Tuesday, January 31, 2006
hullo duck.
Butterfly effect
From Wikipedia, the free encyclopedia.
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searchFor other uses of this term, see
Butterfly effect (disambiguation).
Point
attractors in 2D
phase spaceThe 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.”to emily soh ee ling and amy fairuza whatever ur whole name is.
haha. beat that. i told u such a phenomenon existed.
u know the three of us were at the 24-hour seremban highway Mac's once and i told them about this butterfly effect thing and they have since proclaimed me crazy and the product of a weird education system.
so this is for the both of u. next time when i talk about smth like this, dont give me that incredulous go-back-to-that-weird-country-of-yours look.
posted R @
3:27 am
