----- Original Message ----- 
From: "Russell Standish" <[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.)

>> 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...". 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). (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.)

>> I understand that one can think of the universe as a set of cohering
>> OM's,
>> but the minimal specification of them should be something like a TOE
>> (otherwise why do we see neurons and brains etc, if we care to look?), so
>> 'physical universe' should normally be a relevant concept. And (under the
>> above scenario) it is the simplest universe that counts for measure
>> purposes, not the simplest OM - this explains the lack of white rabbits,
>> but
>> compression of the description of the world and 'random data' being
>> discarded by our senses has nothing to do with the WR issue, as far as I
>> can see.
> The idea of cohering OMs forming a universe relates to the Anthropic
> principle. By having phenomenal correlata, one can deduce that there
> are other OMs that share a reality, and that which remains invariant
> under shifts to different OMs become the law of physics. This is, in
> essence Vic Stenger's Point of View Invariance (POVI) principle. This
> set of laws of physics is the physical Universe inhabited by the
> observers - there's nothing else I can imagine it to be.

I have concerns about this kind of approach, but I really ought to take
another look at your book before considering comment on this.

> So, it seems you are suggesting that time translation invariance (of
> the same observer, but successive OMs) is enough therefore to banish
> the white rabbits. But it does hinge on the anthropic principle, which
> we need for other things.

My '(under the above scenario)' was intended to refer to the whole scenario
covered by my earlier comments. Apologies for the ambiguity there. I hope my
comments this time around explain my (preferred) criteria for white rabbit


> The argument in sect 4.2 does not hinge on the AP, but does rely upon
> the property of robustness of the observer, which I haven't completely
> formalised, but I have made a couple of attempts in postings on this
> list. Unfortunately, I just did a quick search in GoogleGroups, and
> can't lay my hands on them just at the minute.
> Perhaps there is some connection between robustness and the AP?
> I really should write up a formal version of the robustness concept
> somewhere more permanent, and also try to develop a formal model of
> the process to see what happens in the face of pure white noise. I'm
> sure it won't be white rabbits, as the argument in section 4.2 still
> seems valid to me, but whether it is anything interpretable as a
> universe is another thing.
> -- 
> ----------------------------------------------------------------------------
> A/Prof Russell Standish                  Phone 0425 253119 (mobile)
> Mathematics
> UNSW SYDNEY 2052                  [EMAIL PROTECTED]
> Australia                                http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
> ----- End forwarded message -----
> >

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