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Mandelbrot set & Platonic mathematics

Leon Avery leon at eatworms.swmed.edu
Sun Feb 6 08:46:56 EST 1994


In article <CKsLoL.8J4 at kaiwan.com>, ming at kaiwan.com (ming of mongo) writes:
|> 	On the eyeball fractals, I am reminded of some good advice: 
|> Always keep an open mind, but not so open that your brain falls out.
|> 	There are plenty of goofy pop science books on the subject of 
|> fractals and chaos, mostly writen by people who read other goofy pop 
|> science books.  Chaos theory, or the little I understand of it, seems to 
|> be the most beautifull, and interesting branch of mathematics that i have 
|> ever seen.  But, it's hard, much to hard to get from a dime novel science 
|> book.  It is based on non-linear equasions, which are so dificult that 
|> approximation is the accepted way to deal with them, even among advanced 
|> mathematicians.

This is a bit of an overstatement.  Like all of the most fundamental
mathematical problems, chaos theory is simple at the core.  Robert
May's Nature paper (long time ago, 1980 or so?) on the logistic
equation sets forthe the basic problems and some of the prettiest
early results is a very simple way.  I seem to remember there was also
a Scientific American article, perhaps Mathematical Games, about the
time.

|> 	I hope you retain your objectivity while reading on the subject.  
|> there are some good books on the subject, although they treat it only in 
|> a very general way.  "Chaos" by James Gliek, is one that doesn't get 
|> bogged down in fantasy.  It is mostly, however, about the scientists that 
|> brought chaos theory about, and not so much about the math.

I've read Gleick.  I wasn't too impressed.  The problem with
chaologists is that they've all read Thomas Kuhn, and they're all
convinced they're scientific revolutionists, and they attribute any
criticism whatever of what they do to Incomensurability.  Gleick
swallowed this whole line.

Still, I haven't read any of the pop books you talk about, the ones
that are in the shelves next to literature on the occult.  I suppose
if I had I might feel as charitable towards Gleick as you do.

-- 
Leon Avery
Department of Biochemistry
University of Texas Southwestern Medical Center
5323 Harry Hines Blvd
Dallas, TX  75235-9038
(214) 648-2420 (office)
         -2768 (lab)
         -8856 (fax)
leon at eatworms.swmed.edu



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