On Fri, Sep 28, 2007 at 06:56:43PM +0200, Bruno Marchal wrote:
>
>
> Le 27-sept.-07, à 12:43, Russell Standish a écrit :
>
> >
> > It may well be that Darwinism is some marriage of information theory
> > with a multiverse idea, but it is not obvious how this works. I'd take
> > it as a fairly fundamental building block at this stage.
>
>
> Hmmm.... What could that mean? Darwinism by itself is a fuzzy theory
> with a lot of presuppositions. What does mean "all the infinite
> strings" + Darwinism?
> It seems to me like (exagerating a bit for being clear) I presuppose
> string theory + the existence of the moon.
>
Sure - the theories exist at different ontological levels. But a
fairly major point of my book is that it is essential to take this
into account, and is also fundamental to the 1-3 distinction.
Not that I think that string theory + lunar existence will get you
anywhere, of course (but you never know!).
Where evolutionary process come into the picture is generating
information.
In the Multiverse, all irreversible processes look like
evolution: branching of worlds gives variation, differing measure and
anthropic selection gives the selection part and determinism of the
Schroedinger equation gives heritability.
What is more, even without considering the Multiverse, all creative
processes we know about (ones generating information) appear to be
evolutionary. So it is not too much of a stretch to conclude that all
creative processes must be evolutionary.
Having established Occam's razor as a theorem in the Multiverse, there
is the immediate problem of the Occam catastrophe. This is resolved by
requiring a minimal complexity of the observed universe. The simplest
(and most probable by Occam) scheme for generating this complexity is
a creative process operating within a simple universe, and is far
simpler than an ab initio complex universe (a Boltzmann brain).
So the assumption that all creative processes are evolutionary (which
one might hope will be better established than that in the future)
endows evolution with a pivotal role in these grand theories of
everything. Its particularly interesting that the evolutionary
concepts map directly to the fundamental postulates of QM.
>
>
>
>
> >
> > Your problem may be in the lack of formal precision.
>
> No. Conceptual precision. I still don't know what you postulate and
> what you consider as derivable from the postulates.
>
Well obviously, I cannot at this stage explain more clearly than in
my book. However, feel free to ask questions, as in asking questions I
understand better your conceptual framework, and may well be able to
connect to it.
As for results, I would list them as:
Zero information principle
Occams razor
Elimination of white rabbits (these are 1st person white rabbits - I
have no idea what a 3rd person white rabbit could be).
Necessity of self awareness for consciousness
3 out of 4 postulates of QM, namely:
1) Hilbert state space
2) Schroedinger equation
3) Born rule
>
>
> >>> As is stated in "Why Occams Razor", and made more explicit in
> >>> "Importance of the Observer" and "Theory of Nothing", what is the U
> >>> used in computing the universal prior? It can be nothing other than
> >>> the observer. U needn't even be a machine, any partition of the
> >>> strings into measurable subsets suffices.
> >>>
> >>
> >>
> >> ?
> >
> > Which part didn't you understand? The partition bit? If S is the set
> > of strings, with a measure mu such that mu(S)=1, then a function
> > f:S->N such that
> >
> > mu( f^{-1}(N) ) = 1
> >
> > defines a partition { S_i = { x\in S| f(x)=i } | i \in N} of S.
>
>
> And what if U is a machine?
It works if f is a machine, although not all machines satisfy the
above partitioning requirements, in particular non-halting machines.
> What are the relations with the partitions.
> What is an observer (in the all infinite strings context)?
>
Whatever else an observer is, it does map strings to interpretations.
>
>
>
>
> >>> And this identification turns an essentially 3rd person account
> >>> into a
> >>> 1st person account. To talk about ASSA or RSSA one has to introduce
> >>> some notion of time, or at least successor states.
> >>>
> >>
> >>
> >> Which we have without ay physical time notion, nor subjective time
> >> notion with comp. Successor states are definable by use of numbers and
> >> successor of numbers. This can be important given that everybody
> >> agrees
> >> on numbers (except ultrafinitist, but I know only one in Russia), but
> >> nobody agrees on what "time" could be (even the third person physical
> >> one, or first person plural).
> >>
> >
> > Well I, for one, have not made the connection between the successor of
> > a number, and subjective time in COMP.
>
>
>
> Me neither. The successor function is just what we need conceptually to
> talk about the steps of the Universal Dovetailer. Subjective time is a
> much higher level concept related to the 3rd hypostasis (aka first
> person, knower).
>
In the UDA, you do make use of time, in particular the seperation
between 1st person time (duration experienced by the conscious
observer) and 3rd person time (measured by the running of the UD). One
of the lessons I draw from this is the irrelevancy of 3rd person time,
which comes about in step 8 of the argument (in the SANE version) in
the move to a completely Platonic basis. Obviously, 1st person time
remains, and appears to be explicitly assumed ISTM.
I understand S4Grz has Kripke frames, and so one would expect that
hypostasis to have a time-like structure. However, it is not clear to
me how this might relate to the subjective time of the UDA. But wait,
you say there is more on this in your Brussel's thesis...
> >
> > Don't you see that the UD* is just the set of infinite strings?
