Chaos - James Gleick [159]
WHEN FEIGENBAUM CAME TO LOS ALAMOS Feigenbaum, Carruthers, Cvitanović, Campbell, Farmer, Visscher, Kerr, Hasslacher, Jen.
“IF YOU HAD SET UP” Carruthers.
THE MYSTERY OF THE UNIVERSE Feigenbaum.
OCCASIONALLY AN ADVISOR Carruthers.
AS KADANOFF VIEWED Kadanoff.
“THE CEASELESS MOTION” Gustav Mahler, letter to Max Marschalk.
“WITH LIGHT POISE” Goethe’s Zür Farbenlehre is now available in several editions. I relied on the beautifully illustrated Goethe’s Color Theory, ed. Rupprecht Matthaei, trans. Herb Aach (New York: Van Nostrand Reinhold, 1970); more readily available is Theory of Colors (Cambridge, Mass.: The M.I.T. Press, 1970), with an excellent introduction by Deane B. Judd.
THIS ONE INNOCENT-LOOKING EQUATION At one point, Ulam and von Neumann used its chaotic properties as a solution to the problem of generating random numbers with a finite digital computer.
TO METROPOLIS, STEIN, AND STEIN This paper—the sole pathway from Stanislaw Ulam and John von Neumann to James Yorke and Mitchell Feigenbaum—is “On Finite Limit Sets for Transformations on the Unit Interval,” Journal of Combinatorial Theory 15 (1973), pp. 25–44.
DOES A CLIMATE EXIST “The Problem of Deducing the Climate from the Governing Equations,” Tellus 16 (1964), pp. 1–11.
THE WHITE EARTH CLIMATE Manabe.
HE KNEW NOTHING OF LORENZ Feigenbaum.
ODDLY May.
THE SAME COMBINATIONS OF R’S AND L’S “On Finite Limit Sets,” pp. 30–31. The crucial hint: “The fact that these patterns … are a common property of four apparently unrelated transformations … suggests that the pattern sequence is a general property of a wide class of mappings. For this reason we have called this sequence of patterns the U-sequence where ‘U’ stands (with some exaggeration) for ‘universal.’” But the mathematicians never imagined that the universality would extend to actual numbers; they made a table of 84 different parameter values, each taken to seven decimal places, without observing the geometrical relationships hidden there.
“THE WHOLE TRADITION OF PHYSICS” Feigenbaum.
HIS FRIENDS SPECULATED Cvitanović.
SUDDENLY YOU COULD SEE Ford.
PRIZES AND AWARDS The MacArthur fellowship; the 1986 Wolf Prize in physics.
“FEIGENBAUMOLOGY” Dyson.
“IT WAS A VERY HAPPY” Gilmore.
BUT ALL THE WHILE Cvitanović.
WORK BY OSCAR E. LANFORD Even then, the proof was unorthodox in that it depended on tremendous amounts of numerical calculation, so that it could not be carried out or checked without the use of a computer. Lanford; Oscar E. Lanford, “A Computer-Assisted Proof of the Feigenbaum Conjectures,” Bulletin of the American Mathematical Society 6 (1982), p. 427; also, P. Collet, J.P. Eckmann, and O. E. Lanford, “Universal Properties of Maps on an Interval,” Communications in Mathematical Physics 81 (1980), p. 211.
“SIR, DO YOU MEAN” Feigenbaum; ”The Discovery of Universality,” p. 17.
IN THE SUMMER OF 1977 Ford, Feigenbaum, Lebowitz.
“MITCH HAD SEEN UNIVERSALITY” Ford.
“SOMETHING DRAMATIC HAPPENED” Feigenbaum.
THE EXPERIMENTER
“ALBERT IS GETTING MATURE” Libchaber, Kadanoff.
HE SURVIVED THE WAR Libchaber.
“HEUUM IN A SMALL BOX” Albert Libchaber, “Experimental Study of Hydrodynamic Instabilities. Rayleigh-Benard Experiment: Helium in a Small Box,” in Nonlinear Phenomena at Phase Transitions and Instabilities, ed. T. Riste (New York: Plenum, 1982), p. 259.
THE LABORATORY OCCUPIED Libchaber, Feigenbaum.
“SCIENCE WAS CONSTRUCTED” Libchaber.
“BUT YOU KNOW THEY DO!” Libchaber.
“THE FLECKED RIVER” Wallace Stevens, “This Solitude of Cataracts,” The Palm at the End of the Mind, ed. Holly Stevens (New York: Vintage, 1972), p. 321.
“INSOLID BILLOWING OF THE SOLID” “Reality Is an Activity of the Most August Imagination,” Ibid., p. 396.
“BUILDS ITS OWN BANKS” Theodor Schwenk, Sensitive Chaos (New York: Schocken, 1976), p. 19.
“ARCHETYPAL PRINCIPLE” Ibid.
“THIS PICTURE OF STRANDS” Ibid., p. 16.
“THE INEQUALITIES” Ibid., p. 39.
“IT MAY BE” D