BLOGS

Lorenz Attractor - the never-repeating trajectory of a single chaotic orbit, figure 2 (see link)

At the time, most meteorologists predicted weather using linear procedures, which were based on the premise that tomorrow’s weather is a well-defined linear combination of features of today’s weather. By contrast, an emerging school of dynamic meteorologists believed that weather could be more accurately predicted by simulating the fluid dynamical equations underlying atmospheric flows. Lorenz, who had just purchased his first computer, a Royal McBee LGP-30 with an internal memory of 4096 32-bit words, decided to compare the two approaches by pitting the linear procedures against a simplified 12-variable dynamical model. (Lorenz’s computer, though a thousand times faster than his desk calculator, was still a million times slower than a current laptop.)

In classical physics, one is taught that given the initial state of a system, all of its future states can be calculated. In the celebrated words of Pierre Simon Laplace, “An intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis . . . for it, nothing would be uncertain and the future, as the past, would be present to its eyes.”1 Or, put another way, the clockwork universe holds true.

Herein lies the rub: Exact knowledge of a real-world initial state is never possible—the adviser can always demand a few more digits of experimental precision from the student, but the result will never be exact. Still, until the 19th century, the tacit assumption had always been that approximate knowledge of the initial state implies approximate knowledge of the final state. Given their success describing the motion of the planets, comets, and stars and the dynamics of countless other systems, physicists had little reason to assume otherwise.

Starting in the 19th century, however, and culminating with a 1963 paper by MIT meteorologist Edward Lorenz, a series of developments revealed that the notion of deterministic predictability, although appealingly intuitive, is in practice false for most systems. Small uncertainties in an initial state can indeed become large errors in a final one. Even simple systems for which all forces are known can behave unpredictably. Determinism, surprisingly enough, does not preclude chaos.