Chaos - James Gleick [157]
THE EIFFEL TOWER Fractal Geometry, p. 131, and “On Fractal Geometry,” p. 1663. 102 ORIGINATED BY MATHEMATICIANS F. Hausdorff and A. S. Besicovich.
“THERE WAS A LONG HIATUS” Mandelbrot.
IN THE NORTHEASTERN Scholz; C. H. Scholz and C. A. Aviles, “The Fractal Geometry of Faults and Faulting,” preprint, Lamont-Doherty Geophysical Observatory; C. H. Scholz, “Scaling Laws for Large Earthquakes,” Bulletin of the Seismological Society of America 72 (1982), pp. 1–14.
“A MANIFESTO” Fractal Geometry, p. 24.
“NOT A HOW-TO BOOK” Scholz.
“IT’S A SINGLE MODEL” Scholz.
“IN THE GRADUAL” William Bloom and Don W. Fawcett, A Textbook of Histology (Philadelphia: W. B. Saunders, 1975).
SOME THEORETICAL BIOLOGISTS One review of these ideas is Ary L. Goldberger, “Nonlinear Dynamics, Fractals, Cardiac Physiology, and Sudden Death,” in Temporal Disorder in Human Oscillatory Systems, ed. L. Rensing, U. An der Heiden, M. Mackey (New York: Springer-Verlag, 1987).
THE NETWORK OF SPECIAL FIBERS Goldberger, West.
SEVERAL CHAOS-MINDED CARDIOLOGISTS Ary L. Goldberger, Valmik Bhargava, Bruce J. West and Arnold J. Mandell, “On a Mechanism of Cardiac Electrical Stability: The Fractal Hypothesis,” Biophysics Journal 48 (1985), p. 525.
WHEN E. I. DUPONT Barnaby J. Feder, “The Army May Have Matched the Goose,” The New York Times, 30 November 1986, 4:16.
“I STARTED LOOKING” Mandelbrot.
HIS NAME APPEARED I. Bernard Cohen, Revolution in Science (Cambridge, Mass.: Belknap, 1985), p. 46.
“OF COURSE, HE IS A BIT” Mumford.
“HE HAD SO MANY DIFFICULTIES” Richter.
IF THEY WANTED TO AVOID Just as Mandelbrot later could avoid the credit routinely given to Mitchell Feigenbaum in references to Feigenbaum numbers and Feigenbaum universality. Instead, Mandelbrot habitually referred to P. J. Myrberg, a mathematician who had studied iterates of quadratic mappings in the early 1960s, obscurely.
“MANDELBROT DIDN’T HAVE EVERYBODY’S” Richter.
“THE POLITICS AFFECTED” Mandelbrot.
EXXON’S HUGE RESEARCH FACILITY Klafter.
ONE MATHEMATICIAN TOLD FRIENDS Related by Huberman.
“WHY IS IT THAT” “Freedom, Science, and Aesthetics,” in Schönheit im Chaos, p. 35.
“THE PERIOD HAD NO SYMPATHY” John Fowles, A Maggot (Boston: Little, Brown, 1985), p. 11.
“WE HAVE THE ASTRONOMERS” Robert H. G. Helleman, “Self-Generated Behavior in Nonlinear Mechanics,” in Fundamental Problems in Statistical Mechanics 5, ed. E. G. D. Cohen (Amsterdam: North-Holland, 1980), p. 165.
BUT PHYSICISTS WANTED MORE Leo Kadanoff, for example, asked “Where is the physics of fractals?” in Physics Today, February 1986, p. 6, and then answered the question with a new “multi-fractal” approach in Physics Today, April 1986, p. 17, provoking a typically annoyed response from Mandelbrot, Physics Today, September 1986, p. 11. Kadanoff’s theory, Mandelbrot wrote, “fills me with the pride of a father—soon to be a grandfather?”
STRANGE ATTRACTORS
THE GREAT PHYSICISTS Ruelle, Hénon, Rössler, Sinai, Feigenbaum, Mandelbrot, Ford, Kraichnan. Many perspectives exist on the historical context for the strange-attractor view of turbulence. A worthwhile introduction is John Miles, “Strange Attractors in Fluid Dynamics,” in Advances in Applied Mechanics 24 (1984), pp. 189, 214. Ruelle’s most accessible review article is “Strange Attractors,” Mathematical Intelligencer 2 (1980), pp. 126–37; his catalyzing proposal was David Ruelle and Floris Takens, “On the Nature of Turbulence,” Communications in Mathematical Physics 20 (1971), pp. 167–92; his other essential papers include “Turbulent Dynamical Systems,” Proceedings of the International Congress of Mathematicians, 16–24 August 1983, Warsaw, pp. 271–86; “Five Turbulent Problems,” Physica 7D (1983), pp. 40–44; and “The Lorenz Attractor and the Problem of Turbulence,” in Lecture Notes in Mathematics No. 565 (Berlin: Springer-Verlag, 1976), pp. 146–58.
THERE WAS A STORY Many versions of this exist. Orszag cites four substitutes for Heisenberg—von Neumann, Lamb, Sommerfeld, and von Karman—and adds, “I imagine if God actually gave an answer to these four people it would