Strogatz - Sync: the emerging science of spontaneous order

PENGUIN BOOKS

SYNC

Steven Strogatz is Professor of Applied Mathematics at Cornell University and one of the worlds leading researchers into chaos, complexity and synchronization. His seminal research has been featured in Nature, Science, Scientific American, The New York Times, the New Yorker, and the Daily Telegraph.

STEVEN STROGATZ

The Emerging Science of Spontaneous Order

PENGUIN BOOKS

PENGUIN BOOKS

Published by the Penguin Group

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Published in the United States of America by Hyperion 2003

Published in Great Britain by Allen Lane 2003

Published in Penguin Books 2004

Copyright Steven Strogatz, 2003

All rights reserved

The moral right of the author has been asserted

Grateful acknowledgement is made for permission to reprint excerpts from the following copyrighted works: Out of Step on the Bridge and Physics and the Nobel Prizes copyright Brian Josephson, 2000, 2001. Reprinted by permission of Brian Josephson

Illustrations by Margaret Nelson

Illustration credits p.80 Figure 1.9 of Martin Moore-Ede, Frank M. Sulzman, and Charles A. Fuller, The Clocks That Time Us (Cambridge, Massachusetts: Harvard University Press, 1982), adapted by permission of Martin Moore Ede; p. 282 Figure 1 of Eugenio Rodriguez et al., Perceptions Shadow: Long-distance synchronization of human brain activity, Nature 397 (1999) pp. 43033, adapted by permission of Jacques Martinerie

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 publishers 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

ISBN: 978-0-14-193318-4

To Art Winfree
Mentor, inspiration, friend

A T THE HEART OF THE UNIVERSE IS a steady, insistent beat: the sound of cycles in sync. It pervades nature at every scale from the nucleus to the cosmos. Every night along the tidal rivers of Malaysia, thousands of fireflies congregate in the mangroves and flash in unison, without any leader or cue from the environment. Trillions of electrons march in lockstep in a superconductor, enabling electricity to flow through it with zero resistance. In the solar system, gravitational synchrony can eject huge boulders out of the asteroid belt and toward Earth; the cataclysmic impact of one such meteor is thought to have killed the dinosaurs. Even our bodies are symphonies of rhythm, kept alive by the relentless, coordinated firing of thousands of pacemaker cells in our hearts. In every case, these feats of synchrony occur spontaneously, almost as if nature has an eerie yearning for order.

And that raises a profound mystery: Scientists have long been baffled by the existence of spontaneous order in the universe. The laws of thermodynamics seem to dictate the opposite, that nature should inexorably degenerate toward a state of greater disorder, greater entropy. Yet all around us we see magnificent structuresgalaxies, cells, ecosystems, human beingsthat have somehow managed to assemble themselves. This enigma bedevils all of science today. Only in a few situations do we have a clear understanding of how order arises on its own. The first case to yield was a particular kind of order in physical space involving perfectly repetitive architectures. Its the kind of order that occurs whenever the temperature drops below the freezing point and trillions of water molecules spontaneously lock themselves into a rigid, symmetrical crystal of ice. Explaining order in time, however, has proved to be more problematic. Even the simplest possibility, where the same things happen at the same times, has turned out to be remarkably subtle. This is the order we call synchrony.

It may seem at first that theres little to explain. You can agree to meet a friend at a restaurant, and if both of you are punctual, your arrivals will be synchronized. An equally mundane kind of synchrony is triggered by a reaction to a common stimulus. Pigeons startled by a car backfiring will all take off at the same time, and their wings may even flap in sync for a while, but only because they reacted the same way to the same noise. Theyre not actually communicating about their flapping rhythm and dont maintain their synchrony after the first few seconds. Other kinds of transient sync can arise by chance. On a Sunday morning, the bells of two different churches may happen to ring at the same time for a while, and then drift apart. Or while sitting in your car, waiting to turn at a red light, you might notice that your blinker is flashing in perfect time with that of the car ahead of you, at least for a few beats. Such sync is pure coincidence, and hardly worth noting.

The impressive kind of sync is persistent. When two things keep happening simultaneously for an extended period of time, the synchrony is probably not an accident. Such persistent sync comes easily to us human beings, and, for some reason, it often gives us pleasure. We like to dance together, sing in a choir, play in a band. In its most refined form, persistent sync can be spectacular, as in the kickline of the Rockettes or the matched movements of synchronized swimmers. The feeling of artistry is heightened when the audience has no idea where the music is going next, or what the next dance move will be. We interpret persistent sync as a sign of intelligence, planning, and choreography.

So when sync occurs among unconscious entities like electrons or cells, it seems almost miraculous. Its surprising enough to see animals cooperatingthousands of crickets chirping in unison on a summer night; the graceful undulating of schools of fishbut its even more shocking to see mobs of mindless things falling into step by themselves. These phenomena are so incredible that some commentators have been led to deny their existence, attributing them to illusions, accidents, or perceptual errors. Other observers have soared into mysticism, attributing sync to supernatural forces in the cosmos.

Until just a few years ago, the study of synchrony was a splintered affair, with biologists, physicists, mathematicians, astronomers, engineers, and sociologists laboring in their separate fields, pursuing seemingly independent lines of inquiry. Yet little by little, a science of sync has begun coalescing out of insights from these and other disciplines. This new science centers on the study of coupled oscillators. Groups of fireflies, planets, or pacemaker cells are all collections of oscillatorsentities that cycle automatically, that repeat themselves over and over again at more or less regular time intervals. Fireflies flash; planets orbit; pacemaker cells fire. Two or more oscillators are said to be coupled if some physical or chemical process allows them to influence one another. Fireflies communicate with light. Planets tug on one another with gravity. Heart cells pass electrical currents back and forth. As these examples suggest, nature uses every available channel to allow its oscillators to talk to one another. And the result of those conversations is often synchrony, in which all the oscillators begin to move as one.