Einstein, the searcher

by Alexander Moszkowski

Einstein smiled, and, with a touch of sarcasm, said, "Hate is presumably a privilege of the 'cultured,' who have the time and the energy for it, and who are not the slaves of care." His tone indicated clearly that he used the generic term "cultured" to denote the Philistines of culture, its snobbish satellites, but not those whose intensive work aimed at increasing and deepening the fields of culture. In general he maintained his view that it is an illusion to expect "discoveries" in the realm of ethics, since every real discovery belonged alone to the sphere of truth in which the division only into right and wrong, not that into good and evil, holds good.

This led us to the old question of Pilate: What is Truth? In seeking an answer to this question Einstein first called special attention to the conception of "approximation," which plays a great part in the actual search for truth, inasmuch as every physical truth, expressed in measures and numbers, always leaves some remainder, that marks its distance from the unattainable truth of reality. This conception, which manifests itself so prominently in the relation of Einstein's own researches to the older, so-called classical, mechanics, will be developed here according to his line of thought as far as I can recollect from a number of conversations.

Let us suppose that we overhear two people arguing about the shape of the earth's surface. The one affirms that it is an unlimited plane, whilst the other maintains that it is a sphere. We should not hesitate a moment to say that the first is in error, and that the second gives the true answer. As long as the question was to be decided in favour of a "Plane or a Sphere," the sphere would represent the absolute truth. Yet it would be only relative, for these two statements are contradictory only between themselves, but will no longer be so if a third assertion is made which opposes a new alternative to "sphere."

If this alternative objection is actually raised, the third person would be quite justified in saying that the "sphere" explanation is wrong. For the conception "sphere" requires that all diameters be equal, whereas we know that they are not so, since the distance from pole to pole has been proved to be smaller than that between opposite points on the equator. The earth is an ellipsoid of rotation, and this truth is absolute in the face of the errors which are expressed by the terms, plane and sphere.

It would again have to be added that this absoluteness would stand only as long as this contradiction is regarded as being one between a definite sphere and a definite ellipsoid. If, as in the case of the earth, there are quite different diameters in the equatorial and the diametral planes, then there is complete contradiction between the two statements, and as the supporter of the ellipsoid is right, the one who supported the sphere must now give in, although he previously triumphed over his first opponent. His statement was true compared with the latter, but showed itself to be an error when compared with the statement of the third person.

This does not run counter to the laws of elementary logic. One of these, somewhat inadequately called the Law of Contradiction, states that two directly contrary statements—e.g. this figure is a circle, and this figure is not a circle—cannot both be true simultaneously. The truth of the one implies necessarily the falseness of the other. As this cannot be disputed, it follows in our case that we cannot have been confronted with contradictory judgments at all concerning the figure of the earth.

This is to be understood in a geometrical sense. The sphere does not entirely contradict the ellipsoid, since it is a limiting case of the latter: and the plane is likewise a limiting case of the sphere, as well as of the surface of ellipsoids.

But we are not concerned with purely geometrical considerations, for the earth is a definite body, and not a limiting configuration derived from abstraction. We are here dealing with measurable quantities, whose difference can be proved, and hence we must have one of the disputants proclaiming the absolute truth, whilst the other proclaims an absolute error. This, however, again is incompatible with our result that the second person is right in the one case and wrong in the other.

The logical Law of Contradiction overcomes the dilemma in the simplest way. None of these assertions contains the truth, hence none of these judgments allows the falseness of the others to be deduced. Only this may be said, that there is a fraction of truth in each judgment. The true shape of the earth is given by the plane to a first, the sphere to a second, the ellipsoid of rotation to a third, degree of approximation: we reserve the right of further approximations, each of which in succession approaches a higher degree of correctness, but none attains the absolute truth.

This reflection on a particular case may be generalized, and remains when we extend it to our attempts at grasping the states, changes, and occurrences of Nature. Whenever we talk of physical laws, we must bear in mind that we are dealing with human processes of thought, that are subjected to a succession of judgments, courts of appeal, as it were, excluding, however, a final court beyond which no appeal is possible. Each new experience in the course of natural phenomena may render necessary a new trial before a higher court, whose duty is then to give a more definite or different form to the law formulated by us, so as to attain a still higher degree of approximation to the truth.