.2.95 c^ Fantasia B'lh 'HI Mathematica *s Being a set of lilt 111 stories, together with a group ss 'iS I! Ill of oddments and diversions, all drawn from the - universe of mathe- mat i c s , As sembled and edited , with an introduction, by »«*m Clifton Fadiman A Fireside Book OTHER BOOKS BY CLIFTON FADIMAN BOOKS OF ESSAYS Any Number Can Play Party of One ANTHOLOGIES The American Treasury {with Charles Van Doren) Reading I've Liked FANTASIA mathematka BEING A SET OF STORIES, TOGETHER WITH A GROUP OF ODDMENTS AND DIVERSIONS, ALL DRAWN FROM THE UNIVERSE OF MATHEMATICS ASSEMBLED AND EDITED, WITH AN INTRODUCTION, BY CLIFTON FADIMAN A Fireside Book Published by SIMON AND SCHUSTER • NEW YORK COPYRIGHT © 1958 BY CLIFTON FADIMAN ALL RIGHTS RESERVED INCLUDING THE RIGHT OF REPRODUCTION IN WHOLE OR IN PART IN ANY FORM A FIRESIDE BOOK PUBLISHED BY SIMON AND SCHUSTER A GULF + WESTERN COMPANY ROCKEFELLER CENTER, 63O FIFTH AVENUE NEW YORK, N.Y. 10020 ISBN 0-671-24450-7 ISBN O-67I-2445I-5 PBK. LIBRARY OF CONGRESS CATALOG CARD NUMBER: 58-6269 MANUFACTURED IN THE UNITED STATES OF AMERICA 9 10 11 12 13 14 15 FOR Scott Buchanan, MOVER OF MINDS, WHO STARTED THIS CONTENTS Introduction by clifton fadiman xiii 1. ODD NUMBERS Young Archimedes by aldous huxley 3 The deeply moving classic about an Italian peasant boy who might have been a mathematical genius. Pythagoras and the Psychoanalyst by Arthur koestler 35 Why the Pythagorean theorem was never found. Mother and the Decimal Point by richard llewellyn 37 She tries to find out who is in charge of it. Jurgen Proves It by Mathematics by james branch cabell 40 He demonstrates for the beautiful Queen Dolores nine deeply penetrating propositions. Peter Learns Arithmetic by h. g. wells 46 How to be sure that 3 plus 4 always equal 7. Socrates and the Slave by plato 49 In which the Socratic method proves that an ignorant boy really knew all about the Pythagorean theorem all the time. All he had to do was remember it. Hie Death of Archimedes by karel capek 57 What really happened when that Roman centurion found the mathematician of Syracuse at work on circles. vii FANTASIA MATHEMATICA II. IMAGINARIES The Devil and Simon Flagg by Arthur porges 63 Mephisto in search of a mathematical truth. —And He Built a Crooked House by Robert a. heinlein 70 Adventures in fourth-dimensional architecture. Inflexible Logic by russell maloney 91 Remember those six chimpanzees with six typewriters . ? Well, here they start writing. No-Sided Professor by martin Gardner 99 What happens when a professor of topology is punctu- ated by a strip-tease act. Superiority by Arthur c. clarke no Showing how, in a war of the universe, it's the interior science that may win. The Mathematical Voodoo by h. nearing, jr. 121 How to make a mathematical genius by magic. Expedition by fredric brown 1 38 If you fill one spaceship with twenty-nine women and one man, how many . ? The Captured Cross-Section by miles j. breuer, m.d. 140 In which a young mathematician goes chasing his fiancee into the fourth dimension. A. Botts and the Moebius Strip by william hazlett upson 155 Showing how a simple demonstration in topology saved the lives of several Australian soldiers. God and the Machine by nigel balchin 171 On the relative inhumanity of electronic computers. The Tachypomp by edward page Mitchell 182 From 1873 comes a device for achieving infinite speed. The Island of Five Colors by martin Gardner 196 A tale in which five countries apparently really had com- mon borders—a topological impossibility. viii Contents The Last Magician by bruce elliott 211 . and how he faced a mathematical problem that Houdini was born too early to solve. A Subway Named Moebius by a. j. deutsch 222 In which a Harvard professor of mathematics is called upon to solve a mysterious disaster in Boston's under- ground transportation system. The Universal Library by kurd lasswitz 2 37 If every book that could possibly be printed in one language were aligned in a row, how long would it take to walk past them? Postscript to 'The Universal Library" by willy ley 244 In which the translator of the previous story gives not only the history of the problem but other solutions as well. John Jones's Dollar by harry Stephen keeler 248 Showing how universal socialism was attained through a simple problem in sixth-grade arithmetic. III. FRACTIONS A New Ballad of Sir Patrick Spens by 261 ARTHUR T. QUHXER-COUCH The Unfortunate Topologist by cyril kornbluth 266 There Once Was a Breathy Baboon ... by 267 SIR ARTHUR EDDINGTON Yet What Are All . by lewis carroll 268 Twinkle, Twinkle, Little Star by ralph barton 269 Mathematical Love by Andrew marvell 