Russell Standish schreef:

> On Mon, Dec 11, 2006 at 03:26:59PM -0800, William wrote:
> >
> > > If the universe is computationallu simulable, then any universal
> > > Turing machine will do for a "higher hand". In which case, the
> > > information needed is simply the shortest possible program for
> > > simulating the universe, the length of which by definition is the
> > > information content of the universe.
> >
> > What I meant to compare is 2 situations (I've taken an SAS doing the
> > simulations for now although i do not think it is required):
> >
> > 1) just our universe A consisting of minimal information
> > 2) An interested SAS in another universe wants to simulate some
> > universes; amongst which is also universe A, ours.
> >
> > Now we live in universe A; but the question we can ask ourselves is if
> > we live in 1) or 2). (Although one can argue there is no actual
> > difference).
> >
> > Nevertheless, my proposition is that we live in 1; since 2 does exist
> > but is less probable than 1.
> >
> > information in 1 = inf(A)
> > information in 2 = inf(simulation_A) + inf(SAS) + inf(possible other
> > stuff) = inf(A) + inf(SAS) + inf(possible other stuff) > inf(A)
> >
>
> You're still missing the point. If you sum over all SASes and other
> computing devices capable of simulating universe A, the probability of
> being in a simulation of A is identical to simply being in universe A.
>
> This is actually a theorem of information theory, believe it or not!

I think I'm following your reasoning here, this theorem could also be
used to prove that any probability distribution for universes, which
gives a lower or equal probability to a system with fewer information;
must be wrong. Right ?

But in this case, could one not argue that there is only a small number
(out of the total) of "higher" universes containing an SAS, and then
rephrase the statement to "we are not being simulated by another SAS" ?


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