>
> ----- Original Message -----
> From: Russell Standish <R.Standish.domain.name.hidden>
> > > >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.
>
> 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.
In any case (a point I make below), the measure can be relative to the
observer (ie the SAS), rather than absolute.
>
> > > The answer is that the UTM is not important, but information is.
> Information
> > > is only information when interpreted by something, and the only things
> > > interpreting the universes are precisely the self-aware substructures
> > > inhabiting the universes. We should expect to find ourselves in a
> universe
> > > with one of the simplest underlying structures, according to our own
> > > information processing abilities.>>
> > >
> > > I can't agree with this, if I understand you correctly. This implies
> that as
> > > our information processing abilities increase, we could in principle
> expect
> > > to find ourselves in another kind of universe.
> >
> > That is an interesting thought. Maybe Hans Morevic should run with it!
> > Actually, I find it hard to see how we could change the information
> > processing done by us --- based as it is on brains, eyes, ears etc (I
> > could quite believe our descendants may have a completely different
> > view of the world). But assuming that we could augment our
> > intelligence and our sensory receptors in such a radically different way,
> > then all bets are off. Why assume that we will still see much the same
> > sort of universe? One of the authors in "Minds I" asked "What is it
> > like to be a bat?" In actual fact, bats have a pretty similar
> > information processing system to us, so they would probably have a
> > similar view of the world to us. Try and imagine being something far
> > more alien than that. Not so easy.
> >
> > Or another,
> > > not-too-dissimiliar SAS in our universe, with a different kind of
> > > information theory, could disagree with us as to what kind of universe
> we
> > > should expect to be in.
> >
> > I'd be surprised if it depended on information theory. Any different
> > information theory from the one we currently have is bound to be a
> > refinement, and thus would largely agree on what universe we inhabit.
>
> The underlying problem here (as I see it) is that if one admits into
> existence other SAS's in (say) more complex universes according to *our*
> criteria, but which nevertheless correctly assess themselves as in the
> simplest SAS-compatible universes according to *their* criteria (and all
> because their TM/inference-engines are different - not the same situation as
> my first comment above), it seems we are back with an all-possible-TM's
> situation, which you have rejected. If these other SAS's *aren't* admitted
> into existence, we are back with the question I asked earlier (and you
> answered by indicating this part of your paper): why *this* particular TM
> (the inference engine), and no other?
>
Why do you think we're back to the all-possible-TM situation? And even
if we were, all we need to explain is why the universe we exist in
appears simple to us. Surely, that is what I've explained.
> > > It has already been established that each element of the 'Schmidhuber
> > > plenitude' is representable by a mathematical structure. So there must
> be
> > > such a structure corresponding to a 'buggy' program. Hence 2. is just
> > > another form of 1.
> >
> > No - I have only established the converse. (That each element of
> > Tegmark's ensemble is representable in Schmidhuber's).
>
> I took my assertion directly from the end of your introduction ('An
> alternative connection between the two ensembles is that the Schmidhuber
> ensemble is a self-consistent mathematical structure, and is therefore an
> element of the Tegmark one'), but from your more recent remarks I now
> understand in what sense you choose to separate 1. and 2.
>
I'm glad you understand, because it is a subtle point. Tegmark is
embedded in Schmidhuber, but Schmidhuber is but one element of
Tegmark. This naturally implies an infinite recursion of Tegmark's ensemble
containing an element which generates whole ensemble over again, just
as Schmidhuber's ensemble contains the "Great programmer" generating
the whole ensemble again. There doesn't appear to be any problems with
this remarkable fact though.
> Alastair
>
>
>
>
>
>
>
>
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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 Thu Nov 18 1999 - 15:30:44 PST