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Date: 1991 


Question:
I see the words 'chaos' and 'fractals' very often here. and somehow I get a vague impression, that they are some kind of buzz words, that have become popular simpley because they have a certain 'sex appeal' a look good on a graphics screen. Some (several) years ago, when I last read anything about these things, was in 'The mathematical Intelligenser' from Springer, and what I read was a not very kind article about Mandelbrot and the fuzz about fractals. So what is the truth about it?



Replies:
Chaos theory: a system behaves chaotically if it behaves reproducibly given the same initial conditions, given slightly different initial conditions, it behaves very differently. In other words, it is very sensitive to initial conditions. This is completely distinct from randomness or noise. fractals: popularized by Mandelbrot who treated them like a business instead of science for which he was criticized. We have all seen the pretty pictures. The essential ingredient is self-similarity which means the pattern looks the same no matter what size scale you use. fuzzy logic: (I am a truck) if I am going 20 MPH and the driver is applying the brakes, then I should apply light braking pressure with a probability of 20%, medium pressure with a probability of 50%, and high pressure with a probability of 30%.

John Hawley


The important thing about chaos (and to a lesser extent fractals) is that they give us a new mathematically based picture of certain ways in which the real world behaves, which is probably obvious to most people without the mathematics. The old ideas (since Newton himself!) were that the universe ran like clockwork - if you knew well enough what everything in the universe was doing at a particular time, you could predict the future of everything arbitrarily far. That is still sort of true (barring randomness from quantum mechanics) - but chaos theory tells us the immense precision that would be required to do that sort of precision - basically it is the reason we will probably never be able to predict the weather more than a week in advance, unless we control it in some way... Chaos theory (and fractlas) tell us more though - that even with this hopelessness of prediction of specifics (where every single particle will be indefinitely into the future) we still can get pictures of patterns that tell us qualitatively what will happen, and that is better than nothing!

Arthur Smith



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