On Jul 6, 2005, at 10:37 AM, Stephen Paul King wrote:
But isn't the use of time as the dimension along which things vary  (or are 'processed') a somewhat arbitrary choice?

   Please notice that the identification of "time" with a "dimension" involves the identification with each moment in time with some positive Real number. Thus the entire set of moments is identified with R^+. The problem with this identification is that the notion of a well ordering, an a priori aspect of the Real numbers, is not necessarily a priori for moments of time. AFAIK, the paradoxical nature of McTaggart's A and B series follows from a neglect of this issue.

I think Natural numbers suffice here, but I may be wrong (my background is molecular biology, not math).    

   Time, from what I have studied so far, involves two distinct notions: a "measure of change" and an "order of succession". The idea that it is merely a dimension and related to the dimensions of "space", as considered and promulgated by Minkowski, requires the assumption of classical physics and strict local realism. We know (I would hope!) that the former assumption is flawed, but the second is still being debated.

I recognize that time is different than space.  But it strikes me as at least problematic that time must be assumed to have properties which space does not in order for consciousness to exist.  To me, consciousness is nothing special - just one kind of pattern (one that supports robust predictions from the intentional stance) among many.  I think that pattern can exist in a natural number.  The intentional stance (a philosophical view of Daniel Dennett) is key to my views here, so I'll have to expound on it later.


   Please notice in your example that the automata had to be implemented by some process in order to render the results. The resulting "checker board" like picture is a result of the process, it can not be said to have one pattern or some other prior to and absent the computational process.
   Where would a SAS "fit" into the automata? What would its Observer Moments include?

You have a good point here; in the example as I gave it, a temporal process comes first, the result of which is then instantiated in a 3d-structure at a single time.  But I think it would be possible to surmount this objection with the use of a lookup table.  You could have a lookup table large enough to calculate the next N steps all at once, for any N - and then it's a matter of setting N large enough to calculate a block of the automaton that *would have* sufficed to produce a noticeable length of experience by the SAS, had the process been calculated for one step at a time.  Of course, now you can ask where the the lookup table came from -- and it looks like it must have been generated by a temporal process...

Well at any rate, I am trying to glean some conclusions from the existence of the stack >after< it has been created by whatever process - after all, if a simple algorithmic process is capable of generating it, it already exists in Platonia, at very high measure.  This example assumes a strong Platonism for its conclusions - but I think it does go some way toward approaching the problem of how the real numbers (or in this case, I think, even the natural numbers) can give rise to observers, time, consciousness, etc.  Some of those numbers can be interpreted as a Game of Life containing one or more SASs (and I'll assume the question of where the SAS fits into it answered already, by the fact that UTMs can be impemented in the Game of Life, and these UTMs must include ones that can pass the Turing Test.  Many references exist for this claim which you will find if you google ["game of life" "turing machine"]).

Best regards

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