# Re: Is the mandelbrot set real?

Hara Ra (harara@shamanics.com)
Sat, 16 Aug 1997 22:10:16 -0700

John K Clark wrote:
>
> 44 bits per proton. If the Beckenstein bound is true <snip>
> so a hydrogen atom can store 4*10^6 bits.

OK. With 10^80 particles, 4.4 x 10^81, or 10^86 - no matter, both are
finite numbers. BTW, thanks for doing the calculations.

> >Even if the Universe has infinite data storage capacities (which
> >aleph is the next question here)
>
> If we have an omega point then countable infinity is all I can guarantee, but
> maybe by then we'll think of something.

Well, I wouldn't know about Omega Points - if they exist, it's a long,
long
way off from now. My focus is on the present limits to what can be
represented
in this universe, pretty much as it is now.

> Mine too. The idea that you can tell if something is real by examining it's
> complexity, and the simpler the realer, is confusing. A perfect geometric
> line is much simpler than the tree trunk of a pine tree, yet I think you
> would say the tree was more real. Why? The shape of the Mandelbrot Set is
> more complex than the shape of a grape, yet you say the grape is real and the
> set is not. Exactly what is the relationship between complexity and reality?
>
A Preal object is represented by the particles which comprise it. This
implies that repesenting this object at most requires about the same
number of bits. Note that I am content to use the value you cited for a
hydrogen atom, so n*10^6 bits will do.

Your example of a line vs a pine tree is just a bit misleading. The
definition of the line is very simple, a true line is not a Preal
object. Obviously a pine tree is more complex than a definition of a
line.

A Real object such as the Mandelbrot set's shape cannot be directly
represented. Its abstract definition is easily stated in a few hundred
bytes, and this definition is therefore Preal. In fact, the Mandelbrot
set is a rather simple object in terms of complexity theory since its
description is very much smaller than its resulting representation!

O---------------------------------O
| Hara Ra <harara@shamanics.com> |
| Box 8334 Santa Cruz, CA 95061 |
O---------------------------------O