“The concepts of modern mathematics project the individual out of the world of reality into a pure fiction of thought, and lead to what Einstein calls the most degenerate form of imagination—pathological individualism. Silberstein, for instance, argues the possibility of five- and six-dimensional space, and speculates on one’s ability to see an event before it happens. The conclusions contingent on the conception of Flammarion’s Lumen—a fictive person who travels faster than the velocity of light and is therefore able to experience time extending in a reverse direction—are in themselves enough to distort any natural and sane point of view.[32] But there is another conceptual Homunculus even weirder than Lumen from the standpoint of rational thinking. This hypothetical creature can traverse all worlds at once with infinite velocity, so that he is able to behold all human history at a glance. From Alpha Centauri he can see the earth as it was four years ago; from the Milky Way he can see it as it was 4,000 years ago; and he can also choose a point in space where he can witness the ice-age and the present day simultaneously! . . .”
Vance settled himself more deeply in his chair.
“Toying with the simple idea of infinity is enough to unhinge the average man’s mind. But what of the well-known proposition of modern physics that we cannot take a straight and ever-advancing path into space without returning to our point of departure? This proposition holds, in brief, that we may go straight to Sirius and a million times further without changing direction, but we can never leave the universe: we at last return to our starting-point from the opposite direction! Would you say, Markham, that this idea is conducive to what we quaintly call normal thinking? But however paradoxical and incomprehensible it may seem, it is almost rudiment’ry when compared with other theorems advanced by mathematical physics. Consider, for example, what is called the problem of the twins. One of two twins starts to Arcturus at birth—that is, with accelerated motion in a gravitational field—and, on returning, discovers that he is much younger than his brother. If, on the other hand, we assume that the motion of the twins is Galilean and that they are therefore travelling with uniform motion relative to each other, then each twin will find that his brother is younger than himself! . . .
“These are not paradoxes of logic, Markham: they’re only paradoxes of feeling. Mathematics accounts for them logically and scientifically.[33] The point I’m trying to make is that things which seem inconsistent and even absurd to the lay mind, are commonplaces to the mathematical intelligence. A mathematico-physicist like Einstein announces that the diameter of space—of space, mind you—is 100,000,000 light-years, or 700 trillion miles; and considers the calculation abecedarian. When we ask what is beyond this diameter, the answer is: ‘There is no beyond: these limitations include everything.’ To wit, infinity is finite! Or, as the scientist would say, space is unbounded but finite.—Let your mind meditate on this idea for half an hour, Markham, and you’ll have a sensation that you’re going mad.”
He paused to light a cigarette.
“Space and matter—that’s the mathematician’s speculative territ’ry. Eddington conceives matter as a characteristic of space—a bump in nothingness; whereas Weil conceives space as a characteristic of matter,—to him empty space is meaningless. Thus Kant’s noumenon and phenomenon become interchangeable; and even philosophy loses all significance. But when we come to the mathematical conceptions of finite space all rational laws are abrogated. De Sitter’s conception of the shape of space is globular, or spherical. Einstein’s space is cylindrical; and matter approaches zero at the periphery, or ‘border condition.’ Weyl’s space, based on Mach’s mechanics, is saddle-shaped. . . . Now, what becomes of nature, of the world we live in, of human existence, when we weigh them against such conceptions? Eddington suggests the conclusion that there are no natural laws—namely, that nature is not amenable to the law of sufficient reason. Alas, poor Schopenhauer![34] And Bertrand Russell sums up the inevitable results of modern physics by suggesting that matter is to be interpreted merely as a group of occurrences, and that matter itself need not be existent! . . . Do you see what it all leads to? If the world is non-causative and non-existent, what is a mere human life?—or the life of a nation?—or, for that matter, existence itself? . . .”
Vance looked up, and Markham nodded dubiously.
“So far I follow you, of course,” he said. “But your point seems vague—not to say esoteric.”
“Is it surprising,” asked Vance, “that a man dealing in such colossal, incommensurable concepts, wherein the individuals of human society are infinitesimal, might in time lose all sense of relative values on earth, and come to have an enormous contempt for human life? The comparatively insignificant affairs of this world would then become mere petty intrusions on the macrocosmos of his mental consciousness. Inevitably such a man’s attitude would become cynical. In his heart he would scoff at all human values, and sneer at the littleness of the visual things about him. Perhaps there would be a sadistic element in his attitude; for cynicism is a form of sadism. . . .”
“But deliberate, planned murder!” objected Markham.