Chaos - James Gleick [161]
“PERHAPS WE SHOULD BELIEVE” The Beauty of Fractals, p. 136.
WHEN HE WROTE ABOUT e.g., “Iterated Function Systems and the Global Construction of Fractals,” Proceedings of the Royal Society of London A 399 (1985), pp. 243–75.
“IF THE IMAGE IS COMPLICATED” Barnsley.
“THERE IS NO RANDOMNESS” Hubbard.
“RANDOMNESS IS A RED” Barnsley.
THE DYNAMICAL SYSTEMS COLLECTIVE
SANTA CRUZ Farmer, Shaw, Crutchfield, Packard, Burke, Nauenberg, Abrahams, Guckenheimer. The essential Robert Shaw, applying information theory to chaos, is The Dripping Faucet as a Model Chaotic System (Santa Cruz: Aerial, 1984), along with “Strange Attractors, Chaotic Behavior, and Information Theory,” Zeitschrift für Naturforschung 36a (1981), p. 80. An account of the roulette adventures of some of the Santa Cruz students, conveying much of the color of these years, is Thomas Bass, The Eudemonic Pie (Boston: Houghton Mifflin, 1985).
HE DID NOT KNOW Shaw.
WILLIAM BURKE, a SANTA CRUZ COSMOLOGIST Burke, Spiegel.
“COSMIC ARRHYTHMIAS” Edward A. Spiegel, “Cosmic Arrhythmias,” in Chaos in Astrophysics, J. R. Buchler et al., eds. (New York: D. Reidel, 1985), pp. 91–135.
THE ORIGINAL PLANS Farmer, Crutchfield.
BY BUILDING UP Shaw, Crutchfield, Burke.
A FEW MINUTES LATER Shaw.
“ALL YOU HAVE TO DO” Abraham.
DOYNE FARMER Farmer is the main figure and Packard is a secondary figure in The Eudemonic Pie, the story of the roulette project, written by a sometime associate of the group.
PHYSICS AT SANTA CRUZ Burke, Farmer, Crutchfield.
“GIZMO-ORIENTED” Shaw.
FORD HAD ALREADY DECIDED Ford.
THEY REALIZED THAT MANY SORTS Shaw, Farmer.
INFORMATION THEORY The classic text, still quite readable, is Claude E. Shannon and Warren Weaver, The Mathematical Theory of Communication (Urbana: University of Illinois, 1963), with a helpful introduction by Weaver.
“WHEN ONE MEETS THE CONCEPT” Ibid., p. 13.
NORMAN PACKARD WAS READING Packard.
IN DECEMBER 1977 Shaw.
WHEN LORENZ WALKED INTO THE ROOM Shaw, Farmer.
HE FINALLY MAILED HIS PAPER “Strange Attractors, Chaotic Behavior, and Information Flow.”
A. N. KOLMOGOROV AND YASHA SINAI Sinai, private communication.
AT THE PINNACLE Packard.
“YOU DON’T SEE SOMETHING” Shaw.
“IT’S A SIMPLE EXAMPLE” Shaw.
SYSTEMS THAT THE SANTA CRUZ GROUP Farmer; a dynamical systems approach to the immune system, modeling the human body’s ability to “remember” and to recognize patterns creatively, is outlined in J. Doyne Farmer, Norman H. Packard, and Alan S. Perelson, “The Immune System, Adaptation, and Machine Learning,” preprint, Los Alamos National Laboratory, 1986.
ONE IMPORTANT VARIABLE The Dripping Faucet, p. 4.
“A STATE-OF–THE-ART COMPUTER CALCULATION” Ibid.
A “PSEUDOCOLLOQUIUM” Crutchfield.
“IT TURNS OUT” Shaw.
“WHEN YOU THINK ABOUT A VARIABLE” Farmer.
RECONSTRUCTING THE PHASE SPACE These methods, which became a mainstay of experimental technique in many different fields, were greatly refined and extended by the Santa Cruz researchers and other experimentalists and theorists. One of the key Santa Cruz proposals was Norman H. Packard, James P. Crutchfield, J. Doyne Farmer, and Robert S. Shaw [the canonical byline list], “Geometry from a Time Series,” Physical Review Letters 47 (1980), p. 712. The most influential paper on the subject by Floris Takens was “Detecting Strange Attractors in Turbulence,” in Lecture Notes in Mathematics 898, D. A. Rand and L. S. Young, eds. (Berlin: Springer-Verlag, 1981), p. 336. An early but fairly broad review of the techniques of reconstructing phase-space portraits is Harold Froehling, James P. Crutchfield, J. Doyne Farmer, Norman H. Packard, and Robert S. Shaw, “On Determining the Dimension of Chaotic Flows,” Physica 3D (1981), pp. 605–17.
“GOD, WE’RE STILL” Crutchfield.