2014 May 26
Einstein: Einblicke in seine Gedankenwelt --
Gemeinverständliche Betrachtegung über
die Relativitätstheorie und ein neues Weltsystem
entwickelt aus Gesprächen mit Einstein
von Alexander Moszkowski
[Hamburg: Hoffmann und Campe, 1921]
English translation: Einstein the Searcher translated by Henry L. Brose [New York: E. P. Dutton, 1922], with a few additions and modifications.
Moszkowski's words are in bold.
Relation of Discovery and Philosophy in History. --- The Absolute and the Relative. --- The Creative Act. --- Value of Intuition. --- Constructive Activity. --- Invention. --- The Artist as Discoverer. --- Theory and Proof. --- Classical Experiments. --- Physics in Primitive Ages. --- Experimentum Crucis. --- Spectral Analysis and Periodic System. --- The Role of Chance. --- Disappointed Expectations. --- The Michelson-Morley Experiment and the New Conception of Time.
"Next time" --- so one of our talks ended --- "next time, as you insist on it, we shall talk of discovery in general."
This was a promise of special import for me, for it meant that I was to draw near to a fountain-head of instruction, and to have an opportunity of hearing the pronouncements of one whose authority could scarcely be transcended.
We are precluded from questioning Galilei personally about the foundations of Mechanics, or Columbus about the inner feelings of a navigator who discovers new lands, or Sebastian Bach about the merits of Counterpoint, but a great discoverer lives among our contemporaries who is to give us a clue to the nature of discovery. Was it not natural that I should feel the importance of his acceptance of my proposal ?
Before meeting him again I was overwhelmed with ideas that arose in me at the shghtest echo of the word "discovery" in my mind. Nothing, it seemed to me, could be higher : man's position in the sphere of creation and the sum of his knowledge can be deduced from the sum of his discoveries which find their climax in the conceptions "civilization" [Kultur] and "philosophy" [Weltanschauung], just as they are partly conditioned by the philosophies of the time. We might be tempted to ask : which of these two precedes, and which follows? And perhaps the ambiguous nature of this question would furnish us with the key to the answer. For, ultimately, these two elements cannot at all be resolved into the relationship of cause and effect, antecedent and consequent.
Neither is primary, and neither secondary : they are intimately interwoven with one another, and are only different aspects of one and the same process. At the root of this process is our axiomatic belief that the world can be comprehended, and the indomitable will of all thinking men, acting as an elementary instinct, to bring the perceptual events in the universe into harmony with the inner processes of thought. This impulse is eternal ; it is only the form of these attempts to make the world fully intelligible that alters and is subject to the change of time. This form finds expression in the current philosophy which brings each discovery to fruition, just as philosophy bears in itself constituents of the ripe discovery.
It seemed to me that even at this stage of my reflections I was somewhere near interpreting Einstein's intellectual achievement. For his principle of relativity is tantamount to a regulative world-principle that has left a mighty mark in the thought of our times. We have lived to see the death of absolutism ; the relativity of the constituents of political power, and their mutability according to view-point and current tendencies, become manifest to us with a clearness unapproached by any experience of earlier historical epochs. The world was far enough advanced in its views for a final achievement of thought which would demohsh the absolute also from the mathematico-physical aspect. This is how Einstein's discovery appeared as inevitable.
Yet a shadow of doubt crossed my mind. Einstein's discoveries came to light in the year 1905 -- that is, at a time when hardly a cloud was visible to forewarn us of the storms which were to uproot absolutism in the world. But what if a different kind of necessity had imposed itself on world-history, and hence on the world-view ? Nowadays we know from authentic accounts, which no one doubts, that all that we have experienced during the war and the revolution has hung upon the activities of one frail human being of quite insignificant exterior, a bureaucrat of the Wilhelmstraße, a choleric eccentric who succeeded in frustrating the Anglo-German alliance which was unceasingly being pressed upon us for six long years after the beginning of the century.
Amid the noisy progress of universal evolution the secret and insignificant nibbling of a mole cannot be regarded as of momentous importance for history, and yet if we eliminate it from the complete picture of events we find as a result that all our experiences have been inverted. Absolutism would not have been thrown overboard, but would probably have kept the helm with greater mastery than ever as the exponent of an Anglo-German hegemony of the world, and a political outlook fundamentally different in tendency would now have been prevailing on the earth.
[This is a curious anticipation of the tornado-inducing butterfly, but the allusion is obscure to me. While there were indeed efforts to establish an Anglo-German alliance in the years around 1900, their failure is attributed by most historians to opposition on the British end. I do not know what German "bureaucrat" Moszkowski had in mind; perhaps Alfred von Kiderlen-Waechter.]
But Einstein's Theory of Relativity would not have taken the slightest heed of this. It would have arisen independently of the current forms of political conceptions, simply because we had reached that point in our intellectual development and because Einstein was living and thinking. And the question whether his theory would also have crushed absolutism for the non-physicist cannot be answered. [I have made several significant changes to Brose's translation of this paragraph.]
It may indeed be doubted whether its time had already come. In the case of many important events in the history of thought their moment of birth can be fixed to within about ten years, as for example the Theory of Evolution, which had been conceived in several minds at the same time and had of necessity to come to life in one of them, even if it had failed in the case of the others. I venture to say that without Einstein, the Theory of Relativity in its widest sense, that is, including the new doctrine of gravitation, would perhaps have had to wait another two hundred years before being born.
[It is interesting that Moszkowski, despite his hero worship, was perceptive enough to add the qualifying phrase "including the new doctrine of gravitation". Many later and more knowledgeable historians have reached the same conclusion : special relativity was "in the air", but general relativity was probably attainable only by Einstein or Hilbert.]
This contradiction is cleared up if we use sufficiently great time intervals. History does not adapt itself to the time measures of politics and of journalism, and philosophies are not to be calculated in terms of days. The philosophy of Aristotle held sway right through the Middle Ages, and that of Epicurus [i.e. atomism] will gain its full force only in the coming generation. But if we make our unit a hundred years the connexion between philosophies and great discoveries remains true.
