down. For, apart\nfrom the solar energy converted into coal, the warmth of our mother\nplanet radiates on us, and furnishes us with the possibility of work.\nSiemens' conclusion, from the point of view of logic, is tantamount to;\nGraphite is solar energy; hence graphite is necessary, if we are to be\nable to work. The true expression of the state of affairs is: Coal is,\nfor our present conditions of life, the most important, if not the\nexclusive, preliminary for human work.\n\nAnd when we learn from political economy that \"in a social state only\nthe necessary human labour and the demand for power-installations which\nrequire coal, and hence again labour for their production, come into\nquestion,\" this in no way implies the assertion, as Siemens appears to\nassume, that coal can be made out of labour. But it does signify that\nwork founded on the sun's energy need not necessarily be reducible to\ncoal. And this probably coincides with Einstein's opinion, which is so\nmuch the more significant, as his own doctrine points to the highest\nmeasure of effect in forces, even if only theoretically.*\n\nNevertheless, it is a fact that every increase in the quantity of power\nderived, when expressed per kilo, denotes a mitigation of life's\nburdens; it is only a question of the limits involved.\n\nFirstly, is technical science with its possibilities, as far as they can\nbe judged at present, still able to guarantee the future for us? Can it\nspread out the effective work so far that we may rely peacefully on the\ntreasures of coal slumbering in the interior of the earth?\n\nEvidently not. For in this case we are dealing with quantities that may\nbe approximately estimated. And even if we get three times, nay ten\ntimes, as many useful calories as before, there is a parallel\ncalculation of evil omen that informs us: there will be an end to this\nfeast of energy.\n\nIn spite of all the embarrassments due to the present shortage of coal\nwe have still always been able to console ourselves with the thought\nthat there is really a sufficiency, and that it is only a question of\novercoming stoppages. It is a matter of fact that from the time of the\nfoundation of the German Empire to the beginning of the World War coal\nproduction had been rising steadily, and it was possible to calculate\nthat in spite of the stupendous quantities that were being removed from\nthe black caves of Germany, there remained at least 2000 milliards of\nmarks in value (taken at the nominal rate, that is, \u00a3100,000,000,000).\nNevertheless, geologists and mining experts tell us that our whole\nsupply will not last longer than 2000 years, in the case of England 500\nyears, and in that of France 200 years. Even if we allow amply for the\nopening up of new coal-fields in other continents, we cannot get over\nthe fact that in the prehistoric fern forests the sun has stored up only\na finite, exhaustible amount of energy, and that within a few hundred\nyears humanity will be faced with a coal famine.\n\nNow, if coal were really the measure of all things, and if the\npossibility of life depended only on the coal supply, then our distant\ndescendants would not only relapse into barbarity, but they would have\nto expect the absolute zero of existence. We should not need to worry at\nall about the entropy death of the universe, as our own extinction on\nthis earthly planet beckons to us from an incomparably nearer point of\ntime.\n\nAt this stage of the discussion Einstein revealed prospects which were\nentirely in accordance with his conviction that the whole argument based\non the coal assumption was untenable. He stated that it was by no means\na Utopian idea that technical science will yet discover totally new ways\nof setting free forces, such as using the sun's radiation, or water\npower, or the movement of the tides, or power reservoirs of Nature,\namong which the present coal supply denotes only one branch. Since the\nbeginning of coal extraction we have lived only on the remains of a\nprehistoric capital that has lain in the treasure-chests of the earth.\nIt is to be conjectured that the interest on the actual capital of force\nwill be very much in excess of what we can fetch out of the depositories\nof former ages.\n\nTo form an estimate of this actual capital, entirely independent of\ncoal, we may present some figures. Let us consider a tiny water canal, a\nmere nothing in the watery network of the earth, the Rhine-falls at\nSchaffhausen, that may appear mighty to the beholder, but only because\nhe applies his tourist's measure instead of a planetary one. But even\nthis bagatelle in the household of Nature represents very considerable\neffectual values for us: 200 cubic metres spread over a terrace 20\nmetres high yield 67,000 horse-power, equivalent to 50,000 kilowatts.\nThis cascade alone would suffice to keep illuminated to their full\nintensity 1,000,000 glowlamps, each of 50 candle-power, and according to\nour present tariff we should have to pay at least 70,000 marks (\u00a33500\nnominally) per hour. The coal-worshipper will be more impressed by a\ndifferent calculation. The Rhine-falls at Schaffhausen is equivalent in\nvalue to a mine that yields every day 145 tons of the finest brown coal.\nIf we took the Niagara Falls as an illustration, these figures would\nhave to be multiplied by about 80.\n\nAnd by what factor would we have to multiply them, if we wished to get\nonly an approximate estimate of the energy that the breathing earth\nrolls about in the form of the tides? The astronomer Bessel and the\nphilosopher-physicist Fechner once endeavoured to get at some\ncomparative picture of these events. It required 360,000 men twenty\nyears to build the greatest Egyptian pyramid, and yet its cubical\ncontents are only about the millionth of a cubic mile, and perhaps if we\nsum up everything that men and machinery have moved since the time of\nthe Flood till now, a cubic mile would not yet have been completed. In\ncontrast with this, the earth in its tidal motion moves 200 cubic miles\nof water from one quadrant of the earth's circumference to another _in\nevery quarter of a day_. From this we see at once that all the\ncoal-mines in the world would mean nothing to us if we could once\nsucceed in making even a fraction of the pulse-beat of the earth\navailable for purposes of industry.\n\nIf, however, we should be compelled to depend on coal, our imaginations\ncling so much more closely to that enormous quantity given by the\nexpression _mc_^2, which was derived from the theory of relativity.\n\nThe 20 billion calories that are contained in each gramme of coal\nexercise a fascination on our minds. And although Einstein states that\nthere is not the slightest indication that we shall get at this supply,\nwe get carried along by an irresistible impulse to picture what it would\nmean if we should actually succeed in tapping it. The transition from\nthe golden to the iron age, as pictured in Hesiod, Aratus, and Ovid,\ntakes shape before our eyes, and following our bent of continuing this\ncyclically, we take pleasure in fancying ourselves being rescued from\nthe serfdom of the iron and of the coal age to a new golden age. A\nsupply, such as is piled up in an average city storing-place, would be\nsufficient to supply the whole world with energy for an immeasurable\ntime. All the troubles and miseries arising from the running of\nmachines, the mechanical production of wares, house-fires would vanish,\nand all the human labour at present occupied in mining coal would become\nfree to cultivate the land, all railways and boats would run almost\nwithout expense, an inconceivable wave of happiness would sweep over\nmankind. It would mean an end of coal-, freight-, and food-shortage! We\nshould at last be able to escape out of the hardships of the day, which\nis broken up by strenuous work, and soar upwards to brighter spheres\nwhere we would be welcomed by the true values of life. How alluring is\nthe song of Sirens chanted by our physics with its high \"C,\" the\nvelocity of light to the second power, which we have got to know as a\nfactor in this secret store of energy.\n\nBut these dreams are futile. For Einstein, to whom we owe this formula\nso promising of wonders, not only denies that it can be applied\npractically, but also brings forward another argument that casts us down\nto earth again. Supposing, he explained, it were possible to set free\nthis enormous store of energy, then we should only arrive at an age,\ncompared with which the present coal age would have to be called golden.\n\nAnd, unfortunately, we find ourselves obliged to fall in with this view,\nwhich is based in the wise old saw \u03bc\u03b7\u03b4\u1f72\u03bd \u1f04\u03b3\u03b1\u03bd, _ne quid\nnimis_, nothing in excess. Applied to our case, this means that when\nsuch a measure of power is set free, it does not serve a useful purpose,\nbut leads to destruction. The process of burning, which we used as an\nillustration, calls up the picture of an oven in which we can imagine\nthis wholesale production of energy, and experience tells us that we\nshould not heat an oven with dynamite.\n\nIf technical developments of this kind were to come about, the energy\nsupply would probably not be capable of regulation at all. It makes no\ndifference if we say that we only want a part of those 20 billion\ncalories, and that we should be glad to be able to multiply the 8000\ncalories required to-day by 100. That is not possible, for if we should\nsucceed in disintegrating the atom, it seems that we should have the\nbillions of calories rushing unchecked on us, and we should find\nourselves unable to cope with them, nay, perhaps even the solid ground,\non which we move, could not withstand them.\n\nNo discovery remains a monopoly of only a few people. If a very careful\nscientist should really succeed in producing a practical heating or\ndriving effect from the atom, then any untrained person would be able to\nblow up a whole town by means of only a minute quantity of substance.\nAnd any suicidal maniac who hated his fellows and wished to pulverize\nall habitations within a wide range would only have to conceive the plan\nto carry it out at a moment's notice. All the bombardments that have\ntaken place ever since fire-arms were invented would be mere child's\nplay compared with the destruction that could be caused by two buckets\nof coal.\n\nAt intervals we see stars light up in the heavens, and then become\nextinguished again; from these we infer that world catastrophes have\noccurred. We do not know whether it is due to the explosion of hydrogen\nwith other gases, or to collisions between two stellar bodies. There is\nstill room for the assumption that, immeasurably far away in yonder\nregions of celestial space, something is happening which a malevolent\ninhabitant of our earth, who has discovered the secret of smashing the\natom, might here repeat. And even if our imaginations can be stretched\nto paint the blessings of this release of energy, they certainly fail to\nconjure up visions of the disastrous effects which would result.\n\nEinstein turned to a page in a learned work of the mathematical\nphysicist Weyl of Z\u00fcrich, and pointed out a part that dealt with such\nan appalling liberation of energy. It seemed to me to be of the nature\nof a fervent prayer that Heaven preserve us from such explosive forces\never being let loose on mankind!\n\nSubject to present impossibility, it is possible to weave many parallel\ninstances. It is conceivable that by some yet undiscovered process\nalcohol may be prepared as plentifully and as cheaply as ordinary water.\nThis would end the shortage of alcohol, and would assure delirium\ntremens for hundreds of thousands. The evil would far outweigh the good,\nalthough it might be avoidable, for one can, even if with great\ndifficulty, imagine precautionary measures.\n\nWar technique might lead to the use of weapons of great range, which\nwould enable a small number of adventurers to conquer a Great Power. It\nwill be objected: this will hold vice versa, too. Nevertheless, this\nwould not alter the fact that such long-range weapons would probably\nlead to the destruction of civilization. Our last hope of an escape\nwould be in a superior moral outlook of future generations, which the\noptimist may imagine to himself as the _force majeure_.\n\nThere are apparently only two inventions, in themselves triumphs of\nintellect, against which one would have no defence. The first would be\nthought-reading made applicable to all, and with which Kant has dealt\nunder the term \"thinking aloud.\" What is nowadays a rare and very\nimperfect telepathic \"turn\" may yet be generalized and perfected in a\nmanner which Kant supposed not impossible on some distant planet. The\nassociation and converse of man with his fellows would not stand the\ntest of this invention, and we should have to be angels to survive it\neven for a day.\n\nThe second invention would be the solution of this _mc_^2-problem, which\nI call a problem only because I fail to discover a proper term, whereas\nso far was it from being a problem for Einstein that it was only in my\npresence he began to reckon it out in figures from the symbolic formula.\nTo us average beings a Utopia may disclose itself, a short frenzy of joy\nfollowed by a cold douche: Einstein stands above it as the pure\nsearcher, who is interested only in the scientific fact, and who, even\nat the first knowledge of it, preserves its essentially theoretical\nimportance from attempts to apply it practically. If, then, another\nwishes to hammer out into a fantastic gold-leaf what he has produced as\na little particle of gold in his physical investigations, he offers no\nopposition to such thought-experiments, for one of the deepest traits of\nhis nature is tolerance.\n\nA. Pfl\u00fcger, one of the best qualified heralds of the new doctrine, has\ntouched on the above matter in his essay, _The Principle of Relativity_.\nEinstein praised this pamphlet; I mentioned that the author took a view\ndifferent from that of Einstein, of the possibility of making accessible\nthe _mc_^2. In discussing the practical significance of this\neventuality, Pfl\u00fcger says: \"It will be time to talk of this point again\na hundred years hence.\" This seems a short time-limit, even if none of\nus will live to be present at the discussion. Einstein smiled at this\npause of a hundred years, and merely repeated, \"A very good essay!\" It\nis not for me to offer contradictions; and, as far as the implied\nprognostication is concerned, it will be best for mankind if it should\nprove to be false. If the optimum is unattainable, at least we shall be\nspared the worst, which is what the realization of this prophecy would\ninflict on us.\n\nSome months after the above discussion had first been put to paper, the\nworld was confronted by a new scientific event. The English physicist\nRutherford had, with deliberate intention, actually succeeded in\nsplitting up the atom. When I questioned Einstein on the possible\nconsequences of this experimental achievement, he declared with his\nusual frankness, one of the treasures of his character, that he had now\noccasion to modify somewhat the opinion he had shortly before expressed.\nThis is not to mean that he now considered the practical goal of getting\nunlimited supply of energy as having been brought within the realm of\npossibility. He gave it as his view that we are now entering on a new\nstage of development, which may perhaps disclose fresh openings for\ntechnical science. The scientific importance of these new experiments\nwith the atom was certainly to be considered very great.\n\nIn Rutherford's operations the atom is treated as if he were dealing\nwith a fortress: he subjects it to a bombardment and then seeks to fire\ninto the breach. The fortress is still certainly far from capitulating,\nbut signs of disruption have become observable. A hail of bullets caused\nholes, tears, and splinterings.\n\nThe projectiles hurled by Rutherford are alpha-particles shot out by\nradium, and their velocity approaches two-thirds that of light. Owing to\nthe extreme violence of the impact, they succeeded in doing damage to\ncertain atoms enclosed in evacuated glass tubes. It was shown that atoms\nof nitrogen had been disrupted. It is still unknown what quantities of\nenergy are released in this process. This splitting up of the atom\ncarried out with intention can, indeed, be detected only by the most\ncareful investigations.\n\nAs far as practical applications are concerned, then, we have got no\nfurther, although we have renewed grounds for hope. The unit of measure,\nas it were, is still out of proportion to the material to be cut. For\nthe forces which Rutherford had to use to attain this result are\nrelatively very considerable. He derived them from a gramme of radium,\nwhich is able to liberate several milliard calories, whereas the net\npractical result in Rutherford's experiment is still immeasurably small.\nNevertheless, it is scientifically established that it is possible to\nsplit up atoms of one's own free will, and thus the fundamental\nobjection raised above falls to the ground.\n\nThere is also another reason for increased hope. It seems feasible that,\nunder certain conditions. Nature would automatically continue the\ndisruption of the atom, after a human being had intentionally started\nit, as in the analogous case of a conflagration which extends, although\nit may have started from a mere spark.\n\nA by-product of future research might lead to the transmutation of lead\ninto gold. The possibility of this transformation of elements is subject\nto the same arguments as those above about the splitting up of the atom\nand the release of great quantities of energy. The path of decay from\nradium to lead lies clearly exposed even now, but it is very\nquestionable whether mankind will finally have cause to offer up hymns\nof thanksgiving if this line from lead on to the precious metals should\nbe continued, for it would cause our conception of the latter to be\nshattered. Gold made from lead would not give rise to an increase in the\nvalue of the meaner metal, but to the utter depreciation of gold, and\nhence the loss of the standard of value that has been valid since the\nbeginning of our civilization. No economist would be possessed of a\nsufficiently far-sighted vision to be able to measure the consequences\non the world's market of such a revolution in values.\n\nThe chief product would, of course, be the gain in energy, and we must\nbear this in mind when we give ourselves up to our speculations, however\noptimistic or catastrophic they may be. The impenetrable barrier\n\"impossible\" no longer exists. Einstein's wonderful \"Open Sesame,\" mass\ntimes the square of the velocity of light, is thundering at the portals.\n\nAnd mankind finds a new meaning in the old saw: One should never say\n_never_!\n\n\n\n\nCHAPTER III\n\nVALHALLA\n\nOrder of Distinction and Characteristics of Great Discoverers.--Galilei\nand Newton.--Forerunners and Priority.--Science and Religion.--Inheritance\nof Talent.--A Dynasty of Scholars.--Alexander von Humboldt and\nGoethe.--Leonardo da Vinci.--Helmholtz.--Robert Mayer and D\u00fchring.--Gauss\nand Riemann.--Max Planck.--Maxwell and Faraday.\n\n\nI HAD made up my mind to question Einstein about a number of famous men,\nnot concerning mere facts of their lives and works, for these details\nwere also procurable elsewhere, and, moreover, I was not ignorant of\nthem, but what attracted me particularly was to try to discover how the\ngreatness of one might be compared with that of another. This sometimes\nhelps us to see a personality in a different light and from a new\nperspective, which leads us to assign to him a new position in the\nseries of orders of merit.\n\nI had really sketched out a list for this purpose, including a great\nnumber of glorious names from the annals of physics and regions just\nbeyond: a table, as it were, from which one might set up a directory for\nValhalla! It seemed to me a pleasing thought to roam through this hall\nof celebrities in company with Einstein, and to pause at the pedestal of\nthe busts of the great, who, in spite of their number, are still too\nfew, far too few, in comparison with the far too many who populate the\nearth like so many factory-produced articles. If we set to work to draw\nup a list of this sort, we soon find that there is no end to these\nheroes of Valhalla, and we are reminded of the hall of fame of the\nNorthern Saga, of the mythological Valhalla, whose ceiling was so high\nthat the gable was invisible, and whose extent was so great that anyone\nwishing to enter could choose from five hundred and forty entrances.\n\nIn reality our little excursion was far from taking these dimensions,\nthe chief reason being probably that we had begun at Newton. However\nattractive it may be to hear Einstein talk of Newton, a disadvantage\narises in that we find it hard to take leave of his bust situated at the\nmain portal, and that we continually revert to it even when we call to\nmind the remaining paths free for our choice and stretching out of\nsight.\n\nReality, even figuratively, offered a picture which differed\nconsiderably from the measures of greatness apportioned by legendary\naccounts. In Einstein's workroom, certainly, a visitor encounters\nportraits, not busts, and it would be rash to speak of this little\ncollection of portraits as of a miniature museum. No, it is certainly\nnot that, for its catalogue numbers only to three. But here they act as\na trinity with a special significance under the gaze of Einstein, who\nlooks up to them with reverence. To him their contribution of thought is\nimmeasurable; Faraday, Maxwell with his rich coils of hair, and between\nthem, Newton with his flowing wig, represented in an excellent English\nengraving, whose border consists of symbolic insignias encircling his\ndistinguished-looking countenance.\n\n     *     *     *     *     *     *     *     *\n\nAccording to Schopenhauer, the measure of reverence that one can feel is\na measure of one's own intrinsic value. Tell me how much respect you can\nfeel, and I shall tell you what is your worth. It is certainly not\nnecessary to emphasize this quality specially in the case of Einstein,\nfor there are other points of vantage from which we may form an estimate\nof his excellence. Nevertheless, I make special mention of the\ncircumstance to give an indication of the difference between a\nrevolutionary discoverer and revolutionary pioneers in other fields. It\nis particularly noticeable that inborn respect is seldom found in\nmodernists of Art. The only means of propaganda known to them consists\nin a passionate denunciation of what has been developed historically by\ngradual and patient effort; their retrospect consists of unmitigated\ncontempt; they profess to be disciples only of what is most recent,\nremaining confined within the narrow circle surrounding their own ego.\nThe horizon of the discoverer has a different radius. He takes over\nresponsibility for the future by never ceasing his offerings at the\naltar of the Past. There is probably no discoverer who is devoid of this\ncharacteristic, but I should like to emphasize that, among all the\nscientists with whom I am acquainted, no one recognizes the merit of\nothers so warmly as Einstein. He becomes carried away with enthusiasm\nwhen he talks of great men, or of such as appear great to him. His\nValhalla is not, of course, the same as that favoured by Encyclop\u00e6dias,\nand many a one whom we rank as a Sirius among men is to be found lower\nthan the sixth order of magnitude in Einstein's list. Nevertheless, the\nnumber of selection of constellations is no mean one, and the reverence\nthat was originally inspired by reasoned thought has become infused in\nhis temperament and become a part of his emotional self.\n\nOne need only mention the name of Newton--and even this is scarcely\nnecessary, for Newton seems always near at hand; if I happen to start\nwith Descartes or Pascal, it does not take long before we arrive at\nNewton, \u1f04\u03bd\u03b4\u03c1\u03b1 \u03bc\u03bf\u1fd0 \u1f14\u03bd\u03bd\u03b5\u03c0\u03b7!\n\nOnce we began with Laplace; and it seemed almost as if the \"Trait\u00e9 de\nla m\u00e9chanique c\u00e9leste\" was to become the subject of discussion. But\nEinstein left his seat, and, taking up a position in front of his series\nof portraits on the wall, he meditatively passed his hand through his\nhair, and declared:\n\n\"In my opinion the greatest creative geniuses are Galilei and Newton,\nwhom I regard in a certain sense as forming a unity. And in this unity\nNewton is he who has achieved the most imposing feat in the realm of\nscience. These two were the first to create a system of mechanics\nfounded on a few laws and giving a general theory of motions, the\ntotality of which represents the events of our world.\"\n\nInterrupting his remarks, I asked: \"Can Galilei's fundamental law of\ninertia (Newton's First Law of Motion) be said to be a law deduced from\nexperience? My reason for asking is that the whole of natural science is\na science of experience, and not merely something based on speculation.\nIt might easily suggest itself to one that an elementary law like that\nof Galilei or Newton could be derived from our everyday experience. But,\nif this is the case, how is it that science had to wait so long before\nthis simple fact was discovered? Experience is as old as the hills; why\ndid the law of inertia not make its appearance at the very beginning,\nwhen Nature was first subjected to inquiry?\"\n\n\"By no means!\" replied Einstein. \"The discovery of the law of\nrectilinear motion of a body under no external influences is not at all\na result of experience. On the contrary! A circle, too, is a simple line\nof motion, and has often been proclaimed as such by predecessors of\nNewton, for example, by Aristoteles. It required the enormous power of\nabstraction possessed only by a giant of reason to stabilize rectilinear\nmotion as the fundamental form.\"\n\nTo this may be added that before and even after the time of Galilei, not\nonly the circle but also other non-rectilinear lines have been regarded\neven by serious thinkers as the primary lines given by Nature; these\nthinkers even dared to apply their curvilinear views to explaining world\nphenomena that could be made clear only after Galilei's abstraction had\nbeen accepted.\n\nI asked whether the theory of gravitation was already implicitly\ncontained in Galilei's Laws of Falling Bodies. Einstein's answer was in\nthe negative: the gravitational theory falls entirely to the credit of\nNewton, and the greatness of this intellectual achievement remains\nunimpaired even if the efforts of certain forerunners are recognized. He\nmentioned Robert Hooke, whom, among others, Schopenhauer sets up against\nNewton, with absolute injustice and from petty feelings of antipathy,\nwhich takes its origin from Schopenhauer's unmathematical type of mind.\nThe vast difference between Hooke's preliminary attempts at explaining\ngravitation, and Newton's monumental structure, was beyond his power of\ndiscernment.\n\n*Schopenhauer (vol. II. of the _Parerga_) uses two arguments to\ndiscredit Newton. Firstly, he refers to two original works, both of\nwhich he misinterprets; secondly, he undertakes a psychological analysis\nof Newton. He uses psychological means, which would be about equally\nreasonable as applying the Integral Calculus to proving facts of Ethical\nPsychology, and he arrives at the conclusion that priority in\ndiscovering the law of gravitation is due to some one else; Hooke is\npictured as having been treated like Columbus: we now hear of \"America,\"\nand likewise \"Newton's Gravitational System\"!\n\nSchopenhauer has, however, quite forgotten that he himself, some pages\nearlier, trumpeted forth Newton's imperishable fame with the words: \"To\nform an estimate of the great value of the gravitational system which\nwas at least completed and firmly established by Newton, we must remind\nourselves how entirely nonplussed about the origin of the motion of\ncelestial bodies thinkers had previously been for thousands of years.\"\nThat bears the ring of truth. Newton's greatness can be grasped only if\nthousands of years are used as a measure.\n\nWhereas Schopenhauer argued from grounds drawn from psychology and the\nprinciple of universal knowledge, his antagonist Hegel, who was still\nmore vague in these fields, sought to dispense with both Newton and\nKepler by calling to his aid the so-called pure intuition of the curved\nline. In an exposition of truly comical prolixity, such as would have\ndelighted the hearts of scholiasts, he proves that the ellipse must\nrepresent the fundamental type of planetary motion, this being quite\nindependent of Newton's laws, Kepler's observations, and resulting\nmathematical relationships. And Hegel actually succeeds, with a nebulous\nverbosity almost stultifying in its unmeaningness, in paraphrasing\nKepler's second law in his own fashion. It reads like an extract from\nsome carnival publication issued by scientists in a bibulous mood to\nmake fun of themselves.\n\nBut these extravagances, too, serve to add lustre to Newton, for his\ngenius shines out most brilliantly when it is a question of expressing\nclearly, and without assumptions, a phenomenon of cosmic motion. Here\nthere are no forerunners, not even with regard to his own law of\ngravitation. Newton showed with truly triumphant logic that Kepler's\nsecond law belongs to those things that are really self-evident.\n\nThis law, taken alone, offers considerable difficulties to anyone who\nlearns of it for the first time. Every planet describes an ellipse; that\nis accepted without demur. But the uninitiated will possibly or even\nprobably deduce from this that the planet will pass over equal lengths\nof arc in equal times. By no means, says Kepler; the arcs traversed in\nequal times are unequal. But if we connect every point of the elliptic\npath with a definite point within the curve (the focus of the ellipse)\nby means of straight lines, each of which is called a radius vector, we\nget that the areas swept out by the radius vector in equal times (and\nnot the arcs) are equally great.\n\nWhy is this so? This cannot be understood _a priori_. But one might\nargue that since the attraction of the sun is the governing force, this\nwill probably have something to do with Newton's law of gravitation, in\nparticular with the inverse square of the distance. And one might\nfurther infer that, if a different principle of gravitation existed,\nKepler's law would assume a new form.\n\nA fact amazing in its simplicity here comes to light. Newton states the\nproposition: \"According to whatever law an accelerating force acts from\na centre on a body moving freely, the radius vector will always sweep\nout equal areas in equal lengths of time.\"\n\nNothing is assumed except the law of inertia and a little elementary\nmathematics, namely, the theorem that triangles on the same base and of\nthe same altitude are equal in area. The form in which this theorem\noccurs in Newton's simple drawing is certainly astonishing. One feels\nthat there in a few strokes a cosmic problem is solved; the impression\nis ineffaceable.\n\nThis theorem together with its proof is contained in Newton's chief\nwork, _Philosophi\u00e6 naturalis principia mathematica_. The interfusion of\nphilosophy and mathematics furnished him with the natural principles of\nknowledge.*\n\nEinstein made some illuminating remarks about Newton's famous phrase:\n\"Hypotheses non fingo.\" I had said that Newton must have been aware that\nit is impossible to build up a science entirely free from hypotheses.\nEven geometry itself has arrived at that critical stage at which Gauss\nand Riemann discovered its hypothetical foundations.\n\nEinstein replied: \"Accentuate the words correctly and the true sense\nwill reveal itself!\" It is the last word that is to be stressed and not\nthe first. Newton did not want to feel himself free from hypotheses, but\nrather from the assumption that he invented them, except when this was\nabsolutely necessary. Newton, then, wished to express that he did not go\nfurther back in his analysis of causes than was absolutely inevitable.\n\nPerhaps, I allowed myself to interject, a more violent suspicion against\nthe word \"hypotheses\" was prevalent with scholars in Newton's time than\nnow. Newton's emphatic defence would then appear a shade more\nintelligible. Or did he cherish the belief that his world-law was the\nonly possible one in Nature?\n\nEinstein again referred to the universality of Newton's genius, saying\nthat Newton was doubtless aware of the range within which his law was\nvalid: this law applies to the realm of observation and experience, but\nis not given _a priori_, no more than Galilei's Law of Inertia. It is\ncertainly conceivable that beyond the domain of human experience there\nmay be an undiscoverable universe in which a different fundamental law\nholds, and one which, nevertheless, does not contradict the principle of\nsufficient reason.\n\nThe antithesis: Simplicity--Complexity, led the conversation into a\nshort bypath; it arose out of an example which I quoted and that I shall\nrepeat here even if it may seem irrelevant.\n\nOne might well expect that just as for attraction there must be a\ngeneral law for resistance or repulsion. And if attraction occurs\naccording to the inverse square of the distance, then it would be an\nextremely interesting parallel if a similar law were to hold for\nrepulsion except that the proportionality were direct instead of\ninverse. There have actually been physicists who have proclaimed a\ndirect square law of repulsion; I have heard it in lectures myself. The\naction of a resisting medium, as, for example, the resistance of the air\nto the flight of a cannon-ball, is stated to be proportional to the\nsquare of the velocity of the projectile.\n\nThis theorem is wrong. If it were correct, and verified by experiment,\nwe should have to regard it as being presumably the only possible and\ndirectly evident form of the law of repulsion or resistance. There\nwould, at least, be no logical reason for contradicting it.\n\nBut here we have a mixed relationship, as Einstein calls it--that is, we\nare unable to express an exact connexion between the velocity of a body\nin flight and the air resistance.\n\nThis fallacious assumption by no means proceeded from illogical\nreasoning, and it seemed to rest on a sound physical basis. For, so it\nwas argued, if the velocity is doubled, there is twice as much air to be\ndisplaced, so that the resistance will be four times as great. But this\nwas contradicted outright by experimental evidence. One cannot even call\nit an approximate law, except for very low speeds. For greater speeds we\nfind, instead of a quadratic relation, a cubical one, or one of a more\ncomplex nature. Photographs have demonstrated that the resistance\nexperienced by a projectile in flight is due to the excitation of a\npowerful central wave, to the friction between the air and the surface\nof the projectile, and to eddies produced behind the projectile--that\nis, to various conjoined factors, each of which follows a different law,\nand such that the combined effect cannot be expressed by a simple\nformula at all. This phenomenon is thus very complicated and offers\nalmost insuperable difficulties to analysis. A beautiful remark was once\nmade, which characterizes such events in Nature.\n\nDuring a conversation with Laplace, Fresnel said that Nature does not\nworry about analytical difficulties. There is nothing simpler than\nNewton's Law in spite of the complicated nature of planetary motions.\n\"Nature here despises our analytical difficulties,\" said Fresnel; \"she\napplies simple means, and then by combining them produces an almost\ninextricable net of confusion. Simplicity lies concealed in this chaos,\nand it is only for us to discover it!\" But this simplicity when it is\ndiscovered is not always found to be expressible in simple formulae, not\nmust it be forgotten that even the ultimate discoverable simplicity\npoints to certain hypothetical assumptions.\n\n\"Hypotheses non fingo!\" This phrase of Newton's remains true, if we\nmaintain Einstein's interpretation: \"He did not wish to go further back\nin his analysis of causes than was absolutely inevitable.\" It interested\nme to pursue this line of thought suggested by Einstein still further,\nand I discovered that these words of Newton had actually been falsely\naccentuated and hence misinterpreted by many authorities on science.\nEven Mill and the great scholar, William Whewell, succumbed to this\nmisunderstanding. Credit must be given to a more modern scholar,\nProfessor Vaihinger of Halle, for being sufficiently keen of hearing to\ndetect the true accentuation; and now that Einstein has corroborated\nfully this explanation, doubts as to the true sense of the words are no\nlonger to be feared.\n\nThe trend of our talk brought us to a discussion of the conception, \"law\nof nature.\" Einstein recalled Mach's remarks, and indicated that the\npoint was to determine how much we read out of Nature; and these\nobservations made at least one thing clear, namely, that every law\nsignifies some limitation; in the case of human laws, expressed in the\ncivil and penal code, the limitation affects the will, and possible\nactions, whereas natural laws signify the limitations which we, taught\nby experience, prescribe to our expectations. Nevertheless, the\nconception remains elastic, for the question will always intrude itself:\nWhat does prescription mean? Who prescribes? Kant has assigned to Man\nthe foremost position inasmuch as it is he who is regarded by Kant as\nprescribing laws to Nature. Bacon of Verulam emphasizes the ambiguous\npoint of view by asserting: \"Natura non vincitur nisi parendo,\" Man\nconquers Nature only by obeying her, that is, by conforming to her\nimmanent norms. Thus the laws exist without us, and we have only to\ndiscover them. When they have been found, Man can react by applying them\nto subdue Nature. Man becomes the dictator and dictates to Nature the\nlaws according to which she for her part has to subjugate mankind.\nWhether we adopt the one view or the other, there is a vicious circle,\nfrom which there is no escape. A law is a creation of intellect, and\nMephisto's words remain true: \"In the end we depend on the creatures of\nour own making!\"\n\nIn Newton's soul obedience and the wish to obey must have been\npre-eminent traits. Is he not reputed to have been pious and strong of\nfaith?\n\nEinstein confirmed this, and, raising his voice, he generalized from it,\nsaying: \"In every true searcher of Nature there is a kind of religious\nreverence; for he finds it impossible to imagine that he is the first to\nhave thought out the exceedingly delicate threads that connect his\nperceptions. The aspect of knowledge which has not yet been laid bare\ngives the investigator a feeling akin to that experienced by a child who\nseeks to grasp the masterly way in which elders manipulate things.\"\n\nThis explanation implied a personal confession. For he had spoken of the\nchildlike longing felt by all, and had interpreted the subtle\nintricacies of the scientist's ideas in particular as springing from a\nreligious source. Not all have confessed this; we know, indeed, that the\nconvictions of many a one were not so. Let us cling to the fact that the\ngreatest in the realm of science--Newton, Descartes, Gauss, and\nHelmholtz--were pious, although their faith varied in degree. And let us\nnot forget that the most bitter opponent of this attitude of mind, the\noriginator of \"Ecrasez l'infame,\" finally had a temple built bearing the\ninscription: \"Deo erexit Voltaire.\"\n\nIn Newton positivism found its most faithful disciple, and his research\nwas directly affected by his religious attitude. He, himself, was the\nauthor of that beautiful thought: \"A limited measure of knowledge takes\nus away from God; an increased measure of knowledge takes us back to\nHim.\" It was he who considered that the world-machine that he had\ndisclosed was not sufficiently stabilized by his mathematical law, and\nso he enlisted the intermittent help of an assistant for the Creator,\nConcursus Dei, to attend to the functioning of the machine. Finally, he\nslipped from the path of na\u00efve faith on to theological bypaths and\nwrote devout essays on apocalyptic matters. On the other hand,\nDescartes' piety, which was genuine at root, exhibited suspicious\noffshoots, and one cannot shake off the feeling that he was smiling up\nhis sleeve when he was making some of his solemn declarations. He was a\nmaster of compromise, and gave due expression to its spirit, which F. A.\nLange bluntly stated was merely a veil for \"Cowardice towards the\nChurch.\" Voltaire, an apostle of Newton's system of natural philosophy,\nwent so far in his condemnation of Descartes' confession of faith that\nhe affirmed: \"The Cartesian doctrine has been mainly instrumental in\npersuading many not to recognize a God.\"\n\nAs Einstein had called special attention to the childlike nature of the\nscientist's root-impulse, I quoted a remark of Newton that seemed to me\nat the moment to be a confirmation of Einstein's attitude:\n\n\"I do not know what I may appear to the world, but to myself I seem to\nhave been only like a boy playing on the seashore, and diverting myself\nin now and then finding a smoother pebble or a prettier shell than\nordinary, whilst the great ocean of truth lay all undiscovered before\nme.\"\n\nAre we not to regard this analogy of Newton's as being intended to\nconvey a religious meaning?\n\n\"There is no objection to this,\" said Einstein, \"although it seems to me\nmore probable that, in saying this, Newton set down the view only of the\npure investigator. The essential purpose of his remarks was to express\nhow small is the range of the attainable compared with the infinite\nexpanse offered for research.\"\n\nThrough some unexpected phrase that was dropped, the conversation took a\nnew turn at this point, which I should not like to withhold, inasmuch as\nit gave rise to a noteworthy observation of Einstein about the nature of\ngenius. We were talking about the \"possibility of genius for science\nbeing inherited\" and about the comparative rareness with which it\noccurs. There seems to have been only one case of a real dynasty of\ngreat minds, that of the ten Bernoullis who were descended of a line of\nmathematicians, and all of them achieved important results, some of them\nmaking extraordinary discoveries. Why is this exception unique? In other\nexamples we do not get beyond three or four names in the same family,\neven if we take Science and Art conjointly. There were two Plinys, two\nGalileis, two Herschels, two Humboldts, two Lippis, two Dumas, several\nBachs, Pisanos, Robbias, and Holbeins--the net result is very poor, even\nif we count similar names, disregarding the fact of relationship; there\nis no recognizable dynasty except in the case of the ten Bernoullis.[2]\n\"And so,\" I continued, \"the conclusion seems justified that Nature has\nnothing to do with a genealogy of talents, and that, if we happen to\nnotice manifestations of talent in one and the same family, this is a\nmere play of chance.\"\n\n[Footnote 2: The Roman family Cosmati (of the thirteenth century), which\ngave us seven splendid representatives of architecture and mosaic work,\nhardly comes into consideration, since not one of them is regarded in\nthe history of art as a real genius.]\n\nEinstein, however, contradicted this emphatically: \"Inherited talent\ncertainly occurs in many cases, where we do not observe it, for genius\nin itself and the possibility of genius being apprehended are certainly\nfar from always appearing in conjunction. There are only insignificant\ndifferences between the genius that expresses itself in remarkable\nachievements and the genius that is latent. At a certain instant,\nperhaps, only some impulse was wanting for the latent genius to burst\nforth with all clearness and brilliance; or, perhaps, it required only\nan unusual situation in the development of science to call into action\nhis special talents, and thus it remained dormant, whereas a very slight\nchange of circumstances would have caused them to assert themselves in\ndefinite results.\n\n\"In passing I should like to remark that you just now mentioned the two\nHumboldts; it seems to me that Alexander von Humboldt, at least, is not\nto be counted as a genius. It has struck me repeatedly that you\npronounced his name with particular reverence----\"\n\n\"And I have observed equally often, Professor, that you made a sign of\ndisapproval. For this reason slight doubts have gradually been rising in\nme. But it is difficult to get free from the orders of greatness that\none has recognized for decades. In my youth people spoke of 'a Humboldt'\njust as we speak of 'a C\u00e6sar' or 'a Michelangelo,' to denote some\npinnacle of unrivalled height. To me at that time Humboldt's Kosmos was\nthe Bible of Natural Science, and probably such memories have a certain\nafter-effect.\"\n\n\"That is easy to understand,\" said Einstein. \"But we must make it clear\nto ourselves that for us of the present day Humboldt scarcely comes into\nconsideration when we direct our gaze on to the great seers. Or, let us\nsay more clearly, he does not belong to this category. I certainly grant\nhim his immense knowledge and his admirable faculty of getting into\ntouch with the unity of Nature, which reminds us of Goethe.\"\n\n\"Yes; this feeling for the uniformity of the cosmos had probably\npersuaded me in his favour,\" I answered, \"and I am glad that you draw a\nparallel with Goethe in this respect. It reminds me of Heine's story: If\nGod had created the whole world, except the trees and the birds, and had\nsaid to Goethe: 'My dear Goethe, I leave it to you to complete this\nwork,' Goethe would have solved the problem correctly and in a god-like\nmanner--that is, he would have painted the trees green and given the\nbirds feathers.\n\n\"Humboldt could equally well have been entrusted with this task. But\nvarious objections may be raised against such reflections of a playful\npoetic character ... one objection being that Goethe's own knowledge of\nornithology was exceedingly limited. Even when nearly eighty he could\nnot distinguish a lark from a yellow-hammer or a sparrow! Is that a\nfact?\"\n\n\"Fully confirmed: Eckermann gives a detailed report of it in a\nconversation which took place in 1827. As I happened to come across the\npassage only yesterday, I can quote the exact words if you will allow\nme: 'Great and good man,' thought Eckermann, 'who hast explored Nature\nas few have ever done, in ornithology thou seemest still a child!'\"\n\nFor a speculative philosopher, it may here be interposed, this might\nwell serve as the starting-point of an attractive investigation. Goethe,\non the one hand, cannot recognize a lark, but would have been able to\ngrasp the Platonic idea of the feathered species, even if there had been\nno such things as birds: Humboldt, on the other hand, would perhaps have\nbeen able to create the revolving planets, if Heaven had commanded it;\nbut he would never have succeeded in becoming the author of what we call\nan astronomical achievement, such as that of Copernicus or of Kepler.\n\nAnd with reference to certain other men I elicited from Einstein\nutterances that reduced somewhat my estimate of their importance.\n\nWe were speaking of Leonardo da Vinci, omitting all reference to his\nsignificance in the world of Art--that is, only of Leonardo the Scholar\nand the Searcher. Einstein is far from disputing his place in the\nValhalla of great minds, but it was clear that he wished to recommend a\nre-numbering of my list, so that the Italian master would not occupy a\nposition in just the first rank.\n\nThe problem of Leonardo excited great interest in me, and it deserves\nthe consideration of every one. The further the examination of his\nwritings advances, the more does this problem resolve itself into the\nquestion: How much altogether does modern science owe to Leonardo?\nNowadays it is declared in all earnestness that he was a painter and a\nsculptor only by the way, that his chief profession was that of an\nengineer, and that he was the greatest engineer of all times. This has\nin turn given rise to the opinion that, as a scientist, he is the light\nof all ages, and in the abundance of his discoveries he has never been\nsurpassed before or after his own time.\n\nAs this question had arisen once before, I had come equipped with a\nlittle table of facts, hastily drawn from special works to which I had\naccess. According to my scheme, Leonardo was the true discoverer and\nauthor of the following things:\n\n    Law of Conservation of Momentum.\n\n    Law of Virtual Velocities (before Ubaldi and Galilei).\n\n    Wave Theory (before Newton).\n\n    Discovery of the Circulation of the Blood (before\n        Harvey).\n\n    Laws of Friction (before Coulomb).\n\n    Law of Pressure for connected Tubes containing\n        Fluid (before Pascal).\n\n    Action of Pressure on Fluids (before Stevin and Galilei).\n\n    Laws of Falling Bodies (before Galilei).\n\n    True interpretation of the twinkling of stars (before\n        Kepler, who, moreover, did not succeed in finding\n        the real explanation).\n\n    Explanation of the reflected light of the moon (before\n        Kepler).\n\n    Principle of Least Action (before Galilei).\n\n    Introduction of the plus and the minus signs into\n        calculations.\n\n    Definition of kinetic energy from mass and velocity.\n\n    Theory of Combustion (before Bacon).\n\n    Explanation of the motion of the sea (before Maury).\n\n    Explanation of the ascent of fluids in plants (before\n        Hales).\n\n    Theory of Fossilization (before Palissy).\n\nAdded to these there are a great number of inventions, in particular\nthose connected with problems of aviation, such as the parachute (before\nLenormand), and so forth.\n\nThis fist aroused great distrust in Einstein: he regarded it as the\noutcome of an inquisitive search for sources, excusable historically,\nbut leading to misrepresentation. We are falsely led to regard slightly\nrelated beginnings, vague tracks, hazy indications, which are found, as\nevidences of a real insight, which disposes us to \"elevate one above all\nothers.\" Hence a mythological process results, comparable to that which,\nin former times, thrust all conceivable feats of strength on to one\nHercules.\n\nI learned that recently a strong reaction has asserted itself in\nscientific circles against this one-sided hero-worship; its purpose is\nto reduce Leonardo's merits to their proper measure. Einstein made it\nquite clear that he was certainly not to be found on the side of the\nultra-Leonardists.\n\nIt cannot be denied that the latter have valuable arguments to support\ntheir case, and that these arguments become multiplied in proportion as\nthe publication of Leonardo's writings (in the _Codex Atlanticus_,\netc.), which are so difficult to decipher, proceeds. The partisans of\nLeonardo derive considerable support in many points from recognized\nauthorities, as in the case of Cantor, the author of the monumental\nhistory of mathematics. We there read: \"The greatest Italian painter of\nthe fifteenth century was not less great as a scientist. In the history\nof science his name is famous and his achievements are extolled,\nparticularly those which give him a claim to be regarded as one of the\nfounders of Optics.\" He is placed on a level with Regiomantus as one of\nthe chief builders of mathematics of that time. Nevertheless, Cantor\nraises certain doubts by remarking that the results of investigations\nmade up to the present do not prove Leonardo to be a great\nmathematician. On another page he is proclaimed simultaneously with\nArchimedes and Pappus as a pioneer of the doctrines of the centre of\ngravity.\n\nWith regard to the main points, Leonardo's priority in the case of the\nLaws of Falling Bodies, the Theory of Wave-motion, and the other\nfundamental principles of physics, Einstein has the conviction that the\npartisans of Leonardo are either mistaken in the facts or that they\noverlook forerunners. In the case of these principles, above all, there\nis always _some_ predecessor, and it is almost impossible to trace the\nline of discoveries back to the first source. Just as writers have\nwished to deprive Galilei, Kepler, and Newton of their laurels in favour\nof Leonardo, so the same might be done with Copernicus.\n\nThis has actually been attempted. The real Copernicus, so one reads, was\nHipparchus of Nic\u00e6a, and if we go back still further, a hundred years\nearlier, two thousand years ago, we find that Aristarchus of Samos\ntaught that the world rotated about its own axis and revolved round the\nsun.\n\nAnd we need not even stop there, in Einstein's opinion. For it is open\nto conjecture that Aristarchus in his turn has drawn on Egyptian\nsources. This retrogressive investigation may excite the interest of\narch\u00e6ologists, and in particular cases perhaps lead to the discovery of\na primary claim to authorship, but it cannot fail to excite suspicion\nagainst the conscious intention of conferring all the honours of science\non an individual discoverer. Leonardo's superlative constructive genius\nis not attacked in these remarks, and there seems no reason for\nobjecting if anyone wishes to call him the most ingenious engineer of\nall times.\n\nAll the pressures and tensions occurring in Nature seemed to be repeated\nin him as \"inner virtues,\" an expression borrowed from Helmholtz, who\nused it with reference to himself. This analogy might be extended by\nsaying that, in the works of both, Man himself with his organic\nfunctions and requirements plays an important r\u00f4le. For them the\nabstract was a means of arriving at what was perceptual, physiologically\nuseful, and stimulating in its effect on life. Leonardo started out from\nArt, and throughout the realm of mechanics and machines he remained an\nartist in method. Helmholtz set out from the medical side of physiology\nand transferred the valuations of beauty derived from the senses to his\npictures of mechanical relationships. The life-work of each has an\n\u00e6sthetic colouring, Leonardo's being of a gloomy hue, that of Helmholtz\nexhibiting brighter and happier tints. Common to both is an almost\ninconceivable versatility and an inexhaustible productivity.\n\nWhenever Einstein talks of Helmholtz he begins in warm terms of\nappreciation, which tend to become cooler in the course of the\nconversation. I cannot quote his exact words, and as I cannot thus give\na complete account for which full responsibility may be taken, it may be\nallowable to offer a few important fragments that I have gathered.\n\nJudged by the average of his accomplishments, Helmholtz is regarded by\nEinstein as an imposing figure whose fame in later times is assured;\nHelmholtz himself tasted of this immortality while still alive. But when\nefforts are made to rank him with great thinkers of the calibre of\nNewton, Einstein considers that this estimate cannot be fully borne out.\nIn spite of all the excellence, subtlety, and effectiveness of\nHelmholtz's astoundingly varied inspirations, Einstein seems to fail to\ndiscover in him the source of a really great intellectual achievement.\n\nAt a Science Congress held in Paris in 1867, at which Helmholtz was\npresent, a colleague of his was greeted with unanimous applause when he\ntoasted him with the words: \"L'ophthalmologie \u00e9tait dans les\nt\u00e9n\u00e8bres,--Dieu parla, que Helmholtz naqu\u00eet--Et la lumi\u00e8re \u00e9tait\nfaite!\" It was an almost exact paraphrase of the homage which Pope once\naddressed to Newton. At that time the words of the toast were re-echoed\nthroughout the world; ophthalmology was enlarged to science generally,\nand the apotheosis was applied universally. Du Bois-Reymond declared\nthat no other nation had in its scientific literature a book that could\nbe compared with Helmholtz's works on Physiological Optics and on\nSensations of Tone. Helmholtz was regarded as a god, and there are not a\nfew to whom he still appears crowned with this divine halo.\n\nA shrill voice pierced the serene atmosphere, attacking one of his main\nachievements. The dissentient was Eugen D\u00fchring, to whose essay on the\nPrinciples of Mechanics a coveted prize was awarded, a fact which seemed\nto stamp him as being specially authorized to be a judge of pre-eminent\nachievements in this sphere. D\u00fchring's aim was to dislodge one of the\nfundamental supports of Helmholtz's reputation by attacking his \"Law of\nthe Conservation of Energy.\" If this assault proved successful, the god\nwould lie shattered at his own pedestal.\n\nD\u00fchring, indeed, used every means to bespatter his fair name in\nscience; and it is hardly necessary to remark that Einstein abhors this\nkind of polemic. What is more, he regards it as a pathological symptom,\nand has only a smile of disdain for many of D\u00fchring's pithy sayings. He\nregards them as documents of unconscious humour to be preserved in the\narchives of science as warnings against future repetitions of such\nmethods.\n\nD\u00fchring belonged also to those who wished to exalt one above all\nothers. He raised an altar to Robert Mayer, and offered up sanguinary\nsacrifices. Accustomed to doing his work thoroughly, he did not stop at\nHelmholtz in choosing his victims. No hecatomb seemed to him too great\nto do honour to the discoverer of the Mechanical Equivalent of Heat, and\nso his next prey was Gauss and Riemann.\n\nGauss and Riemann! Each was a giant in Einstein's opinion. He knew well\nthat this raging Ajax had also made an assault against them, but he had\nno longer a clear recollection of the detailed circumstances; as the\nreferences were near at hand, he allowed me to repeat a few lines of\nthis tragi-comedy.\n\nHelmholtz, according to D\u00fchring (who also calls him \"Helmklotz\"), has\ndone no more than distort Mayer's fundamental mechanical idea, and\ninterpret it falsely. By \"philosophizing\" over it, he has completely\nspoilt it, and rendered it absurd. It was the greatest of all\nhumiliations practised on Mayer that his name had been coupled with that\nof one whom he had easily out-distanced, and whose clumsy attempts at\nbeing a physicist were even worse than those by which he sought to\nestablish himself as a philosopher.\n\nThe offences of Gauss and Riemann against Mayer are shrouded in\ndarkness. But there was another would-be scientist, Justus von Liebig,\nwho, being opposed to Mayer, aroused the suspicions of D\u00fchring,\nparticularly as he had used his \"brazen-tongue\" to defend the two\nrenowned mathematicians. After he, and Clausius too, had been brought to\nearth, D\u00fchring launched out against the giants of G\u00f6ttingen. In the\nchapter on Gauss and \"Gauss-worship,\" we read: \"His megalomania rendered\nit impossible for him to take exception to any tricks that the deficient\nparts of his own brain played on him, particularly in the realm of\ngeometry. Thus he arrived at a pretentiously mystical denial of Euclid's\naxioms and theorems, and proceeded to set up the foundations of an\napocalyptic geometry not only of nonsense but of absolute stupidity....\nThey are abortive products of the deranged mind of a mathematical\nprofessor, whose mania for greatness proclaims them as new and\nsuperhuman truths!... The mathematical delusions and deranged ideas in\nquestion are the fruits of a veritable _paranoia geometrica_.\"\n\nAfter Herostratus had burnt to ashes the consecrated temple, the Ionian\ncities issued a proclamation that his name was to be condemned to\nperpetual oblivion! The iconoclast D\u00fchring is immortalized, for, apart\nfrom the charge of arson, he is notable in himself. In his case we found\nourselves confronted with unfathomable problems of a scholar's complex\nnature, problems which even a searcher like Einstein failed to solve.\nThe simplest solution would be to turn the tables and to apply the term\n\"paranoia\" as a criticism to the book on Robert Mayer, and thus demolish\nit. But this will not do, for if we merely pass over the pages of\ndistorted thought, we are still left with a considerable quantity of\nvaluable material.\n\nDoes D\u00fchring, after all, himself deserve a place in our Valhalla? The\nquestion seems monstrous, and yet cannot be directly answered in the\nnegative. The individual is to be judged according to his greatest\nachievement, and not according to his aberrations. The works of\nAristotle teem with nonsensical utterances, and Leonardo's _Bestiarius_\nis an orgy of abstruse concoctions. If D\u00fchring had written nothing\nbeyond his studies of personalities ranging from Archimedes to Lagrange,\nthe portals would yet have been open to him. Even in his eulogy of\nRobert Mayer, which is besmirched with unseemly remarks, he displays at\nleast the courage of his convictions.