On 02 Oct 2013, at 03:56, Russell Standish wrote:

On Tue, Oct 01, 2013 at 02:54:51PM +0200, Bruno Marchal wrote:

On 01 Oct 2013, at 01:30, Russell Standish wrote:

The real universe is likely to be 11 dimensional, nonlocal with around 10^{122} states, or 2^{10^{122}} possible universes, if indeed it is a
CA at all. Needles in haystacks is a walk in the park by comparison.

CA are local. The universe cannot be a CA if comp is correct, and
the empirical violation of Bell's inequality confirms this comp


There is no particular requirement for CAs to be local, although local
CAs are by far easier to study than nonlocal ones, so in practice they
usually are (cue obligatory lamp post analogy).

We can easily conceive quantum CA.
But those are not what is named simply CA (which locality is quite typical).
You will not find quantum CA in Wolfram (well, in my edition).

Unless you mean something else by locality. I mean that there is some
neighbourhood radius such that the update function for a given cell
only access the states of cells within the given radius.

Having said that - I notice that Wikipedia, Wolfram.com and also Andy
Wuensche's article on Discrete Dynamical Networks
(http://www.complexity.org.au/ci/vol06/wuensche/) all state that the
update function must be local in the manner described above in their
definitions of "cellular automata". In which case, you are correct.


I am clearly taking about a more general subset of discrete dynamical
networks in which the cells are still tiling an n-dimensional space,
but that the update function does not depend on a local neighbourhood
of the cell to be updated.

Better not to call them CA, but quantum CA, or why not comp-CA, as comp entails non locality, non cloning, indeterminacy, etc.

I don't know what Wolfram was talking about though - I just assumed he
wouldn't be thinking in terms of local update functions for his "CA of
the universe".

Alas, that is what he does, or did.
At the time he wrote his books, he put all the QM weirdness under the rug. He said that if non-locality is a real consequence of QM, it means that QM is false.

There are just very few people who grasp those three things at once:

- the mind-body problem
- the conceptual QM astonishing features (non locality, non cloning, indeterminacy, etc) - Church thesis and the non triviality of the discovery of the universal machine and its fundamental "creative limitations".



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