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HISTORIAN OF SCIENCE Kuhn’s understanding of scientific revolutions has been widely dissected and debated in the twenty-five years since he put it forward, at about the time Lorenz was programming his computer to model weather. For Kuhn’s views I have relied primarily on The Structure of Scientific Revolutions, 2nd ed. enl. (Chicago: University of Chicago Press, 1970) and secondarily on The Essential Tension: Selected Studies in Scientific Tradition and Change (Chicago: University of Chicago, 1977); “What Are Scientific Revolutions?” (Occasional Paper No. 18, Center for Cognitive Science, Massachusetts Institute of Technology); and Kuhn, interview. Another useful and important analysis of the subject is I. Bernard Cohen, Revolution in Science (Cambridge, Mass.: Belknap Press, 1985).

“I CAN’T MAKE Structure, pp. 62–65, citing J. S. Bruner and Leo Postman, “On the Perception of Incongruity: A Paradigm,” Journal of Personality XVIII (1949), p. 206.

MOPPING UP OPERATIONS structure, p. 24.

EXPERIMENTALISTS CARRY OUT Tension, p. 229.

IN BENJAMIN FRANKLIN’S STRUCTURE, pp. 13–15.

“UNDER NORMAL CONDITIONS TENSION, p. 234.

A PARTICLE PHYSICIST Cvitanović

TOLSTOY Ford, interview and “Chaos: Solving the Unsolvable, Predicting the Unpredictable,” in Chaotic Dynamics andFractals, ed. M. F. Barnsley and S. G. Demko (New York: Academic Press, 1985).

SUCH COINAGES But Michael Berry notes that the OED has “Chaology (rare) ‘the history or description of the chaos.’” Berry, “The Unpredictable Bouncing Rotator: A Chaology Tutorial Machine,” preprint, H. H. Wills Physics Laboratory, Bristol.

“IT’S MASOCHISM Richter.

THESE RESULTS APPEAR J. Crutchfield, M. Nauenberg and J. Rudnick, “Scaling for External Noise at the Onset of Chaos,” Physical Review Letters 46 (1981), p. 933.

THE HEART OF CHAOS Alan Wolf, “Simplicity and Universality in the Transition to Chaos,” Nature 305 (1983), p. 182.

CHAOS NOW PRESAGES Joseph Ford, “What is Chaos, That We Should Be Mindful of It?” preprint, Georgia Institute of Technology, Atlanta.

REVOLUTIONS DO NOT “What Are Scientific Revolutions?” p. 23.

“IT IS RATHER AS IF” Structure, p. 111.

THE LABORATORY MOUSE Yorke and others.

WHEN ARISTOTLE LOOKED “What Are Scientific Revolutions?” pp. 2–10.

“IF TWO FRIENDS” Galileo Opere VIII: 277. Also VIII: 129–30.

“PHYSIOLOGICAL AND PSYCHIATRIC” David Tritton, “Chaos in the swing of a pendulum,” New Scientist, 24 July 1986, p. 37. This is a readable, nontechnical essay on the philosophical implications of pendulum chaos.

THAT CAN HAPPEN In practice, someone pushing a swing can always produce more or less regular motion, presumably using an unconscious nonlinear feedback mechanism of his own.

YET, ODD AS IT SEEMS Among many analyses of the possible complications of a simple driven pendulum, a good summary is D. D’Humieres, M. R. Beasley, B. A. Huberman, and A. Libchaber, “Chaotic States and Routes to Chaos in the Forced Pendulum,” Physical Review A 26 (1982), pp. 3483–96.

SPACE BALLS Michael Berry researched the physics of this toy both theoretically and experimentally. In “The Unpredictable Bouncing Rotator” he describes a range of behaviors understandable only in the language of chaotic dynamics: “KAM tori, bifurcation of periodic orbits, Hamiltonian chaos, stable fixed points and strange attractors.”

FRENCH ASTRONOMER Hénon.

JAPANESE ELECTRICAL ENGINEER Ueda. 45 A YOUNG PHYSICIST Fox.

SMALE Smale, Yorke, Guckenheimer, Abraham. May, Feigenbaum; a brief, somewhat anecdotal account of Smale’s thinking during this period is “On How I Got Started in Dynamical Systems,” in Steve Smale, The Mathematics of Time: Essays on Dynamical Systems, Economic Processes, and Related Topics (New York: Springer-Verlag, 1980), pp. 147–51.

THE SCENE IN Moscow Raymond H. Anderson, “Moscow Silences a Critical American,” The New York Times, 27 August 1966, p. 1; Smale, “On the Steps of Moscow University,” The Mathematical Intelligencer 6:2, pp. 21–27.

WHEN HE RETURNED Smale.

A LETTER FROM A COLLEAGUE The colleague was N. Levinson. Several threads of mathematics, running back