Whoever undertakes to explore the necessity of this connexion cannot evade the fact that the lines of the result had been marked out in the region of pure thought, as can be proved, before even the great discovery or invention was able to present it in a fully intelligible form. Even the achievement of Copernicus would follow this general rule of development : it was the last consequence of the belief in the Sun Myth which had never been forsaken by man in spite of the violent efforts of the Church and of man himself to force the geocentric view. Copernicus concentrated what had survived of the wisdom of the earliest priests --- which includes also the germ of our modern ideas of energy and electricity --- of the teachings of Anaxagoras and the Eleatics which had remained latent in our consciousness : his discovery was the transformation of a myth into science. Mankind, whose wandering fancy first feels presentiments, then thinks and wishes to know, is a large edition of the individual thinker. The latter sees further only because he, so to speak, stands on the shoulders of a sum-total of beings with a world-view.
Let us turn our attention to an example from the most recent history of philosophy and discovery. The absolute continuity of events was one of the generally accepted canons of thought, and is even nowadays taught by serious philosophers as an incontrovertible element in our knowledge. The old quotation Nature makes no leaps, popularized by Linné, is one of the formulæ of this apparently invincible truth. But deep down in the consciousness of man there has always been an opposition to it, and when the French philosopher Henri Bergson set out to break up this line of continuity by metaphysical means in ascribing to human knowledge an intermittent, cinematographic character, he was proclaiming in an audible and eloquent form only what had lain latent in a new but as yet incomplete philosophy. Bergson made no new "discovery," he felt his way intuitively into a new field of knowledge and recognized that the time was ripe for the real discovery. This was actually presented to us in our day by the eminent physicist Max Planck, the winner of the Nobel Prize for Physics in 1919, in the form of his "Quantum Theory."
This is not to be taken as meaning that a revolutionary philosophy and a triumph of scientific research now become coincident, but only that a discontinuous, intermittent sequence, an atomistic structure, was proved by means of the weapons of exact science, to be true of energies which, according to current belief, were expected to be radiated regularly and connectedly. This was probably not a case of the accidental coincidence of a new philosophical view with the results of reasoning from physical grounds, but a demand of Time, exacting that the claims of a new principle of thought be recognized.
As above suggested, it is more difficult to find a link between Einstein's discoveries and antecedent presentiments of relativity. For a mere reference to the downfall of absolutism in the world of human events will not suffice. In the case of Einstein, we see such a tremendous rush of thought in one being that we almost feel compelled to recognize an analogy with the Quantum Theory and believe in a discontinuity in the course of intellectual history ! Yet there are certainly threads that connect Einstein's achievement with a prophetic insight. In this case, however, we must spread out over centuries what in the case of other discoveries extends, in comparison, only over decades.
That doubt of Faust [II, iv], which troubles the spirit of every thinker : "whether in yonder spheres there is also an Above and a Below," and which goes back as far as Pyrrhon and Protagoras, is itself relativistic ; it expresses doubt whether the co-ordinate system passing through our own lives as centres is valid. It is ultimately a matter of point of view, and the mathematico-physical consequences of the endless series of questions, and the relation, which arises from the couple, Above-Below, probably leads to a new mode of comprehending the constitution of the world, for which Einstein's creative work found the adequate expression in abstract terms. And from this point onwards, in accordance with the principle of reciprocal action, a new stream of knowledge will pour itself into the hazy stretches of philosophy. A fundamental and radical reform of our philosophy seems inevitable, particularly with respect to our conceptions of Space and Time, perhaps, too, even with respect to Infinity and Causality. Much dross will have to be sifted out of our old categories of thought and out of our world wisdom, which once served as material for fine structures. What will the finer ones look like that are to take their places in obedience to the command of physics ? Who would care to take it upon himself to form an estimate ?
Much will be uprooted, and it is possible that even the defiant "ignorabimus," the antipole of the search for truth from Pyrrhon to Dubois, will again take up the cudgel. For in the face of despairing uncertainty there is the one certainty : what cannot be comprehended is being encircled more and more by the great discoverers ! And even if the absolute point of convergence can never be reached, there is within our reach at least another point which is a haven of rest in the passing stream of philosophies, namely, a moral centre around which eddies of happiness circle. At the heart of this world-view there is the uplifting belief in an advance of knowledge in spite of all, and a belief in the vanishing of age-long problems and difficulties under the flood of discoveries. And even if afterwards and concurrently ever new problems and difficulties arise, these do not suppress our feeling of triumph.
Every achievement in this field gives us a sense of enfranchisement from prejudices, not the least of which is narrowness of national outlook. Not only do discoverers construct bridges of thought that stretch to astronomical distances, but, what is more difficult, they build bridges for our feelings, that surmount political obstacles. Every thinking being who plays a part in the making of some great discovery and who, with deepened vision, bows before a new achievement of mind, gradually becomes a disciple of the religion of universal politics, the creed of which is faith in the brotherhood of thought. The nucleus of a philosophy that belongs to the future is the recognition that differing national views must be compounded into a unity, and that every great discovery means a step towards attaining this end.
Even if we accept Pascal's wonderful dictum that human knowledge is represented by a sphere which is continually growing and increasing its points of contact with the unknown, we must not interpret it as a sign of despair. It is not the enlargement of the unknown, but only that of knowledge that stirs our feelings with ethical forces. The positive calls up in us a living force by inspiring in us the feeling that the sphere of knowledge is destined to grow, and that there can be no higher duty for all the energies of mind than to obey the call for combined action towards this growth which will bring the world into harmony.
What a very different picture many an outsider draws of the manner in which a seeker in the heavens works ! He is imagined like Tycho Brahe to be in a domed observatory, surrounded by unusual pieces of apparatus, spying through the ocular of a long range refractor into the universe, seeking to unravel its ultimate secrets. The true picture does not correspond to this fancy in the slightest. Nothing in the make-up of the room reminds one of super-earthly sublimity, no abundance of instruments or books is to be seen, and one soon becomes aware that here a thinker reigns whose only requirement for his work, which encompasses the world, is his own mind, plus a sheet of paper and a pencil.
