Chaos - James Gleick [152]
Stephen H. Schneider
Christopher Scholz
Robert Shaw
Michael F. Shlesinger
Yasha G. Sinai
Steven Smale
Edward A. Spiegel
H. Bruce Stewart
Steven Strogatz
Harry Swinney
Tomas Toffoli
Felix Villars
William M. Visscher
Richard Voss
Bruce J. West
Robert White
Gareth P. Williams
Kenneth G. Wilson
Arthur T. Winfree
Jack Wisdom
Helena Wisniewski
Steven Wolfram
J. Austin Woods
James A. Yorke
PROLOGUE
LOS ALAMOS Feigenbaum, Carruthers, Campbell, Farmer, Visscher, Kerr, Hasslacher, Jen.
“I UNDERSTAND YOU’RE” Feigenbaum, Carruthers.
GOVERNMENT PROGRAM Buchal, Shlesinger, Wisniewski.
ELEMENTS OF MOTION Yorke.
PROCESS RATHER THAN STATE F. K. Browand, “The Structure of the Turbulent Mixing Layer,” Physica 18D (1986), p. 135.
THE BEHAVIOR OF CARS Japanese scientists took the traffic problem especially seriously; e.g., Toshimitsu Musha and Hideyo Higuchi, “The 1/f Fluctuation of a Traffic Current on an Expressway,” Japanese Journal of Applied Physics (1976), pp. 1271–75.
THAT REALIZATION Mandelbrot, Ramsey; Wisdom, Marcus; Alvin M. Saperstein, “Chaos—A Model for the Outbreak of War,” Nature 309 (1984), pp. 303–5.
“FIFTEEN YEARS AGO” Shlesinger.
JUST THREE THINGS Shlesinger.
THIRD GREAT REVOLUTION Ford.
“RELATIVITY ELIMINATED” Joseph Ford, “What Is Chaos, That We Should Be Mindful of It?” preprint, Georgia Institute of Technology, p. 12.
THE COSMOLOGIST John Boslough, Stephen Hawking’s Universe (Cambridge: Cambridge University Press, 1980); see also Robert Shaw, The Dripping Faucet as a Model Chaotic System (Santa Cruz: Aerial, 1984), p. 1.
THE BUTTERFLY EFFECT
THE SIMULATED WEATHER Lorenz, Malkus, Spiegel, Farmer. The essential Lorenz is a triptych of papers whose centerpiece is “Deterministic Nonperiodic Flow,” Journal of the Atmospheric Sciences 20 (1963), pp. 130–41; flanking this are “The Mechanics of Vacillation,” Journal of the Atmospheric Sciences 20 (1963), pp. 448–64, and “The Problem of Deducing the Climate from the Governing Equations,” Tellus 16 (1964), pp. 1–11. They form a deceptively elegant piece of work that continues to influence mathematicians and physicists twenty years later. Some of Lorenz’s personal recollections of his first computer model of the atmosphere appear in “On the Prevalence of Aperiodicity in Simple Systems,” in Global Analysis, eds. Mgrmela and J. Marsden (New York: Springer-Verlag, 1979), pp. 53–75.
THEY WERE NUMERICAL RULES A readable contemporary description by Lorenz of the problem of using equations to model the atmosphere is “Large-Scale Motions of the Atmosphere: Circulation,” in Advances in Earth Science, ed. P. M. Hurley (Cambridge, Mass.: The M.I.T. Press, 1966), pp. 95–109. An early, influential analysis of this problem is L. F. Richardson, Weather Prediction by Numerical Process (Cambridge: Cambridge University Press, 1922).
PURITY OF MATHEMATICS Lorenz. Also, an account of the conflicting pulls of mathematics and meteorology in his thinking is in “Irregularity: A Fundamental Property of the Atmosphere,” Crafoord Prize Lecture presented at the Royal Swedish Academy of Sciences, Stockholm, Sept. 28, 1983, in Tellus 36A (1984), pp. 98–110.
“IT WOULD EMBRACE” Pierre Simon de Laplace, A Philosophical Essay on Probabilities (New York: Dover, 1951).
“THE BASIC IDEA” Winfree.
“THAT’S THE KIND OF RULE” Lorenz.
SUDDENLY HE REALIZED “On the Prevalence,” p. 55.
SMALL ERRORS PROVED CATASTROPHIC Of all the classical physicists and mathematicians who thought about dynamical systems, the one who best understood the possibility of chaos was Jules Henri Poincaré. Poincaré remarked in Science and Method:
“A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still know the situation