----- Original Message -----
From: Russell Standish <R.Standish.domain.name.hidden>
> My much hyped paper is now available for review and criticism
> (hopefully constructive). The URLs are
> http://parallel.hpc.unsw.edu.au/rks/docs/ps/occam.ps.gz or
> http://parallel.hpc.unsw.edu.au/rks/docs/occam/ depending on whether
> you like your papers in postscript or HTML.
I think this is generally a very good paper - probably because I agree with
most of what I can understand of it! My comments follow.
<<Introduction
.
.
Note that there is no need for the UTM to actually exist, nor is there any
need to specify which UTM is to be used -- a program that is meaningful on
UTM1can be executed on UTM2 by prepending it with another program that
describes UTM1 in terms of UTM2's instructions, then executing the
individual program. Since the set of all programs (infinite length
bitstrings) is isomorphic to the set of whole numbers N, an enumeration of
N is sufficient to generate the ensemble that contains our universe.>>
For me, 'generate' is far too strong. I would only allow something like
'index' here.
<<
.
.
In this paper, we adopt the Schmidhuber ensemble as containing all possible
descriptions of all possible universes, whilst remaining agnostic on the
issue of whether this is all there is.1 Each self-consistent mathematical
structure (member of the Tegmark ensemble) is completely described by a
finite set of symbols, and a finite set of axioms encoded in those symbols,
and a set of rules (logic) describing how one mathematical statement may be
converted into another.>>
There will be structures with an infinite number of axioms, but not
functionally (ie visibly) for our kind of universe.
<<Universal Prior
.
.
where |p| means the length of p, gives the size of the equivalence class of
all halting programs generating the same output s under the UTM U. This
measure distribution is known as a universal prior, or alternatively a
Solomonoff-Levin distribution.>>
Reference to, say, L&V here?
<<
.
.
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. 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. We can only attempt to find natural bases for
measures that are anthropically unbiassed and have sufficient generality to
cater for all logically possible universes. Of those that seem to qualify,
TM's en masse can only lead to a rough guide to the simplicity of a TOE, as
you have shown; a basis involving axioms and symbols *may* be better.
<<The White Rabbit Paradox
A criticism levelled at ensemble theories is to consider universes
indistinguishable from our own, except for the appearance of something that
breaks the laws of physics temporarily, e.g. a white rabbit is observed to
fly around the room at specific time and place. There are two possible
explanations for this:
1.
that there is some previously unknown law of physics that caused this rather
remarkable phenomenon to happen. However, it would have to be an extremely
complex law, and thus belong to a rather unlikely universe. >>
Presumably this follows from the last section on the Universal Prior.
<<2.
that there is some ``glitch'' or ``bug'' in the program governing the
universe, that allows some of the ``don't care'' bits to be interpreted.
Since there are many more ways a program can fail, than be correct, surely
then, the ``White Rabbit'' universes should outnumber the lawlike ones.>>
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.
<<Consider more carefully the latter scenario. In most of the universes
where the ``don't care'' bits are interpreted, the ``don't care'' bits will
be devoid of information, and appear as random noise to the self-aware
entity, and thus the universe is indistinguisable from a law-like one.>>
'random noise' implies that it is part of the universe. Again, if it affects
the world, even if not discernable to a SAS, it will be covered by a
physical law, and so come under 1. above.
<<Quantum Mechanics
In this section, I ask the question of what is the most general (i.e.
minimum infomration content) description of an ensemble containing
self-aware substructures. Firstly, it seems that time is critical for
consciousness -- i.e. in order for there to be a ``flow of consciousness''.
Denote the state of an ensemble by phi. This induces an evolution equation
d phi
------ = i H (phi, t)
d t >>
It seems to me that some QM is assumed to generate this - surely other
equations can model time dependency (eg without an imaginary component).
(Also you may wish to clarify that the ensembles of this section aren't the
ensembles of the introduction.)
Typo's (easily missed!): Intro/par 4/line 3; UP/2/1-2; QM/1/1;QM/3/4; Ack -
my name...
Alastair
Received on Tue Nov 16 1999 - 10:43:00 PST