THE BUTTERFLY EFFECT

THE BUTTERFLY EFFECT Étienne GHYS CNRS-UMPA ENS Lyon etienne.ghys@ens-lyon.fr It is very unusual for a mathematical idea to disseminate into the society at large. An interesting example is chaos theory, popularized by Lorenz’s butterfly effect: “does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” A tiny cause can generate big consequences! Can one adequately summarize chaos theory in such a simple minded way? Are mathematicians responsible for the inadequate transmission of their theories outside of their own community? What is the precise message that Lorenz wanted to convey? Some of the main characters of the history of chaos were indeed concerned with the problem of communicating their ideas to other scientists or non-scientists. I’ll try to discuss their successes and failures. The education of future mathematicians should include specific training to teach them how to explain mathematics outside their community. This is more and more necessary due to the i...

Yes there’s a difference. The butterfly effect is just one example that shows why it’s difficult to model complex systems. That’s why it’s a good way to explain what chaos theory “is,” because chaos theory is a certain perspective on trying to model complex systems. Most people who model the weather are not exactly chaos theorists, although some of them know a lot about chaos theory. Chaos theory is a branch of physics and mathematics that tries to unify and make general statements about modeling complex systems.

The Butterfly Effect Weather prediction is an extremely difficult problem. Meteorologists can predict the weather for short periods of time, a couple days at most, but beyond that predictions are generally poor. Edward Lorenz was a mathematician and meteorologist at the Massachusetts Institute of Technology who loved the study of weather. With the advent of computers, Lorenz saw the chance to combine mathematics and meteorology. He set out to construct a mathematical model of the weather, namely a set of differential equations that represented changes in temperature, pressure, wind velocity, etc. In the end, Lorenz stripped the weather down to a crude model containing a set of 12 differential equations. On a particular day in the winter of 1961, Lorenz wanted to re-examine a sequence of data coming from his model. Instead of restarting the entire run, he decided to save time and restart the run from somewhere in the middle. Using data printouts, he entered the conditions at som...