\n\nThe attempt at a comparison between Robert Mayer and Helmholtz is doomed\nto failure even when considered dispassionately, inasmuch as the\ndisturbing factor of priority here intrudes itself. The definite fixing\nof the Law of Energy is certainly to the credit of Helmholtz, but\nperhaps he would have gained by laying more stress on the discovery of\nit five years earlier by the doctor in Heilbronn. And again, this would\nnot have been final, for the invariance of the sum of energy during\nmechanical actions was known even by Huyghens. The Heilbronn doctor\nperformed one act of genius in his life, whereas Helmholtz during his\nwhole life moved asymptotically to the fine of genius without ever\nreaching it. If my interpretation of Einstein's opinion is correct,\nHelmholtz is to be credited with having the splendour of an overpowering\ngift for research predominant in his nature, but is not necessarily to\nbe given a seat among the most illustrious of his branch of science.\nEinstein wishes to preserve a certain line of demarcation between this\ntype and not only the Titans of the past, but also those of the present.\nWhen he speaks of the latter, his tone becomes warmer. He does not need\ncircuitous expressions, each syllable rings with praise. He has in mind,\nabove all, Hendrik Antoon Lorentz in Leyden, Max Planck, and Niels Bohr;\nwe then see that he feels Valhalla about him.\n\n     *     *     *     *     *     *     *     *\n\nThe reason that I have tried to maintain the metaphor of a Temple of\nFame is due to an echo of Einstein's own words at a celebration held in\nhonour of the sixtieth birthday of the physicist Planck in the May of\n1918. This speech created the impression of a happy harmony resulting\nfrom a fusion of two melodies, one springing from the intellect, the\nother rising from the heart. We were standing as at the Propylons with a\nnew Heraclitus uttering the cry: Introite, nam et hic dii sunt!\n\nI should like to give the gist of this beautiful address in an extract\nuninterrupted by commentaries.\n\n\"The Temple of Science\"--so Einstein began--\"is a complex structure of\nmany parts. Not only are the inmates diverse in nature, but so also are\nthe inner forces that they have introduced into the temple. Many a one\namong them is engaged in Science with a happy feeling of a superior\nmind, and finds Science the sport which is congenial to him, and which\nis to give him an outlet for his strong life-forces, and to bring him\nthe realization of his ambitions. There are, indeed, many, too, who\noffer up their sacrifice of brain-matter only in the cause of useful\nachievements. If now an angel of heaven were to come and expel all from\nthe temple who belonged to these two categories, a considerable\nreduction would result, but there would still remain within the temple\nmen of present and former times: among these we count our Planck, and\nthat is why he has our warm affection.\n\n\"I know full well that, in doing this, we have light-heartedly caused\nmany to be driven out who contributed much to the building of the\ntemple; in many cases our angel would find a decision difficult.... But\nlet us fix our gaze on those who find full favour with him! Most of them\nare peculiar, reserved, and lonely men, who, in spite of what they have\nin common, are really less alike than those who have been expelled. What\nled them into the temple?... In the first place, I agree with\nSchopenhauer that one of the most powerful motives that attract people\nto Science and Art is the longing to escape from everyday life with its\npainful coarseness and unconsoling barrenness, and to break the fetters\nof their own ever-changing desires. It drives those of keener\nsensibility out of their personal existence into the world of objective\nperception and understanding. This motive force is similar to the\nlonging which makes the city-dweller leave his noisy, confused\nsurroundings and draws him with irresistible force to restful Alpine\nheights, where his gaze covers the wide expanse lying peacefully before\nhim on all sides, and softly passes over the motionless outlines that\nseem created for all eternity. Associated with this negative motive is a\npositive one, by virtue of which Man seeks to form a simplified\nsynoptical view of the world in a manner conformable to his own nature,\nin order to overcome the world of experience by replacing it, to a\ncertain degree, by this picture. This is what the painter does, as also\nthe poet, the speculative philosopher, and the research scientist, each\nin his own way. He transfers the centre of his emotional existence into\nthis picture, in order to find a sure haven of peace, one such as is not\noffered in the narrow limits of turbulent personal experience.\n\n\"What position does the world-picture of the theoretical physicist\noccupy among all those that are possible? He demands the greatest rigour\nand accuracy in his representation, such as can be gained only by using\nthe language of mathematics. But for this very reason the physicist has\nto be more modest than others in his choice of material, and must\nconfine himself to the simplest events of the empirical world, since all\nthe more complex events cannot be traced by the human mind with that\nrefined exactness and logical sequence which the physicist demands....\nIs the result of such a restricted effort worthy of the proud name\n'world-picture'?\n\n\"I believe this distinction is well deserved, for the most general laws\non which the system of ideas set up by theoretical physics is founded\nclaim to be valid for every kind of natural phenomenon. From them it\nshould be possible by means of pure deduction to find the picture, that\nis, the theory, of every natural process, including those of living\norganism, provided that this process of deduction does not exceed the\npowers of human thought. Thus there is no fundamental reason why the\nphysical picture of the world should fall short of perfection....\n\n\"Evolution has shown that among all conceivable theoretical\nconstructions there is at each period one which shows itself to be\nsuperior to all others, and that the world of perception determines in\npractice the theoretical system, although there is no logical road from\nperception to the axioms of the theory, but rather that we are led\ntowards the latter by our intuition, which establishes contact with\nexperience....\n\n\"The longing to discover the _pre-established harmony_ recognized by\nLeibniz is the source of the inexhaustible patience with which we see\nPlanck devoting himself to the general problems of our science, refusing\nto allow himself to be distracted by more grateful and more easily\nattainable objects.... The emotional condition which fits him for his\ntask is akin to that of a devotee or a lover; his daily striving is not\nthe result of a definite purpose or a programme of action, but of a\ndirect need.... May his love for Science grace his future course of\nlife, and lead him to a solution of that all-important problem of the\nday which he himself propounded, and to an understanding of which he has\ncontributed so much! May he succeed in combining the Quantum Theory with\nElectrodynamics and Mechanics in a logically complete system!\"\n\n     *     *     *     *     *     *     *     *\n\n\"What grips me most in your address,\" I said, \"is that it simultaneously\nsurveys the whole horizon of science in every direction, and traces back\nthe longing for knowledge to its root in emotion. When your speech was\nconcluded, I regretted only one thing--that it had ended so soon.\nFortunate is he who may study the text.\"\n\n\"Do you attach any importance to it?\" asked Einstein; \"then accept this\nmanuscript.\" It is due to this act of generosity that I have been able\nto adorn the foregoing description of the excursion into Valhalla with\nsuch a valuable supplement.\n\n     *     *     *     *     *     *     *     *\n\nThe conversation had begun with the brilliant constellation\nGalilei-Newton, and near the end inclined again towards the\nconsideration of a double-star: the names of Faraday and Maxwell\npresented themselves.\n\n\"Both pairs,\" Einstein declared, \"are of the same magnitude. I regard\nthem as fundamentally equal in their services in the onward march of\nknowledge.\"\n\n\"Should we not have to add Heinrich Hertz as a third in this bond? This\nassistant of Helmholtz is surely regarded as one of the founders of the\nElectromagnetic Theory of Light, and we often hear their names coupled,\nas in the case of the Maxwell-Hertz equations.\"\n\n\"Doubtless,\" replied Einstein, \"Hertz, who is often mentioned together\nwith Maxwell, has an important rank and must be placed very high in the\nworld of experimental physics, yet, as regards the influence of his\nscientific personality, he cannot be classed with the others we have\nnamed. Let us, then, confine ourselves to the twin geniuses Faraday and\nMaxwell, whose intellectual achievement may be summarized in a few\nwords. Classical mechanics referred all phenomena, electrical as well as\nmechanical, to the direct action of particles on one another,\nirrespective of their distances from one another. The simplest law of\nthis kind is Newton's expression: 'Attraction equals Mass times Mass\ndivided by the square of the distance.' In contradistinction to this,\nFaraday and Maxwell have introduced an entirely new kind of physical\nrealities, namely, _fields of force_. The introduction of these new\nrealities gives us the enormous advantage that, in the first place, the\nconception of action at a distance, which is contrary to our everyday\nexperience, is made unnecessary, inasmuch as the fields are superimposed\nin space from point to point without a break; in the second place, the\nlaws for the field, especially in the case of electricity, assume a much\nsimpler form than if no field be assumed, and only masses and motions be\nregarded as realities.\"\n\nHe enlarged still further on the subject of fields, and while he was\ndescribing the technical details, I saw him metaphorically enveloped in\na magnetic field of force. Here, too, an influence, transmitted through\nspace from point to point, made itself felt, and there could be no\nquestion of action \"at a distance\" inasmuch as the effective source was\nso near at hand. His gaze, as if drawn magnetically, passed along the\nwall of the room and fixed affectionately on Maxwell and Faraday.\n\n\n\n\nCHAPTER IV\n\nEDUCATION\n\nSchool Curricula and Reform of Teaching.--Value of Language Study.--Economy\nof Time.--Practice in Manual Work.--Picturesque Illustrations.--Art\nof Lecturing.--Selection of Talents by Means of Examinations.--Women\nStudents.--Social Difficulties.--Necessity as Instructress.\n\n\nOUR conversation turned towards a series of p\u00e6dagogic questions, in\nwhich Einstein is deeply interested. For he himself is actively engaged\nin teaching, and never disguises the pleasure which he derives from\nimparting instruction. Without doubt he has a gift of making his spoken\nwords react on wide circles anxious to be instructed, composed not only\nof University students, but of many others quite outside this category.\nWhen, recently, popular lectures on a large scale were instituted, he\nwas one of the first to offer his services in this sound undertaking. He\nlectured to people of the working class, who could not be assumed to\nhave any preliminary information on the subject, and he succeeded in\npresenting his lectures so that even the less trained minds could easily\nfollow his argument.\n\nHis attitude towards general questions of school education is, of\ncourse, conditioned by his own personality and his own work in the past.\nHis first care is that a young person should get an insight into the\nrelationship underlying natural phenomena, that is, that the curricula\nshould be mapped out so that a knowledge of facts is the predominating\naim.\n\n\"My wish,\" Einstein declared to me, \"is far removed from the desire to\neliminate altogether the fundamental features of the old grammar\nschools, with their preference for Latin, by making over-hasty reforms,\nbut I am just as little inclined to wax enthusiastic about the so-called\nhumanistic schools. Certain recollections of my own school life suffice\nto prevent this, and still more, a certain presentiment of the\neducational problems of the future.\"--\"To speak quite candidly,\" he\nsaid, \"in my opinion the educative value of languages is, in general,\nmuch over-estimated.\"\n\nI took the liberty of quoting a saying that is still regarded as\nirrefutable by certain scholars. It was Charles V who said: \"Each\nadditional acquired language represents an additional personality\"; and\nto suggest the root of language formation he said it in Latin: \"Quot\nlinguas quis callet, tot homines valet.\" This saying has been handed\ndown through the ages in German in the form: \"Soviel Sprachen, soviel\nSinnen\" (An added language means an added sense).\n\nEinstein replied: \"I doubt whether this aphorism is generally valid, for\nI believe that it would at no time have stood a real test. All\nexperience contradicts it. Otherwise we should be compelled to assign\nthe highest positions among intellectual beings to linguistic athletes\nlike Mithridates, Mezzofanti, and similar persons. The exact opposite,\nindeed, may be proved, namely, that in the case of the strongest\npersonalities, and of those who have contributed most to progress, the\nmultiplicity of their senses in no wise depended on a comprehensive\nknowledge of languages, but rather that they avoided burdening their\nminds with things that made excessive claims on their memories.\"\n\n\"Certainly,\" said I, \"it may be admitted that this gives rise to\nexaggeration in some cases, and that the linguistic sort of sport\npractised by many a scholar degenerates to a mere display of knowledge.\nAn intellectual achievement of lasting merit has very rarely or never\nbeen the result of a superabundance of acquired linguistic knowledge. An\ninstance occurs to me at this moment. Nietzsche became a philosopher of\nfar-reaching influence only after he had passed the stage of the\nphilologist. As far as our present discussion is concerned, the question\nis narrowed down considerably: it reduces itself to inquiring whether we\ndo sufficient, too little, or too much Greek and Latin. I must remark at\nthe very outset that, formerly, school requirements went much further in\nthis respect than nowadays, when we scarcely meet with a scholar even in\nthe upper classes who knows Latin and Greek perfectly.\"\n\nIt is just this fact that Einstein regards as a sign of improvement and\na result of examining the true aims of a school. He continued: \"Man must\nbe educated to 'react delicately'; he is to acquire and develop\n'intellectual muscles'! And the methods of language drill are much less\nsuited to this purpose than those of a more general training that gives\ngreatest weight to a sharpening of one's own powers of reflection.\nNaturally, the inclination of the pupil for a particular profession must\nnot be neglected, especially in view of the circumstance that such\ninclination usually asserts itself at an early age, being occasioned by\npersonal gifts, by examples of other members of the family, and by\nvarious circumstances that affect the choice of his future life-work.\nThat is why I support the introduction into schools, particularly\nschools devoted to classics, of a division into two branches at, say,\nthe fourth form, so that at this stage the young pupil has to decide in\nfavour of one or other of the courses. The elementary foundation to the\nfourth form may be made uniform for all, as they are concerned with\nfactors on education that are scarcely open to the danger of being\nexaggerated in any one direction. If the pupil finds that he has a\nspecial interest in what are called _humaniora_ by the educationist, let\nhim by all means continue along the road of Latin and Greek, and,\nindeed, without being burdened by tasks that, owing to his disposition,\noppress or alarm him.\"\n\n\"You are referring,\" I interposed, \"to the distress which pupils feel in\nthe time allotted to mathematics. There are actually people of\nconsiderable intelligence who seem to be smitten with absolute stupidity\nwhen confronted with mathematics, and whose school-life becomes poisoned\nowing to the torment caused by this subject. There are many cases of\nliving surgeons, lawyers, historians, and litterateurs, who, till late\nin life, are visited by dreams of their earlier mathematical ordeals.\nTheir horror has a very real foundation, for, whereas the pupil who is\nbad at Latin yet manages to get an idea of the language, and he who is\nweak in history has at least a notion of what is being discussed, the\none who is unmathematical by nature has to worry his way through\nnumberless lessons in a subject which is entirely incomprehensible to\nhim, as if belonging to another world and being presented to him in a\ntotally strange tongue. He is expected to answer questions, the sense of\nwhich he cannot even guess, and to solve problems, every word and every\nfigure of which glares at him like a sphinx of evil omen. Sitting on\neach side of him are pupils to whom this is merely play, and some of\nwhom could complete the whole of school mathematics within a few months\nat express rate. This leads to a contrast between the pupils, which may\npress with tragical force on the unfortunate member throughout his whole\nschool existence. That is why a reform is to be welcomed that sifts out\nin time those who should be separated from the rest, and which adapts\nthe school curriculum as closely as possible to individual talents.\"\n\nEinstein called my attention to the fact that this division had already\nbeen made in many schools in foreign countries, as in France and in\nDenmark, although not so exclusively as suggested by him. \"Moreover,\" he\nadded, \"I am by no means decided whether the torments that you mentioned\nare founded primarily on absence of talent in the pupil. I feel much\nmore inclined to throw the responsibility in most cases on the absence\nof talent in the teacher. Most teachers waste their time by asking\nquestions which are intended to discover what a pupil does _not_ know,\nwhereas the true art of questioning has for its purpose to discover what\nthe pupil knows or is capable of knowing. Whenever sins of this sort are\ncommitted--and they occur in all branches of knowledge--the personality\nof the teacher is mostly at fault. The results of the class furnish an\nindex for the quality of the preceptor. All things being taken into\nconsideration, the average of ability in the class moves, with only\nslight fluctuations, about mean values, with which tolerably\nsatisfactory results may be obtained. If the progress of the class is\nnot up to this standard, we must not speak of a bad year but rather of\nan inefficient instructor. It may be assumed that, as a rule, the\nteacher understands the subject with which he is entrusted, and has\nmastered its content, but not that he knows how to impart his\ninformation in an interesting manner. This is almost always the source\nof the trouble. If the teacher generates an atmosphere of boredom, the\nprogress is stunted in the suffocating surroundings. To know how to\nteach is to be able to make the subject of instruction interesting, to\npresent it, even if it happens to be abstract, so that the soul of the\npupil resonates in sympathy with that of his instructor, and so that the\ncuriosity of the pupil is never allowed to wane.\"\n\n\"That is in itself an ideal postulate. If we assume it to be fulfilled,\nhow do you wish to see the subjects distributed in the curriculum?\"\n\n\"We must leave the detailed discussion of this question for another\noccasion. One of the main points would be the economy of time; all that\nis superfluous, vexatious, and only intended as a drill must be\ndropped. At present the aim of the whole course is the leaving\ncertificate. This test must be given up!\"\n\n\"Is that serious. Professor? Do you wish to do away with the examination\nfor matriculation?\"\n\n\"Exactly. For it is like some fearful monster guarding our exit from\nschool, throwing its shadow far ahead, and compelling teacher and pupil\nto work incessantly towards an artificial show of knowledge. This\nexamination has been elevated by forcible means to a level which the\nviolently drilled candidates can keep only for a few hours, and is then\nlost to sight for ever. If it is eliminated, it will carry away with it\nthis painful drilling of the memory; it will no longer be necessary to\nhammer in for years what will be entirely forgotten within a few months,\nand what deserves to be forgotten. Let us return to Nature, which\nupholds the principle of getting the maximum amount of effect from the\nminimum of effort, whereas the matriculation test does exactly the\nopposite.\"\n\n\"Yes, but who is then to be allowed to enter the university?\"\n\n\"Every one who has shown himself to be capable not only in a crucial\ntest of an accidental kind, but in his whole behaviour. The teacher will\nbe the judge of this, and if he does not know who is qualified, he again\nis to be blamed. He will find it so much the easier to decide who is\nsufficiently advanced to obtain a leaving certificate, in proportion as\nthe curriculum has weighed less on the minds of the young people. Six\nhours a day should be ample--four at school and two for home-work; that\nshould be the maximum. If this should appear too little to you, I must\nask you to bear in mind that a young mind is being subjected to strain\neven in leisure hours, as it has to receive a whole world of\nperceptions. And if you ask how the steadily increasing curriculum is to\nbe covered in this very moderate number of hours, my answer is: Throw\nall that is unnecessary overboard! I count as unnecessary the major part\nof the subject that is called 'Universal History,' and which is, as a\nrule, nothing more than a blurred mass of history compressed into dry\ntables of names and dates. This subject should be brought within the\nnarrowest possible limits, and should be presented only in broad\noutline, without dates having to be crammed. Leave as many gaps as you\nlike, especially in ancient history; they will not make themselves felt\nin our ordinary existences. In nowise can I regard it as a misfortune if\nthe pupil learns nothing of Alexander the Great, and of the dozens of\nother conquerors whose documentary remains burden his memory like so\nmuch useless ballast. If he is to get a glimpse of the grey dawn of\ntime, let him be spared from Cyrus, Artaxerxes, and Vercingetorix, but\nrather tell him something of the pioneers of civilization, Archimedes,\nPtolemy, Hero, Appolonius, and of inventors and discoverers, so that the\ncourse does not resolve into a series of adventures and massacres.\"\n\n\"Would it not be expedient,\" I interrupted, \"to take some of the history\ntime to branch off into an elementary treatment of the real evolution of\nthe state, including sociology and the legal code?\"\n\nEinstein does not consider this desirable, although he himself is deeply\ninterested in all manifestations of public life. He does not favour an\nelementary political training received at school, presumably above all\nowing to the fact that in this branch the instruction cannot be removed\nfrom official influences, and because political questions require the\nattention of a mature mind. His picture of how a youth is to meet the\nrequirements of modern life is something quite different, far removed\nfrom all theories. His whole efforts are directed at finding a means of\ncounteracting the tendency to overburden one side of the youthful mind.\n\"I should demand the introduction of compulsory practical work. Every\npupil must learn some _handicraft_. He should be able to choose for\nhimself which it is to be, but I should allow no one to grow up without\nhaving gained some technique, either as a joiner, bookbinder, locksmith,\nor member of any other trade, and without having delivered some useful\nproduct of his trade.\"\n\n\"Do you attach greater importance to the technique itself or to the\nfeeling of social relationship with the broad masses of the people which\nit engenders?\"\n\n\"Both factors are equally important to me,\" said Einstein, \"and others\nbecome added to these which help to justify my wish in this respect. The\nhandiwork need not be used as a means of earning money by the pupil of\nthe secondary school, but it will enlarge and make more solid the\nfoundation on which he will rest as an ethical being. In the first\nplace, the school is not to produce future officials, scholars,\nlecturers, barristers, and authors, but human beings, not merely mental\nmachines. Prometheus did not begin his education of mankind with\nastronomy, but by teaching the properties of fire and its practical\nuses....\"\n\n\"This brings to my mind another analogy,\" I continued, \"namely, that of\nthe old _Meistersinger_, who were, all of them, expert smiths, tinkers,\nor shoemakers, and yet succeeded in building a bridge to the arts. And\nat bottom, the sciences, too, belong to the category of free arts. Yet,\na difficulty seems to me to arise. In demanding a compulsory handicraft,\nyou lay stress on practical use, whereas in your other remarks you\ndeclared science in itself as being utterly independent of practice.\"\n\n\"I do this,\" replied Einstein, \"only when I speak of the ultimate aims\nof pure research, that is, of aims that are visible to only a vanishing\nminority. It would be a complete misconception of life to uphold this\npoint of view and to expect its regulative effectiveness in cases in\nwhich we are dealing only with the preliminaries of science. On the\ncontrary, I maintain that science can be taught much more practically at\nschools than it is at present when bookwork has the upper hand. For\nexample, to return to the question of mathematical teaching: it seems to\nme to be almost universally at fault, if only for the reason that it is\nnot built up on what is _practically_ interesting, what appeals directly\nto the senses, and what can be seized intuitively. Child-minds are fed\nwith definitions instead of being presented with what they can grasp,\nand they are expected to be able to understand purely conceptual things,\nalthough they have had no opportunity given them of arriving at the\nabstract by way of concrete things. It is very easy to do the latter.\nThe first beginnings should not be taught in the schoolroom at all, but\nin open Nature. A boy should be shown how a meadow is measured and\ncompared with another. His attention must be directed to the height of a\ntower, to the length of his shadow at various times, to the\ncorresponding altitude of the sun; by this means he will grasp the\nmathematical relationships much more rapidly, more surely, and with\ngreater zeal, than if words and chalk-marks are used to instil into him\nthe conceptions of dimensions, of angles, or perchance of some\ntrigonometrical function. What is the actual origin of such branches of\nscience? They are derived from practice, as, for example, when Thales\nfirst measured the height of the pyramids with the help of a short rod,\nwhich he set up at the ultimate point of the pyramid's shadow. Place a\nstick in the boy's hand and lead him on to make experiments with it by\nway of a game, and if he is not quite devoid of sense, he will discover\nthe thing for himself. It will please him to have discovered the height\nof the tower without having climbed it, and this is the first thrill of\nthe pleasure which he feels later when he learns the geometry of similar\ntriangles and the proportionality of their sides.\"\n\n\"In the matter of physics,\" pursued Einstein, \"the first lessons should\ncontain nothing but what is experimental and interesting to see. A\npretty experiment is in itself often more valuable than twenty formul\u00e6\nextracted from our minds; it is particularly important that a young mind\nthat has yet to find its way about in the world of phenomena should be\nspared from formul\u00e6 altogether. In his physics they play exactly the\nsame weird and fearful part as the figures of dates in Universal\nHistory. If the experimenter is ingenious and expert, this subject may\nbe begun as early as in the middle forms, and one may then count on a\nresponsiveness that is rarely observable during the hours of exercise in\nLatin grammar.\"\n\n\"This leads me,\" said Einstein, \"to speak in this connexion of a means\nof education that has so far been used only by way of trial in\nclass-teaching, but from an improved application of which I expect\nfruitful results later. I mean the school cinema. The triumphal march of\nthe cinematograph will be continued into pedagogic regions, and here it\nwill have a chance to make good its wrongs in thousands of picture shows\nin showing absurd, immoral, and melodramatic subjects. By means of the\nschool-film, supplemented by a simple apparatus for projection, it would\nbe possible firstly to infuse into certain subjects, such as geography,\nwhich is at present wound off organ-like in the form of dead\ndescriptions, the pulsating life of a metropolis. And the lines on a map\nwill gain an entirely new complexion in the eyes of the pupil, if he\nlearns, as if during a voyage, what they actually include, and what is\nto be read between them. An abundance of information is imparted by the\nfilm, too, if it gives an accelerated or retarded view of such things as\na plant growing, an animal's heart beating, or the wing of an insect\nmoving. The cinema seems to me to have a still more important function\nin giving pupils an insight into the most important branches of\ntechnical industry, a knowledge of which should become common property.\nVery few hours would suffice to impress permanently on the schoolboy's\nmind how a power-station, a locomotive, a newspaper, a book, or a\ncoloured illustration is produced, or what takes place in an electrical\nplant, a glass factory, or a gasworks. And, to return to natural\nscience, many of the rather difficult experiments that cannot be shown\nby means of school apparatus may be shown with almost as great clearness\non a film. Taken all in all, the redeeming word in school-teaching is,\nfor me: an increased appeal to the senses. Wherever it is possible,\nlearning must become living, and this principle will predominate in\nfuture reforms of school-teaching.\"\n\n     *     *     *     *     *     *     *     *\n\nUniversity study was only touched on lightly during this talk. It has\nbecome known that Einstein is a very strong supporter of the principle\nof free learning, and that he would prefer to dispense entirely with the\nregular documents of admission which qualify holders to attend lecture\ncourses. This is to be interpreted as meaning that as soon as anyone\ndesirous of furthering his studies has demonstrated his fitness to\nfollow the lecturer's reasoning by showing his ability in class\nexercises or in the laboratory, he should be admitted immediately.\nEinstein would not demand the usual certificate of \"general education,\"\nbut only of fitness for the special subject, particularly as, in his own\nexperience, he has frequently found the cleverest people and those with\nthe most definite aims to be prone to one-sidedness. According to this,\neven the intermediate schools should be authorized to bestow a\ncertificate of fitness to enter on a course in a single definite subject\nas soon as the pupil has proved himself to have the necessary ability.\nIf he earlier spoke in favour of abolishing the matriculation\nexamination, this is only an indication of his effort to burst open the\nportals of higher education for every one. Nevertheless, I remarked\nthat, in the course of university work itself, he is not in favour of\ngiving up all regulation concerning the ability of the student--at\nleast, not in the case of those who intend to devote themselves to\ninstruction later. He does not desire an intermediate examination (in\nthe nature of the _tentamen physicum_ of doctors), but he considers it\nprofitable for the future schoolmaster to have an opportunity early in\nhis course to prove his fitness for teaching. In this matter, too,\nEinstein reveals his affectionate interest in the younger generation,\nwhose development is threatened by nothing so much as by incapable\nteachers: the sum of these considerations is that the pupil is examined\nas little as possible, but the teacher so much the more closely. A\ncandidate for the teaching profession, who in the early stages of his\nacademic career fails to show his fitness, his individual _facultas\ndocendi_, should be removed from the university.\n\nThere can be no doubt but that Einstein has a claim to be heard as an\nauthority on these questions. There are few in the realm of the learned\nin whose faces it is so clearly manifest that they are called to excite\na desire for knowledge by means of the living word, and to satisfy this\ndesire. If great audiences assemble around him, if so many foreign\nacademies open their arms to him to make him their own, these are not\nonly signs of a magnetic influence that emanates from the famous\ndiscoverer, but they are indications that he is far famed as a teacher\nwith a captivating personality. Let us consider what this signifies in\nhis profession. Philosophers, historians, lawyers, doctors, and\ntheologians have at their disposal innumerable words which they merely\nneed to pronounce to get into immediate contact with their audiences. In\nEinstein's profession, theoretical physics, man disappears; it leaves no\nscope for the play of emotion; its implement mathematics--and what an\ninstrument it is!--bristles with formal difficulties, which can be\novercome only by means of symbols and by using a language which has no\nmeans of displaying eloquence, being devoid of expression, emotion, and\nregular periods. Yet here we have a physicist, a mathematician, whose\nfirst word throws a charm over a great crowd of people, and who extracts\nfrom their minds, so to speak, what, in reality, he alone works out\nbefore them. He does not adhere closely to written pages, nor to a\nscheme which has been prepared beforehand in all its details; he\ndevelops his subject freely, without the slightest attempt at rhetoric,\nbut with an effect which comes of itself when the audience feels itself\nswept along by the current. He does not need to deliver his words\npassionately, as his passion for teaching is so manifest. Even in\nregions of thought in which usually only formul\u00e6, like glaciers, give\nan indication of the height, he discovers similes and illustrations with\na human appeal, by the aid of which he helps many a one to conquer the\nmountain sickness of mathematics. His lectures betray two factors that\nare rarely found present in investigators of abstract subjects; they are\ntemperament and geniality. He never talks as if in a monologue or as if\naddressing empty space. He always speaks like one who is weaving threads\nof some idea, and these become spun out in a fascinating way that robs\nthe audience of the sense of time. We all know that no iron curtain\nmarks the close of Einstein's lecture; anyone who is tormented by some\ndifficulty or doubt, or who desires illumination on some point, or has\nmissed some part of the argument, is at liberty to question him.\nMoreover, Einstein stands firm through the storm of all questions. On\nthe very day on which the above conversation took place he had come\nstraight from a lecture on four-dimensional space, at the conclusion of\nwhich a tempest of questions had raged about him. He spoke of it not as\nof an ordeal that he had survived, but as of a refreshing shower. And\nsuch delights abound in his teaching career.\n\n     *     *     *     *     *     *     *     *\n\nIt was the last lecture before his departure for Leyden (in May 1920),\nwhere the famous faculty of science, under the auspices of the great\nphysicist Lorentz, had invited him to accept an honorary professorship.\nThis was not the first invitation of this kind, and will not be the\nlast, for distinctions are being showered on him from all parts of the\nworld. It is true that the universities who confer a degree on him\n_honoris causa_ are conferring a distinction on themselves, but Einstein\nfrankly acknowledges the value of these honours, which he regards as\nreferring only to the question in hand, and not the person. It gives him\npleasure on account of the principle involved being recognized, and he\nregards himself essentially only as one whom fate has ordained as the\npersonal exponent of these principles.\n\nWhat this life of hustle and bustle about a scientist signifies is\nperhaps more apparent to me, who have a modest share in these\nconversations, than to Einstein himself, for I am an old man\nwho--unfortunately--have to think back a long way to my student days,\nand can set up comparisons which are out of reach of Einstein. Formerly,\nmany years ago, but in my own time, there was an _auditorium maximum_\nwhich only one man could manage to fill with an audience, namely, Eugen\nD\u00fchring, the noted scholar, who was doomed to remain a lecturer\ninasmuch as he went under in his quarrels with confr\u00e8res of a higher\nrank. But before he made his onslaught against Helmholtz, he was\nregarded as a man of unrivalled magnetic power, for his philosophical\nand economical lectures gathered together over three hundred hearers, a\nrecord number in those times. Nowadays, in the case of Einstein, four\ntimes this number has been surpassed, a fact which has brought into\ncirculation the playful saying: One can never miss his auditorium;\nwhither all are hastening, that is the goal! To make just comparisons,\nwe must take account of the faithfulness of the assembled crowd, as well\nas its number. Many an eminent scholar has in earlier times had reason\nto declare, like Faust: \"I had the power to attract you, yet had no\npower to hold you.\" Helmholtz began regularly every term with a crowded\nlecture-hall, but in a short time he found himself deserted, and he\nhimself was well aware that no magnetic teaching influence emanated from\nhim. There is yet another case in university history of a brilliant\npersonality who, from similar flights of ecstasy, was doomed to\ndisappointment. I must mention his name, which, in this connexion, will\nprobably cause great surprise, namely, Schiller! He had fixed his first\nlecture in history at Jena, to which he was appointed, and had prepared\nfor an audience of about a hundred students. But crowd upon crowd\nhustled along, and Schiller, who saw the oncoming stream from his\nwindow, was overcome with the impression that there was no end to it.\nThe whole street took alarm, for at first it was imagined that a fire\nhad broken out, and at the palace the watch was called out--yet, a\nlittle later in the course, there was a depressing ebb of the tide,\nafter the first curiosity had been appeased; the audience gradually\nvanished into thin air, a proof of the fact that the nimbus of a name\ndoes not suffice to maintain the interest between the lecturer's desk\nand the audience.\n\nI mentioned this example at the time when Einstein's gift for teaching\nhad gradually increased the number of his hearers to the record figure\nof 1200, yet I did not on this occasion detect any inordinate joy in him\nabout his success. I gained the impression that he had strained his\nvoice in the vast hall. His mood betrayed in consequence a slight\nundercurrent of irritation. In an access of scepticism he murmured the\nwords, \"A mere matter of fashion.\" I cannot imagine that he was entirely\nin earnest. It goes without saying that I protested against the\nexpression. But, even if there were a particle of truth in it, we might\nwell be pleased to find such a fashion in intellectual matters, one that\npersists so long and promises to last. The world would recover its\nnormal healthy state if fashions of this kind were to come into full\nswing. It is, of course, easy to understand on psychological grounds\nthat Einstein himself takes up a sort of defensive position against his\nown renown, and that he occasionally tries to attack it by means of\nsarcasm, seeing that he cannot find serious arguments to oppose it.\n\n     *     *     *     *     *     *     *     *\n\nWhether Einstein's ideas and proposals concerning educational reform\nwill be capable of realization throughout is a question that time alone\ncan answer. We must make it clear to ourselves that, if carried out\nalong free-thinking lines, they will demand certain sacrifices, and it\ndepends on the apportionment of these sacrifices as to what the next, or\nthe following, generation will have to exhibit in the way of mental\ntraining.\n\nAn appreciable restriction will have to be imposed on the time given to\nlanguages. It is a matter of deciding how far this will affect the\nfoundations that, under the collective term _humaniora_, have supported\nthe whole system of classical schools for centuries. The fundamental\nideas of reform, which, owing to the redivision of school-hours and the\neconomy of work, no longer claim precedence for languages, indicate that\nnot much will be left of the original Latin and Greek basis.\n\nWe have noticed above that Einstein, although he does not, in principle,\noppose the old classicism, no longer expects much good of it. But\nnowadays the state of affairs is such that it is hardly a question of\nsupporting or opposing its retention in fragmentary form. Whoever does\nnot support it with all his power strengthens indirectly the mighty\nchorus of those who are radically antagonistic to it. And it is a\nremarkable fact that this chorus includes many would-be authorities on\nlanguages who have influence among us because they are champions of the\ncause of retaining languages.\n\nThey do not wish to rescue languages as such, but only the German\ntongue; they point to the _humaniora_ of classical schools, or to\n_Humanisterei_, as they call it, as the enemy and corrupter of their\nlanguage. In what sense they mean this is obvious from their articles of\nfaith, of which I should like to cite a few in the original words of one\nof their party-leaders:\n\n\"Up to the time of the hazardous enterprise of Thomasius (who first\nannounced lectures in the German language in 1687) German scholars as a\nbody were the worst enemies of their own tongue.--Luther did not take\nhis models for writing German from the humanistic mimics who aped the\nold Latins. In the case of many, including Lessing and Goethe, we\nobserve them making a definite attempt to shake themselves free from the\nchaos of humanistic influences in Germany--The inheritance of\npseudo-learned concoctions of words stretches back to pretentious\nhumanism as do most of essential vices of learned styles.--The\nfar-reaching and lasting corruption of the German language by this\npoisonous Latin has its beginnings in the humanism of the sixteenth\ncentury.\"\n\nAnd, quite logically, these heralds extend their attacks along the whole\nacademic front. For, according to their point of view, the whole army of\nprofessors is deeply immersed in the language slime of the traditional\nhumanism of the Greeks and Latins. \"The whole language evil of our\ntimes,\" so these leaders say, \"is at bottom due to scientists, who, in\nthe opinionated guise of a language caste, and without enriching our\nconceptions in the slightest, seek by tinkling empty words to give us\nthe illusion of a new and particularly mysterious occult science, an\nimpression which is unfortunately often produced on ignorant minds....\nHowever many muddy outlets official institutions and language\nassociations may purge and block up, ditch-water from ever new quagmires\nand drains pours unceasingly into the stately stream of our language.\"\n\nThus the attack on the Latin and Greek language foundation in schools\nidentifies itself with the struggle against the academic world as a\nwhole, and a scholar who does defend the classical system of education\nwith all his might finds himself unconsciously drifting into the ranks\nof the brotherhood which in the last instance is seeking his own\nextermination.\n\nThis danger must not be under-estimated. It is just this peril, so\nthreatening to our civilization, that moves me to show my colours\nfrankly here. I am not a supporter of bookworm drudgery in schools, but\nI feel myself impelled to use every effort in speech and writing to\ncombat the anti-humanists whose password, \"For _our_ language,\" at root\nsignifies \"Enemies of Science!\"\n\nWe must put no weapons into their hands, and the only means to avoid\nthis is, in my opinion, to state our creed emphatically and openly after\nthe manner of almost all our classical writers.\n\nThis creed, both as regards language and substance, is to be understood\nas being based on the efficacy of the old classical languages. It is the\nluminous centre of the life and work of the men who caused Bulwer to\nproclaim our country the country of poets and thinkers. The\nsuperabundance of these is so excessive that it is scarcely fair to\nmention only a few names such as Goethe, Lessing, Schiller, Wieland,\nKant, and Schopenhauer. Our literature would be of a provincial standard\nand not a world possession if this creed had not asserted its sway at\nall times.\n\nIf the question is raised as to where our youth is to find time for\nlearning ancient languages under the present conditions of crowded\nsubjects, the answer is to be furnished by improved methods of\ninstruction. My personal point of view is that even the older methods\nwere not so bad. Goethe found himself in no wise embarrassed through\nlack of time in acquiring all sorts of knowledge and mental equipment,\nalthough even as a boy of eight years he could write in Latin in a way\nwhich, compared with the bungling efforts of the modern sixth-form boy,\nseems Ciceronian. Montaigne could express himself earlier in Latin than\nin French, and if he had not had this \"Latin poison\" injected into his\nblood he would never have become Montaigne.\n\nIt seems to me by no means impossible that the cultured world will one\nday in the distant future return to the once self-evident view of\nclassical languages, and indeed just for reasons of economy of time,\nunless the universal language so ardently desired by Hebbel--not to be\nconfused with the artificial patchwork called Esperanto--should become a\nreality. But even this language, at present Utopian, but one which will\nhelp to link together the nations, will disclose the model of the\nancient languages in its structure. Scientific language of the present\nday shows where the route lies; and this route will be made passable in\nspite of all the efforts of Teutonic language saints and assassins of\nhumanism to block it.\n\nThe working out of ideas by research scientists leads to enrichment of\nlanguage. And since, as is quite natural, they draw copiously on antique\nforms of expression, they are really the trustees of an instruction that\nmakes these expressions intelligible not merely as components of an\nartificial language like Volap\u00fck but as organic growths. That is how\nthey proceed when they carry on their research, or describe it and\nlecture on their own subject. But if they are to decide how the school\nis to map out its course in actual practice, the problem of time again\nbecomes their chief consideration--that is, they feel in duty bound to\ngive preference to what is most important. Hence there results the wish\nto reduce the hours apportioned to the language subjects as much as\npossible.\n\nOn this matter we have a detailed essay by the distinguished Ernst Mach\nmentioned earlier, who exposes the actual dilemma with the greatest\nclearness. He treats this exceedingly important question in all its\nphases, and arrives at almost the same conclusion as Einstein. At the\noutset he certainly chants a Latin psalm almost in the manner of\nSchopenhauer. Its lower tones represent an elegy lamenting that Latin is\nno longer the universal language among educated people, as it was from\nthe fifteenth to the eighteenth century. Its fitness for this purpose is\nquite indisputable, for it can be adapted to express every conception\nhowever modern or subtle it may be.\n\nWhat a profusion of new conceptions was introduced into science by Sir\nIsaac Newton, to all of which he succeeded in giving correct and precise\nLatin names! The natural inference suggests itself to us that young\npeople should learn the ancient classical tongues--and yet a different\nresult is coming about; the modern child is to be content with\nunderstanding words with a world-wide currency, without knowing their\nphilological origin.\n\nIt is not necessary to be a schoolmaster to feel the inadequacy of this\nproceeding. It is true that without knowing Arabic we can grasp the\nsense and meaning of the word \"Algebra,\" and in the same way we can\nextract the essence of a number of Greek and Latin expressions without\ndigging at their etymological roots. But these expressions are to be\ncounted in hundreds and thousands, and are increasing daily, so that we\nare put before the question whether, merely from the point of view of\ntime, it is practicable to learn them as individual foreign terms or as\nnatural products of a root language with which we have once and for all\nbecome familiar.\n\nIt is scarcely necessary for me to point out that Einstein himself is\nnot sparing in the use of these technical expressions, even when he is\nusing popular language. He assumes or introduces terms of which the\nfollowing are a few examples: continuum, co-ordinate system,\ndimensional, electrodynamics, kinetic theory, transformation, covariant,\nheuristic, parabola, translation, principle of equivalence, and he is\nquite justified in assuming that every one is fully acquainted with such\ngenerally accepted expressions as: gravitation, spectral analysis,\nballistic, phoronomy, infinitesimal, diagonal, component, periphery,\nhydrostatics, centrifugal, and numberless others which are diffused\nthrough educated popular language in all directions. Taken all together\nthese represent a foreign realm in which the entrant can always succeed\nin orientating himself when he receives explanations, examples, or\ntranslations, whereas with a little preliminary knowledge of the ancient\nlanguages he immediately feels himself at home with them; in this we\nhave not even taken into consideration the general cultural value of\nthis training in view of the access it gives to the old literature and\nto Hellenic culture.\n\nPerhaps I am going too far in adopting the attitude of a _laudator\ntemporis acti_ towards Einstein's very advanced opinion. We are here\ndealing with a question in which nothing can be proved, and in which\neverything depends on disposition and personal experiences. In my own\ncase this experience includes the fact that at a very early age, in\nspite of the very discouraging school methods, I enjoyed the study of\nLatin and Greek, and that I learned Horatian odes by heart, not because\nI had to, but because they appealed to me, and finally that Homer opened\nup a new world to me. When Einstein expresses his abhorrence of drill, I\nagree with him; but these languages need not be taught as if we are on\nparade. We see thus that it is a question of method and not of the\nsubject involved. Einstein gives the subject its due by recommending a\ndouble series of classes. He allows the paths to diverge, giving his\nspecial blessing to the group along the one without setting up obstacles\nto prevent the other pilgrims from attaining happiness in their own way.\n\n     *     *     *     *     *     *     *     *\n\nWe spoke of higher education for women, and Einstein expressed his views\nwhich, as was to be expected, were tolerant, and yet did not suggest\nthose of a champion of the cause. It was impossible to overlook the fact\nthat in spite of his approval he had certain reservations of a\ntheoretical nature.\n\n\"As in all other directions,\" he said, \"so in that of science the way\nshould be made easy for women. Yet it must not be taken amiss if I\nregard the possible results with a certain amount of scepticism. I am\nreferring to certain obstacles in woman's organization which we must\nregard as given by Nature, and which forbid us from applying the same\nstandard of expectation to women as to men.\"\n\n\"You believe, then, Professor, that high achievements cannot be\naccomplished by women? To keep our attention on science, can one not\nquote Madame Curie as a proof to the contrary?\"\n\n\"Surely only as one proof of brilliant exceptions, more of which may\noccur without refuting the statute of sexual organization.\"\n\n\"Perhaps this will be possible after all if a sufficient time for\ndevelopment be allowed. There may be much fewer geniuses among the other\nsex, but there has certainly been a concentration of talent. Or, in\nother words, totally ignorant women have become much rarer. You,\nProfessor, are fortunate in not being in a position to compare young\nwomen of to-day with those of forty or more years ago. This I can do,\nand just as once I found it natural that there should be swarms of\nlittle geese and peacocks, I never recover from my astonishment nowadays\nat the amount of knowledge acquired by young womanhood. It requires a\nconsiderable effort on my part very often to avoid being completely\novershadowed by a partner at dinner. The more this stratum of talent\nincreases, the more we have reason to expect a greater number of\ngeniuses from them in the future.\"\n\n\"You are given to prognostication,\" said Einstein, \"and calculate with\nprobabilities which sometimes are lacking in foundation. Increased\neducation and even an increase of talents are quantitative assumptions\nthat make an inference regarding higher quality reaching to genius\nappear very bold.\"--A passing look of ominous portent flashed over his\nface, and I noticed that he was preparing to launch a sarcastic\naphorism. So it was, for the next words were: \"It is conceivable that\nNature may have created a sex without brains!\"\n\nI grasped the sense of this grotesque remark, which was in no way to be\ntaken literally. It was intended as an amusing exaggeration of what he\nhad earlier called the reason for his failing expectation: the organic\ndifference which, being rooted in the physical constitution, had\nsomewhere to express itself on the mental plane, too. The soul of woman\nstrong in impulse shows a refinement of feeling of which we men are not\nsusceptible, whereas the greatest achievements of reason probably depend\non a preponderance of brain substance. It is this plus beyond the normal\namount that gives promise of great discoveries, inventions, and\ncreations. We can just as little imagine a female Galilei, Kepler, and\nDescartes, as a female Michelangelo or Sebastian Bach. But when we think\nof these extreme cases, let us also recall the balance on the other\nside: although a woman could not create the differential calculus, it\nwas she that created Leibniz; similarly she produced Kant if not the\nCritique of Pure Reason. Woman, as the author of all great minds, has at\nleast a right of access to all means of education and to all advancement\nthat is proffered by universities. And in this connexion Einstein\nexpressed his wish clearly enough.\n\n     *     *     *     *     *     *     *     *\n\nOne of the most discussed themes in matters touching school education is\nat the present time: \"the selection of gifted pupils.\" It has developed\ninto a principle that is generally recognized by the great majority, the\nonly point of disagreement being in respect to the number that is to be\nselected.\n\nThe idea running through it is that derived from Darwin's theory of\nselection: man completes the method of selection practised by Nature. He\nsifts and chooses, and allows those that are more talented to come to\nthe fore more rapidly and more decidedly; he favours their advancement\nand makes easy their ascent.\n\nThis principle has really always been in existence. It started with the\ndistribution of prizes in ancient Olympia and reaches to the present-day\nexaminations that are clearly intended as a means of selecting talents.\nA greater discrimination based on a systematic search for talents was\nreserved for our own day.\n\nIt was scarcely a matter of doubt to me what attitude Einstein would\ntake up towards this matter. I had already heard him say hard words\nabout the system of examinations, and knew his leaning towards allowing\neach mind to develop its power freely and naturally.\n\nIn effect, Einstein declared to me that he would hear nothing of a\nbreeding of talents in a sort of sporting way. The dangers of the\nmethods of sport would creep in and lead to results that had only the\nappearance of truth. From the results so far obtained it was impossible\nto come to a final decision about it. Yet it was conceivable that a\nselective process conducted along reasonable lines would in general\nprove of advantage in education, particularly in the respect that many a\ntalent that would ordinarily become stunted owing to its being kept in\ndarkness would now have an opportunity of coming to light.\n\nThis resolved itself into a talk bearing on many questions, and of which\nI should like to state the main issue here. It was specially intended to\nmake clear the gambling method that Einstein repudiates, and the danger\nof which seems still more threatening to me than to him.\n\nIf certain pedagogues, whose creed is force, were to have their way, the\n\"most gifted\" pupils would be able, or would be compelled, to rush\nthrough school at hurricane speed, and, at an age at which their fellows\nwere still spending weary hours at their desks, they would have to\nclamber to the topmost branches of the academic tree. All things are\npossible, and history even furnishes cases of such forced marches.\nLuther's friend Melanchthon qualified at the age of thirteen to enter\nthe University of Heidelberg, and at the age of seventeen he became a\nprofessor at T\u00fcbingen, where he gave lectures on the most difficult\nproblems of philosophy, as well on the Roman and Greek writers of\nclassical antiquity. This single instance need only be generalized, and\nwe have the new ideal rising up before our astonished gaze: a race of\nprofessorial striplings whose upper lips are scarcely darkened with the\ndown of youth! It is a mere matter of making an early discovery of the\nmost gifted, and then raising the scaffolding up which the precocious\nknow-alls can climb as easily as possible.\n\n[Interposed query: Where are these discoverers of talent, and how do\nthey prove their own talent? There was a good opportunity for them in a\ncase which I must here mention. Einstein told me in another connexion\nthat, as early as 1907, that is, when he was still very young in years,\nhe had not only succeeded in successfully representing the Principle of\nEquivalence, one of the main supports of the General Principle of\nRelativity, but had even published it; yet it made not the slightest\nimpression on the learned world. No one suspected the far-reaching\nconsequences, and no one pointed out this flaming up of a new talent of\nthe highest order. And just as this was able to remain concealed from\nthe learned Areopagus of the world at that time, so a similar lack of\nunderstanding may easily be possible on a smaller scale at school. We\nknow actually that among the recognized great men of science, there were\nmany who did only moderately well at school; as, for example, Humphry\nDavy, Robert Mayer, Justus Liebig, and many others. Wilhelm Ostwald goes\nso far as to affirm: \"Boys ordained to be discoverers later in life\nhave, almost without exception, been bad at school! It is just the most\ngifted young people who have resisted most strongly the form of\nintellectual development prescribed by the school! Schools never cease\nto show themselves to be the bitter, unrelenting enemies of genius!\"--in\nspite of all efforts at selection which have always been in vogue in the\nguise of advancement into higher forms.]\n\nBut the new mode of selection is intended to prevent mistakes and\noversights. Is this possible? Do not the traces of previous attempts\ninspire distrust? There was once a very ideal selection that had to\nstand the test of one of the most eminent bodies in existence, the\nFrench Academy. Its duty was to discover geniuses on an incomparably\nhigher plane. It, however, repudiated or overlooked: Moli\u00e8re,\nDescartes, Pascal, Diderot, the two Rousseaus, Beaumarchais, Balzac,\nB\u00e9ranger, the Goncourts, Daudet, Emile Zola, and many other extremely\ngifted people, whom it should really have been able to find.