Chaos - James Gleick [162]
SOME PROFESSORS DENIED e.g., Nauenberg.
“WE HAD NO ADVISOR” Shaw.
MORE INTERESTED IN REAL SYSTEMS Not that the students ignored maps altogether. Crutchfield, inspired by May’s work, spent so much time in 1978 making bifurcation diagrams that he was barred from the computer center’s plotter. Too many pens had been destroyed laying down the thousands of dots.
LANFORD LISTENED POLITELY Farmer.
“IT WAS MY NAIVETÉ” Farmer.
“AUDIOVISUAL AIDS” Shaw.
ONE DAY BERNARDO HUBERMAN crutchfield, huberman.
“IT WAS ALL VERY VAGUE” Huberman.
THE FIRST PAPER Bernardo A. Huberman and James P. Crutchfield, “Chaotic States of Anharmonic Systems in Periodic Fields,” Physical Review Letters 43 (1979), p. 1743.
FARMER WAS ANGERED Crutchfield.
CLIMATE SPECIALISTS This is a continuing debate in the journal Nature, for example.
ECONOMISTS ANALYZING STOCK MARKET Ramsey.
FRACTAL DIMENSION, HAUSDORFF DIMENSION J. Doyne Farmer, Edward Ott, and James A. Yorke, “The Dimension of Chaotic Attractors,” Physica 7D (1983), pp. 153–80.
“THE FIRST LEVEL OF KNOWLEDGE” Ibid., p. 154.
INNER RHYTHMS
HUBERMAN LOOKED OUT Huberman, Mandell (interviews and remarks at Conference on Perspectives in Biological Dynamics and Theoretical Medicine, Bethesda, Maryland, 11 April 1986). Also, Bernardo A. Huberman, “A Model for Dysfunctions in Smooth Pursuit Eye Movement,” preprint, Xerox Palo Alto Research Center, Palo Alto, California.
“THREE THINGS HAPPEN” Abraham. The basic introduction to the Gaia hypothesis—an imaginative dynamical view of how the earth’s complex systems regulate themselves, somewhat sabotaged by its deliberate anthropomorphism—is J. E. Lovelock, Gaia: A New Look at Life on Earth (Oxford: Oxford University Press, 1979).
RESEARCHERS INCREASINGLY RECOGNIZED A somewhat arbitrary selection of references on physiological topics (each with useful citations of its own): Ary L. Goldberger, Valmik Bhargava, and Bruce J. West, “Nonlinear Dynamics of the Heartbeat,” Physica 17D (1985), pp. 207–14. Michael C. Mackay and Leon Glass, “Oscillation and Chaos in Physiological Control Systems,” Science 197 (1977), p. 287. Mitchell Lewis and D. C. Rees, “Fractal Surfaces of Proteins,” Science 230 (1985), pp. 1163–65. Ary L. Goldberger, et al., “Nonlinear Dynamics in Heart Failure: Implications of Long-Wavelength Cardiopulmonary Oscillations,” American Heart Journal 107 (1984), pp. 612–15. Teresa Ree Chay and John Rinzel, “Bursting, Beating, and Chaos in an Excitable Membrane Model,” Biophysical Journal 47 (1985), pp. 357–66. A particularly useful and wide-ranging collection of other such papers is Chaos, Arun V. Holden, ed. (Manchester: Manchester University Press, 1986).
“A DYNAMICAL SYSTEM OF VITAL INTEREST” Ruelle, “Strange Attractors,” p. 48.
“IT’S TREATED BY PHYSICIANS” Glass.
“WE’RE AT A NEW FRONTIER” Goldberger.
MATHEMATICIANS AT THE COURANT INSTITUTE Peskin; David M. McQueen and Charles S. Peskin, “Computer-Assisted Design of Pivoting Disc Prosthetic Mitral Valves,” Journal of Thoracic and Cardiovascular Surgery 86 (1983), pp. 126–35.
A PATIENT WITH A SEEMINGLY HEALTHY HEART Cohen.
“THE BUSINESS OF DETERMINING” Winfree.
A STRONG SENSE OF GEOMETRY Winfree develops his view of geometric time in biological systems in a provocative and beautiful book, When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias (Princeton: Princeton University Press, 1987); a review article on the applications to heart rhythms is Arthur T. Winfree, “Sudden Cardiac Death: A Problem in Topology,” Scientific American 248 (May 1983), p. 144.
“I HAD A HEADFUL” Winfree.
“YOU GO TO A MOSQUITO” Winfree.
SHE REPORTED FEELING GREAT Strogatz; Charles A. Czeisler, et al., “Bright Light Resets the Human Circadian Pacemaker Independent of the Timing of the Sleep-Wake Cycle,” Science 233 (1986), pp.
667–70. Steven Strogatz, “A Comparative Analysis of Models of the Human Sleep-Wake Cycle,” preprint, Harvard University, Cambridge, Massachusetts.
HE HAD GAINED Winfree.
“WHEN MINES DECIDED” “Sudden Cardiac Death.”
TO DO SO, HOWEVER Ideker.