On 17 Sep 2012, at 22:25, meekerdb wrote:

But did anybody think z' = z^2 + c was interesting before that?


Yes. This was known by people like Fatou and Julia, in the early 1900. Iterating analytical complex functions leads to the Mandelbrot fractal sets, or similar.

The computer has made those objects famous, but the mathematicians know them both from logic (counterexamples to theorem in analysis, like finding a continuous function nowhere derivable), or from dynamic system and iteration.

If you iterate the trigonometric cosec function on the Gauss plane C, you can't miss the Mandelbrot set.

In nature too as the following video does not illustrate too much seriously :)

http://www.youtube.com/watch?v=JGxbhdr3w2I

Bruno


Bretn

On 9/17/2012 1:17 PM, Terren Suydam wrote:
I would say computers were the tool that allowed us to see it, like a
microscope allowed us to see bacteria, and a telescope stars.

On Mon, Sep 17, 2012 at 3:14 PM, meekerdb<meeke...@verizon.net> wrote:
On 9/17/2012 10:36 AM, Terren Suydam wrote:

Rex,

Do you have a non-platonist explanation for the "discovery" of the
Mandelbrot set and the infinite complexity therein? How can you make
sense of that in terms of the constructivist point of view


How can you make sense of it otherwise.  The Mandelbrot set is only
interesting because it became possible to construct it by use of computers.

Brent


that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

Terren


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