Archives for 6.25.11

Have you heard of Edward Lorenz? During WWII, he served as a weather forecaster for the U.S. Army Air Corps. When he came home from the war, he decided to study meteorology. He studied at MIT where, in the early 60s, he set out to construct a mathematical model of the weather. He managed to narrow all weather down to a set of 12 differential equations.

On one particular day, Lorenz wanted to re-examine a sequence of data from his model. Instead of starting at the very beginning, he decided to save time and restart the run in the middle. He entered the conditions at some point near the middle of the previous run and restarted his calculations. The data from the second run should have exactly matched the data from the first run. But, that’s not what happened. They matched at first; but, then, the runs eventually began to diverge and not just slightly but dramatically. The further the data progressed, the less resemblance between them until they were nothing at all alike. They looked a bit like this:

At first, Lorenz thought something had gone wrong with his computer. Then, he realized that when he started the second run, he had used numbers rounded off to three digits, assuming that anything beyond that was inconsequential. But, his computer used six digits, not three. And, apparently even .000001 is far from inconsequential.

He concluded that long-term weather forecasting was impossible and pioneered the phenomenon known as “sensitive dependence on initial conditions,” meaning that the slightest difference in initial conditions, even ones beyond human ability to measure, made prediction of past or future outcomes impossible. He proclaimed, “a single flap of a single seagull’s wings would be enough to change the course of all future weather systems on the earth.” The seagull was changed to the more poetic sounding butterfly and the theory became well known as the butterfly effect, causing quite a stir in modern science. After all, this theory violated the basic conventions of physics. Science teaches that small initial changes lead to small changes in behavior. Every high school student knows well that for every action there is an equal and opposite reaction. But, Lorenz’s findings showed something different. Even the very smallest disturbance, even the very smallest action, one perhaps no one would ever notice, could cause major change and have a dramatic future effect on the world around it.

So, what is your .000001?