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By Root 878 0

Shaw’s dripping faucet the pictures illustrated the point. In three dimensions, especially, the patterns emerged, resembling loopy trails of smoke left by an out-of–control sky-writing plane. Shaw was able to match plots of the experimental data with data produced by his analog computer model, the main difference being that the real data was always fuzzier, smeared out by noise. Even so, the structure was unmistakable. The Santa Cruz group began collaborating with such experienced experimentalists as Harry Swinney, who had moved to the University of Texas in Austin, and they learned how to retrieve strange attractors from all kinds of systems. It was a matter of embedding the data in a phase space of enough dimensions. Soon Floris Takens, who had invented strange attractors with David Ruelle, independently gave a mathematical foundation for this powerful technique of reconstructing the phase space of an attractor from a stream of real data. As countless researchers soon discovered, the technique distinguishes between mere noise and chaos, in the new sense: orderly disorder created by simple processes. Truly random data remains spread out in an undefined mess. But chaos—deterministic and patterned—pulls the data into visible shapes. Of all the possible pathways of disorder, nature favors just a few.

THE TRANSITION FROM REBEL to physicist was slow. Every so often, sitting in a coffeehouse or working in their laboratory, one or another of the students would have to fight back amazement that their scientific fantasy had not ended. God, we’re still doing this and it still makes sense, as Jim Crutchfield would say. We’re still here. How far is it going to go?

Their chief supporters on the faculty were the Smale protégé Ralph Abraham in the mathematics department and in the physics department Bill Burke, who had himself made “czar of the analog computer” to protect the collective’s claim to this piece of equipment, at least. The rest of the physics faculty found itself in a more difficult position. A few years later, some professors denied bitterly that the collective had been forced to overcome indifference or opposition from the department. The collective reacted just as bitterly to what it considered revisionist history on the part of belated converts to chaos. “We had no advisor, nobody telling us what to do,” said Shaw. “We were in an adversary role for years, and it continues to this day. We were never funded at Santa Cruz. Every one of us worked for considerable periods of time without pay, and it was a shoestring operation the entire way, with no intellectual or other guidance.”

By its lights, though, the faculty tolerated and even abetted a long period of research that seemed to fall short of any substantial kind of science. Shaw’s thesis advisor in superconductivity kept him on salary for a year or so, long after Shaw had veered away from low-temperature physics. No one ever quite ordered the chaos research to stop. At worst the faculty reached an attitude of benevolent discouragement. Each member of the collective was taken aside from time to time for heart-to–heart talks. They were warned that, even if somehow a way could be found to justify doctorates, no one would be able to help the students find jobs in a nonexistent field. This may be a fad, the faculty would say, and then where will you be? Yet outside the redwood shelter of the Santa Cruz hills, chaos was creating its own scientific establishment, and the Dynamical Systems Collective had to join it.

One year Mitchell Feigenbaum came by, making the rounds of the lecture circuit to explain his breakthrough in universality. As always, his talks were abstrusely mathematical; renormalization group theory was an esoteric piece of condensed matter physics that these students had not studied. Besides, the collective was more interested in real systems than in delicate one-dimensional maps. Doyne Farmer, meanwhile, heard that a Berkeley mathematician, Oscar E. Lanford III, was exploring chaos, and he went up to talk. Lanford listened politely and then looked at Farmer