how nature works c Springer Science+Business Media, LLC PERBAK how nature works © 1996 Springer Science+Business Media New York Originally published by Springer-Verlag New York Inc. in 1996 Softcover reprint of the hardcover 1st edition 1996 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. All characters except for historical personages are ficticious. Library of Congress Cataloging-in-Publication Data Bak,P. (Per), 194?- How nature works: the science of self-organized criticality/ Per Bak. p. em. Includes bibliographical references and index. ISBN 978-0-387-98738-5 ISBN 978-1-4757-5426-1 (eBook) DOI 10.1007/978-14757-5426-1 r. Critical phenomena (Physics) 2. Complexity (Philosophy) 3· Physics-Philosophy. I. Title. QC173+C74B34 1996 00 31 .7-dc2o Printed on acid-free paper. Designed by N ikita Pristouris 9 8 7 6 5 4 3 2 SPIN 10523741 ISBN 978-o-387-98738-5 Who could ever calculate the path of a molecule? How do we know that the creations of worlds are not determined by falling grains of sand? -Victor Hugo, Les M;serables Contents Preface and Acknowledgments Xl Chapter 1 Complex~ty and Cr~t~cal~ty 1 The Laws of Physics Are Simple, but Nature Is Complex . .3 . Storytelling Versus Science . 7. What Can a Theory of Complexity Explain? . 9 Power Laws and Criticality . .27 . Systems in Balance Are Not Complex . .28 . Chaos Is Not Complexity ................................ 29 Self-Organized Criticality . .3 . 1 . Chapter 2 The D~scovery ofSelf-Organ~zed Cr~ t~cal~ ty 33 Science at Brookhaven . 3. .3 . Where Does 1 /f "Noise" Come From? . 3. .7 . Susan Coppersmith's Dog Model ........................ 37 On Coupled Pendulums . 3 9 The Philosophy of Using Simple Models: On Spherical Cows ................................... 41 The Pendulums Become Critical......................... 45 Chapter 3 The Sandpae Parad~gm 49 The Sandpile Model ..................................... 52 Vlll How Nature Works Life in the Sandpile World ............................... 59 Can We Calculate the Power Laws with Pen and Paper? ....................................... 62 Chapter4 Real Sandpaes and Landscape Formation 65 Real Sand . 66. Norwegian Rice Piles ..................................... 69 Vicsek' s Landslide Experiment: The Origin of Fractals .................. ; . 5. 7 Himalayan Sandpiles . .77 . Sediment Deposition . .78 . Geomorphology: Landscapes Out of Balance . .8o . Chapter 5 Earthquakes, Starquakes, and Solar Flares 85 Self-Organization of Earthquakes ....................... 88 A Misprint Leads to Progress . 9 3 Rumbling Around Stromboli . 97. The Crust of the Earth Is Critical . 99. Pulsar Glitches and Starquakes . 1oo. Black Holes and Solar Flares............................ 1oo Chapter6 The "Game of Life": Complexity Is Criticality 105 Chapter 7 Is Life aSelf-Organized Critical Phenomenon? 113 The Santa Fe Institute................................... 114 Sand piles and Punctuated Equilibria .................. 117 Interacting Dancing Fitness Landscapes . .18 . 1 Chapter8 Mass Extinctions and Punctuated Equai hria in a Simple Model of Evolution 129 Can We Model Darwin? . 1 3 2 A Science Project for a Sunday Afternoon . .13 . .5 Contents 1x Life at a Cold Place . I43 Comparison with Real Data ............................ I44 On Dinosaurs and Meteors . I 5 I Dante Chialvo's Evolutionary Game . I5 3 Self-Organized Criticality and Gaia . I 54 Replaying the Tape of Evolution . I 56 Chapter 9 Theory of the Punctuated Equili bri urn Model 161 Whatls a Theory? ....................................... I62 The Random Neighbor Version of the Evolution Model ............................ I63 The Self-Organization Process . I67 The Critical State . I69 Revisiting the Game of Life . I70 Revisiting Earthquakes .................................. 172 Chapter 10 The Brain 175 Why Should the Brain Be Critical? . r 76 The Monkey Problem .................................. I78 The Brain and River Networks ......................... r8o Chapter 11 On Economics and Traffic Jams 183 Equilibrium Economics Is Like Water . I8 3 Real Economics Is Like Sand . I8 5 Simple Toy Model of a Critical Economy.............. I87 Fluctuations and Catastrophes Are Unavoidable ...... I9I Traffic Jams .............................................. I92 Bibliography I99 Index 207 preface and acknowledgments Self-organized criticality is a new way of viewing nature. The basic picture is one where nature is perpetually out of balance, but organized in a poised state-the critical state-where anything can happen within well-defined statistical laws. The aim of the science of self-organized criticality is to yield insight into the fundamental question of why nature is