Chaos - James Gleick [163]
“THE CARDIAC EQUIVALENT” Winfree.
IDEKER’S IMMEDIATE INTENTION Ideker.
THEY USED TINY AGGREGATES Glass.
“EXOTIC DYNAMIC BEHAVIOR” Michael R. Guevara, Leon Glass, and Alvin Schrier, “Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac Cells,” Science 214 (1981), p. 1350.
“MANY DIFFERENT RHYTHMS” Glass.
“IT IS A CLEAR INSTANCE” Cohen.
“PEOPLE HAVE MADE THESE WEIRD” Glass.
“DYNAMICAL THINGS ARE GENERALLY” Winfree.
“SYSTEMS THAT NORMALLY OSCILLATE” Leon Glass and Michael C. Mackay, “Pathological Conditions Resulting from Instabilities in Physiological Control Systems,” Annals of the New York Academy of Sciences 316 (1979), p. 214.
“FRACTAL PROCESSES” Ary L. Goldberger, Valmik Bhargava, Bruce J. West, and Arnold J. Mandell, “Some Observations on the Question: Is Ventricular Fibrillation ‘Chaos,’” preprint.
“IS IT POSSIBLE” Mandell.
“WHEN YOU REACH AN EQUILIBRIUM” Mandell.
MANDELL OFFERED HIS COLLEAGUES Arnold J. Mandell, “From Molecular Biological Simplification to More Realistic Central Nervous System Dynamics: An Opinion,” in Psychiatry: Psychobiological Foundations of Clinical Psychiatry 3:2, J. O. Cavenar, et al., eds. (New York: Lippincott, 1985).
“THE UNDERLYING PARADIGM REMAINS” Ibid.
THE DYNAMICS OF SYSTEMS Huberman.
SUCH MODELS SEEMED TO HAVE Bernardo A. Huberman and Tad Hogg, “Phase Transitions in Artificial Intelligence Systems,” preprint, Xerox Palo Alto Research Center, Palo Alto, California, 1986. Also, Tad Hogg and Bernardo A. Huberman, “Understanding Biological Computation: Reliable Learning and Recognition,” Proceedings of the National Academy of Sciences 81 (1984), pp. 6871–75.
“ASTONISHING GIFT OF CONCENTRATING” Erwin Schrödinger, What Is Life? (Cambridge: Cambridge University Press, 1967), p. 82.
“IN PHYSICS WE HAVE DEALT” Ibid., p. 5.
CHAOS AND BEYOND
“WHEN I SAID THAT?” Ford.
“IN A COUPLE OF DAYS” Fox.
THE WORD ITSELF (Holmes) SIAM Review 28 (1986), p. 107; (Hao) Chaos (Singapore: World Scentific, 1984), p. i; (Stewart) “The Geometry of Chaos,” in The Unity of Science, Brookhaven Lecture Series, No. 209 (1984), p. 1; (Jensen) “Classical Chaos,” American Scientist (April 1987); (Crutchfield) private communication; (Ford) “Book Reviews,” International Journal of Theoretical Physics 25 (1986), No. 1.
TO HIM, THE OVERRIDING MESSAGE Hubbard.
TOO NARROW A NAME Winfree.
“IF YOU HAD A TURBULENT RIVER” Huberman.
“LET US AGAIN LOOK” Gaia, p. 125.
THOUGHTFUL PHYSICISTS P. W. Atkins, The Second Law (New York: W. H. Freeman, 1984), p. 179. This excellent recent book is one of the few accounts of the Second Law to explore the creative power of dissipation in chaotic systems. A highly individual, philosophical view of the relationships between thermodynamics and dynamical systems is Ilya Prigogine, Order Out of Chaos: Man’s New Dialogue With Nature (New York: Bantam, 1984).
GROWTH OF SUCH TIPS Langer. The recent literature on the dynamical snowflake is voluminous. Most useful are: James S. Langer, “Instabilities and Pattern Formation,” Reviews of Modern Physics (52) 1980, pp. 1–28; Johann Nittmann and H. Eugene Stanley, “Tip Splitting without Interfacial Tension and Dendritic Growth Patterns Arising from Molecular Anisotropy, Nature 321 (1986), pp. 663–68; David A. Kessler and Herbert Levine, “Pattern Selection in Fingered Growth Phenomena,” to appear in Advances in Physics.
IN THE BACK OF THEIR MINDS Gollub, Langer.
ODD-SHAPED TRAVELING WAVES An interesting example of this route to the study of pattern formation is P. C. Hohenberg and M. C. Cross, “An Introduction to Pattern Formation in Nonequilibrium Systems,” preprint, AT&T Bell Laboratories, Murray Hill, New Jersey.
IN ASTRONOMY, CHAOS EXPERTS Wisdom; Jack Wisdom, “Meteorites May Follow a Chaotic Route to Earth,” Nature 315 (1985), pp. 731–33, and “Chaotic Behavior and the Origin of the 3/1 Kirkwood Gap,” Icarus 56 (1983), pp. 51–74.
STRUCTURES THAT REPLICATE THEMSELVES As Farmer and Packard put it: “Adaptive behavior is an emergent property which spontaneously arises through the interaction