Saturday, April 19, 2008

Edward Lorenz: Rest in Equilibrium

Meteorologist Edward Lorenz has died at the age of 90. The theories of deterministic chaos/dynamic systems and their associated applications in complexity theory have been pretty seminal in my thinking (as anyone who's endured me droning on about attractors and emergent phenomena can testify), and I've always admired Lorenz as one of the first to see into the tangled relationships between chaos and deep order in the universe.

Lorenz was one of that rare breed of researchers who could look at anomalous findings and not simply write them off to faulty experimental design or human error. Better still, he could detect the presence of those factors and still have the presence of mind to discern that something deeper was afoot anyway:

As recounted in the book “Chaos” by James Gleick, Dr. Lorenz’s accidental discovery of chaos came in the winter of 1961. Dr. Lorenz was running simulations of weather using a simple computer model. One day, he wanted to repeat one of the simulations for a longer time, but instead of repeating the whole simulation, he started the second run in the middle, typing in numbers from the first run for the initial conditions.

The computer program was the same, so the weather patterns of the second run should have exactly followed those of the first. Instead, the two weather trajectories quickly diverged on completely separate paths.

At first, he thought the computer was malfunctioning. Then he realized that he had not entered the initial conditions exactly. The computer stored numbers to an accuracy of six decimal places, like 0.506127, while, to save space, the printout of results shortened the numbers to three decimal places, 0.506. When typing in the new conditions, Dr. Lorenz had entered the rounded-off numbers, and even this small discrepancy, of less than 0.1 percent, completely changed the end result.

Even though his model was vastly simplified, Dr. Lorenz realized that this meant perfect weather prediction was a fantasy.

A perfect forecast would require not only a perfect model, but also perfect knowledge of wind, temperature, humidity and other conditions everywhere around the world at one moment of time. Even a small discrepancy could lead to completely different weather.
It was Lorenz who coined the term "butterfly effect" to refer to this phenomenon of "sensitive dependency on initial conditions." With the advent of more powerful computers and their ability to perform intensive iterations and so reveal the complexity which could emerge from relatively simple parameters, the storm of profound insights into nature which arose from his elegant formulations has enriched our lives in ways even he could not have foreseen.

His was a life well and fully lived, and we owe him much.

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