>
>
> I don't see, and I don't think so. UD* is the infinite running of the
> UD. Now, what is true is that the UD dovetails on all portion of
> generable infinite (even uncountable sets) so that all programs will be
> executed relatively of all infinite strings, but also infinite trees,
> graph, etc.
A UD based on a Turing machine only works on strings. Did you have
some other machine in mind - Lisp perhaps?
> And all this each time relatively to the execution of a
> programs, and this only from the first person point of view. UD* as
> seen from a third person perspective never goes to the uncountable.
I don't see why not. It all depends on what you allow in Platonia.
I remember we had a lengthy discussion with Schmidhuber, who was
arguing as you are now.
> Eventually UD* endows all the non trivial constraints from computer
> science/mathematical logic.
>
>
I assume this relates cryptically to the previous in some way.
...
>
>
> So now, you assume things like Church thesis. But then there are others
> statements which makes no sense (if only like: only the strings).
How is the CT incompatible with the set of all strings?
> I understand many of your answer locally, but do not succeed in
> relating them coherently, (and thus the problem of conceptual clarity)
> except by assuming comp, and correcting a few bit your intuition by
> using my own work.
>
It is a worthwhile exercise to do this.
> > Are you really sure of this? What if it is a newborn child placed
> > inside the W-M duplication experiment, that repeats (100 times a
> > second might be fast enough). Don't you think the child might end up
> > distilling some sort of reality from what it observes? ...
>
>
> This is an ASSA type of reasoning, and I don't see how this could work
> (even without comp).
No - it is SSA based, not SSSA (ie reasoning on birth moments).
> Even a new born baby would experiment the quasi
> exact splitting in two of a flux of z-photons send on an x-analyser (to
> take the quantum version of the WM iterated duplication).
> In the WM iteration, most of the mutiplied baby will be in front of
> incompressible WM-strings independently of the fact that they can read
> it or not due to the contingent fact that babies cannot read).
>
>
>
>
> > ... Perhaps most don't, but only those that manage to build up some
> > kind of coherent
> > reality from the random sequences of W's and M's ever become conscious.
>
>
> That is a move like "white rabbit does not exist because they make no
> sense". But both by UDA and AUDA, all the problems is that white rabbit
> does makes sense. They does not entail inconsistency, and they can only
> be avoided by a (absolute and/or relative) measure.
>
No White Rabbits are not experienced because they're immensely complex
relative to what we normally observe. Small amounts of noise (relative
to the wabbity stuff) seen in the context of consistent world views are
simply filtered out. It has to be that way, as otherwise we'd be
hopelessly distracted by contingent data in the natural environment,
and effectively non-functional.
> >
> > OK - but then you can never know that you know something.
>
>
> This is a subtle point. Formally you *can* know that you know something
> (Know p -> Know Know p). But indeed, you cannot know *for sure* that
> you know for sure something.
Umm - what's the difference?
> That is why comp prevents us to ever know
> we are awake or sound, or things like that, although we can know to be
> wrong or dreaming, etc.
> The price of attaching knowledge to the (unameable, undefinable) truth,
> is that we loose the connection of knowledge with certainty.
> But this is like in "real life" where you can still have the memory of
> having believe knowing something, and then changing your mind. If not,
> we would always say "believe" in place of "know".
>
To the intense frustration of my wife!
>
>
> >
> >> Confirmation is provided by the fact that that doing this
> >> gives an unameable (by itself) self quite similar to Brouwer's theory
> >> of consciousness (which has given birth to intutionnist math and
> >> philo). Much much more can be said here.
> >
> > This I've never really understood. What is this unnameable self, if
> > not a logic statement, or a system of logic statements?
>
>
> I will try to come back on this. It is explained in my SANE and
> PLOTINUS paper (and the theses (in french)).
>
Ah - in that paper you use "to name" to mean "assert by a consistent
machine". This is not an everyday use of the verb, but maybe it makes
sense in the context of Plotinus theology, a subject I have little
interest in.
> >
> > Where is the justification of this? I'm not trying to be
> > argumentative, but I missed seeing this justification in both your
> > Lille thesis and your SANE paper.
>
>
> This is what I explained in 300 pages in "Conscience et Mécanisme", but
> has been replaced in the Lille thesis by "see Godel, Lob, Solovay".
> It is pure computer science/mathematical logic.
>
It can't be pure logic, as it forms a bridge between the formal world
and the "baggage" by which we understand things. It should be in the
form of an intuition pump like the UDA, or some handwaving description like
much of ToN.
But I do need to read the Brussels thesis one day. I was hoping you
might take me up on my offer to translate it - it would force me to
read it thoroughly!
> >>
> >> Experiences are the roots of incorrigible knowledge.
> >>
> >
> > It seems one can be wrong about one's experiences.
> > How is this
> > incorrigible knowledge then?
>
>
> It is incorrigible for the reason that it is attached to truth by
> definition.
We're not apriori talking about the same thing. There is incorrigible
knowledge, defined by the formula Bp & p. There are experiences, which
are what the observer experience - related to OMs, qualia and all that
stuff. Where's the connection?
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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Received on Sun Sep 30 2007 - 21:44:29 PDT