比特币做空杠杆:跪求蝴蝶效应的一些英文资料~

Butterfly effect - the phenomenon whereby a small change at one place in a complex system can have large effects elsewhere, e.g., a butterfly flapping its wings in Rio de Janeiro might change the weather in Chicago
蝴蝶效应
蝴蝶效应是气象学家洛伦兹1963年提出来的。

其大意为：一只南美洲亚马孙河流域热带雨林中的蝴蝶，偶尔扇动几下翅膀，可能在两周后引起美国德克萨斯引起一场龙卷风。其原因在于：蝴蝶翅膀的运动，导致其身边的空气系统发生变化，并引起微弱气流的产生，而微弱气流的产生又会引起它四周空气或其他系统产生相应的变化，由此引起连锁反映，最终导致其他系统的极大变化。

此效应说明，事物发展的结果，对初始条件具有极为敏感的依赖性，初始条件的极小偏差，将会引起结果的极大差异。

“蝴蝶效应”在社会学界用来说明：一个坏的微小的机制，如果不加以及时地引导、调节，会给社会带来非常大的危害，戏称为“龙卷风”或“风暴”；一个好的微小的机制，只要正确指引，经过一段时间的努力，将会产生轰动效应，或称为“革命”。

One of the great modern science stories is the so-called "Butterfly Effect". It suggests that the weather is so sensitive to tiny changes, that something as microscopic as a butterfly flapping its wings in Brazil could set off a tornado in Texas. It's a great bit of Pop Science that has entered the common consciousness - but it's probably wrong.

Weather is that stuff that happens in the 5 million billion tonnes of air and water vapour that wraps around our planet in a thin layer.

Weather is big business on our planet. According to the World Meteorological Organisation, accurate weather forecasts improve the global economy by about $80 billion each year. Every time an aeroplane flight cancellation is avoided, that saves around $80,000 - and every time a flight is not diverted, that saves $300,000.

The modern science of weather predictions probably began in 1913, with the pacifist, physicist and mathematician, Lewis Fry Richardson. World War I broke out the next year, and he found a way to help without violating his personal beliefs - he enlisted as an ambulance driver with the French Army. In his spare time, he would sit down and work out tens of thousands of laborious pencil-and-paper weather calculations. A Norwegian meteorologist had already published very detailed weather data for an area in and around central Germany on May 20, 1910 - some four years earlier. Richardson knew what the weather turned out to be, and he was trying to develop a mathematical model that could successfully use this data to "predict" what actually turned out. But he never could get his model to work.

Richardson thought it was because he didn't have enough data. He proposed to divide the surface of the Earth into tens of thousands of little cells, and gather all possible weather data from each cell. He wrote about this in 1922 in his book called Weather Prediction By Numerical Process. Unfortunately, it was impossible to do the calculations fast enough by pencil and paper.

But then came the Second World War and "unbustable" German war codes and the Atom Bomb - and computers were invented to solve both those problems. In 1950, John von Neumann, one of the fathers of modern computing, realised that his computers were fast enough to solve Richardson's weather problem. By 1953, the ENIAC computer at Princeton University had run Richardson's equations to make moderately successful predictions of the weather. And so the modern age of weather prediction was born.

Today we have a massive network of weather stations on land and buoys at sea, planes and balloons in the air, and satellites looking down from space. They all gather data to feed into these increasingly sophisticated mathematical models of the weather.

But in 1972, Ed Lorenz, a meteorologist at the Massachusetts Institute of Technology said it might be impossible to be truly accurate. He was the first to point out the role of Chaos in weather forecasting, and he came up with that imaginative example of the butterfly wing in Brazil. In fact, he invented the term, "butterfly effect".

Now here's a very important point.

With Chaos Theory, the error starts small and then gets bigger with time and then gets huge. But this is not, repeat NOT, what happens with the weather.

In weather forecasts, the error becomes very large very rapidly, and then begins to tail off - so most of the error in the weather forecasts is not related to Chaos Theory.

This really bothered David Orrell, a mathematician at the University College in London. He and his fellow mathematicians started thinking about what would happen if the actual mathematical models that the meteorologists use to predict the weather were wrong. They proved a mathematical theorem that predicted exactly how, if a model really was wrong, its errors would grow as time progressed. In fact, these errors should follow a "Square Root Law" - growing very rapidly at first, and then slowing down after a few days. And believe it or not, this is how the errors in the weather forecasts behave.

In other words, according to David Orrell, the main thing stopping us from getting accurate weather forecasts three days down the line is not the Butterfly Effect (which is real), but the errors in the models.

His theory can't say where the errors are, only that there are errors. And once the mathematicians and the meteorologists get together and come up with better models of the weather, they should be able to make dead accurate forecasts up to three days down the line. The Chaos effects will then begin to kick in after about a week or so.

Now David Orrell might be wrong, or he might be right. But if he is right, the meteorologists shouldn't feel too worried. After all, trying to mathematically model the 5 million billion tonnes of turbulent atmosphere and water vapour is probably one of the most difficult computing problems ever attempted in the history of the human race.

The only thing that we can be sure of is that the weather will always give us something to talk about...

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. 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.

Illustration
The butterfly effect in the Lorenz attractor
time 0 ≤ t ≤ 30 (larger) z coordinate (larger)

These figures show two segments of the three-dimensional evolution of two trajectories (one in blue, the other in yellow) in the Lorenz attractor starting at two initial points that differ only by 10-5 in the x-coordinate. Initially, the two trajectories seem coincident, as indicated by the small difference between the z coordinate of the blue and yellow trajectories, but for t > 23 the difference is as large as the value of the trajectory. The final position of the cones indicates that the two trajectories are no longer coincident at t=30.
A Java animation of the Lorenz attractor shows the continuous evolution.

Mathematical definition
A dynamical system with evolution map ft displays sensitive dependence on initial conditions if points arbitrarily close become separate with increasing t. If M is the state space for the map ft, then ft displays sensitive dependence to initial conditions if there is a δ>0 such that for every point x∈M and any neighborhood N containing x there exist a point y from that neighborhood N and a time τ such that the distance

The definition does not require that all points from a neighborhood separate from the base point x.

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.