All that acts on the observatories outside, that gives rise to great scientific expeditions, that, indeed, ultimately regulates the relationship of mankind to the constitution of the universe, the revolution in the knowledge of things connecting heaven and earth, all this is here concentrated in the simple figure of a still youthful scholar, who spins out endless threads from the fabric of his mind : the words of a poet are recalled to our memory, which, addressed to all of us, have been fulfilled to the last degree by one living among us : ---
Whereso thou roamest in space, thy Zenith and Nadir unite thee ---
This to the heavenly height, that to the pole of the world, ---
Whatsoever thou do, let thy will mount up into Heaven ---
But let the pole of the world still o'er thine actions preside.
(Schiller, "Zenith und Nadir" ; Translation by Merivale.)
And this one helped to fulfil this aim, and I must break off his thread of thought to put the question : What is Discovery, and what does it signify ?
It is a purely abstract question that may appear to many to be devoid of content. Such will repeat to themselves, as best they can, the list of discoveries, and think a man makes a discovery when he finds out something important, such as the Laws of Falling Bodies, the formation of Rainbows, or the Origin of Species : a general denomination may be found for it perhaps only by ascribing to Discovery something requiring a powerful mind, a creative genius.
At first it staggered me to hear Einstein say : "The use of the word 'Discovery' in itself is to be deprecated. For discovery is equivalent to becoming aware of a thing which is already formed ; this links up with proof, which no longer bears the character of 'discovery' but, in the last instance, of the means that leads to discovery." He then stated (at first in blunt terms, which he afterwards elaborated by giving detailed illustrations): "Discovery is really not a creative act!"
Arguments for and against this view flashed through my mind, and I thought involuntarily of a great master of music who, when he was asked : "What is Genius?", answered : "A genius is one to whom ideas occur." This parallel might be carried still further, for I have repeatedly heard Einstein call "ideas" [Einfälle, from einfallen, "to occur to"] what we would regard as wonderful thoughts.
Does not the philosopher Fritz Mauthner speak of the discovery of gravitation as being an "aperçu" of Newton ; yes, in the sense of aperçus as applied in ancient Greek philosophy, and which included almost everything that was left by Pythagoras, Heraclitus, etc., as a token of their genius. On the other hand, we are all possessed of the desire to differentiate clearly between an idea and a creative act of thought, as occurs in Grillparzer's aphorism : "Ideas are not thoughts; the thought respects the boundaries that the idea ignores, thereby failing to realize itself."
Here, then, we must revise our view. We know, for example, how much Einstein's "ideas," felt by him to be such and named so accordingly, accomplished. Let us hear how he characterizes in a few words his own "idea" which shook the world :
"The underlying thought of relativity," he said, in connexion with this question, "is that there is physically no unique (specially favoured) state of motion. Or, more exactly, among all states of motion there is none that is favoured in the sense that, in contradistinction to the others, it may be said to be a state of rest. Rest and Motion are not only by formal definition but also by their intrinsic physical meaning relative conceptions."
"Well, then," I interposed, "surely this was a creative act ! This first flashed across your mind, Professor ; it represents your discovery, so that we may well let the word retain the meaning usually associated with it!"
"By no means," answered Einstein, "for it is not true that this fundamental principle occurred to me as the primary thought. If this had been so, perhaps it would be justifiable to call it a 'discovery.' But the suddenness with which you assume it to have occurred to me must be denied. Actually, I was lead to it by steps arising from the individual laws derived from experience."
Einstein supplemented this by emphasizing the conception "invention," and ascribed a considerable importance to it : "Invention occurs here as a constructive act. This does not, therefore, constitute what is essentially original in the matter, but the creation of a method of thought to arrive at a logically coherent system . . . the really valuable factor is intuition !"
I had thought, long and intently, about these theses to discover as nearly as possible what distinguished their content from the usual view. The fundamental differences suggest an abundance of ideas whose importance grows in value as we apply them to various cases as illustrations. And I feel convinced that we shall yet have to occupy ourselves with these words of Einstein, which present themselves as a confession, as with the famous "hypotheses non fingo" that Newton set up as the idea underlying his work.
The latter as well as the former implies something negative : it denies something. In Einstein's words there is apparently a repudiation of the really creative act in discovery ; he lays stress on the gradual, methodical constructive factors, not omitting to emphasize intuition. There is no other course open to us but to seek indirectly a synthesis of these conceptions, and to eliminate what is apparently contradictory in them.
I consider this possible if we decide to subdivide the discovery into a series of individual acts in which succession takes the place of instantaneous suddenness. The creative factor may then remain intact ; indeed, it attains a still higher degree of importance, if we imagine to ourselves that a series of creative ideas must be linked together to make possible a single important discovery.
The original idea never springs fully equipped and armed like Minerva out of the head of its creator. And it is wise to bear in mind that even Jupiter had to suffer in his head a period of pregnancy accompanied with great pain. It is only in the after-picture that Pallas Athene appears with the attribute of suddenness. It is the nature of our myth-building imagination to leap over the actual act of birth so as to give a more brilliant form to the finished creation.
We feel great satisfaction when we learn that Gauss, the Prince of Mathematicians, declared in one of his valuable flashes of insight : "I have the result, only I do not yet know how to get to it." For in this utterance we see above all that he emphasizes a lightning-like intuition. He has possession of a thing, which is, however, not yet his own, and which can only become his own when he has found the way to it. Is this contradictory ? From the point of view of elementary logic, certainly ; but methodologically, by no means. Here it is a question of : Erwirb es um es zu besitzen ! [Faust I, 683: "Wouldst thou posses thy heritage? Essay by use to render it thine own!" (Swanwick tr.)] This makes necessary a series of further intuitions along the road of invention, and of construction.
This is, then, where that phase commences, which Einstein denotes by the word "gradual," or "by steps." The first intuition must be present ; its presence as a rule usually guarantees that further intuition will follow in logical sequence.
This does not always happen. In passing, we discussed
several special cases from which particular inferences may
be drawn. The powerful mathematician Pierre Fermat has
presented the world with a theorem of extremely simple form
which he discovered, a proof of which is being sought even
nowadays, two and a half centuries after he stated it. In
easy language, it is this : the sum of two squares may again
be a square, for example,
This is certainly true ; it is an intuitive discovery. But Fermat's assertion that he possessed a "wonderful proof," is for very good reasons open to contradiction. No one doubts the absolute truth of the theorem. But the later inspiration, the next step after the intuition, has occurred neither to Fermat nor to anyone else. It cannot be established whether his remark about the proof was due to a subjective error, or was baseless. In any case it seems probable that Fermat had arrived at the result per intuitionem without knowing the way to it. His creative act stopped short ; it was only a first flare of a conflagration, and did not fulfil the condition that Einstein associates with the conception of a logically complete method.
