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

From: Russell Standish <r.standish.domain.name.hidden>
Date: Tue, 20 Jun 2006 09:18:01 +1000

On Tue, Jun 20, 2006 at 11:43:08AM +0200, Bruno Marchal wrote:
>
>
> Le 19-juin-06, 15:31, Russell Standish a crit :
>
> > I'm not so sure. At heart, I suspect he is a computationalist, however
> > what he assumes in his papers is that the universe (that we see) is a
> > single
> > specific computation selected from the dovetailer algorithm. With COMP
> > (and
> > with functionalism too) we assume that consciousness supervenes on all
> > consistent computations, which leads to your famous first person
> > indeterminism result. Schmidhuber's assumption directly implies
> > determinism (we are living inside one particular computation only).
> >
> > I do not see Schmidhuber's argument as inconsistent, but it does seem
> > to contradict COMP, so Schmidhuber may have inconsistent faiths if he
> > insists both on this argument and COMP.
>
>
> I agree here. I still don't understand why you call "description" what
> is really just a real number (or a real number from the unit interval).

Sets of descriptions are more or less isomorphic to set of real numbers, but
not actually the same. In fact there is even a difference - the strings
0111111... and 100000.... are different descriptions, but correspond
to the same real number (0.5), but this difference is only on a set of
measure 0 (rational numbers with denominator that is a power of two).

So we a need a name. Bitstrings is too specific, since we could also
be referring to strings from other alphabets. The word description
seems to fit the concept, and wasn't otherwise used in literature.

> I will try to read my Levin Solomonov literature, if only to see if we
> are just quibbling on terminology or on something more fundamental. To
> see program as prefix of infinite string is interesting if you are
> interested in Kolmogorov-Chaitin-Solovay-Martin-Lf sort of (quasi
> absolute) probability measure, like in the search of a Bayesian sort of
> ASSA Udist (which, I have often argue miss the relative self-sampling
> assumption forced by the 1-3 distinction).

Whereas I don't think it does. It can be applied in an absolute way
(such as you refer) or in a relative subjective way (which is how I do
it). In fact I make the point that absolute measures aren't meaningful
- there just isn't an absolutely given UTM.

>
> I disagree (but this I already told you) with your mention of universal
> dovetailing in Schmidhuber, given that if you select a specific
> computation there is no more need to dovetail.

The dovetailing provides the simpler ensemble from which the specific
computation is selected. This is right there in the first paper. In
the second paper, the dovetailing is assumed to run on an actual
resource limited computer - hence the speed prior.

> This is, at the least,
> pedagogically confusing. Sure, Church Thesis and Universal Machine
> should play an important role in Schmidhuber, but there is no reason to
> dovetail universally. This appears when you realize comp makes it
> impossible to attach consciousness to any specific computation
> (material or not) that is when you get the comp first person
> indeterminacy.
>
> A last note: speed prior, like in Schmidhuber second paper, seems to
> contradict the basic idea of its first paper. With notion of prior we
> can just go back to (theoretical) physics. QM is easily derivable from
> few assumptions on probability and symmetry and math, but this I take
> as cheating when asking fundamental questions. More technically the
> speed prior seems to be in contradiction with the fact that "universal
> machine" can be sped up infinitely (Blum speed up theorem). Speed prior
> would favorize *big* programs. We can come back later on this more
> technical issue.
>

Perhaps, although it is not a burning interest of mine :(

> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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Received on Tue Jun 20 2006 - 07:54:26 PDT

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