Non-Euclidean Mathematics and Fiction

Notes on Recently Published Books

EDMUND WILSON

EINSTEIN'S lectures on The Meaning of Relativity published by the Princeton University Press are almost completely incomprehensible to a non-mathematical reader. The book to read is his Relativity, published two or three years ago by Holt. Here Einstein provides an abstract of his theory' with as few mathematical and physical formulae as possible, and communicates to us some of the exhilaration of moving in the high breathless regions of thought, where, not only, as in Dante's Paradise, do we apprehend without the aid of the senses, but where we arrive, through calculation, at conclusions which are not even capable of being imagined—like Einstein's universe, which manages to be both finite and unbounded.

Unimaginable, at least, by anyone except the Einsteins—except the builders of the crystal ladder beyond the needs and the images of the earth. Yet in another fifty years Einstein's abstruse physics and his non-Euclidcan geometry will no doubt be taught in the schools; all ideas become common property, provided someone has had the intellectual energy to conceive them: it is not that ideas are difficult to grasp, but that men will not think for themselves; the people we call intellectuals are usually people who are merely familiar with other peopie's ideas and the one thing that man is most reluctant to do is reason beyond the exigencies of his environment. I am told by the philosophers that it is less a question of Einstein's theories being.difficult in themselves to follow than of the scholastic world's being untrained in the physics which enables him to arrive at them.

So the Greeks, who invented geometry and carried several branches of it to completion (see Mr. David Eugene Smith's admirable little history of Ancient Mathematics recently published by Marshall Jones in the Our Debt to Greece and Rome series), and who in their treatment of certain geometrical problems provided the germs which the Arabs afterwards elaborated into algebra, never discovered algebra themselves because its peculiar abstractions lay outside their intellectual vision, which was based, as the name of their great science, geometry, indicates, on the more practical problems which had their rise in the measurement of the earth, The minus quantities and negative roots which are now the commonplaces of algebra would have seemed as queer and as inaccessible to a second century student of Euclid as Einstein's conception of a curvature in space does to a contemporary student of physics. Our intellectual processes, whatever we may flatter ourselves by thinking, arc pretty narrowly limited to what we have been taught at school and to what we have found it absolutely necessary to make the effort to compass for ourselves in order to adjust ourselves to our surroundings and to survive among our neighbors.

Fiction vs. Mathematics

IN any case, mathematics and physics seem to have become by far the most exciting of the forms of creative activity which find their expression in printed books. Poetry has practically expired (since the modern world no longer inspires thc emotions which arc proper to poetry); history and criticism are not going very strong; and I have even of late been having disquieting doubts about the great modern literary form of the novel. These doubts, I confess with regret, have recently been raised anew by reading Mr. Waldo Frank's Holiday (Boni and Liveright). Mr. Frank seems to have arrived on the literary scene at an unfortunate period for a noveliest. Looking about him, he sees that the novel is tending to become a more or less stereotyped species of journalism and, being of rather a serious turn of mind, Mr. Frank is naturally reluctant to write an ordinary novel. On the other hand, he has a curiosity about character and a taste for telling a story. So what does he do? He tries to transmogrify the old-fashioned fiction by presenting it in a novel manner—by ornamenting it with all the jagged graces of the painting of Picasso and Braque. The house does not stand on the hill in the novels of Mr. Frank: it drags the hill up by the roots and explodes into a thousand splinters; a man does not make a remark: he gives vent to a hurricane of flint. It is not that, under certain circumstances, a remark or a house might not conceivably be likened to these things; it is that Mr. Frank has overintensified everything. His landscapes never have a moment's quiet; one of his characters cannot walk down the street without shaking the language like an El train. And the story which occasions this terrific literary vibration is certainly no titan in itself. It is a simple melodrama of the race problem—The Birth of a Nation upside down,

I do not know if anybody will attempt to justify Mr. Frank by an analogy with certain phases of Mr. Joyce's Ulysses. If he does, I should consider him illadvised for the following reasons: In the first place, Mr. Joyce's constant effort is to make the manner fit the matter; his eccentricities arise in the attempt to meet some emergency; he is not straining a tout propos like Mr. Frank; in a word, he is not precious. In the second place, the great thing about Joyce is his magnificent grasp of his characters; they are never sentimentalized or simplified; we see them as we see real living entities; they survive and very far overshadow any tricks which he can play in presenting them. But Mr. Frank's have a slightly flimsy look— rather as if they had been cut out of pasteboard and painted with a box of colors, I have even read a story by him which, but for its recherche manner, might well have been written by O. Henry.

I state all this with some pain because Mr. Frank has the sensitivity of an artist and has the courage of his sensitivity and what we miss in the perusal of his works we may gain in the dignity of his exampic. Nonetheless, after the clashing colors and the warring juices of Holiday, I can, as I hinted earlier, think of nothing I should like better than a nice cool quadratic equation. I am sure that it is more beautiful and it would appear, just now, to be up to something more interesting,

Speaking of Euclid, as I was above, Mr. E. M. Forster's Pharos and Pharillon (Knopf) is a charming, lively and witty book on ancient and modern Alexandria. Though one identifies very early the slight touch of Mr. Lytton Strachey which seems to have become inevitable nowadays in biography or history, Mr. Forster has a brilliance and distinction which arc unmistakably his own. I don't know that there is any English writer living who could better such perfectly aimed strokes as the following: "Hardness and poverty edged it (the Western Harbor of Alexandria) as they do today, and Christianity had settled here early, as she settled on all spots where the antique civilization had failed to make men dignified." " But what impresses us most in the scene is the quiet persistence of the earth. . . . Year after year . . . she has covered the Mareotic civilization with dust and raised flowers from its shards, Will she do the same to our own tins and barbed wire? Probably not, for man has now got so far ahead of other forms of life that he will scarcely permit the flowers to grow over his works again. His old tins will be buried under new tins. This is the triumph of civilization. . ."