Mandelbrot set & Platonic mathematics

john baez baez at
Sun Jan 30 19:32:58 EST 1994

In article <7572 at> mrw at (M.R.Watkins) writes:
>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 described with 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.    

The Mandelbrot set, charming as it is, is in no *special* position to
shed light on this issue.  It is simply one of zillions of complicated
mathematical objects that mathematicians study, most of which keep on
revealing ever-deeper layers of interesting structure the more one
studies them.  Most of these objects are a lot harder to "show" to the
layman since they aren't subsets of the plane.  Whether these objects
are inhabitants of a supernal realm "out there" or simply creations of
our cunning is one of those questions that will never be answered until
people ask it more clearly.  What, for example, does one really mean by
a mathematical world "out there"?  

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