>
> ----- Original Message -----
> From: Russell Standish <R.Standish.domain.name.hidden>
> > > > > [AM:]This only goes some way to clarify matters for me - can the
> > > same output
> > > > > bitstrings have different interpretations? (eg could the very same
> bits
> > > > > specify two different sets of SAS's, each in their own physical
> > > universes?)
> > > > > If so, it could at the least complicate the measure (equivalence
> class)
> > > > > calculation, since then nonsense bitstrings (failed outputs of the
> > > inference
> > > > > engine) could in principle be interpreted as SAS-universes. If on
> > > the other
> > > > > hand there are no multiple interpretations for the same bits, then
> > > there is
> > > > > no such problem.
> > > >
> > > > I would wager (if I was a betting man) that any SAS within a bitstring
> > > > was unique (within an isomorphic equivalence class). However, at this
> > > > stage I have no proof of this assertion - it would an interesting
> > > > proof to try to find.
> > >
> > > This implies a partial restriction on the possible (objective)
> > > interpretations of output bit strings - just saying *any* interpretation
> > > that generates a SAS is no good, because it makes the TM redundant
> except as
> > > an artifact to solve the WR problem. I prefer a single possible
> > > interpretation which is defined by the theorems generated by the
> inference
> > > engine. The only other possibility is that the structure of the output
> > > string admits certain possible different interpretations - rather messy,
> and
> > > bringing in a new (and unnecessary) ontology.
> >
> > I'm not quite sure where you are leading with this. Can you elaborate?
>
> We are focussing here on the output bit string of the inference engine (the
> 's' of your Universal Prior section). The fact that you don't dismiss *in
> principle* the possibility of multiple interpretations of the same bit
> string implies that the specific theorems that would specify a particular
> SAS aren't the only possible interpretation of that string. (I hope you
> agree that we can't have *any* interpretation, for reasons given above.) So,
> if we don't have a single interpretation, then it seems that the *structure*
> of the output string must in some way restrict the range of its possible
> interpretations; this in turn means we have to give some special 'reality'
> status to this structure (as well as explaining the nature of the
> restriction), because this structure would be separate from (/ not uniquely
> associated with) the direct SAS (frog) view we (collectively) have of the
> world, and *this* is because there could, *in principle*, be two different
> such views (ie two different SAS-sets) resulting from the same string
> segment (although I agree that in 'practice' this would be highly unlikely);
> neither could the output string structure be deemed uniquely equivalent to
> an 'explicated bird-view' (ie all theorems explicitly specified), since
> other interpretations would be possible. Hence the requirement for an extra
> ontology (the ontology of output string structures) for the multiple
> interpretation case that you have implied. It is for this reason (among
> others) that I prefer the single interpretation version.
>
> Speaking generally, I would just like to say that, apart from the last few
> sentences of the Universal Prior section, I am largely in agreement with
> your paper as far as it goes, and wish it well - I also think there could be
> a book in this later on.
>
> Alastair
>
There may be a problem with this Universal Prior scheme if just any
interpretation of a bitstring is allowed. (eg one can somehow interpret
the string containing an infinite number of zeros as encoding
Shakespeares "Romeo and Juliet"). Because of this rather bizarre
"counter-example" I assume that there is some restriction on how
bitstrings can be interpreted. I'm not sure how to formalise this, but
perhaps Shannon entropy (which is meaning free) provides a measure of
the "information carrying capacity" of a given strings, therefore
constraining possible interpretations.
However should we go all the way to requiring a single interpretation
as you propose? It certainly would be neat and it gives us an objective
universal measure, however as I point out is not necessary to explain
the facts. If a given bitstring has potentially two or more
interpretations giving rise to SASes, then the only problem is that
there is no measure giving the relative probability of being one SAS
or the other - each is equally as likely. However, the result that each
such SAS sees a minimally complex universe, and no "white rabbits"
still applies.
Thanks for your words of encouragement. It might be a while though
before I start thinking of a book!
Cheers
----------------------------------------------------------------------------
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 Wed Nov 24 1999 - 18:26:11 PST