Butterfly effect - Encyclopedia

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. Sensitive dependence is also found in non-dynamical systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position.

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. In all practical cases, defects in the knowledge of the initial conditions and deficiencies in the model are equally important sources of error. 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.

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 idea is now often stated something to the effect of, “a butterfly flapping its wings in Tokyo could cause tornadoes in California.”

The concept of the Butterfly effect is sometimes used in popular media dealing with the idea of time travel, though not always accurately. For example, in the movie A Sound of Thunder the characters are determined not to change anything in the past – but in reality their mere presence could be enough to change short-term events (such as the weather), and could also have an unpredictable impact on the distant future.

In many cases, minor and seemingly inconsequential actions in the past are extrapolated over time and can have radical effects on the present time of the main characters. In the movie The Butterfly Effect, Evan Treborn (Ashton Kutcher), when reading from his adolescent journals, is able to essentially "redo" parts of his past. As he continues to do this, he realizes that even though his intentions are good, the actions he takes always have unintended consequences.

• Chaos theory

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