Game of Life is an example 2D system capable of universal computation. I'm not sure this implies consciousness is possible in 2D, but it needs to be considered.

I think Turing machines are impossible in 1D, however... Cheers On Fri, Nov 04, 2005 at 10:52:39PM -0500, Stephen Paul King wrote: > Hi George, > > It seems to me that the notion of "storing" and communication 1 bit > explicitly requires some form of stable structure over multiple queries. Does > this not lead to the requirement of some form of physicality, a physicality > that is epiphenomena at best in the ideal monism (everything is Numb3rs) > theory? > > As to the question of the smallest dimension that can support life and > consciousness; this has been considered by many people. My own ideas consider > the smallest dimension that allows for the greatest diversity of forms, forms > available to instantiate and represent ideal Forms. We find that in 3 > dimensions there exists at least a countable infinity of topologically > distinct objects that require non-trivial computational resources to sort and > categorize. > > Onward! > > Stephen > > ----- Original Message ----- > From: George Levy > To: Everything List > Sent: Friday, November 04, 2005 6:17 PM > Subject: Re: Let There Be Something > > > 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 -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

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