• KUDOS FOR CHAOS "Highly entertaining ... a startling look at newly discovered universal laws" —Chicago Tribune Book World "I was caught up and swept along by the flow of this astonishing chronicle of scientific thought. It has been a long, long time since I finished a book and immediately started reading it all over again for sheer pleasure." —Lewis Thomas, author of Lives of a Cell "Chaos is a book that deserves to be read, for it chronicles the birth of a new scientific technique that may someday be important." —The Nation "Gleick's Chaos is not only enthralling and precise, but full of beautifully strange and strangely beautiful ideas." —Douglas Hofstadter, author of Godel, Escher, Bach "Taut and exciting ... it is a fascinating illustration of how the pattern of science changes." —The New York Times Book Review "Admirably portrays the cutting edge of thought" —Los Angeles Times "This is a stunning work, a deeply exciting subject in the hands of a first-rate science writer. The implications of the research James Gleick sets forth are breathtaking." —Barry Lopez, author of Arctic Dreams "An ambitious and largely successful popular science book that deserves wide readership" — Chicago Sun-Times "There is a teleological grandeur about this new math that gives the imagination wings." —Vogue "It is a splendid introduction. Not only does it explain accurately and skillfully the fundamentals of chaos theory, but it also sketches the theory's colorful history, with entertaining anecdotes about its pioneers and provocative asides about the philosophy of science and mathematics." —The Boston Sunday Globe PENGUIN BOOKS CHAOS James Gleick was born in New York City and lives there with his wife, Cynthia Crossen. / /' / / • • • • - C H AO S Making a New Science JAMES GLEICK / f PENGUIN BOOKS To Cynthia PENGUIN BOOKS Published by the Penguin Group Viking Penguin Inc., 40 West 23rd Street, New York, New York 10010, U.S.A. Penguin Books Ltd, 27 Wrights Lane, London W8 5TZ, England Penguin Books Australia Ltd, Ringwood, Victoria, Australia Penguin Books Canada Ltd, 2801 John Street, Markham, Ontario, Canada L3R1B4 Penguin Books (N.Z.) Ltd, 182-190 Wairau Road, Auckland 10, New Zealand Penguin Books Ltd, Registered Offices: Harmondsworth, Middlesex, England First published in the United States of America by Viking Penguin Inc. 1987 Published in Penguin Books 1988 5 7 9 10 8 6 Copyright © James Gleick, 1987 All rights reserved Portions of this book first appeared, in different form, in The New York Times Magazine, as "Solving the Mathematical Riddle of Chaos" and "The Man Who Reshaped Geometry." • Pages 353-54 constitute an extension of this copyright page. LIBRARY OF CONGRESS CATALOGING IN PUBLICATION DATA Gleick, James. Chaos: making a new science/James Gleick. p. cm. ISBN 0 14 00.9250 1 1. Chaotic behavior in systems. I. Title. [Q172.5.C45G54 1988] 003—dc!9 88-17448 Printed in the United States of America Set in Melior Except in the United States of America, this book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. human was the music, natural was the static . —JOHN UPDIKE \ Contents Prologue 1 The Butterfly Effect 9 Edward Lorenz and his toy weather. The computer misbehaves. Long-range forecasting is doomed. Order masquerading as randomness. A world of nonlinearity. "We completely missed the point." Revolution 33 A revolution in seeing. Pendulum clocks, space balls, and playground swings. The invention of the horseshoe. A mystery solved: Jupiter's Great Red Spot. Life's Ups and Downs 57 Modeling wildlife populations. Nonlinear science, "the study of non-elephant animals." Pitchfork bifurcations and a ride on the Spree. A movie of chaos and a messianic appeal. A Geometry of Nature 81 A discovery about cotton prices. A refugee from Bourbaki. Transmission errors and jagged shores. New dimensions. The monsters of fractal geometry. Quakes in the schizosphere. From clouds to blood vessels. The trash cans of science. "To see the world in a grain of sand." x Contents Strange Attractors 119 A problem for God. Transitions in the laboratory. Rotating cylinders and a turning point. David Ruelle's idea for turbulence. Loops in phase space. Mille-feuilles and sausage. An astronomer's mapping. "Fireworks or galaxies." Universality 155 A new start at Los Alamos. The renormalization group. Decoding color. The rise of numerical experimentation. Mitchell Feigenbaum's breakthrough. A universal theory. The rejection letters. Meeting in Como. Clouds and paintings. The Experimenter 189 Helium in a Small Box. "Insolid billowing of the solid." Flow and form in nature. Albert Libchaber's delicate triumph. Experiment joins theory. From one dimension to many. Images of Chaos 213 The complex plane. Surprise