Re: White Rabbits and QM/Flying rabbits and dragons

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Thu, 18 Nov 1999 20:56:19 -0000

----- 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.

> > 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?

> > 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.

Alastair
Received on Thu Nov 18 1999 - 13:02:23 PST