On Tue, Jul 31, 2007 at 04:06:10PM +0200, Bruno Marchal wrote:
> Le 31-juil.-07, à 00:08, Russell Standish a écrit :
> >
> > On Mon, Jul 30, 2007 at 11:47:48AM +0200, Bruno Marchal wrote:
> >>
> >> If this is not relevant in this context, I ask what is relevant ... ?
> >> The problem you mention is at the cross of my work and the everything
> >> list. Now, as I said some days ago, I think that a way to link more
> >> formally my work and the everything discussion can consist in defining
> >> a notion of basic atomic third person observer moment. The UDA, plus
> >> Church thesis + a theorem proved in Boolos and Jeffrey (but see also
> >> and better perhaps just Franzen's appendix A) makes it possible to
> >> define the comp third person OMs by the Sigma1 sentences of
> >> arithmetical language. Those have the shape ExF(x) with F(x) 
> >> decidable.
> >> For example ExPrime(x) (a prime number exists), Ex(x = code of
> >> triple(a,b,c) and machine a gives c on argument b), ... This last
> >> example show that the notion of Sigma1 sentences is rather rich and
> >> encompasses full computability. So the very restricted notion of
> >
> > Interesting. Since an observer moment contains all information that is
> > known about the universe,
> ? I guess you mean ... about the observer.

No, I mean all information known by the observer (including, but not
exclusively information know by the observer about erself).

> > this led me to identify the observer moment
> > and the quantum state vector.
> ... and the partial relative quantum state vector corresponding to the 
> observer. OK, but at this stage this would be cheating. We can not yet 
> explain why the quantum histories wins over the comp/number relations.

Well I have my own reasons, considering knowledge acquisition as an
evolutionary process. But I disagree about it being cheating, because
I don't a priori assume quantum states are elements of a Hilbert
space. That is a derived property.

> > This is not incompatible with with your
> > notion of the OM being a Sigma1 sentence, but it places severe
> > restrictions on the form of the quantum state vector.
> The OM are the Sigma1 sentences, when they are considered as third 
> person constructs. 

Third person is that which is accessible to all observers. Do you mean
0th person perhaps?

> Those are really the states accessible by the UD. To 
> get the quantum we have to reconsider those OMs from the points of 
> view. In the arithmetical comp setting this corresponds to looking to 
> the views expressed by the intensional variants of the logic of 
> prpvability (p, Bp, Bp & p, Bp & Dp, Bp & Dp & p, ...) with p 
> restricted to the (arithmetical) Sigma1 sentences. This gives the 
> second row of the 16 hypostases described in your book, page ? (my 
> exemplar is at home!).
> > There can only
> > be aleph_0 of them for instance.
> Not really because the Sigma1 sentences are (a priori) weighted by the 
> computations going through, including those who does not terminate, if 
> only because they dovetail on the reals, and this is enough to suspect 
> that there could be  a continuum (aleph1). Of course it could be less 
> by the existence of some yet unknown equivalence relations (which I 
> succeeded not using thanks to the lobian interview). More on this when 
> David is back.

Alright, but it would be nice to know. There are only a countable
number of machines, so I thought there'd only be a countable no. of
Sigma1 sentences.

> > Perhaps these restrictions are
> > testable? Perhaps there is something wrong with identifying the state
> > vector with the OM?
> Comp is really "I am a machine", and not at all "the universe is a 
> machine". The UDA shows that, unless "I am the universe", the 
> proposistion "I am a machine" and "the physical universe is a machine" 
> are incompatible. Indeed the UDA forces the physical laws to emerge 
> locally from *all computations"? A priori again this makes the universe 
> a non computational  object, it seems to me (by UDA).

But the OM is actually the "universe", or at least a snapshot
thereof. So we would expect it to be uncomputable. Is that also the
case of the Sigma1 sentences?

> Bruno
> http://iridia.ulb.ac.be/~marchal/

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

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