November, 1896.
XIV
SOME CRANKS AND THEIR CROTCHETS
"Now, by two-headed Janus,
Nature hath framed strange fellows in her time!"
Merchant of Venice, I. i.
About five-and-twenty years ago, when I was assistant librarian at Harvard University, much of my time was occupied in revising and bringing toward completion the gigantic pair of twin catalogues—of authors and subjects—which my predecessor, Dr. Ezra Abbot, had started in 1861. Twins they were in simultaneity of birth, but not in likeness of growth. Naturally, the classified catalogue was much bigger than its brother, filled more drawers, cost more money, and made a vast deal more trouble. For while some books were easy enough to classify, others were not at all easy, and sometimes curious questions would arise.
One day, for example, I happened to be looking at a pamphlet on the value of Pi; and, should any of my readers ask what that might mean, I should answer that Pi (pi ) is the Greek letter which geometers use to denote the ratio of the circumference of a circle to its diameter. The arithmetical value of this symbol is 3.1415926536, and so on in an endless fraction. Is it not hard to see what there can be in such an innocent decimal to irritate human beings and destroy their peace of mind? Yet so it is. Many a human life has been wrecked upon Pi. To a certain class of our fellow-creatures its existence is maddening. It interferes with the success of a little scheme on which they have set their hearts,—nothing less than to construct a square which shall be exactly equivalent in dimensions to a given circle. Nobody has ever done such a thing, for it cannot be done. But when mathematicians tell these poor people that such is the case, they howl with rage, and, dipping their pens in gall, write book after book bristling with figures to prove that they have "squared the circle." The Harvard library does not buy such books, but it accepts all manner of gifts, and has thus come to contain some queer things.
When I consulted the subject catalogue, to see under what head it had been customary to classify these lucubrations on Pi, I found, sure enough, that it was Mathematics § Circle-Squaring. Following this cue, I explored the drawers in other directions, and found books on "perpetual motion" formed a section under Physics, while crazy interpretations of the book of Daniel were grouped along with works of solid Biblical scholarship by such eminent writers as Reuss and Kuenen and Cheyne. Clearly, here was a case for reform. The principle of classification was faulty. In one sense, the treatment of the quadrature of the circle may be regarded as a section under the general head of mathematics; as, for example, when Lindemann, in 1882, showed that Pi cannot be represented as the root of any algebraic equation with rational coefficients. But our circle-squaring literature is very different. It is usually written by persons whose mathematical horizon scarcely extends beyond long division: just as the writers on perpetual motion know nothing of physics; just as so many expositors have dealt with the ten-horned beast in blissful ignorance alike of ancient history and of the principles of literary criticism. What all such books illustrate, however various may be their ostensible themes, is the pathology of the human mind. They are specimens of Insane Literature. As such they have a certain sort of interest; and to any rational being it is the only sort they can have.