>
> Russell,
>
> There seems to me to be an underlying inconsistency in what you have been
> saying in this thread, or else there is some kind of misunderstanding
> between us. So, if I may, I will pursue matters a little further, but try to
> focus just on this main point.
>
> > > (1) Role of TM solely as an inference engine (implementing the specific
> > > transition rules of Modus Ponens, substitutivity and so on) - this
> creates
> > > at least two problems if it is applied to your scheme:
> > > (a) An inference engine can do nothing with a non-wff (it is outside the
> > > context of its application).
> > > (b) Why do we have this specific TM - why not others? So we have to go
> to
> >
> > This is indeed the role of the TM. As far as problem a) is concerned,
> > all bitstrings are interpretable as valid programs. However, the
> > output couble be rubbish, and may correspond to a non-wff, an
> > illogical universe, or even "nothing at all" - complete
> > randomness.
>
> The picture I am getting here, in simple terms, is of one program (the
> inference engine) operating as best it can on all possible sequences of
> bits - some of these sequences will be 'lucky' enough to be converted to
> bitstrings corresponding to theories (consistent theorem sets), but most
> will be gobble-de-gook (there will also be inconsistent theories - this is
> where your 'illogical universes' come in, I presume).
>
Right on the nose!
> However, previously you have said:
>
> >>[AM:] 3) Whether bitstrings could be immediately interpreted as anything
> other
> >> than symbol strings.
> >
> >You could interpret them as anything you like - UTM programs, axioms
> >of a mathematical theory, the works of Shakespeare.
>
> So, apparently, if the inference engine generates bitstrings corresponding
> to theories, they could just as easily be interpreted as rubbish. Conversely
> gobble-de-gook strings could be interpreted as consistent theories - again
> we descend to unanalysable anarchy.
>
The fact that some of the bitstrings can be interpreted as universes
containing SASes is enough to imply the reality of those universes
to the SASes they contain. It doesn't matter if that bitstring
appears gobble-de-gook to an external observer (although I can't
imagine it would appear completely random, there must be various
patterns and correlations that the external observer will see). This
is the beauty of the Schmidhuber approach. Tegmark's scheme works in a
very similar way.
> I think this is the main problem I have with your scheme. Less important
I'd like to think of it as my scheme, but Schmidhuber and Tegmark got
there first.
> ones are the ontological credentials of rubbish and inconsistent-theory
> bitstrings/universes, and the subjective information theory problem which I
> mention in my comments on your paper.
>
> Alastair
>
>
>
>
>
>
>
----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Tue Nov 16 1999 - 18:04:02 PST