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.

> 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.

> 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. 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.

> 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).



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