We may, indeed, pursue this case of Fermat still further. He had enunciated another theorem, per intuitionem, namely, that it was possible to construct prime numbers of any magnitude by a formula he gave. Euler later showed by a definite example that the theorem was false. It was stated in a letter to Pascal written in 1654 in the words : the result of squaring 2 continuously and then adding 1 must in each case be a prime number, that is, two to the power 2k, plus one, must always be a prime no matter what value k may have. Fermat added : "This is a property for the truth of which I answer." Euler chanced to try k=5, and found that 232 + 1 = 4,294,967,297, which may be represented as the product of 641 and 6,700,417, and hence is not a prime.
It is conceivable that no Euler might have lived, and that no one else might have discovered this contradiction. What would then have been the position of this "discovery" of Fermat ?
We should certainly not have disputed its creative character, for we should have said that it corresponds to a fact which is fully formed, but cannot be proved. But now that we know that the fact does not exist at all, the thing assumes a different colour. It was not a discovery at all, but an erroneous conjecture. But one would never be able to arrive at an erroneous conclusion of this sort without being a mathematical genius, and having the inspiration of the moment. And from this again it follows that to make a discovery in the full sense of the word the intuition of the moment does not suffice, but must be supported by a series of intuitions, and this is the condition that it become a permanent component of universal truth.
The fact that Einstein refers to the action of "inventing" in his explanation, gives support, it seems to me, to the view that, strictly speaking, "discovering" and "inventing" are never to be regarded as being separable. In "discovering", what has to be constructed persists, and in "inventing", it is a question of finding the path along which there is the promise of success, be it by a method, a proof, or by some general work.
We spoke of works of art, and I was delighted to see that Einstein was by no means disinclined to claim certain works of pure thought, which are usually placed in the category of scientific discovery, as works of art. In the latter, however, the pure process of invention plays the prominent part, for in them something is represented that did not exist at all before ; this has repeatedly led to the artist's achievement being given the higher rank, as being properly and exclusively creative.
The argument runs somewhat along these lines : the infinitesimal calculus would certainly have been discovered even if there had been no Newton and no Leibniz, but without Beethoven we should never have had a C Minor Symphony, and never in the future would it have appeared, for it was a subjective, absolutely personal, and unique product of its creator.
I believe this may be admitted, and that we may nevertheless retain the view that in the work of art, too, the act of discovering is to be found. Let us consider for a moment the elementary substance of the first movement of this Fifth Symphony, a colossal movement of 500 bars, which expresses itself quite definitely in four notes, of which one is repeated three times. Thus Destiny thunders at the gates is Beethoven's motto for this section ; it is expressed tonally in a succession of notes which through all eternity existed among the possible permutative arrangements of these sounds.
Beethoven, one says, "invented" it. But it is just as correct to say --- in Einstein's words --- "he became aware of what was already formed" --- that is, he "discovered" the fundamental theme, and afterwards musicologically "proved it" by a method of incredible beauty . [The exact meaning of this flowery sentence is obscure to me, as it apparently was to Brose who translates it with a string of words: "afterwards proved it in terms of musical logic unheard-of beauty in a methodical elaboration."]
We may, indeed, go further still. This motif of four tones was not only extant as an abstractum, as a possible mathematical arrangement, but also as something natural. Czerny, a pupil of Beethoven, to whom the master confided many a remark about the origin of his compositions, reports that a bird, the yellow-hammer, had sung this theme to Beethoven in the woods. But neither the bird nor any other living creature had invented it ; rather what could not be created (because it had always been in existence) became objectified in the medium of sound. Beethoven found it ; it was res nullius when he found it, and when he discovered simultaneously with the succession of tones that they were appropriate for a powerful nmsical representation of sombre Destiny.
Every theme, be it of Beethoven, Bach, Wagner, or anyone else, may be represented graphically by a curve (in the case of Bach's fugal themes this has, in fact, been done for special purposes), and just as it is certain that every elliptic-arc existed before all geometry, so it may be affirmed with equal certainty that everything musical was in existence before the advent of composition, and was merely waiting for a discoverer whom we designate the "inventor", the creative organ.
But may not some of this glory be reflected on to scientific discovery ? When we are in an ecstasy of admiration, we talk of a creative act as of something divine ; may we not also grant to the scientist this tribute which, owing to a slight confusion of conceptions, we shower on the artists ? And I believe that Einstein's definition does not set up an insuperable barrier in this respect to our admiration, which exerts every effort to pass beyond, refuses to come to a standstill before the rigid fact that the discoverer reveals only what is pre-formed ; our emotions prove to be stronger than our minds with their objective valuation. In the last instance, we opine, the scientific discoverer, too, creates something new, namely a piece of knowledge that was previously not in existence. And we obey the impulse of hero-worship, when we call a definite first discoverer a creator.
This silences opposition certainly only for a time, without vanquishing it. For this knowledge, too, lay ready before the first discoverer appeared : he did not create it, but merely drew back the veil that enveloped it. So that, ultimately, we get back to "intuition" in its literal sense, a becoming aware of things, an exact consideration of things, states, and relationships ; and this intensive consideration, full of wonderment, has always been a privilege of a very few chosen men.
It might be asked : Was there any knowledge of Pythagoras' Theorems before Pythagoras gave us his proof ? We should have to answer : It was in existence at least in the still dark field of vision of Pythagoras, which became illumined one day when he took such a view of the number-ratios 3 : 4 : 5 that an exact intuition could actually come about. It is erroneous to assume that a creative act suddenly called up before his soul as if by magic the figure with the three squares drawn externally on the sides of a triangle. Rather, he "took his stride" (as we know from Vitruvius [ De Architectura IX. ii]) by considering a triangle whose sides were of a definite length ; and the well-known proof, which is linked indissolubly in our minds with his work, is not his at all, but Euclid's. Yet our annals grow musty, centuries pass by, and the credit of being the creator rests with the man who first succeeded in getting a clear picture of such a triangle.
