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C00002 00002		#. The "Life" cellular automaton.  This example,
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	#. The "Life" cellular automaton.  This example,
which was invented for quite a different purpose by John Conway,
can be used as a simplified model of the world as a whole and
illustrates some phenomena that occur in the real world, but without
all of the real world's complexity.

	At each point %2(x,y)%1 in the plane with integer co-ordinates an
automaton with two possible states 0 and 1 is attached.  The state of
each automaton at time %2t+1%1 is determined from its state at time %2t%1
and the states of its eight neighbors
as follows:
A point whose state is 0 will become 1 if exactly three of its neighbors
are in state 1.  A point whose state is 1 will remain 1 if 2 or 3 of
its neighbors are in state 1.
In all other cases the state becomes or remains 0.

	Conway's original question was whether an initial
configuration  with only a finite  set of 1's would  remain that way.
After Gosper and others discovered infinitely growing configurations,
the questions changed,  and it was eventually proved  that the "life"
automaton is universal for computation, i.e. an initial configuration
can be found that will  interpret a suitably encoded data  in another
part  of the plane  as an  arbitrary computer  program and  its data.
Moreover,  it  was  discovered  that  such  computers  can  be   made
self-reproducing  as  well,  i.e.    they  can  make  new  copies  of
themselves if suitably  programmed, and these copies can also compute
and reproduce.

	(The fact that the "life" configurations can be universal
computers and constructors is one formulation of the idea that
"life" cell is a universal cell for cellular automata.  It seems to
me more natural to define a universal cell as one such that a suitable
square array of them can simulate the basic cell of any other cellular
automaton, but no such theorem has been proved as far as I know).

	Now imagine such a computer constructed of "life" elements.
Among the things it can be programmed to do is to simulate the "life"
automaton system, i.e. it can know the fundamental physics of its
world.  Moreover, it can be told the initial configuration of its
world by storing in a strip of data a list of all cells
outside the strip that are in state 1.  It doesn't need a separate
description of the states of the cells inside the strip, since
it knows the code.  Therefore, it can simulate its world and
answer any question about the state of the world at a definite time.
Of course, it must compute so slowly that it can never predict its own
future.

	Now suppose we have several such "computers" that interact
with each other, but each one knows the entire initial configuration
and the "law of motion" of "life".  Suppose further that we program
each of them to try to achieve certain goals and that to do this they
must communicate with each other and co-operate and compete.
It seems evident that effective behavior will require that a computer
ascribe beliefs and purposes to the others even though it knows
the fundamental physics of the world and could "in principle"
predict the other's behavior from any known initial state.
It will have to formulate theories about how these beliefs arise
and how they affect action.  How these beliefs and wants
%2reduce%1 to configurations of 0's and 1's in the "life" automata
may be neither useful nor easily determined either by the computer
itself or by ourselves as external observers.

	The moral of this example is to emphasize that the problem
of the relation of mental qualities to physical states arises in
physical systems of the most determinate kind possible.