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From: <juergen.domain.name.hidden>

Date: Thu, 21 Jun 2001 17:06:14 +0200

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

*> Subject: Re: Countable vs Continuous
*

*> Date: Thu, 21 Jun 2001 08:41:13 -0400
*

*>
*

*> Juergen:
*

*> > There is the rather harmless kind: the countable one. And some say
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*> > there is another kind, a strange one, the one associated with the
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*> > uncountable continuum, the one whose very existence many deny.
*

*> >
*

*> > Do not lump them together.
*

*>
*

*> Yes, I can see how this distinction might be useful in some esoteric
*

*> discussions. But it seems (to me) to have little relevance to achieving a
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*> successful Theory of Everything. And it might even distract us..
*

*>
*

*> Both kinds of infinities are inaccessible to humans. So they can play no
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*> part in our theories. In this sense, I think it's fair to lump them into
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*> the pile of things that are not helpful.
*

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.

*> We cannot build the universe out of pieces themselves we cannot construct.
*

*> (e.g. Pi)
*

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.

Really bad are those things that do not have ANY finite representation.

*> 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?

Juergen

http://www.idsia.ch/~juergen/

http://www.idsia.ch/~juergen/everything/html.html

http://www.idsia.ch/~juergen/toesv2/

Received on Thu Jun 21 2001 - 08:07:18 PDT

Date: Thu, 21 Jun 2001 17:06:14 +0200

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.

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.

Really bad are those things that do not have ANY finite representation.

it depends - minimal for what purpose?

Juergen

http://www.idsia.ch/~juergen/

http://www.idsia.ch/~juergen/everything/html.html

http://www.idsia.ch/~juergen/toesv2/

Received on Thu Jun 21 2001 - 08:07:18 PDT

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