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
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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Received on Mon Jun 19 2006 - 19:25:01 PDT