Excerpt

The realization in the late twentieth century that deterministic dynamics can be chaotic fundamentally changed our view of predictability vs. unpredictability. Although pieces of the puzzle were understood in the late nineteenth century, Ed Lorenz’s famous 1963 paper brought it all together, explaining the how, why and “so what” of chaos in one fell swoop. In this essay I will explain what chaos is, why this paper was a key original contribution, why it triggered a revolution, how chaos fits into the broader framework of complex systems, and its practical and philosophical implications.

As most readers will know, chaos implies fundamental limits to prediction, but it is more than that: Chaos is a remarkable example of endogenous motion, that is, motion that spontaneously emerges in an otherwise static environment. It is also an example of an unsolvable phenomenon, the dynamical systems analog of Gödel’s proof or Turing’s halting problem. In fact, chaos is a double-edged sword: In some circumstances, the realization that chaos underpins random-looking phenomena leads to vastly improved predictions (Farmer and Sidorowich 1987).

Many phenomena in nature and social science are chaotic. Fluid turbulence and weather are the most famous examples, but there are many others. Celestial mechanics is the canonical example of predictability, but, nonetheless, chaos places a fundamental limit on predicting motion in the solar system of about 20 million years. The first experimental system to be definitively shown to be chaotic was a chemical oscillator, in which the chemical composition fluctuates irregularly in time—a phenomenon that was believed to be theoretically impossible until past the middle of the twentieth century. Chaos explains why populations of species can change spontaneously and unpredictably. Though this is controversial, many (like me) believe that business cycles are due at least in part to chaotic dynamics. At a more theoretical level, the ergodic hypothesis, which underpins all of statistical mechanics, depends on chaotic behavior at the microscopic level. And there are important implications for free will.

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