PERPETUAL MOTION The Making of a Mathematical Logician by John L. Bell Llumina Press © 2010 John L. Bell All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from both the copyright owner and the publisher. Requests for permission to make copi es of any part of this work should be mailed to Permissions Department, Llumina Press, 7915 W. McNab Rd., Tamarac, FL 33321 ISBN: 978-1-60594-589-7 (PB) Printed in the United States of America by Llumina Press PCN 2 Contents New York and Rome, 1951-53 14 The Hague, 1953-54 18 Bangkok, 1955-56 28 San Francisco, 1956-58 34 Millfield, 1958-61 54 Cambridge, 1962 93 Exeter College, Oxford, 1962-65 101 Christ Church, Oxford, 1965-68 146 London, 1968-73 178 Obituary of E. H. Linfoot 225 3 My mother in the 1940s My parents in the 1950s 4 Granddad England and I, Rendcomb, 1945 5 Myself, age 3 My mother and myself, age 3 6 Myself, age 6, with you-know who 7 Granddad Oakland and his three sons, 1938 8 The Four Marx Brothers, 1969 9 Mimi and I (The Three “Me’s”), 1969 10 Myself, 2011 11 When you’re both alive and dead, Thoroughly dead to yourself, How sweet The smallest pleasure! —Bunan Some men a forward motion love, But I by backward steps would move; And when this dust falls to the urn, In that state I came, return. —Henry Vaughan We shall not cease from exploration And at the end of all our exploring Will be to arrive where we started And know the place for the first time —T.S. Eliot My past grows vast My future’s much diminished Everything considered It looks as if I’m finished. — J. Bennhall 12 WHEN I WAS A CHILD I entertained the fantasy of travelling somehow into the future so as to be able to view my life as a whole, from the other end, as it were, so placing the exigencies of day- to-day living safely behind me. (Perhaps this was an unconscious death-wish.) But now that I have reached the dispiriting age at which one’s hopes for the future begin to fade, looking forward offers little attraction. I therefore throw in the existential towel and take refuge in time past—no longer at one with Magritte who bravely declared that he despised everybody’s past, his own included. On the contrary: as my mental horizon contracts and what remains of my life slowly congeals around me, I embrace the idea of alleviating tedium vitae by squeezing the desiccated lemon of memory. Here, for better or worse, is the result. My parents met during World War II while my father was stationed in England as an officer in the U.S. Army. My mother, Helen Lane (1920–1960) was a pianist, and my father, John Wright Bell (1918–2003), a civil engineer. After a whirlwind courtship they were married in 1943. On 25 March 1945 I was born in Cheltenham, a genteel town in Gloucestershire (my mother’s family’s county of origin) noted both for its posh Ladies’ College and for its numerous retired colonels reclining in Bath chairs. At war’s end my father returned to the United States along with the bulk of the American army, and a year later my mother and I travelled to join him in California, crossing the Atlantic on the Queen Mary, which had been requisitioned for the express purpose of reuniting the many European war brides with their American husbands. This was to be the first journey of a childhood spent in a state of perpetual motion. A mnemonic fog quickly gathers in my mind when I try to recall details of my family life in California before attaining the age of seven1, a life which seems to have been spent on the move. Nevertheless a few isolated memories stand out from the mist: of a childhood friend, Richard Gilliland, whose mother, I was later informed, committed suicide by throwing herself off the Golden Gate Bridge; of my father’s running children’s story, “Stripy the Skunk,” written in his flowing hand on ruled sheets of yellow paper; of my father describing to me the various sorts of clouds—cumulus, stratus, cirrus, nimbus, etc.—and of his pointing out constellations such as the Pleiades; of a book of dinosaurs, in which both the name and the squat form of the Eryops I found amusing; of “Tootle”, the cautionary tale of a locomotive that strayed off the tracks; of a Halloween skeleton suit and a T-shirt from the period of World War II bearing the repeated message “Keep ’em flying”; of my fascination with the curious names of the colors in my crayon set—magenta, gamboge, burnt umber, ochre, sienna; of a plain grey teddy-bear. My chronicle begins in earnest with our move to New York in 1951. 