Perhaps, I allowed myself to interject, a more violent suspicion against the word "hypotheses" was prevalent with scholars in Newton's time than now. Newton's emphatic defence would then appear a shade more intelligible. Or did he cherish the belief that his world-law was the only possible one in Nature?
Einstein again referred to the universality of Newton's genius, saying that Newton was doubtless aware of the range within which his law was valid: this law applies to the realm of observation and experience, but is not given a priori, no more than Galilei's Law of Inertia. It is certainly conceivable that beyond the domain of human experience there may be an undiscoverable universe in which a different fundamental law holds, and one which, nevertheless, does not contradict the principle of sufficient reason.
The antithesis: Simplicity—Complexity, led the conversation into a short bypath; it arose out of an example which I quoted and that I shall repeat here even if it may seem irrelevant.
One might well expect that just as for attraction there must be a general law for resistance or repulsion. And if attraction occurs according to the inverse square of the distance, then it would be an extremely interesting parallel if a similar law were to hold for repulsion except that the proportionality were direct instead of inverse. There have actually been physicists who have proclaimed a direct square law of repulsion; I have heard it in lectures myself. The action of a resisting medium, as, for example, the resistance of the air to the flight of a cannon-ball, is stated to be proportional to the square of the velocity of the projectile.
This theorem is wrong. If it were correct, and verified by experiment, we should have to regard it as being presumably the only possible and directly evident form of the law of repulsion or resistance. There would, at least, be no logical reason for contradicting it.
But here we have a mixed relationship, as Einstein calls it—that is, we are unable to express an exact connexion between the velocity of a body in flight and the air resistance.
This fallacious assumption by no means proceeded from illogical reasoning, and it seemed to rest on a sound physical basis. For, so it was argued, if the velocity is doubled, there is twice as much air to be displaced, so that the resistance will be four times as great. But this was contradicted outright by experimental evidence. One cannot even call it an approximate law, except for very low speeds. For greater speeds we find, instead of a quadratic relation, a cubical one, or one of a more complex nature. Photographs have demonstrated that the resistance experienced by a projectile in flight is due to the excitation of a powerful central wave, to the friction between the air and the surface of the projectile, and to eddies produced behind the projectile—that is, to various conjoined factors, each of which follows a different law, and such that the combined effect cannot be expressed by a simple formula at all. This phenomenon is thus very complicated and offers almost insuperable difficulties to analysis. A beautiful remark was once made, which characterizes such events in Nature.
During a conversation with Laplace, Fresnel said that Nature does not worry about analytical difficulties. There is nothing simpler than Newton's Law in spite of the complicated nature of planetary motions. "Nature here despises our analytical difficulties," said Fresnel; "she applies simple means, and then by combining them produces an almost inextricable net of confusion. Simplicity lies concealed in this chaos, and it is only for us to discover it!" But this simplicity when it is discovered is not always found to be expressible in simple formulae, not must it be forgotten that even the ultimate discoverable simplicity points to certain hypothetical assumptions.
"Hypotheses non fingo!" This phrase of Newton's remains true, if we maintain Einstein's interpretation: "He did not wish to go further back in his analysis of causes than was absolutely inevitable." It interested me to pursue this line of thought suggested by Einstein still further, and I discovered that these words of Newton had actually been falsely accentuated and hence misinterpreted by many authorities on science. Even Mill and the great scholar, William Whewell, succumbed to this misunderstanding. Credit must be given to a more modern scholar, Professor Vaihinger of Halle, for being sufficiently keen of hearing to detect the true accentuation; and now that Einstein has corroborated fully this explanation, doubts as to the true sense of the words are no longer to be feared.
The trend of our talk brought us to a discussion of the conception, "law of nature." Einstein recalled Mach's remarks, and indicated that the point was to determine how much we read out of Nature; and these observations made at least one thing clear, namely, that every law signifies some limitation; in the case of human laws, expressed in the civil and penal code, the limitation affects the will, and possible actions, whereas natural laws signify the limitations which we, taught by experience, prescribe to our expectations. Nevertheless, the conception remains elastic, for the question will always intrude itself: What does prescription mean? Who prescribes? Kant has assigned to Man the foremost position inasmuch as it is he who is regarded by Kant as prescribing laws to Nature. Bacon of Verulam emphasizes the ambiguous point of view by asserting: "Natura non vincitur nisi parendo," Man conquers Nature only by obeying her, that is, by conforming to her immanent norms. Thus the laws exist without us, and we have only to discover them. When they have been found, Man can react by applying them to subdue Nature. Man becomes the dictator and dictates to Nature the laws according to which she for her part has to subjugate mankind. Whether we adopt the one view or the other, there is a vicious circle, from which there is no escape. A law is a creation of intellect, and Mephisto's words remain true: "In the end we depend on the creatures of our own making!"