★★☆☆☆ Good on the facts, bad on interpretation

Chaos: Making a New Science

James Gleick

Chaos: Making a New Science was the first book by James Gleick I read. I read one other book of his subsequently, his biography of Richard Feynman, Genius. I hope never to read another book by Gleick, because, while informative, they are annoying and misleading.

What I liked about Chaos: I learned a lot about the history of chaos theory research by reading Chaos. For instance, I didn't realize that as great deal of chaos research was done at the University of California at Santa Cruz. I even learned a little about chaos theory, but not much, because it's a subject I have been interested in for many years.

What I didn't like: Gleick tells about chaos research as a Scientific Revolution, of the type Thomas S. Kuhn wrote about in his famous book The Structure of Scientific Revolutions. It is my opinion that Kuhn was mostly wrong. But that is less important than the observation that chaos research clearly was not a scientific revolution of the type described by Kuhn. It was exciting mainstream mathematical research that was welcomed and encouraged by the math establishment. I was there and watching.

I was a 20-year-old brand-new grad student when Robert M. May published his famous 1976 Nature review paper, "Simple mathematical models with very complicated dynamics". This paper is now esteemed a classic of chaos research. It described the onset of chaos in what we now call the Logistic Map, one of the simplest chaotic systems. May left a lot unexplained, because at that time no one understood the Logistic Map or chaos very well. I thought it was a terrific paper. I gobbled it down with enthusiasm and for weeks after bored my fellow grad students (who, being Biochemistry students were less interested in math than I) by gassing about it.

In 1981 Douglas R. Hofstadter wrote an excellent column in Scientific American on the subject of "Strange attractors: mathematical patterns delicately poised between order and chaos", which once again tackled the logistic map, but with far more resolution, since chaos research had progressed a lot in the meantime. Hofstadter was able at this time to point out the connection to fractals and to mention Benoît B. Mandelbrot. "Strange attractors" was an installment of Hofstadter's monthly recreational mathematics column "Metamagical Themas".

By 1986 it had become clear that the logistic map is closely connected to a particular fractal, the Mandelbrot Set. Heinz-Otto Peitgen and Peter H. Richter produced a book, The Beauty of Fractals: Images of Complex Dynamical Systems, of beautiful pictures of the Mandelbrot set and other fractals, and Mandelbrot screensavers were seen on computers all over the world. Also in 1986 Scientific American published a regular research article on chaos theory simply entitled "Chaos" that extended it beyond the logistic map. Gleick published Chaos in 1987.

I mentioned these things to make a point. If your field of research is introduced by a review article in Nature (there was in 1976 no more prestigious venue for a scientific publication), is written up in the world's best-known popular mathematics column, is published in a full research paper in Scientific American, and is the source of screensavers and a coffee table book of pictures, you are not the Plucky Young Revolutionaries -- you're the Entrenched Establishment.

Now, Gleick did not entirely imagine the revolutionary narrative. In my experience, chaologists were (and are) apt to whine about old-time mathematicians who fail to recognize the significance of their (the chaologists') work. But, Mr Gleick, have you met humans? Feeling underappreciated is their thing! Well, it's ONE of their things. Of course, they didn't entirely imagine the resistance, some old-time mathematicians didn't fully appreciate chaos theory at the start, although my impression is that the resistance was mainly against the practice of doing math by computer, not chaos theory itself. Conservative reaction to novelty is another of those human things. And of course the chaologists would complain, because complaining is yet another of those human things.

Gleick is too credulous. I'm not suggesting that anyone meant to fool Gleick, but in looking for a Good Story he nevertheless fooled himself. He took the whining at face value and improved it with Kuhnian special sauce.

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