The Butterfly Effect (Edward N. Lorenz)

Edward Lorenz, best known for the notion of the "butterfly effect," died last Wednesday. From the New York Times obituary:

In discovering “deterministic chaos,” Dr. Lorenz established a principle that “profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind’s view of nature since Sir Isaac Newton,” said a committee that awarded him the 1991 Kyoto Prize for basic sciences.
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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.

Dr. Lorenz published his findings in 1963. “The paper he wrote in 1963 is a masterpiece of clarity of exposition about why weather is unpredictable,” said J. Doyne Farmer, a professor at the Santa Fe Institute in New Mexico.

The following year, Dr. Lorenz published another paper that described how a small twiddling of parameters in a model could produce vastly different behavior, transforming regular, periodic events into a seemingly random chaotic pattern.

At a meeting of the American Association for the Advancement of Science in 1972, he gave a talk with a title that captured the essence of his ideas: “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”