in Newton's method. The Mandelbrot set: sprouts and tendrils. Art and commerce meet science. Fractal basin boundaries. The chaos game. The Dynamical Systems Collective 241 Santa Cruz and the sixties. The analog computer. Was this science? "A long-range vision." Measuring unpredictability. Information theory. From microscale to macroscale. The dripping faucet. Audiovisual aids. An era ends. Inner Rhythms 273 A misunderstanding about models. The complex body. The dynamical heart. Resetting the biological clock. Fatal arrhythmia. Chick embryos and abnormal beats. Chaos as health. Contents xi Chaos and Beyond 301 New beliefs, new definitions. The Second Law, the snowflake puzzle, and loaded dice. Opportunity and necessity. Notes on Sources and Further Reading 318 Acknowledgments 341 Index 343 x / i X CO O < E U [_____._......._ ___..... Prologue THE POLICE IN THE SMALL TOWN of Los Alamos, New Mexico, worried briefly in 1974 about a man seen prowling in the dark, night after night, the red glow of his cigarette floating along the back streets. He would pace for hours, heading nowhere in the starlight that hammers down through the thin air of the mesas. The police were not the only ones to wonder. At the national laboratory some physicists had learned that their newest colleague was experimenting with twenty-six-hour days, which meant that his waking schedule would slowly roll in and out of phase with theirs. This bordered on strange, even for the Theoretical Division. In the three decades since J. Robert Oppenheimer chose this unworldly New Mexico landscape for the atomic bomb project, Los Alamos National Laboratory had spread across an expanse of desolate plateau, bringing particle accelerators and gas lasers and chemical plants, thousands of scientists and administrators and technicians, as well as one of the world's greatest concentrations of supercomputers. Some of the older scientists remembered the wooden buildings rising hastily out of the rimrock in the 1940s, but to most of the Los Alamos staff, young men and women in college-style corduroys and work shirts, the first bombmakers were just ghosts. The laboratory's locus of purest thought was the Theoretical Division, known as T division, just as computing was C division and weapons was X division. More than a hundred physicists and mathematicians worked in T division, well paid and free of academic pressures to teach and publish. These scientists 2 Prologue had experience with brilliance and with eccentricity. They were hard to surprise. But Mitchell Feigenbaum was an unusual case. He had exactly one published article to his name, and he was working on nothing that seemed to have any particular promise. His hair was a ragged mane, sweeping back from his wide brow in the style of busts of German composers. His eyes were sudden and passionate. When he spoke, always rapidly, he tended to drop articles and pronouns in a vaguely middle European way, even though he was a native of Brooklyn. When he worked, he worked obsessively. When he could not work, he walked and thought, day or night, and night was best of all. The twenty-four-hour day seemed too constraining. Nevertheless, his experiment in personal quasiperiodicity came to an end when he decided he could no longer bear waking to the setting sun, as had to happen every few days. At the age of twenty-nine he had already become a savant among the savants, an ad hoc consultant whom scientists would go to see about any especially intractable problem, when they could find him. One evening he arrived at work just as the director of the laboratory, Harold Agnew, was leaving. Agnew was a pow- erful figure, one of the original Oppenheimer apprentices. He had flown over Hiroshima on an instrument plane that accompanied the Enola Gay, photographing the delivery of the laboratory's first product. "I understand you're real smart," Agnew said to Feigenbaum. "If you're so smart, why don't you just solve laser fusion?" Even Feigenbaum's friends were wondering whether he was ever going to produce any work of his own. As willing as he was to do impromptu magic with their questions, he did not seem interested in devoting his own research to any problem that might pay off. He thought about turbulence in liquids and gases. He thought about time—did it glide smoothly forward or hop discretely like a sequence of cosmic motion- picture frames? He thought about the eye's ability to see consistent colors and forms in a universe that physicists knew to be a shifting quantum kaleidoscope. He thought about clouds, watching them from airplane windows (until, in 1975, his scientific travel privileges were officially suspended on grounds of overuse) or from the hiking trails above the laboratory.