\n\nThe only true, and at the same time necessary as well as sufficient,\nbreeding is carried out by Nature herself in conjunction with social\nconventions, which promise the more success the less they assume the\ncharacter of incubators and breeding establishments. If you wish to\napply tests to discover pupils of genius in any class, examine as much\nas you like, excite interest and ambition, distribute prizes even, but\nnot for the purpose of separating at short intervals the shrewd and\nneedle-witted heads from the rest; and do not lose sight of the fact\nthat among those who appear as the sheep as a result of these\nsystematized tests to discover ingenuity there are many who, ten or\ntwenty years later, will take up their positions as men of eminent\ntalent.\n\nThere is no essential difference between the forced promotion of such\npupils and the breeding of super-men according to Nietzsche's recipe as\nexemplified by his Zarathustra.\n\nAssuming that super-men are justified in existing at all, they will come\nabout of themselves, but cannot simply be manufactured. Workmen, taken\nas a class, represent super-men more definitely than an individual such\nas Napoleon or C\u00e6sar Borgia. So the \"super-scholar\" exists perhaps\nalready to-day, not as an individual phenomenon, but as a whole,\nrepresenting his class. Whoever has had experience in these things will\nknow that nowadays there are difficult subjects in which it is possible\nto apply to pupils of fifteen years of age tests that are far above the\nplane of comprehension of pupils of the same age in former times,\nprovided that the average is considered, that no accidental or\nartificial separation has occurred, that no pretentiously witty\nquestions have had to be answered, and that there has been no systematic\nand inquisitive search for talent.\n\nLet us rest satisfied if we find that the sum-total of talent is\ncontinually on the increase. On the other hand, it is by no means proved\nthat we are doing civilization a service by persisting in the impossible\nproject of abolishing from the world the struggle for existence\nprescribed by Nature. It is an elementary fact, and one that is easy to\nunderstand, that many talents perish unnoticed. On the other hand,\nobserve the long list of eminent men who fought their way upwards out of\nthe lowest stages of existence only to recognize that the difficulties\nthat have been overcome are mostly necessary accompaniments of talent,\nthat is, that Nature's way of selection is to oppose obstacles and raise\ndifficulties in order to test their powers. In the case of the poor\nlens-grinder Spinoza and many others ranging to B\u00e9ranger, who was a\nwaiter, what a chain of desperate experiences, yet what triumphs!\nHerschel, the astronomer, was too poor to buy a refracting telescope,\nand it was just this dispensation of poverty that made him succeed in\nconstructing a reflecting type composed of a mirror. Faraday, the son of\na blacksmith without means, made his way for years as a bookbinder's\napprentice. Joule, one of the founders of the mechanical theory of heat,\nstarted as a beer-brewer. Kepler, the discoverer of the planetary laws,\nwas descended from a poverty-stricken innkeeper. Of the members in\nGoethe's circle, Jung-Stilling, of whom Nietzsche was so fond, was a\ntailor's apprentice; Eckermann, Goethe's intimate associate, was a\nswine-herd, and Zelter was a mason. We could add many recent names to\nthis list, and very many more if we continue the line backwards to\nEuripides, whose father was a publican and whose mother was a vendor of\nvegetables. This might serve as a basis for many reflections about the\n\"upward course of the talented,\" and about its less favourable reverse\nside. For one might put the apparently paradoxical question whether a\nsoaring career for many or all talents is a necessity for our\ncivilization, or whether it would not be better to have a substratum\ninterspersed with talent, to cultivate a mossy undergrowth which is to\nserve as nourishment for the blooming plants of the upper layer.\n\nMaximum is not equivalent to optimum, and we learned elsewhere that\nEinstein is far removed from identifying them. In the previous case it\nwas a question of the problem of population; and in the course of the\ndiscussion he mentioned that we are subject to an old error of\ncalculation when we regard it as a desirable aim to have a maximum\nnumber of human beings on the earth. It seems, indeed, that this false\nconclusion is already in process of being corrected. A beginning is\nbeing made with new and very active organizations and unions whose\nprogramme is to reduce the number so that an optimum may be attainable\nby those left.\n\nIf we extend this line of reasoning still further, we arrive at the\ndepressing question whether too much might not be done for talent, not\nonly as regards breeding it, but also in favouring the greatest number.\nIt is quite possible that in doing so, we might overlook, or take\ninsufficient account of the harm that might be done to the lower\nstratum, in that we should be depriving it of forces which, according to\nthe economy of Nature, should remain and act in concealment.\n\nThis fear, as here expressed, is not shared by Einstein. However\nbrusquely he repudiates breeding, he speaks in favour of smoothing the\nway for talent. \"I believe,\" he said, \"that a sensible fostering of\ngifts is of advantage to humanity generally and prevents injustice being\ndone to the individual. In great cities which give such lavish\nopportunities of education, this injustice manifests itself less often;\nbut it occurs so much the more in rural districts, where there are\ncertainly many cases of gifted youths who, if recognized as such at the\nright age, would attain to an important position, but who, together with\ntheir gifts, become stunted, nay, go to ruin, if the principle of\nselection does not penetrate to their circle.\"\n\nThis brings us to the most difficult and most dangerous point. The\nspectre of responsibility is rapping at the portals of society, and is\nreminding us insistently that it is our duty to see that no injustice be\ndone to any talent that may be among us. And this duty is but little\nremoved from the demand that it should be disburdened of the worries of\ndaily life, for, so the moral argument runs, talent will ripen the more\nsurely the less it has to combat these ceaseless disturbances of\nordinary life.\n\nBut this thesis, so evident on moral grounds, will never be proved\nempirically. On the contrary, we have good reason to suppose that\nnecessity, the mother of invention on the broader scale, will often in\nthe case of the individual talent prove to be the mother of its best\nresults. Goethe required for his development an unchallenged life of\nease, whereas Schiller, who never emerged from his life of misery, and\nwho, up to the time when he wrote _Don Carlos_, had not been able to\nearn sufficient with his pen to buy a writing-desk, required distress to\nmake his genius burst into flower. Jean Paul recognized this blessing of\ngloomy circumstances when he glorified poverty in his novels. Hebbel\nfollowed him along this path by saying that it is more fruitful to\nrefuse the most talented person the necessities of life than to grant\nthem to the least gifted. For among a hundred who have been chosen by\nthe method of sifting, there will be only one on the average who will\nreceive the certificate of excellence in the test of future generations,\nfor the latter use entirely different methods of sifting from that\npractised by a committee of examiners who expect ready answers to\nprepared questions.\n\nThis projects us on to the horns of a severe dilemma that scarcely\nallows of escape. The consciousness of duty towards the optimum\nexpresses itself only in a maximum of assistance, and overhears the\nwhispered objection of reason that Nature has also coarser means at her\ndisposal to attain her ends; in her own cruelty of selection she often\nenough proves the truth of Menander's saying, which, freely translated,\nsays: to be tormented is also part of man's education. The fact that\nEinstein--with certain reservations--favours the giving of help to the\nselected few, it is for me a proof, among many others, of his love\ntowards his fellow-men, which fills his heart absolutely, all questions\nof relativity notwithstanding.\n\n\n\n\nCHAPTER V\n\nTHE DISCOVERER\n\nRelation of Discovery and Philosophy in History.--The Absolute and the\nRelative.--The Creative Act.--Value of Intuition.--Constructive\nActivity.--Invention.--The Artist as Discoverer.--Theory and\nProof.--Classical Experiments.--Physics in Primitive Ages.--_Experimentum\nCrucis_.--Spectral Analysis and Periodic System.--The R\u00f4le of\nChance.--Disappointed Expectations.--The Michelson-Morley Experiment\nand the New Conception of Time.\n\n\nNEXT time--so one of our talks ended--next time, as you insist on it, we\nshall talk of discovery in general. This, was a promise of special\nimport for me, for it meant that I was to draw near to a fountain-head\nof instruction, and to have an opportunity of hearing the pronouncements\nof one whose authority could scarcely be transcended.\n\nWe are precluded from questioning Galilei personally about the\nfoundations of Mechanics, or Columbus about the inner feelings of a\nnavigator who discovers new lands, or Sebastian Bach about the merits of\nCounterpoint, but a great discoverer lives among our contemporaries who\nis to give us a clue to the nature of discovery. Was it not natural that\nI should feel the importance of his acceptance of my proposal?\n\nBefore meeting him again I was overwhelmed with ideas that arose in me\nat the slightest echo of the word \"discovery\" in my mind. Nothing, it\nseemed to me, could be higher: man's position in the sphere of creation\nand the sum of his knowledge can be deduced from the sum of his\ndiscoveries which find their climax in the conceptions civilization and\nphilosophy, just as they are partly conditioned by the philosophy of the\ntime. We might be tempted to ask: which of these two precedes, and which\nfollows? And perhaps the ambiguous nature of this question would furnish\nus with the key to the answer. For, ultimately, these two elements\ncannot at all be resolved into the relationship of cause and effect,\nantecedent and consequent.\n\nNeither is primary, and neither secondary: they are intimately\ninterwoven with one another, and are only different aspects of one and\nthe same process. At the root of this process is our axiomatic belief\nthat the world can be comprehended, and the indomitable will of all\nthinking men, acting as an elementary instinct, to bring the perceptual\nevents in the universe into harmony with the inner processes of thought.\nThis impulse is eternal; it is only the form of these attempts to make\nthe world fully intelligible that alters and is subject to the change of\ntime. This form finds expression in the current philosophy which brings\neach discovery to fruition, just as philosophy bears in itself\nconstituents of the ripe discovery.\n\nIt seemed to me that even at this stage of my reflections I was\nsomewhere near interpreting Einstein's intellectual achievement. For his\nprinciple of relativity is tantamount to a regulative world-principle\nthat has left a mighty mark in the thought of our times. We have lived\nto see the death of absolutism; the relativity of the constituents of\npolitical power, and their mutability according to view-point and\ncurrent tendencies, become manifest to us with a clearness unapproached\nby any experience of earlier historical epochs. The world was far enough\nadvanced in its views for a final achievement of thought which would\ndemolish the absolute also from the mathematico-physical aspect. This is\nhow Einstein's discovery appeared as inevitable.\n\nYet a shadow of doubt crossed my mind. Einstein's discoveries came to\nlight in the year 1905--that is, at a time when hardly a cloud was\nvisible to forewarn us of the storms which were to uproot absolutism in\nthe world. But what if a different kind of necessity had imposed itself\non world-history, and hence on the world-view? Nowadays we know from\nauthentic accounts, which no one doubts, that all that we have\nexperienced during the war and the revolution has hung upon the\nactivities of one frail human being of quite insignificant exterior, a\nbureaucrat of the Wilhelm-Strasse, a choleric eccentric who succeeded in\nfrustrating the Anglo-German alliance which was unceasingly being\npressed upon us for six long years after the beginning of the century.\n\nAmid the noisy progress of universal evolution the secret and\ninsignificant nibbling of a mole cannot be regarded as of momentous\nimportance for history, and yet if we eliminate it from the complete\npicture of events we find as a result that all our experiences have been\ninverted. Absolutism would not have been thrown overboard, but would\nprobably have kept the helm with greater mastery than ever as the\nexponent of an Anglo-German hegemony of the world, and a political\noutlook fundamentally different in tendency would now have been\nprevailing on the earth.\n\nBut Einstein's Theory of Relativity would not have taken the slightest\nheed of this. It would have arisen independently of the current forms of\npolitical conceptions, simply because we had reached that point in our\nintellectual development and because Einstein was living and spinning\nhis webs of thought. And the question whether his theory will also have\ncrushed absolutism for the non-physicist cannot be answered.\n\nIt may indeed be doubted whether its time had already come. In the case\nof many important events in the history of thought their moment of birth\ncan be fixed to within about ten years, as for example the Theory of\nEvolution, which had been conceived in several minds at the same time\nand had of necessity to come to life in one of them, even if it had\nfailed in the case of the others. I venture to say that without\nEinstein, the Theory of Relativity in its widest sense, that is,\nincluding the new doctrine of gravitation, would perhaps have had to\nwait another two hundred years before being born.\n\nThis contradiction is cleared up if we use sufficiently great time\nintervals. History does not adapt itself to the time measures of\npolitics and of journalism, and philosophies are not to be calculated in\nterms of days. The philosophy of Aristotle held sway right through the\nMiddle Ages, and that of Epicurus will gain its full force only in the\ncoming generation. But if we make our unit a hundred years the connexion\nbetween philosophies and great discoveries remains true.\n\nWhoever undertakes to explore the necessity of this connexion cannot\nevade the fact that the lines of the result had been marked out in the\nregion of pure thought, as can be proved, before even the great\ndiscovery or invention was able to present it in a fully intelligible\nform. Even the achievement of Copernicus would follow this general rule\nof development: it was the last consequence of the belief in the Sun\nMyth which had never been forsaken by man in spite of the violent\nefforts of the Church and of man himself to force the geocentric view.\nCopernicus concentrated what had survived of the wisdom of the earliest\npriests--which includes also the germ of our modern ideas of energy and\nelectricity--of the teachings of Anaxagoras and the Eleatics which had\nremained latent in our consciousness: his discovery was the\ntransformation of a myth into science. Mankind, whose wandering fancy\nfirst feels presentiments, then thinks and wishes to know, is a large\nedition of the individual thinker. The latter sees further only because\nhe, so to speak, stands on the shoulders of a sum-total of beings with a\nworld-view.\n\nLet us turn our attention to an example from the most recent history of\nphilosophy and discovery. The absolute continuity of events was one of\nthe generally accepted canons of thought, and is even nowadays taught by\nserious philosophers as an incontrovertible element in our knowledge.\nThe old quotation _Natura non facit saltus_, popularized by Linn\u00e9, is\none of the formulae of this apparently invincible truth. But deep down\nin the consciousness of man there has always been an opposition to it,\nand when the French philosopher Henri Bergson set out to break up this\nline of continuity by metaphysical means in ascribing to human knowledge\nan intermittent, cinematographic character, he was proclaiming in an\naudible and eloquent form only what had lain latent in a new but as yet\nincomplete philosophy. Bergson made no new \"discovery,\" he felt his way\nintuitively into a new field of knowledge and recognized that the time\nwas ripe for the real discovery. This was actually presented to us in\nour day by the eminent physicist Max Planck, the winner of the Nobel\nPrize for Physics in 1919, in the form of his \"Quantum Theory.\" This is\nnot to be taken as meaning that a revolutionary philosophy and a triumph\nof scientific research now become coincident, but only that a\ndiscontinuous, intermittent sequence, an atomistic structure, was proved\nby means of the weapons of exact science, to be true of energies which,\naccording to current belief, were expected to be radiated regularly and\nconnectedly. This was probably not a case of the accidental coincidence\nof a new philosophical view with the results of reasoning from physical\ngrounds, but a demand of time, exacting that the claims of a new\nprinciple of thought be recognized.\n\nAs above suggested, it is more difficult to find a link between\nEinstein's discoveries and antecedent presentiments of relativity. For a\nmere reference to the downfall of absolutism in the world of human\nevents will not suffice. In the case of Einstein, we see such a\ntremendous rush of thought in one being that we almost feel compelled to\nrecognize an analogy with the Quantum Theory and believe in a\ndiscontinuity in the course of intellectual history. Yet there are\ncertainly threads that connect Einstein's achievement with a prophetic\ninsight. In this case, however, we must spread out over centuries what\nin the case of other discoveries extends, in comparison, only over\ndecades. That doubt of Faust, which troubles the spirit of every\nthinker: \"whether in yonder spheres there is also an Above and a Below,\"\nand which goes back as far as Pyrrhon and Protagoras, is itself\nrelativistic; it expresses doubt whether the co-ordinate system passing\nthrough our own lifes as centres is valid. It is ultimately a matter of\npoint of view, and the mathematico-physical consequences of the endless\nseries of questions, and the relation, which arises from the couple,\nAbove-Below, probably leads to a new mode of comprehending the\nconstitution of the world, for which Einstein's creative work found the\nadequate expression in abstract terms. And from this point onwards, in\naccordance with the principle of reciprocal action, a new stream of\nknowledge will pour itself into the hazy stretches of philosophy. A\nfundamental and radical reform of our philosophy seems inevitable,\nparticularly with respect to our conceptions of Space and Time, perhaps,\ntoo, even with respect to Infinity and Causality. Much dross will have\nto be sifted out of our old categories of thought and out of our world\nwisdom, which once served as material for fine structures. What will the\nfiner ones look like that are to take their places in obedience to the\ncommand of physics? Who would care to take it upon himself to form an\nestimate?\n\nMuch will be uprooted, and it is possible that even the defiant\n\"ignorabimus,\" the antipole of the search for truth from Pyrrhon to\nDubois, will again take up the cudgel. For in the face of despairing\nuncertainty there is the one certainty: what cannot be comprehended is\nbeing encircled more and more by the great discoverers! And even if the\nabsolute point of convergence can never be reached, there is within our\nreach at least another point which is a haven of rest in the passing\nstream of philosophies, namely, a moral centre around which eddies of\nhappiness circle. At the heart of this world-view there is the uplifting\nbelief in an advance of knowledge in spite of all, and a belief in the\nvanishing of age-long problems and difficulties under the flood of\ndiscoveries. And even if afterwards and concurrently ever new problems\nand difficulties arise, these do not suppress our feeling of triumph.\nEvery achievement in this field gives us a sense of enfranchisement from\nprejudices, not the least of which is narrowness of national outlook.\nNot only do discoverers construct bridges of thought that stretch to\nastronomical distances, but, what is more difficult, they build bridges\nfor our feelings, that surmount political obstacles. Every thinking\nbeing who plays a part in the making of some great discovery and who,\nwith deepened vision, bows before a new achievement of mind, gradually\nbecomes a disciple of the religion of universal politics, the creed of\nwhich is faith in the brotherhood of thought. The nucleus of a\nphilosophy that belongs to the future is the recognition that differing\nnational view must be compounded into a unity, and that every great\ndiscovery means a step towards attaining this end.\n\nEven if we accept Pascal's wonderful dictum that human knowledge is\nrepresented by a sphere which is continually growing and increasing its\npoints of contact with the unknown, we must not interpret it as a sign\nof despair. It is not the enlargement of the unknown, but only that of\nknowledge that stirs our feelings with ethical forces. The positive\ncalls up in us a living force by inspiring in us the feeling that the\nsphere of knowledge is destined to grow, and that there can be no higher\nduty for all the energies of mind than to obey the call for combined\naction towards this growth which will bring the world into harmony.\n\nFull of such reflections I entered the home of the great discoverer,\nwhose activities unceasingly hovered before my vision as ideal examples\nof creative effort. I discovered him, as almost always, seated before\nloose sheets of paper which his hand had covered with mathematical\nsymbols, with hieroglyphics of that universal language in which,\naccording to Galilei, the great book of Nature is written.\n\nWhat a very different picture many an outsider draws of the manner in\nwhich a seeker in the heavens works! He is imagined like Tycho Brahe to\nbe surrounded by unusual pieces of apparatus, spying through the ocular\nof a long range refractor into the universe, seeking to unravel its\nultimate secrets. The true picture does not correspond to this fancy in\nthe slightest. Nothing in the make-up of the room reminds one of\nsuper-earthly sublimity, no abundance of instruments or books is to be\nseen, and one soon becomes aware that here a thinker reigns whose only\nrequirement for his work, which encompasses the world, is his own mind,\nplus a sheet of paper and a pencil. All that acts on the observatories\noutside, that gives rise to great scientific expeditions, that, indeed,\nultimately regulates the relationship of mankind to the constitution of\nthe universe, the revolution in the knowledge of things connecting\nheaven and earth, all this is here concentrated in the simple figure of\na still youthful scholar, who spins out endless threads from the fabric\nof his mind: the words of a poet are recalled to our memory, which,\naddressed to all of us, have been fulfilled to the last degree by one\nliving among us:--\n\n\n   \"Whereso thou roamest in space, thy Zenith and Nadir unite thee--\n    This to the heavenly height, that to the pole of the world,--\n    Whatsoever thou do, let thy will mount up into Heaven--\n    But let the pole of the world still o'er thine actions preside.\"\n\n                            (Schiller: _Translation by Merivale_.)\n\n\nAnd this one helped to fulfil this aim and I must break off his thread\nof thought to put the question: What is Discovery, and what does it\nsignify?\n\nIt is a purely abstract question that may appear to many to be devoid of\ncontent. Such will repeat to themselves, as best they can, the list of\ndiscoveries and think a man makes a discovery when he finds out\nsomething important, such as the Laws of Falling Bodies, the formation\nof Rainbows, or the Origin of Species: a general denomination may be\nfound for it perhaps only by ascribing to Discovery something requiring\na powerful mind, a creative genius.\n\nAt first it staggered me to hear Einstein say: \"The use of the word\n'Discovery' in itself is to be deprecated. For discovery is equivalent\nto becoming aware of a thing which is already formed; this links up with\nproof, which no longer bears the character of 'discovery' but, in the\nlast instance, of the means that leads to discovery.\" He then stated at\nfirst in blunt terms, which he afterwards elaborated by giving detailed\nillustrations: \"Discovery is really not a creative act!\"\n\nArguments for and against this view flashed through my mind, and I\nthought involuntarily of a great master of music who, when he was asked:\n\"What is Genius?\" answered: \"A genius is one to whom ideas occur.\" This\nparallel might be carried still further, for I have repeatedly heard\nEinstein call \"ideas\" what we would regard as wonderful thoughts. Does\nnot the philosopher Fritz Mauthner speak of the discovery of gravitation\nas being an \"aper\u00e7u\" of Newton; yes, in the sense of _aper\u00e7us_ as\napplied in ancient Greek philosophy, and which included almost\neverything that was left by Pythagoras, Heraclitus, etc., as a token of\ntheir genius. On the other hand, we are all possessed of the desire to\ndifferentiate clearly between an idea and a creative act of thought, as\noccurs in Grillparzer's aphorism: \"An idea is not a thought; a thought\nknows its bounds, whereas the idea leaps over them and succeeds in\naccomplishing nothing!\"\n\nHere, then, we must revise our view. We know, for example, how much\nEinstein's \"ideas,\" felt by him to be such and named so accordingly,\naccomplished. Let us hear how he characterizes in a few words his own\n\"idea\" which shook the world:\n\n\"The underlying thought of relativity,\" he said, in connexion with this\nquestion, \"is that there is physically no unique (specially favoured)\nstate of motion. Or, more exactly, among all states of motion there is\nnone that is favoured in the sense that, in contradistinction to the\nothers, it may be said to be a state of rest. Rest and Motion are not\nonly by formal definition but also by their intrinsic physical meaning\n_relative conceptions_.\"\n\n\"Well, then,\" I interposed, \"surely this was a creative act! This first\nflashed across _your_ mind, Professor; it represents your discovery, so\nthat we may well let the word retain the meaning usually associated with\nit!\"\n\n\"By no means,\" answered Einstein, \"for it is not true that this\nfundamental principle occurred to me as the primary thought. If this had\nbeen so perhaps it would be justifiable to call it a \"discovery.\" But\nthe suddenness with which you assume it to have occurred to me must be\ndenied. Actually, I was lead to it by _steps_ arising from the\n_individual_ laws derived from experience.\"\n\nEinstein supplemented this by emphasizing the conception \"invention,\"\nand ascribed a considerable importance to it: \"Invention occurs here as\na constructive act. This does not, therefore, constitute what is\nessentially original in the matter, but the creation of a method of\nthought to arrive at a logically coherent system ... the really valuable\nfactor is _intuition_!\"\n\nI had thought, long and intently, about these theses to discover as\nnearly as possible what distinguished their content from the usual view.\nThe fundamental differences suggest an abundance of ideas whose\nimportance grows in value as we apply them to various cases as\nillustrations. And I feel convinced that we shall yet have to occupy\nourselves with these words of Einstein, which present themselves as a\nconfession, as with the famous \"hypotheses non fingo\" that Newton set up\nas the idea underlying his work.\n\nThe latter as well as the former implies something negative: it denies\nsomething. In Einstein's words there is apparently a repudiation of the\nreally creative act in discovery; he lays stress on the gradual,\nmethodical constructive factors, not omitting to emphasize intuition.\nThere is no other course open to us but to seek indirectly a synthesis\nof these conceptions, and to eliminate what is apparently contradictory\nin them.\n\nI consider this possible if we decide to subdivide the discovery into a\nseries of individual acts in which succession takes the place of\ninstantaneous suddenness The creative factor may then remain intact;\nindeed, it attains a still higher degree of importance if we imagine to\nourselves that a series of creative ideas must be finked together to\nmake possible a single important discovery.\n\nThe original idea never springs fully equipped and armed like Minerva\nout of the head of its creator. And it is wise to bear in mind that even\nJupiter had to suffer in his head a period of pregnancy accompanied with\ngreat pain. It is only in the after-picture that Pallas Athene appears\nwith the attribute of suddenness. It is the nature of our myth-building\nimagination to leap over the actual act of birth so as to give a more\nbrilliant form to the finished creation.\n\nWe feel great satisfaction when we learn that Gauss, the Prince of\nMathematicians, declared in one of his valuable flashes of insight: \"I\nhave the result, only I do not yet know how to get to it.\" For in this\nutterance we see above all that he emphasizes a lightning-like\nintuition. He has possession of a thing, which is, however, not yet his\nown, and which can only become his own when he has found the way to it.\nIs this contradictory? From the point of view of elementary logic,\ncertainly; but methodologically, by no means. Here it is a question of:\n_Erwirb es um es zu besitzen_! This makes necessary a series of further\nintuitions along the road of invention, and of construction.\n\nThis is, then, where that phase commences, which Einstein denotes by the\nword \"gradual,\" or \"by steps.\" The first intuition must be present; its\npresence as a rule usually guarantees that further intuition will follow\nin logical sequence.\n\nThis does not always happen. In passing, we discussed several special\ncases from which particular inferences may be drawn. The powerful\nmathematician Pierre Fermat has presented the world with a theorem of\nextremely simple form which he discovered, a proof of which is being\nsought even nowadays, two and a half centuries after he stated it. In\neasy language, it is this: the sum of two squares may again be a square,\nfor example, 5^2 + 12^2 = 13^2, since 25 + 144 = 169; but the sum of two\ncubes can _never_ be a cube, and, more generally, as soon as the exponent,\nthe power index _n_, is greater than 2, the equation _x_^_n_ + _y_^_n_ =\n_z_^_n_ can never be satisfied by whole number values for _x_, _y_, and\n_z_; it is impossible to find three whole numbers for _x_, _y_, and _z_,\nwhich, when substituted in the equation, give a correct result.\n\nThis is certainly true; it is an intuitive discovery. But Fermat's\nassertion that he possessed a \"wonderful proof,\" is for very good\nreasons open to contradiction. No one doubts the absolute truth of the\ntheorem. But the later inspiration, the next step after the intuition,\nhas occurred neither to Fermat nor to anyone else. It cannot be\nestablished whether his remark about the proof was due to a subjective\nerror, or was baseless. In any case it seems probable that Fermat had\narrived at the result _per intuitionem_ without knowing the way to it.\nHis creative act stopped short; it was only a first flare of a\nconflagration, and did not fulfil the condition that Einstein associates\nwith the conception of a logically complete method.\n\nWe may, indeed, pursue this case of Fermat still further. He had\nenunciated another theorem, again _per intuitionem_, namely, that it was\npossible to construct prime numbers of any magnitude by a formula he\ngave. Euler later showed by a definite example that the theorem was\nfalse. It was stated in a letter to Pascal written in 1654 in the words:\nthe result of squaring 2 continuously and then adding 1 must in each\ncase be a prime number, that is, 2^(2^_k_) + 1 must always be a prime no\nmatter what value _k_ may have. Fermat added: \"This is a property for\nthe truth of which I answer.\" Euler chanced to try _k_ = 5, and found\nthat 2^32 + 1 = 4,294,967,297, which may be represented as the product\nof 641 and 6,700,417, and hence is not a prime.\n\nIt is conceivable that no Euler might have lived, and that no one else\nmight have discovered this contradiction. What would then have been the\nposition of this \"discovery\" of Fermat?\n\nWe should certainly not have disputed its creative character, for we\nshould have said that it corresponds to a fact which is fully formed,\nbut cannot be proved. But now that we know that the fact does not exist\nat all, the tiling assumes a different colour. It was not a discovery at\nall, but an erroneous conjecture. But one would never be able to arrive\nat an erroneous conclusion of this sort without being a mathematical\ngenius, and having the inspiration of the moment. And from this again it\nfollows that to make a discovery in the full sense of the word the\nintuition of the moment does not suffice, but must be supported by a\nseries of intuitions, and this is the condition that it become a\npermanent component of universal truth.\n\nThe fact that Einstein refers to the action of \"inventing\" in his\nexplanation, gives support, it seems to me, to the view that, strictly\nspeaking, discovering and inventing are never to be regarded as being\nseparable. In discovering, what has to be constructed persists, and in\ninventing, it is a question of finding the path along which there is the\npromise of success, be it by a method, a proof, or by some general work.\nWe spoke of works of art, and I was delighted to see that Einstein was\nby no means disinclined to claim certain works of pure thought, which\nare usually placed in the category of scientific discovery, as works of\nart. In the latter, however, the pure process of invention plays the\nprominent part, for in them something is represented that did not exist\nat all before; this has repeatedly led to the artist's achievement being\ngiven the higher rank, as being properly and exclusively creative. The\nargument runs somewhat along these lines: the infinitesimal calculus\nwould certainly have been discovered even if there had been no Newton\nand no Leibniz, but without Beethoven we should never have had a C Minor\nSymphony, and never in the future would it have appeared, for it was a\nsubjective, absolutely personal, and unique product of its creator.\n\nI believe this may be admitted, and that we may nevertheless retain the\nview that in the work of art, too, the act of discovering is to be\nfound. Let us consider for a moment the elementary substance of the\nfirst movement of this fifth symphony, a colossal movement of 500 bars,\nwhich expresses itself quite definitely in four notes, of which one is\nrepeated three times. \"Thus Destiny thunders at the gates\" is\nBeethoven's motto for this section; it is expressed tonally in a\nsuccession of notes which through all eternity existed among the\npossible permutative arrangements of these sounds.\n\nBeethoven, so it is expressed, invented it. But it is just as correct to\nsay--in Einstein's words--\"he became aware of what was already\nformed\"--that is, he \"discovered\" the fundamental theme, and afterwards\n\"proved it\" in terms of musical logic unheard-of beauty in a methodical\nelaboration. We may, indeed, go further still. This _motif_ of four\ntones was not only extant as an abstractum, as a possible mathematical\narrangement, but also as something natural. Czerny, a pupil of\nBeethoven, to whom the master confided many a remark about the origin of\nhis compositions, reports that a bird, the yellow-hammer, had sung this\ntheme to Beethoven in the woods. But neither the bird nor any other\nliving creature had invented it; rather what could not be created,\nbecause it had always been in existence, became objectified in the\nmedium of sound. Beethoven found it; it was _res nullius_ when he found\nit and when he discovered simultaneously with the succession of tones\nthat they were appropriate for a powerful musical representation of\nsombre Destiny. Every theme, be it of Beethoven, Bach, Wagner, or anyone\nelse, may be represented graphically by a curve (in the case of Bach's\nfugal themes this has, in fact, been done for special purposes), and\njust as it is certain that every elliptic-arc existed before all\ngeometry, so it may be affirmed with equal certainty that everything\nmusical was in existence before the advent of composition, and was\nmerely waiting for a discoverer whom we designate the inventor, the\ncreative organ.\n\nBut may not some of this glory be reflected on to scientific discovery?\nWhen we are in an ecstasy of admiration, we talk of a creative act as of\nsomething divine; may we not also grant to the scientist this tribute\nwhich, owing to a slight confusion of conceptions, we shower on the\nartists? And I believe that Einstein's definition does not set up an\ninsuperable barrier in this respect to our admiration, which exerts\nevery effort to pass beyond, refuses to come to a standstill before the\nrigid fact that the discoverer reveals only what is preformed; our\nemotions prove to be stronger than our minds with their objective\nvaluation. In the last instance, we opine, the scientific discoverer,\ntoo, creates something new, namely, a piece of knowledge that was\npreviously not in existence. And we obey the impulse of hero-worship,\nwhen we call a definite first discoverer a creator.\n\nThis silences opposition certainly only for a time, without vanquishing\nit. For this knowledge, too, lay ready before the first discoverer\nappeared: he did not create it, but merely drew back the veil that\nenveloped it. So that, ultimately, we get back to \"intuition\" in its\nliteral sense, a becoming aware of things, an exact consideration of\nthings, states, and relationships; and this intensive consideration,\nfull of wonderment, has always been a privilege of a very few chosen\nmen.\n\nIt might be asked: Was there any knowledge of Pythagoras' Theorems\nbefore Pythagoras gave us his proof? We should have to answer: It was in\nexistence at least in the still dark field of vision of Pythagoras,\nwhich became illumined one day when he took such a view of the\nnumber-ratios 3--4--5 that an exact intuition could actually come about.\nIt is erroneous to assume that a creative act suddenly called up before\nhis soul as if by magic the figure with the three squares drawn\nexternally on the sides of a triangle. Rather, he \"took his stride\" (as\nwe know from Vitruvius) by considering a triangle whose sides were of a\ndefinite length; and the well-known proof, which is linked indissolubly\nin our minds with his work, is not his at all, but Euclid's. Yet our\nannals grow musty, centuries pass by, and the credit of being the\ncreator rests with the man who first succeeded in getting a clear\npicture of such a triangle.\n\nIt seems natural to test discoveries by experiments. The first result of\ndoing this is a very remarkable increase in the rate at which the\nintuitive process has developed. In ancient times, intuition, it seems,\nscarcely felt the need of proving things by experiment; all that was\ndiscovered by Archimedes in mechanics, by the Pythagoreans in acoustics,\nby Euclid in optics, may be reduced practically to the formula\n\"heureka,\" and it is probably scarcely an exaggeration to say that more\nand more fruitful experiments are performed in one week nowadays than in\nthe whole of the classical age taken together.[3]\n\n[Footnote 3: Recently certain precisians in definition have been seeking\nto establish a fundamental difference between physicists of reality,\nexperimental physicists, and \"blackboard-physicists.\" The last term is\ngiven jeeringly to theoretical physicists because they, in the opinion\nof these critics, wish to found Nature entirely on formul\u00e6 argued out\non the blackboard. The history of science does recognize this\ndistinction, although it is, of course, quite possible for a physicist\nto arrive at important discoveries without making any experiments.\n\nOne might be more justified in asserting that the great theorist need\nnot necessarily be a great experimenter and vice versa. But I can quote\nno example of a physicist who confined himself obstinately to blackboard\ndiscussion, and on principle disowned all experimental work.\n\nI must add that Einstein himself is fond of experimenting, and has had\nmuch success in experimental work. The amount of advice and\nencouragement that he has given, and still gives, to many workers in\nthis field is very considerable. But he does not practise experimental\nwork regularly, and remarked that he is obliged to appeal to outside\nhelp for certain practical tests. There are specific experimental\ngeniuses, whose activity assumes the happiest and most fruitful form\nwhen it supplements that of the theorist and fertilizes it.]\n\nExperiments have become, if not the sole, yet the most definite, test of\nintuition. I need only recall the observations of the solar eclipse of\n1919, which were of an experimental character inasmuch as they used\napparatus to question Nature. To the world generally, they gave the\nirrefutable confirmation of Einstein's Theory of Gravitation, but not to\nEinstein himself, whose intuition felt itself so certain that the\nconfirmation was a mere matter of course.\n\nBut this is not the average case; in many cases the intuition of the\ndiscoverer appeals to experiment as a judge of great authority, who is\nto confirm, reject, or correct.\n\nLet us take some examples of cases in which the intensity and the value\nof intuition were measured by the experimental results. Benjamin\nFranklin's Kite Experiment may be taken as a classical instance. Here is\na man in whose head the idea takes root that lightning and electricity\nare one and the same thing. Innumerable persons before and after his\ntime might have hit on the same idea, which is now the common knowledge\nof children. Yet, a single man had to appear who became aware of this\npre-formed fact and who simultaneously thought out a method of putting\nit to proof. In 1752 he constructed a kite, sent it up into the clouds\nduring a storm, and caught up sparks on the ground by a metallic\ncontrivance, and, as d'Alembert so aptly described it to the French\nAcademy:\n\n\n    \"Eripuit coelo fulmen ...\"\n\n\nHe wrested the lightning from the heavens. Jupiter Tonans illuminated a\ngreat discovery, a mighty intuition which had entered like a lightning\nstroke into the brain of a discoverer.\n\nThis case would be classical, were it not that nine-tenths of it is\nbased on legend. Franklin was by no means the first who had this\nintuition, and his experimental test was so full of faults that it was\nwithin an ace of failing. Franklin used a dry thread of hemp, which he\nthought to be a conductor, but which became a conductor only after it\nhad been made wet by rain. Till that moment the exhibition of sparks on\nthe ground had been poor enough, and little was wanting for Franklin to\ngive up his attempt and confess that he had been inspired, not with an\nintuition, but with a hallucination.\n\nBut to whom then is the glory of this discovery due? This is a difficult\npoint to decide. As early as 1746, that is, six years before Franklin's\nkite made its ascent in Philadelphia, Professor Winkler of Leipzig had\nasserted in a dissertation that the two phenomena were identical, and\nhad proved this theoretically; and three years earlier still Abb\u00e9\nNollet had declared the storm clouds to be the conductors of an\nelectrical induction machine. Almost simultaneously with Franklin,\nDalibard, Delor, Buffon, Le Monnier, Canton, Bevis, and Wilson made\nexperiments on an elaborate scale, which far exceeded that of Franklin\nin their results. To this must be added that the experiment was\nconducted with evident success only in 1753, when de Romas of Nerac in\nSouth France wove a real conductor of thin annealed wire into the\nkite-string, and succeeded in bringing down a regular thunderstorm with\nflashes of lightning ten feet long, accompanied by a deafening uproar.\nIt was only then that the track of the inspiration was traced back\nthrough time to the Roman Kings, Numa Pompilius and Tullus Hostilius, as\nthe first experimenters with lightning. And then the physicist\nLichtenberg sought to furnish a proof that the old Hebrew ark of the\nCovenant, together with the tabernacle, were nothing other than great\npieces of electrical apparatus highly charged with electricity derived\nfrom the air; thus the first intuition, and the priority of discovery,\nwould have to be ascribed to Moses or Aaron! And connected with this was\nthe fact, supported by substantial proof, that the Temple of Solomon was\nprotected by lightning-conductors.\n\nI must not omit to mention that Einstein regards this whole chain of\nproofs stretching back to early times as by no means established,\nalthough besides Lichtenberg, other important scholars, such as Bendavid\nin Berlin and Michaelis in G\u00f6ttingen, have vouched for their truth. And\nas it is a matter of electrical relationships, Einstein's doubts cannot\nbe passed over. As far as I recollect, they were not directed against\nthe rough facts in themselves, but against the sense that is construed\ninto them--that is to say, in the case of both the ancient Roman and the\nBiblical data, the conception of discovery must be excluded, and must be\nawarded rather to those intellectual efforts which have led to the\ncreation of a method of thought. None the less, we may uphold our\nstatement that in this case, presumed to be classical, neither Franklin\nnor anyone else is to be claimed as the discoverer or as the central\nfigure in a creative act.\n\nThe experimental case of spectral analysis is incomparably simpler and\nless open to dispute. It is without doubt a discovery of fundamental\nimportance bearing all the characteristics of originality, for no\npredecessors are discernible. I have always felt a little dissatisfied\nwith the fact that it required two men to think it out, that a duo of\nminds was necessary for one act of thought which appears quite uniform,\nelementary and inseparable from the intuition of a single mind. But it\nseems possible that tradition has not handed the facts down to us\nfaithfully, and that the two men, with a unanimity arising from their\npartnership in work, combined their results, which were not, at the\nbeginning, of a dual character. This possibility became clear to me from\na remark of Einstein which made it plain to me that the conjunction\nKirchhoff and Bunsen is to be taken as denoting Kirchhoff and then,\nafter a pause, Bunsen in the next breath! But if we discard this\nquestion of unity or duality, we are left with the fact that the idea of\na spectral analysis occurred to some one (as a result of preceding\noptical experiments with Fraunhofer lines), and was fully confirmed by\nlater experiments. Only fully confirmed? No, the classic rank of this\ncase manifested itself in a much more triumphant manner, for it is\nimpossible that the intuition of Kirchhoff and Bunsen could have grasped\nthe whole significance and range of their discovery even after they had\nmade it their own.\n\nEvery discovery encloses a germ of hope. However great this may have\nbeen in the case of Kirchhoff, it could not by any stretch of\nimagination approach the degree of its fulfilment. The fundamental\ntheoretical idea that \"a vapour absorbs from the ray-complex of white\nlight only those wave-lengths which it can emit\" gave rise to a process,\nthe ingenuity, delicacy, and certainty of which is almost inconceivable.\nWhen rays of light emitted by incandescent vapour were separated by a\nprism, there were discovered fine coloured lines that betrayed some\nunknown mystery. The spectroscopic experiments proved, in a succession\nof results, that the author of the above idea had made not only one\ndiscovery, but a whole host of them. For example, it was observed that,\nin burning minute residues obtained by evaporating certain mineral\nwaters, a red line and a blue line that had never been seen before\nappeared in the spectrum. One knew immediately that an element, hitherto\nundiscovered, was proclaiming its presence. In this way in quick\nsuccession the element C\u00e6sium was discovered, then Rubidium, Thallium,\nIndium, Argon, Helium, Neon, Krypton, Xenon--certainly things that were\nalready pre-formed in Nature, just as the idea of a bridge from Optics\nto Chemistry lay all ready in the heart of Nature; but no blame can be\ngiven to the astonished contemporaries who regarded this fundamental\ndiscovery of spectroscopic analysis as a creative achievement of the\nintellect.\n\nThis ray of hope gave a glimpse of the degree of accuracy attainable. In\nthis connexion the experiment confirmed infinitely more than the boldest\nimagination could ever have dreamed. A yellow line was detected in the\nspectrum of sodium. And it was found experimentally that the\nthree-millionth part of a thousandth of a gramme of a sodium salt is\nsufficient to produce this sodium line in the spectrum of a Bunsen\nburner. There commenced a dizzying passage in the Calculus of\nProbabilities for, since it was found that in the sun's atmosphere\nhydrogen, carbon, iron, aluminium, calcium, sodium, nickel, chromium,\nzinc, and copper were present, the question arose as to how great was\nthe possibility of an error in this observation. Kirchhoff calculated it\nas a chance of a trillion to one that these substances are actually\npresent in the sun!\n\nNever before had an experiment verified to such an extreme degree a\ndiscoverer's idea. It seems appropriate at this stage to deal with a\ndoctrine which seeks to shed light into the deepest recesses of the\nconnexion between experiment and discovery. It teaches that an\n_experimentum crucis_, an experiment that verifies absolutely, is\n_impossible_ in physics. That is to say, every idea of a discoverer\ninvolves a hypothesis, and, however the experiment that follows may turn\nout, there still remains the possibility that this hypothesis was false,\nand may later have to make way for another essentially contradictory\nhypothesis which will be valid again only for a limited time.\n\nThe chief exponent of this theory is the eminent scholar, Pierre Duhem,\nMembre de l'Institut. He draws a parallel between experiment and\nmathematical proof, particularly with the indirect, apagogic form which\nhas been so successfully applied in Euclidean geometry. In this method\nit is assumed that a certain statement is erroneous; it is then shown\nthat it leads to an obvious contradiction; consequently the statement\nwas correct provided that a certain doubt be excluded. Thus in the\ndomain of mathematics we have a real _experimentum crucis_.\n\nIn accordance with this, Duhem tests the validity of two physical\ntheories, both of which were put forward and claimed as discoveries.\nNewton had discovered the nature of light to consist in \"emission\"; to\nhim, as well as to Laplace and Biot, light consists of projectiles that\nare emitted with very great velocity. The discovery of Huyghens,\nsupported by Young and Fresnel, substitutes wave-motion in place of\ncorpuscular emission. Hence, according to Duhem, we have, or we had,\nhere two hypotheses which appear to be the only ones possible.\nExperiment was to pronounce a judgment, and at first it decided\nirrefutably in favour of the wave-theory. Therefore, the discovery of\nHuyghens is alone true, and that of Newton is shown to be an error;\nthere is no third outlet, and so we have quite certainly an\n_experimentum_ crucis before us.\n\nThe term itself originates in Bacon's _Novum Organum_. Contrary to\nDuhem's assumption, it does not refer to a signpost at cross-roads\ngiving various routes, nor is it connected with _croix ou pile_, heads\nor tails. _Experimentum crucis_ denotes rather a divine judgment at the\ncross, that is a test that is absolutely decisive and beyond further\nappeal. But no! adds Duhem, there is no room for a third judgment in the\ncase of two contradictory statements in geometry, but there is between\ntwo contradictory statements in physics. And, in fact, this third\npossibility has manifested itself in the discovery of Maxwell, who has\nshown that the nature of light is founded on a process of periodic\nelectromagnetic disturbances. Hence, so concludes Duhem, experiment can\nnever decide whether a certain theory is alone valid. The physicist is\nnever certain that he has exhausted all conceivable possibilities, of\nthought. The truth of a physical statement, the validity of a discovery,\ncannot be confirmed by any _experimentum crucis_.\n\nAccording to this argument, therefore, it is also possible that the\nscientific grounds of spectral analysis do not conform to truth. A\ncontradictory hypothesis may, indeed, be set up, with the result that\nthe same experiments that had led Kirchhoff's discovery from one triumph\nto another would have to be interpreted in a totally different sense.\n\nI must frankly confess that I cannot subscribe to such an extreme\neventuality, since, in my opinion, Duhem's analogy with mathematics\nexcludes this possibility. For if a certain probability is expressed by\na trillion to one, then I venture to state that even in the case of\nmathematical truths certainty reaches no higher degree of probability.\nFrom the history of mathematics we know of theorems which were\nenunciated and provided with complete proofs, and yet did not succeed in\nestablishing themselves; hence we see that, however evident a\nmathematical theorem may be, it is still only a matter of very great\nprobability.\n\nIf, following our usual habits of thought, we take this for absolute\ncertainty, then we may also consider the sum-total of experiments in the\nrealm of spectral analysis to be a great _experimentum crucis_ for the\ncorrectness of the theory itself.\n\nFar removed from it, and yet connected with it, there is the \"Periodic\nSystem of the Elements,\" the discovery of Mendelejew and Lothar Meyer.\nIt, too, offered prophetic glances into the future, foretold the\nunknown, hinted at things that were present only in imagination in a\nscheme of thought that assigned definite places of existence to\nundiscovered things. The Periodic System is represented by a table\ncontaining vertical and horizontal rows, in the squares of which the\nelements are entered according to certain rules depending on their\natomic weights. The discovery consisted theoretically in stating that\nthe physical and chemical properties of each element is the arithmetic\nmean between the properties of its horizontal and vertical neighbours.\nThis gave rise to predictions concerning the unoccupied squares. These\ngaps, these blank spaces in the table, seem to say prophetically: There\nare elements missing here that must be discoverable. The neighbours will\nbetray them, and the empty space itself shows by what means they are to\nbe found. With the shrewdness of a detective, Mendelejew was able to\nsay: There must be elements of the atomic weights 44, 70, and 72; we do\nnot know them yet, but we are in a position to determine the properties\nof these foundlings of the future, and, what is more, the properties of\ntheir compounds with other elements. Later researches, which led to the\ndiscovery of the elements. Scandium, Gallium, and Germanium, have\nactually confirmed all these predicted properties.\n\nThe metal Gallium was discovered in 1875 by spectroscopic means. Its\nproperties are the mean of those of Aluminium and Indium, and this\nplaces it in a position which had already been assigned to it in the\nperiodic table before its discovery; for, owing to a gap in the system,\nMendelejew had asserted its existence five years previously, although he\nthen knew nothing of its characteristic spectral signs, namely, two\nbeautiful violet lines. Radium, too, which was discovered in 1900 and\nwas found to have the atomic weight 226, completely satisfied this test\nand fitted exactly into the place which this number reserved for it in\nthe table. Thus prediction and confirmatory discovery were fully\ncongruent in this case; the experiment followed on the visionary insight\njust as a Euclidean proof follows on a mathematical assertion, and we\nhave every reason to say that the system of Mendelejew and Lothar Meyer\nhas stood the crucial test. Future hypotheses will perhaps supplement\nthe system or enlarge our knowledge of it, but will certainly not reduce\nit _ad absurdum_.\n\n     *     *     *     *     *     *     *     *\n\nApart from these cases, there are achievements by men who may be called\n_lucky_ discoverers, although they displayed no genius for finding nor\nfor creating. The philosopher-physicist, Ernst Mach, has devoted a\nlecture to such intellects, which seems to me very valuable, if only for\nthe reason that he traces back the conceptions of discovery and\ninvention to one common root of knowledge, and explains their difference\nas being due only to a difference in the application of this discovery.\n\nBut when Ernst Mach in this lecture, \"On the Influence of Accidental\nCircumstances on the Development of Inventions and Discoveries,\" extends\nthe influence of chance to include accidental circumstances that can\nonly enter when the discoverer is closely attentive, it seems to me that\ncertain limitations are advisable. Otherwise, if we pursue Mach's line\nof thought to its extreme, we could declare every discovery to be due to\nchance, and this would be the end of the intuitive-creative idea. This\nassertion would ultimately mean that genius owes its achievements to the\naccidental arrangement of the molecules in the brain-cells of its\nassociated body. This would be just as wrong as saying that chess is a\ngame of chance because we lose a game when, by chance, we come up\nagainst a better player.\n\nHuyghens, the great discoverer and inventor, says, in his _Dioptrica_,\nthat he would have to consider anyone who invented the telescope without\nthe favourable intervention of chance to be a superhuman genius. Why\nshould he choose just the telescope? To many the invention of the\nDifferential Calculus will appear grander and due to a higher degree of\ningenuity. And since it was produced quite methodically, and since\nchance was excluded, we may follow Huyghens and with good reason\nproclaim its authors superhuman geniuses.\n\n     *     *     *     *     *     *     *     *\n\nMany a true inspiration is dependent on some impulse from without. Who\ndiscovered Electromagnetism? The world-echo answers, \"Oersted,\" with the\nsame confidence that it couples together the names America and Columbus.\nThis shows how enormously important was the achievement. Next to\nsteam-power nothing has exerted such a revolutionary influence in all\nbranches as electromagnetism. Without it, the world of to-day would\npresent a totally different aspect. Without it, we should have no\ndynamos, no electric trams, no telegraphy, no electric-power stations,\nall of which are due to the work of Arago, Gay-Lussac, Amp\u00e8re, Faraday,\nGramme, and Siemens. Without it, there would be none of the abundance of\nbrilliant discoveries that are associated with the names of Maxwell,\nHertz, and Einstein. The fact that physics used to be divided into three\nparts--Mechanics, Optics, Electrodynamics--and that, since then, the\ncoherent unity of the physical picture of the world has been developed,\nshows us a picture in the background of which we see the illuminating\nfigure of Hans Christian Oersted. It must not be overlooked, however,\nthat in the case of his great discovery, too, chance played a definite\npart. It occurred one day when Oersted was holding a lecture in the\nwinter of 1819-20; a magnetic needle situated near his Volta-battery\nbegan to vibrate irregularly. This apparently unimportant trembling of\nthe metal points contained the key to a fact, the whole consequences of\nwhich could in no conceivable way have entered the mind of this observer\nof a hundred years ago, in spite of the genius of the Danish scientist,\nwhich is documented in the classical and far-famed dissertation,\n\"Experimenta circa effectum conflictus electrici in Acum magneticam,\"\nwhich appeared in July 1820. It cleared the way for intuitions that were\nequally as fruitful for theory as for practice. Thirteen years after\nthis initial discovery the world saw the first very important\nconsequence in Gauss' and Weber's electric telegraph, and a little later\nthe eminent discoverer Fechner, in Leipzig, proclaimed it as his\nconviction that, within two years, electromagnetism would entirely\nreform the world of machines, and would entirely supersede steam- and\nwater-power. Of course, his time estimate fell far short of the mark. It\nhas been reserved for the present generation to realize that we live in\nan electromagnetic world, and that we have, theoretically and\npractically, to spend our life electromagnetically. The first indication\nof this knowledge hung upon the quivering point of a magnetic needle,\nand from it there evolved the electromagnetic ideas that we are so fond\nof picturing as our handmaids, but which, in reality, are sovereign over\nus all.