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

From: Russell Standish <>
Date: Mon, 19 Jun 2006 23:31:58 +1000

On Mon, Jun 19, 2006 at 11:12:52AM +0200, Bruno Marchal wrote:
> ?

I'm not sure which bit you were having trouble with. A description is
an infinite length bitstring. It is therefore equivalent to a point in
the unit interval [0,1] (modulo a little bit of funny stuff on a set of
measure zero). The uniform measure on the unit interval is equivalent
to the Levin-Solomonoff distribution, or universal prior, were sets of
descriptions are partitioned by a UTM. Information (or complexity) is
simply the negative logarithm of the set's measure:

I = -log mu(S)

Clearly, the set of all descriptions is equivalent to the unit
interval, and has I=0. This is the zero information object. Subsets of
the unit interval have smaller measure than 1, so the equivalent sets
of descriptions have larger information content.

A finite string can be thought of as a set of descriptions that share the
same finite prefix, and so have I <= length of string.

> > I think he
> > is wrong too, and agree with you, however I'm not so sure his
> > arguments are this easy to dismiss.
> Which argument in particular?

The speed prior argument (advanced in his "Algorithmic Theories of
Everything") paper.

> > 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).
> Remember Schmidhuber assumes comp.

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'm thinking out loud here, so I welcome comments and corrections, of course.

> Bruno
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.
A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                         	       0425 253119 (")
UNSW SYDNEY 2052                      
            International prefix  +612, Interstate prefix 02
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to
To unsubscribe from this group, send email to
For more options, visit this group at
Received on Mon Jun 19 2006 - 19:25:01 PDT

This archive was generated by hypermail 2.3.0 : Fri Feb 16 2018 - 13:20:11 PST