Re: Is the Mandelbrot Set real?
Sat, 26 Jul 1997 13:18:48 -0400 (EDT)

In a message dated 7/26/97 8:12:37 AM, wrote:

(peripherally, John, you probably shouldn't indent when you quote. My lines
are, if anything, too long to start with.)

> On Fri, 25 Jul 1997 Wrote:
>>things which don't exist in reality can exist only as concepts in
>>our mind.

>Unclear. Do these things exist or not, what does "exist" even mean?

A trip to metaphysics doesn't seem necessary. I'll go with Websters: "to
have reality or being".

>>>is there any reason to think that The Mandelbrot Set is less real
>>>than the chair you're sitting on right now?

>>Yes. I can find a chair in physical reality. I've yet to find a
>>Mandelbrot set, and have strong reasons to believe I'll never find one.
>That's just passing the buck, you arbitrarily decree that one is in physical

>reality and one is not, but the very thing we're discussing is what physical

>reality is and is not. When I sit in a chair I can't detect it directly,
>through the agency of nerve impulses from my ass. I can't see bacteria
>directly, only through a magnifying lens. I can't detect the Virgo cluster
>directly, only through a light gathering lens, and even then not as it is
>only as it was 2 billion years ago.

You're redirecting the discussion into the limits of our epistemology. Yes,
we know things only through sense data; yes we are fallible. But,
nonetheless, there is a universe out there, independent of us. If all humans
died tomorrow the bacteria and the Virgo cluster would still be there, and
the chair would last quite a while.

I am as confident of the chair as I can be of anything; I have extensive
sense evidence of its endelbrot set, and strong theoretical reasons to
believe it can't exist in this universe.

>I can't detect The Mandelbrot Set
>directly, only through the "lens" of a computer, but at least it shows me
>the set as it is now.

The sense impressions of the real things you mentioned were formed from the
actual things. The Mandelbrot set sense impressions were formed from a
finite approximation to the Mandelbrot set. And, as you pointed out, finite
representations of the Mandelbrot set are *very* different from the actual
Mandelbrot set. I can make a program that creates the sense impressions I'd
get from the Easter Bunny, and use it for wallpaper, but there's still no
Easter Bunny.