\n\n     *     *     *     *     *     *     *     *\n\nA great deal of the history of discovery must be revised and corrected.\nThe Spiral of Archimedes is not due to Archimedes, nor Marriotte's Law\nto Marriotte, nor Cardan's formula to Cardan, nor Crookes' Tube to\nCrookes, and Galvanism is only related to Galvani by the following\nanecdote. It arose from an accidental experience of Madame Galvani in\nthe kitchen: a half-skinned frog that was to be fried for the evening\nmeal happened to rest between a scalpel and a tin plate, which brought\nit into metallic contact with an accidental discharge of electricity;\nthe frog twitched; the head of the house gave a very na\u00efve\ninterpretation to the phenomenon; and it was under such auspices that\nGalvanism made its entry into the world. It would be a futile task to\nendeavour to trace the connexion between experiment and the underlying\nidea, which, in this case, first came to life in Alexander Volta. What\nwould have remained a mere frog-dance if left to Galvani now acquired\nthe rank of a discovery through the work of a thinking physicist, who\nset up a \"Voltaic series\"; this discovery then assumed power and dignity\nin the hands of Nicholson, Davy, Thomson, Helmholtz, and Nernst. The\nwords Galvanic Electricity should be made to give way entirely to\nVoltaic Electricity,[4] as in the case of many another expression for\nwhich chance and insufficient thought have stood sponsor.\n\n[Footnote 4: The usual term in England is Voltaic Electricity, or,\nsimply, Current Electricity.--H. L. B.]\n\nIt often happens that experiment acts as a corrective of the underlying\nidea, neither confirming nor contradicting, but nursing it, as it were,\nstrengthening, and purging it of errors. Such experiments, partly in\nconjunction with chance, play an important, sometimes a decisive, r\u00f4le\nin the works of Dufay, Bradley, Foucault, Fresnel, Fraunhofer, and\nR\u00f6ntgen. Faraday, who was incapable of observing otherwise than\nintensively, found himself compelled, whilst studying induction\nphenomena, to alter his initial view, and it is just this correction by\nexperiment that constitutes Faraday's real discovery. In many cases the\ninitial idea is corrected, nay surpassed, by the result. Columbus worked\nmethodically when he set out to reach the East Indies by travelling\nwestwards; but what he discovered was not a confirmation of his nautical\nidea only, but something much greater, which certainly did not lie in\nhis calculation. Thus he became the archetype of all searchers, who had\nthought out and anticipated essentially different conditions from those\nthat were afterwards discovered to be prevalent. Among these are to be\ncounted Priestley and Cavendish, who clung to the erroneous notion of\nphlogiston, even when they had the evidence to the contrary in the\nelements they had themselves discovered, namely, oxygen and hydrogen.\nGraham Bell, the inventor, was seeking something quite different from\nwhat he later hit on: as a teacher of the deaf and dumb he was trying to\ngive a visual picture of sounds, in order to make clear the formation of\nsounds to his pupils; this led him to construct an electrical apparatus,\nwhich finally led to the discovery of the telephone.\n\nThe truest and sharpest contrast with the _experimentum crucis_ is\nfurnished by experiment when it shows the exact opposite of what the\nexplorer was expecting. But since an absolute No entails a very decisive\nYes--namely, in this case, the affirmation of a relationship that was\npreviously held to be impossible--a negative experiment of this kind,\nwhen it occurs, will be followed by momentous consequences; these will\nbe the more important in proportion as the question, the affirmation of\nwhich was expected by the physicist, is of a fundamental character.\n\nThe experiments of Michelson and Morley, directed at proving the\nexistence of the ether, are to be regarded as the true classical\ninstances of these experiments answering with an overwhelming negative.\nTheir first effect was to produce a sense of helplessness, a check to\nthought, a void in the chamber of ideas. And to fill this void there\narose new views of the world in which we nowadays recognize the true\nthought-pictures of the universe. The great names--Lorentz, Minkowski,\nAlbert Einstein--shone out!\n\nAs there are forerunners for almost every Important event, so also in\nthe case of the _experimentum crucis_ of Michelson and Morley. Henri\nPoincar\u00e9, the famous mathematician, whilst still a student of the\n\u00c9cole Polytechnique, had initiated experiments with his fellow-student\nFav\u00e9, which followed the same object. The Michelson-Morley experiment\nwas at least a hundred times more accurate. In each case the conclusion\nwas that the laws of optics are not disturbed by a motion of\ntranslation, such as that of the earth through space this is, however,\ncontrary to what the old physical ideas lead us to expect.\n\nIf we assume the existence of a space-filling ether, the earth, owing to\nits own velocity of nineteen miles per second, would have to pass\nthrough a hurricane just as in the case of travellers sitting in an open\ntrain rushing along at very great speed. If we send out light rays in\nall directions simultaneously from any point on the earth's surface,\nsome will travel in the teeth of the ether-storm, others will experience\nonly a part of the storm's power; so that of two light-rays travelling\nin exactly opposite directions the retardation of the one should be\nequal to the acceleration of the other; and yet they are not quite\nequal, for a simple calculation shows that in every case the retardation\nis slightly more than the acceleration.\n\nThis may be made clear by means of a model of easy construction, or,\nbetter still, by considering a ship that is subject to a constant\ncurrent and, simultaneously, to a pressure of the wind. The time taken\nby the boat in making a trip up and down stream can never be the same\nfor the cases when the wind is in the direction of the current, and vice\nversa.\n\nIn the case of the ray of light, which is sent backwards and forwards by\nmeans of a contrivance of mirrors, this fact should be clearly\ndemonstrated by means of the interference-fringes, which are able to\nshow much smaller effects than the experiment demands. The experimental\noracle was to speak, but it remained silent. This portentous silence\nsignified: no interference-effect, no action of the ether-current, no\ninfluence due to translation--nothing!\n\nThis \"nothing\" compelled a decision of a very startling kind, for the\nresult of this experiment was in direct contradiction to another famous\nexperiment. Fizeau had proved that the ether is practically rigid and\nremains fixed in interstellar space. A decision had to be taken in\nfavour of Fizeau or Michelson and Morley. Yet this was impossible, for\nboth had operated with unsurpassable accuracy. It was impossible to\nreconcile both views as they were diametrically opposed. This\ncontradiction remains, even if we assume a different hypothesis, not\ninvolving the ether, for Fizeau's experiment. A solution was impossible\nwithout undertaking revolutionary changes in the whole of physical\nthought.\n\nThis radical change was effected by Einstein; and this mysterious\ncontradiction disappeared in the resulting revolution of thought.\nEinstein supplanted the absolute time-conception by a new relative\nconception, and thus the perplexing problem disappeared. Two great\nprinciples arose as regulative factors in thought, and wherever these\nwere applied, they achieved wonders: one was the new conception of time\nthat deprived the earth of her unique position as the sovereign of time\nby the introduction of the principle that the rate at which time elapses\nis different in media moving at different speeds; the other is the\nprinciple of the constancy of the velocity of light. One feels a\ntemptation to apply a mythical allegory: just as the world, according to\nthe Biblical story, originated from nothing, so there arose from the\n\"nothing\" of the Michelson-Morley experiment a new world, a world of\nknowledge, a cosmos of thought, in which perfect harmony reigns.\n\nIts truth was contained in itself before the experimental proof was\nfurnished. And this realization of truth has become a fact in the\n_experimentum crucis_ for which the sun and stars formed the material.\nThis will be discussed in another part of the book.\n\n\"The really important factor is ultimately intuition,\" Einstein had said\nto me. It made me think of Huyghens' remark about the genius who would\nhave been able to create the telescope without the help of chance. Was\nnot this intellect, imagined by Huyghens, sitting opposite me at that\nmoment? An inner voice answered in the affirmative, for Einstein's\nthought-complex seemed to me at that moment a kind of telescope for the\nhuman mind, a telescope that had arisen out of pure intuition, and whose\nrange stretched to the limits of the universe.\n\n\n\n\nCHAPTER VI\n\nOF DIFFERENT WORLDS\n\nImaginary Experiment with \"Lumen.\"--Impossibilities.--A Destroyed\nIllusion.--Is the World Infinite?--Surface Creatures and Shadow\nRambles.--What is the Beyond?--Action at a Distance.--Ideas of\nMulti-dimensional Regions.--Hypnotism.--Recollections of Z\u00f6llner.--Science\nand Dogma.--The Trial of Galilei.\n\n\nCONVERSATION held during April 1920 destroyed an illusion which had\nbecome dear to me.\n\nIt concerned the fantastic figure, \"Lumen,\" conceived as an actual\nhuman being, imagined as endowed with an extraordinary power of motion\nand keenness of sight. Mr. Lumen is supposed to be the invention of the\nastronomer Flammarion, who produced him in the retort of fancy, as Faust\nproduced Homunculus, to use him to prove the possibility of very\nremarkable happenings, in particular, the reversal of Time.\n\nEinstein declared outright: \"Firstly, Lumen is not due to Flammarion,\nwho has derived him from other sources; and secondly. Lumen can in no\nway be used as a means of proving things.\"\n\nMOSZKOWSKI: \"It is at least very interesting to operate with him. Lumen\nis supposed to have a velocity greater than that of light. Let us assume\nthis as given, then the rest follows quite logically. If, for example,\nhe leaves the earth on the day of a great event, such as the battle of\nWaterloo, and---- May I trace out this example, at the risk of tiring\nyou?\"\n\nEINSTEIN: Do repeat it, and act as if you were telling something\nentirely new. It is clear that the Lumen-story gives you great\namusement, so please talk quite freely. But I cannot forgo the privilege\nof showing later how the whole adventure and its consequences must be\ndemolished.\n\nM.: Well then, the person, Lumen, sets off at the end of the battle of\nWaterloo to make an excursion into space with a speed of 250,000 miles\nper second. He thus catches up all the light-rays that left the field of\nbattle and moved in his direction. After an hour he will already have\nattained a lead of about twenty minutes. This lead will be gradually\nincreased, so that at the end of the second day he will no longer be\nseeing the end of the battle, but the beginning. What has Lumen been\nseeing in the meantime? Clearly he has been observing events happening\nin the reverse direction, as in the case of a cinematograph which is\nexhibiting pictures backwards. He saw the projectiles leaving the\nobjects they had struck, and returning into the mouths of the cannon. He\nsaw the dead come to life, arise, and arrange themselves into battalion\norder. He would thus arrive at an exactly opposite view of the passing\nof time, for what he observes is as much his experience as what we\nobserve is ours. If he had seen all the battles of history and, in fact,\nall events happening in the reverse order, then in his mind \"before\" and\n\"after\" would be interchanged. That is, he would experience time\nbackwards; what are causes to us would be effects to him, and our\neffects would be his causes; antecedents and consequents would change\nplaces, and he would arrive at a causality diametrically opposite to our\nown. He would be quite as justified in adopting his view of the\nhappening of things, according to his experiences, and of the causal\nnexus as it appears to him, as we are justified in adopting ours.\n\nEINSTEIN: And the whole story is mere humbug, absurd, and based on false\npremises, leading to entirely false conclusions.\n\nM.: But it is only to be taken as an imaginary experiment that plays\nwith fantastic impossibilities to direct our ideas on to the relativity\nof time by a striking illustration. Did not Henri Poincar\u00e9 adduce this\nextreme example to discuss the \"reversal\" of time?\n\nEINSTEIN: You may rest assured that Poincar\u00e9, even if he used this\nexample as an entertaining digression in his lectures, took the same\nview of Lumen as I do. It is not an imaginary experiment: it is a farce,\nor, to express it more bluntly, it is a mere swindle! These experiences\nand topsy-turvy perceptions have just as little to do with the\nrelativity of time, such as it is taught by the new mechanics, as have\nthe personal sensations of a man, to whom time seems long or short\naccording as he experiences pain or pleasure, amusement or boredom. For,\nin this case, at least the subjective sensation is a reality, whereas\nLumen cannot have reality because his existence is based on nonsense.\nLumen is to have a speed greater than that of light. This is not only an\nimpossible, but a foolish assumption, because the theory of relativity\nhas shown that the velocity of light cannot be exceeded. However great\nthe accelerating force may be, and for however long it may act, it\ncannot cause this limit to be transcended. Lumen is supposed to be\nequipped with the organ of sight, that is, he is supposed to have a\ncorporal existence. But the mass of a body becomes infinitely great when\nit reaches the velocity of light, so that it is quite absurd to go\nbeyond this stage. It is admissible to operate with impossibilities in\nimagination, that is, with things that contradict our practical\nexperience, but not with absolute nonsense. That is why the other\nadventure of Lumen, in which he jumps to the moon, is also an absurdity.\nIn this, he is supposed to leap with a speed greater than light, and,\nwhen he reaches the moon, to turn round instantaneously, with the result\nthat he sees himself jumping from the moon to the earth backwards! This\njump is logically meaningless; and if we try to make deductions of an\noptical nature from such a nonsensical assumption, we deceive ourselves.\n\nM.: Nevertheless, I should claim extenuating circumstances for this case\non the ground that I am enlisting the help of the conception of\nimpossibility. A journey even at a speed of only 1000 miles per second\nis impossible for a man or a homunculus.\n\nEINSTEIN: Yes, according to our experience, if we measure it against\nfacts. We cannot state definitely that a journey into the universe at an\nenormous yet limited velocity is absolutely impossible. Within the\nindicated bounds every play of thought that is argued correctly is\nallowable.\n\nM.: Now, suppose that I strip Lumen of all bodily organs and take him as\nbeing a pure creature of thought, entirely without substance. A velocity\ngreater than that of light can be imagined, even if it cannot be\nrealized physically. If, for example, we think of a lighthouse with a\nrevolving light, and consider a beam of light about 600 miles long,\nwhich rotates 200 times per second. Then we could represent to ourselves\nthat the light at the circumference of this beam travels with a speed of\nnearly 760,000 miles per second.\n\nEINSTEIN: As for that, I can give you a much better example of the same\nthing. We need only imagine that the earth is poised in space,\nmotionless, and non-rotating. This is physically admissible. Then the\nmost distant stars, as judged by us, would describe their paths with\nalmost unlimited velocities. But this projects us right out of the world\nof reality into a pure fiction of thought, which, if followed to its\nconclusion, leads to the most degenerate form of imagination, namely, to\npathological individualism. It is in these realms of thought that such\nperversities as the reversal of time and causality occur.\n\nM.: Dreams, too, are confined to the individual. Reality constrains all\nhuman beings to exist in one and the same world, whereas, in dreams,\neach one has his own world with a different kind of causality.\nNevertheless, dreams are a positive experience, and signify a reality\nfor the dreamer. Even for waking reality it would be easy to construct\ncases in which the causal relationship is shattered. Suppose a person\nwho has grown up in a confined retreat, such as Kaspar Hauser, looks in\na mirror for the first time in his life. As he knows nothing of the\nphenomena of optical reflexion, he sees in it a new, objective world\nthat gives a shock to, or even subverts, his own idea of causality in so\nfar as it may have become developed in him. Lumen sees himself jump\nbackwards, whereas Kaspar Hauser sees himself performing gestures on the\nwrong side of his body; should it not be possible to draw a reasonable\nparallel between these two cases?\n\nEINSTEIN: Quite impossible. However you set about it, your Lumen will\ninevitably come to grief on the conception of time. Time, denoted in\nphysical expressions by the symbol \"t,\" may, indeed, be given a negative\nvalue in these equations, so that an event may be calculated in the\nreverse direction. But then we are dealing with pure matters of\ncalculation, and in this case we must not allow ourselves to be drawn\ninto the erroneous belief that time itself may travel negatively, that\nis, retrogressively. This is the root of the misapprehension: that what\nis allowable and indeed necessary in calculations is confused with what\nmay be thought possible in Reality.[5] Whoever seeks to derive new\nknowledge from the excursions of a creature like Lumen into space,\nconfuses the time of an experience with the time of the objective event;\nbut the former can have a definite meaning only if it is founded on a\nproper causal relation of space and time. In the above imaginary\nexperiment the order of the experiences in time is the reverse of that\nof the events. And as far as causality is concerned, it is a scientific\nconception that relates only to events ordered in space and time, and\nnot to experiences. In brief, the experiments with Lumen are swindles.\n\n[Footnote 5: Perhaps an analogy will serve to make this clear. Suppose\nthat a certain quantity of some foodstuff is consumed by \u2152 head of\npopulation. The false inference would be that a population is possible\nwhich has \u2152 heads! In the same way the statistics may be quite correct\nin arriving at the figure \u2155 suicides, but if we leave the realms of\ncalculation, then the \u00a3 suicide loses its meaning entirely.]\n\nM.: I must resign myself to giving up these illusions. I must frankly\nconfess that I do so with a certain sadness, for such bold flights of\nconstructive fancy exert a powerful attraction on me. At one time I was\nnear outdoing Lumen by assuming a Super-Lumen, who was to traverse all\nworlds at once with infinite velocity. He would then be in a position to\ntake a survey of the whole of universal history at a single glance. From\nthe nearest star, Alpha Centauri, he would see the earth as it was four\nyears ago; from the Pole Star, as it was forty years ago; and from the\nboundary of the Milky Way, as it was four thousand years ago. At the\nsame moment he could choose a point of observation that would enable him\nto see the First Crusade, the Siege of Troy, the Flood, and also the\nevents of the present day simultaneously.\n\nEINSTEIN: And this flight of thought, which, by the way, has been\nindulged in repeatedly by others too, has much more sense in it than the\nformer one, because you may make an abstraction which disregards speed\naltogether. It is only a limiting case of reflection.\n\nM.: I should like to touch on other limiting cases, in particular two\nthat I find it impossible to interpret. Lotze mentions them in his\nLogic. The first concerns the infinitely long lever whose fulcrum, or\nturning-point, is at the confines of the universe. According to the Laws\nof Levers, a mass of magnitude zero will suffice to keep in equilibrium\nat the end of the other lever-arm any weight, no matter whether it is a\nmillion times heavier than the earth. Our imaginations cannot even\npicture this. Yet I cannot feel satisfied with the mere explanation that\nit is an exceptional case, an extension of a general law to a case in\nwhich it is no longer applicable. The second example is still more\nperplexing because it does not require a journey into other worlds, but\nleads us into inconceivable consequences even if we remain on the earth.\nLotze considers this second limiting case easier; to me it seems more\ndifficult. It is this: The force that a wedge exerts is inversely\nproportional to its thickness. If it is infinitely thin, this formula\ngives an infinitely great result, whereas, actually, the force exerted\nis nil. This very thin wedge, transformed finally into a geometrical\nplane, should be able to split in twain any wooden or even steel block.\nAnd now, consider a special arrangement of this wedge in which it is\nresting with its extremely sharp edge vertically downwards, whereas at\nthe top it broadens to a little ledge which supports a weight. We then\nget the incredible result that this wedge, which can be imagined\nconcretely, should be able to cut through the whole earth with its\nextremely fine edge, if placed on some base. Where is the fallacy in\nthis case?\n\nEINSTEIN: The mechanical facts have not been taken sufficiently into\nconsideration.--He illustrated his further remarks by drawing a few\nstrokes with his pen, and proved from his diagram that a wedge of this\nsort would be able to perform what I assumed, only if the base on which\nit is placed is composed of separate laminae. Otherwise the assumption\nthat the force is infinitely great would be erroneous.\n\n     *     *     *     *     *     *     *     *\n\nAfter this digression to a limiting case on the earth we returned to\nmore general problems, and the question of the finitude or infinitude of\nthe universe. Shortly before, Einstein had given an address to the\nBerlin Academy on this point, involving difficult calculations, and I\nhoped to hear from him an easy explanation at least in general terms.\n\nIt is one of the ultimate problems. Whoever talks of the limits of the\nworld endeavours also to mark off the bounds of the understanding. The\naverage person, at first sight, almost always decides in favour of an\ninfinite universe, on the ground that a finite world is inconceivable.\nHe argues that, if it were considered finite, we should immediately be\nconfronted with the question: What lies _beyond_ the finite boundary?\nSomething must be present, even if it is only empty space. This brings\nus into an inevitable conflict with the first of Kant's \"antinomies,\"\nwith the thesis and antithesis, from which there is no escape. What is\nthe meaning of the fact that the apprehensive understanding seeks refuge\nin \"Infinity\"? It signifies that he gets entangled in the folds of a\nnegative conception, that furnishes him with no explanation at all, and\nexpresses merely that his first assumption of finitude cannot be thought\nout to its conclusion.\n\nBesides this, a second disturbing question arises. Is there a finite or\ninfinite number of stellar bodies? If this question refers to an assumed\ninfinite space, even if such space is inconceivable, then there are two\npossible answers. For it would be possible to imagine a finite number of\nstars even if no limit could be found for space.\n\nWhereas the general question of space in the universe belongs\nexclusively to speculative philosophy, the star-question is not purely\nmetaphysical, but is physical, too, and has accordingly been treated by\nphysicists. The great astronomer Herschel imagined he could solve it by\nmeans of optical principles, and he arrived at the conclusion that the\nnumber of heavenly bodies must be finite, as otherwise the aspect of the\nstarry firmament, from the point of view of illumination, would be\nentirely different. But this proof did not establish itself among\nscientists, for the number of stars of the type of the sun might be\nfinite, whilst there was an infinite number of _dark_ stars.\n\nA further question presented itself: Would it be possible for a definite\npart of the heavens (say, that north of the ecliptic) to contain an\ninfinite number of stars, whilst other parts contained only a finite\nnumber? At first this sounds very extraordinary, but it is by no means\nunreasonable, as a concrete example will show: If, on a scale of\ntemperature, we count the degrees of heat from a certain point, then\nthey stretch apparently to infinity in one direction, whereas they\nextend only to -273\u00b0 (Centigrade) in the other direction, that is, to\nthe absolute zero. Thus we can imagine an arrangement which stretches to\ninfinity only in one direction.\n\nTo get an insight into the discussion by Einstein which is about to\nfollow, we must first dispose of a certain arbitrariness of language,\nlying in the customary indiscriminate use of the terms, infinite,\nimmeasurable, and unbounded. Suppose we have a globe about one foot in\ndiameter, the surface of which is inhabited by extremely small,\nultramicroscopic creatures that can move about freely and can think. The\nsurface of the sphere constitutes the world of the micro-men, and he has\na very good reason for considering it infinite, for, however far and in\nwhatever direction he may move, he never encounters a boundary. But we,\nwho live in our space, look on to this spherical surface, and recognize\nthat his judgment is erroneous. To us his spherical world seems\ndecidedly finite and quite measurable, although it has no determinable\nbeginning and no end, and thus must appear unbounded to the micro-man.\nIn fact, we ourselves may regard it as boundless, if we can succeed in\nforming an abstraction that leaves out of account its limitations in our\nown space.\n\nNow, it might occur to a particularly intelligent micro-being to\nundertake a voyage for the purpose of making measurements. He carefully\nmarks his point of departure, walks Straight ahead in a certain\ndirection, describing a circle on his sphere--a circle which he will\nnecessarily regard as a straight line. He continues ever onwards in the\nfirm conviction that he is getting farther and farther away from his\nstarting-point. Suddenly, he discovers that he has reached it again. He\ndiscovers, by the mark he made, that he has not been describing a\nstraight line, but a line that merges into itself.\n\nThe micro-professor would be compelled to declare: Our world, the only\none known to me, is not infinite, although in a certain sense boundless.\nMoreover, it is not immeasurable, since it can be measured in at least\none direction by the number of steps I have walked. From this we may\ninfer that our former geometrical view was either wrong or incomplete,\nand that, in order to understand our world properly, we must build up a\nnew geometry.\n\nWe may assume that the majority of the remaining micro-inhabitants would\nat first protest strongly against this decision. The idea that a line,\nwhich appears to them to be pointing always in the same direction, is\ncurved, seems to them inconceivable and absurd. They would only\ngradually overcome their scruples of thought by getting an insight into\na newly developed geometry that makes clear to them for the first time\nthe conception of a sphere.\n\nIn our world of space, which includes all stars, we are the\nmicro-inhabitants. We have been born with, or have inherited, the idea\nof a straight and ever-advancing path in space, and we become filled\nwith the utmost astonishment if some one asks us to believe that if we\nundertake a voyage in one direction out into the universe, beyond Sirius\nand a million times farther, we should finally arrive at our\nstarting-point again, although we had not changed our direction. But the\nmacro-being, who belongs to a universe of higher dimensions and who\nlooks on our world as we looked on the above spherical world one foot in\ndiameter, sees the narrowness of our view. We, too, are in a position to\nrise above this narrow view by means of a theory founded on our\nexperience, which will lead us to an extended world-geometry, just as\nthe micro-professor used his experience to extend his theory of the\ncircle to include the conception of a sphere.\n\nAfter these preliminary remarks we shall endeavour to get an insight\ninto Einstein's reasoning, not in the form in which it was originally\npresented (in the Report of the Proceedings of the Berlin Academy of\nScience of 8th February 1917), but in a very easy description which was\ngiven to me during a conversation. Here, too, I shall try to preserve\nthe sense of Einstein's remarks without binding myself strictly to his\nwords. For although I am indebted to him for his efforts to avoid\ndifficult points, yet the aim of this book is, if possible, to make the\nexplanation still easier. Any lack of accuracy arising from this last\nsimplification is to be debited to me. The new form of representing the\nargument, which is as important as it is fascinating, is, of course, due\nto Einstein.\n\nThe final result stated by Einstein was: The universe, both as regards\nextent and mass, has finite limits and can be measured. If anyone asks\nwhether this can be pictured, I shall not deprive him of the hope. All\nthat is required is a power of imagination that is great enough to\nfollow a pictorial description and that can take up the right attitude\ntowards a sort of figurative representation.\n\nLet us again imagine a sphere of modest dimensions with its\ntwo-dimensional surface. We are concerned only with the latter, and not\nwith the cubical content. The sphere is to be considered as resting on\nan absolutely plane white table of unlimited extent in all directions.\nThe sphere touches the table at a single point which we shall call its\nSouth Pole; on the top side directly opposite, we have the North Pole.\nTo simplify matters we may make a sketch on paper of a vertical section\nthrough the centre of the sphere. This profile-picture will show us the\nsphere as a circle, and the white table as a straight line; the line\njoining the two poles is the axis of the globe, and the sectional circle\nis a meridian.\n\nLet us further suppose a creature (resembling, say, a ladybird in shape)\nhaving length and breadth, but no thickness, to crawl along this\nmeridian. Although it has no thickness, we shall imagine it to have one\nproperty of a solid body, that of being opaque, so that it can throw a\nshadow if properly illuminated. We assume the globe itself to be\ntransparent. At the North Pole we suppose a very strong point-source of\nlight, a little electric lamp, that sends out rays freely in all\ndirections.\n\nThe insect begins its journey at the South Pole and sets out along the\nmeridian to reach the North Pole. It is illuminated by the lamp all the\nway, so that it continually throws a shadow on the white table. The\nshadow moves along the table farther and farther from the South Pole, in\nproportion as the insect moves up the meridian, with the difference that\nwhile the insect is describing an arc of a circle, its shadow moves\nalong a straight line. The position of the shadow can be determined at\nany moment by drawing the straight line connecting the lamp to the\ninsect, and producing it to meet the white surface of the table; the\npoint of intersection is the projection of the insect on the plane.\n\nAt the beginning of the excursion the shadow is exactly as large as the\nflat insect itself, if we assume that its dimensions are negligible\ncompared with the surface of the sphere, for it will then coincide with\nits own shadow. But when the insect crawls upwards, its shadow will\nincrease, because of the shortened distance between the insect and the\nlamp, and because the points of projection on the table separate more\nand more as their distances from their corresponding points on the\nsphere become greater. There is thus a twofold increase. The shadows\nmove away more and more rapidly, and at the same time increase in size.\n\nWhen the insect gets very near the North Pole, its shadow, now of\nenormous dimensions, has moved to a very great distance; and when\nfinally it reaches the Pole, its shadow becomes infinitely great and\nthus stretches to infinity.\n\nBut let the insect wander on along the meridian, past the North Pole,\ndown towards the South. At the moment when it passes the upper Pole its\nshadow jumps from the right side to the left. Its shadow now emerges\nfrom an infinite distance to the left, and, instead of being infinite\nsize, again becomes finite in dimensions as it approaches. It contracts\nas it approaches, and, in short, the same process as occurred during the\nfirst half of the journey now occurs in the reverse order.\n\n[If we fix on the critical moment of the jump from the right to the\nleft, that is, from plus infinity to minus infinity, we may encounter\ndifficulties. For the surface-creature pursues its way without\ninterruption and continuously, and we experience a wish to ascribe to it\na shadow-path that is also unbroken and continuous. This is possible\nonly if we assume the two points at infinity to be connected, that is,\nif we consider them identical. This assumption will seem more natural if\nwe reason as follows. In the profile-picture the table is represented as\na straight line, and it is along this line that the shadow travels. We\nmay regard this line as an infinitely great circle, for an infinitely\ngreat circle has zero curvature, just as the straight line, from which\nit is therefore indistinguishable. The infinitely great circle has,\nhowever, only one point situated at an infinite distance, that is, it\nassociates together the two apparent points at infinity of the straight\nline with which we identify it. Accordingly, we preserve the continuity\nof the shadow-journey, too. Einstein considers it allowable to say that\nthe right and the left portion each represent a half of the infinite\nprojection, which becomes complete only when the two ends are joined.]\n\nNow we must be prepared for an effort of thought which will need\nconsiderable help from our imaginations. Firstly, instead of one\nsurface-creature, we shall suppose several crawling about on different\nmeridians, so that a series of shadows will be moving about along\nstraight lines radiating from the South Pole. Next, let us imagine the\nwhole picture to have its dimensions increased by one, that is, we\ntransform the plane-picture into a space model. The phenomena are to\nremain the same, except that they are to be strengthened by one\ndimension, surface conditions becoming space conditions, and surfaces\nbecoming solids.\n\nWhat we now see are actual insects with round bodies (if we retain our\noriginal type of creatures), or, since there is no restriction as to\ntheir size--the shadows have assumed all possible sizes--we may assume\nany solid bodies whatsoever, stars or even star-systems. Their motions\ntake place in exactly the same way as those of the shadows previously\nthrown by the flat bodies.\n\nThis means that, if a stellar body moves, its size increases until it\nreaches the spherical boundary of space, where it becomes infinitely\ngreat, and, at the same moment, passes from plus infinity to minus\ninfinity, that is, it enters the universe from the opposite direction;\nthen, if it continues moving in its original direction (as it has been\ndoing all along), it gradually becomes smaller in size until, finally,\nit reaches its original position and its original size. If we suppose\nthe body to be endowed with the power of sensation, it would not be able\nto observe its own changes of size, since all its scale-measures would\nbe altered in the same proportion. This whole complex of phenomena would\nstill be taking place in an infinite world of space, but, according to\nthe General Theory of Relativity, the geometry that is valid in this\nworld would no longer be that of Euclid; it is replaced by a system of\nlaws that arise from physics as a geometric necessity. In this new\ngeometry, a circle described with unit radius is a little smaller than\nit would be in Euclidean geometry, with the result that the greatest\nconceivable circle in this world cannot assume an infinite size.\n\nThus we have to imagine that our solid bodies, say stars, arrive at a\npoint in their travels which we may term only \"enormously distant.\" If\nwe call the directions right and left instead of positive and negative,\nthen the process reduces itself to this: the moving body reaches the\npoint, which is enormously distant on the right, and which is identical\nwith the point enormously distant on the left; this means that the body\nnever moves out of the space continuum of this world, but returns to its\ninitial point of departure even when it moves ever onward in what is\napparently a straight line. It moves in a \"warped\" space.\n\nEinstein has succeeded in finding an approximate value for this\nnon-infinite universe, from the fact that there is a determinable\ngravitational constant. In the constitution of the universe it denotes\nthe same for the mass-relationships of the earth as the gravitational\nconstant of the earth denotes for us, namely, the quantity from which we\ncan calculate the final velocity attained by a freely falling body\nduring a unit of time. He also assumes a probable average for the\ndensity of distribution of matter in the universe, by supposing that it\nis about the same as that of the Milky Way. On this basis Einstein has\narrived at the following result by calculation:\n\nThe whole universe has a diameter of 100 million light-years, in round\nnumbers. That amounts to about 700 trillion miles.\n\nM.: Does this follow from the discussion you entered on just now?\n\nEINSTEIN: It follows from the mathematical calculations which I\npresented in \"Cosmological Considerations arising from the General\nTheory of Relativity,\" in which the figure I have just quoted is not\ngiven. The exact figure is a minor question. What is important is to\nrecognize that the universe may be regarded as a closed continuum as far\nas distance-measurements are concerned. Another point, too, must not be\nforgotten. If, in deference to your wish, I used an easy illustration,\nthis must not be regarded otherwise than as an improvised bridge to\nassist the imagination.\n\nM.: Nevertheless, it will be very welcome to many, who are unable to\ngrasp the difficult Cosmological Considerations. The number that you\nmention is overwhelming in the extreme. Indeed, it seems to me that a\ndiameter of 100 million light-years suggests an infinitely great\ndistance more than the word \"infinity\" itself, mentioned _per\ndefinitionem_, which conveys nothing to the ordinary mind. It calls up a\nregular carnival of numbers, particularly in those to whom the immense\nnumber alone gives a certain pleasure. But you were going to give me the\nnumber expressing the mass, too?\n\nAnd then I learned that the weight of the whole universe, expressed in\ngrammes, was 10 multiplied by itself 54 times, that is 10^54 (453\ngrammes = 1 lb., roughly). This seems rather disappointing at first, but\nassumes a different aspect when we represent to ourselves what this\nfigure signifies. It means that the weight of the universe in\nkilogrammes is high in the octillions. The earth itself weighs six\nquadrillion kilogrammes, hence the weight of the Einstein universe bears\nthe same relation to the weight of the whole earth as the latter bears\nto a kilogramme. Again, the earth's weight to that of the sun is as 1 is\nto 324,000. Hence we should have to take at least a trillion, that is, a\nmilliard times a milliard, suns to get the weight of the universe. And\nas far as the linear extent is concerned, let us consider the most\ndistant stars of the Milky Way, which are at an inconceivable distance,\nexpressible only in light-years. If we place 10,000 such Milky Ways end\nto end we shall arrive at this diameter of the universe, which,\naccordingly, will have a cubical content a thousand milliard times\ngreater than the region accessible to astronomical observation.\n\nThus we have a very spacious universe. Yet it is not spacious enough to\nsatisfy all the demands that a mathematician interested in permutations\nand combinations might make. One of such combinations is exemplified in\nthe so-called _Universal Book_, that originated in an imaginary\nexperiment of Leibniz. If we picture to ourselves the sum-total of all\nbooks that can be printed by making all possible arrangements and\nsuccessions of our letters, each book differing from any other even if\nonly in one symbol, then, together, they must contain all that can be\nexpressed in sense and nonsense, and everything that is ever realizable\nactually or in dreams. Hence, among other things, they would include all\nworld-history, all literature, and all science, even from the beginning\nof the world to the end. If we agree to the convention of operating with\n100 different printed signs (letters, figures, stops, spacings, etc.),\nand of allowing each such book a million paces for signs, so that each\nbook will still be of a handy size, then the number of these books would\namount to exactly 10 to the two-millionth power, or, in figures, _i.e._\n10^2,000,000.\n\nThis fully exhaustive universal library containing all wisdom would\nconsist of so many volumes that it could not be contained in a case of\nthe size of the entire stellar universe. And, unhappily, it must be\nadded that the closed universe, just described by Einstein and having a\ndiameter of a hundred million light-years would be much too small to\ncontain this library.\n\n\"Nevertheless,\" said I, \"your universe pictures something inconceivably\ngreat; one might call it an infinity expressed in figures. For in your\nworld there still remains one property of infinity, namely, that it\nimposes no limitations on motion of any kind. On the other hand, the\nfigures proclaim a limited measure in the mathematical sense, however\ngreat this measure may be. This calls up the old restlessness of mind,\ndue to the persistent question: What lies beyond? The absolute Nothing?\nOr is it a something which yet does not occupy space? Descartes and many\nother great thinkers have never overcome this difficulty, and have\nalways affirmed that a closed world is impossible. How, then, is the\naverage person to reconcile himself with the dimensions you have\nestablished?\"\n\nEinstein gave an answer which, it seemed to me, offered a last escape to\napprehensive minds. \"It is possible,\" so he said, \"that other universes\nexist independently of our own.\"\n\nThat is to say, it will never be possible to trace a connexion between\nthem. Even after an eternity of observation, calculation, and\ntheoretical investigation, no glimpse or knowledge of any of these\nultra-worlds will ever enter our consciousness. \"Imagine human creatures\nto be two-dimensional surface-creatures,\" he added, \"and that they five\non a plane of indefinite extent. Suppose that they have organs,\ninstruments, and mental attitude adapted strictly to this\ntwo-dimensional existence. Then, at most, they would be able to find out\nall the phenomena and relationships that objectify themselves in this\nplane. They would then have an absolutely perfect science of two\ndimensions, the fullest knowledge of their cosmos. Independent of this,\nthere might be another cosmic plane with other phenomena and\nrelationships, that is, a second analogous universe. There would then be\nno means of constructing a connexion between these two worlds, or even\nof suspecting such a connexion. We are in just the same position as\nthese plane-inhabitants except that we have one dimension more. It is\npossible, in fact, to a certain degree probable, that we shall by means\nof astronomy discover new worlds far beyond the limits of the region so\nfar investigated, but no discovery can ever lead us beyond the continuum\ndescribed above, just as little as a discoverer of the plane-world would\never succeed in making discoveries beyond his own world. Thus we must\nreckon with the finitude of our universe, and the question of regions\nbeyond it can be discussed no further, for it leads only to imaginary\npossibilities for which science has not the slightest use.\"\n\n     *     *     *     *     *     *     *     *\n\nEinstein left me for a while to the tumult of ideas that he had roused\nup in me. After I had overcome the first shock, I sought to gain a haven\nin the idea that arose out of the first shadow-argument, in which the\nspherical bodies occurred that seek to escape towards infinity on the\nright but reappear, instead, at enormous distances on the left. Has\nanyone ever had presentiments of this kind of world? Perhaps something\nof the sort is to be found in earlier books of science? If so, they have\nescaped my notice. Yet, a passage of a poet occurs to me. It is to be\nfound in a volume by Heinrich von Kleist; it is a volume dealing only\nwith earthly matter and bare of astronomical ideas. Imagine a book the\nsubject of which is a puppet-show, containing, in the middle of it, a\nsection foreshadowing Einstein's universe! Quite by chance Kleist comes\nto speak of \"the intersection of two lines which, after passing through\ninfinity, suddenly appear on the other side, like a picture in a concave\nmirror, which moves away to infinity and suddenly returns again and is\nquite close,\" and, quite in accordance with our new cosmology, he\ndeclares: \"Paradise is locked and barred, and the cherub is behind us;\nwe must make a voyage round the world, and see whether we cannot\ndiscover an exit elsewhere at the other end perhaps.\"\n\nPerhaps poets of the future will busy themselves with this universe; not\nlyrical poets, but descendants of Hesiod, Lucretius, or R\u00fcckert. They\nwill express in verse that Einstein's world offers a source of\nconsolation to tormented spirits which have sickened of Kant's\nantinomies. For in this still almost immeasurable world the fateful\nconception \"infinite\" has been made bearable for the first time. In a\ncertain way it relieves us from what is quite inconceivable, yet into\nwhich we are usually driven, and forms a bridge between the thesis\n\"finite\" and the antithesis infinite. We are brought to a common stream,\nin which both conceptions peacefully flow together. There was no mention\nof this in our talk, and I had good reason for being cautious about\nfollowing out the theme along these lines. I must not allow any doubts\nto arise on this point: Einstein, himself, clings with unerring logic to\nthe strict mathematically defined conception of infinity, and allows no\ncompromise with the non-infinite.\n\nWhen I, on some previous occasion, sought to lead him on to a\ncompromise, involving a transition-boundary, it availed me nothing that\nI quoted Helmholtz to support the possibility of such an operation: my\neffort came to an abrupt end.\n\n     *     *     *     *     *     *     *     *\n\nIn pursuing these considerations about the universe, we arrived at\nthings which, in ordinary language, are usually called \"occult.\" In\nconnexion with this, these remarks ensued: \"I am, of course, far from\ntrying to trace out a connexion between the four-dimensionality that you\nestablish, Professor, and the four-dimensionality of certain spiritistic\npseudo-philosophers, yet it suggests itself to me that in such occult\ncircles efforts will be made to derive advantage from the fact that the\nsame word is used in both cases. This is more than a conjecture, indeed,\nfor there are no misgivings among the ignorant, and so we actually find\nthe name Einstein quoted in connexion with mediumistic experiments that\nare flavoured with four-dimensionality.\"\n\n\"It will not be expected of me,\" said Einstein, \"to enter into\ndiscussion with ignoramuses and misinterpreted. Discarding them, then,\nlet us confine ourselves to a brief consideration of the conception\n'occult,' as this has played a part in serious science. The chief\nexample of this in history is gravitation. Huyghens and Leibniz refused\nto accept gravitation, for, so they said, according to Newton's view, it\nis an action at a distance and hence belongs to the realm of the occult.\nLike everything occult, it contradicts the causal order in Nature. We\nmust not regard Huyghens' and Leibniz's contradiction as being due to\nlack of perspicacity; rather, they objected on grounds which, as\ninvestigators, they had every right to uphold. For, as far as our\neveryday experience is concerned, every mutual influence of things in\nNature occurs only by direct contact, as by pressure or impact, or by\nchemical action, as when a flame is lit. The fact that sound and light\napparently form exceptions is not usually felt as a contradiction to the\npostulate of contact. The case of a magnet appears much more striking\nbecause its effect asserts itself as a direct manifestation of force. I\nmust mention that when I, as a child, made my first acquaintance with a\ncompass--and this was before I had ever seen a magnet--it created a\nsensation in me, which I consider to have been a dominant factor in my\nlife up to the very present. There is, indeed, a fundamental difference\nbetween pressure and impact on the one hand, and what we hear and see on\nthe other, even in everyday experience. In the case of light and sound,\nsomething must be 'happening' continually, if the effect is to occur and\ncontinue....\"\n\n\"Yet another difference seems to enter here,\" I interposed. \"Is it\npossible to give a full explanation of gravitation by using only the\nconceptions pressure and impact? Perhaps 'pressure at a distance' would\nnot have seemed to contemporaries of Newton as unintelligible as a\n'tension or pull at a distance.' It seems to me that it is particularly\ndifficult to imagine a pull or an attraction towards a distant object.\"\n\nEinstein does not consider this difference considerable, and regards it\nas possible to overcome it even in a manner which can be directly\npictured. \"If the force is exerted by a corpuscular transmission,\" he\nexplained, \"we may imagine a 'force-shadow' into which the bombarding\ncorpuscles cannot penetrate. Thus if an obstacle, which produces such a\nshadow, becomes interposed between a body A and a body B, then there\nwill be a lesser pressure on the side of B facing A, and hence B will\nexperience a greater corpuscular pressure on the other side, with the\nresult that B will be forced in the direction of A, and the observer\nwould gain the impression of a pull from B to A. Nowadays, when the\ntheory of 'fields of force' dominates our physical views, we need\ntrouble just as little about using corpuscular pressures and impacts as\nabout the vortices which Descartes once considered as the ultimate\ncauses of the motions of the heavenly bodies. The efforts of certain\nreformers to reintroduce these vortices and whirlpools as explanations\nmust be regarded as futile.\"\n\n\"Nevertheless,\" I answered, \"it seems admissible to say that,\nultimately, there is always an occult element in every physical\nexplanation, an absolutely final and elementary something which we\nrecognize as a principle, without concealing from ourselves that we have\nreached the limit of explanation, and our knowledge avails no further.\nThis brings me to another question the discussion of which, as I clearly\nperceive, leads us on to dangerous ground.\"\n\nEINSTEIN: Don't hesitate to say what is troubling you. I cannot yet see\nwhat you are aiming at.\n\nM.: I am referring to certain phenomena which are also called\n\"occult\"--with the object of discrediting them. They may at times\ndegenerate to hocus-pocus and fall into the category of dubious arts. It\nseems to me, however, that scientists have not always drawn the line\nwith sufficient care, and that they have been disposed to reject as\nhumbug, without examination, everything inexplicable that dares to\npresent itself in the form of open display.\n\nEINSTEIN: In general, they will be in the right, for investigators\ncannot be expected to occupy themselves with things bolstered up by\nadvertisement, and which are supposed to be connected with some\nfabulous, occult regions.\n\nM.: Nevertheless, in my opinion even among such displays there sometimes\noccur phenomena which scientists should not pass over with contempt. I,\nmyself, have experienced such cases, and have said to myself: There are\nstranger happenings here----\n\nEINSTEIN:--than are dreamt of in your philosophy, you were about to say?\n\nM.: Exactly. These are things that in the guise of sensationalism often\nhide a physical truth well worthy of study.\n\nEINSTEIN: But you must not overlook the fact that in such cases you have\nmostly played the part of an onlooker, and hence were exposed to all\npossible manner of deception. You are baffled on all sides by\nundiscoverable tricks and by other persons, whose collusion you do not\nsuspect. This renders an objective criticism impossible.\n\nM.: This presumes that the performing artist is not entirely isolated.\nIt is possible to bring about conditions that positively eliminate all\ntricks from the very outset.\n\nEINSTEIN: If you have experienced any such cases, relate them by all\nmeans.\n\nM.: I shall be brief, and shall state only facts....\n\nEINSTEIN: Or, expressed more accurately, only things which seem to have\nbeen facts as far as you can trust to memory. Well then, you think that\nyou have grounds for saying that you caught a glimpse of a mysterious\nworld at that time.\n\nM.: It is certainly long ago, more than thirty years. Hansen, the freak,\none of the most eminent of his profession, was showing hypnotic and\ntelepathic experiments that were partly identical with experiments that\nthe celebrated scientist Charcot at Paris was performing for purposes of\npathology.\n\nEINSTEIN: Well, then, why did you hesitate before? These experiments\ncome under the head of science, and require no occult veil to appear in\nthe open.\n\nM.: This touches the main issue. Hansen did not work in the interests of\nscience, but wished, above all, to earn money. Nevertheless he had in\nhis own way produced marvellous results that were used later for\nscientific work. Unfortunately in his case, owing to the fact that he\ncloaked it in occultism at the outset, he was brusquely repudiated by\nscientists. The result was that Hansen was condemned to a long period of\nimprisonment in Dresden, thanks to the recommendation of scientists who\ndeclared that the experiments were only possible if deception was\npractised, and hence that Hansen was an impostor who should be made\nharmless by being incarcerated.\n\nEINSTEIN: And how did you yourself seek to discover whether his\nexperiments were genuine?\n\nM.: Very easily and with absolute certainty. One of my acquaintances,\nthe wealthy race-horse owner, von Oelschl\u00e4ger, had induced him by means\nof a high fee to experiment at his country house, at some distance from\nBerlin, in the presence of persons, not one of whom Hansen knew, and in\nthe case of whom there could be no question of secret collaboration. I\ncan assure you that everything succeeded without exception. A single\nsecond was sufficient for him to communicate his will to each subject of\nexperiment. He operated like a supernatural being on those present.\n\nEINSTEIN: I should like to hear examples.\n\nM.: Herr von Oelschl\u00e4ger introduced four jockeys, and suggested a race\nin the great salon. Hansen placed them astride over chairs, hypnotized\nthem on the spot, described the shape of the course, giving distances in\nkilometres, curves, and even the value of the prizes. He then gave the\nsignal for starting. The jockeys immediately began treating their chairs\nas race-horses, exhibiting all the signs of extreme strain which\naccompany the actual ride.\n\nEINSTEIN: This is not yet a positive proof. The subjects of experiment\nmay have become cognizant of the fact that they were to serve some\neccentric display. Their acquiescence in a prescribed part need by no\nmeans signify that they were subjectively convinced of the genuineness\nof the affair.\n\nM.: There could be not the slightest doubt on this point. After a few\nseconds perspiration was streaming over their faces as a result of the\nexertion, a symptom that exhibits itself only when the participants are\nconvinced of the absolute earnestness of their undertaking. All that\ngazed on this baffling ride made the acquaintance of a grotesque\nreality, and were looking into a strange world of dreams, which\ntransformed wooden chairs into living thoroughbreds. In the course of\nhis following experiments in the transference of his will-power, Hansen\nexperimented with an actress who was famous at that time, and with whom\nhe had no more acquaintance than with the others. He again produced deep\nhypnosis, and gave the order: I shall ask you various questions, all of\nwhich you will be able to answer correctly, with one exception: you will\nhave forgotten your name. And so it happened. In her trance the actress\ngave correct answers, until, when the question, \"What is your name?\" was\nasked, her own name, Helene Odilon, had vanished from her memory. And\nimmediately afterwards, she told me herself that, in spite of her state\nof coma, she had retained full consciousness, had understood everything,\nand had been possessed of her memory until it came to the critical\nmoment when, in spite of extreme efforts, she could not recollect the\nwords Helene Odilon. But Hansen did not stop at dictating his thoughts\nto others, he also transformed corporate things. By a single motion of\nhis hand he converted a stable-boy into a rigid block, devoid of\nsensation. Never would I have thought such an intense state of cramp\npossible. He placed the boy with his feet and head alone resting on two\nsupports, so that the body itself was poised in space. He then stood on\nthe body with his whole weight, without the rigid body of the boy\nbending even an inch.\n\nEINSTEIN: How did he, in all these cases, restore the normal state?\n\nM.: Always by a single gesture, which, like everything that he did,\nworked at lightning speed. I must admit that his display became a little\nmonotonous after a while, and that his programme did not seem capable of\nmuch variation. Things were different, however, in the case of a man\nwho, some years previously, had toured the world as an exponent of\noccult phenomena, and to whom scientists will some time in the future\nlook back with regret. When he appeared, most academicians took only\nsufficient notice of him to reject him without having given him a trial.\nIt was Henry Slade, the American, who is not to be confused with other\nSlades who appropriated his name in order to dupe people whose\ninsatiable curiosity was aroused.\n\nEINSTEIN: One might almost suppose that your genuine Henry Slade served\nas a model for them.\n\nM.: For certain reasons I regard this as out of the question, mainly\nbecause the true Slade gave \"demonstrations\" only occasionally, his\nchief object being to interest scientists. He, himself, repeatedly\nasserted that he did not understand his own achievements, and he\nunceasingly requested the supervision of professional physicists and\nphysiologists, to whom the unusual phases in his nature were to serve as\nobjects of study. The result was that people like Dubois-Reymond,\nHelmholtz, and Virchow refused to see him, not to mention experiment\nwith him.