Re: Is the Mandelbrot Set real?

Hara Ra (
Wed, 06 Aug 1997 23:49:27 -0700

Eliezer S. Yudkowsky wrote:
> Hara Ra wrote:
> > They are not physical particles. However, the strings which state the
> > Postulates are finite and representatable within the physical universe.
> > The longest Preal string has as many characters as there are particles
> > in the universe, approximately.
> Who says this is constant? Virtual particles are popping in and out of
> existence all the time. A lot of my workarounds to the Laws of Physics rely
> on creating equal amounts of negative and positive mass/energy - since even
> negative mass represents a positive amount of information. (I don't think
> there's any way to represent a negative amount of information, which is too
> bad, because otherwise there'd be a REALLY INTERESTING form of matter out
> there somewhere! Anti-real matter!)

Presuming the Big Bang is true, the mass of the Universe is around 10^80
protons. This limits the largest Preal string to 10^80 characters or so,
certainly less than 10^100, the googol. Forget the virtual particles, I
am just suggesting a number which is large, fits in the Universe and
very very definitely NOT infinite.

> Anyway, I don't know if there's a genuine upper bound on the amount of
> information the Universe can store. Unless the Universe is quantized, the
> amount is equal to - at least - aleph-2. (All those fields of real
> numbers...) Even supposing the Bekenstein Bound - what about all the digits
> of pi? Even excluding "Platonic" information, what about virtual particles
> and negative matter? Would there still be some physical bound on the number
> of positive and negative "particles"? I sure don't know.
Ok, to get really gritty - the maximum amount of bits storable if you
converted the entire universe into data storage using nanotechnology. 1
per proton.

> And - out of curiosity - there can't possible be a sharp distinction between
> "Preal" things and "Punreal" things.
Prove this. There are many infinite objects, all of which are Punreal.

> Even if there is a sharp physical
> bound... wouldn't it be essentially arbitrary in some way?

Yes it is arbitrary. My real interest is in the limits of what is
physically representable.

> I cannot see any
> reason why there would be a limit on how much information can be "real". At
> worst, we might be ontologically restricted to some low number or ordinal of
> aleph-infinity.

A googol will do just fine.

> So if Preal and Punreal don't describe any testable or
> fundamental quality of a string... what's the point?

If length(string) > googol, string = Punreal

I think that is testable.

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