In response to the variety of comments on the weblog of October 6, 2005 entitled “What is the Butterfly Effect”, I asked Associate Professor Richard Eykholt of the Department of Physics at Colorado State University to provide his perspective on the discussion. Professor Eykholt is an internationally respected expert on chaos and nonlinear dynamical systems. His website provides information on his excellent professional and academic credentials.
His response to my request (dated October 11, 2005) is reproduced, with his permission;
I think that you captured the key features and misconceptions pretty well. The butterfly effect refers to the exponential growth of any small perturbation. However, this exponential growth continues only so long as the disturbance remains very small compared to the size of the attractor. It then folds back onto the attractor. Unfortunately, most people miss this latter part and think that the small perturbation continues to grow until it is huge and has some large effect. The point of the effect is that it prevents us from making very detailed predictions at very small scales, but it does not have a significant effect at larger scales.
This summary should put to rest the misconception about the “butterfly effect.” In answer to the question presented in the original weblog on this subject, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?”, the answer is absolutely no.
Roger A. Pielke Sr.