Re: *THE* PUZZLE (was: ascension, Smullyan, ...)

From: Russell Standish <>
Date: Sun, 18 Jun 2006 09:55:45 +1000

On Thu, Jun 15, 2006 at 04:29:18PM +0200, Bruno Marchal wrote:
> Le 14-juin-06, à 07:31, Russell Standish a écrit :
> >
> > On Mon, Jun 12, 2006 at 03:52:15PM +0200, Bruno Marchal wrote:
> >>
> >> In general, an infinite programs can still be written with a finite
> >> number of symbols, like a real number can be written with a finite
> >> number of symbols chosen among {0,1,2,3,4,5,6,7,8,9}. Of course in
> >> general it will need an infinite number of occurences of those
> >> symbols.
> >> It is the length of the program which is infinite.
> >> But there is no infinite programs (in arithmetical Platonia). Of
> >> course
> >> like Russell, you can conceive and study them but it in general the
> >> whole motivation of the notion of programs/names/description is really
> >> to capture something infinite by something finite.
> >
> > This is an interesting comment, that I hadn't appreciated before. The
> > Plenitude I study has infinite length "description", precisely because
> > this plenitude is the zero information object.
> Could you explain what is your conception of the relation between a
> description and an object?

A description is an infinite length (bit)string (bits in brackets,
because any other alphabet will do also). This use does sometimes fly
in face of what people expect, but I define this explicitly - it is a
useful term.

I'm just using the term "object" informally. The zero information object is in
fact a set of descriptions.

> I can understand "an infinite length object", like some putative
> infinite physical universe for example. I can understand "a zero
> information description"; for example the empty program or some empty
> theory (I will address "theories" later though). It is harder for me to
> understand what can be the use of infinite description or a
> zero-information object.

Only sets of descriptions (remember infinite length bitstrings) can
have finite information.

This looks like a terminological issue...

> >
> > However, computable things are indeed finite in size, which implies
> > that the arithmetical Platonia is smaller, and consequently a richer
> > set of things.
> >
> > The universal dovetailer, however, executes everything in the infinite
> > bitstring Plenitude does it not, or is this a misunderstanding of
> > Schmidhuberian proportions?
> I think the only trouble with Schmidhuber, and then with many people to
> be sure, is that they find hard to take seriously enough the
> distinction between first and third person point of views.
> The UD is a (finite) program, and when it runs, like any program
> running on some universal machine, it uses only at each time a finite
> piece of its (potentially infinite) tape, etc.
> Now, indeed, once you grasp that the probabilities of relative
> histories relies on the first person point of view, the case can been
> made that the infinite computations have a higher measure that the
> finite one, so that somehow physicalities emerges from the infinite set
> of those infinite (crashing-like) computations.

You're talking here of his speed prior argument of course. I think he
is wrong too, and agree with you, however I'm not so sure his
arguments are this easy to dismiss. It is related again to the ancient
debate on ASSA vs RSSA - Schmidhuber's argument works if you assume
just one computation is selected as your universe, which is rather
contrary to functionalism (and COMP).


A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                         	       0425 253119 (")
UNSW SYDNEY 2052                      
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Received on Sat Jun 17 2006 - 19:56:49 PDT

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