On Sat, Nov 05, 2005 at 09:57:17AM -0500, Bob Hearn wrote:
> On Nov 5, 2005, at 2:22 AM, Russell Standish wrote:
> >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.
> It does imply that if the Game of Life is the laws of physics of your  
> universe, then consciousness is possible, because at the very least a  
> 3D physics could be simulated. Whether that should be interpreted as  
> consciousness in 2D may be a subtle issue, because the perceptual  
> world of the conscious entities would be 3D - perhaps that was your  
> point?

Yes - assuming some version of comp, then yes, an entire 3D universe
can be simulated, including consciousness such as our own. The more
interesting question is whether conscious entites can exist the
experience a 2D world, and if so what is their relative measure to
those experiencing 3D environments.

> However, one can easily imagine a perceptual 2D world existing for  
> conscious entities. Even if there is no self-consistent 2D physics  
> leading to atoms, planets, etc., one can computationally simulate  
> Flatland (a la Abbott) or a Planiverse (a la Dewdney) in a 3D  
> universe, with no requirement for a consistent micro-physics. (In  
> fact the Planiverse is my simulation domain for my AI work.)

Assuming computationalism, I would argue that conscious observers
experiencing 2D environment are possible, but perhaps unlikely. Why?
Because 2D networks are highly constrained, and so it is difficult to
evolve complex structures in 2D. 3D and higher is not so constrained,
so evolution is possible.

This is, of course, mere speculation at this stage - I'd love someone
to develop these ideas further.

> So, whether it's the base physical reality you care about, or the  
> perceived reality of the conscious entities, I would say 2D  
> consciousness is possible. (Admittedly, in the latter case, one has  
> to consider whether the 2D creatures could at some point develop  
> science sufficient to prove that they must be simulated in some  
> higher-dimensional physics!)
> >I think Turing machines are impossible in 1D, however...
> No, there are 1D cellular automata that are computation universal.  
> Here's an abstract from a paper showing it; I don't seem to be able  
> to find the paper online. The paper is from 1990. However, there are  
> references to earlier constructions, e.g. here: http:// 
> www.stephenwolfram.com/publications/articles/mathematics/85-twenty/18/ 
> text.html . Again, I can't find the cited paper online.

Interesting - I might follow these refs further...

> The relevant Mathworld page is rather confused and misleading: http:// 
> mathworld.wolfram.com/UniversalCellularAutomaton.html
> There it seems that by "universal" they mean that there is a certain  
> class of 1D CA that can simulate any other 1D CA in that class. Hmm,  
> so what? Cute, but hardly surprising. Mathworld is a great site, but  
> it's too bad in some ways it's so tied in with the Wolfram mythos.  
> There's a huge spin put on pages like the one above that you have to  
> try to penetrate.
> Bob
> ---------------------------------------------
> Robert A. Hearn
> http://www.swiss.ai.mit.edu/~bob/

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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
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