On Tue, Jun 21, 2005 at 09:06:22PM -0700, Jonathan Colvin wrote:
> Russell Standish wrote:
>
> Are you familiar with Wolframian CI systems?
Yes of course. Wolfram did not invent the term.
> The idea of CI is that while
> the system evolves deterministically, it is impossible (even in principle)
> to determine or predict the outcome without actually performing the
> iterations. I'm not at all sure that the idea of block representation works
> in this case.
>
Easy. Run your computer simulation for an infinite time, and save the
output. There is your block representation. Computational
irreducibility has nothing to do with whether the block representation
is possible - only indeterminism. And even then, if you include all the
counterfactuals, a block representation is possible too.
> >In any case, computational irreducibility does not imply that
> >the the state of the universe at T+x is unknowable. In loose
> >terms, computational irreducibility say that no matter what
> >model of the universe you have that is simpler to compute than
> >the real thing, your predictions will ultimately fail to track
> >the universe's behaviour after a finite amount of time.
> >
> >Of course up until that finite time, the universe is highly
> >predictable :)
>
> I'm thinking of Wolframian CI. There seem to be no short-cuts under that
> assumption (ie. No simpler model possible).
There are always simpler models. CI implies that no simpler model
remains accurate in the long run. But in the short term it is entirely
possible.
An example: Conways Game of Life is a computationally irreducible
system. Yet you can predict the motion of a glider most accurately
while it is in free space. Only when it runs into some other
configuration of blocks does it become unpredictable.
> >
> >In any case, whatever the conditions really turn out to be,
> >there has to be some causal structure linking now with the
> >future. Consequently, this argument would appear to fail. (But
> >interesting argument anyway, if it helps to clarify the
> >assumptions of the DA).
>
> I don't see that causal structure is key. My understanding of the standard
> DA is that the system (universe) itself has knowledge of its future that the
> observer lacks (sort of bird's eye vs. frog's eye situation), which avoids
> the reverse -causation problem.
I've never thought of the DA in that way, but it might be valid.
Analytic functions have the property that all information about what
that function does everywhere is contained within the derivatives all
evaluated at one point.
Whilst I don't expect population curves to be analytic, I am saying
the DA probably implicitly assumes some constraints, which act as
information storage about the future in the here and now.
> Wolframian CI seems like it might be
> problematic for that account.
>
> Jonathan Colvin
>
Even a computationally irreducible system contains information about
the future. Its just that much of it is inaccessible.
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Received on Wed Jun 22 2005 - 00:28:03 PDT