\n\nEINSTEIN: These men cannot be reproached for acting in this way. Slade\nwas regarded as a representative of a four-dimensional world in the\nspiritistic sense; serious scientists must avoid all humbug of this\nsort, since even slight interest in it can easily be misinterpreted by\nthe ignorant public.\n\nM.: Not every one was afraid of compromising himself. After closed doors\nhad greeted Slade in Berlin, he went to Leipzig, where he became an\nobject of study for one important scientist.\n\nEINSTEIN: You are referring to Friedrich Z\u00f6llner, who undoubtedly had a\nreputation as an astrophysicist to preserve. But he would have served\nhis reputation better if he had not entered into this adventure with the\nAmerican spiritist.\n\nM.: Perhaps there will some day be cause for a revision of opinion on\nthis point. The documents are extant, even if, half forgotten, they are\nreposing in various libraries. A renewed investigation of Z\u00f6llners\n_Scientific Dissertations_, dating from 1878 to 1891, might lead to the\njudgment that his ghostly interpretations are to be regarded as occult\nin the worst sense, and yet one would marvel that a great scientist,\nsuch as he was, should have felt himself at a complete loss with his\nknowledge, so that he was forced to resort to abstruse methods in order\nto escape from the mental confusion into which Slade had plunged him.\n\nEINSTEIN: That merely shows that Slade, as a cunning practician,\nsurpassed him, and that Z\u00f6llner did not succeed in seeing through his\nmachinations.\n\nM.: This would lead one to assume that Slade knew more physics than the\nLeipzig professor. For in a great number of experiments Z\u00f6llner himself\nhad prescribed the conditions, including all contrivances which made\ndeception so much the more unlikely, since Slade himself could not know\nwhat Z\u00f6llner's intentions were. It was a question of Electricity,\nMagnetism, Optics including prepared conditions of polarization,\ninvolved Mechanics, in short, things that Z\u00f6llner as a professional\nphysicist understood thoroughly, and which, moreover, were controlled by\nothers of his profession. Among the latter was the celebrated professor\nof Electricity, Wilhelm Weber, who, like Z\u00f6llner, found himself faced\nby phenomena that were utterly incomprehensible to him. It would be a\nprofitable undertaking to bring these dissertations to light again, and\nit would easily be recognized that the things described actually deal\nwith scientific problems and have not the remotest connexion with tricks\nof magic. For example, there is an account of an incredible anatomical\nfeat. On flour which had been placed carefully in a dish beforehand,\nthere suddenly appeared the imprint of a naked human foot, whilst Slade\nwas present at a certain distance, being fully clothed and subject to\ncareful scrutiny. The footprint showed all the surface-details of the\nskin, as was confirmed by authorities, just as only a left foot could\nproduce them, but not an artificial copy.\n\nEINSTEIN: And from this Z\u00f6llner inferred the intervention of\nsupernatural beings? He would have done better to measure the dimensions\nof the foot.\n\nM.: So he did--at once. A difference of four centimetres between the\nlength of Slade's foot and the copy was disclosed. This riddle, like so\nmany others, remained unexplained. I must repeat that I am not in the\nslightest degree disposed to assert that occult phenomena really occur,\nbut am interested only in seeing that they are investigated carefully by\nqualified persons.\n\nEINSTEIN: Your remarks show that Leipzig scientists did so at that time\nwith no better result than that Z\u00f6llners mental confusion became still\ngreater.\n\nM.: The conjecture remains that the Leipzig experiments, abundant as\nthey were, did not suffice. Allow me to ask a direct question,\nProfessor. Supposing another such agent of miracles should appear, would\nyou yourself feel impelled to test him experimentally?\n\nEINSTEIN: Your question is misdirected. I explained above that I share\nthe point of view taken up by Dubois-Reymond and his colleagues.\n\nM.: The following case may be conceived. A certain man, X, might\nsuddenly appear, who has control of a certain natural force that has\nnever before been investigated; like one who knew how to use electricity\nat a time when people had never experienced any electrical phenomenon.\nHe would be able to give hundreds of demonstrations, all of which we\nshould relegate to the realm of inexplicable magic. We should, for\ninstance, be much astonished if he were to draw sparks from a living\nperson. Now, suppose two professors express an opinion. Professor A\ndeclares the whole thing to be a farce, and refuses to look into it at\nall. Professor B is ready to investigate the achievements of X only if\nthe latter subjects himself from the beginning to all the physical\nconditions that are to be determined beforehand. And suppose the\nprofessor arranges his conditions so that they make impossible the\noccurrence of electrical phenomena. If, now, all scientists were to\nbehave like A and B, the consequences would be very depressing. For here\nwas an important field of investigation, which is cut off owing to the\ndistrust or obstinacy of scientists, who should have been the first to\nopen it up. It is quite irrelevant whether X had the character of a\ncharlatan or not, for behind his charlatanism there were facts which\nclamoured for investigation.\n\nEINSTEIN: The most that I can grant is that your imagined case does not\nlie outside the scope of possibility. Yet the chance that there is such\na \"natural force\" hitherto undiscovered by Man, that is, one that is a\n\"secret force\" as far as we are concerned, is so vanishingly small that\nit may be set down as equal to impossible. I should refuse to take part\nin any such practices, served up in the form of sensation, for one\nreason that I should regret the waste of time, as there are better\nthings to do. It is a different matter if the mood takes me to visit a\nvariety entertainment, in order to derive amusement from such\nmystifications. For example, only yesterday I was in a little theatre,\nin which, among diverse items, a thought-reading woman was performing.\nShe correctly guessed the numbers 61 and 59 that I had in my mind. But\nlet no one mention this as a case of telepathic actions at a distance or\nwireless communication between minds, for an intermediate person, the\nmanager, was present, and I had to whisper the numbers to him. The\ndistance to the stage was certainly too great to allow the sound to be\nconveyed directly to an audible degree. Hence there must have been a\ndifferent, very cunningly arranged code of signals, which eluded the\nnotice of people in the stalls. The process consists actually in an\nextraordinary refinement of observation, which does not, however, seem\nto me any more wonderful than the training of a reckoner who extracts\ncubic roots mentally, or than the practised muscles of a juggler all\nworking in unison to enable him to perform feats with twelve plates\nsimultaneously.\n\nM.: It gives me enough satisfaction, Professor, that you conceded me\nbefore a certain limited chance of finding a last refuge in occultism.\nAnd even if you, yourself, as a representative of the most rigorous\nresearch of physical reality, refuse to consider it, yet the fact that\nmany others are drawn irresistibly towards mysterious phenomena cannot\nbe denied. Should one feel shame on this account? I believe that, in\nthis matter, we are touching on inner confessions that are quite\nindependent of the standard of the mind in which they are embedded.\nNewton considered the key of the universe to be a personal God, whereas\nLaplace proclaimed: _Dieu--je n'avais pas besoin de cette hypoth\u00e8se_:\nthis contrast allows no inference to be drawn as to their relative\nkeenness of mind. And probably the same may be said of the question\nwhether there are other hidden universes besides the one in which we\nlive. In any case, those who feel enthusiasm for such questions can\nquote in their support good names from the learned world. Immanuel Kant\noccupied himself seriously and intensively with the wonders of\nSwedenborg, Kepler practised Astrology, in which he had a firm belief,\nRoger Bacon, Cardanus, Agrippa, Nostradamus, van Helmont, Pascal, and,\namong the modern, Fechner, Wallace, Crookes, are to be counted among the\nmystics. No matter whether the views they held were theosophical,\noccult, four-dimensional in the spiritistic sense, or coloured by any\nother superstition; they proclaimed that things that could be rigorously\nproved were, alone, insufficient for them. Out of presentiment and\nconjecture they constructed wings with which to fly into regions _extra\nnaturam_. This is how it happened that, as the common folk could not\nfind a place in science for many extraordinary achievements, they\nassigned their authors to the realm of magicians, as in the case of\nParacelsus, Albertus Magnus, Raimundus Lullus, Sylvester II, who were\nregarded as sorcerers. And this coin is still current: to Edison, of our\ntimes, the term, \"sorcerer of Menlo-Park,\" has become attached. In the\nminds of the populace discovery and invention, works of genius and\nsupernatural phenomena, become confused and indistinguishable; it may\neven happen to you. Professor, that your works will become invested with\nlegend. I should not like to conjure up what your fate would have been\nif your theory of relativity had originated at the time of the\nInquisition. For the views put forward by Giordano Bruno are mere\nchild's play compared with your theory of the universe as a\nquasi-spherical closed space of hyper-Euclidean character. The tribunal\nof the Inquisition would not have understood your differential equation,\ngravitational potentials, tensors, and equivalence theory; they would\nabruptly have declared the whole theory to be a magical formula or a\nmanifestation of the devil, and would have honoured it and you with a\nfuneral pyre.\n\nEINSTEIN: This is clearly a slight exaggeration. Mathematico-physical\nand astronomical works have never been attacked by the Papal courts,\nbut, on the contrary, have been much encouraged by them down to the\npresent day. This is abundantly clear from the fact that we can set up a\nwhole list of Brothers of Orders, particularly Jesuits, who have made\neminent discoveries in natural science. From my personal knowledge of\nyou, I foresee that you will one day sketch a fantastic trial, in which\nthe new world-system will have to defend itself against the _Sanctum\nOfficium_.\n\nM.: This would be a very grateful task, judged from the literary point\nof view. What a splendid colouring could be obtained by bringing these\ntwo worlds of thought into conflict with one another, the Relative\nagainst the Absolute, which has been established in tradition and dogma.\nBut we need not even call the historical fancy into action, for,\nactually, the theory of the structure of the world is even now still at\nvariance with traditional ideas, that act with dogmatic violence. There\nis no need to deny the fact that every person of education, who makes\nthe acquaintance of Lorentz's, Minkowski's, Einstein's ideas for the\nfirst time, feels excited to offer contradictions, and becomes involved\nin a tumult of pros and cons, and each one experiences in himself the\nexcitement of an inquisitorial tribunal. The triumph of the new theory\npasses over the corpses of conceptions that lie at the cross-roads of\nthought and, long after, retain a ghostly existence. Only very few of us\nare aware of the further inner revolution that awaits us along the line\nof development of Einsteinian ideas; we have only vague presentiments\nthat whisper to us that the end of forms of thought once considered as\nirrefragable is drawing nigh. When once the principle of causality has\nbeen set on a relative base, and all \"properties\" have been resolved\ninto occurrence, and all that is three-dimensional has come to be\nrecognized as an abstraction from the four-dimensional world that is\nalone valid, then the time will have come to arrange for, the death\nprocession of all the philosophies that once served as the main pillars\nof thought.\n\nA retrospect of the trials of Giordano Bruno and of Galileo Galilei\noffers certain parallels other than those usually discovered by\nscholars. And if, to-day, we proclaim Einstein as the Galilei of the\ntwentieth century, it must be added that in character he is fortunately\na Bruno and not a Galilei. For it is not true that the latter came out\nof the persecution as a moral victor with an _eppur si muove_, rather,\nin spite of the protection of influential prelates and dignitaries, even\nof the entourage of the Pope, he lacked courage and bowed his head,\nbetraying his science and denying himself as well as Copernicus. Are we\nto picture how Einstein would have acted under similar circumstances,\neven if they cannot recur again?\n\nWhoever has even an inkling of his character will entertain no doubts.\nAt that time, three hundred years ago, the materials for a magnificent\nscene, \"one world _versus_ the other,\" lay ready. Only one condition was\nwanting, the moral courage of the hero. The lack of this one factor\nspoilt the final act for the history of that time. The fine ethical\nfeelings of later generations have had to be propitiated by improvising\na legend iridescent with beautiful colours.\n\n\n\n\nCHAPTER VII\n\nPROBLEMS\n\nQuestions of the Future.--Problem of Three Bodies.--Conception of\nApproximation.--Object of Mechanics.--Simplicity of Description.--Limits\nof Proof.--Reflections about the Circle.--From the History of\nErrors.--Causalities.--Relativity on a Physiological Basis.--Physicists\nas Philosophers.\n\n\nWE spoke of the objects and problems of science in general, and touched\non certain recurrent questions with which reputed men of science are\nconfronted from time to time, so that we may ascertain their opinions\nabout immediate as well as more remote aims, and about worthy objects\nand those within reach.\n\n\"Such stimuli,\" said Einstein, \"may be quite interesting inasmuch as\nthey sharpen the appetite of the public for the works of investigators,\nand give the latter the opportunity of making wider circles acquainted\nwith their plans. Yet the value of their suggestions must not be\noverrated, when they are directed at giving trustworthy information\nabout the future lines of development of science. Every scientist, in\nworking out his own research, gravitates to particular points on the\nboundary which separates the known from the unknown, and becomes\ninclined to take his particular perspective from these points. It must\nnot, however, be expected that these individual aspects will form a\ncomplete picture, and will indicate the only paths along which science\ncan or will advance.\"\n\n\"May I suggest, Professor,\" I answered, \"that we select certain answers\nthat have been given to these recurrent questions for discussion? I have\nbrought along a whole series of them; it would be of value to know what\nattitude you take up towards some of the statements that have been made\nabout future possibilities.\"\n\nEinstein acquiesced, and so I read out a number of expressions of\nopinion, given by eminent authorities, particularly in natural science\nand mathematics. They came under the heading, \"The Future Revolution of\nScience.\" At the outset we encountered arguments by Bailhaud, the\ndirector of the Paris Observatory; he dealt with the so-called \"Problem\nof Three Bodies,\" and with \"The Finitude or Infinitude of the Universe.\"\n\nEinstein elucidated these questions as follows. The celebrated Problem\nof Three Bodies is a special case of the general problem of Many Bodies,\nthe object of which is to discover the exact paths of the heavenly\nbodies. If we suppose that the planets and the comets are subject only\nto the attraction of the central body, the sun, then their paths would\nbe exactly those given by Kepler's Laws--that is, they would move about\nthe central body, or, more precisely, about the common centre of gravity\nin perfectly elliptical orbits. The same result would happen if we\nregard the orbit of a moon to depend solely on its parent planet. But\nthis assumption is not in agreement with reality, since all the bodies\nof our system are also subject to their mutual attraction depending on\ntheir masses and distances. Consequently we have the so-called\ndisturbances, perturbations, and divergences from the ideal paths; and\nthe problem of ascertaining these disturbances is essentially identical\nwith the Problem of Three Bodies. Regarded from the point of view of\npure mechanics, this problem may be considered solved in so far as we\nare able to write down the equations of motion. But, in addition to this\npurely mechanical process, there is a mathematical problem which has not\nbeen completely solved--that is to say, the integral expressions that\noccur in it can be calculated only approximately. This makes no\ndifference to the practical calculation, since the degree of\napproximation, according to the present methods, may be carried as far\nas we wish. The error may be reduced to any desirable extent, so that it\nis probably wrong to expect new revelations on this point from future\nupheavals in physics. We read on and discovered that several of the\nscientists mentioned did not stop at expecting all advances of the\nfuture from pure theory. They had visions of an optimum of happiness, to\ngain which the increase of knowledge alone did not suffice. Thus the\ncelebrated Swedish astrophysicist Svante Arrhenius had summarized his\njudgment in a few lines: \"After the stupendous progress that has been\nmade in the physical and chemical sciences in recent times, it seems to\nme that the moment has come for attacking the most important problems of\nmankind with full success, namely, those of biology, and in particular\nof the art of healing, with the weapons that are furnished by the\narsenal of the exact sciences.\" And the mathematician, Emile Picard,\nMembre de l'Acad\u00e9mie, expressed himself in still more hopeful terms:\n\"There is no doubt but that the discoveries which the human race is\nawaiting with impatience are those that are seeking to eliminate\nsickness and the decrepitude of old age. Injections giving immunity\nagainst all diseases, an elixir of life (_une eau de Jouvence_) for\npersons of advancing age--these are the discoveries that are longed for\nby every one. There are also sciences that are to be termed 'moral,'\nfrom which we are impatiently expecting that guidance which will\ndiminish the hate which seems to be increasing from day to day among the\nnations. That would be a splendid discovery.\"\n\n\"These are, indeed, noble and inspiring words,\" said I. \"It shows how\ndeeply rooted is the demand for ethical values in human nature, when\neven a mathematician, whose intellectual interests are directed\nprimarily towards exact results, ranks the discoveries of ethics above\nall others.\"\n\nEinstein answered: \"We must carefully distinguish between what we wish\nfor in general and what we have to investigate as belonging to the world\nof knowledge. The question under consideration is not one of wishes and\nfeelings, but was unmistakably aimed at the advances and revolutions in\nthe realm of science. It does not come within the scope of science at\nall to make moral discoveries! Its one aim is rather the Truth. Ethics\nis a science about moral values, but not a science to discover moral\n'truths.' Ethics, conceived as a science in the usual way, can therefore\nserve to discover or to promote truth only indirectly. To illustrate my\npoint of view I shall quote an example taken from a totally different\nfield; it is merely to serve as an analogy. Let us consider the game of\nchess. Its value and its meaning is not to be sought in scientific\nfactors, but in something entirely different, in a struggle which takes\nplace according to definite rules. But even chess, inasmuch as it\nsharpens the intellect, may exhibit an indirect value for promoting\ntruth. It may, for instance, suggest examples in permutations, which may\ncontain mathematical, that is, purely scientific, truths. I certainly\ndo not deny that there is an ethical factor in all genuine sciences. For\nbeing occupied with things for the sake of truth alone emancipates and\nennobles the mind.\"\n\n\"This ennobling effect,\" I interposed, \"should surely show itself in a\nmoderation of the passions which were mentioned in the above expression\nof opinion. With Picard we should expect above all things to see a\ndiminution in the feelings of hate between peoples, the tragic\nconsequences of which we have experienced.\"\n\nEinstein smiled, and, with a touch of sarcasm, said, \"Hate is presumably\na privilege of the 'cultured,' who have the time and the energy for it,\nand who are not the slaves of care.\" His tone indicated clearly that he\nused the generic term \"cultured\" to denote the Philistines of culture,\nits snobbish satellites, but not those whose intensive work aimed at\nincreasing and deepening the fields of culture. In general he maintained\nhis view that it is an illusion to expect \"discoveries\" in the realm of\nethics, since every real discovery belonged alone to the sphere of truth\nin which the division only into right and wrong, not that into good and\nevil, holds good.\n\nThis led us to the old question of Pilate: What is Truth? In seeking an\nanswer to this question Einstein first called special attention to the\nconception of \"approximation,\" which plays a great part in the actual\nsearch for truth, inasmuch as every physical truth, expressed in\nmeasures and numbers, always leaves some remainder, that marks its\ndistance from the unattainable truth of reality. This conception, which\nmanifests itself so prominently in the relation of Einstein's own\nresearches to the older, so-called classical, mechanics, will be\ndeveloped here according to his line of thought as far as I can\nrecollect from a number of conversations.\n\nLet us suppose that we overhear two people arguing about the shape of\nthe earth's surface. The one affirms that it is an unlimited plane,\nwhilst the other maintains that it is a sphere. We should not hesitate a\nmoment to say that the first is in error, and that the second gives the\ntrue answer. As long as the question was to be decided in favour of a\n\"Plane or a Sphere,\" the sphere would represent the absolute truth. Yet\nit would be only relative, for these two statements are contradictory\nonly between themselves, but will no longer be so if a third assertion\nis made which opposes a new alternative to \"sphere.\"\n\nIf this alternative objection is actually raised, the third person would\nbe quite justified in saying that the \"sphere\" explanation is wrong. For\nthe conception \"sphere\" requires that all diameters be equal, whereas we\nknow that they are not so, since the distance from pole to pole has been\nproved to be smaller than that between opposite points on the equator.\nThe earth is an ellipsoid of rotation, and this truth is absolute in the\nface of the errors which are expressed by the terms, plane and sphere.\n\nIt would again have to be added that this absoluteness would stand only\nas long as this contradiction is regarded as being one between a\ndefinite sphere and a definite ellipsoid. If, as in the case of the\nearth, there are quite different diameters in the equatorial and the\ndiametral planes, then there is complete contradiction between the two\nstatements, and as the supporter of the ellipsoid is right, the one who\nsupported the sphere must now give in, although he previously triumphed\nover his first opponent. His statement was true compared with the\nlatter, but showed itself to be an error when compared with the\nstatement of the third person.\n\nThis does not run counter to the laws of elementary logic. One of these,\nsomewhat inadequately called the Law of Contradiction, states that two\ndirectly contrary statements--_e.g._ this figure is a circle, and this\nfigure is not a circle--cannot both be true simultaneously. The truth of\nthe one implies necessarily the falseness of the other. As this cannot\nbe disputed, it follows in our case that we cannot have been confronted\nwith contradictory judgments at all concerning the figure of the earth.\n\nThis is to be understood in a geometrical sense. The sphere does not\nentirely contradict the ellipsoid, since it is a limiting case of the\nlatter: and the plane is likewise a limiting case of the sphere, as well\nas of the surface of ellipsoids.\n\nBut we are not concerned with purely geometrical considerations, for the\nearth is a definite body, and not a limiting configuration derived from\nabstraction. We are here dealing with measurable quantities, whose\ndifference can be proved, and hence we must have one of the disputants\nproclaiming the absolute truth, whilst the other proclaims an absolute\nerror. This, however, again is incompatible with our result that the\nsecond person is right in the one case and wrong in the other.\n\nThe logical Law of Contradiction overcomes the dilemma in the simplest\nway. None of these assertions contains the truth, hence none of these\njudgments allows the falseness of the others to be deduced. Only this\nmay be said, that there is a fraction of truth in each judgment. The\ntrue shape of the earth is given by the plane to a first, the sphere to\na second, the ellipsoid of rotation to a third, degree of approximation:\nwe reserve the right of further approximations, each of which in\nsuccession approaches a higher degree of correctness, but none attains\nthe absolute truth.\n\nThis reflection on a particular case may be generalized, and remains\nwhen we extend it to our attempts at grasping the states, changes, and\noccurrences of Nature. Whenever we talk of physical laws, we must bear\nin mind that we are dealing with human processes of thought, that are\nsubjected to a succession of judgments, courts of appeal, as it were,\nexcluding, however, a final court beyond which no appeal is possible.\nEach new experience in the course of natural phenomena may render\nnecessary a new trial before a higher court, whose duty is then to give\na more definite or different form to the law formulated by us, so as to\nattain a still higher degree of approximation to the truth.\n\nIf we call to mind some of the most valuable statements made by modern\ninvestigators about the nature of natural laws, we recognize that they\nare all connected by a single thread of thought, namely, that even in\nthe most certain law there is left a remainder that has not been\naccounted for, and that obliges us to consider a greater approximation\nto the truth as possible, even if a final stage is not attainable.\n\nMechanics furnishes us with the expression of its laws in equations,\nwhose importance Robert Kirchhoff explained in 1874 by a definition that\nhas been considered conclusive by scientists. According to him, it is\nthe object of mechanics to describe completely (and not to explain) in\nthe simplest manner the motions that occur in Nature.\n\nThe postulate of simplicity is derived from the fundamental view of\nscience as an economy of thought. It expresses the will of man's mind to\narrive at a maximum of result by using a minimum of effort, and to\nexpress the greatest sum of experience by using the smallest number of\nsymbols. Let us consider two simple examples quoted by Mach. No human\nbrain is capable of grasping all the possible circumstances of bodies\nfalling freely, and it may well be doubted whether even a supernatural\nmind like that imagined by Laplace could succeed in doing so. But if we\ntake note of Galilei's Law for Falling Bodies and the value of the\nacceleration due to gravity, which is quite an easy matter, we are\nequipped for all cases, and have a compendious formula, accessible to\nany ordinary mind, that allows us to picture to ourselves all possible\nmotions of falling bodies. In the same way no memory in the world could\nretain all the different cases of the refraction of light. Instead of\ntrying to do the impossible task of grasping this infinite abundance, we\nsimply take note of the sine law, and the indices of refraction of the\ntwo media in question; this enables us to picture any possible case of\nrefraction, or to complete it, since we are free to relieve our memories\nentirely by having the constants in a book. Thus we have here natural\nlaws that give us a comprehensive yet abbreviated statement of facts,\nand satisfy the postulate of simplicity to a high degree.\n\nBut these facts are built up on experiences, and it is not impossible\nthat some new unexpected experience will reveal a new fact, which is not\nsufficiently taken into account in the law. This would compel us to\ncorrect the expression for the law, and to seek a closer approximation\nfor the enlarged number of facts.\n\nThe Law of Inertia, according to our human standard, seems unsurpassable\nin simplicity and completeness; it seems to us fundamental. But this\nlaw, which prescribes uniform rectilinear motion to a body subject to no\nexternal forces, selects only one possibility out of an infinite number\nas being valid for us. It does not seem evident to a child, and it is\neasy to imagine a good scholar in some branch of knowledge other than\nphysics, to whom it would likewise not seem evident. For it is by no\nmeans necessary a priori that a body will move at all when all forces\nare absent. If the law were self-evident, it would not need to have been\ndiscovered by Galilei in 1638. Nevertheless, it appears to us, now, to\nbe absolutely self-evident, and we can scarcely imagine that it can ever\nbe otherwise. This is simply because we are bound to the current set of\nideas that cannot extend beyond the sum of sense-data and experiences\nthat have been inculcated into us by heredity and environment. At a very\ndistant date in the future the average mind may surpass that of Galilei\nto the same extent as Galilei's surpasses that of a child, or of a\nPapuan native. And of all the infinite possibilities one may occur to a\nGalilei of the distant future, which, when formulated as a law, may\nserve to describe motions of a body subject to no forces better than the\nlaw of inertia, proposed in 1638.\n\nThese reflections are not mere hallucinations, but have to do with\nscientific occurrences that we have observed in the twentieth century.\nNewton's equation that gives the Law of Attraction is beyond doubt a\nmodel of simplicity, and it would have occurred to no thinking person of\neven the last generation to doubt its accuracy. The easily grasped\nexpression k (m.m^1\u2044r^2) apparently expresses truth in a law which is\nvalid for all eternity. In this expression, he denotes a gravitational\nconstant, that is, a quantity which is invariable in the whole universe;\n_m_ and _m_^1 are two masses that act attractively on one another; and\n_r_ is the distance between them. But Newton has been followed by\nEinstein, who has proved that this expression represents only an\napproximate value, that leaves a small remainder as an error that may be\ndetected if the greatest refinement be made in our methods of\nobservation. The equations that have been set up by Einstein represent\nthe approximation that is to be considered final for the present, and\nthat may remain valid for thousands of years. They are certainly very\ncomplicated, being included in a system of differential equations of\nawe-inspiring length, and we may feel tempted to object with the\nquestion: how do they agree with Kirchhoff's postulate that the simplest\ndescription of the motions must be sought? But this objection falls to\nthe ground if we look carefully into the question. For simplicity\nconsists not merely in being brief or in excluding difficulty from a\nformula, but rather in asserting the simplest relation to the universe\nas a whole, which is independent of all systems of reference. When this\nindependence is proved--and in Einstein's case it is so--the complicated\naspect of the formula disappears entirely in the light of the higher\nsimplicity and unity of the world-system that presents itself--a\nworld-system that is directed in conformity with the one fundamental law\nof general relativity as well in the motion of the electrons as in\nmotion of the most distant stars. With regard to the other postulate,\nthat of completeness, _i.e._ absolute accuracy, we have been furnished\nwith proofs that have rightly excited the wonder of the present\ngeneration. But are we then to recognize the Principle of Approximation\nin every direction? Is there then nothing that can be proved rigorously,\nnothing that is unconditionally valid in the form of knowledge that\ncorresponds exactly to truth?\n\nWe are led to think of mathematical theorems, which, when they have once\nbeen proved, are evident to the same degree as the axioms from which\nthey have been derived, by virtue of logic which cannot be disputed\nsince a contradiction leads to absurdity. It has been said that\nmathematics _est scientia eorum_, _qui per se clara sunt_, that is, is\nthe science of what is self-evident.\n\nBut here again doubts arise. If we should get to know only a single\ncase, in which the self-evident came to grief, the road to further\ndoubts becomes open. Such a case will now be quoted.\n\nAs we know, a tangent is a straight line, which makes contact with a\ncurve at two coincident (or infinitely near) points without actually\ncutting the curve. The simplest case of this is the perpendicular at the\nextremity of a radius of a circle. And it agrees fully with what our\nfeeling leads us to expect when it is stated that every curved line that\nis \"continuous,\" that is, which discloses no break and no sudden bend,\nhas a tangent at every point. Analysis, which treats plane curves as\nequations in two variables, gives the direction of the tangent in terms\nof the differential coefficient, and declares accordingly that every\ncontinuous function has a differential coefficient, that is, may be\ndifferentiated, at every point. The one statement amounts to the same as\nthe other, since there must be an equivalent graphical picture\ncorresponding to every functional expression.\n\nBut this apparently rudimentary theorem involves an error, which was not\ndiscovered before the year 1875. The theory of curves has been in\nexistence for centuries, but it occurred to no one to doubt the general\nvalidity of this theorem of tangents. It was regarded as self-evident,\nas a mathematical intuition. And certainly neither Newton, nor Leibniz,\nnor Bernoulli, not to mention the mathematicians of olden times, even\ndreamed that a continuous curve without a tangent, or a continuous\nfunction without a differential coefficient, was possible.\n\nMoreover, a proof of the theorem had been accepted. It appeared in\ntext-books, and was often to be heard in lecture rooms; nor was a shadow\nof a doubt suggested. For it was not merely a _demonstratio ad oculos_,\nbut it appeared directly to our sense of intuition. And we may safely\nsay that up to the present day no one has ever been able to _imagine_ a\ncontinuously curved line which has no tangent; no one has been able to\npicture even one point of such a curve at which no tangent could be\ndrawn.\n\nNevertheless, scientists appeared who began to entertain doubts. In the\ncase of Riemann and Schwarz these doubts assumed a concrete form, in\nthat they proved that certain functions are refractory at certain\npoints. But Weierstrass was the first to make a real breach in the old\nbelief that was so firmly rooted. He set up a function that is\ncontinuous at every point, but differentiable at no point. The graphical\npicture would thus have to be a continuous curve having no tangent at\nall.\n\nWhat is the appearance of such a configuration? We do not know, nor\nshall we presumably ever get to know. During a conversation in which\nthis problem of Weierstrass arose, Einstein said that such a curve lay\nbeyond the power of imagination. It must be remarked that, although the\nmathematical expression of the Weierstrass function is not exactly\nsimple, it is not inordinately complex. Moreover, seeing that one such\nfunction (or curve) exists, others will soon be added to it (Poincar\u00e9\nmentions that Darboux actually gave other examples even in the same year\nthat the first was discovered); there will, indeed, be found an infinite\nnumber of them. We may go still further, and say that, corresponding to\neach curve that has tangents, there are an infinite number that have no\ntangents, so that the former form the exception and not the rule. This\nis an overwhelming confession that shakes the foundations of our\nmathematical convictions, yet there is no escape.\n\nHow may we apply the principle of \"approximation\" to these\nconsiderations? May we say that the theorem that was believed earlier is\nan approximation to a mathematical truth?\n\nThis is possible only conditionally, in a certain extremely limited\nsense, namely, if we picture to ourselves that point in the development\nof science at which the conception and properties of tangents first\nbegan to be investigated. Compared with this stage of science, the above\ntheorem denotes a first approximation to the truth, in spite of its\nincorrectness; for it makes us acquainted with a great abundance of\ncurves that are very important for us and that exhibit tangents at every\npoint. This knowledge brings us a step nearer to the more approximate\ntruth given by Weierstrass's example. In the distant future, the earnest\nstudent will learn this theorem only as a curious anecdote, just as we\nhear of certain astrological and alchemistic fallacies. He will learn,\nin addition, other theorems that are looked on as proved by us of the\npresent day, although actually they were proved only approximately. For\nwhat does it mean when Gauss, for example, repudiated certain proofs of\nearlier algebraists as being \"not sufficiently rigorous,\" and replaced\nthem by more rigorous proofs? It signifies no more than that, in\nmathematics, too, what appears to one investigator as flawless, strict,\nand evident, is found by another to have gaps and weaknesses. Absolute\ncorrectness belongs only to identities, tautologies, that are absolutely\ntrue in themselves, but cannot bear fruit. Thus at the foundation of\nevery theorem and of every proof there is an incommensurable element of\ndogma, and in all of them taken together there is the dogma of\ninfallibility that can never be proved nor disproved.\n\nIt must appear extremely interesting that, at first sight, this example\nof the tangent has its equivalent in Nature herself, namely, in\nmolecular motions the investigation of which is again largely due to\nEinstein.\n\nJean Perrin, the author of the famous book, _Atoms_, describes, in the\nintroduction, the connexion between this mysterious mathematical fact\nand results that are visible and may be shown by experiment, to which we\nhave been led by the study of certain milky-looking (colloidal) liquids.\n\nIf, for example, we look at one of those white flakes, which we get by\nmixing soap solution with common salt, we at first see its surface\nsharply outlined, but the nearer we approach to it, the more indistinct\nthe outline becomes. The eye gradually finds it impossible to draw a\ntangent to a point of the surface; a straight line which, viewed\nsuperficially, seems to run tangentially, is found on closer examination\nto be oblique or even perpendicular to the surface. No microscope\nsucceeds in dispelling this uncertainty. On the contrary, whenever the\nmagnification is increased, new unevennesses seem to appear, and we\nnever succeed in arriving at a continuous picture. Such a flake\nfurnishes us with a model for the general conception of a function which\nhas no differential coefficient. When, with the help of the microscope,\nwe observe the so-called Brownian movement, which is molecular by\nnature, we have a parallel to the curve which has no tangent, and the\nobserver is left only with the idea of a function devoid of a\ndifferential coefficient.... We find ourselves obliged, ultimately, to\ngive up the hope of discovering homogeneity at all in studying matter.\nThe farther we penetrate into its secrets, the more we see that it,\nmatter, is spongy by nature and infinitely complex; all indications tend\nto show that closer examination will reveal only more discontinuities.\n\nI have not yet had an opportunity of seeing these Brownian movements\nunder the microscope, but I must mention that Einstein has repeatedly\nspoken to me of them with great enthusiasm, of an objective kind, as it\nwere, for he betrayed neither by word nor by look that he himself has\ndone research leading to definite laws that have a recognized place in\nthe history of molecular theory.\n\nAs soon as we approach the question of molecular irregularities we\nrecognize that, when we earlier spoke of the figure of the earth in\ndiscussing the principle of \"approximation,\" we were still very far from\nthe limit that may be imagined. We had set up the three stages:\nplane--sphere--ellipsoid of revolution, as relative geometrical steps,\nbeyond which there must be still further geometrical approximations. If\nwe imagine all differences of level due to mountains and valleys to be\neliminated, for example, and if we suppose the earth's surface to\nconsist entirely of liquid, undisturbed by the slightest breath of wind,\neven then, the ellipsoid is by no means the final description. For now\nthe discontinuities from molecule to molecule begin, the infinite number\nof configurations without tangents, the macroscopic parallels of what\nthe white flake soap solution showed as microscopically, and no\nconceivable geometry would ever be adequate to grasp these phenomena. We\narrive at a never-to-be-completed list of functions which can never be\ndescribed either in words or in symbolic expressions of analysis.\n\nBut even if the ultimate geometrical truth is hidden behind the veils of\nMaya,[6] we are yet left with the consolation that the method of\napproximation, even when applied to a relatively modest degree, produces\nremarkable results in the realm of numbers. Let us consider for a moment\nin the simple figure of a circle the ratio between the circumference and\nthe radius.\n\n[Footnote 6: Maya = appearance.]\n\nAs we know, this ratio is constant, and is called in honour of the man\nwho first gave a trustworthy value for it, Ludolf's number, namely, \u03c0\n(pi). Thus it makes no difference whether we consider a circle as small\nas a wedding-ring, or as large as a circus arena, or even one the radius\nof which is as great as the distance of Sirius. And it makes just as\nlittle difference what happens to the circle whilst it is being\nmeasured; the above ratio must remain constant.\n\nBut here, too, a contradiction makes itself heard, issuing from one\nsection of modern science. It calls to mind the saying of Dove that when\nprofessors are not quite sure about a thing they always preface their\nremarks with the phrase: \"it is well known that\" ... We should be well\nadvised in avoiding this method of expression altogether, for even when\nwe feel quite sure, the ghost of the unknown lurks behind what we fain\nwould call well known.\n\nThe theorem that all circles without exception are subject to the same\nmeasure-relation belongs _a priori_ to the synthetic judgments. But\nfields of thought have been discovered in which the _a priori_ has lost\nits power. Mathematics--once a quintessence of synthetic statements _a\npriori_--is now regarded as being dependent on physical conditions.\nPhysical conditions, however, are empirical and subject to change.\nTherefore, since the _a priori_ is not subject to change, we encounter a\ndiscrepancy. It leads to the question: Is the Euclidean geometry with\nwhich we are familiar the only possible geometry? Or, in particular: Is\n\u03c0 the only possible measure-relation?\n\nEinstein replies in the negative. He not only shows how another geometry\nis possible, but he also discloses what once seemed inconceivable,\nnamely, that if we wish to describe the course of the phenomena of\nNature exactly by means of the simplest laws, it is not only impossible\nto do so with the help of Euclidean geometry alone, but that we have to\nuse a different geometry at every point of the world, dependent on the\nphysical condition at that point.\n\nFrom the comparatively simple example of two systems rotating relatively\nto one another, Einstein shows that the peripheral measurement of a\nrotating circle, as viewed from the other system, exhibits a peculiarity\nwhich does not accompany the radial measurement. For, according to the\ntheory of relativity, the length of a measuring rod is to be regarded as\nbeing dependent on its orientation. In the case quoted, the rod\nundergoes a relative contraction only when applied along the\ncircumference, so that we count more steps than when we measure the\ncircumference of the same circle at rest, that is, in non-rotation.\nSince the radius remains constant in each case, we get a relatively\ngreater value for \u03c0, which shows that we are no longer using Euclidean\ngeometry.\n\nYet, formerly, before such considerations could even be conceived in\ndreams, this \u03c0 was regarded as absolutely established and immutable;\nand observers used every possible means of determining its value as\naccurately as possible.\n\nIn Byzantium there lived during the eleventh and twelfth centuries a\nlearned scholar, Michael Psellus, whose fame as the \"Foremost of\nPhilosophers\" stretched far and wide, and whose mathematical researches\nwere regarded as worthy of great admiration. This grand master had\ndiscovered by analytical and synthetical means that a circle is to be\nregarded as the geometric mean between the circumscribed and the\ninscribed square, which gives to the above quantity, as may easily be\ncalculated, the value \u221a8, that is, 2.8284271.... In other words, the\nlength of the circumference is not even three times that of the radius.\n\nWe have the choice of regarding the result of Psellus as an\napproximation, or as mere nonsense. Every schoolboy who, in a spirit of\nfun, measures a circular object, say a top, with a piece of string,\narrives at a better result, but the contemporaries of Psellus accepted\nthis entirely wrong figure with credulous reverence, and continued to\nburn incense at the feet of the famous master. It is all very well for\nus of the present to call him a donkey. We have just as much right in\nsaying that mathematicians differ, not in their natures, but only in the\norder of their brain functions. If a man like Psellus missed the mark by\nso much, it is possible that men like Fermat or Lagrange may also have\nerred occasionally or even consistently.\n\nNo heavenly power will give us a definite assurance to the contrary, and\nall of us may be just as false in our judgment of accepted celebrities\nas were the Byzantines eight hundred years ago in their estimate of\nPsellus.\n\nWhereas the latter had obtained a value \"less than 3,\" there are learned\ndocuments of about the same date that have been preserved, according to\nwhich the value of \u03c0 comes out as exactly 4. Compared with this\ngrandiose bungling, even the observations mentioned in the Old Testament\nare models of refinement. For, as early as three thousand years ago, it\nis stated of the mighty basin in the temple of Solomon (First Book of\nKings, chapter VII.): \"And he made a molten sea, ten cubits from the one\nbrim to the other: it was round all about, and his height was five\ncubits; and a line of thirty cubits did compass it round about.\" Thus \u03c0\nhere appears as 3, an approximation which no longer satisfied later\ngenerations. The wise men of the Talmud went a step further, in saying 3\nplus a little more; and this agrees roughly with the actual value.\n\nThe view became more and more deeply rooted that this \u03c0 was a main\npillar of mathematical thought and calculation. The more the problem of\nthe quadrature of the circle seized on men's minds, the greater were the\nefforts made to find the exact value of this \"little more\" of the\nTalmud. Since 1770 we know that this is not possible, for \u03c0 is not\nrational, that is, it can be represented only as an infinite and\nirregular (that is, non-repeating) decimal expression. It occupies,\nfurther, a special rank as a transcendental quantity; this fact was\nproved by Lindemann as late as 1882 for the first time. Yet, even\nnowadays, there are incorrigible devotees of quadrature, who are still\nhunting a solution because they cannot rid themselves of the\nhallucination that such a simple figure as the circle must submit\nultimately to a constructive process.\n\nThe correct way was to carry out an even more accurate determination of\nthe decimal figures. The above-mentioned Ludolf van Ceulen got as far as\nthe 35th place of decimals; at the turn of the eighteenth century the\n100th decimal place was reached. Since 1844, thanks to the lightning\ncalculator Dase, we have its value to the 200th decimal place, and this\nshould satisfy even the most extravagant demands. This number,\nassociated with the circle, is a classical example of how an\napproximation that is expressible in figures of very small value gives\nan order of accuracy that can be described only by using fantastic\nillustrations.\n\nIf we take a circle of the size of the equator, and also multiply the\nvalue of the diameter of the earth by \u03c0, we know that the latter result\nwill not be exactly equal to the former, and that there will always be a\nsmall remainder. If this discrepancy were less than a metre, the order\nof exactness would be extraordinarily high, for a metre is practically\ninsignificant compared with a mighty circle of the dimensions of the\nearth's circumference.\n\nLet us stipulate still greater accuracy. We demand that the error is to\nbe less than the thickness of the thinnest human hair. We find, then,\nthat we must take for \u03c0 at most 15 places of decimals. Thus, if we use\n\u03c0 = 3.14159265358973, we are applying a means of calculation that\nreduces the possible error in all measurements of circles on the earth\nto a degree beyond the limits of human perception.\n\nIf we pass beyond the world out into celestial space, and consider\ncircles of the dimensions of a planetary orbit, nay, further, if we pass\non to the Milky Way or even to the limit of visible stars, to find space\nfor our circle, and if in this case we still reduce the discrepancy so\nas to be less than any length that is observable under a microscope,\nthen the last given value of \u03c0 still suffices. Yet we must not forget\nthe proviso: _semper aliquid haeret_, something unsolved still clings to\nthe problem.\n\nSuch numerical approximations, however instructive they may be,\nnevertheless retain a comparatively playful character, and furnish only\na superficial analogy to the most important approximations that are\ncontained in our natural laws themselves. It is these, above all, that\nmanifest themselves so clearly in Einstein's life-work, and they bear\nthe same relation to the former as truth bears to correctness. Truth\ncomprises the greatest conceivable circle of ideas and passes far beyond\nthe sphere of correctness, which deals only with measure-relations, and\nnot with the things in themselves. If Einstein, as we learn,\nemphatically declares truth to be the only object of science, he means\nthe strictly objective truth that is to be derived from Nature, the true\nrelationship of phenomena and occurrences, independently of whether\nrestless philosophy assigns a question mark to this ultimate\nobjectivity. A great discoverer in the realm of Nature cannot and dare\nnot proceed otherwise. For him there is behind the veil of Maya not a\nphantom that finally vanishes, but something knowable, that becomes ever\nclearer and more real as he detaches each successive veil in his process\nof approximation.\n\nDuring this conversation, when we were talking of the \"Future of the\nSciences,\" Einstein gave his ideas free rein, shooting far ahead of the\nviews and prognostications of the above-mentioned scientists:\n\n\"Hitherto we have regarded physical laws only from the point of view of\n_Causality_, inasmuch as we always start from a condition known at a\ndefinite cross-section of time, that is, by taking a time-section of\nphenomena in the universe, as, for example, a section corresponding to\nthe present moment. But, I believe,\" he added, with earnest emphasis,\n\"that the laws of Nature, the processes of Nature, exhibit a much higher\ndegree of uniformity of connexion than is contained in our\ntime-causality! This possibility suggests itself to me particularly as\nthe result of certain reflections concerning Planck's Quantum Theory.\nThe following may be conceived: What belongs to a definite cross-section\nof time may in itself be entirely devoid of structure, that is, it might\ncontain everything that is physically conceivable, even such things (so\nI understood him to say) as, in our ordinary physical thought, we\nconsider impossible of realization, for example, electrons of arbitrary\nsize, and having an arbitrary charge, iron of any specific gravity, etc.\nBy our causality we have adjusted our thought to a lower order of\nstructural limitations than seems realized in Nature. Real Nature is\nmuch more limited than our laws imply. To use an allegory, if we regard\nNature as a poem, we are like children who discover the rhyme but not\nthe prosody and the rhythm.\" I interpret this as meaning that children\ndo not suspect the restrictions to which the form of the poem is\nsubject, and just as little do we, with our causality, divine the\nrestrictions which Nature imposes on occurrences and conditions even\nwhen we regard them as governed by the natural laws we have found.\n\nThus a leading problem of science in the future will be to discover the\nrestrictions of Nature as compared with the apparent causality implied\nin physical laws.\n\nWe have in this an example of the transcendental perspectives that are\nopened up when we accompany Einstein on one of his excursions of\nthought. In this case it is actually a question of ultimate things, of a\nregion of discovery of which we cannot yet form a conception, and it\nappears doubtful whether the problems latent in it are to be treated by\nmaking investigations into physical nature, or whether they are to be\nallotted to speculative philosophy.\n\nIn the first place, Einstein's remark seems to aim at nothing less than\na revision of the conception of causality. However much has been done to\npurify this conception and to make it clear, we have here, perhaps, a\nnew possibility of refining it by making a synthesis of scientific and\nabstract philosophical views. We shall just touch very lightly and\nsuperficially on the possibility of a synthesis giving us an avenue to\ntruth. Whoever has heard these words of Einstein, feels the need of\ngetting on to firm ground to rescue himself out of the turmoil of ideas\ninto which he has been plunged.\n\nWhat is Causality? A physiological answer may be given by saying that it\nis the irrepressible animal instinct, rooted in our brain-cells, that\ncompels us to connect together things that we have experienced and\nimagined. Poets have defined Hunger and Love as the fundamental elements\nof our social lifes; we need only add the thirst for causality to this\nto complete the list of primary instincts. For this mental thirst is not\nless intense than our bodily hunger, and is even greater in that it\nnever forsakes us for a moment. It is easier for the body to check\nbreathing than for the soul to still the question of the why and\nwherefore, of the cause and effect, of the antecedent and consequent.\n\nThis ceaseless search for a connexion between occurrences has become\norganized into a fixed and immovable form of thought, which remains\nmysterious even when we imagine that we have eliminated all the mystery\nfrom it. The relations that we seek and that we regard as being of an\nelementary character are totally foreign to Nature herself. David Hume,\nthe first real, and at the same time the most penetrating, explorer into\nthis form of thought, said that, in the whole of Nature not a single\ncase of connexion is disclosed which we are able to grasp. All\nhappenings appear, in reality, disconnected and separate. One \"follows\non\" another, but we can never detect a connexion between them. They\nappear \"co-joined,\" but never \"connected.\" And since we can form no idea\nof what has never presented itself to our outer or inner perception, the\nnecessary conclusion seems to be that we have absolutely no idea of\ncausal connexions or causative forces, and that these expressions are\nquite devoid of meaning, however much they may be used in philosophical\ndiscussions or in ordinary life. This \"Inquiry concerning Human\nUnderstanding,\" with its atmosphere of resignation, has been elaborated\nin manifold ways, particularly by Kant and the Kantians; for it is\nimpossible to take up a philosophic thread without entering on an\nexamination of the fundamental question concerning the existence of a\ncausality which lies outside our instinct for causality. It is also\ninevitable that, whenever we start out in this direction, we encounter\nthe further question: What is Time? For causality directs itself to the\nproblem of succession, both of sensations and phenomena, consequently\nthe two questions are not only intimately connected, but are really only\ndifferent expressions of one and the same question. Time, which\naccording to Descartes and Spinoza is a _modus cogitandi_, not an\n_affectio rerum_, and, according to Kant, is an _a priori_ form of\nthought, dominates our intelligence with the same sovereign power, as\nthe imagined course of things: what we perceive in the corresponding act\nof thought is regarded as temporal and causal, and impossible of further\nanalysis.\n\nNow, the conception of time has been entirely revolutionized by Einstein\nhimself; and it may be expected that the conception of causality,\ntoo--which, in accordance with custom, we still endow with a separate\nexistence--will also be affected by this revolution.\n\nWe thus approach a relativization of causality, and we may advance a\nstep further in this direction, if we call to mind the differences of\ntime-perception that Nature herself leaves open to us. It must be\nclearly understood that we are not dealing at present with the\ntheoretical time of physics, in the sense of Einstein's theory, but with\nsomething physiological that ultimately, however, resolves itself into a\nrelativization of time, and hence also of the causal connexions in time.\n\nTo do this, we have to follow the lines of reasoning developed by the\ncelebrated St. Petersburg academician, K. E. von Baer, and we need\nextend it only very little to get at the heart of causality, if we start\nfrom his address of 1860: \"Which View of Living Nature is correct?\" For\nthe human brain is a part of living nature, and hence the processes of\nthought may also be conceived as expressions of life.\n\nThe starting-point is a figment, the fictitious character of which\nvanishes as soon as we approach its results. The bridge of thought may\nbe destroyed later; it suffices to carry us temporarily, as long as it\nlands us in safety on the other side.\n\nThe rapidity of perception, of the arbitrary motions, of intellectual\nlife seems in the case of various animals to be proportional\napproximately to the rapidity of their pulse-beats. Since, for example,\nthe pulse of a rabbit beats four times as quickly as that of a bull, it\nwill, in the same interval of time, also perceive four times as quickly,\nand will be able to execute four times as many acts of will, and will\nexperience four times as much as the bull. In the same astronomical\nlength of time the inner life and perceptual world, in the case of\nvarious animals, including Man, will take place at different specific\nrates, and it is on these rates that each of these living creatures\nbases its subjective measure of time. Only when compared with our own\nmeasure of time does an organic individual, say, a plant, appear as\nsomething permanent in size and shape, at least within a short interval.