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. >

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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) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---