I conjecture that if one can design physical laws for a universe capable of 1) supporting the NAND function 2) storing (locally) 1 bit, 3) transmitting 1 bit from one point to another point, then one could also generate a Turing machine in this universe which would then be capable of supporting machine duplication (life) and AI (consciousness.) The basic physical laws (TOE) in such a universe would be very simple. One would need 1) a logical law: NAND; 2) a state law to allow the existence of "states"; and a concept of extension or space such that different states can exist at different locations and be transmitted from one location to another location.

A related question is what is the smallest number of dimension for such a universe, that can support life and consciousness.

George



Russell Standish wrote:
On Fri, Nov 04, 2005 at 12:18:01AM +0100, Quentin Anciaux wrote:
  
Hi Russel,

Le Jeudi 03 Novembre 2005 22:11, Russell Standish a ??crit??:

    
Even then, there is still a loophole. I suspect that 3D environment
are far more likely to evolve the complex structures needed for
consciousness, so that conscious GoL observers are indeed a rare
thing. I don't know if this is the case or not, but if true it would
make a GoL example irrelevant. More interesting is to look at some 3D
CA rules that appear to support universal computation - Andy Wuensche
had a paper on this in last year's ALife in Boston. No arXiv ref I'm
afraid, but you could perhaps email him for an eprint...

Cheers
      
But 3D, 2D CA is of no relevance... the way we see the computation through the 
gol as nothing in common with how hypothetical living being inside the gol 
would perceive their environment.

Quentin
    

True, but I suspect it does have impact on the likelihood of conscious
observers arising in such a system. In a plenitude of CAs of different
rules and dimensionality, initialised at random, I suspect that 3D or
higher CAs will dominate the measure of those CAs that generate the
complex data structures needed for conscious observers. Perhaps 3D is
even favoured. This is, of course, a hunch to be proven or disproven
by some future mathematical genius.

Cheers

  

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