Re: Countable vs Continuous

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,
> non-esoteric reasons. Many believe the history of our own universe
> will be infinite - certainly there is no evidence against this
> possibility. Also, any finite never-halting program for a virtual
> reality corresponds to an infinite history. TOEs ignoring this seem
> unnecessarily restrictive.

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

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

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
>> it a good candidate ATOE (algorithmic theory of everything)?
>
> it depends - minimal for what purpose?

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