Chaos - James Gleick [155]
ROBUST AND STRANGE Smale; “On How I Got Started.”
IT WAS JUST A VACUUM TUBE van der Pol described his work in Nature 120 (1927), pp. 363–64.
“OFTEN AN IRREGULAR NOISE” Ibid.
TO MAKE A SIMPLE Smale’s definitive mathematical exposition of this work is “Differentiable Dynamical Systems,” Bulletin of the American Mathematical Society 1967, pp. 747–817 (also in The Mathematics of Time, pp. 1–82).
THE PROCESS MIMICS Rössler.
BUT FOLDING Yorke.
IT WAS A GOLDEN AGE Guckenheimer, Abraham.
“IT’S THE PARADIGM SHIFT Abraham.
A MODEST COSMIC MYSTERY Marcus, Ingersoll, Williams; Philip S. Marcus, “Coherent Vortical Features in a Turbulent Two-Dimensional Flow and the Great Red Spot of Jupiter,” paper presented at the 110th Meeting of the Acoustical Society of America, Nashville, Tennessee, 5 November 1985.
“THE RED SPOT ROARING” John Updike, “The Moons of Jupiter,” Facing Nature (New York: Knopf, 1985), p. 74.
VOYAGER HAD MADE Ingersoll; also, Andrew P. Ingersoll, “Order from Chaos: The Atmospheres of Jupiter and Saturn,” Planetary Report 4:3, pp. 8–11.
“YOU SEE THIS” Marcus.
“GEE, WHAT ABOUT” Marcus.
LIFE’S UPS AND DOWNS
RAVENOUS FISH May, Schaffer, Yorke, Guckenheimer. May’s famous review article on the lessons of chaos in population biology is “Simple Mathematical Models with Very Complicated Dynamics,” Nature 261 (1976), pp. 459–67. Also: “Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos,” Science 186 (1974), pp. 645–47, and May and George F. Oster, “Bifurcations and Dynamic Complexity in Simple Ecological Models,” The American Naturalist 110 (1976), pp. 573–99. An excellent survey of the development of mathematical modeling of populations, before chaos, is Sharon E. Kingsland, Modeling Nature: Episodes in the History of Population Ecology (Chicago: University of Chicago Press, 1985).
THE WORLD MAKES May and Jon Seger, “Ideas in Ecology: Yesterday and Tomorrow,” preprint, Princeton University, p. 25.
CARICATURES OF REALITY May and George F. Oster, “Bifurcations and Dynamic Complexity in Simple Ecological Models,” The American Naturalist 110 (1976), p. 573.
BY THE 1950s May.
REFERENCE BOOKS J. Maynard Smith, Mathematical Ideas in Biology (Cambridge: Cambridge University Press, 1968), p. 18; Harvey J. Gold, Mathematical Modeling of Biological Systems.
IN THE BACK May.
HE PRODUCED A REPORT Gonorrhea Transmission Dynamics and Control. Herbert W. Hethcote and James A. Yorke (Berlin: Springer-Verlag, 1984).
THE EVEN-ODD SYSTEM From computer simulations, Yorke found that the system forced drivers to make more trips to the filling station and to keep their tanks fuller all the time; thus the system increased the amount of gasoline sitting wastefully in the nation’s automobiles at any moment.
HE ANALYZED THE MONUMENT’S SHADOW Airport records later proved Yorke correct.
LORENZ’S PAPER Yorke.
“FACULTY MEMBERS” Murray Gell-Mann, “The Concept of the Institute,” in Emerging Syntheses in Science, proceedings of the founding workshops of the Santa Fe Institute (Santa Fe: The Santa Fe Institute, 1985), p. 11.
HE GAVE A COPY Yorke, Smale.
“IF YOU COULD WRITE” Yorke.
HOW NONLINEAR NATURE IS A readable essay on linearity, non-linearity, and the historical use of computers in understanding the difference is David Campbell, James P. Crutchfield, J. Doyne Farmer, and Erica Jen, “Experimental Mathematics: The Role of Computation in Nonlinear Science,” Communications of the Association for Computing Machinery 28 (1985), pp. 374–84.
“IT DOES NOT SAY” Fermi, quoted in S. M. Ulam, Adventures of a Mathematician (New York: Scribners, 1976). Ulam also describes the origin of another important thread in the