Thanks for your comments, Hal!
Your point on the dovetailer is well taken. I modified the text:
"If Zuse's thesis is correct, then which is our universe's program? It
may come as a surprise to some that we already know at least one
algorithm that does compute our universe (and several others)..."
Ed Clark has a nice review page on Wolfram's book:
http://www.math.usf.edu/~eclark/ANKOS_reviews.html
It includes Scott Aaronson's interesting review which also
addresses the issue of Bell's inequality.
Best,
Juergen
http://www.idsia.ch/~juergen/digitalphysics.html
> Juergen Schmidhuber writes:
>
>>I welcome feedback on a little web page on Zuse's 1967 thesis
>>(which states that the universe is being computed on a cellular automaton):
>>
>>http://www.idsia.ch/~juergen/digitalphysics.html
>
>
> That's very interesting; I was not aware of Zuse. Unfortunately I
> don't know German so I can't read his paper.
>
> Regarding the question of the compatibility of CA models with relativity
> and QM, Wolfram looks into this in some detail. He essentially abandons
> a simple CA model in favor of a more complex network of interacting
> nodes, which has some features similar to the Lorentz transformation of
> relativity. Then to address the EPR style long-distance correlations of
> QM, he proposes that while the network is mostly local, it has occasional
> nodes which get stretched apart and are connected to distant nodes.
> These are rare but allow for the type of information flow necessary to
> reproduce long-distance QM correlations. All in all it is a pretty ad
> hoc and unconvincing model.
>
> I tried to read the t'Hooft paper referenced here but it was over my
> head. It also struck me though as not really addressing the discrepancy
> between long-distance correlations and local CA models. It seems very
> much an open and difficult question to me to show how a local CA model
> can reproduce relativity and QM.
>
> One issue which CA models tend to ignore is the MWI. Most CA models
> are built as hidden variable theories which define a single universe.
> Some multiverse models have that structure as well. But it seems to me
> that this is an entirely unnecessary restriction. If a CA can model
> a universe, it can model a multiverse, and likewise with any other
> computing model like TMs.
>
> The MWI is fully deterministic, which may make it a more attractive
> target for modelling with a deterministic computational theory than
> attempting to reproduce the statistical phenomena of QM, essentially
> via hidden variables. Any hidden variable theory, CA based or not,
> has two strikes against it from the beginning due to the the many well
> known difficulties of Bell inequalities and EPR correlations.
>
> Regarding entropy, it is pointed out that entropy does not grow in a
> CA model. Wolfram discusses this as well. While entropy technically
> does not grow, you can get phenomena that look very much like entropy
> growth in a CA model. Eventually you will get a Poincare recurrence
> if the universe is finite. But if you start in a sufficiently simple
> state, there are many CA models which will mimic entropy growth into a
> more complex state. And this may be close enough to explain our universe.
>
> Alternatively, of course the MWI as a deterministic theory also does
> not have entropy growth. As mentioned above, computational models of
> our universe might well do better to aim towards an MWI world.
>
> As far as the claim that we already know the algorithm that runs our
> universe, and it is the UD: I think this is amusing but ultimately
> misleading. It's true that a dovetailer which runs all programs will
> indeed run our own universe's program (assuming it has one), but I think
> it is a misuse of terminology to say that the UD is the algorithm that
> is running our universe. I would reserve that phrase to refer to the
> specific program that generates our universe and no others. It will be a
> tremendous accomplishment of physics and philosophy when that program is
> discovered, but it is misleading to give the impression that we already
> know what it is.
>
> I think a better terminology here would be something like, we don't
> need to know the specific program that describes our universe in order
> to imagine how to program a computer that would in fact generate our
> experiences, at least in theory. And then go on and explain about
> running all programs at once, etc.
>
> Hal Finney
>
Received on Wed Nov 06 2002 - 03:39:55 PST