Can atoms exist in a 2D universe? AFAIK, physics is very different when
constrained to only 2D. My point is that the notion of computation is
meaningless if there is no possibility of a stable structure on and in which
to implement the computation. Platonic Numbers or bit-strings have no
ability to do anything by themselves (by definition!) and thus appeals to
their existence are vacuous.
----- Original Message -----
From: "Russell Standish" <[EMAIL PROTECTED]>
To: "Stephen Paul King" <[EMAIL PROTECTED]>
Sent: Saturday, November 05, 2005 2:22 AM
Subject: Re: Let There Be Something
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...
On Fri, Nov 04, 2005 at 10:52:39PM -0500, Stephen Paul King wrote:
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.