Einstein, the searcher

by Alexander Moszkowski

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

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

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

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

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

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

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

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

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

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