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
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