270 From The Definition of Love The Circle by Christopher morley 271 The Circle and the Square by thomas dekker 272 From The Honest Whore ix FANTASIA MATHEMATICA Euclid Alone Has Looked on Beauty Bare by 273 EDNA ST. VINCENT MILLAY Euclid by vachel lindsay 274 To Think That Two and Two Are Four by a. e. housman 275 The Uses of Mathematics by samuel butler 276 From Hudibras Arithmetic by carl sandburg 277 Threes (To Be Sung by Niels Bohr) by john atherton 278 Plane Geometry by emma rounds 279 He Thought He Saw Electrons Swift by Herbert dingle 281 Fearsome Fable by bruce elliott 282 Bertrand Russell's Dream by g. h. hardy 283 From A Mathematician's Apology For All Practical Purposes by c. Stanley ogilvy 284 From Through the Mathescope Eternity: A Nightmare by lewis carroll 285 From SyJvie and Biuno Concluded An Infinity of Guests by george gamow 286 From One, Two, Three . Infinity 00 by SIR ARTHUR EDDINGTON 287 From New Pathways in Science No Power on Earth by william whewell 288 (X -f 1 ) by EDGAR ALLAN POE 289 From James Russell Lowell The Receptive Bosom by edward shanks 290 Leinbach's Proof by Arthur schnitzler 291 From Flight into Darkness Problem from The New Yorker: "Talk of the Town" 292 Contents A Letter to Tennyson from Mathematical Gazette 293 A Fable from Mathematical Gazette 294 There Was a Young Man from Trinity 295 ANONYMOUS There Was an Old Man Who Said, "Do" 296 ANONYMOUS Relativity 297 ANONYMOUS There Was a Young Fellow Named Fisk 298 ANONYMOUS XI INTRODUCTION About twenty-five years ago I spent a weekend at the country home of the poet and critic Mark Van Doren. Among my fellow- guests was an old friend of my college days, Scott Buchanan, to whom this collection is dedicated and who was then and remains today one of the most remarkable men I have ever met I should like some day to write at length about him. He is the only dis- tinguished representative I know of a species practically extinct, or in any case obsolescent—the vagabond intellectual. I do not mean that he is a bohemian, only that his life has been guided by the behests of his curious mind rather than strait-jacketed by the usual limitations of a "career." He has had a brilliant career nevertheless, but only as a by-product. Though he is a philosopher by training, his real interest is simply in thought, thought in ah most any area. Wherever intellectual curiosity has led him, there he has strayed, as reveler or as ponderer. He has been a professor, a writer, a dabbler in politics, a sociological analyst, many other things. But at bottom he is an itinerant mind, not unlike those attractive wandering students of the twelfth century who have immortalized themselves in the Goliardic Songs. Among other things he is a good mathematician. Should you ever come across his out-of-print Poetry and Mathematics you will End its witty and occasionally obscure pages more than re- xiii FANTASIA MATHEMATICA warding. On this particular sunny afternoon he amused us by the display of a few topological tricks which have long been familiar both to mathematicians and to stage magicians, but which were new to us. One oi these tricks involved the Moebius strip, ex- ploited by several stories in this volume, and clearly described and explained by Mr. Gardner in his delightful "No~Sided Pro- fessor." It was at this point that I suddenly realized that I was inter- ested in mathematics. An indifferent student of the subject in high school, I had not thought about mathematics for years, feeling it to be beyond my mental capacities. But Mr. Buchanan's parlor trick, with its revelation of the fact, for example, that a surface can exist with only one side and one edge (try it yourself) aroused a curiosity which I have been gratifying ever since. I still know no real mathematics; but I know what mathematics is about, and something of the way in which the mathematical mind seems to work, and a fair amount about the lives of the great mathematicians. I have written elsewhere, in an essay called "Meditations of a Mathematical Moron," 1 of the pleasures of reading about mathematics, pleasures open to anyone who has received a conventional secondary-school education, and is will- ing to do a little mental work. One of the by-products of this interest is now in your hands. For about five years I have been collecting stories and imaginative oddments, often trivial, about mathematics. The stories are suit- able not for mathematicians, who will be bored by their naivete, but for non-mathematicians capable of being amused or surprised by the devious connections between the imagination and what would appear to be a discipline of the utmost rigor.