修改了发票金额怎么查:谁能告诉我“蝴蝶效应”这个词相关的英文资料

The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system. This is sometimes presented as esoteric behavior, but can be exhibited by very simple 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.

Recurrence, the approximate return of a system towards its initial conditions, together with the sensitive dependence on initial conditions, are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range—approximately a week, in the case of weather.

History
Sensitive dependence on initial conditions was first described in the literature by Hadamard and popularized by Duhem's 1906 book. The term butterfly effect is related to the work of Lorenz, who in a 1963 paper for the New York Academy of Sciences noted that "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. According to Lorenz, upon failing to provide a title for a talk he was to present at the 139th meeting of the AAAS in 1972, Philip Merilees concocted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? as a title.

Popular media
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 1952 short story by Ray Bradbury, "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.

The Butterfly effect was also invoked by the fictional mathematician, Ian Malcolm, in both the novel and film versions of Jurassic Park. He used it to explain the inherent instability of (among other things) an amusement park with dinosaurs as the attraction.

更多参考资料：
http://www.monochrom.at/butterfly/
http://www.fortunecity.com/emachines/e11/86/beffect.html
http://www.news.cornell.edu/releases/Feb04/AAAS.Kleinberg.ws.html
http://necsi.org/guide/concepts/butterflyeffect.html
http://www.butterflyeffectmovie.com/
http://hypertextbook.com/chaos/
http://mathworld.wolfram.com/ButterflyEffect.html

The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system. This is sometimes presented as esoteric behavior, but can be exhibited by very simple 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.

Recurrence, the approximate return of a system towards its initial conditions, together with the sensitive dependence on initial conditions, are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range—approximately a week, in the case of weather.

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中文参考：何谓蝴蝶效应？先从美国麻省理工学院气象学家洛伦兹（Lorenz）的发现谈起。为了预报天气，他用计算机求解仿真地球大气的13个方程式。为了更细致地考察结果，他把一个中间解取出，提高精度再送回。而当他喝了杯咖啡以后回来再看时竟大吃一惊：本来很小的差异，结果却偏离了十万八千里！计算机没有毛病，于是，洛伦兹（Lorenz）认定，他发现了新的现象：“对初始值的极端不稳定性”，即：“混沌 ”，又称“蝴蝶效应”，亚洲蝴蝶拍拍翅膀，将使美洲几个月后出现比狂风还厉害的龙卷风！

这个发现非同小可，以致科学家都不理解，几家科学杂志也都拒登他的文章，认为“违背常理”：相近的初值代入确定的方程，结果也应相近才对，怎幺能大大远离呢。desperate 的理解可能放在整体上，可是蝴蝶效应说的就是“一件事”对结果的影响，就象只改动了一点数据计算的结果都会相差十万八千里。“蝴蝶效应”之所以令人着迷、令人激动、发人深省，不但在于其大胆的想象力和迷人的美学色彩，更在于其深刻的科学内涵和内在的哲学魅力。而恰好就是这一点让人很难理解。

butterfly effect

Point attractors in 2D phase space.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 Japan could cause a tornado in California.”

Popular media
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.

butterfly effect

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