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By Root 875 0

1960s. He had made it his business to pursue clues to the possibility of erratic behavior in models of star motion, and he kept in touch with the French mathematicians. Eventually, as a professor at Columbia University, he made turbulence in space—“cosmic arrhythmias”—the focus of his astronomical study. He had a flair for captivating his colleagues with new ideas, and as the night wore on he captivated Burke. Burke was open to such things. He had made his reputation by working through one of Einstein’s more paradoxical gifts to physics, the notion of gravity waves rippling through the fabric of space-time. It was a highly nonlinear problem, with misbehavior related to the troublesome nonlinearities in fluid dynamics. It was also properly abstract and theoretical, but Burke liked down-to-earth physics, too, at one point publishing a paper on the optics of beer glasses: how thick could you make the glass and still leave the appearance of a full portion of beer. He liked to say that he was a bit of a throwback who considered physics to be reality. Furthermore, he had read Robert May’s paper in Nature, with its plaintive plea for more education about simple nonlinear systems, and he, too, had taken a few hours to play with May’s equations on a calculator. So the Lorenz attractor sounded interesting. He had no intention of listening to it. He wanted to see it. When he returned to Santa Cruz, he handed Rob Shaw a piece of paper on which he had scrawled a set of three differential equations. Could Shaw put these on the analog computer?

In the evolution of computers, analog machines represented a blind alley. They did not belong in physics departments, and the existence of such things at Santa Cruz was pure happenstance: the original plans for Santa Cruz had included an engineering school; by the time the engineering school was canceled, an eager purchasing agent had already bought some equipment. Digital computers, built up from circuitry that switched off or on, zero or one, no or yes, gave precise answers to the questions programmers asked, and they proved far more amenable to the miniaturization and acceleration of technology that ruled the computer revolution. Anything done once on a digital computer could be done again, with exactly the same result, and in principle could be done on any other digital computer. Analog computers were, by design, fuzzy. Their building blocks were not yes-no switches but electronic circuits like resistors and capacitors—instantly familiar to anyone who played with radios in the era before solid-state, as Shaw had. The machine at Santa Cruz was a Systron-Donner, a heavy, dusty thing with a patch panel for its front, like the patch panels used by old–fashioned telephone switchboards. Programming the analog computer was a matter of choosing electronic components and plugging cords into the patch panel.

By building up various combinations of circuitry, a programmer simulates systems of differential equations in ways that happen to be well-suited to engineering problems. Say you want to model an automobile suspension with springs, dampers, and mass, to design the smoothest ride. Oscillations in the circuitry can be made to correspond to the oscillations in the physical system. A capacitor takes the place of a spring, inductors represent mass, and so forth. The calculations are not precise. Numerical computation is sidestepped. Instead you have a model made of metal and electrons, quite fast and—best of all—easily adjustable. Simply by turning knobs, you can adjust variables, making the spring stronger or the friction weaker. And you can watch the results change in real time, patterns traced across the screen of an oscilloscope.

Upstairs in the superconductivity laboratory, Shaw was making his desultory way to the end of his thesis work. But he was beginning to spend more and more time playing with the Systron-Donner. He had got far enough to see phase-space portraits of some simple systems—representations of periodic orbits, or limit cycles. If he had seen chaos, in the form of strange attractors,