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© Copyright 1997, Jim Loy
Imagine a flat surface with nails driven in it. The surface is slanting, so that a marble will roll down it. A marble hits one of the nails, and momentarily stops, before falling to one side or the other. The situation is chaotic. A very small change in the marble's initial trajectory will make a big change in its final trajectory. The phenomenon is called "sensitivity to initial conditions," and is one pervasive feature of chaos. The study of chaos has become the science of the unpredictable. And sensitivity to initial conditions is a chief source of that unpredictability. And sensitivity to initial conditions is the main way in which you can recognize a chaotic system.
Chaos was first studied seriously when Edward Lorenz tried to model the earth's weather on a computer. The computer program could simulate realistic weather. It could even predict the weather for a time into the future. But sooner or later, the predicted weather became much different from the actual weather. More accurate data did not solve the problem.
Then an experiment was done. The program was given certain initial conditions (the accurate data), and was instructed to predict the weather. Then the initial conditions were changed very slightly, a seemingly insignificant amount. And the program was again instructed to predict the weather. And the new prediction was nearly identical to the first prediction, for a while, then it diverged, becoming totally different. So, weather predicting is inaccurate, not so much because of lack of data, but because the weather is chaotic. It is unpredictable, by its very nature. It was even said (half jokingly, half seriously) that the movements of a butterfly's wing in South America would eventually, and drastically change the weather in North America. This "butterfly effect" is an example of sensitivity to initial conditions.
Sensitivity to initial conditions appears everywhere. A decision that you make, with insufficient information, may change your life forever. Whether a baseball player hits the ball or not (a difference of fractions of an inch), may determine who wins the World Series, and whether another baseball player "earns" millions of dollars or not. Sports are designed to be chaotic. A defective circuit breaker, or a bug in a computer program, may cause a massive blackout and even deaths. The world's political situation is chaotic, often intentionally so.
But chaos is strangely predictable, as well. The above-mentioned marble hitting the nail is chaotic and unpredictable. But, many marbles hitting nails are very predictable, statistically. When a given nucleus of uranium decays or not is totally unpredictable. But, in a quantity of uranium, the radioactive decay is very very predictable. And the study of chaos gives us ways of predicting things about chaos itself.
According to Greek myth, everything emerged from chaos. In physics and chemistry, the word "gas" comes from the word "chaos". A gas is indeed a chaotic form of matter, compared to a liquid or a solid. The motion of an individual molecule is chaotic.
In The Discworld Series, by Terry Pratchett, a series of humorous fantasy novels, there is a species of butterfly, the "Quantum Butterfly" which has the disturbing characteristic of making massive changes to the weather, at great distances, every time it flaps its wings.
Addendum:
I have come up with this imitation Rube Goldberg (see Rube Goldberg Inventions) scenario:
My version of the Butterfly Effect: Butterfly (A) flaps wings (B), distracting archer (C) who misses target (D) and shoots bull (E) who charges through fence (F) striking automobile (G) of Ambassador from Zukistan (backward nation with 1/7 of world's nuclear weapons), causing rear-view mirror (H) to break, giving Zukistan (I) seven years bad luck (J). Zukistan blames the USA (K), and declares war (L). Massive thermonuclear exchange (M) destroys civilization (N) and causes nuclear winter (O).
We also have the inverse butterfly effect: Nuclear winter (O) kills butterfly (A).