Re: Is the Mandelbrot Set real?

Hara Ra (
Thu, 31 Jul 1997 21:03:38 -0700

John K Clark 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?

> 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.

> This is the exact opposite of the spirit (I don't have a definition) of the
> word "real", at least as I use it.

And thus the confusion. So, let's try a few definitions on here:

Real - anything one says is same....
PReal - Physically Real. Representable by a one to one mapping
onto the set of all physical particles in the Universe.
Mreal - Representable by a functioning brain.

Now, mentally real is representable by mapping into our brains, probably
limited to about the number of synapses in the brain.

This yields the usual kind of numbers - 10^13 neurons, 10^4 synapses per
neuron, 10^3 states per synapse, so some 10^20 in all, with 10^20!
combinations of connections (way too many, but no matter here).

The set of integers can be defined by the Peano axioms in about 200
bytes. Representing the entire set, one integer per particle, is of
course impossible.
So, the concept of integers is easily held in our brains, but the set
itself cannot be held in our brains. Ditto for the Mandelbot Set. So,

Concept of Integers = Preal
Set of Integers != Preal

I think the notion of "Real" is a dead end, with no real consequences.
Now Preal gives some hope towards knowing the limits of our
understanding, even if we have a Universe Mind (Extropian Jupiter Mind
boundlessly expanded) to do it with.

| Hara Ra <> |
| Box 8334 Santa Cruz, CA 95061 |