I was once shown a statement made by an eminent mathematician of Cambridge from which one would conclude that this mathematician thought that finite distances became infinite when they were great enough. In one of those splendidly printed books, bound in blue, published by the University Press, and sold at about a guinea as a guide to some advanced branch of pure mathematics, one may read, even in the second edition published in 1900, the words: "Representation [of a complex variable] on a plane is obviously more effective for points at a finite distance from the origin than for points at a very great distance." Plainly some of the points at a very great distance are at a _finite_ distance, for the same author mentions that Neumann's sphere for representing the positions of points on a plane "has the advantage ... of exhibiting the uniqueness of _z_ = [infinity symbol] as a value of the variable." CHAPTER XXXI THE MATHEMATICAL ATTAINMENTS OF TRISTRAM SHANDY Tristram Shandy[82] said that his father was sometimes a gainer by misfortune; for if the pleasure of haranguing about it was as ten, and the misfortune itself only as five, he gained "half in half," and was well off again as if the misfortune had never happened. Suppose that the unit (arbitrary) of pleasure is denoted by A, Tristram Shandy, by neglecting, in this ethical discussion, to introduce negative quantities (Kant's pamphlet advocating this introduction into philosophy was made subsequently[83]), apparently made 15A to result, and this can hardly be maintained to be the half of 10A. It is possible, however, that Tristram Shandy succeeded in proving the apparently paradoxical equation 15A = 5A by remarking that the axiom "the whole is greater than the part" does not always hold. This remark follows at once from what Mr. Russell[84] has called "The Paradox of Tristram Shandy." This paradox is described by Mr. Russell as follows: "Tristram Shandy, as we know, took two years writing the history of the first two days of his life, and lamented that, at this rate, material would accumulate faster than he could deal with it, so that he could never come to an end. Now I maintain that, if he had lived for ever, and not wearied of his task, then, even if his life had continued as eventfully as it began, no part of his biography would have remained unwritten."