It seems natural to test discoveries by experiments. The first result of doing this is a very remarkable increase in the rate at which the intuitive process has developed. In ancient times, intuition, it seems, scarcely felt the need of proving things by experiment ; all that was discovered by Archimedes in mechanics, by the Pythagoreans in acoustics, by Euclid in optics, may be reduced practically to the formula Eureka, and it is probably scarcely an exaggeration to say that more and more fruitful experiments are performed in one week nowadays than in the whole of the classical age taken together.
Recently certain precisians in definition have been seeking to establish a fundamental difference between physicists of reality, experimental physicists, and "blackboard-physicists." The last term is given jeeringly to theoretical physicists because they, in the opinion of these critics, wish to found Nature entirely on formulæ argued out on the blackboard. The history of science does recognize this distinction, although it is, of course, quite possible for a physicist to arrive at important discoveries without making any experiments.
[These "precisians in definition", obviously, included the founders of what would become the Third Reich's "Aryan physics", supposedly distinguished from "Jewish theorising" by its empirical character.]
One might be more justified in asserting that the great theorist need not necessarily be a great experimenter and vice versa. But I can quote no example of a physicist who confined himself obstinately to blackboard discussion, and on principle disowned all experimental work.
(I must add that Einstein himself is fond of experimenting, and has had much success in experimental work. The amount of advice and encouragement that he has given, and still gives, to many workers in this field is very considerable. But he does not practise experimental work regularly, and remarked that he is obliged to appeal to outside help for certain practical tests. There are specific experimental geniuses, whose activity assumes the happiest and most fruitful form when it supplements that of the theorist and fertilizes it.)
Experiments have become, if not the sole, yet the most definite, test of intuition. I need only recall the observations of the solar eclipse of 1919, which were of an experimental character inasmuch as they used apparatus to question Nature. To the world generally, they gave the irrefutable confirmation of Einstein's Theory of Gravitation, but not to Einstein himself, whose intuition felt itself so certain that the confirmation was a mere matter of course.
But this is not the average case ; in many cases the intuition of the discoverer appeals to experiment as a judge of great authority, who is to confirm, reject, or correct.
Let us take some examples of cases in which the intensity and the value of intuition were measured by the experimental results. Benjamin Franklin's Kite Experiment may be taken as a classical instance. Here is a man in whose head the idea takes root that lightning and electricity are one and the same thing. Innumerable persons before and after his time might have hit on the same idea, which is now the common knowledge of children. Yet, a single man had to appear who became aware of this pre-formed fact and who simultaneously thought out a method of putting it to proof. In 1752 he constructed a kite, sent it up into the clouds during a storm, and caught up sparks on the ground by a metallic contrivance, and, as d'Alembert so aptly described it to the French Academy, eripuit coelo fulmen: He wrested the lightning from the heavens. Juppiter tonans illuminated a great discovery, a mighty intuition which had entered like a lightning stroke into the brain of a discoverer.
This case would be classical, were it not that nine-tenths of it is based on legend.
Franklin was by no means the first who had this intuition, and his experimental test was so full of faults that it was within an ace of failing. Franklin used a dry thread of hemp, which he thought to be a conductor, but which became a conductor only after it had been made wet by rain. Till that moment the exhibition of sparks on the ground had been poor enough, and little was wanting for Franklin to give up his attempt and confess that he had been inspired, not with an intuition, but with a hallucination.
But to whom then is the glory of this discovery due ? This is a difficult point to decide. As early as 1746, that is, six years before Franklin's kite made its ascent in Philadelphia, Professor Winkler of Leipzig had asserted in a dissertation that the two phenomena were identical, and had proved this theoretically ; and three years earher still Abbé Nollet had declared the storm clouds to be the conductors of an electrical induction machine. Almost simultaneously with Franklin, Dalibard, Delor, Buffon, Le Monnier, Canton, Bevis, and Wilson made experiments on an elaborate scale, which far exceeded that of Franklin in their results.
To this must be added that the experiment was conducted with evident success only in 1753, when de Romas of Nerac in South France wove a real conductor of thin annealed wire into the kite-string, and succeeded in bringing down a regular thunderstorm with flashes of lightning ten feet long, accompanied by a deafening uproar. It was only then that the track of the inspiration was traced back through time to the Roman Kings, Numa Pompilius and Tullus Hostilius, as the first experimenters with lightning. And then the physicist Lichtenberg sought to furnish a proof that the old Hebrew ark of the Covenant, together with the tabernacle, were nothing other than great pieces of electrical apparatus highly charged with electricity derived from the air ; thus the first intuition, and the priority of discovery, would have to be ascribed to Moses or Aaron ! And connected with this was the fact, supported by substantial proof, that the Temple of Solomon was protected by lightning-conductors.
[Lichtenberg's idea lived on long after 1800. In the 1970s, it was a component of the "ancient astronauts" mythology -- who but aliens could have revealed the secrets of electricity to Moses? -- and there are websites on the Internet today devoted to the supposed electrical and radioactive properties of the Ark.]
I must not omit to mention that Einstein regards this whole chain of proofs stretching back to early times as by no means established, although besides Lichtenberg, other important scholars, such as Bendavid in Berlin and Michaelis in Göttingen, have vouched for their truth. And as it is a matter of electrical relationships, Einstein's doubts cannot be passed over. As far as I recollect, they were not directed against the rough facts in themselves, but against the sense that is construed into them --- that is to say, in the case of both the ancient Roman and the Biblical data, the conception of discovery must be excluded, and must be awarded rather to those intellectual efforts which have led to the creation of a method of thought.
None the less, we may uphold our statement that, in this case, presumed to be classical, neither Franklin nor anyone else is to be claimed as the discoverer or as the central figure in a creative act.
The experimental case of spectral analysis is incomparably simpler and less open to dispute. It is without doubt a discovery of fundamental importance bearing all the characteristics of originality, for no predecessors are discernible. I have always felt a little dissatisfied with the fact that it required two men to think it out, that a duo of minds was necessary for one act of thought which appears quite uniform, elementary and inseparable from the intuition of a single mind. But it seems possible that tradition has not handed the facts down to us faithfully, and that the two men, with a unanimity arising from their partnership in work, combined their results, which were not, at the beginning, of a dual character. (This possibility became clear to me from a remark of Einstein which made it plain to me that the conjunction "Kirchhoff and Bunsen" is to be taken as denoting "Kirchhoff", and then, after a pause, "Bunsen" in the next breath !)
