# Is the mandelbrot set real?

John K Clark (johnkc@well.com)
Sat, 9 Aug 1997 20:57:55 -0700 (PDT)

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On Fri, 08 Aug 1997 Hara Ra <harara@shamanics.com> Wrote:

>It's very tempting to snipe at Tipler and how many bits per proton

44 bits per proton. If the Beckenstein bound is true (probably is, but it has
never been rigorously proved) then the amount of information inside a sphere
of radius R that contains energy E is less than or equal to 2*PI*E*R/(h *ln2),
h is really h bar. For meters (R) and kilograms (M) that works out to
2.577 *10^43* M*R bits. A proton has a radius of 10^-15 meters and a mass of
1.67 *10^-27 kilograms, plug that in and you get 44 bits. You'd do a lot
better with a Hydrogen atom. The mass is almost the same but it's a lot
bigger, about 10^-10 meters, so a hydrogen atom can store 4*10^6 bits.

>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.

>but this diverges from my point.

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?

John K Clark johnkc@well.com

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