Mandelbrot set & Platonic mathematics

George Hrabovsky george at fullfeed.fullfeed.com
Mon Feb 7 16:11:52 EST 1994


In article <CKsLoL.8J4 at kaiwan.com> ming at kaiwan.com (ming of mongo) writes:
>	I'm glad you disagree with the Platonic view of mathmatics. 
>(Plato was a professional wrestler, who's name translates roughly to "Big 
>Guy", making him dangerously simmilar to Hulk Hogan! (How's that for an 
>ad hominum argument?))
>
>	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.
>	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 hope this helps
>

I have foud two really good books on Fractals and Chaos.
The first is Ott's "Chaos in Dynamical Systems" which introduces the subject
in a very clear way.
The second (which I have loaned out and can't cite adequately) is
Falconer's "Fractal Geometry" which is very deep and I suggest you study
a little general topology before you tackle it.
Both of these books I consider to be basic introductions, but you need to
have a firm grasp of both ODE and PDE and a good grounding in topology and
abstract (or modern) algebra would be good.

	GEH




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