complex, not simple, as the laws of physics imply. Self-organized criticality explains some ubiquitous patterns existing in nature that we view as complex. Fractal structure and catastrophic events are among those regularities. Applications range from the study of pulsars and black holes to earthquakes and the evolution of life. One intriguing conse­ quence of the theory is that catastrophes can occur for no reason whatsoever. Mass extinctions may take place without any external triggering mechanism such as a volcanic eruption or a meteorite hitting the earth (although the the­ ory of course cannot rule out that this has in fact occurred). xu How Nature Works Since we first proposed the idea in 1987, more than 2,ooo papers have been written on self-organized criticality, making ours the most cited paper in physics during that period. How Nature Works is the first book to deal with the subject. The basic idea is simple, and most of the mathematical models that have been used in the implementation of the theory are not complicated. Any­ one with some computer literacy and a PC can set the models up on his own to verifY the predictions. Often, no more than high school mathematics is needed. Some of the computer programs are even available on the Internet. Some of the sandpile experiments are of no greater cost and difficulty than the dedi­ cated reader can perform him or hersel£ Unlike other subjects in physics, the basic ideas are simple enough to be made accessible to a non-scientific audience without being trivialized. Many friends and colleagues have helped me, with both the research and the book. The science has been all fun-in particular I am grateful to Kurt Wiesenfeld and Chao Tang, with whom I collaborated on the original idea, and to Kan Chen, Kim Christensen, Maya Paczuski, Zeev Olami, Sergei Maslov, Michael Creutz, Michael Woodford, Dimitris Stassinopolous, and Jose Scheinkman, who participated in the research that followed, bringing the idea to life by applying it to many different phenomena in nature. Thanks are due to Elaine Wiesenfeld for drawing the logo of self-organized criticality, the sandpile, shown in Figure 1; to Ricard Sole for drawing the dog-pulling Figure 9; to Arch Johnston for providing Figure 2; to Jens Feder and his group in Oslo for Figure 6 and the figures on their ricepile experiment, Figures 15-17 and Plate 4; to Daniel Rothman and John P. Grotzinger for the photos of the Kings Peak formation, Figure r8; to Peter Grassberger for the office version of the sandpile model, Figure 13; and to Paolo Diodati for providing the original figures on the measurements of acoustic emission from Stromboli, Figure 23. The impressive computer graphics on the sandpile in Plate r, and the "Game of Life," Plates 6-8, are due to Michael Creutz. A number of persons helped me increase the literary qualities of the manuscripr-unfortunately, the brevity of precise form that is suitable for scientific journals does not do well when addressing a broader audience. First Preface and Acknowledgments xm of all, I am grateful to Maya Paczuski and Jim Niederer who spent endless hours improving the presentation and helping with organizing the material. My children, Tine and Jakob and Thomas, checked the manuscript for read­ ability for non professionals, leading to revisions of several unclear passages. Finally, I am indebted to Jerry Lyons, William Frucht, and Robert Wexler of Copernicus Books for substantial and invaluable help with the manuscript at all stages. chapter 1 complexity and criticality How can the universe start with a few rypes ofelementary particles at the big bang, and end up with life, history, economics, and literature? The question is screaming out to be answered bur it is seldom even asked. Why did the big bang not form a simple gas of particles, or condense into one big crystal? We see complex phenomena around us so often that we rake them for granted without looking for further explanation. In fact, until recently very little sci­ entific effort was devoted to understanding why nature is complex. I will argue that complex behavior in nature reflects the tendency of large systems with many components ro evolve into a poised, "critical" state, way out of balance, where minor disturbances may lead to events, called avalanches, of all sizes. Most of the changes take place through catastrophic events rather than by following a smooth gradual path. The evolution to this very delicate state occurs without design from any outside agent. The state is estab­ lished solely because of the dynamical interactions among individual elements ofrhe system: rhe critical 2 How Nature Works state is selj-organiztd.