\nFor we may look at it a hundred times and more in a minute, and yet\nnotice no external change in it. Now, if we suppose the pulse-beat, the\nrate of perception, the external course of life, and the mental process\nof Man, very considerably accelerated or retarded, the state of affairs\nbecomes greatly changed, and phenomena then occur, which we, fettered by\nour physiological structure, should have to reject as being fantastic\nand supernatural, although, on the supposition of a new structure they\nwould be quite logical and necessary. If we suppose human life from\nchildhood to old age to be compressed into a thousandth part of its\npresent duration, say, into a month, so that the pulse beats a thousand\ntimes more quickly than occurs in our own experience, we should be able\nto follow the course of a discharged bullet very exactly from point to\npoint with our eyes, more easily than we can at present observe the\nflight of a butterfly. For now the motion of the bullet in a second will\nbe distributed among at least 1000 pulse-beats, and will induce at least\n1000 perceptions, and accordingly, in comparison with our everyday\nperception, it will appear 1000 times slower. If the duration of our\nlife were again to be reduced to a thousandth of its first reduced\nvalue, that is, shortened to about forty minutes, then our flowers and\nherbs would seem just as motionless and immutable as rocks and\nmountains, in which we only infer the changes without having directly\nobserved them. We would in the course of our lifes see little more of\nthe growth and decay of a bud and a flower in full bloom than we at\npresent see of the geological changes in the earth's crust. The acts of\nanimals would be much too slow to be seen; at most, we could infer them\nas we do the motions of the stars at present. If life were shortened\nstill further in the same way, light would cease to be an optical\noccurrence to us. Instead of seeing the things on which light falls, we\nshould become aware of them as being audible, and what we at present\ncall tones and noises would long have ceased to have an effect on the\near.\n\nIf, however, we let our fancy roam in the opposite direction, that is,\nif, instead of compressing the duration of human life, we expand it\nenormously, what a different picture of the world would present itself!\nIf, for example, the pulse-beat, and hence the rate of perception, were\nto be made a thousand times slower, so that the average human life would\nbe spread out over, say, 80,000 years, and that we should experience in\none whole year only as much as we now experience in a third of a day,\nthen, in every four hours winter or any other season would pass by,\nvegetation would spring up and as rapidly die. Many a growth would not\nbe perceptible, on account of its relative rapidity compared with the\nrate of the pulse-beat. For example, a mushroom would suddenly come into\nexistence, like a newly formed spring. Day and night would alternate as\na light and a dark minute; and the sun would appear to fly over the\nheavens like a fiery projectile. If we were again to make the duration\nof human life a thousand times longer still, and hence the rate of life\na thousand times slower still, we should, during the whole of an\nordinary year, be able to have only 190 distinct perceptions, so that\nthe difference between day and night would vanish entirely, and the\nsun's path would be a glowing circular band in the heavens, and all\nchanges of form that seem to us to happen quietly and regularly, and to\npreserve a certain permanency, would melt together in the wild stream of\nhappening, engulfed in its onward rush.\n\nAre we justified in opposing to this relative perception of time \"our\nown\" time, which is something specific and dependent on our constitution\nas human beings? Should we not rather adopt the view that this specific\ntime, adapted to our particular pulse-beat, gives only a very limited\npicture of the world, which is conditioned and determined by the\nlimitations of our own definite intelligence? Is it, perhaps, only a\ndistorted picture, a caricature, of actual occurrences?\n\nAn intelligence infinitely superior to our own would no longer be\ndependent on the separate sensations such as are presented to us with\nthe rhythm of the pulse. For such a mind there would be no metronomic\nfoundation in the sequence of occurrences, beyond what represents itself\nas time to our understanding. He would be situated outside of time in\nwhat Thomas Aquinas called the _nunc stans_, in the stationary present,\nwithout a retrospect of the past and without expectation of a future.\nWithout the Before and the After, the occurrences of the world would\nacquire the clearest and simplest meaning, like that given by an\nequation of identity. What presents itself to us as a \"succession\" of\nevents would merge together into one whole, just as a succession of\nnumerical calculations become summarized in a rule of calculation, or as\na series of logical operations resolves into a logical self-evident\ntruth. If the mind conceived by Laplace actually existed, it would stand\nabove the necessity of introducing time as a quantity into its\nworld-equations, for time is a purely anthropomorphic quantity, produced\nby our perception, and regulated by our own characteristic pulses.\nAccordingly, the conception of causality, too, which is indissolubly\nconnected with time, must be regarded as anthropomorphic, as something\nthat we read into, and not out of Nature. We should at least have to\nrecognize that if there is a causality outside ourselves, then we can\nlearn only a minimum about it, and even this only in a world displaced\nor distorted by the accidental rate of our pulse-beat.\n\nLet us now repeat Einstein's assertion \"that the laws of Nature, the\nprocesses of Nature, exhibit a much higher degree of uniformity of\nconnexion than is contained in our time-causality! It is possible that\nwhat belongs to a definite cross-section of time may in itself be\nentirely devoid of structure, that is, it might contain everything that\nis physically conceivable, even such things as, in our ordinary physical\nthought, we consider impossible of realization, for example, iron of any\narbitrary specific gravity.\" It seems to me that the non-physicist will,\nperhaps, gain a clearer insight into these highly significant words of\nEinstein, now that he has received the assistance of these physiological\nconsiderations. It must be granted that the philosophic grounds of\nEinstein are quite different and lie much deeper than those of von Baer,\nwho starts from organic functions and ends by arriving at a mysterious\nrelativity that is yet consistent in itself. Nevertheless, there is one\npoint of contact, inasmuch as in each case possibilities that lie\napparently _extra naturam_ are suggested.\n\nEinstein says: \"Hitherto we have regarded physical laws only from the\npoint of view of _causality_, inasmuch as we always start from a\ncondition known at a definite cross-section of time, as, for example, a\nsection corresponding to the present moment.\" At our own risk an easy\nparaphrase of his words will be attempted:\n\nThe time-section of the present contains for us the sum of all previous\nexperiences, out of which the necessary course of our thought sifts out\nthe category of causality.\n\nWhat is not present in experience cannot appear in our causality. Let us\nconsider for a moment Hume's example of the Indian who has never known\nice. Without being told, and if he is dependent only on his own\nsensations, he would never learn that water freezes in cold climates.\nThe influence of cold on water is not gradual, corresponding to an\nincrease of cold, and not one that may be anticipated in all its\nconsequences, but at the freezing-point water, which a moment before was\na very mobile liquid, passes into a very rigid solid. The causality of\nthe Indian cannot account for this. If we tell him of this phenomenon,\nhe has two courses open to him. Either he refuses to believe it--and\nthis would be quite natural, since rigid water is to him as meaningless\nas is a square circle to us. Or else he believes the story, and then his\nlist of categories incurs a break, passing through the middle of\ncausality. He has then to reconcile himself to the assumption that\nsomething that is meaningless to him and that stands outside the\nconnexion of cause and effect is possible of realization. Up to that\nmoment, in his time-section of the present, there was no room for it in\nhis causality. To Torricelli the conception of liquid air, which we have\nbeen able to prepare only since 1883, would have appeared impossible and\nincompatible with his causality.\n\nSo there is no room in our causality for the idea of iron with the\nspecific gravity of air, or with one several times that of gold. For,\nreasoning along the lines of our causality, we should conclude that a\nsubstance that is so light or so heavy may, indeed, exhibit chemical\nrelationship with iron, but it would not itself be sufficiently defined\nby the term _iron_.\n\nNow Einstein also said: \"Real Nature is much more limited (or bound)\nthan our laws imply.\" A sceptic might be disposed to take these\nstatements separately in order to construe a contradiction out of them.\nFor, if there are limiting conditions in Nature, which are foreign to\nthe views expressed in our laws, how would it then be possible for\nphenomena, which cannot be imagined, to become realized? If Nature can\ndo this, surely she must have more liberty than we seek to impose on\nher. This apparent contradiction vanishes if we treat the conception of\nstructural design or uniformity as something distinct from the measure\nof all experience up to the present. This would give us the following\ninterpretation:\n\nOut of the manifold of occurrences that are possible in mechanical\nNature, real Nature selects a very closely defined manifold. Thus the\ntrue laws imply a much greater degree of limitation than those known to\nus. For example, the laws known to us at present would not be affected\nif we should discover electrons of arbitrary size or iron of arbitrary\nspecific weight. But Nature realizes only electrons of a quite definite\nsize and iron of a definite specific weight.\n\n     *     *     *     *     *     *     *     *\n\nLet us bear in mind that in aiming at ultimate truths we have no final\ncourts of appeal. Nor are the latter to be assumed even when, in\npursuing a theory, we encounter a difficulty, which at first exhibits\nall the signs of a direct conceptual contradiction. It should rather be\nrealized that a fiction containing an initial but only provisional\ncontradiction serves as a starting-point for just those investigations\nthat are most subtle and that have far-reaching consequences. We should\nhave no Infinitesimal Calculus, no Algebra, no Atomic Theory, no Theory\nof Gravitation if, to avoid all initial contradictions, we surrender the\nfiction of differentials, of imaginary quantities, of the atom, of\naction at a distance. In short, it may, indeed, be said that not only\nknowledge, but also life, the holding together of people by convention,\nlaw, and duty, would become impossible if we did not accept the fiction\nof free will, which directly contradicts the determinate character of\nall happening, including actions and motives, which, physically, alone\nseems recognizable.\n\nFiction (not to be confused with hypothesis) and anthropomorphism, in\nspite of their inner inconsistency, are the two poles about which our\nthoughts and our lives revolve. And no doctrine will ever soar to such\nheights that it will be able to deny completely its origin from these\nroots of all thought. The Archimedean thought-centre of the universe,\nwhich would enable us to lift the world out of its hinges, is\nunattainable, because it does not exist at all.\n\nIs this also to apply to the new physics, whose results are to be\nregarded as the last word in scientific knowledge? Many a hypercritical\nthinker might be led away by the current of the preceding statement, and\nfeel disposed to answer in the affirmative, were it not that, here too,\na contradiction intrudes itself. This is expressed in the fact that not\none of the present-day philosophers is in a position to pursue the\nthreads of this theoretical fabric to their hidden ends.\n\nThus we arrive at a parting of the ways. Whoever aims at becoming\nthoroughly familiar with Einstein's new world-system finds that the\nstudy of the theory claims so much attention that there is scarcely a\npossibility left of proceeding to an ultimate philosophical analysis.\nAnd whoever is absorbed only by the desire of making philosophic\ninvestigations soon enough arrives at border-lines of thought, at which\nhis conscience warns him to beware of insufficient scientific knowledge.\nHe will be attacked by doubts as to whether he has properly understood\nthe theory. And he will be confronted with the question whether he is\njustified in drawing ultimate philosophical conclusions before he has\nmastered all the mathematical details.\n\nAs far as can be judged at present, only one thinker has, so far, had\nsufficiently wide knowledge to enable him to correlate the physical\ntheory methodically with the theory of knowledge. I mean Professor\nMoritz Schlick of Rostock, who has set out his ideas systematically in\nhis book _Erkenntnislehre_, which is extraordinary in itself and in its\ngreat scope; it takes us beyond Kant. In Schlick's opinion Einstein's\ntheory furnishes us with the key to new and unexpected chambers of\nthought; it is a wonderful instrument for opening up new avenues, and\nwould appear more wonderful still if we could use this instrument\nwithout having recourse to anthropomorphism. This limitation may lead to\na Utopia, or may entail a _circulus vitiosus_. But we have one\nphilosophy nowadays which applies to what cannot be fulfilled \"AS IF\" it\nreally is capable of fulfilment. Among the disciples of Vaihinger, the\nfounder of the As-If-doctrine of thought, we, however, notice the\ntendency to follow anthropomorphic and fictitious paths also in his\nfield of thought.\n\nFrom numerous utterances of Einstein, I have gathered that he himself\ndoes hot give his unqualified approval to all attempts at unravelling\nthe ultimate problems by means of philosophy, that is, by using\nmetaphysics alone. He does not deprecate these endeavours, but even\nexpresses admiration for some of the newer works, as for that of\nSchlick, yet he sees certain obstacles in the purely philosophical\nmethods, that at least restrain him from taking a systematic interest in\nthem. This reluctant acceptance of, and doubt in, the processes of\nphilosophy, that has never forsaken the exact investigator, this\nsuspicious attitude which scents traces of sophistic and scholastic\nmachinations in all metaphysical arguments, also asserts itself in him\nin a noticeable form. He feels the absence of rigour and of consistency\nof direction, which is a guarantee of progress in passing from one\nresult to another, in the method of thought of those who are pure\nphilosophers: and he deplores the spongy and murky appearance of certain\nexpressions of thought, which, it must be admitted, form a poor contrast\nto the completeness and the crystal clearness of mathematico-physical\nreasoning. There was an inscription on the portals of the Athenian\nAcademy which stated that entrance was forbidden to all who had had no\nmathematical training; we may imagine next to it an academy of pure\ntranscendental philosophy, bearing the inscription: No exact research\nallowed! I believe that this clear-cut distinction would tally with\nEinstein's view.\n\nIn the case of the great Ernst Mach, for whom Einstein has intense\nadmiration, we observe a similar attitude, or we may say that, in the\nlanguage of allegory, he sang openly the same refrain in another key. He\nnever ceased reiterating that he was properly \"no philosopher at all,\nbut only an investigator of Nature.\" At the beginning of the\nintroduction to one of his works we read his confession: \"Without in the\nslightest degree being a philosopher, or even wishing to be one ...\";\nand some lines further on he calls himself sarcastically \"a mere amateur\nsportsman\" in philosophical regions. Yet, Mach's initial remark is\nfollowed by a remarkable result, for the book in question, _Knowledge\nand Error_ (Erkenntnis und Irrtum), is to be reckoned among the most\nimportant works in philosophical literature; and he himself, the amateur\nsportsman, who did not even desire to be called a philosopher, accepted\nin 1895 the post of Professor of Philosophy at Vienna University. It was\nmerely his timidity in the face of the philosophical fraternity that had\nmade him emphasize repeatedly the distinction between his own work and\nthat of the philosophers, whereas in his heart he had nourished a\npassion for Philosophy, the first mother of Science. And in my opinion\nsuch a moment may arrive for even the most rigorous investigator when he\nsuccumbs to the siren strains from the shores of philosophy.\n\nAs far as Einstein himself is concerned, I cannot venture on a\nprognostication. Even though he belongs to the category and rank of\nDescartes, Pascal, d'Alembert, and Leibniz, in whom Mathematics and\nspeculative Philosophy are intermingled, he is yet characterized by such\na pronounced individuality, that it is quite inadmissible to draw\nconclusions about him from others. He has no need to experience a day of\nDamascus, for he carries the gospel of salvation in himself, and it\nradiates from him. One thing seems possible, in my opinion, namely, that\nEinstein will occasionally roam into the neighbouring realm merely from\n\u00e6sthetic motives. Although the means of philosophy are nebulous and\nmore indefinite than those of exact science, which are almost glaringly\ndistinct, philosophy itself for this reason is the more closely related\nto Art. And a theory that applies to the whole universe must assuredly\ncontain many germs that may come to life if subjected to the methods of\nArt. The connecting link between Kant and Schiller shows in what sense\nthis is to be understood. Even at present there are indications in Art\nwhich tend to show that it is ready to establish points of contact with\nKnowledge. In France symphonic poems were written on the measure\nrelations of the circle, and on logarithms: these are at present only\ncuriosities, but may in future become models. At a much later date,\nperhaps, the four-dimensional universe may become ripe for treatment by\nsuch methods of Art. On the way to this goal there is the treatment with\nthe symbolic, non-rigorous, and semi-poetic means of expression used by\nPhilosophy. Many will use their efforts to achieve this, and perhaps\nthey will come within closer range of success, if Einstein himself lends\na helping hand. It will not be possible to arrive at new physical truths\nby following this path, but those that are actually known will be traced\nmore readily to the great mainstream of philosophy. To fathom the\nsecrets of the world is the work of a recluse, but to make it\ncomprehensible to a wide circle, a preacher is necessary, who uses the\nbeautiful methods of philosophical rhetoric. Cosmos denotes the World\nand its Ornamentation; its creator, Demiurge, is a master who fashions\nhis forms along the lines of Art.\n\nThus we have learned what Einstein regards as the sole purpose of\nScience, namely, the search after Truth. For him, the latter is\nsomething absolute in itself, and the possibility of getting nearer to\nit is as great as the impossibility of deriving results of scientific\nuse from, say, ethical discoveries. For ethics is a field which is\nhaunted by the conceptual ghosts, and the manner of treatment, _ordine\ngeometrico_, that Spinoza wished to apply to it, is reserved for\nphysics. Einstein leaves the inverse philosophical query: \"Is not Truth\nin itself only something that we have constructed in imagination?\" to\nthose who find pleasure in sauntering along paths of thought that are\ntotally unconnected, whereas he himself advances in a straight line with\nthe consciousness that even if the goal is unattainable, he will at\nleast not lose the right direction!\n\n\n\n\nCHAPTER VIII\n\nHIGHWAYS AND BY-WAYS\n\nPractical Aims of Science.--Pure Search for Truth.--Retrospective\nConsiderations.--The Practical Side of Kepler.--A Saying of\nKant.--Mathematics as a Criterion of Truth.--Deductive and Inductive\nMethods.--Conceptual and Perceptual Knowledge.--Happiness and the\nPleasures of Theory.--Achievements of Science and Works of Art.--Ethical\nResults.--Minor Questions.\n\n\nAGAIN we chanced to refer to the great subject: Can or should\ntheoretical science also pursue practical aims?\n\nIt is impossible to overrate the importance of this question. It haunts\nus daily and often enough looms up threateningly on the horizon of\nmankind. Observe what form the discussions of educated people take when\nthe finest and most sublime achievements of mind are being debated: one\ntalks of the wonders of research in the remotest corners of astronomy\nwhere the structures of world-wide star-systems are being investigated;\nwe hear observations about the theories that aim at tracing the\ncosmogonic development of universes from the original chaos of countless\nages ago. We hear mention of exalted sciences, the Theory of Functions\nand Numbers, whose founders and representatives are just as remarkable\nin propounding problems as in solving them, and inevitably the following\nquestion obtrudes itself: Of what use is it, ultimately? What can one do\nwith it? Can it be admitted that theoretical science has an object of\nits own, or have we at least the right to maintain the hope that, sooner\nor later, it will bring us a real \"Utility\" expressible in practical\nterms?\n\nAnd just as the devotees of pure art have framed the expression, \"L'art\npour l'art,\" so Einstein proclaims that science is its own object,\n\"Science for its own sake!\" It carries its aims absolutely in itself and\nmust not, through aiming at other purposes, stray from its own highways.\n\"It is my inner conviction,\" said he, \"that the development of science\nitself seeks in the main to satisfy the longing for pure knowledge,\nwhich, psychologically, asserts itself as religious feeling.\"\n\n\"To yourself, Professor, the practical aspect seems comparatively\ninsignificant?\"\n\n\"I did not say that, and it was not implied in the question. We must not\nlose sight of our premises. As long as I am interested in working along\nlines of research--this was the assumption--the practical aspect, that\nis, every practical result that is found simultaneously or arises out of\nit later, is a matter of complete indifference to me.\"\n\nFar be it from me, even in thought, to wish to question this confession\nof faith, particularly as the fact that it comes from a searcher of the\ntruth gives it the more weight. Yet a certain uneasiness has crept over\nme because voices have recently made themselves heard that demand for\nscience a totally different tendency. They arise not only from the\npublic at large, but also from academic circles. Just a short time ago\nI read an exposition by a well-known scientist, W. Wien, in which he\nindulged in a violent polemic against the view that purely scientific\nobjects are alone valid. Professor Wien addressed himself particularly\nto German physicists, reproaching them with underestimating technical\nscience, and with regarding it as a \"lowering of status\" when a\nphysicist enters into practical life.\n\nTo this Einstein remarked: \"I do not know at whom this reproach is\naimed, but I venture to think that my own attitude can never have given\nrise to an attack of this kind. For I make no divisions of rank, and\nrecognize no higher and no lower status. I affirm only what is the\nnature of science herself, and the objects according to which she,\nobjectively, has to direct her gaze. Whatever further orientation\nindividual investigators may seek for themselves depends on the\ndetermining conditions of life of each, although these conditions do not\nserve as a means for deducing the main lines of research. The accusation\nthat I am unwarranted in putting forward this view will, I hope, not be\nlevelled at me, for my connexions with practice are manifold enough, and\nup to the present moment I have often collaborated with practical\nphysicists....\"\n\n\"As I have regretfully observed when you were obliged to interrupt a\nconversation with me to give an audience to impatient persons seeking\nadvice in technical matters!\"\n\n\"My own associations with the world of practice are not, indeed, of\nrecent date. My own parents originally wanted me to become a technical\nscientist, and I was expected to choose this profession to earn my\nlivelihood. I was not, however, sympathetically inclined to it, for even\nat an early age these practical aims were to me, on the whole,\nindifferent and depressing. My idea of human culture did not coincide\nwith the current view, that cultural development is to be measured in\nterms of technical progress. Doubts, indeed, arose in me as to whether\ntechnical improvements and advances would actually contribute to the\nwell-being of mankind. I must add that, later, when I came into actual\ntouch with technical science, my opinion became somewhat modified, for\nthe reason that, here too, pleasures of theory often visited me.\"\n\nThe true position is probably that the technical worker who does not\nmerely think out improvements for machines, but occupies himself with\ninventions on a higher plane, never ceases to feel himself a theorist,\nsince his achievements are dependent for their inspiration on the fruits\nof theory. The practical results of to-day are rooted in the theoretical\nresults of decades ago, and what is nowadays regarded as an idea of pure\nresearch may in later decades acquire practical value. Whether it\nactually becomes of value, or not, is of little account in judging the\nidea. At any rate experience has shown that the beginning of theoretical\ninvestigations hardly ever gives us the chance of making\nprognostications. We spoke of the discoveries of Volta, Amp\u00e8re, and\nFaraday. When these were first known, the world might have asked: Why\nhave they been disclosed? To what can they be applied? Of what use are\nthey? Nowadays we know the answers that still lay hidden at that time,\nand we proudly point to modern dynamos. But does a dynamo really\nrepresent the significance of these discoveries? Would the importance\nand rank of Volta, Amp\u00e8re, and Faraday be less if the dynamo had not\ncome into existence? Only an out-and-out materialist would affirm this,\nand, strictly speaking, the question should not even be raised. For it\nis in a sense equivalent to wishing to judge of the importance and\nsignificance of the Polar Star from its usefulness to the navigator on\nthe earth's surface in finding his bearings. We may put the question\n(although only in the spirit of psychological curiosity, and without\nexpecting much elucidation): Would these discoverers have been\nparticularly happy if they had divined the far-reaching consequences of\ntheir work? Did they, indeed, in the course of their abstract\nresearches, have a pre-vision of the future dominated by the dynamo?\nEinstein refused to answer this in the decisive negative. He left room,\nif ever so little, for doubts--that is, he considered that, in all\nprobability, these three discoverers had no presentiment of these\nconsequences, and even if they had in a dream caught a glimpse of our\npresent electrical age, their zest for discovery, their \"pleasure in\ntheory,\" could scarcely have been increased; for they were discoverers\nby nature, who, swept along by their own spirits, did not need to wait\nto satisfy the desires of practical application.\n\nIn Einstein's opinion, the presentiment that a discovery may have\npractical applications in the future may react on pure research. He\nquoted bacteriology as a proof of this. In the series of eminent\nbacteriologists, ranging from Spallanzani to Schwann and Pasteur, there\nwere certainly some whose desire for knowledge was directed primarily\ntowards discovering purely scientific relationships. Pasteur himself\nstarted from the theoretical question of the creation of life, that is,\nfrom the problem of the origin of organic creatures from inorganic\nmatter without the medium of parent organisms. As a pan-spermist he took\nup a negative attitude, that is, he tried to prove that it is impossible\nto discover a bridge between organic and inorganic matter. Yet he\ndoubtless knew that his theoretical efforts stretched out into practical\nregions, and he may easily have foreseen that they would exert a very\nimportant influence on Medicine and Hygiene, although he could not\nmeasure its full extent. In this case, then, we cannot fail to recognize\nthat a certain connexion between the desire for pure knowledge and the\nimpulse to apply it practically is possible, serviceable, and justified\nin itself.\n\nAn influence in the opposite direction is also possible, and when,\nduring the course of our conversation, we went in search of examples, we\ncame across one of great interest. It shows us that a question may arise\nout of ordinary practice that may open up an immense field of pure\nknowledge, nay, it may lead to a science of very wide scope. As this\nexample is not well known, I shall mention it here; I do so with\nadditional pleasure as the scientist involved is one of those whom\nEinstein quotes most frequently and for whom he has the greatest\nadmiration, namely, Johannes Kepler. First we have the surprising fact\nthat Kepler, who, even when at the height of his fame, was not free from\ncare, was once the possessor of some money. In the year 1615, his\nblessed year of fortune, the great astronomer owned a comfortable home\nin Linz, and even dared to conceive the idea of placing some well-filled\ncasks in his cellar; nay, more, he was in a position to publish a new\nscientific work at his own expense, and thus appear as his own\npublisher.\n\nThis production of Kepler and his casks of wine are directly connected,\nas we see clearly from the title: _Doliometrie_, literally, \"The\nMeasurement of Casks.\" But the title of the work gives not the slightest\nhint of its importance. For these investigations relating to wine-casks\nactually became the foundation of a science of sovereign power, the\n_Infinitesimal Calculus_.\n\nWhat was Kepler's aim? It was something entirely practical, and directed\nto a definite purpose, quite independent of \"pleasures of theory,\" to\nrepeat Einstein's expression. His problem was a question of economy, of\nusing material sparingly and appropriately, in accordance with the\nrequirements of the careful head of a house. How must such a cask be\nconstructed from a minimum of wood to give the greatest cubical content?\n\nHis deliberations began by regarding wine as the precious content\nenclosed by a figure in space, and then conceiving the cask as\nrepresenting a particular class of \"bodies of revolution,\" that is, of\nfigures in space that may be regarded as produced by the revolution of a\ncurved line about an axis. At this point he at first endeavoured to gain\na complete survey of the question. He varied the boards along the sides,\nthe staves, and formed successively ninety-two such bodies of\nrevolution, some of which he named after the fruits which they resembled\nin shape, as, for example, apple-shaped, lemon-shaped, olive-shaped\nbodies. He started out by measuring casks, and the final result was that\nhis work, _Doliometrie_, became the source of all future cubatures or\nmeasurements of volume.\n\nNow we come to the deciding point. What conditions has the limiting\nsurface of such a cask-like body of revolution to fulfil, if the body is\nto have a maximum volume? An epochal discovery here came to light. The\npractical head of the house soars up into the sublime realms of the\ntheory of magnitudes. Kepler discovered the conception of changes in\nfunctions, and their peculiarities at the maximum point. (He did not, of\ncourse, use these modern terms.) By this means, long before Newton and\nLeibniz, he laid the foundations of Infinitesimal Calculus, which later\nbecame the heart and soul of mathematics, of astronomy, of theoretical\nphysics, and of technical science, in so far as it is founded in\nmechanical relations.\n\nOn the other hand, Einstein who now, three hundred years later, has set\nup his differential equations, and, with them, a new world-system,\nstands before us as a pure discoverer, devoid of practical aims. But in\nthese equations there are elements of analysis that once came to light\nin a happy idyll. This event did not come out of the grey obscurity of\nabstraction, but out of a region of earthly happiness, when a ray of\nlight found its way into Kepler's gloomy existence. No poet has yet\nexpressed this curious complex of events in a ballad, telling how Truth,\nthe only object of Science, was pressed out of the grape, and how\nPractice, inspired by the inquiry of a cooper, found its way to a Theory\nthat stretches to the confines of the Universe.\n\n\n\n\nII\n\n\nThe conversation touched on famous expressions, words carved in stone,\nin particular a saying of Kant which seeks to fix the foundation and the\nlimits of knowledge. \"Every science of Nature,\" the great philosopher of\nK\u00f6nigsberg had said, \"contains just as much Truth as it contains\nmathematics.\" And since, ultimately. Nature includes everything--for a\ndemarcation between physical and mental science no longer seems\npossible--then, if we follow Kant, we should have to regard mathematics\nas the sole measure of science.\n\nIt is certainly not yet possible to enter into a discussion on this\npoint with historians, medical or legal practitioners. They would be\njustified in refusing it, since, in their subjects, \"truth\" is not the\nsole factor, and because we cannot see at present how the conception of\na comprehensive mathematical truth is to find a place in them. But when\nwe question a physicist on this point, who unceasingly uses mathematics\nas his chief instrument, we should surely expect him to answer with an\nunconditional affirmative. At least, I should not have been surprised if\nEinstein had answered in this way, and if he had indeed claimed its\nvalidity for every branch of science.\n\nBut Einstein considered this quotation to be true only conditionally, in\nthat he accepted it as a principle, but did not regard it as universal.\nThat is, he does not recognize mathematics as the only test of truth.\n\n\"The sovereignty of mathematics,\" said Einstein, \"is based on very\nsimple assumptions; it is rooted in the conception of magnitude itself.\nIts dominant position is due to the fact that it gives us much more\ndelicate means of distinguishing between infinitely varied possibilities\nthan any other method of thought that expresses itself in language and\nis restricted to the use of words. The greater the field taken into\nconsideration, the clearer does this become; but even in such a narrow\nrange as 1 to 100, an estimate such as 27 is incomparably more exact\nthan can be expressed in words in any other way. If we think of a series\nof sensations, ranging from pleasure to pain, or from sweet to bitter,\nwe find that words leave us in an uncertain, confused state, and we do\nnot succeed in fixing on a point of the series with the same precision\nas we above fixed on the 27 out of the 100. But when the theory of\nmagnitude plays a part in the question, as, for example, in a series of\ntones, whose vibrations exhibit a mathematical sequence, we immediately\nattain a much higher order of precision by using numbers....\"\n\nThat is why there is a sort of scientific pleasure in the sequence of\ntones, so my thoughts ran on. Leibniz remarks that \"Music is the\npleasure of the human soul, which arises from counting without knowing\nthat it is counting.\" Here Pythagoras' \"Number is the essence of all\nthings\" is verified. As soon as we arrive at the stage at which we feel\nthe psychological essence of number, we fall into a sort of ecstasy,\nbecause, in our subconscious minds, we experience not only the pleasure\nof sense but also the underlying truth.\n\nEinstein resumed: \"Kant's remark is correct in the sense that it sets up\ntwo things in clear contradiction to one another. On the one hand, he\nhas in view the fruits of knowledge of ordinary life, in which our\nordinary perceptions and experiences are intermingled and cannot be\ndisentangled by inductive methods and deductive considerations. Opposed\nto these, and to be regarded of higher rank, are the properly scientific\nconstructions\u2014that is, such in which we find a neat differentiation of\nconnected thoughts that are based on regular foundations and that form\nthe links of a chain of deduction. Whenever our science succeeds in\ndetaching this logically ordered knowledge from its sense-sources, it\nhas a mathematical character, and the amount of truth contained in it\nwill accordingly be determined by Kant's criterion. But Kant demands too\nmuch when he asks us to apply this scale to all attainable knowledge of\nscience. It would seem advisable to draw limitations if his remark is to\nserve as a regulative measure. A great part of biological science will\nin future still be obliged to make its way independently of purely\nmathematical considerations.\"\n\n\"Your reflections, Professor, would then also apply to the saying of\nGalilei: The book of Nature lies open before us, but is written in\nletters other than those of our alphabet; its characters are composed of\ntriangles, quadrilaterals, circles, and spheres.\"\n\n\"With all due honour to the beauty of this observation, I cannot refrain\nfrom doubting its universal validity. If we were to accept it\nunconditionally we should have to regard the paths of all research as\npurely mathematical, and this would exclude certain very important\npossibilities, above all, certain forms of intuition that have shown\nthemselves to be extremely fruitful. Thus, according to Galilei's\ninterpretation, the book of Nature would have been illegible for Goethe,\nfor his spirit was entirely non-mathematical, indeed anti-mathematical.\nBut he possessed a particular form of intuition that expressed itself as\na feeling which put him into direct contact with Nature, with the result\nthat he obtained a clearer vision than many an exact investigator.\"\n\n\"Do you then consider intuitive gifts to be separable at all in form and\nin kind?\"\n\n\"It would be pedantic to seek to establish a fundamental difference,\neven if we may regard the non-mathematical intuition of Goethe as a very\nstriking case. Moreover, as I have often emphasized, all great\nachievements of science start from intuitive knowledge, namely, in\naxioms, from which deductions are then made. It is possible to arrive at\nsuch axioms only if we gain a true survey of thought-complexes that are\nnot yet logically ordered; so that, in general, intuition is the\nnecessary condition for the discovery of such axioms. And it cannot be\ndenied that, in the great majority of minds with a mathematical\ntendency, this intuition exhibits itself as a characteristic of their\ncreative power.\"\n\n\"From these remarks it would appear that you value deduction\nconsiderably higher than induction. Perhaps in using these catchwords I\nam expressing myself a little vaguely; it seems to me that great things\nhave been achieved, too, by using inductive processes.\"\n\n\"Let us first define what each of these terms means. Deduction is the\nderivation of the particular from the general, whereas induction is the\nprocess of deriving the general from the particular case. Now, quote any\nexample of a brilliant achievement, which you feel illustrates the power\nof the inductive method. Of whatever kind your example may be, you will\nsoon become aware of the difference in the significance of the two\nprocesses.\"\n\n\"For me the most perfect example of induction is given by certain\nreasoning of Euclid. The question was whether there is a finite or an\ninfinite number of primes (that is, numbers that cannot be divided\nwithout leaving a remainder except by unity). Euclid found an elegant\nproof that the total number is infinite by the following strictly\ninductive reasoning. If the total number were finite there would have to\nbe a _greatest_ prime. Let us call it _n_, and then form the product of\nall primes up to _n_ and including it, finally adding one, thus:\n2 x 3 x 5 x 7 x 11 x 13 ... _n_, plus 1. This new number, say Y, is\ncertainly greater than _n_, and now there are two possibilities, either\n_n_ is prime or it is not prime.\n\n\"If it is not prime, it must be divisible by some existing prime. But\nthe primes up to and including _n_ cannot divide exactly into Y, as\nthere is always a remainder, namely, 1. Hence Y must be divisible by an\nexisting prime X greater than _n_. This contradicts the assumption that\n_n_ is the greatest prime, for X is shown to be greater than _n_.\n\n\"Secondly, if Y _is_ a prime, it immediately follows that _n_ cannot be\nthe greatest prime, for Y is greater than _n_. Hence, however great may\nbe any prime that we may assume, there will always be one that is\ngreater, and even if we do not succeed in expressing it in figures, we\nsee that it must certainly exist. Thus by studying carefully a\nparticular case--the prime _n_, which was assumed to be the greatest\npossible one--we have arrived at a general theorem which states that\nthere is no limit to the number of primes. Is not that, too, a triumph\nof intuition?\"\n\n\"Certainly,\" said Einstein. \"But you must not overlook the fact that a\ntheorem of this kind cannot be ranked with a theorem of a fundamentally\naxiomatic character. The one you have discussed has been derived by a\nclever process of reasoning, but it does not exhibit the characteristic\nof a momentous discovery. This theorem of Euclid can be imagined absent\nfrom science without the content of truth in science being essentially\neffected. Compare with it a theorem of axiomatic significance, such as\nGalilei's Law of Inertia, or Newton's Law of Gravitation. Theorems such\nas the latter are characterized by being starting-points of knowledge\nthat are inexhaustible in the consequences that may be deduced from\nthem. Your question, earlier, as to whether I consider the deductive\nmethod superior to the inductive, was not formulated in correct terms.\nTo this I answered above that the inductive method as a means of\ndiscovering general truths usually appears over-estimated. The proper\nform of the question is: Which truths are of the higher order, those\nthat are found inductively, or those that lead to further deduction?\nThere can scarcely be doubt about the answer.\"\n\n\"No, that is certainly true. If I understand your meaning rightly, the\nanswer may be expressed by an allegory. Intuition of the highest order\ncreates treasure-mines, those of lesser degree individual articles of\nvalue that are significant in themselves, although they cannot be\ncompared with the inestimable value of the mines. The fact that the\nhighest intuition is found in minds with a mathematical trend makes it\nappear possible that Kant's remark may gain more and more credence in\nthe future. It already applies in a measure to subjects to which it\nseemed inapplicable during Kant's lifetime, for example, in Psychology,\nin which the relations between stimulus and response have been\nestablished mathematically only since the Weber-Fechner Law was set up;\nand also, since the time of Quetelet, in Moral Science and Sociology, we\nlearn from mathematical methods of statistics and probability that even\nMan as an active being is subjected to mechanical causality. At any rate\nit seems manifest that Kant's remark, that in every science there is\njust as much truth as there is mathematics, has received additional\nsupport in recent times.\"\n\n\"That may be admitted,\" concluded Einstein, \"without recognizing his\nremark as an axiom. It is still far removed from making possible\nunassailable deductions, and will never quite succeed in doing so; yet\nit may claim equal significance as a beautifully expressed idea with\nthat of Pythagoras, which asserts number to be the nature of all\nthings.\"\n\n\n\n\nIII\n\n\n\"The lines of demarcation between 'conceptual knowledge' (_Erkennen_)\nand 'perceptual knowledge' (_Kennen_) are being drawn more and more\nclosely nowadays. The former is regarded as being the exclusive\npossession of the highly developed human mind, and the latter as being\ncharacteristic of the lower intelligence of other living creatures. Is\nthis not a pronounced case of anthropomorphism, and does it not mislead\nus to form opinions that we should at once disown if we succeed in\nstepping out of our human frames even for a moment?\"\n\n\"We have to rest satisfied with anthropomorphism once and for all,\"\nanswered Einstein, \"and there is no sense in wishing to escape from it,\nfor the arguments about anthropomorphism are necessarily also diffused\nwith it, itself. We are thus moving in a circle if we imagine we can\ndeduce something outside of human knowledge. As soon as we have argued\naround the circle, we find ourselves again at the starting-point, and so\nwe are compelled to mark clear lines of division between instinctive\nknowledge, derived directly by perception, from conceptual knowledge,\nderived by processes of abstraction and reflection; in this way we award\nthe palm of supremacy to the human mind.\"\n\n\"But what if the following contradiction were to assert itself? Suppose\nthat the logical 'circle' is not a circle at all, but a spiral, so that\nthe final point of the argument lies just a trifle above the initial\npoint. I feel instinctively that such apparently fruitless circuitous\narguments might finally lead to a definite piece of knowledge. For\nexample, a certain insect, the ichneumon-fly, although devoid of a\nknowledge of science in our sense, infallibly plants its sting in a\ndefinite point in the rings of a caterpillar, at just the point that\nserves its purpose of paralysing the caterpillar without killing it. It\nacts instinctively, and it is open to me to interpret this occurrence in\nother words. The fly discloses that it 'knows' the anatomy of the\nforeign creature, although it has no conceptual knowledge of it in our\nsense. But it immediately follows from this analogy that, from the point\nof view of the fly, its _perceptual_ intelligence stands higher than our\n_conceptual_ intelligence--that is, by changing the perspective, I am\nled to declare the anatomical knowledge of the fly to be of higher rank\nthan the analogous knowledge of the most learned anatomist. In the same\nway I might persuade myself that the mathematics of a bird of passage\nstands above the cartographic knowledge of any human explorer. The\nmigratory bird that flies from the interior of Africa in a straight fine\nto its nest in Mecklenburg must have something in the nature of a\nco-ordinate system in its organism. The real reason that we assign a\nhigher position to our conceptual knowledge is that we are equally proud\nof our intelligence as of our science; this is perhaps a deception\ndepending on some compromise, a sort of illicit deal in which the mind\ndraws bills of exchange on science, and, as a return, science meets its\nobligations by paying in cheques drawn on the mind!\"\n\nI must confess that these hazardous suggestions received no welcome from\nEinstein, and were not even met with the friendly smile with which he\nusually accompanies his refutations. Nor do I disguise from myself that\nthe question of conceptual or perceptual knowledge can in no way serve\nas a basis of proof; we may at most base certain conjectures on the\ndifference of these types of knowledge, conjectures that suggest in\nwords what eludes our clear comprehension. Einstein's refusal to allow\nthis possibility certainly rests on much firmer ground than the somewhat\nBergsonian views that I tried to present. Perhaps they are of a\nhair-splitting nature, and deal with things lying on different planes;\nand are deduced by unjustifiably altering the perspective with a sort of\nsophistic somersault; perhaps I may be reproached with seeking, like\nM\u00fcnchhausen, to reach a higher standpoint without having a support from\nwhich to start. Yet how is it that I find it impossible to free myself\nfrom this chain of thought? No reason is forthcoming, for it is a purely\nmetaphysical question, and there has never yet been a clear system of\nmetaphysics free from ambiguities and sophism.\n\nLet us rather confine ourselves to the conceptual intelligence\ncharacteristic of human beings, with which, according to Einstein, so\nmany pleasures of theory are available. I asked him whether he would\nrecognize differences of degree in these pleasures, dependent on their\nintensities. Although I rightly felt that he would answer in the\naffirmative, his answer took a totally different turn from what I had\nexpected. It was, indeed, a great surprise, for in the matter of\nhappiness of spirit he expressed a view, according to which he--a great\ndiscoverer!--does not regard Science as the deepest source of happiness!\n\n\"Personally,\" said Einstein, \"I experience the greatest degree of\npleasure in getting contact with works of Art. They furnish me with\nhappy feelings of an intensity such as I cannot derive from other\nrealms.\"\n\n\"This is indeed a remarkable revelation, Professor!\" I exclaimed. \"Not\nthat I have ever doubted your receptivity for products of art, for I\nhave often enough observed how you are affected by good music, and with\nwhat interest you yourself practise music. But even at such moments when\nyou gave yourself up to the pleasures of the Muses, and were soaring in\nregions far removed from the earth, I used to say to myself: This is a\ndelightful arabesque in Einstein's existence; but I should never have\nsurmised that you regard this decorative side-issue as the greatest\nsource of happiness. But your confession seems to go further, perhaps\neven beyond music?\"\n\n\"At the moment I was thinking particularly of literature.\"\n\n\"Do you mean literature in general? Or had you a definite writer in\nmind, when you were speaking of the felicitous effect of works of art?\"\n\n\"I meant it generally, but if you ask in whom I am most interested at\npresent, I must answer: Dostojewski!\" He repeated the name several times\nwith increasing emphasis. And, as if to deal a mortal blow at every\nconceivable objection, he added: \"Dostojewski gives me more than any\nscientist, more than Gauss!\"\n\n\"If, Professor,\" said I, after a pause that may easily be accounted\nfor--\"if you mention in the same breath the names of two such powerful\nbut essentially different intellects, you open the way to a discussion\nthat cannot be settled by a mere positive assertion. It is possible to\nadmire intensely Dostojewski as one who moulds personalities and who\nanalyses the inner struggles of the soul, and yet to deny him perpetual\nfame. This depends on individual judgment, and, as for my own, I believe\nthat Dostojewski, in spite of his direct artistic appeal, will not have\nhis name perpetuated through the centuries like that of many another\nmember of Parnassus. It seems to me to be a more important matter\nwhether a common measure can be found for Art and Discovery at all.\nPerhaps the test of how far a work can be replaced may be regarded as\nvalid for each. When you say that Dostojewski gives you more than Gauss,\nthis probably corresponds with the feeling that without Dostojewski you\nwould have no 'Karamasoffs' and hence would lack a certain life-value\nthat cannot be replaced. But if Gauss had failed to produce one of his\nfundamental theorems of Algebra, probably some other Gauss would have\nappeared, who would have achieved this result. According to this, then,\nour instinct increases the value of a work of art, as we feel that we\nare dependent on one being alone for its creation.\"\n\n\"But this is only to be admitted conditionally,\" said Einstein, \"for the\nbest that Gauss has given us was likewise an exclusive production. If he\nhad not created his geometry of surfaces, which served Riemann as a\nbasis, it is scarcely conceivable that anyone else would have discovered\nit. I do not hesitate to confess that to a certain extent a similar\npleasure may be found by absorbing ourselves in questions of pure\ngeometry.\"\n\n\"Perhaps we may use a different characteristic as a means of\ncomparison,\" I suggested, \"namely, the permanency of the impression\nproduced on the subject receiving it. For example, a fine piece of music\nnever loses its influence. We can listen to the first movement of\nBeethoven's Ninth Symphony a hundred times, and, although we know at\nevery beat what will follow, the state of pleasure continues unweakened;\nindeed, it might rather be said that the expectation of pleasure\nincreases from one hearing to the next.\"\n\n\"This characteristic, too,\" answered Einstein, \"cannot be claimed as the\nexclusive property of works of art. Its existence cannot be doubted,\ninasmuch as it belongs to every eminent example of art. Yet we encounter\nit outside the realm of art, too, in great advances of science, with\nwhich we never cease occupying ourselves, and yet the impression\ncontinues unweakened.\"\n\n\"Do you include among them the impressions that a discoverer experiences\nwhen he reviews in his mind the progress due to his own efforts?\"\n\n\"Naturally, and these, indeed, quite particularly; and if this question\nwere put to me directly, I should answer unhesitatingly that I find\npleasure in reflecting on my own discoveries, and never experience\nfeelings of weariness in passing over them again. So that, to return to\nour original thesis, we must adopt a new basis of value if we wish to\naccount for the fact that the greatest degree of happiness is to be\nexpected of a work of art. It is the moral impression, the feeling of\nelevation, that takes hold of me when the work of art is presented. And\nI was thinking of these ethical factors when I gave preference to\nDostojewskis works. There is no need for me to carry out a literary\nanalysis, nor to enter on a search for psychological subtleties, for all\ninvestigations of this kind fail to penetrate to the heart of a work\nsuch as \"The Karamasoffs.\" This can be grasped only by means of the\nfeelings, that find satisfaction in passing through trying and difficult\ncircumstances, and that become intensified to exultation when the author\noffers the reader ethical satisfaction. Yes, that is the right\nexpression, 'ethical satisfaction'! I can find no other words for it.\"\n\nHis whole face lit up, and I was deeply touched by his expression. At\nthat moment it seemed to me that he had drawn the last veil from his\nsoul to allow me to share in his ecstasy. Was that the same physicist\nwho interprets the events of the world in terms of mathematics, and\nwhose equations encompass phenomena from electrons to universes? If so,\nit was a different soul; one which gave utterance, like that of Faust,\nto the words:\n\n\n   \"And when in the feeling wholly blest thou art,\n    Call it then what thou wilt.\n    Call it Bliss! Heart! Love! God!\n    I have no name for it!\n    Feeling is all in all!\n    Name is but sound and reek,\n    A mist round the glow of heaven!\"\n\n\nAnd, certainly, the book need not have been one of Dostojewski's to\nexcite this feeling in him. He chose the latter to give expression to a\nmood that may change according to what he reads, but undergoes no\nfluctuations in its ethical foundation. From other occasions we know how\nlittle ethics, that is conducted along systematic lines, signifies to\nhim, and that he does not even include it in the sciences. But at the\nsame time we see now that his inner life is dominated entirely by the\nethical principle. His deep love of Art is characterized by it, and\nreceives full satisfaction from the source of ethical joy of which Art\nis the centre.\n\n\n\n\nIV\n\n\nDuring the autumn of 1918 Einstein was feeling indisposed, and, on the\nadvice of his doctor, did not leave his bed. When I entered his room, I\nsaw at once that there was no reason for alarm, for pieces of paper\ncovered with mysterious symbols were lying about, and he was absorbed in\nmaking additions to some of them. Nevertheless, I considered it my duty\nto treat him as a patient under medical care, and did not conceal my\nintention of leaving him after having inquired about his condition. But\nhe would not accept my visit as a mere call to ascertain his progress\ntowards recovery, and insisted that I should remain with him a while, to\nconverse about amusing little problems as usual.\n\nI pointed out to him that there were two objections to this, the first\nbeing that he was unwell, and the second that I was intruding on his\nwork.\n\n\"How illogical!\" he answered. \"If I interrupt my work to chat with you,\nI am putting aside exactly what the doctor would deny me if I were to\nallow him. So, let us make a start. You have probably some conundrum\nweighing on your mind.\"\n\n\"That may not be far wrong. I have been troubled by something in\nconnexion with Kepler's second law. It almost robbed me of my night's\nsleep. My thoughts kept returning to a certain question, and I should\nlike to know whether there is any sense in the question itself at all.\"\n\n\"Let us hear it!\"\n\n\"The law in question states that every planet in describing its elliptic\npath, sweeps out with its radius vector equal sectorial areas in equal\nintervals of time. But this seems only half a law, for the radius\nvectors are only considered drawn from the one focus of the ellipse,\nnamely, the gravitational centre. Now, another focus exists, that may be\nsituated in space somewhere, perhaps far away in totally empty regions,\nif we assume the orbit to be very eccentric. My question is: What form\ndoes this law take if the radius vectors are drawn from this second\nfocus and if the corresponding sectorial areas are considered, instead\nof these quantities being referred to the first focus exclusively?\"\n\n\"This question is not devoid of sense, but it serves no useful purpose.\nIt may be solved analytically, but would probably lead to very\ncomplicated expressions, that would be of no interest for celestial\nmechanics. For the second focus is only a constructive addition, that\nhas nothing real in space corresponding to it. What else is troubling\nyou?\"\n\n\"My next difficulty is a little problem that sounds quite simple and yet\nis sufficiently awkward to make one rack one's brains. It was suggested\nto me by an engineer who certainly has a keen mind for such things, and\nyet, as far as I could judge, he did not get a solution for it. It\nconcerns the position of the hands of a clock.\"\n\n\"You surely are not referring to the children's puzzle of how often and\nwhen both hands coincide in position?\"\n\n\"By no means. As I said just now, it is really quite perplexing. Let us\nassume the position of the hands at twelve o'clock, when both hands\ncoincide. If they are now interchanged, we still have a possible\nposition of the hands, giving an actual time. But, in another case, say,\nexactly six o'clock, we get a false position of the hands, if we\ninterchange them, for on a normal clock it is impossible for the large\nhand to be on the six whilst the small hand is on the twelve. The\nquestion is now: When and how often are the two hands situated so that\nwhen they are interchanged, the new position gives a possible time on\nthe clock?\"\n\n\"There, you see,\" said Einstein, \"that is just the right kind of\ndistraction for an invalid. It is quite interesting, and not too easy.\nBut I am afraid the pleasure will not be of great duration, for I\nalready see a way to solve it.\"\n\nSupporting himself on his elbow, he sketched a diagram on a sheet of\npaper that gave a clear picture of the conditions of the problem. I can\nno longer recollect how he arrived at the terms of his equation. At any\nrate, the result soon came to hand in a time not much longer than I had\ntaken to enunciate the problem to him. It was a so-called indeterminate\n(Diophantic) equation between two unknowns, that was to be satisfied by\nsimple integers only. He showed that the desired position of the hands\nwas possible 143 times in 12 hours, an equal interval separating each\nsuccessive position; that is, starting from twelve o'clock, the two\nhands may be interchanged every 5 minutes \u00b2\u2044\u2081\u2084\u2083 seconds, and yet give a\npossible time.\n\n     *     *     *     *     *     *     *     *\n\nI mention this little episode, which is insignificant in itself, merely\nto give an example of how a great discoverer, too, finds amusement in\nsuch distractions. In Einstein's case this tendency to practise his\ningenuity on unimportant trifles is so much the more pronounced from the\nfact that he requires an outlet for his virtuosity in calculation, and\ngratefully welcomes every suggestion that helps him to relieve his\nmental tension. Similar characteristics are reported of the great Euler,\nas well as of Fermat, whereas many another eminent mathematician feels\ndecidedly unhappy if he drifts within reach of the realm of actual\nnumerical calculation. In my mind's eye I still see Ernst Kummer, the\nsplendid savant (who, in his time, conferred distinction on Berlin\nUniversity by his very presence), suffering agonies whenever ordinary\narithmetical tables threatened to appear in the working-out of his\nformulae. As a matter of fact, these two things, a mastery over\nmathematics and a talent for ingenious calculation, are to be considered\nas quite independent, even if we now and then find them present in the\nsame person.