Mandelbrot set & Platonic mathematics
M.R.Watkins
mrw at ukc.ac.uk
Sun Jan 30 18:07:17 EST 1994
As far as i know, in his book _The Emperor's New Mind_, Roger Penrose argues for
a platonic philosophy of mathematics, and as evidence points to the Mandelbrot
set. This incomprehensibly intricate & beautiful object, which can be describedwith a minimal mathematical effort, seems to prove beyond a shadow of a doubt
that there is a mathematical world "out there" somewhere, as real (or perhaps
more real) than the physical world we inhabit, and that through some mysterious
process, human consciousness is able to gain access to this world. This seemed
quite convincing when i read the book a couple of years ago, but i recently
read _Pi In the Sky_ by John D. Barrow, which points out some serious difficulties with the platonic approach. There's an interesting footnote on p.261 where
the author attempts to tackle the issue of the Mandelbrot set. He points out
that unlike a telescope or Geiger counter, which are examples of tools used
to *explore* the physical universe, the computer is used to *construct* the
Mandelbrot, and goes on to hypothesise that the "impressiveness" of such
fractal structures is a subtle consequence of natural selection - nature
settles on fractal designs, as they are the most economical in certain situations, hence their familiarity and "beauty".
i'd be very interested to hear other peoples opinions on these matters. email me directly if you can, as i'm not able to keep up with all of these newsgroups.
There's a second, almost-related question that seems worth asking: people in
altered states of consciousness often report "seeing" fractal-like images
behind their closed eyelids (this can be most safely experienced via the
"Dreamachine" designed by Brion Gysin, a strobe-like device which supposedly
synchronises ones alpha waves). Is it possible that these images have a
truly fractal origin (patterns of electrical activity in the brain, i suppose
it would have to be), and has anyone done any research on this (the difficulty
would be graphically reproducing the images for analysis, of course) ??
m a t t h e w
A
"Dreamachin
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