But if we discard this question of unity or duality, we are left with the fact that the idea of a spectral analysis occurred to some one (as a result of preceding optical experiments with Fraunhofer lines), and was fully confirmed by later experiments. Only fully confirmed ? No, the classic rank of this case manifested itself in a much more triumphant manner, for it is impossible that the intuition of Kirchhoff and Bunsen could have grasped the whole significance and range of their discovery even after they had made it their own.
Every discovery encloses a germ of hope. However great this may have been in the case of Kirchhoff, it could not by any stretch of imagination approach the degree of its fulfilment. The fundamental theoretical idea that ''a vapour absorbs from the ray-complex of white light only those wave-lengths which it can emit" gave rise to a process, the ingenuity, deficacy, and certainty of which is almost inconceivable. When rays of light emitted by incandescent vapour were separated by a prism, there were discovered fine coloured lines that betrayed some unknown mystery. The spectroscopic experiments proved, in a succession of results, that the author of the above idea had made not only one discovery, but a whole host of them.
For example, it was observed that, in burning minute residues obtained by evaporating certain mineral waters, a red line and a blue line that had never been seen before appeared in the spectrum. One knew immediately that an element, hitherto undiscovered, was proclaiming its presence. In this way in quick succession the element Cæsium was discovered, then Rubidium, Thallium, Indium, Argon, Helium, Neon, Krypton, Xenon ... certainly things that were already pre-formed in Nature, just as the idea of a bridge from Optics to Chemistry lay all ready in the heart of Nature ; but no blame can be given to the astonished contemporaries who regarded this fundamental discovery of spectroscopic analysis as a creative achievement of the intellect.
This ray of hope gave a glimpse of the degree of accuracy attainable. In this connexion the experiment confirmed infinitely more than the boldest imagination could ever have dreamed. A yellow line was detected in the spectrum of sodium. And it was found experimentally that the three-millionth part of a thousandth of a gramme of a sodium salt is sufficient to produce this sodium line in the spectrum of a Bunsen burner. There commenced a dizzying passage in the Calculus of Probabilities for, since it was found that in the sun's atmosphere hydrogen, carbon, iron, aluminium, calcium, sodium, nickel, chromium, zinc, and copper were present, the question arose as to how great was the possibility of an error in this observation. Kirchhoff calculated it as a chance of a trillion to one that these substances are actually present in the sun !
Never before had an experiment verified to such an extreme degree a discoverer's idea. It seems appropriate at this stage to deal with a doctrine which seeks to shed light into the deepest recesses of the connexion between experiment and discovery. It teaches that an experimentum crucis, an experiment that verifies absolutely, is impossible in physics. That is to say, every idea of a discoverer involves a hypothesis, and, however the experiment that follows may turn out, there still remains the possibility that this hypothesis was false, and may later have to make way for another essentially contradictory hypothesis which will be valid again only for a limited time.
The chief exponent of this theory is the eminent scholar, Pierre Duhem, Membre de l'Institut. He draws a parallel between experiment and mathematical proof, particularly with the indirect, apagogic form which has been so successfully applied in Euclidean geometry. In this method it is assumed that a certain statement is erroneous ; it is then shown that it leads to an obvious contradiction ; consequently the statement was correct provided that a certain doubt be excluded. Thus in the domain of mathematics we have a real experimentum crucis.
In accordance with this, Duhem tests the validity of two physical theories, both of which were put forward and claimed as discoveries. Newton had discovered the nature of light to consist in "emission" ; to him, as well as to Laplace and Biot, light consists of projectiles that are emitted with very great velocity. The discovery of Huyghens, supported by Young and Fresnel, substitutes wave-motion in place of corpuscular emission. Hence, according to Duhem, we have, or we had, here two hypotheses which appear to be the only ones possible. Experiment was to pronounce a judgment, and at first it decided irrefutably in favour of the wave-theory. Therefore, the discovery of Huyghens is alone true, and that of Newton is shown to be an error ; there is no third outlet, and so we have quite certainly an experimentum crucis before us.
The term itself originates in Bacon's Novum Organum. Contrary to Duhem's assumption, it does not refer to a signpost at cross-roads giving various routes, nor is it connected with croix ou pile, "heads or tails". Experimentum crucis denotes rather a divine judgment at the cross, that is a test that is absolutely decisive and beyond further appeal. But no ! adds Duhem, while there is no room for a third judgment in the case of two contradictory statements in geometry, there is between two contradictory statements in physics. And, in fact, this third possibility has manifested itself in the discovery of Maxwell, who has shown that the nature of light is founded on a process of periodic electromagnetic disturbances.
Hence, so concludes Duhem, experiment can never decide whether a certain theory is alone valid. The physicist is never certain that he has exhausted all conceivable possibilities of thought. The truth of a physical statement, the validity of a discovery, cannot be confirmed by any experimentum crucis.
According to this argument, therefore, it is also possible that the scientific grounds of spectral analysis do not conform to truth. A contradictory hypothesis may, indeed, be set up, with the result that the same experiments that had led Kirchhoff' s discovery from one triumph to another would have to be interpreted in a totally different sense.
I must frankly confess that I cannot subscribe to such an extreme eventuality, since, in my opinion, Duhem's analogy with mathematics excludes this possibility. For if a certain probability is expressed by a trillion to one, then I venture to state that even in the case of mathematical truths certainty reaches no higher degree of probability. From the history of mathematics we know of theorems which were enunciated and provided with complete proofs, and yet did not succeed in establishing themselves ; hence we see that, however evident a mathematical theorem may be, it is still only a matter of very great probability.
If, following our usual habits of thought, we take this for absolute certainty, then we may also consider the sum-total of experiments in the realm of spectral analysis to be a great experimentum crucis for the correctness of the theory itself.
["Cournot's Principle" asserts that an event is completely certain if it is "morally certain", that is, if its non-occurence is so rare as never actually to be observed. This is one of the cornerstones of modern science, and yet, as the unfamiliarity of its name will already have suggested to many readers, it is not much discussed. The reason, of course, is that it contains an embarrassing problem: where does one place the threshold? Moszkowski's "trillion-to-one" odds may seem intuitively reasonable, but why?]
