Day: April 17, 2008

In honor of the passing of Dr. Edward Lorenz yesterday, I heard a butterfly say the entire species will recognize the man by not flapping their wings for a one minute observation today.

Dr. Lorenz is best known for the notion of the “butterfly effect,” the idea that a small disturbance like the flapping of a butterfly’s wings can induce enormous consequences.

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.

When I was in college, one of my math professors taught a chaos theory class.  His term (and I’m sure this is near-universal for chaos theoreticians,  but I’ve only heard him say this) was SDOIC – Situation Dependent on Initial Conditions (we pronounced it stoyk).  In chaotic systems, the results you get are extremely sensitive to changes in initial inputs.  As seen in Dr. Lorenz’s weather simulation, only slightlchanges in the measurements later in the simulation lead to completely different outputs at the end.  Thus the tiniest change in conditions, such as changes to air currents brought about by a butterfly flapping her wings, can lead to massive differences in conditions throughout an entire system.

Clearly, I cannot explain this well enough, but it is a fascinating branch of mathematics, and well worth learning more about if you are interested.  And there is much more to it than what Jeff Goldblum discussed in Jurassic Park.

So remember if the weather is batshit crazy tomorrow, it’s due to the butterflies honoring Dr. Lorenz today.  And that, dear reader, is chaos at work.

[tags]RIP, Dr. Lorenz, Edward Lorenz, Chaos theory, the pirates don’t eat the tourists, Nobody could’ve predicted that[/tags]