\n\nIn the case of Einstein this tendency is a symptom of an incredible\nuniversality of spirit. It moreover presents itself in the pleasantest\nforms, and a character-sketch of Einstein would be incomplete if this\ntrait were not mentioned. Every problem which is in any way amusing\nexcites in him a willing interest and enthusiasm. I once directed our\nconversation to the so-called _Scherenschnitte_. These are made from\nlong strips of paper or canvas, the ends of which are caused to overlap\na little and then pasted together, but instead of being fixed so that a\nflat wheel results, which rolls on one side of the strip, the strip is\ntwisted one or more times before the ends are fastened together. If now\nthe strip is cut lengthwise right along its centre, various unexpected\nresults occur, depending on the number of twists that have been made\nbefore pasting.\n\nSome very complex geometrical difficulties are involved in these\nproblems. This is shown by the fact that learned mathematicians have\nwritten extensive disquisitions on these curious constructions (for\nexample, Dr. Dingeldey's book, published by Teubner, Leipzig). Einstein\nhad never taken notice of these wonders of the scissors, but when I\nbegan to form these strips, to paste them, and to cut them, he\nimmediately became interested in the underlying problem, and predicted\nin a flash what puzzling chain constructions would result in each case,\nwith a certainty that would lead one to imagine that he had spent days\nat it. On another occasion a space-problem dealing with dress came up\nfor discussion: Can a properly dressed man divest himself of his\nwaistcoat without first taking off his coat? One would not have dared to\nconfront Copernicus or Laplace with such a problem. Einstein at once\nattacked it with enthusiasm, as if it were an exercise in mechanics, the\nbody being the object; he solved it in a trice, practically, with a\nlittle energetic manipulation, much to the amazement and joy of the\nbeholder, who asked himself: Is this the same Einstein who developed the\nwork of Copernicus and Newton? A little later, perhaps, the conversation\ncentres around some serious point drawn from politics, political\neconomy, sociology, or jurisprudence. Whatever it may be, he knows how\nto spin out the suggested thread, to establish contact with his partner\nin conversation, to open up his own perspectives without ever insisting\non his point of view, always stimulating and showing a ready sympathy\nfor the subject of discussion and for all the ideas which it\ncrystallizes, the prototype of the scientist, in the mouth of whom\nTerence put the words: \"I am a human being; nothing that is human is\nalien to me!\"\n\n\n\n\nCHAPTER IX\n\nAN EXPERIMENTAL ANALOGY\n\nForms of Physical Laws.--Aids to Understanding.--Popular\nDescriptions.--Optical Signals.--Simultaneity.--Experiments in Similes.\n\n\n\"I WISH to ask you. Professor, to help me over a difficulty and to treat\nme as the spokesman of a great number who are similarly troubled. In\nmost accounts of your theory of relativity, there is a dearth of\ndefinite, concrete, illustrative examples on which we can fix our minds\nwhenever the theorem is to be applied generally without limitation. Let\nme express this more precisely: Your simplified picture of the structure\nof the universe is achieved in the theory of relativity by emancipating\nall observations from fixed co-ordinate systems, and by proclaiming the\nequivalence of all systems of reference. One of your earliest theorems\nstates that physical laws describing how the states of physical systems\nalter, remain the same, no matter to which of two co-ordinate systems\nthese states are referred, provided that the co-ordinate systems are\nmoving rectilinearly and uniformly relatively to one another. This\ntheorem entails the following statement. If we--erroneously--adopt a\nnon-relativistic view, we shall come to the conclusion that physical\nlaws depend on the particular system of reference chosen, and will thus\nassume a different form for each different system. At this point we\nexperience a desire to hear definite examples. What varying forms may a\ncertain given physical law, known under a definite form, assume, and how\ncan we use this law to show that it must adapt itself to the postulate\nof relativity?\"\n\nEinstein explained that such examples cannot be given in special cases,\nbut only in very general terms. If we were to suggest the elliptic\norbits of the planets (at which I had hinted in my remarks), we should\nfall into error, for the law of elliptic orbits is no such law. For,\nfrom another point of view, the elliptic paths of the planets might be\ndrawn out into wavy lines, or into spirals, and they would remain\nellipses only as long as the lines of motion are referred to the central\nattracting body. But the constancy of the velocity of light is such a\nlaw, as also is the law of inertia, according to which a body that is\nleft to itself moves uniformly in a straight line.\n\nI confessed to him that this limitation to a few very general laws would\nbe a painful matter for many an enthusiast of average attainments, who\nhas great difficulty in distinguishing the laws that are _generally_\nvalid from those that hold only within circumscribed limits. But if this\nwere not so, we should have to alter our conception of what is conveyed\nby a popular exposition. For it is called _popular_, not because it now\nand then uses the patronizing words \"dear reader,\" but because it\nanticipates the questions and doubts of the man of average sense, and\nexamines them, proving some to be unjustified and others to be\nreasonable or unreasonable, as the case may be. \"Then there is a further\nmatter that troubles me,\" I continued. \"Let us suppose an ordinary\nreader of such a popular account to get a first insight into the new\nconception of Time. He is glad to feel the ideas dawning in him, and, to\nget a more lasting view of the idea, he repeats the arguments through\nwhich he has just threaded his way, and, in doing so, again encounters\nthe phrase 'uniform motion.' At the first reading he imagined that he\nunderstood the expression quite well, but the second time he pauses and\nconsiders. For now that he knows how much depends on it, he is anxious\nto find out the exact meaning of a 'uniform motion.' He looks for a\ndefinition, and if he cannot find one in the book he is perusing, he\nendeavours to reason it out for himself. With good luck he arrives at\nthe usual statement: a body moves with 'uniform motion' if it traverses\nequal distances in equal intervals of time. But equal intervals of time\nare clearly those during which a body in uniform motion traverses equal\ndistances. In other words, he explains A by means of B, and B by means\nof A, so that he has involved himself in a vicious circle from which he\ncannot escape. This is his hour of need, due to the difficulty of\n'time.'\n\n\"He hopes that further study will remove this obstacle. He meets with\nthe conception of 'simultaneity,' which is defined for him anew, and is\ndisclosed as being 'relative.' He man\u0153uvres further towards the\nfundamental theorem that every body of reference has its own particular\ntime.\n\n\"His popular booklet makes this clear to him by quoting the example of a\nflying-machine, or, better still, a railway train that is rushing along\nan embankment at a very great speed, and that carries a passenger. Two\nstrokes of lightning I and II are to take place at two widely distant\npoints on the embankment. The question is then: When are these two\nflashes of lightning to be considered 'simultaneous'? What conditions\nmust be fulfilled to ensure this? It is found--incontrovertibly--that\nthe light-rays starting out from the two strokes of lightning must meet\nat the mid-point of the embankment.\n\n\"It now follows from a short chain of argument that the observer in the\ntrain will see flash II earlier than flash I, if they reach the\nobserver, who is at rest, at the same moment. That is, two events that\nare simultaneous with respect to the embankment are not simultaneous for\na moving system (such as a train or a flying-machine); the converse is,\nof course, also true.\n\n\"Here, again, the eager layman encounters difficulty, for he asks\nhimself: Why should the two events be characterized or defined by\nlightning-flashes in particular? If acoustic signals were used instead,\nnothing would be altered in the fundamental determination, for the sound\nrays (sound-waves) would likewise meet at the mid-point of the line\njoining the sources of disturbance. What is the reason that the\nrelativity of time arises only when phenomena are regarded optically,\nand that rays of light play the deciding part in all later developments?\n\n\"And this particular query is followed by one which is more general: Why\ndoes the popular pamphlet not read this question in my mind? I know that\nthe author of it is more skilled in these matters than I, but just this\nsuperiority should help him to divine what is passing in my mind when I\nmake efforts to follow his reasoning.\"\n\nEinstein had listened to me patiently, and then he explained to me at\nconsiderable length why in this case optical signals cannot be replaced\nby sound signals: light is the only mode of motion that shows itself to\nbe entirely independent of the carrier of the motion, of the\ntransmitting medium. Thus the constancy of velocity is assumed in the\nabove argument, and as this constancy is an exclusive property of light,\nevery other method must be discarded as unallowable for investigating\nthe conception \"simultaneity.\" Furthermore, he showed me how, on the\nbasis of relativity, starting from the embankment-experiment, we may\narrive at a perfectly consistent representation of the conception of\nTime. He certainly did this by applying subtle physical arguments that\nexceed the scope of the present book.[7] He added, in substance, that it\nwas futile and impossible to discuss in detail all the conceivable\nobjections that might arise in the mind of one reading a popular work of\nthis kind: it was a futile undertaking, because the true purpose was\ndefeated, inasmuch as a clear development of the fundamental thought\nwould be almost impossible under the cross-fire of so many random\nquestions.\n\n[Footnote 7: In these arguments, arrangements of synchronous clocks\noccur, which are fixed into the co-ordinate systems, the positions of\ntheir hands being compared with one another. The \"time\" of an event is\nthen defined as the position of the hands of a clock immediately\nadjacent to the scene of the event.]\n\nThus, in this matter, Einstein takes the same stand as Schopenhauer in\nthe preface of his chief work, in which he says: \"To understand this\nwork no better way can be advised than to read it twice (at least),\ninasmuch as the beginning assumes the end, almost as much as the end\nassumes the beginning; the smallest part cannot be understood if the\nwhole has not already been understood.\" Whoever accepts and follows this\nadvice will find that the intermediate objections will gradually balance\nand cancel one another, and that it is not necessary that they should\ninterrupt the steady and consistent line of development.\n\nThe position would be different if a disciple of the new theory should\nresolve to dispense with strictly scientific reasoning altogether, and\nshould wish to meet the wishes of his readers or hearers by discarding\naccuracy entirely. Such a programme seems quite feasible.\n\n\"This would be merely following the sketchy method of a magazine,\"\nEinstein remarked, \"but you do not seriously think that it would lead to\nanything?\"\n\n\"It would not be a true explanation, which is reserved for technical\nproductions. But I can imagine that it would not be unprofitable to help\none who is entirely ignorant on these questions by using makeshifts, in\nthe form of allegories or analogies, which will serve as supports if he\nshould take fright during the course of his earlier studies. These\nshocks are bound to occur, as, for instance, when he learns that a\nmoving rigid rod undergoes contraction in the direction of motion.\"\n\n\"But this is _proved_ to him!\"\n\n\"Nevertheless, he does not easily accept it. For the general reader will\nsay to himself: 'A superhuman effort is imposed on my mind. A rigid rod\nis the most constant of all things, and never before has one been\ncompelled to regard something that is constant as variable.'\"\n\n\"If he does not grasp it, no analogy will teach him.\"\n\n\"But perhaps it is possible. The analogy is to show him that the effort\nis not _superhuman_, and that thinking Man has already had occasion to\nbecome familiar with such transformations from constant to variable\nfactors.\"\n\n\"I am afraid your analogy will prove a failure.\"\n\n\"From the scientific point of view this is probably true, inasmuch as\nall comparisons are imperfect, but the analogy may yet be of service as\na last resort. For example, I should say to my general reader: 'Picture\nto yourself a savant of the Middle Ages who reflects on the constitution\nof animals and plants. One fact seems to him to be irrevocably true,\nnamely, that the species are unchangeable! A palm tree is a palm tree, a\nhorse is a horse, a worm a worm, and what is once a reptile remains a\nreptile. A species in itself denotes something absolutely _invariant_.'\"\n\n\"The expression is wrong when taken in this connexion; you mean\n_invariable_.\"\n\n\"A little inaccuracy more or less does not affect the analogy. For the\nsake of my picture I should like to retain the conception-couple,\n_variable_ and _invariant_. Well, then, the species give our savant the\nimpression of invariance, as in the view that was held by Linn\u00e9 and\nCuvier. This view necessarily has its counterpart in his thought. He\nargues that every species has its own original root, and that, in this\nsense, there is very extensive variation. The fundamental roots are\nextremely manifold; Nature has produced innumerable variations in her\nindividual acts of creation. But now the _Theory of Descent_ of Lamarck,\nGoethe, Oken, Geoffroy St. Hilaire, enters the field and produces a\ncomplete inversion of these two elements; the two parts of the earlier\npoint of view change places. Our savant has to revise his whole world of\nthought. Now all organisms are to be traced back to a single original\nroot: the latter, which was variable before, becomes an invariable\nunicellular primitive organism, but the apparently unchangeable species\nnow becomes variable, in the widest possible sense. And even if this\nsavant should exclaim: 'How am I to reconcile myself to this view?' his\ndescendants later find no difficulty in accepting the idea that the\norganic roots are uniform, and that it is the species that are subject\nto all manner of variation as a compensating feature.\"\n\nEinstein expressed himself very little pleased with this attempt at an\nanalogy, and found that it was so far fetched that it could not be\nconsidered admissible.\n\n\"Then I must ask your permission to continue my attempt; perhaps\nsomething useful may yet result from it. I now picture to myself a human\nbeing who lived in classical times and who, following Ovid and the great\nmajority of his contemporaries, regards the earth as a disc. On this\ndisc, each inhabitant of the earth has his own particular position, for\nthe disc has a centre with reference to which the position of a person\ncan be specified if his distance and his angular displacement from a\ngiven initial radius is specified. Thus, there is a variation of\nposition if various persons are considered. On the other hand, the\n_Above_ and the _Below_ is absolutely invariable for all persons, for\nthe lines running between _Above_ and _Below_ are all parallel for them,\nsince they all have uniformly the same disc under their feet and the\nsame heaven above their heads. Ovid would therefore have refused to\nentertain for a moment the suggestion that _Above-Below_ is a variable.\nBut his distant descendants accepted the view that the earth is\nspherical and that there are antipodes as self-evident, and they found\nnot the slightest difficulty in considering the line _Above-Below_ to\nvary with their own position, making all possible angles with an initial\nline extending to direct oppositeness. Referred to the centre of the\nsphere, all people have now an 'invariant' position, whereas, in\ncompensation, the _Above-Below_ is subject to every conceivable\nvariation. And now I again address myself to the average reader, and say\nthat the meaning of these analogies is that every doctrine that leads to\na great _uniformity_ converts what was formerly invariant into a\nvariable quantity, and vice versa. The theory of relativity makes all\nconsiderations about the physical world independent of all co-ordinate\nsystems; it establishes completely invariable uniformity, removed from\nall changes due to varying points of view. Hence what was previously\ninvariable--such as a rigid measuring-rod--will now become variable. It\nis not surprising that this requires a new method of thought, a revision\nof our mode of reasoning, for the above analogies show that these\nradical adjustments are characteristically necessary in the case of\ncomprehensive theories, and that such theories are able to overcome\napparently firmly established ideas. The parallels that I drew above\nwill at least inspire the average reader with a certain confidence, for\nthey show him how results of reasoning that were once considered\nincredible were regarded as self-evident by later generations.\"\n\nI have already emphasized sufficiently that Einstein regards as\ninadequate these auxiliary pictures that have presented themselves to\nme. Yet in the course of the conversation I gained the impression that\nhis judgment grew somewhat milder, and that, with certain reservations,\nhe was disposed to let them pass as tolerably useful helps--and they are\nnot intended to be more than this. I think, therefore, that I am not\nacting counter to his wishes in citing these allegorical examples here,\nparticularly as they arose in the course of our talks.\n\nSince then, I have had many opportunities of testing these examples on\ncertain persons, and may mention that they proved quite useful.\nAnalogies of this kind may offer a friendly help in moments when the\nuninitiated feel themselves in peril, and encounter a difficulty which\nthey imagine to be insurmountable. They do not remove the difficulty,\nbut they impart a certain power of expansion to the intellect and\nencourage a continuation of effort, which would probably otherwise be\nrelaxed at the first sign of something which is imagined to be\ninconceivable. There is thus no room in textbooks for such helps, but\nthey may justifiably find a place in a book that departs from the\nmethodical route, and hopes to discover in by-ways things that are\nsuggestive and instructive.\n\n\n\n\nCHAPTER X\n\nDISCONNECTED SUGGESTIONS\n\nConditionality and Unconditionality of Physical Laws.--Conception of\nTemperature.--Grain of Sand and Universe.--Are Laws\nunalterable?--Paradoxes of Science.--Rejuvenation by Motion.--Gain of a\nSecond.--Deformed Worlds.--Atomic Model.--Researches of Rutherford and\nNiels Bohr.--Microcosmos and Macrocosmos.--Brief Statement of the Principle\nof Relativity.--Science with reduced Sense-Organs.--Eternal\nRepetition.--Higher Types of Culture.\n\n\nIN all branches of reasoning, no word and no conception has played a\nmore important part than that of _law_. Physical laws denote the barrier\nthat separates strictly chance and arbitrariness from necessity, and it\nseems to us that the region of the latter must ever extend so that\nfinally nothing will be left of the former, which will have become\namalgamated with necessity. We shall be constrained to believe more and\nmore in a supreme law that will be a complete expression of all the\npartial laws which science presents to us as more or less permanent\nresults of individual researches.\n\nOur conversation was centred about these individual laws, such as those\nthat are taught in the theory of gases, optics, etc., and that are\nassociated with the names, Boyle, Gay-Lussac, Dalton, Marriotte,\nHuyghens, Fresnel, Kirchhoff, Boltzmann, and others. In connexion with\nthese I asked Einstein whether he regarded the laws as things\nunconditioned in themselves, and capable of proof under every set of\ncircumstances; and whether absolutely valid laws existed or could exist.\n\nEinstein's answer was essentially in the negative. \"A law cannot be\nfinal, if only for the reason that the conceptions, which we use to\nformulate it, show themselves to be imperfect or insufficient as science\nprogresses. Let us consider, for example, an elementary law such as\nNewton's Law of Force. From our more recent point of view we find the\nconception of direct action at a distance to be inexact in Nature. For\nit has been shown that action at a distance is not an ultimate factor,\nbut must be resolved into a multiplicity of actions between immediately\nneighbouring points (The Theory of Action by Contact or Contiguous\nAction). Another example is provided by the conception _Temperature_.\nThis conception becomes meaningless if we endeavour to apply it to\nmolecules: it leads to no result if we try to impose it on the smallest\nparts of matter as such. The reason is that the state, the velocity, and\nthe inner energy of the individual molecules fluctuates between very\nwide limits. The conception 'temperature' is applicable only to a\nconfiguration composed of many molecules, and even then it is not\napplicable quite generally. For let us picture to ourselves an extremely\nrarefied gas contained in a closed receiver. Two opposite walls are to\nbe at different temperatures, the one being cold and the other being hot\nIn a gas at such very low pressure the molecules come into collision so\nseldom that, practically, we have to take into account only the\ncollisions of the molecules with the confining walls. The molecules that\nrebound from the hot wall have greater velocities than those coming from\nthe colder wall, and hence the conception of temperature becomes\nuntenable for this gas.\"\n\n\"Would the temperature-scale on the thermometer then denote nothing?\" I\nasked. \"The greater or lesser degree of warmth of a body, in this case\nof the mass of gas, depends on the more rapid or less rapid motion of\nits smallest parts. The motions are in any case present, so what would a\nthermometer indicate?\"\n\n\"It would betray only that it had nothing to indicate. If a thermometer\nthat is blackened on one side were inserted into the vessel containing\nthe gas, then _different_ temperatures would be recorded if the\nthermometer were gradually turned about its own axis; and this signifies\nthat the conception of temperature has become meaningless for this\nconfiguration of molecules. And passing beyond the quoted examples, I\nshould maintain that all our conceptions, however subtly they may have\nbeen thought out, are shown in the course of progressive knowledge to be\ntoo rough hewn, that is, too little differentiated.\"\n\n     *     *     *     *     *     *     *     *\n\nWe spoke of the \"Properties of Things,\" and of the degree to which these\nproperties could be investigated. As an extreme thought, the following\nquestion was proposed:\n\nSupposing it were possible to discover _all_ the properties of a _grain\nof sand_, would we then have gained a complete knowledge of the _whole\nuniverse_? Would there then remain no unsolved component of our\ncomprehension of the universe?\n\nEinstein declared that this question was to be answered with an\nunconditional affirmative. \"For if we had completely and in a scientific\nsense learned the processes in the grain of sand, this would have been\npossible only on the basis of an exact knowledge of the laws of\nmechanical events in time and space. These laws, differential equations,\nwould be the most general laws of the universe, from which the\nquintessence of all other events would have to be deducible.\"\n\n[This thought may be spun out in yet another direction. Every piece of\nresearch, however specialized it may appear and of whatever minor\nimportance it may be, retains a relationship with researches into the\nuniverse, and may prove to be valuable for this latter task. If we\naccept the view that science is capable of realizing perfection, then\nevery contribution to knowledge, even the most insignificant, is\nessentially indispensable for attaining this goal.]\n\n     *     *     *     *     *     *     *     *\n\nCan a physical law alter with time? In more precise language, can time,\nas such, enter explicitly into laws, so that, for example, an experiment\nthat is carried out at different times leads to different results? This\nquestion has been treated several times, among others, by Poincar\u00e9, who\nanswered it with an emphatic \"No!\" but also by others to whom the\ninvariability of physical laws did not seem to hold for all eternity. If\nmy memory does not play me false, Helmholtz once expressed faint doubts\nabout the constancy of laws.\n\nEinstein answered this question with a decided negative. \"For a law of\nphysical nature is, by definition, a rule to which events conform\nwherever and whenever they take place. Thus, if we were to be compelled\nas a result of experience to make a law dependent on time, it would be a\nnecessary step to seek a law independent of time, which would include in\nitself the law dependent on the time as a special case. The latter would\nbe excluded from the category of physical laws, and would henceforward\nplay the part only of a result deduced from the law which is independent\nof the time.\"\n\n     *     *     *     *     *     *     *     *\n\nWhat attitude should we adopt if, in studying a scientific doctrine, we\nencounter paradoxical results even though the inferences have been drawn\ncorrectly--that is, if we meet with a deduction to which our reasoning\npowers object, although no fallacy is discoverable in the argument?\n\nBefore we deal with cases which seem to me, personally, to be\ninteresting, let us hear what is Einstein's attitude in general. \"As\nsoon as a paradox presents itself, we may, as a rule, infer that\ninaccurate reasoning is the cause, and should thus examine in each\nparticular case whether an error of logic is discoverable, or whether\nthe paradoxical result denotes only a violent contrast with our present\nviews.\"\n\nLet us first take examples from an entirely modern science, from the\n_Theory of Aggregates_ founded by Georg Cantor of Halle. We shall follow\nthe argument by the only possible method for this book, namely, by rough\nindications that will serve our purpose and do not claim to be accurate\nin expression or in sense.\n\nIf we take an aggregate of three objects, for example, an apple, a pear,\nand a plum, we may, by definition, form six partial aggregates, namely:\n\n    the apple\n    the pear\n    the plum\n    the apple and the pear\n    the apple and the plum\n    the pear and the plum.\n\nThe aggregate of the partial aggregates, which contains six elements, is\nthus greater than (actually twice as great as) the original aggregate,\nin which only three elements occur.\n\nIf the original aggregate contains an additional element, for example, a\nnut, the following partial aggregates may be formed:\n\n    the apple\n    the pear\n    the plum\n    the nut\n    the apple and the pear\n    the apple and the plum\n    the apple and the nut\n    the pear and the plum\n    the pear and the nut\n    the plum and the nut\n    the apple, the pear, and the plum\n    the apple, the pear, and the nut\n    the apple, the plum, and the nut\n    the pear, the plum, and the nut.\n\nThus, in this case, the aggregate of the partial aggregates is already\nconsiderably greater than the original aggregate. This numerical excess\nincreases rapidly with each successive increase in the original\naggregate, so that if we apply the same reasoning to an infinite\naggregate, the aggregate of partial aggregates becomes an infinity of a\n_higher order_. This is expressed by saying that the infinite aggregate\nof partial aggregates has a greater _potentiality_ than the infinity of\nthe elements of the original aggregate.\n\nSo we see that the one infinity is, in popular language, much more\ncomprehensive, more powerful than the other. Our minds do not find it\nimpossible to grasp this. But in a definite imaginary experiment it is\nfound that this theorem of progression not only fails in its\napplication, but leads to flagrant contradiction.\n\nFor if we start from the primary aggregate of \"all conceivable things,\"\nits infinity can certainly not be transcended by any other infinity. But\naccording to the above theorem the \"aggregate of all partial aggregates\"\nwould have a greater potentiality, although it itself cannot extend\nfurther than to the conception of the maximum of all conceivable things.\nWe thus arrive at an insoluble paradox, a typical example of how, in the\nsystem of conceptions involved, something is insufficient or not in\nconformity with logical thought. And this sceptical view receives\nsupport from various remarks of Descartes, Locke, Leibniz, and\nparticularly Gauss, who, long before the advent of the Theory of\nAggregates, raised a protest against inexact definitions of infinity.\n\nIn another case, however, the same theory seems to arise by perfectly\nlogical processes, although it again leads to a statement that does not\nseem correct to \"common sense.\" For it shows by a very subtle and\ningenious method that all the surface-points of a surface infinitely\nextended in all directions may be brought to correspond in a reversible\nsingle manner to the linear points of a line, however small; so that to\nevery point of the unlimited plane there corresponds a definite point of\nthe line, and vice versa. The same theorem may be extended to\nthree-dimensional space, with the result that we have to reconcile\nourselves with the incredible fact that, expressed in popular language,\na straight line of however small length exhibits the same potentiality\nwith regard to the number of its points, as all the points in the\nuniverse.\n\nFor my own part, I must confess that no means suggests itself to me to\nmake this paradox intelligible. But the _sacrificium intellectus_ comes\nwithin dangerous proximity. Einstein, who values and marvels at the\ntheory of aggregates as a science, or perhaps more as a work of art\nbuilt up from the materials of science, gives whole-hearted support to\nthe proof. He refuses to accept the notion of a paradox--that is, he\nrecognizes a contradiction not in our process of reasoning, but only in\na habit of thought that is open to correction. I should give much to\ndiscover the means of correction!\n\n     *     *     *     *     *     *     *     *\n\nA third example arises out of the special theory of relativity. It has a\nmysterious paradoxical character that vanishes when a clear view of the\nrelationships involved has been obtained.\n\nAccording to this theory the rate at which events happen alters\naccording to the state of motion of the system under consideration. Let\nus now consider two twins A and B, that, although born at one place on\nthe earth, are immediately separated, B remaining at rest, whilst A\nrushes out into space at an enormous rate, describing what, viewed from\nthe earth, is an inconceivably great circle. In this way the rate of\nhappening of all events is reduced very considerably for A in a manner\nthat may be calculated. If A then returns to B, it may happen that the\ntwin who stayed at home is now sixty years old, whereas the wanderer is\nonly fifteen years of age, or is perhaps only an infant still.\n\nThe first introduction to this flight of imagination naturally causes\nprofound perplexity. Nevertheless, we are dealing not with a realm of\nmiracles, but with something that is within the range of comprehension.\n\n\"In the case of these two twins,\" Einstein declared, \"we have merely a\nparadox of _feeling_. It would be a paradox of thought only if no\nsufficient ground could be suggested for the behaviour of these two\ncreatures. This ground, which accounts for the comparative youth of A,\nis given, from the point of view of the special theory of relativity, by\nthe fact that the creature in question, and only this creature, has been\nsubject to accelerations. A proper grasp of the reason is furnished only\nwhen we adopt the _general_ theory of relativity, which tell us that,\nfrom the point of view of A, a centrifugal field exists, whereas it is\nabsent from the point of view of B. This field exerts an influence on\nthe relative rate of happening of the events of life.\"\n\nIt certainly requires a prodigious mechanism to allow the moving twin to\ngain even only one second of time. If he were to spend a year in a\nmerry-go-round whose circumference were about 19 milliard miles in\nlength, he would have to travel in it at the rate of over 600 miles per\nsecond if he is to gain a second on his brother.\n\nThis inevitable result that is immediately apparent to a trained\nscientific mind throws light on the nature of \"common sense,\" the\nvalidity of which, as an ultimate criterion, Kant too has refused to\nrecognize, in so far as this \"common sense\" is incapable of passing\nbeyond the examples offered in its own experience. It circulates, as\nEinstein says, in the \"realms of feeling and analogy.\" It finds no\nanalogy for a phenomenon like that described above, and since it can\napply rules only concretely, many things appear to it paradoxical that,\nin the light of intensified abstraction, appear logical and necessary.\n\n     *     *     *     *     *     *     *     *\n\nLet us speculate on the following question. If all things in the\nuniverse should increase or decrease enormously in dimensions, and if,\nat the same time, in a manner totally concealed from us, certain\nphysical conditions should become changed, we should lack all means of\ndiscovering the difference between things before and after the change.\nFor since all measuring-rods, including those furnished by our senses,\nwould have become changed in the same proportion, the two conditions\ncould not be differentiated from one another. It may easily be shown\nthat this would necessarily occur, if an extramundane power were\nnon-uniformly to displace, deform, compress, or bend all things in the\nuniverse, provided that our instruments and senses participated in this\ntransformation. Accordingly it is permissible also to regard the\nuniverse known to us as one that is deformed, and one that is derived\nfrom another, the original form of which will ever remain a secret to\nus.\n\nIs there any connexion between this grotesque speculation and the theory\nof relativity?\n\nWe can establish only one that is negative and that arises _e\ncontrario_. \"These deformations,\" said Einstein, \"are in themselves\nabstractions that are physically meaningless. Only _relations between\nbodies_ have a physical meaning, for example, the relation between\nmeasuring-rods and the objects they measure. Therefore, it is reasonable\nto talk of deformations only when we are dealing with the deformations\nof two or more bodies with respect to one another, whereas the\nconception of deformation has no sense, unless a real object is\nspecified, to which it is referred. The philosophical merit of the\ngeneral theory of relativity, as compared with previous views of\nphysics, consists in the fact that the former avoids entirely these\nmeaningless abstractions with respect to space and time.\"\n\n[According to this, it is not purposeless to enter on these grotesque\ntrains of thought, even if they are untenable physically. For since the\nnew physics teaches us to avoid these false tracks, it seems of value to\nknow what it is that is to be avoided. Just as we must study scholastic\nthought if we wish to grasp thoroughly the philosophy which sprang up\nafter the scholastic fetters were burst. Moreover, these reflections on\nconcealed universes are not without a certain attraction, reminiscent of\nthe sorcerer's wand, if they pursued any other goal than that of making\nuniverses distorted. It is true that they hold out latent temptations\nthat may in some cases lead us on to dangerous ground, in encouraging us\nto venture on analogies beyond the scope of geometry and physics. Would\nit be possible to enter suddenly into a world that is distorted and\ndeformed with respect to its ethics, its culture, and its reasoning\nintellects, without our observing the difference? Are we ourselves\nperhaps living under such deranged conditions, of which we cannot become\naware, because our perceptual organs have likewise become deformed? I\nmust frankly confess that I do not regard it as quite inconceivable that\nthis argument of deformation may be spun out in this direction, but I\nmust add that Einstein rejects absolutely all such extensions, since,\nas he emphasizes, they lead to regions that are merely fields for the\nexhibition of \"verbal gymnastics.\"]\n\n     *     *     *     *     *     *     *     *\n\nThe question whether Nature makes leaps or not is very old. In the\ntheory of descent it forms the foundation of the difference between\nrevolutionists and the evolutionists, who uphold the axiom _natura non\nfacit saltus_, with all its consequences. Recently attempts have been\nmade, particularly by psychologists, to propound and justify a natural\nprinciple of discontinuity. They assert that our own perceptions and\nsensations are discontinuous in themselves, and that the mechanism of\nevery perception is akin to that of a cinematograph with its extremely\nrapid interruptions. If this should actually be the case, we should\nscarcely have a means of solving definitely the question whether\ncontinuity reigns, or not, in Nature.\n\nEinstein does not recognize the possibility of this alternative for a\nmoment. If a doubt had ever arisen, the researches of Maxwell would in\nthemselves have been sufficient to dispel it. Our universe that is to be\ndescribed in terms of differential equations is absolutely continuous.\n\n\"But,\" I interjected, \"does not modern physics offer a certain support\nto the assumption of a discontinuity? Does not the Quantum Theory point\nto an atomistic structure of energy, and hence also of events that are\nto be imagined as happening in jerks and as involving relations\nexpressible in whole numbers?\"\n\nEinstein gave an answer of epigrammatic brevity and flavour. \"The fact\nthat these phenomena are expressible in whole numbers must not be\nconstrued into an argument against continuous happening. Just imagine to\nyourself for a moment that beer is sold only in whole litres; would you\nthen infer that beer, as such, is discontinuous?\"\n\n     *     *     *     *     *     *     *     *\n\nWhat achievements are to be expected of astronomy in the present era?\n\nThis question would have a special meaning if it were assumed that the\nastronomer who works in observatories is surrounded by solved problems,\nand can no longer hope to solve problems having the universal\nsignificance of those of Copernicus or Kepler. This assumption, however,\nwould not be in agreement with the actual state of affairs.\n\nEinstein indicated to me a number of fundamental problems that present\nthemselves to modern astronomy, and the solution of which he expected of\nfuture times.\n\nAbove all, the geometrical and physical constitution of the stellar\nsystems will, in the main, become revealed.\n\nAt present we do not yet know whether Newton's Law of Attraction holds,\nat least approximately, for configurations of the type of the Milky Way\nand of the spherical clusters of stars--that is, in extents of space in\nwhich the influence of space-curvature would become appreciable. The\nrapid progress of recent astronomy justifies our great hopes that the\nsolution of this universal problem will be found within the coming\ndecades.\n\nIn distant connexion with this we also touched on the question of the\nhabitability of other worlds. This theme of Fontenelle, \"la pluralit\u00e9\ndes mondes habit\u00e9s,\" which has again become a centre of public\ninterest, owing to investigations of Mars, has evoked a storm of\ndiscussion. We hear the noisy war-cries of geocentric scientists who\nwish to regain for the earth her shattered supremacy in astronomy, and\nwho claim the existence of organic forms as the sole prerogative of our\nplanet. It is scarcely necessary to mention that Einstein rejects the\nmotives of these human and all-too-human individuals as small-minded and\nshort-sighted. Creatures in distant worlds are derived from, and are\nsubject to, conditions of organic nature, of which we can form no idea\nby deductions from the world which we inhabit. But to deny their\nexistence on numberless constellations, or to demand an ocular proof of\ntheir presence, is no better than to assume the point of view of an\ninfusoria to whom there is no life other than that in a dirty drop of\nditch-water.\n\n     *     *     *     *     *     *     *     *\n\nThe idea of the atom as the ultimate structural element involves a\nphilological as well as a conceptual contradiction. For _atomos_\nsignifies the indivisible, the no-further-divisible, whereas the idea of\na body, however small, an element of structure differing from zero,\ndemands, at least geometrically, further divisibility. Even the original\nfounders of the theory of atoms, Leukippus, Epicurus, and Democritus,\nassigned definite forms to the ultimate components, and we may read in\nthe splendid work of Lucretius how he infers from the nature of\nsubstance that the ultimate particles are smooth, round, or rough, or\nhave the shapes of hooks and eyes. The further analysis pressed forward,\nthe more the simplicity of the original idea vanished. Microcosms came\nto be regarded as copies of macrocosms, and the atoms of present-day\nscience actually exact from us that we should regard them as worlds in\nthemselves.\n\nEinstein acceded to my request that he might give a sketch of the latest\nachievements of science sufficient to provide an approximate idea of the\n_atomic model_. According to the researches of Rutherford and Niels\nBohr, we are to picture it as a planetary system.\n\nThe central body of this system is represented by a positively charged\nnucleus, which constitutes almost the whole mass of the atom, surrounded\nby a certain number of electrons, negative charges, that move in uniform\ncircular or elliptic orbits about the nucleus. There is thus a certain\nanalogy that allows us to regard the nucleus as the sun, and the\nelectrons as the planets of this system.\n\nThe number of these electrons varies between the limits 1 and 92,\naccording to the chemical constitution of the element. The smallest\nnumber occurs in the case of helium (in which there are two), and of the\nhydrogen atom, in which only one electron-planet describes its circular\npath about the nucleus. In other atoms there are probably more\ncomplicated orbits, although they are more or less approximately\ncircular. According to this still very new theory, which is supported by\nvery convincing facts, the electrons are to be imagined as arranged in\nconcentric shells (like the layers of an onion), among which the\ninnermost shell plays a distinctive part inasmuch as the number of the\nelectrons arranged in it decides the chemical character of the atom in\nquestion. It sometimes occurs that electrons spring, under external\ninfluence, from one orbit to another; when the electron jumps back to\nthe original orbit, light is emitted. An essential fact is to be noted:\nWhereas any arbitrary orbits of any arbitrary radius may occur in a\nplanetary system of the celestial regions, the manifold of these orbits\nin the case of the electrons is restricted, in that only certain orbits\nare possible, namely, those that are determined mathematically by the\nquantum condition.\n\n\"Perhaps,\" I interrupted, \"the whole analogy may be inverted. If the\natom is considered analogous to a planetary system in the model, it\nshould be admissible to regard our true planetary system as a cosmic\natom. And then, long after we have become accustomed to regard our earth\nas playing the part of a grain of sand, the sovereignty of the sun, too,\nwould be past. The whole majesty of the solar system as far as the orbit\nof Neptune would then shrink to a configuration compared with which the\nworld of a grain of sand would be infinitely complex.\"\n\n\"This fantastic inversion is permissible up to a certain extent,\" said\nEinstein, \"but we must not lose sight of the fact that there is a\ncardinal difference. If we disregard the enormous disparity in\ndimensions, the analogy is far from exact owing to the circumstance that\nthe atom is only an element of structure, whereas the true planetary\nsystem is an extraordinarily complex structure in itself. Thus the\ndifference between a simple thing and one that is very highly complex\nstill remains.\"\n\n\"But, Professor, may not a similar complexity yet be discovered in the\natom? It may be merely a difference of philosophical view from the\nprimary idea to that of regarding the electrons as circulating like\nplanets. May we not conjecture that in each successive step we are\nmerely carrying out a true _regressus in infinitum_?\"\n\n\"That seems highly improbable,\" he replied, \"although, of course,\nstructural investigations can never cease. At first they are directed at\nthe more remote object of finding out why certain atoms are radioactive,\nthat is, exhibit a tendency to disintegrate. It has already been\nestablished that this tendency is a property of the positive nucleus, of\nwhich little is as yet known. This means that the nucleus is not simple,\nyet it does not open up the possibility of an unending regression. Our\naim must be to get a clear insight into the constitution of the nucleus,\nas regards the positive and negative charges, and it is my opinion,\" he\nconcluded, \"that beyond this there will be no further subdivision of\nmatter.\"\n\nWhen Goethe writes of the immovable pole in the flux of phenomena, we\nrecognize that his beautiful remark pronounces an elegy to the\npossibility of attaining ultimate simplicity. Einstein's utterance, if I\nunderstand him aright, converts this elegy into a song of hope. If the\nsubdivision of matter actually has an end somewhere, then we are now on\nthe threshold of ultimate things, we are near the immovable pole, which\nwe are capable of reaching.\n\n     *     *     *     *     *     *     *     *\n\n\"Every new truth of science must be such that, in ordinary writing, it\nmay be communicated completely within the space of a quarto leaf.\"\nKirchhoff made this remark, and gave a sufficient, if not literal,\ndemonstration of its truth. When Bunsen and he published the first\nnotice about spectral analysis, they compressed their publication into\nthe small space of three printed pages.\n\nBut what is to happen if the new truth should be built up of very\ncomprehensive materials, when it requires many links, of which none can\nbe omitted if the truth is to be made intelligible? Would Kirchhoffs\nquarto page still be sufficient?\n\n\"Certainly,\" said Einstein, \"provided, of course, that it is addressed\nto a reader who has already mastered what went before--that is, to one\nwho is so far acquainted with the older facts that he has to learn only\nthe really new part of the new truth.\"\n\n\"That sounds very hopeful,\" I remarked, \"for then it should also be\npossible to describe very briefly the theory of relativity.\"\n\n\"Let us rather say its essentials--the heart of the matter. Well, then,\nget your Kirchhoff page ready. We shall see whether we can set out on it\nthe special theory of relativity.\"\n\nThe totality of our experience compels us to assume that light travels\nwith a constant velocity in empty space. Likewise, our whole experience\nin optics compels us to recognize that all inertial systems are\nequivalent; these are systems that are produced from an allowable one by\nmeans of a uniform translation. An allowable system is one in which\nGalilei's and Newton's Law of Inertia holds. (This law states that a\nmoving body that is left to itself retains its direction and velocity\npermanently.)\n\nNow, the law of the constancy of light propagation seems to conflict\nwith the classical principle of relativity, according to which the\nvelocity of a ray of light assumes different values in the moving system\naccording to the direction of the ray.\n\nThis apparent incompatibility arises from the following unproved\nassumptions:\n\n(_a_) If two events are simultaneous with regard to one inertial system,\nthey are also simultaneous with regard to any other inertial system.\n\n(_b_) The length of a measuring-rod, the shape and size of a rigid body,\nand the rate of a clock are independent of their motion with respect to\nthe system of reference used, provided this motion is rectilinear and\nnon-rotational.\n\nThese assumptions must be discarded if this disagreement is to be\neliminated. If we substitute for them the assumption that all inertial\nsystems are equivalent and that the velocity of light _in vacuo_ is\nconstant, we get:\n\n(1) That the dimensions of bodies and the rate of clocks have a\nfunctional relation to the motion.\n\n(2) That the equations of motion of Newton require to be modified; this\nmodification leads to results that, for rapid motions, differ\nappreciably from those of Newton.\n\nThis is, in a very compressed form, the meaning of the special theory of\nrelativity.\n\n\nAs there is still some space left on our quarto page, we may add a\nremark that, it is hoped, will make a little clearer the above-mentioned\ndiscrepancy.\n\nLet us choose as our system of reference an express train 18 miles long.\nThere are two passengers--Mr. Front, right at the front of the train,\nand Mr. Back, at the extreme end of the train, so that a rigid distance\nof 18 miles separates the two passengers. The carriages are transparent,\nso that the two passengers can signal to one another. They are,\nmoreover, furnished with ideal clocks that run at exactly the same rate.\n\nFirst, suppose that the train is at rest. Back is just opposite\nmilestone 100, whilst Front is opposite milestone 118. By means of a\nflash, Back signals to Front his time, exactly 12 o'clock. It takes\nlight very nearly \u00b9\u2044\u2081\u2080\u2080\u2080\u2080 second to traverse the length of\nthe train--18 miles; hence the flash will reach Front at 12 o'clock\n\u00b9\u2044\u2081\u2080\u2080\u2080\u2080 second. Exactly the same result would have come\nabout if Front had signalled his time to Back. Light makes no difference\nin travelling forwards and backwards. If the train moves at a great\nspeed, the two travellers can conduct the same experiment as when the\ntrain was at rest. They will then set the time that light takes to\ntravel from Back to Front equal to the time that it takes to traverse\nthe same way in the reverse direction. But this phenomenon will assume a\ndifferent aspect if viewed from the railway embankment. An observer on\nthe latter would affirm that light does not take the same time in\ntravelling the length of the train in one direction as it does when\ntravelling in the opposite direction.\n\nFor the ray of light moving in the forward direction has to traverse not\nonly the distance between Back and Front, but also the very short\ndistance that Front has moved forward during the interval that the light\nhas been moving; whereas, inversely, the flash sent out by Front to Back\nwill traverse a distance that is correspondingly less than that between\nthe passengers, since Back is moving towards the signal.\n\nThus the duration of the two phenomena of light propagation is the same\nor different, respectively, according as it is judged from the train or\nfrom the embankment. In other words, _the judgment of the length of time\ndepends on the state of motion of the observer_.\n\nAll further pronouncements of the special theory of relativity are based\non the preceding arguments of the relativity of time.\n\n     *     *     *     *     *     *     *     *\n\nWould Man be able to construct a Science if he possessed one sense less\nthan at present--for example, if he were deprived of sight? Let us apply\nthis to a definite case. In the new physics the velocity of light plays\na decisive part as a world-constant. At first sight it would appear\nimpossible for us to determine it and recognize its importance, if we\nhad not at our disposal some organ which enabled us to become aware of\noptical phenomena.\n\nBut, as Einstein explained to me, even under such difficult\ncircumstances, it would be possible to build up a science, for the\nreason that phenomena, as far as they are perceptible, may be\ntransformed so that they become manifest to other senses if one sense\nshould be absent. For example, the electrical conductivity of selenium\nis strongly influenced by the amount of illumination that falls on it.\nThus light acts on a selenium cell, causing changes of current\nintensity, which in their turn may be perceived by feeling, or by\nchemical action on the mucous fluid of the tongue. Ultimately we are\nconcerned only with a differentiation that enables us to refer identical\nexperiences to identical events. We should certainly encounter enormous\ndifficulties in endeavouring to form a physical picture of our\nsurrounding world if the number of our senses should become less than\nthe organs with which we actually operate. Yet, in principle, we should\nbe able to overcome all difficulties by means of much lengthened and\ncomplicated lines of research, even if we should have only a single\nsense left, or if we had only one at the very outset. The construction\nof a Science would then be possible, and would give the same results,\nalthough it might be propounded only after a delay of perhaps millions\nof years.\n\n[It is naturally assumed that the intellect is retained, as this is the\nnecessary condition for all scientific research. Since the degree of\nunderstanding depends on the senses--_nihil est in intellectu, quod non\nprius fuerit in sensu_--we may conjecture that a human being with only\none sense organ would work with a minimum degree of understanding, which\nwould be insufficient for the acquirement of any knowledge whatsoever.\nThis transcendental question, which lies almost beyond the bounds of\ndiscussion, was not touched on in our conversation, as the subject was\nrestricted so that it should not drift into metaphysical regions.\n\nNevertheless, I should like to mention that a speculation of this kind\nis recorded in the history of science. Condillac, in a study teeming\nwith ideas, investigates the behaviour of a \"Statue,\" that he represents\nas a human being, with the assumption that there is at first no idea in\nthe soul of this statue-person. This living creature is enclosed in a\nmarble envelope, the sole exterior organ of which is at first the organ\nof smell. He then shows that by means of this single sense all manner of\nsensations and expressions of will may develop in his \"statue.\"\nCondillac does not, however, undertake to give a convincing proof that\nthis creature, restricted to the organ of smell, would be able to\ndiscover physically the relationships that hold in physical nature, and\nthus to build up a scientific system. Thus Einstein, in his discussion,\ngoes considerably further than the author of this statue.]\n\n     *     *     *     *     *     *     *     *\n\nHas the \"eternal repetition,\" as outlined by Nietzsche, any meaning?\n\nThe sage of Sils-Maria tells us that this revelation came to him midway\nbetween tears and ecstasy, as a fantasy with a real meaning. The crux of\nhis idea is a finite world built up of a finite number of atoms. From\nthe fact that the present state emerges out of the immediately preceding\none, the latter from the one just before, and so on, he concludes that\nthe present state exhibits repetition both forwards and backwards. All\nbecoming recurs and moves in a multiple cycle of absolutely identical\nstates.\n\nLet us discard for the moment all philosophical objections, above all\nthis, that the recurrence of the same disposition of atoms may not\nnecessarily entail the recurrence of the same psychical states.\nFurthermore, let us suppress the cynical thought that in the return to\nthe same state the world would have reason to enjoy extreme happiness\nonly for moments, but to lament for aeons. Then we are left with the\ncomparatively simple question: Is this repetition, from the point of\nview of physics, conceivable and possible?\n\nIt would be the death-knell of Nietzsche's idea if the answer of a great\nphysical research scientist were entirely in the negative. But Einstein\nstill allows it a small measure of life. \"Eternal repetition,\" so he\nexpressed himself, \"cannot be denied by science with absolute\ncertainty.\" The disciples of Nietzsche will have to rest satisfied with\nthis very small concession. For what, in Nietzsche's eyes, is a logical\nnecessity becomes transformed by Einstein's supplementary remark into a\nvague assumption, the product of fantasy. From the point of view of\nphysics the recurrence of the same condition is to be regarded as\n\"enormously improbable.\" This statement is founded chiefly on the famous\nsecond Law of Thermodynamics, according to which the processes of Nature\nare in the main irreversible, so that a one-sided tendency is expressed\nin natural phenomena. The fact that the course of phenomena is in only\none sense or direction speaks in favour of the view that the events of\nthe world are to be regarded as occurring only once.\n\nSo that when Nietzsche, in contradistinction to this, vigorously\nsupported the doctrine of repetition, he contradicted at least one\nimportant recognized theorem of physics. The fact that he did not become\nconscious of this contradiction, but that, on the contrary, he regarded\nhis idea as the most important event in the development of his\nintellect, may be regarded as an example of a _docta ignorantia_. But it\nis allowable, too, that philosophic fantasies that complete the poetical\npicture of the universe should be given expression. And Nietzsche would\npresumably have been deprived of a degree of pleasure if he had been\naware of this second law.\n\n\"Truth is the most expedient error\"; this statement may be traced back\nto a sequence of thought developed by Nietzsche. But the Eternal\nRepetition is shattered by just this remark, for judged by its\nconsequences it would be a very inexpedient error.\n\n     *     *     *     *     *     *     *     *\n\nSupposing we should succeed in exchanging thoughts with the inhabitants\nof distant worlds and should, through them, acquire the elements of a\ncivilization _superior to our own_, would this knowledge prove a\nblessing to us or the reverse?\n\nThe word \"superior\" must, of course, be treated circumspectly. It is to\ndenote only that, relatively, this distant civilization bears somewhat\nthe same relation to our civilization of to-day as our own bears to that\nof an Australasian negro or an anthropoid ape. There are fanatics of\nprogress whose wishes plunge headlong and without restraint into the\nfuture, and to whom nothing could be more desirable than the sudden\nappearance of a civilization that, as they opine, would at one stroke\ncarry us \"forward\" many thousands of years.\n\nBut the view of these magicians with their seven-league boots is\nuntenable. Let me cite a mere outline of the many opposing arguments in\na few words of Einstein. \"Every sudden change in the conditions of\nexistence, even if it occurred in the form of a higher development,\nwould come upon us like a doom, and would probably annihilate us, just\nas the Indians succumb to the civilization that has outstripped them.\nThe tragedy of our own highly civilized times is that we cannot create\nthe social organizations that have become necessary as a consequence of\nthe technical advances of the last century. This has given rise to the\ncrises, impasses, and senseless competition between nations, and to the\nimpoverishment of defenceless individuals. These deplorable conditions\nwould become inconceivably accentuated if we were to be invaded by\nextra-mundane technical sciences of a higher order.\"\n\n     *     *     *     *     *     *     *     *\n\nNevertheless, there is still a possibility that the \"superior\ncivilization\" might contain indications of the organizations which we\nlack. Instead of entering on the question of this Utopia, we confined\nourselves to comparing past conditions in our world with present ones.