by Brian Awehali

When Edward Lorenz gave a talk in 1972 entitled “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?,” he distilled the main essence of his thoughts on predictability, interdependence and “chaos theory” in one pithy question.

Lorenz was a mathemetician and a meteorologist who, in the early 1960s, discovered that weather simulation models he was developing were exhibiting chaotic, non-predictive behavior, despite a fixed set of variables and no apparent equipment malfunction. Two identical weather simulation machines, side-by-side, given the same variables to process. Wildly different results. How?

Lorenz eventually concluded that it was a “dependence on initial conditions” — in this case, the fact of computers rounding variables to decimal points: 3.12879 expressed as 3.13, etc. Even extending the number of decimal points in the simulators did not produce matching results from the weather machines. Minute variations gave rise to wildly different chains of events.

Lorenz also advanced work on what came to be known as the Lorenz Attractor, or Strange Attractor, which describes the behavior of chaotic flow in lasers, dynamos, and water wheels. The mathematical expression of Lorenz’s Strange Attractor is (seemingly coincidentally) shaped like a butterfly, and some Java programmer in Japan was kind enough to create an animated demonstration of it.

Contrary to some popular misconceptions about chaos theory, it doesn’t mean randomness prevails. Rather, it means that things occur in a non-linear, but deterministic fashion, with an extreme sensitivity to initial conditions. Fractal geometry in nature, as well as Mandelbrot sets, illustrate the mathematics of chaos theory.

French mathematician Henry Poincaré is really the “father” of chaos theory; Lorenz mostly re-popularized an idea that had merely fallen from the limelight. At the end of the 19th century, Poincaré, encouraged by an award offered by King Oscar II of Sweden, looked into how to explain the erratic orbit of Neptune and the broader question, is the solar system stable? (Poincaré’s eventual conclusion was no, but the preceding link provides a far more satisfying overview of his voyage to that conclusion.)

I was first exposed to chaos theory through James Gleick’s excellent book, Chaos: The Making of a New Science. The notion of a greater complexity and deeper order underlying the observable surface of things is great on many levels beyond the scholarly realm. Chaos theory is a rich metaphor for our present moment, which promises to impress upon quite a few people, in ways both small and large, pleasant and unpleasant, that everything is connected and even, to some extent, interdependent. And, apropos of our time in my opinion, this understanding now raises far more questions than it provides answers.