Re: White Rabbits and QM/Flying rabbits and dragons

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Tue, 23 Nov 1999 17:46:56 -0000

----- 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
Received on Tue Nov 23 1999 - 14:16:33 PST