Far removed from it, and yet connected with it, there is the "Periodic System of the Elements," the discovery of Mendeleef and Lothar Meyer. It, too, offered prophetic glances into the future, foretold the unknown, hinted at things that were present only in imagination in a scheme of thought that assigned definite places of existence to undiscovered things.
The Periodic System is represented by a table containing vertical and horizontal rows, in the squares of which the elements are entered according to certain rules depending on their atomic weights. The discovery consisted theoretically in stating that the physical and chemical properties of each element is the arithmetic mean between the properties of its horizontal and vertical neighbours. This gave rise to predictions concerning the unoccupied squares. These gaps, these blank spaces in the table, seem to say prophetically : There are elements missing here that must be discoverable. The neighbours will betray them, and the empty space itself shows by what means they are to be found. With the shrewdness of a detective, Mendeleef was able to say : There must be elements of the atomic weights 44, 70, and 72 ; we do not know them yet, but we are in a position to determine the properties of these foundlings of the future, and, what is more, the properties of their compounds with other elements. Later researches, which led to the discovery of the elements. Scandium, Gallium, and Germanium, have actually confirmed all these predicted properties.
The metal Gallium was discovered in 1875 by spectroscopic means. Its properties are the mean of those of Aluminium and Indium, and this places it in a position which had already been assigned to it in the periodic table before its discovery ; for, owing to a gap in the system, Mendeleef had asserted its existence five years previously, although he then knew nothing of its characteristic spectral signs, namely, two beautiful violet lines.
Radium, too, which was discovered in 1900 and was found to have the atomic weight 226, completely satisfied this test and fitted exactly into the place which this number reserved for it in the table. Thus prediction and confirmatory discovery were fully congruent in this case ; the experiment followed on the visionary insight just as a Euclidean proof follows on a mathematical assertion, and we have every reason to say that the system of Mendeleef and Lothar Meyer has stood the crucial test. Future hypotheses will perhaps supplement the system or enlarge our knowledge of it, but will certainly not reduce it ad absurdum.
Apart from these cases, there are achievements by men who may be called lucky discoverers, although they displayed no genius for finding nor for creating. The philosopher-physicist, Ernst Mach, has devoted a lecture to such intellects, which seems to me very valuable, if only for the reason that he traces back the conceptions of discovery and invention to one common root of knowledge, and explains their difference as being due only to a difference in the application of this discovery.
But when Ernst Mach in this lecture, "On the Influence of Accidental Circumstances on the Development of Inventions and Discoveries," extends the influence of chance to include accidental circumstances that can only enter when the discoverer is closely attentive, it seems to me that certain limitations are advisable. Otherwise, if we pursue Mach's line of thought to its extreme, we could declare every discovery to be due to chance, and this would be the end of the intuitive-creative idea. This assertion would ultimately mean that genius owes its achievements to the accidental arrangement of the molecules in the brain-cells of its associated body. This would be just as wrong as saying that chess is a game of chance because we lose a game when, by chance, we come up against a better player.
Huyghens, the great discoverer and inventor, says, in his Dioptrica, that he would have to consider anyone who invented the telescope without the favourable intervention of chance to be a superhuman genius. Why should he choose just the telescope ? To many the invention of the Differential Calculus will appear grander and due to a higher degree of ingenuity. And since it was produced quite methodically, and since chance was excluded, we may follow Huyghens and with good reason proclaim its authors superhuman geniuses.
Many a true inspiration is dependent on some impulse from without. Who discovered Electromagnetism ? The world-echo answers, "Oersted," with the same confidence that it couples together the names America and Columbus. This shows how enormously important was the achievement. Next to steam-power nothing has exerted such a revolutionary influence in all branches as electromagnetism. Without it, the world of to-day would present a totally different aspect. Without it, we should have no dynamos, no electric trams, no telegraphy, no electric-power stations, all of which are due to the work of Arago, Gay-Lussac, Ampere, Faraday, Gramme, and Siemens. Without it, there would be none of the abundance of brilliant discoveries that are associated with the names of Maxwell, Hertz, and Einstein. The fact that physics used to be divided into three parts --- Mechanics, Optics, Electrodynamics --- and that, since then, the coherent unity of the physical picture of the world has been developed, shows us a picture in the background of which we see the illuminating figure of Hans Christian Oersted.
It must not be overlooked, however, that in the case of his great discovery, too, chance played a definite part. It occurred one day when Oersted was holding a lecture in the winter of 1819-20 ; a magnetic needle situated near his Volta-battery began to vibrate irregularly. This apparently unimportant trembling of the metal points contained the key to a fact, the whole consequences of which could in no conceivable way have entered the mind of this observer of a hundred years ago, in spite of the genius of the Danish scientist, which is documented in the classical and far-famed dissertation, Experimenta circa effectum conflictus electrici in Acum magneticara, which appeared in July 1820. It cleared the way for intuitions that were equally as fruitful for theory as for practice.
Thirteen years after this initial discovery the world saw the first very important consequence in Gauss' and Weber's electric telegraph, and a little later the eminent discoverer Fechner, in Leipzig, proclaimed it as his conviction that, within two years, electromagnetism would entirely reform the world of machines, and would entirely supersede steam- and water-power. Of course, his time estimate fell far short of the mark. It has been reserved for the present generation to realize that we live in an electromagnetic world, and that we have, theoretically and practically, to spend our life electromagnet ically. The first indication of this knowledge hung upon the quivering point of a magnetic needle, and from it there evolved the electromagnetic ideas that we are so fond of picturing as our handmaids, but which, in reality, are sovereign over us all.
