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