“Our criminal is supersane, Markham. And his acts are not senseless: they’re hideously logical and precise. True, they have been conceived with a grim and terrible humor, with a tremendously cynical attitude; but within themselves they are exact and rational.”
Markham regarded Vance thoughtfully.
“How can you reconcile these Mother-Goose crimes with the mathematical mind?” he asked. “In what way can they be regarded as logical? To me they’re nightmares, unrelated to sanity.”
Vance settled himself deeper in his chair, and smoked for several minutes. Then he began an analysis of the case, which not only clarified the seeming madness of the crimes themselves, but brought all the events and the characters into a uniform focus. The accuracy of this analysis was brought home to us with tragic and overwhelming force before many days had passed.[30]
“In order to understand these crimes,” he began, “we must consider the stock-in-trade of the mathematician, for all his speculations and computations tend to emphasize the relative insignificance of this planet and the unimportance of human life.—Regard, first, the mere scope of the mathematician’s field. On the one hand he attempts to measure infinite space in terms of parsecs and light-years, and, on the other, to measure the electron which is so infinitely small that he has to invent the Rutherford unit—a millionth of a millimicron. His vision is one of transcendental perspectives, in which this earth and its people sink almost to the vanishing point. Some of the stars—such as Arcturus, Canopus and Betelgeuse—which he regards merely as minute and insignificant units, are many times more massive than our entire solar system. Shapleigh’s estimate of the diameter of the Milky Way is 300,000 light-years; yet we must place 10,000 Milky Ways together to get the diameter of the universe—which gives us a cubical content a thousand milliard times greater than the scope of astronomical observation. Or, to put it relatively in terms of mass:—the sun’s weight is 324,000 times greater than the weight of the earth; and the weight of the universe is postulated as that of a trillion[31]—a milliard times a milliard—suns. . . . Is it any wonder that workers in such stupendous magnitudes should sometimes lose all sense of earthly proportions?”
Vance made an insignificant gesture.
“But these are element’ry figures—the every-day facts of journeyman calculators. The higher mathematician goes vastly further. He deals in abstruse and apparently contradict’ry speculations which the average mind can not even grasp. He lives in a realm where time, as we know it, is without meaning save as a fiction of the brain, and becomes a fourth co-ordinate of three-dimensional space; where distance also is meaningless except for neighboring points, since there are an infinite number of shortest routes between any two given points; where the language of cause and effect becomes merely a convenient shorthand for explanat’ry purposes; where straight lines are non-existent and insusceptible of definition; where mass grows infinitely great when it reaches the velocity of light; where space itself is characterized by curvatures; where there are lower and higher orders of infinities; where the law of gravitation is abolished as an acting force and replaced by a characteristic of space—a conception that says, in effect, that the apple does not fall because it is attracted by the earth, but because it follows a geodesic, or world-line. . . .
“In this realm of the modern mathematician, curves exist without tangents. Neither Newton nor Leibnitz nor Bernoulli even dreamed of a continuous curve without a tangent—that is, a continuous function without a differential co-efficient. Indeed, no one is able to picture such a contradiction,—it lies beyond the power of imagination. And yet it is a commonplace of modern mathematics to work with curves that have no tangents.—Moreover, pi—that old friend of our school-days, which we regarded as immutable—is no longer a constant; and the ratio between diameter and circumference now varies according to whether one is measuring a circle at rest or a rotating circle. . . . Do I bore you?”
“Unquestionably,” retorted Markham. “But pray continue, provided your observations have an earthly direction.”
Vance sighed and shook his head hopelessly, but at once became serious again.