Re: White Rabbits and QM

From: Russell Standish <>
Date: Wed, 17 Nov 1999 13:15:28 +1100 (EST)

> ----- Original Message -----
> From: Russell Standish <>
> > My much hyped paper is now available for review and criticism
> > (hopefully constructive). The URLs are
> > or
> > 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.

Good point. Actually, according to my embedding, they will have
measure zero.

> <<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?

I'll see what I can find.

> <<
> .
> .
> 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.

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.

Maybe its a matter of preference, but axioms and symbols assume that
the universe must be logical, and describable by a well formed
formula. To me, the information theoretic description of Schmidhuber
is far more basic and justifiable than assuming a logical nature to
the universe.

> <<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.

No - I have only established the converse. (That each element of
Tegmark's ensemble is representable in Schmidhuber's). Unless you are
aware of some other result showing the opposite, I would assume that
Schmidhuber's ensemble has elements not in Tegmark's (corresponding
precisely to those nonlogical universes you would have me drop).

> <<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 I confused readers by writing the RHS as iH. I should have
used another symbol, e.g. {\cal H}, and then later on, once linearity
is introduced, identify {\cal H} = iH, where H is a Hermitian operator.

problem not.

Otherwise, the above equation is the most general way of writing an
evolution equation I think.

> 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

Thanks for your comments.


Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Room 2075, Red Centre
Received on Tue Nov 16 1999 - 18:28:13 PST

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