Einstein, the searcher

by Alexander Moszkowski

CHAPTER VII
PROBLEMS

Questions of the Future.—Problem of Three Bodies.—Conception of Approximation.—Object of Mechanics.—Simplicity of Description.—Limits of Proof.—Reflections about the Circle.—From the History of Errors.—Causalities.—Relativity on a Physiological Basis.—Physicists as Philosophers.

WE spoke of the objects and problems of science in general, and touched on certain recurrent questions with which reputed men of science are confronted from time to time, so that we may ascertain their opinions about immediate as well as more remote aims, and about worthy objects and those within reach.

"Such stimuli," said Einstein, "may be quite interesting inasmuch as they sharpen the appetite of the public for the works of investigators, and give the latter the opportunity of making wider circles acquainted with their plans. Yet the value of their suggestions must not be overrated, when they are directed at giving trustworthy information about the future lines of development of science. Every scientist, in working out his own research, gravitates to particular points on the boundary which separates the known from the unknown, and becomes inclined to take his particular perspective from these points. It must not, however, be expected that these individual aspects will form a complete picture, and will indicate the only paths along which science can or will advance."

"May I suggest, Professor," I answered, "that we select certain answers that have been given to these recurrent questions for discussion? I have brought along a whole series of them; it would be of value to know what attitude you take up towards some of the statements that have been made about future possibilities."

Einstein acquiesced, and so I read out a number of expressions of opinion, given by eminent authorities, particularly in natural science and mathematics. They came under the heading, "The Future Revolution of Science." At the outset we encountered arguments by Bailhaud, the director of the Paris Observatory; he dealt with the so-called "Problem of Three Bodies," and with "The Finitude or Infinitude of the Universe."

Einstein elucidated these questions as follows. The celebrated Problem of Three Bodies is a special case of the general problem of Many Bodies, the object of which is to discover the exact paths of the heavenly bodies. If we suppose that the planets and the comets are subject only to the attraction of the central body, the sun, then their paths would be exactly those given by Kepler's Laws—that is, they would move about the central body, or, more precisely, about the common centre of gravity in perfectly elliptical orbits. The same result would happen if we regard the orbit of a moon to depend solely on its parent planet. But this assumption is not in agreement with reality, since all the bodies of our system are also subject to their mutual attraction depending on their masses and distances. Consequently we have the so-called disturbances, perturbations, and divergences from the ideal paths; and the problem of ascertaining these disturbances is essentially identical with the Problem of Three Bodies. Regarded from the point of view of pure mechanics, this problem may be considered solved in so far as we are able to write down the equations of motion. But, in addition to this purely mechanical process, there is a mathematical problem which has not been completely solved—that is to say, the integral expressions that occur in it can be calculated only approximately. This makes no difference to the practical calculation, since the degree of approximation, according to the present methods, may be carried as far as we wish. The error may be reduced to any desirable extent, so that it is probably wrong to expect new revelations on this point from future upheavals in physics. We read on and discovered that several of the scientists mentioned did not stop at expecting all advances of the future from pure theory. They had visions of an optimum of happiness, to gain which the increase of knowledge alone did not suffice. Thus the celebrated Swedish astrophysicist Svante Arrhenius had summarized his judgment in a few lines: "After the stupendous progress that has been made in the physical and chemical sciences in recent times, it seems to me that the moment has come for attacking the most important problems of mankind with full success, namely, those of biology, and in particular of the art of healing, with the weapons that are furnished by the arsenal of the exact sciences." And the mathematician, Emile Picard, Membre de l'Académie, expressed himself in still more hopeful terms: "There is no doubt but that the discoveries which the human race is awaiting with impatience are those that are seeking to eliminate sickness and the decrepitude of old age. Injections giving immunity against all diseases, an elixir of life (une eau de Jouvence) for persons of advancing age—these are the discoveries that are longed for by every one. There are also sciences that are to be termed 'moral,' from which we are impatiently expecting that guidance which will diminish the hate which seems to be increasing from day to day among the nations. That would be a splendid discovery."

"These are, indeed, noble and inspiring words," said I. "It shows how deeply rooted is the demand for ethical values in human nature, when even a mathematician, whose intellectual interests are directed primarily towards exact results, ranks the discoveries of ethics above all others."

Einstein answered: "We must carefully distinguish between what we wish for in general and what we have to investigate as belonging to the world of knowledge. The question under consideration is not one of wishes and feelings, but was unmistakably aimed at the advances and revolutions in the realm of science. It does not come within the scope of science at all to make moral discoveries! Its one aim is rather the Truth. Ethics is a science about moral values, but not a science to discover moral 'truths.' Ethics, conceived as a science in the usual way, can therefore serve to discover or to promote truth only indirectly. To illustrate my point of view I shall quote an example taken from a totally different field; it is merely to serve as an analogy. Let us consider the game of chess. Its value and its meaning is not to be sought in scientific factors, but in something entirely different, in a struggle which takes place according to definite rules. But even chess, inasmuch as it sharpens the intellect, may exhibit an indirect value for promoting truth. It may, for instance, suggest examples in permutations, which may contain mathematical, that is, purely scientific, truths. I certainly do not deny that there is an ethical factor in all genuine sciences. For being occupied with things for the sake of truth alone emancipates and ennobles the mind."

"This ennobling effect," I interposed, "should surely show itself in a moderation of the passions which were mentioned in the above expression of opinion. With Picard we should expect above all things to see a diminution in the feelings of hate between peoples, the tragic consequences of which we have experienced."