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
> feature.
> Bruno

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).

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.

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".


Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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