1 Years later I was to learn a little about my five-year-old self from a letter my father sent me just after I received my doctorate. I quote from it: The fruition of your plans in Fresno in 1950 is finally a reality—however a little late. You probably don’t remember do you?… we were discussing atoms and molecules, or at least that’s when you found out about them from me. I can remember verbatim the conversation. You asked what the coffee table…was made of. I said glass & wood—bright eh? Anyway, you said “I know, but what are they made of?” so I said “Little particles” “What are they made of?” “Molecules”, etc. to atoms. At that you asked if everything was made of atoms. Oh yes. You looked at the fire and asked about the flame—yes—gas, etc…. Then, you asked about light, as the lamp was burning—No—but out of the blue, you asked how fast light travelled. Yore ole Dad gave you that answer. Anyway, following that you said that you wanted to be a scientist and get a Ph.D. Where you heard of that I couldn’t figure but you knew what it was in general terms. Then you wanted to know when you could get one and I told you probably under the age of 30. Then you told me that you’d like to have it by the time you were 21. I guess you figured that when you had reached manhood you should have a Ph.D. 13 NEW YORK AND ROME, 1951-53 MY FAMILY TOOK UP RESIDENCE in one of a clutch of high-rise apartment buildings each bearing an English place name—Eton, Middlesex, etc.—I believe ours was called “York.” I can still recall my panic at being trapped in the building’s elevator as the result of a power failure; to this day I cannot enter a lift without a lingering sense of apprehension. I attended a large public school, an experience which evokes no pleasant memories. On the occasions when the school bus failed to show up, I and my fellow enrolees from our apartment complex were paraded to school by a granite-faced guard whose appearance alone would unquestionably have sufficed to deter any potential child molester lurking along our path, or, more pertinently—New York being a far safer city then than now—in our parents’ anxious minds. Much more agreeable is the memory of my violin teacher, a certain Mr. Mendelssohn, whose M-shaped belt-buckle arrestingly proclaimed his common surname, and thereby his family relationship, with the illustrious Felix. Despite my cacophonic efforts on the fiddle, exposure to which may well have caused the unfortunate man to regret his choice of occupation, I have a diffuse recollection of the patience and kindness he showed me. This surely attests to the inherent sweetness of his nature, rather than to his seeing in me a future violinist manqué . I also recall being taken by my parents to see what may have been my first movie, “When Worlds Collide”. Leslie Halliwell may dismiss this film as “stolid science fiction with a spectacular but not marvellous climax following seventy minutes of inept talk,” but I was thrilled when I first saw it! Its final scenes show the protagonists escaping from the earth (in accordance with the film’s title, about to collide with another planet) in a spaceship launched, not vertically— as the space program of the sixties was to make familiar—but on a curious curved ramp, the memorable, if technologically unlikely product of a Hollywood scenarist’s febrile imagination. I recall being presented with a collection of “children’s classics” of which the only volumes I can remember actually reading were Grimm’s and Hans Andersen’s Fairy Tales, which delighted me. I also remember with diffuse affection Richard’s Topical Encyclopedia— a junior edition accompanying the imposing set of Encyclopedia Britannica (complete with its own bookcase) my parents had bought some years before. The front cover of each volume of Richard’s was embossed with what I took to be the image of a Viking ship. I was particularly impressed with the article on “atmosphere” because it began with the striking phrase “We live in an ocean of air.” I can still visualize the curiously unsettling photograph of a chubby young man imprisoned up to his chest in a curious airtight box. He is yawning away, so the photograph’s caption declares, “not because he is tired, but because he is not receiving enough oxygen through his skin.” My favorite book of the time, The Rock Book (no longer in my possession, alas!) had probably been bought for me by my father because of my liking (which I have never lost) for those miniature collections of rock fragments—“jewels in the rough”—attractively displayed on cards and obtainable in tourist gift shops.