\nDid we not have the most promising preliminaries for an organization\nthat was devoid of friction and tended to reduce the competition between\nnations in the numerous international institutions that drew together a\ngreat section of the intellectual world to work in co-operation? Are\nthere hopes that this international coalition will be resumed?\n\nEinstein expressed himself optimistically, not to do homage to an\norganization artificially formed, but to extol the world-wide mastery of\nintellect. \"Even if international congresses were to be swept away,\" he\nsaid, \"international co-operation would not be abolished, as it effects\nitself automatically.\" I should venture to assert that if all these\ncongresses were to cease, we should not even have cause to fear that\nthere would be an appreciable diminution in the combined effort of\nresearch. If certain developments are hindered by political conditions,\nit is only due to the resulting economic hardships affecting individuals\nin their work and robbing them of their intellectual freedom. The real\nfriends of Truth have always clung together, and do so actually now;\nindeed, many feel the tie to be closer than that connecting them to\ntheir own country. In spite of all obstacles and boundaries they will\nnever cease to find contact with one another!\n\n\n\n\nCHAPTER XI\n\nEINSTEIN'S LIFE AND PERSONALITY\n\n\nWE know from the biographies of great thinkers that they seldom\npersonify the character of a dramatic ideal. They are not heroes of\nfiction who pass through complex experiences and struggle with\nmysterious problems of existence that may unduly excite the imagination\nof observers. Whoever follows their development remarks in the majority\nof cases the predominance of the inner life, the course of which is\ndiscoverable only by study of their works, no clue being given in the\nconfusion of ordinary exterior manifestations. An eminent man of\nthought, whose energies are concentrated on mental effort, rarely finds\ntime to present in addition an interesting figure in the epic sense. The\npoet who moulds his forms from life finds little scope in him as a\nmodel, and only in exceptional cases has he succeeded in idealizing the\nsavant in a work of art.\n\nIt would be a fruitless undertaking to treat Einstein's life as one of\nthese exceptional cases. It is possible to trace the various phases of\nhis development, yet neither the writer nor the reader must disguise\nfrom himself the fact that such outlines give only the external picture\nof the man and chronological events of importance. Nevertheless, a book\nof which he forms the theme cannot pass over the task of giving his\n_curriculum vit\u00e6_. And if it should partly appear aphoristic and\ndisjointed, it must be borne in mind that this account originated from\nconversations and scraps of conversation that touched on various\nepisodes of his life, according as they had a bearing on the subject\nunder discussion.\n\nThe story of Einstein's life begins at Ulm, the town which possesses the\nhighest building in Germany. Gladly would I stand on the belfry of the\nUlm Cathedral in order to obtain a general survey of Einstein's youth.\nBut the view discloses nothing beyond the bare fact that he was born\nthere in March 1879. The detail which has already been mentioned above,\nnamely, that it was something physical that first arrested the child's\nattention, remains to be noted. His father once showed the infant, as he\nlay in his cot, a compass, simply with the idea of amusing him--and in\nthe five-year-old boy the swinging metal needle awakened for the first\ntime the greatest wonderment about unknown cohesive forces, a wonderment\nthat was an index of the research spirit that was still lying dormant in\nhis consciousness. The remembrance of this psychical event has a\nsignificant meaning for the Einstein of to-day. In him all the\nimpressions of early childhood seem to be still vivid, the more so as\nall other physical occurrences, such as the falling of an unsupported\nbody, left no impression on him. His attention was fixed on the compass,\nand the compass alone. This instrument addressed him in oracular\nlanguage, indicating to him an electromagnetic field that was in later\nyears to serve him as a domain for fruitful research.\n\nHis father, who had a sunny, optimistic temperament, and was inclined\ntowards a somewhat aimless existence, at this time moved the seat of the\nfamily from Ulm to Munich. They here lived in a modest house in an\nidyllic situation and surrounded by a garden. The pure joy of Nature\nentered into the heart of the boy, a feeling that is usually foreign to\nthe youthful inhabitants of cities of dead stone. Nature whispered song\nto him, and at the coming of the spring-tide infused his being with joy,\nto which he resigned himself in happy contemplation. A religious\nundercurrent of feeling made itself manifest in him, and it was\nstrengthened by the elementary stimulus of the scented air, of buds and\nbushes, to which was added the educational influence of home and school.\nThis was not because ritualistic habits reigned in the family. But it\nhad so happened that he learned simultaneously the teachings of the\nJewish as well as the Catholic Church; and he had extracted from them\nthat which was common and conducive to a strengthening of faith, and not\nwhat conflicted.\n\nYouthful impetuosity, which in boys of a similar age usually expresses\nitself in rash enterprises and loose tricks, did not appear in him. His\nspirit was adjusted to contemplation, and an inborn fatalism, diffused\nwith a super-sensuous element appertaining to dreams, restrained him\nfrom responding to external impulses. He reacted slowly and\nhesitatingly, and he interpreted what his senses offered him and all the\nlittle experiences of early days in terms of a reverence reflected from\nwithin. Words did not easily rise from his lips, and measured by the\nordinary scale of rapidity of learning and readiness in answering\nquestions, he would scarcely have been judged to possess unusual gifts.\nAs an infant he had started to talk so late that his parents had been in\nsome alarm about the possibility of an abnormality in their child. At\nthe age of eight or nine years he presented the picture of a shy,\nhesitating, unsociable boy, who passed on his way alone, dreaming to\nhimself, and going to and from school without feeling the need of a\ncomrade. He was nicknamed \"Biedermaier,\" because he was looked on as\nhaving a pathological love for truth and justice. What at that time\nseemed to be pathological, to-day appears as a deeply rooted and\nirrepressible natural instinct. Whoever has got to know Einstein as a\nman and as a scientist knows that this failing of his boyhood was but\nthe forerunner of a very healthy outlook.\n\nSigns of his love for music showed themselves very early. He thought out\nlittle songs in praise of God, and used to sing them to himself in the\npious seclusion that he preserved even with respect to his parents.\nMusic, Nature, and God became intermingled in him in a complex of\nfeeling, a moral unity, the traces of which never vanished, although\nlater the religious factor became extended to a general ethical outlook\non the world. At first he clung to a faith free from all doubt, as had\nbeen infused into him by the private Jewish instruction at home and the\nCatholic instruction at school. He read his Bible without feeling the\nneed of examining it critically; he accepted it as a simple moral\nteaching and found himself little inclined to confirm it by rational\narguments inasmuch as his reading extended very little beyond its\ncircle.\n\nPainful inner conflicts were not wanting. Jewish children formed a small\nminority in the school, and it was here that the boy Albert felt the\nfirst ripples of the anti-semitic wave that, sweeping on from without,\nwas threatening to overwhelm master and pupil alike. For the first time\nhe felt himself oppressed by something that was not in harmony with his\nsimple temperament. His modesty made him a prey to injustice, and in\ndefending himself his originally gentle and restrained nature gained a\ncertain independence and individuality.\n\nIf one may speak of achievements at all in a preparatory school, those\nof Albert were of the average modest level. He was careful as a pupil,\ngenerally satisfied requirements, but in no way betrayed special\ntalents: indeed, so much the less, as he showed himself to be possessed\nof a very uncertain memory for words. The methodic plan of the\nelementary school that he attended to his tenth year was, however, not\nother than the usual scheme mapped out by drill-masters; it made up for\nwhat was lacking in an understanding of the pupils by applying drastic\nstrictness. The beautiful sentence of Jean Paul: \"Memory is the only\nparadise from which we cannot be banished,\" finds no echo in Einstein's\nschool memories, of which he has often spoken to me without a shadow of\nregret for a lost paradise. He told me with bitter sarcasm that his\nteachers had the character of sergeants--those later in the _gymnasium_\n(secondary school) were of the nature of lieutenants. Both terms are\nused in the pre-armistice sense, and his words were directed against the\nself-opinionated tone and customs of these garrison-schools of earlier\ndays.\n\nThe next stage of his development was a course of study at the\nLuitpold-Gymnasium in Munich, which placed him in the second class. In\nEinstein's retrospect of these days more friendly recollections present\nthemselves, connected, however, only with particular persons, and not\nbreathing praise in general; on the contrary, from his account, it is\nclear that although he conceived affection for individual teachers, he\nfelt the tone of the institute as a whole to be rough. As we know, many\nthings have been changed in these schools since then, following on a\nrevulsion from the convict atmosphere that used to characterize them,\nand which meant suffering enough for the pupils. The result was that the\nschoolboy Einstein developed a contempt for human institutions and\nassigned little value to the subjects of study which he was obliged to\nabsorb in schematic form without the application of his own mental\nenergy. This gloomy picture is relieved at points by the presence of\nseveral teachers, above all, one called Ru\u00ebss, who took pains in\nexposing the beauty of classical antiquity to the fourteen-year-old boy.\nWe learn elsewhere that Einstein at present admits the humanistic ideal\nfor the school of the future only under very restricted limitations. But\nwhen he thinks of this teacher and his influence, a warm appreciation of\nclassical study vibrates in his words, occasionally rising, indeed, to\nan unbounded enthusiasm for the treasures of Greek history and\nliterature. His instruction was not restricted to the acquisition of a\nperspective of the antique. Under the direction of the same teacher, he\nwas introduced into the poetic world of his native country, and learned\nthe magic of Goethe in his \"Hermann and Dorothea\"; this poem, as he\nconfesses, was explained to him in a really model manner. Thus there\nwere some oases in the desert of schematic teaching: they served as\nrefreshing halts for the spirit of the eager young searcher after\nknowledge.\n\nWe must go back one or two years to note a weighty experience, which\noccurred when he made his first acquaintance with elementary\nmathematics; this subject presented itself to him with the intensity of\na revelation. It did not happen in the ordinary course of school-work,\nbut was due to a sort of wizard-like inquiring inner spirit that plied\nhim with questions and that gave him inward thrills of joy when he found\na sharp-witted solution. From the very beginning Albert proved himself\nto be a good solver of problems, even before he achieved an arithmetical\nvirtuosity, and before he knew the technique of equations. He helped\nhimself by means of little tricks, experimented roundabout inventions,\nand was happily excited when they led to the goal. One day he asked his\nuncle, Jacob Einstein, an engineer who lived in Munich, a certain\nquestion. He had heard the word \"algebra\" and surmised that his uncle\nwould be able to explain the term to him. Uncle Jacob answered: \"Algebra\nis the calculus of indolence. If you do not know a certain quantity, you\ncall it _x_ and treat it as if you do know it, then you put down the\nrelationship given, and determine this _x_ later.\" That was quite\nsufficient. The boy received a book containing algebraic problems that\nhe solved all alone in accordance with this not exhaustive but expedient\ndirection. On another occasion Uncle Jacob told him the enunciation of\nPythagoras' theorem without giving him a proof. His nephew understood\nthe relationship involved, and felt that it had to be founded on some\nreasoning. Again he set about all alone to furnish what was wanting.\nThis was, however, not a case for the \"calculus of indolence\" with an\n_x_ that was to be determined. Here it was a question of developing a\nfacility for geometric argument, such as very few possess at such an\nearly stage of development. The boy plunged himself for three weeks into\nthe task of solving the theorem, using all his power of thought. He came\nto consider similarity of triangles (by dropping a perpendicular from\none vertex of the right-angled triangle on to the hypotenuse), and was\nthus led to a proof for which he had so ardently longed! And although it\nconcerned only a very old well-known theorem, he experienced the first\njoy of the discoverer. The proof that he had found proved that the\ningenuity of the worrying young mind was awakening.\n\nA new world was opened for him when he made the acquaintance of A.\nBernstein's comprehensive popular books on scientific subjects. This\nwork is looked on nowadays as being somewhat antiquated and, in the eyes\nof many a professional scientist, has sunk to the level of a\npseudo-scientific \"shocker\"; even when Einstein as a boy made\nexplorations in it, there were signs of rust and decay in the work, for\nit originated in the fifties of the previous century and, in point of\nsubject-matter, had long been transcended. Yet it could be read\nthen--and even now--as a story containing thousands of interspersed\nphysical, astronomical, and chemical wonders, and for the boy Einstein\nit came to be a true book of Nature, which presented to his mind, greedy\nfor knowledge, as much as it did to his imagination.\n\nOther vistas were opened up to him by B\u00fcchner's _Kraft und Stoff_\n(_Force and Substance_), a book the cheapness of which he could not yet\ndiscern, but which called up wonder in him without rousing his\ncriticism. In addition, his attention was chiefly occupied by a handbook\nof elementary planimetry, containing an abundance of geometrical\nexercises, which he fearlessly attacked and within a very short time\nsolved almost in their entirety. His delight grew when he ventured into\nthe difficulties of analytical geometry and infinitesimal calculus quite\napart from the curriculum of his school-work. L\u00fcbsen's textbook had\nfallen into his hands, and these directions sufficed for his audacious\nspirit. Whereas many of his school companions were still standing\nundecidedly before the pools of theorems of congruence and repeating\ndecimals, he was already disporting himself freely in the ocean of\ninfinitesimals. His work did not remain concealed, and gained\nappreciation. His mathematical teacher declared that the\nfifteen-year-old boy was ripe for university study.\n\nYet he was not to find a way into the open by matriculating very early,\nbut through an event that unexpectedly threw him into new surroundings\nof life. In 1894 his parents transferred their abode to Italy. The\nchronicler has nothing to report of pangs of separation in Albert when\nhe left Bavarian soil. He was glad to get away from the drill academy,\nLuitpold, and, as an inhabitant of Milan, he enjoyed the change in his\nexistence, and was not encumbered by attacks of home-sickness. All in\nall, he had felt himself in an unhappy position under school compulsion\nin Munich, in spite of the mathematical delights he had provided for\nhimself, and in spite of the rapturous moments that musical revelations\nhad created for him since his twelfth year. Defiance and distrust\nagainst outside influences had remained active in him as forces that did\nnot allow the happy disposition proper to his age to assert itself. But\nnow the fetters had fallen and the pent-up joy of life burst forth as if\nthrough opened sluices. The sun and landscape of the South, Italian\nmanners of life, art freely displayed in the market-place and on the\nstreet, realized for him dream-pictures that had appeared to him earlier\nduring the hours of oppression. Whatever he saw, felt, and experienced\nlay outside the ordinary course of his life, awakened his sense for\nnatural and human things, and set his spirit free from all bonds. There\nwas no question of his going to school in the first six months. He\nenjoyed complete freedom, occupied himself with literature, and\nundertook extended excursions. Starting from Pavia, he wandered all\nalone over the Apennine to Genoa. Whilst he was being intoxicated with\nthe sublime Alpine landscape, he came into contact with the lower\nstratum of the people, who aroused his deepest sympathy. The tour took\nhim over a short stretch of the Italian Riviera, the beauties of\nwhich, as depicted by B\u00f6cklin, do not seem to have revealed themselves\nto him. At that time he was probably subject to a feeling of upward\nstriving such as possessed Zarathustra.\n\nWith all their joys and inspirations the experiences in Italy remained\nbut a short episode. Einstein resolved on a new tour, which was not\nwithout a professional purpose. He made a pilgrimage to Switzerland with\nthe intention of studying mathematics and physics at the Z\u00fcrich\nPolytechnical Institute. But he was not to be successful in his first\neffort to gain entrance. The conditions of entry required a standard in\ndescriptive sciences and modern languages that he had not yet reached.\nSo he turned to Aarau, where he was allowed to extend his knowledge with\nthe help of excellent methods at the Canton school. Even it the present\nday Einstein talks with extreme enthusiasm of the organization of this\nmodel school that corresponds in rank approximately to a German\nRealgymnasium (or an English Grammar School). There was nothing to\nremind him of the continual manipulation of the sceptre of authority at\nthe Luitpold school barracks; he easily obtained his leaving\ncertificate, and now the portals of the Z\u00fcrich Polytechnicum were open\nfor him.\n\nHe himself was probably not aware that he carried a marshal's baton in\nhis own mathematical equipment. But, in looking back, we come across\nastounding things. For it is a fact that even in the pupil at Aarau\nproblems had taken root that already lay in the vanguard of research at\nthat time. He was not yet a finder, but what he sought as a\nsixteen-year-old boy was already stretching into the realms of his later\ndiscoveries. We have here simply to register facts, and to abstain from\nmaking an analysis of his development, for how are we to trace out the\nintermediate steps, and to discover the sudden phases of thought that\nlead a very young Canton pupil to feel his way into a still undiscovered\nbranch of physics? The problem that occupied him was the optics of\nmoving bodies, or, more exactly, the emission of light from bodies that\nmove relatively to the ether. This contains the first flash of the\ngrandiose complex of ideas that was later to lead to a revision of our\npicture of the world. And if a biographer should state that the first\nbeginnings of the doctrine of relativity occurred at that time, he would\nnot be making an objectively false statement.\n\nThe ambitions of the youth by no means reached these flights of\nimagination, for whereas the latter signified the coming power of his\nwings, he himself set a modest goal. He wished to become a schoolmaster,\nand imagined that in choosing this career he was allowing his hopes to\nrun high. This was in conformity with the esteem in which he held the\nstatus of teachers. In the Z\u00fcrich Technical School there is a section\nequipped as a department for preparing teachers, and in this Einstein\nstudied from the age of seventeen to the age of twenty-one, perfectly\nsatisfied with the thought of sitting, not on the pupil's bench, but at\nthe master's desk, and of exercising a beneficial if limited influence\nas a preceptor of the young.\n\nHe was still under the sway of the feeling that he was not sufficiently\nexperienced in life and that he dare not venture out into the light for\nexistence in the great turmoil of the world. He saw in this struggle,\nwhich pitted man against man, led to exhibitions of violence, and\naroused ambition for glittering unrealities, cause only for disgust and\nalienation. The prospect of personal success did not lure him to try\nforce against force. Thus, for the time being, it was his ideal to lead\na very modest existence. From various quarters he had been given hopes\nof a position as assistant to some professor of physics or mathematics.\nBut for unknown reasons he was everywhere refused. These apparently\nobscure grounds, it must be said with regret, become clearer when we\nbear in mind his confession of faith. Nor did his hopes of teaching at a\ngymnasium seem near fulfilment, as certain conditions of birth raised\nobstacles. In the first place, he was not a Swiss; in fact, since his\nstay in Milan he was without a nationality at all in the bureaucratic\nsense, and then he had no personal connexions, without which, at least\nat that time, there was no chance of progress even for a talented\nperson. Yet the young student who was entirely without protection of any\nsort had to overcome the cares and satisfy the needs of daily life. He\ncould not rely on material help from his parents, who themselves lived\nin restricted circumstances, and thus we find him a little later in\nSchaffhausen and Bern, where he earned a small pittance as a private\ntutor.\n\nHe found consolation in the fact that he preserved a certain\nindependence, which meant the more to him as his instinct for freedom\nled him to discover the essential things in himself. Thus, earlier, too,\nduring his studies at Z\u00fcrich he had carried on his work in theoretical\nphysics at home, almost entirely apart from the lectures at the\nPolytechnic, plunging himself into the writings of Kirchhoff, Helmholtz,\nHertz, Boltzmann, and Drude. Disregarding chronological order, we must\nhere mention that he found a partner in these studies who was working in\na similar direction, a Southern Slavonic student, whom he married in the\nyear 1903. This union was dissolved after a number of years. Later he\nfound the ideal of domestic happiness at the side of a woman whose grace\nis matched by her intelligence, Else Einstein, his cousin, whom he\nmarried in Berlin.\n\nIn 1901, after living in Switzerland for five years, he acquired the\ncitizenship of Z\u00fcrich, and this at last gave him the opportunity of\nrising above material cares. His University friend, Marcel Grossmann,\nlent him a helping hand by recommending him to the Swiss Patent Office,\nthe director of which was his personal friend. Einstein occupied himself\nhere from 1902 to 1905 as a technical expert, that is, as an examiner of\napplications for patents, and this position gave him the chance of\nmoving about in absolute freedom in the realms of technical science.\nWhoever has a strong predilection for discovery will perhaps feel\nestranged to find Einstein so long in the sphere of \"invention,\" but, as\nEinstein himself emphasizes very strongly, both regions make great\ndemands on clearly defined and accurate thought. He recognizes a\ndefinite relationship between the knowledge that he gained at the Patent\nOffice and the theoretical results that appeared at the same time as\nproducts of intensive thought.\n\nIn 1905, in the midst of his work, the storm broke loose in him with the\nsuddenness of a hurricane. In quick succession his mind disburdened\nitself of the abundance of ideas that had stored themselves up in the\nwork of the preceding years, and these ideas signify more to us than a\ndefinite stage in the development of an individual. What physicists have\ncome to regard as an elaboration of the heritage of Galilei and Newton\nhad matured in him. We merely record the title of dissertations, which\nappeared in 1905 in the _Annalen der Physik_: \"Concerning a Heuristic\nStandpoint towards the Production and Transformation of\nLight\"--\"Concerning the Inertia of Energy\"--\"The Law of Brownian\nMovement.\"--Then the most important contribution: \"The Electrodynamics\nof Moving Bodies,\" that contained the revolutionary ideas underlying the\nspecial theory of relativity. To these is to be added a dissertation for\nhis doctorate in the same year: \"A New Determination of Molecular\nDimensions.\"\n\nIn all, these represent a life-work that belongs to the history of\nscience. It was certainly some considerable time before his work began\nits triumphal march in the sight of the world, and it may be added that\ntreasures were hidden in these disquisitions that were not understood\ntill long years afterwards. Yet the youthful discoverer was not passed\nover without signs of friendly appreciation. He received a letter,\ncouched in very warm terms, from the celebrated physicist, Max Planck,\nwho was a complete stranger to him at that time; it spoke in glowing\nwords of his essay, \"The Electrodynamics of Moving Bodies.\" This letter\nwas the first diploma, the forerunner of all the honours that later\nswept over him like a tidal wave.\n\nIt was his intention to obtain a tutorial position at the University. An\nappointment to Bern was at first again hindered by certain obstacles\nwhich he would probably have overcome if he had applied himself\nenergetically to attaining his goal. He finally received his\nappointment, but exercised his duties for only a very short time, as\nZ\u00fcrich now opened her arms to him. In 1909 he accepted the position of\nProfessor extraordinarius there for theoretical physics, and soon\nassembled a grateful audience about himself. Nevertheless, during the\nearlier stages of his professorship he found it difficult to suppress a\nlonging for the quiet, unexcited life of his patent-office work, in\nwhich he seemed to have had a still greater degree of independence. In\n1911 he accepted a new appointment as Professor Ordinarius to Prague,\nwhich offered him more favourable emoluments as an inducement. In the\nautumn of 1912 he returned to Z\u00fcrich as a Professor at the Polytechnic,\nand in the early part of 1914 he was drawn into the strong magnetic\nfield of the northern capital; he arrived at the Spree, and has, since\nthen, lived among us. He is now a Swiss by nationality, a world citizen\nby conviction, and, professionally, a member of the Berlin Academy and\nattached in a lecturing capacity to the University. Here he perfected\nhis works on relativity, ending in the superlative elaboration of the\ntheory of gravitation, the beginnings of which stretch back to the year\n1907. He had spent eight years in a concentrated effort of severe\nthought to bring it to completion, and perhaps centuries will be\nnecessary before the world will gain a complete perspective of all the\nconsequences of his theory.\n\nFor the theory asks us to brush aside habits of thought that have\nclaimed an hereditary position in pre-eminent minds. One of the foremost\nphysicists, Henri Poincar\u00e9, had confessed as late as 1910 that it\ncaused him the greatest effort to find his way into Einstein's new\nmechanics. Another whole year passed before he gave up his last doubts.\nThen he passed with flying colours into Einstein's camp, and recommended\nEinstein's appointment to the Professorship at Z\u00fcrich, in conjunction\nwith the discoverer of radium, Madame Curie, in an exuberant letter\nwhich may add its note of appreciation here:\n\n\"Herr Einstein,\" so wrote the great Poincar\u00e9, \"is one of the most\noriginal minds that I have ever met. In spite of his youth he already\noccupies a very honourable position among the foremost savants of his\ntime. What we marvel at in him, above all, is the ease with which he\nadjusts himself to new conceptions and draws all possible deductions\nfrom them. He does not cling tightly to classical principles, but sees\nall conceivable possibilities when he is confronted with a physical\nproblem. In his mind this becomes transformed into an anticipation of\nnew phenomena that may some day be verified in actual experience.... The\nfuture will give more and more proofs of the merits of Herr Einstein,\nand the University that succeeds in attaching him to itself may be\ncertain that it will derive honour from its connexion with the young\nmaster.\"\n\nWe may be tempted to look back and ask whether the criteria that Wilhelm\nOstwald once set up as a test of great men are verified in Einstein's\ncase. He has certainly not broken the first and most general rule, the\nprinciple of \"early maturity.\" This showed itself clearly when his\nimpulse towards mathematical knowledge and discovery asserted itself,\nand when he penetrated far into the future with his optical problems.\nThe history of science and of art may offer more striking examples in\nthis connexion, but at any rate in Einstein's case the indications are\nsufficient to serve as a confirmation of the rule. On the other hand,\nthe second test of Ostwald seems to be valid only conditionally when\napplied to Einstein. For Ostwald takes up arms against a \"gradual\nintensification\" of ability, and proclaims it as an almost universal\nrule that the exceptional achievement is the privilege of quite young\npersons: \"what he achieves later is seldom as impressive as his first\nbrilliant achievement.\" Thus, in Einstein's case, the exception is\nevident. For if we fix on only two chief discoveries, passing over many\nothers, there is no doubt that the second (the theory of gravitation)\nsurpasses the first (special relativity) in both range and significance.\nIndeed, we cannot escape from the idea of a \"gradual intensification,\"\nfor the second discovery could come about only as a result of the first.\nMoreover, it is not yet night, and there is nothing to refute the\nassumption that there will be a further progression.\n\nFurthermore, Ostwald takes into consideration the tempo of the\nintellectual pulse of inspiration to divide the main types of great men\ninto a classical and a romantic category: this classification cannot,\nhowever, be applied to Einstein. He is decidedly classical, in so far as\nhis work seems calculated to serve later generations as a classical\nfoundation for all mechanical investigations of the macrocosm of the\nheavens and the microcosm of atoms. On the other hand, his versatility,\nthe mobility and resource of his highly imaginative mind, stamp him as a\nromantic spirit. His delight in teaching would also assign him to this\ncategory, for in the case of many classical spirits there is a decided\naversion to imparting instruction. So that, although we might well be\nable to speak of a synthesis of these two forms, it seems better to\nestimate Einstein, not in the light of a ready scheme, but rather as a\ntype of which he is the unique representative.\n\n     *     *     *     *     *     *     *     *\n\nJust as the external contour of his life is on the whole regular and\nunbroken, so also his inner life is attuned to simplicity. Nowhere, it\nmight almost be said, do we observe a break, a spasmodic turn, or a\nsudden intensification. Although he has grasped and suggested so many\nproblems, he himself presents no psychological riddle, and we meet with\nno singularities in analysing his personality. It has already been\nremarked several times that Art plays a part in his life. What I learned\nfrom him himself about his affection for music coincides exactly with\nwhat observation clearly discloses. The expression of his countenance\nwhen he is listening to music is a sufficient indication of the\nresonances induced in him. He is confessedly a classicist, and a sincere\ndevotee of the revelations of Bach, Haydn, and Mozart. What fascinates\nand enraptures him above all is that which is directed inwards, which is\ncontemplative and erected on a religious basis. The simple masterful\nflow in musical development and invention is all-important for him. The\narchitectonic structure that we marvel at in Bach, the Gothic tendency\ntowards heavenly heights, perhaps calls up in him sensations that\nemanate from his hidden wealth of constructive mathematical ideas. It\nseems to me that this possibility is not unworthy of remark. It suggests\na reason for the fact that he gives himself up only unwillingly to the\nnervous strain of drama directed at emotional upheaval. He does not\ngladly overstep the boundary that separates the simple from the\npsychologically subtle, and whenever his desire to understand art\nrequires him to venture beyond it, his appreciation is not accompanied\nby genuine pleasure. His subjectivity does not fix this boundary in\naccordance with the ordinary rules of concert \u00e6sthetics, which are\nactually not rules at all, but only changeable valuations and\ncrystallizations of the feelings of certain groups of people. He gives\nhimself up quietly and freely to what is presented, but makes no special\neffort to assimilate experiences to which his being does not\nspontaneously react. There would be no meaning in seeking to mark off\nthe limits of his receptivity in accordance with this, and to tell him\nthat it is too limited, and that it should be enlarged, and that he\nshould not regard as an opinionated exaggeration what appears to others\nto be a deep and mighty revelation, or seems to be possessed of divine\nsweetness. He would be able to point out that even in the case of\nmasters of the musical art a change of faith was not a rare occurrence,\nand that they learned anew, or rejected what they once idolized, and\nvery often found no permanent haven in their own faith. Whoever, like\nEinstein, gives himself up to the simply contemplative, and feels no\nimpulse towards sensationalism, is spared the task of learning afresh,\nand finds still one world left for him even if many other worlds are\ninaccessible. To mention only the main features, then, neither Beethoven\nas a composer of symphonies, nor Richard Wagner, denote the pinnacles of\nmusic for him; he could live without the Ninth Symphony, but not without\nBeethoven's ensemble music. The number of composers and compositions\nwhich are not a necessity of life for him is very considerable. It\nincludes the majority of romanticists, the erotically inclined school of\nChopin and Schumann, which revels in sensation, and, as already\nmentioned, the neo-German dramatic composers. He has much objective\nadmiration for them, yet he does not conceal the fact that he also feels\nlively opposition in the gamut of his sensations. He regards the\nproperly modern productions as interesting phenomena, and has various\ndegrees of disapproval for them, extending to complete aversion. It\ncosts him an effort to hear an opera of Wagner, and when he has done so,\nhe returns home bearing with him the _leitmotiv_ of Meister Eckhard:\n\"The lust of creatures is intermingled with bitterness.\" In general he\nseems to take up approximately the point of view of Rossini. Wagner\ngives him wonderful moments, followed, however, by periods of acute\nemotional distress. I need hardly add that I myself, who confess to\nbeing an ultra-Wagnerite, never strove in my conversations with Einstein\nto make my opinion prevail against his. For I am deeply convinced that\nin this matter there is no question of right and wrong, and that every\nmusical valuation represents no more than an accidental judgment\ndependent on one's own nature, entirely egocentric and thus objectively\nof no account.\n\nEinstein also occupies himself in an active sense with music, and has\ndeveloped into a very fair violinist, without claiming higher degrees of\nachievement. Among other things I once heard him play the violin part of\na Brahms Sonata, and his performance approached concert standard. He\ndraws a beautiful tone, infuses expression into his rendering, and knows\nhow to overcome the technical difficulties. Among the supreme artists of\nhis instrument who have exerted a personal influence on him, Joachim\nassumes the first place. Einstein still speaks with great enthusiasm of\nJoachim's performance of Beethoven's Tenth Sonata and of Bach's\nChaconne. He himself plays the latter piece, for which the purity and\naccuracy of his double and multiple stopping fits him. Whoever chooses\nthe right moment--this good fortune has not yet befallen me--may\noverhear Einstein at his pianistic studies. As he confessed to me,\nimprovisation on the piano is a necessity of his life. Every journey\nthat takes him away from the instrument for some time excites a\nhome-sickness for his piano, and when he returns he longingly caresses\nthe keys to ease himself of the burden of the tone experiences that have\nmounted up in him, giving them utterance in improvisations.\n\nThe regular run of concerts in which displays of bravura play an\nimportant part finds little favour with him; above all, he is not a\nworshipper of the orchestral conductor, whom he regards only as an\ninterpreter and not as a virtuoso on the orchestral instrument. He\nexpressed this idea in unmistakable words: \"The conductor should keep\nhimself in the background.\" I believe that his dearest wish would be to\nbreathe in the tones without a personal or material medium, merely out\nof the air or out of space. Furthermore, I believe that there is an\nunfathomable connexion between his musical instinct and his nature as a\nresearch scientist. For the ear, as we know from Mach, is the true organ\nthat enables us to experience space, and thus things may occur within\nthe ear of the investigator of space that may have a different\nsignificance from that of music which is representable in tones. I\nstrongly doubt whether traces of compositional form occur in Einstein's\ntone-monologues, but perhaps they contain examples of an art for which\nthe \u00e6sthetics of a distant future may find a name.\n\n     *     *     *     *     *     *     *     *\n\nWith regard to higher literature, and indeed all writings not connected\nwith science, Einstein has little to say. He himself rarely directs\nconversation on to this topic, and still less rarely does he give vent\nto an enthusiastic outburst that betrays warm interest. He restricts\nhimself to making short, aphoristic comments, and now and then allows\nhis listener to gather that he can easily imagine an existence without\nliterature. The number of accepted novels, tales, and poetic works which\nhe has not read is legion, and all the pretentiously artistic,\nhistorical, and critical writings that are added to them have attracted\nonly a very momentary interest from him.\n\nI have never seen him attracted in any way by the promising aspect of\nsome new book intended for diversion. If such a one happens to get into\nhis hands, he merely places it among the others. At times I was\nconstrained to think of Caliph Omar's words: \"If the book contains what\nis already in the Koran, it is unnecessary; if it contains something\nelse, it is harmful.\" It is harmful at least in the sense that it robs\nus of time that may be better spent in another way. I am purposely\nexaggerating here to make it quite clear that Einstein finds full\nsatisfaction in a narrow circle of literature, and that he experiences\nno loss if numerous new works pass by and escape his notice.\n\nNevertheless, he speaks with reverence of a series of authors, to whom\nhe owes enrichment: among them are the classical writers, who naturally\noccupy the highest position, with certain exceptions, which he equally\nnaturally wishes to be taken as a personal opinion and not in the sense\nof a critical valuation. With him the difference reveals itself in the\nintonation from which we may read a greater or lesser measure of\naffection. When he says \"Shakespeare,\" the eternal greatness seems to be\ninherent in the actual sound of the name. When he says \"Goethe,\" we\nnotice a slight undertone of dissonance, which may be interpreted\nwithout difficulty. He admires him with the pathos of distance, but no\nwarmth glows through this pathos.\n\nI had ventured to deduce from my knowledge of his nature the men and the\nworks which, in my opinion, should awaken strong echoes in him. A fairly\nclearly defined line leads to the true path. Outside of any systematic\nseries, I may mention Dostojewski, Cervantes, Homer, Strindberg,\nGottfried Keller in the positive sense, Emile Zola and Ibsen in the\nnegative sense. Taken as a whole, this prognostication does not disagree\nseriously with his own statement, excepting that he lays still greater\nemphasis on Don Quixote and the Brothers Karamasoff than I had surmised.\nHe expressed himself with reserve about Voltaire. He has no belief in\nVoltaire's poetic qualities, and sees in him only a subtle-minded and\namusing writer. Perhaps if Einstein were to devote himself a little more\nintensively to Voltaire and Zola, he would assign a higher value to\nthese related spirits. But there is little hope of this occurring, as\nthe wide range of Voltaire's works tends to restrain him. Time, which\nthe physicist Einstein has shown to be relative, has an absolute value\nfor him when measured in hours, and whoever seeks to persuade him to\nread thick volumes is not likely to gain his goodwill.\n\nOur philosophical literature is not received with acclamation by him. If\nsome one wished to undertake the task of ascertaining Einstein's\nattitude towards philosophy, he would be well advised to plunge into\nEinstein's works rather than to ask him personally. In them the\nquestioner would find ample hints, pointing towards a new theory of\nknowledge, the first indications of which are already perceptible. A\ngreat portion of philosophic doctrine will yet have to pass through the\nEinstein filter to be purified. He himself, it seems to me, leaves this\nprocess of filtering mostly to other thinkers, but we must not lose\nsight of the fact that these others derive their views of space, time,\nand causality from Einstein's physics. It is thus immediately evident\nthat he does not find revelations about ultimate things in already\nextant literature, for the simple reason that they are not to be found\nthere. For him famous works represent, in Kant's language, \"Prolegomena\nto every future system of metaphysics which can claim to rank as a\nscience.\" The accent is to be put on the future that has not yet become\nthe present. He praises many, particularly Locke and Hume, but will\ngrant finality to none, not even to the great Kant, not to mention\nHegel, Schelling, and Fichte, whom he barely mentions in this connexion.\nTo Schopenhauer and Nietzsche he assigns a high position as writers, as\nmasters of language and moulders of impressive thoughts. He values them\nfor their literary excellence, but denies them philosophic depth. As far\nas Nietzsche is concerned, whom, by the way, he regards as too\nglittering, Einstein certainly experiences ethical objections against\nthis prophet of the aristocratic cult whose views are so diametrically\nopposed to Einstein's own opinion of the relations between man and man.\n\nEarlier when we were talking of classical poetry he had particularly\nemphasized Sophocles as one who was dear to him. And this name leads us\nto the innermost source of Einstein as a man. \"I am not here to hate\nwith you but to love with you,\" is the cry of Sophocles' Antigone, and\nthis cry is the keynote of Einstein's emotional existence. I shall not\ngive way to the temptation to follow those who in the turmoil of the\npresent day refer to Einstein as a political figure. That would lead to\na description of policy and party arguments that lie beyond the scope of\nthis book; so much the less am I inclined to do so as Einstein's\nconvictions may be expressed very clearly without reference to schematic\nterms of a very elastic nature. An individuality such as his cannot be\ncompressed into a party programme. And if anyone should insist on\nplacing him among the radicals or on assigning him far to the left, I\nshould suggest that it would be better to choose, instead of the\nclassification right and left, that of above and below. I look up\ntowards his idealism, whose altitude may perhaps be reached one day by\nthe raising of our ethical standards. But not by means of paragraphs of\nlaws. I have seldom heard him talk of such schematic recipes, but so\nmuch the more have I noted utterances which bore witness to a very\nintense and ever-present sympathy with every human creature. His\nprogramme, which is written not in ink but in heart's-blood, proclaims\nin the simplest manner the categorical imperative: Fulfil your duty to\nyour fellow-being: offer help to every one: ward off every material\noppression. \"Well, then, he is a socialist,\" so the cry runs. If it is\nyour pleasure to call him so, he will not deny you it. But to me this\nterm seems to denote too narrow limits for him. I see no contradiction\nin applying the term, but there is no perfect congruence. If one word is\nnecessary, I should be rather more inclined to say that he is in the\nwidest sense a democrat of liberal trend.\n\nFor him the State is not its own aim, nor does he imagine himself to be\nthe possessor of a panacea. \"The attitude of the individual to\nsocialism,\" he said, \"is uncertain owing to the fact that we can never\nascertain clearly how much of the iron compulsion and blind working of\nour economic system may be overcome by appropriate institutions.\" And I\nshould like to add that such institutions would scarcely have a\npermanent result, but that more may be expected from the ethical example\nof those who have the power of renunciation. Whoever realizes the motto\nof Antigone, \"I am here to love with you,\" brings us nearer the goal.\nAll in all, our longing continually flees from the confusion of\npolitical considerations to simple morality. For Einstein this is the\nprimary element, that which is directly evident and not open to\nmisrepresentation. It includes sympathy, and, what is more important,\njoy in conjunction with others. \"The best that life has to offer,\" he\nonce exclaimed, \"is a face glowing with happiness!\"\n\nThis look is expressed on his own face when he discusses his ideals,\nabove all the internationality of all intellectual workers and the\nrealization of eternal peace among the nations. To him pacifism is a\nmatter of mind as well as of heart, and he is of the opinion that the\ncourse of history so far is but the prelude to its realization. The\npast, with its bloodstained fingers that reach into the present, does\nnot discourage him He points to the endless city wars of the Middle Ages\nin Italy, which had finally to cease in answer to the increasing feeling\nof solidarity. So he believes in the victory of peace, which the unified\nconsciousness of all humanity will one day win over the demonic powers\nof tyranny and conquest.\n\nThe pacifistic goal seems to him to be attainable without the\npeculiarities of the various States being destroyed. National\ncharacteristics arising from tradition and hereditary influences do not\nsignify in his eyes a contradiction to the internationalism that\nembraces the common intellectual factors of civilized peoples. Thus the\ndesire for the preservation and care of particularities directs him to\nthe secondary goal of Zionism. His blood asserts itself when he supports\nthe foundation of a State in Palestine, which seems to him to be the\nonly means of preserving the national individuality of his race without\nthe freedom of the individual being affected.\n\nWe had left Art to talk of the State, and then returned to the former\ntheme to touch lightly on the pictorial arts. Painting was allowed to\npass with merely a fleeting remark. It plays no considerable part in\nEinstein's existence, and he would not suffer great grief if it were to\nvanish from the plane of culture, a consummation to which definite signs\nseems to point. I have described these signs in other writings (as in\n_Kunst in 1000 Jahren_), and maintain the point of view that the latest\nbranches of painting as represented by expressionism and cubistic\nfuturism denote, in essence, the last convulsions of a dying surface\nart. And even the chief representatives of former flourishing periods\nare beginning to fade away, and Einstein will not be the only one who\nwill relegate this art, as compared with music, to a lower plane among\nthe inspired arts that bring joy to humanity. He is only more frank than\nothers when he freely confesses that he cannot convince himself that a\nlife without the joys of pictorial art would be hopelessly impoverished.\nBut he bows his head to sculpture, and, for him, architecture is a\ngoddess. It is again his deeply rooted piety that asserts itself when\nmemory recalls to him the Gothic dome with its pinnacles striving\ntowards heaven. Goethe and Schlegel have called architecture \"frozen\nmusic,\" and this picture is present in his mind when he sees Gothic\narchitecture as frozen music of Bach. It is open to anyone to analyse\nthis specific impression in another way by seeking the fundamental\nelements, in which the essence of the art is to provide support for a\nweighty structure and to overcome gravitation. For a spirit that works\nwith mechanics and that feels within itself the pressures and tensions\noccurring in external nature, architecture is a kind of statics and\ndynamics transformed into a thing of beauty, a ravishing picture of his\nown science.\n\n     *     *     *     *     *     *     *     *\n\nEinstein has told me many a story of his travels, and these reports were\ncharacterized by an absence of definite purpose. The conception of\nsomething worth seeing in the tourists' sense does not exist for him,\nand he does not set out in eager pursuit of those things that are marked\nwith two asterisks in Baedeker. The intense romanticism of Swiss\nscenery, that lay within such easy reach for him, has never enticed him\ninto its magic circle, and he has nothing to do with the abysmal terrors\nof glaciers and the world of snow-peaks. His enthusiasm for landscape\nbeauty conforms with the behaviour of the barometer: the greater the\naltitude, the lower the mercury. In simple contact with Nature he\nprefers the lesser mountains, the seashore, and extensive plains,\nwhereas brilliant panoramic contours like those of the Vierwaldstetter\nSee do not rouse him into ecstasy. It is unnecessary to remark that he\ndoes not arrange his living on the standard of the Grand Palace Hotels\nen route. It is nearer the truth to picture him as a vagrant who tramps\nalong without a sense of time and without a goal, in the fairy\natmosphere of a joyous wanderer who has unconsciously adopted the old\nrule of Philander: Walk with a steady step: make your burden small:\nstart early in the morn, and leave home all care!\n\nAm I to record the list of pleasures and hobbies that are foreign to\nhim? The list would be very long, and I should arrive at my goal more\nquickly by setting his sporting tendencies equal to zero. I once\nsuspected him of being given to aquatic sport, as I learned that he had\ntaken part in several yachting excursions. But I was mistaken. He sails\nin the same way as he walks on his tours, without a set purpose,\ndreaming, and uninterested in what is regarded by members of sailing\nclubs as a \"feat.\" In the negative list of his games we see even chess,\nthat usually exerts a strong attraction on natures with a mathematical\ntendency. The particular types of combination offered by this game have\nnever tempted him, and the world of chess has remained _terra incognita_\nfor him. He is just as little interested in every kind of collection,\neven that of books. I have seldom or never met a savant who attaches so\nlittle value to the personal possession of numerous and valuable books.\nThis statement may be extended as far as saying that he experiences no\npleasure at all in possession as such: he says so himself, and his whole\nmanner of life proves it. There seems to me to be an element of\nresignation in his amiable hedonism, a kind of monkish asceticism. He\nnever rids himself of the feeling that he is only paying a visit in this\nworld.\n\nI do not know whether Einstein considers that his life-work can be\ncompleted within the span of this visit. At any rate he makes no attempt\nto extract more out of the day by following a rigid programme of work\nthan the day voluntarily offers. He does not compel himself to cover a\ndefinitely circumscribed piece of ground with chronological exactitude.\nThere are brain-workers, especially artists, who actually never shake\noff the fetters of the twenty-four hours day of work inasmuch as they\nspin on the threads of daily effort into the nightly fabric of dreams.\nEinstein can make a pause, interrupt his work, or divert himself into\nside-channels at leisure and according to the demands of the hour, but\ndreams offer him no inspiration and do not waylay him with problems.\n\nOn the other hand, however, he is waylaid so much the more during the\nday by things and persons that make an assault on him. This starts as\nsoon as the first post arrives, to see through which requires a special\nbureau. In addition to the communications of a professional or official\nnature there appear innumerable letters from everywhere and anywhere\nasking him to grant a little of his time. Whatever each individual\nwriter has thought about the principle of relativity, all his thoughts\nand doubts, additions, and, above all, that which he has not been able\nto understand, all this is to be answered by Einstein. Has he, the child\nof fame, even a quarter of an hour for himself? There they wait in the\nhall, the painter, the photographer, the sculptor, and the interviewer;\nwith whatever powers of persuasion and argumentative subtlety his\nattentive wife may seek to defend his hours of rest, some of these\nvisitors will yet succeed in gaining the upper hand, and will produce\nsomething in oil-colours, in plaster of Paris, in black and white, in\nwater-colours, or in print. Fame, too, demands her sacrifices, and if we\ntalk of a hunt after fame, then Einstein is certainly not the hunter,\nbut the hunted.\n\nHe sighs under the burden of his correspondence, not only as the\nrecipient, but also with the sender, whose letter has to remain\nunanswered. Yet he is never roused to anger by the intruder on his time.\nIf this were not so, the aphorism of Cyrus that patience is the panacea\nof all ills would not hold for him, and how would I myself otherwise\nhave dared to claim so many hours of him? A sense of guilt falls on me!\n\nBut even Einstein's patience can come to an end, and this is at the\npoint where \"society\" begins: I mean the congregation of persons in a\nsalon, society entertainments to which one is invited to be seen, and so\nthat one may claim to have been there. A solemn representation in which\nhe is to be made the cynosure of all eyes is a torture to him. If in a\nvery exceptional case he is compelled to participate in such a\ngathering, the joy of his hosts will not be entirely unmixed, for it\ndoes not require a thought-reader to recognize the longing for solitude\nimprinted on his countenance: \"Could I but escape!\"\n\nSo much the happier does he feel himself in the narrow circle of his\nfriends, who offer what means to him much more than admiration, namely,\naffection, and an appreciation of his human self. He is what one wishes\nhim to be. He is happy when he can forget the doctor profundus, and can\nyield himself up to the atmosphere of stimulating and unconstrained\nconverse. He is a master in the art of listening, and is not averse to\ncontradiction; when possible, he even emphasizes the arguments of his\nopponent. _Audiatur et altera pars_! This is a further manifestation of\nhis altruistic personality, which rejoices when he extracts the true\nkernel from the husk of the opposing opinion. Here he also displays a\ncharacteristic which one does not usually expect to find among abstract\nthinkers, a sense of humour that runs through the whole gamut from a\ngentle smile to hearty laughter, and that is the happy source of many a\nstriking sally. It may happen that the subject of conversation excites\nhis anger, especially in political debates when he calls to mind\nmilitaristic or feudal misgovernment. He then becomes roused, and, as a\ncynical philosopher, sarcastically attacks personalities and points out\nthe primary source of perennial hate, immediately afterwards soaring up\nto happy speculations of the future.\n\nIt is a matter for regret that the subjects that he has discoursed on\nlightly have not been fixed phonographically. Such records would form an\ninteresting supplement to the conversations outlined in this book. It\nwould never occur to him to set down in permanent literary form the\ninspiration of the moment. What he writes emanates from other regions,\nand is, to use his own expression, a precipitate of \"thick ink.\" This is\nobvious, for what he has to proclaim as a scientist cannot be presented\nin a \"thin\" form. But many a so-called writer would have reason to\ncongratulate himself, if so much thinly flowing matter occurred to him\nin writing as to Einstein in speaking.\n\n     *     *     *     *     *     *     *     *\n\nThe record of these conversations was begun in the summer of 1919, and\ncompleted in the autumn of 1920.\n\n\n\n\nINDEX\n\nAristoteles, 41\nArrhenius, 144\n\nBabinet, 25\nBach, 88, 235\nBacon, 46\nBaer, K. E. von, 162\nBailhaud, 144\nBeethoven, 99, 234, 235\nBell, Graham, 25, 111\nB\u00e9ranger, 84\nBergson, 91\nBernoulli, 48\nBernstein, 225\nBessel, 32\nBohr, Niels, 57, 210\nBrahe, Tycho, 94\nBruno, Giordano, 141\nB\u00fcchner, 225\nBulwer, 76\nBunsen, 164\nByron, 9\n\nCantor, 52, 203\nCavendish, 111\nCeulen, Ludolf van, 158\nCondillac, 216\nCopernicus, 6, 90\nCosmati, 48\nCurie, Madame, 79, 231\nCuvier, 196\n\nDarboux, 152\nDase, 158\nDescartes, 47, 133, 162\nDingeldey, 190\nDostojewski, 185, 187\nDove, 21, 155\nDuhem, 105, 106\nD\u00fchring, 54, 56\n\nEckermann, 50, 85\nEdison, 140\nEuclid, 180\nEuler, 98\nEuripides, 85\n\nFaraday, 39, 61, 84\nFechner, 110, 182\nFermat, 97, 190\nFizeau, 113\nFlammarion, 115\nFranklin, 102\nFresnel, 45\n\nGalilei, 6, 40, 150, 179, 181\nGalle, 6\nGalvani, 110\nGauss, 55, 185, 186\nGoethe, 13, 23, 179, 197, 212, 236\n  240\nGrillparzer, 95\nGrossmann, 229\n\nHansen, 134\nHebbel, 77, 86\nHegel, 42\nHeine, 49\nHelmholtz, 25, 26, 53, 73\nHeraclitus, 23\nHerschel, 84\nHertz, 60\nHooke, 41\nHorace, 3\nHumboldt, 49\nHume, 161\nHuyghens, 56, 109, 132\n\nJean Paul, 86, 223\nJoule, 84\nJung Stilling, 84\n\nKant, 35, 121, 170, 177, 179, 237\nKepler, 6, 42, 84, 176, 177\nKirchhoff, 104-107, 148, 212\nKleist, 130\nKummer, 190\n\nLamarck, 197\nLange, 47\nLaplace, 40, 45, 140, 165\nLeibniz, 26, 128\nLeonardo da Vinci, 11, 50-54\nLeverrier, 6, 10\nLiebig, 55\nLindemann, 158\nLinn\u00e9, 196\nLorentz, 57, 72\nLothar Meyer, 107\nLucretius, 210\n\nMach, 46, 77, 108, 149, 169\nMauthner, 95\nMaxwell, 39, 60\nMayer, Robert, 25, 55, 56\nMelanchthon, 82\nMenander, 86\nMendelejew, 107\nMezzofanti, 63\nMichelangelo, 49\nMichelson and Morley, 112\nMill, 45\n\nMithridates, 63\nMontaigne, 77\nMozart, 233\n\nNewton, 2, 6, 8, 39, 40, 43, 96\nNietzsche, 63, 217, 237\nNollet, 103\n\nOdilon, Helene, 135\nOersted, 109\nOstwald, 83, 231, 232\nOvid, 197\n\nPascal, 93, 98\nPasteur, 175\nPerrin, 154\nPfl\u00fcger, 35\nPhilander, 241\nPicard, 144\nPlanck, 57, 59, 91, 230\nPoincar\u00e9, 1, 7, 112, 116, 231\nPope, 54\nPriestley, 111\nPsellus, 156\nPyrrhon, 92\nPythagoras, 101, 179\n\nQuetelet, 182\n\nRegiomantus, 52\nReis, 25\nRiemann, 186\nRiggenbach, 25\nRu\u00ebss, 224\nRutherford, 36, 210\n\nSchiller, 74, 94, 170\nSchlegel, 240\nSchlick, Moritz, 168\nSchopenhauer, 41, 237\nSchwann, 175\nShakespeare, 236\nSiemens, 25, 27-30\nSlade, 136\nSophocles, 238\nSpinoza, 84, 162\nStephenson, 25\n\nTerence, 191\nThomas Aquinas, 165\nTorricelli, 166\n\nVaihinger, 43, 169\nVitruvius, 101\nVolta, 110, 111\nVoltaire, 47, 237\n\nWagner, 234\nWeber, 182\nWeierstrass, 152\nWeyl, 34\nWhewell, 45\nWien, 173\n\nZelter, 84\nZ\u00f6llner, 137","title":"Einstein, the searcher : $b his work explained from dialogues with Einstein","tradition":"philosophy-ethics","translated_text":null,"word_count":93531}