On Thu, Mar 13, 2008 at 07:58:35PM -0000, Alastair Malcolm wrote:
> ----- Original Message ----- 
> From: "Russell Standish" <[EMAIL PROTECTED]>
> To: <[EMAIL PROTECTED]>
> Sent: Wednesday, March 12, 2008 2:56 AM
> Subject: Malcom/Standish white rabbit solution
> .
> .
> .
> >>
> >> (There appears to be a subsidiary issue of 'many description
> >> strings to one OM' (what you seem to be saying in your first email para),
> >> but perhaps that can be dealt with by different definiions of 'OM' - you
> >> seem to think of it as one OM 'type', whereas I think of it as one OM
> >> 'occurrence'.)
> >>
> >
> > Multiple description strings map to a single OM. This is a relatively
> > obvious feature of a functionalist theory, which this theory is.
> >
> > One can certainly think of the OM being an occurrence, but you m ust
> > also realise that there a multiple identical OMs (an uncountable
> > infinity in fact) within the everything.
> 
> Comparing identical OM's/OM sequences, it seems to me that I am most likely
> to be ['in'] that sequence of OM occurrences that is in one of the
> simplest universes that can produce them (cet. par.). (Reason given below.)

You are assuming a measure over all histories, rather than birth
moments or observer moments. This is a rather different SSA than has
been usually proposed (ASSA or RSSA). I can see a possible connection here to
the Schmidhuber II approach (measure over programs), but it is
contradictory to either the Marchal dovetailer (subjective
indeterminism) or my all strings approach (which I consider to be
essentially just starting from the dovetailer trace UD* and assuming a
uniform prior on the strings).

> 
> >> Perhaps the most direct route to the problem is your statement at the end
> >> of
> >> section 4.2 that (paraphrasing), the problem of induction is not a
> >> problem
> >> for the plenitude provided [either the Schmidhuber solution holds or]
> >> observers always tend to model reality, find patterns, theories and so on
> >> that compress the description of the world around them, discarding
> >> non-model-fitting bits as 'noise'.
> >>
> >> The reason that there is no failure of induction (in general), under this
> >> scenario is, as I stated under (b) earlier (which appears to be the one
> >> closest to your view), that we are most likely to be in one of the
> >> simplest
> >> universes that supports SAS's, and it is this that determines the
> >> complexity
> >> of the universe that we are in, and provides order for our universe, and
> >> not
> >> how observers behave/operate in it.
> >>
> >
> > But where does the premise "we are most likely to be in one of the
> > simplest
> > universes that supports SASes" come from, if not from the properties
> > of the observer? That is what 4.1 is all about (coupled with section
> > 5.1 of course).
> >
> > But section 4.1 does not directly answer the failure of induction
> > issue. Nothing about Occam's razor says that a universe has to
> > continue being comprehensible.
> 
> In your 'Why Occam's Razor' paper, sect 2, following a discussion of the
> Schmidhuber ensemble and the Universal Prior, it is stated "If we assume the
> self-sampling asssumption [...t]his implies we should find ourselves in one
> of the simplest (in terms of C-0[Complexity of description x]) possible
> universes capable of supporting self-aware substructures (SASes). This is
> the origin of physical law...". 

The SSA refers to birth moments. The "universe" is sort of code for
the history up to that point in time. The White Rabbit problem
concerns what happens after that point in time.

An assumption of a noumenal reality is enough, of course, to eliminate
white rabbits in conjunction with the arguments in section 2 of Why
Occams Razor. But noumenal reality has its own set of problems,
including being incompatible with quantum facts, something that Bruno
has been at pains to point out.

What I find is that most explanations requiring noumenal reality can
also be explained by simply assuming the anthropic principle. It is
possible that the AP suffices to banish white rabbits also. However,
the AP becomes a little mysterious without noumenal reality, which I
do discuss at several points in my book. It remains, IMHO, an unsolved
problem. 

> If one takes the description string x (up to
> some finite limit) as (minimally) representing a universe (and from which
> OM's are derived), then application of your equivalence class method should
> solve the WR problem directly (check out my roughly equivalent method at
> www.physica.freeserve.co.uk/pa01.htm) - this hopefully answers your point
> above about the origin of our being almost certainly in one of the simplest
> SAS-supporting universes: the premise can be all logically possible
> universes (or just 'entities'), some or all of which are representable by
> description strings (say).

Its been a while since I read your paper, but IIRC it was largely a
paraphrase of the same argument I put in section 3 of Why Occams Razor.

> (From other comments I earlier assumed this is
> what you were actually doing - it seems our ideas in this area are
> significantly different after all.)
> 

It seems to me that you have changed your interpretation of the SSA
(there's nothing wrong with changing your mind, but its always worth
trying to dig into the foundations) as mentioned above.

-- 

----------------------------------------------------------------------------
A/Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
Australia                                http://www.hpcoders.com.au
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