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From: Joel Dobrzelewski <dobrzele.domain.name.hidden>

Date: Thu, 21 Jun 2001 12:42:14 -0400

Juergen:

*> I think we may not ignore infinities for quite pragmatic,
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*> non-esoteric reasons. Many believe the history of our own universe
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*> will be infinite - certainly there is no evidence against this
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*> possibility. Also, any finite never-halting program for a virtual
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*> reality corresponds to an infinite history. TOEs ignoring this seem
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*> unnecessarily restrictive.
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Yes, I agree. I think my objection was to those infinite representations...

*> What you cannot construct in finite time is just a particular
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*> representation of Pi, namely, the one consisting of infinitely many
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*> digits. But this is not a problem of Pi, it is a problem of this
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*> particular representation. There are better, finite, unambiguous
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*> representations of Pi: its programs. You can manipulate them, copy
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*> them, insert into other finite programs and theorem provers, etc.
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*> Proofs of Pi's properties are essentially proofs of properties of
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*> Pi's programs.
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Yes, ok, I see the distinction now.

I think I was arguing against the use of "Pi as a process" as a fundamental

building block of a Theory of Everything. i.e. We cannot reasonably expect

the function Pi() to return a value that we will use during some step in a

series to perform some calculation.

*>> Juergen, what do you think about the minimal cellular automaton? Is
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*>> it a good candidate ATOE (algorithmic theory of everything)?
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*>
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*> it depends - minimal for what purpose?
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Minimal in the sense that the computational process that these automata

represent cannot be simplified. Since there are no unreachable

configurations for a minimal cellular automaton, no part of the computation

can be thrown out.

In contrast, non-minimal automata (most CA) have certain configurations that

are never reached, and thus, we can rewrite them as a new automaton using

fewer states per cell.

Joel

Received on Thu Jun 21 2001 - 09:38:40 PDT

Date: Thu, 21 Jun 2001 12:42:14 -0400

Juergen:

Yes, I agree. I think my objection was to those infinite representations...

Yes, ok, I see the distinction now.

I think I was arguing against the use of "Pi as a process" as a fundamental

building block of a Theory of Everything. i.e. We cannot reasonably expect

the function Pi() to return a value that we will use during some step in a

series to perform some calculation.

Minimal in the sense that the computational process that these automata

represent cannot be simplified. Since there are no unreachable

configurations for a minimal cellular automaton, no part of the computation

can be thrown out.

In contrast, non-minimal automata (most CA) have certain configurations that

are never reached, and thus, we can rewrite them as a new automaton using

fewer states per cell.

Joel

Received on Thu Jun 21 2001 - 09:38:40 PDT

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