H J Ruhl wrote:
>
> At 1/23/02, you wrote:
> >H J Ruhl wrote:
> > >
> > > I have the following question regarding Juergen's paper:
> > >
> > > In the very first sentence of the abstract it is assumed that universes
> > > have histories. If by this it is meant that a particular universe has a
> > > particular unique identifiable history does this not mean that that
> > > universe is computable?
> >
> >
> >Why should it? It seems a universe's history is the only property a
> >universe can have, ie universes are histories.
>
> I do not see that at all. Why does it need a history? All it needs is the
> capability of finding a next state.
It doesn't need the capacity to find the next state. If it has that
capacity, then the history is computable. It is a poor assumption to
assume that the universe is deterministic (history computable from
initial state).
Histories are any description unfolding with time, whatever that
happens to be. Time appears to be necessary for consiousness..
>
>
> >There are plenty of
> >noncomputable descriptions that can serve as histories - for example
> >the binary expansion of Chaitin's Omega.
>
>
>
> That was not my point. The initial state of a universe is not computable -
> it just was. The point is the method of association of any history with a
> particular universe.
>
My point is that any history just is. However, those that are
computable from a simple initial state are dense in a large subset of
such histories (subset proportional to 2^{-C}, where C is the
complexity of the initial state), so we should expect a random sample
to select a history that is approximately a computable outcome from a
simple initial state.
> As to your example how would you parse it into segments each describing a
> state of the universe? The universe may be doing so and thus computing
> Omega and not know it. This as I understand it is possible for non halting
> computers since no selection to compute Omega was made.
Good point - perhaps Omega is a bad example. It is possible that an
algorithm exists for computing the binary expansion of Omega, its just
that you can never prove that it does. However, there are uncountably
infinite number of binary strings for which no algorithm
exists. Choose any one of these.
>
> Hal
>
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Received on Tue Jan 22 2002 - 19:16:19 PST