A great deal of the history of discovery must be revised and corrected. The Spiral of Archimedes is not due to Archimedes, nor Marriotte's Law to Marriotte, nor Cardan's formula to Cardan, nor Crookes' Tube to Crookes, and Galvanism is only related to Galvani by the following anecdote:
It arose from an accidental experience of Madame Galvani in the kitchen : a half-skinned frog that was to be fried for the evening meal happened to rest between a scalpel and a tin plate, which brought it into metallic contact with an accidental discharge of electricity ; the frog twitched ; the head of the house gave a very naïve interpretation to the phenomenon ; and it was under such auspices that Galvanism made its entry into the world. It would be a futile task to endeavour to trace the connexion between experiment and the underlying idea, which, in this case, first came to fife in Alexander Volta. What would have remained a mere frog-dance if left to Galvani now acquired the rank of a discovery through the work of a thinking physicist, who set up a "Voltaic series" ; this discovery then assumed power and dignity in the hands of Nicholson, Davy, Thomson, Helmholtz, and Nernst. The words Galvanic Electricity should be made to give way entirely to Voltaic Electricity, as in the case of many another expression for which chance and insufficient thought have stood sponsor.
It often happens that experiment acts as a corrective of the underlying idea, neither confirming nor contradicting, but nursing it, as it were, strengthening, and purging it of errors. Such experiments, partly in conjunction with chance, play an important, sometimes a decisive, role in the works of Dufay, Bradley, Foucault, Fresnel, Fraunhofer, and Röntgen. Faraday, who was incapable of observing otherwise than intensively, found himself compelled, whilst studying induction phenomena, to alter his initial view, and it is just this correction by experiment that constitutes Faraday's real discovery. In many cases the initial idea is corrected, nay surpassed, by the result. Columbus worked methodically when he set out to reach the East Indies by travelling westwards ; but what he discovered was not a confirmation of his nautical idea only, but something much greater, which certainly did not lie in his calculation. Thus he became the archetype of all searchers, who had thought out and anticipated essentially different conditions from those that were afterwards discovered to be prevalent. Among these are to be counted Priestley and Cavendish, who clung to the erroneous notion of phlogiston, even when they had the evidence to the contrary in the elements they had themselves discovered, namely, oxygen and hydrogen. Graham Bell, the inventor, was seeking something quite different from what he later hit on : as a teacher of the deaf and dumb he was trying to give a visual picture of sounds, in order to make clear the formation of sounds to his pupils ; this led him to construct an electrical apparatus, which finally led to the discovery of the telephone.
The truest and sharpest contrast with the experimentum crucis is furnished by experiment when it shows the exact opposite of what the explorer was expecting. But since an absolute No entails a very decisive Yes --- namely, in this case, the affirmation of a relationship that was previously held to be impossible --- a negative experiment of this kind, when it occurs, will be followed by momentous consequences ; these will be the more important in proportion as the question, the affirmation of which was expected by the physicist, is of a fundamental character.
The experiments of Michelson and Morley, directed at proving the existence of the ether, are to be regarded as the true classical instances of these experiments answering with an overwhelming negative. Their first effect was to produce a sense of helplessness, a check to thought, a void in the chamber of ideas. And to fill this void there arose new views of the world in which we nowadays recognize the true thought-pictures of the universe. The great names --- Lorentz, Minkowski, Albert Einstein --- shone out !
As there are forerunners for almost every important event, so also in the case of the experimentum crucis of Michelson and Morley. Henri Poincaré, the famous mathematician, whilst still a student of the École Polytechnique, had initiated experiments with his fellow-student Favé, which followed the same object. The Michelson-Morley experiment was at least a hundred times more accurate. In each case the conclusion was that the laws of optics are not disturbed by a motion of translation, such as that of the earth through space; this is, however, contrary to what the old physical ideas lead us to expect.
If we assume the existence of a space-filling ether, the earth, owing to its own velocity of nineteen miles per second, would have to pass through a hurricane just as in the case of travellers sitting in an open train rushing along at very great speed. If we send out light rays in all directions simultaneously from any point on the earth's surface, some will travel in the teeth of the ether-storm, others will experience only a part of the storm's power ; so that of two hght-rays travelling in exactly opposite directions the retardation of the one should be equal to the acceleration of the other ; and yet they are not quite equal, for a simple calculation shows that in every case the retardation is slightly more than the acceleration.
This may be made clear by means of a model of easy construction, or, better still, by considering a ship that is subject to a constant current and, simultaneously, to a pressure of the wind. The time taken by the boat in making a trip up and down stream can never be the same for the cases when the wind is in the direction of the current, and vice versa.
In the case of the ray of light, which is sent backwards and forwards by means of a contrivance of mirrors, this fact should be clearly demonstrated by means of the interference-fringes, which are able to show much smaller effects than the experiment demands. The experimental oracle was to speak, but it remained silent. This portentous silence signified : no interference-effect, no action of the ether-current, no influence due to translation --- nothing !
This "nothing" compelled a decision of a very startling kind, for the result of this experiment was in direct contradiction to another famous experiment. Fizeau had proved that the ether is practically rigid and remains fixed in interstellar space. A decision had to be taken in favour of Fizeau or Michelson and Morley. Yet this was impossible, for both had operated with unsurpassable accuracy. It was impossible to reconcile both views as they were diametrically opposed. This contradiction remains, even if we assume a different hypothesis, not involving the ether, for Fizeau's experiment. A solution was impossible without undertaking revolutionary changes in the whole of physical thought.
This radical change was effected by Einstein ; and this mysterious contradiction disappeared in the resulting revolution of thought. Einstein supplanted the absolute time-conception by a new relative conception, and thus the perplexing problem disappeared. Two great principles arose as regulative factors in thought, and wherever these were applied, they achieved wonders : one was the new conception of time that deprived the earth of her unique position as the sovereign of time by the introduction of the principle that the rate at which time elapses is different in media moving at different speeds ; the other is the principle of the constancy of the velocity of light.
One feels a temptation to apply a mythical allegory : just as the world, according to the Biblical story, originated from nothing, so there arose from the "nothing " of the Michelson-Morley experiment a new world, a world of knowledge, a cosmos of thought, in which perfect harmony reigns.
Its truth was contained in itself before the experimental proof was furnished. And this realization of truth has become a fact in the experimentum crucis for which the sun and stars formed the material. This will be discussed in another part of the book.
"The really important factor is ultimately intuition," Einstein had said to me. It made me think of Huyghens' remark about the genius who would have been able to create the telescope without the help of chance. Was not this intellect, imagined by Huyghens, sitting opposite me at that moment ? An inner voice answered in the affirmative, for Einstein's thought-complex seemed to me at that moment a kind of telescope for the human mind, a telescope that had arisen out of pure intuition, and whose range stretched to the limits of the universe