It seems we're in agreement. You are better placed to spread the gospel of
the short program - didn't someone say the 'universe is counting' or
something? And you're the best person to complete the all-important
exercise:
Exercice : From the statement
"LET A=A+1 GOTO START" generates the universe.
Prove (and make precise) that
Universes are related to
other universes only by correlation,
which is a subjective feature.
Regards
James, Eagle and Serpent.
> -----Original Message-----
> From: Marchal [SMTP:marchal.domain.name.hidden]
> Sent: Monday, March 08, 1999 2:52 PM
> To: Higgo James
> Cc: 'everything-list.domain.name.hidden'
> Subject: RE: delayed reply
>
> James Higgo write :
>
> >...I am
> >flabberghasted that anyone could read my "Universes are related to other
> >universes only by correlation, which is a subjective feature...." post
> and
> >agree with it.
>
> I agree with it ... relatively to my (comp-) understanding of it. (Of
> course).
>
> > I thought it was pretty radical. Do you know of anywhere
> >these ideas are developed further?
>
> Difficult question. My feeling is that the idea is, more or less
> explicitly, in Pythagore, Xenocrate, Platon, the neoplatoniste (Plotin
> ...), but also in some idealist school of India and nominalist school of
> China, and also in Descartes, Berkeley, Hume, Leibnitz... (you probably
> knew that).
>
> I mention http://iridia.ulb.ac.be/marchal :)
>
> Some modern analytical approach which bear on causality or explanation
> lends, more or less repulsively, to such ideas. Have you read "David
> Lewis: the plurality of worlds" (Basil Blackwell 1986) or his
> "Counterfactuals" (idem 1973).
>
> Modal logic, (the science of possible "worlds"/relative truth), is, I
> think, an almost unavoidable tool if we hope to make things more precise.
> The best textbook, to my knowledge, is Chellas 1980 "Modal Logic, an
> Introduction".
> This could be premature if you are not logic-minded. Plain english is
> still better than eclectic formal exercices. But I hardly imagine
> many-worlders tripping seriously without modal logical tools at hands in
> the long run.
>
> > Could you refer me to something on the Skolem paradox?
>
> Mmh... It seems you are in a difficult-question mood today.
>
> The search on the net is rather disappointing (today too).
>
> My first encounter with Skolem Paradox (SP) is "Les limitations internes
> des formalismes" from Jean Ladriere 1957. 650 pages in french.
>
> A reinterpretation of SP with comp can be find in my
> Iridia-Technical-report-1995, 750 pages in french (cruel fate!)...
>
> I got it: I realise I have never mentionned "Boolos G.S. & Jeffrey R.C.,
> Computability and Logic, Cambridge University Press, third edition 1989".
> It is a very nice and clear and deep introduction to computability,
> classical logic including modal and provability logic !
> ...and you will find in it more than two pages on
> Skolem Paradox: pp. 152-155.
>
> SP in a nutshell : the Skolem Paradox (paradox means here:
> counter-intuitive result) is a consequence of Loewenheim-Skolem theorem
> (LST): any first-order theory which has a model has a denumerable model
> (among others).
> Now take a model U of a classical first order axiomatisation of set
> theory, like Zermelo-Fraenkel set theory (ZF).
> Such a model U is usually called a universe (sic).
> By LST there is such a denumerable universe U and even transitive one
> (i.e. if x belongs to U then x is included in U). U obeys to the axioms
> and theorems of set theory, so it is easy to prove the existence of a non
> denumerable set y in U (Cantor theorem). So y is non denumerable and is
> included in U which is denumerable.
> Contradiction. Contradiction?
> There is no contradiction. What happens is that bijections between y and
> N (which makes y denumerable) does not belong to U. So "from inside" U, y
> is correctly proved to be non-denumerable, but for an "outside" observer
> of U, y is denumerable. Skolem paradox shows that notion like
> "cardinality" are not absolute but are relative to a model.
>
> > I think I'll pass on the program-writing.
>
> Cool !
>
> >I can't see why you need
> >anything more than "LET A=A+1 GOTO START" to generate the universe.
>
> You are definitely in the difficult-question mood.
> Besides, I tell you I do NOT need anything more than "LET A=A+1 GOTO
> START" to generate the universe ...and other machines's dreams.
>
> The problem is to made that statement both obvious and non trivial, to
> make people understanding the point AND appreciating the richness of the
> point.
>
> The whole thread "information or computation" is all about that. And I
> don't thing we got consensus there.
> I will not repeat statements by Gille Henry or Jacques M Mallah, but most
> of them are founded. Especially if you present such proposition in a so
> provocative statement.
>
> Actually, when you say "LET A=A+1 GOTO START generates the universe", I
> am afraid you are saying something PRESUMPTUOUS, RIDICULOUS, ALMOST UGLY,
> IMPOLITE WITH RESPECT TO DEWITT & WHEELER, Etc. Consolation: it is true,
> (trivially provably so with comp).
> But truth is a meager and even frustrating consolation if you are not
> able to share the "tresor" with others.
> You know, there is a time for coming back from the mountain, ...
>
> Now that you pass on the program-writing I will suggest you the following
> exercice (forgive my teacher-deformation) :
>
> Exercice : From the statement
>
> "LET A=A+1 GOTO START" generates the universe.
>
> Prove (and make precise) that
>
> Universes are related to
> other universes only by correlation,
> which is a subjective feature.
>
> Weak anthropic principle is certainly a powerfull tool here, but that's
> hardly enough.
> I doubt you will ever succeed without the concept of universal turing
> machines, and/or without finding some measure on the set of
> computationnal histories (remember the thought experiments PE-omega), etc.
> And, please, don't underestimate the hardness of making the notion of
> "subjective feature" clearer.
>
> ... An explicit UD, (or a great programmer) on the contrary, makes more
> explicit what is needed for the proof. It is just more pedagogical.
> ...Luckily enough, part of the work appears to be done in some nice books
> like Li and Vityani, Boolos and Jeffrey, etc.
>
> I want add something. When you say, in the preeceding post:
>
> >In an infinite multiverse universes
> >which appear to have any relation you like do in fact exist.
> > We appear to
> >exist in those sets of universes which can be strung
> > together so that the
> >laws of physics appear to emerge (weak anthropic principle, my dear
> > friend).
>
> I agree so much that I believe a big part of the laws of physics can and
> must be derived from
> "a theory of consciousness" which itself can and must be derived, with
> comp,
> from theoretical computer science in the form of what machines can tell
> (AND NOT TELL) correctly about themselves including their most "probable"
> computationnal history.
>
> You can take "theory of consciousness" just in the sense of a theory
> of what you call "subjective feature".
> And I hope you agree that a subjective feature, is a feature relative to
> a subject (alias a person, an observer, a point of view, an "angle"...).
>
> Bruno.
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Received on Mon Mar 15 1999 - 09:47:27 PST