Butterfly effect
The Butterfly Effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. The idea is that small variations in the initial conditions of a dynamical system produce large variations in the long term behavior of the system.
Edward Lorenz first analyzed the effect in a 1963 paper for the New York Academy of Sciences. According to the paper, "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever." Later speeches and papers by Lorenz used the more poetic butterfly, possibly inspired by the diagram generated by the Lorenz attractor, which looks like a butterfly; other theories propose that the phrase's basis is to be found in fiction (Ray Bradbury's 1952 story "A Sound of Thunder"), but there is no proof available that Lorenz was swayed by literary precedent.
The practical consequence of the butterfly effect is that complex systems such as the weather are difficult to predict past a certain time range - approximately a week, in the case of weather. This is because any finite model that attempts to simulate a system must necessarily truncate some information about the initial conditions—for example, when simulating the weather, one would not be able to include the wind coming from every butterfly's wings. Although in all practical cases, deficiencies in the knowledge of the initial conditions are more important source of error, as are model deficiencies. In a chaotic system, these errors are magnified as the simulation progresses. Thus the predictions of the simulation are useless after a certain finite amount of time.
See also
External links
- Butterfly Effect (Mathematical Recreations)
- From butterfly wings to single e-mail (Cornell University)
- The Chaos Hypertextbook. An introductory primer on chaos and fractals.
- The Butterfly Effect. New Line Cinema's feature film Butterfly Effect IMDB