Hi Bruno, Interleaving... From: Bruno Marchal Sent: Sunday, October 10, 2010 11:16 AM To: firstname.lastname@example.org Subject: Re: A paper for your Comments
Hi Stephen, The discussion has evolved enough now from my original topic as to require that I restate my thesis and add some new ideas in a new post with a new subject line, given some new understanding of your ideas. I greatly appreciate your patience and comments as I have learned a great deal from it. I believe that we agree on sufficient points to move forward so that I will leave you comments below stand as a reference for the future. Right now I have one question: Are you familiar with Jaakko Hintikka's idea of game semantics for Logic in which (crudely put) on thinks of a proof is related to the existence of a winning strategy in a 2-person game. What is your opinion of such, if any? For examples please see: http://plato.stanford.edu/entries/logic-games/ http://www.csc.villanova.edu/~japaridz/CL/gsoll.html http://en.wikipedia.org/wiki/Game_semantics [BM] That is very interesting, but with respect to the question I am interested in, this is a question of implementation. The point of mechanism is that the internal views does not depend on the choice of the initial system. [SPK] My idea is that the "top-down" instantiation of proofs from Arithmetic Realism's P.o.V. is reflected in a "bottom-up" way by an infinite number of interactions between many. This sets up a natural symmetry of sorts between the ONE and the MANY, where the "internal views" are within the MANY. There would be no unique "initial system" in the objective sense for the same reason that there can be no first implementation in the objective sense. This has the implication for physical systems that there is no origin for time and space in an objective sense. The Perfect Cosmological Principle that the Universe is homogenous and isotropic in space and time would obtain for an average "observer"; thus a finite space and duration of the world would obtain for any instance. This would solve the initial conditions problem in physics. ** I ask this because it seems that one of the key points of divergence in our discussion is related to my use of ideas that are implicit in game semantic based logics. [BM] All digital parallelism can be emulated by digital sequences. In the mind-body problem parallelism is a red herring, because IF it plays some role for the measure problem, THEN it will be justified by the extraction of space and time. Of course in concrete 3D-time applications, parallelism is without doubt of upmost importance. [SPK] I agree and this goes straight to the root of the idea that I am exploring. This is why I am looking at the duality between Boolean algebras (and their generalizations) and disconnected/scattered spaces that we see in the Stone Representation theorem. Minds would be instances of the former and Bodies would be instances of the latter. The trick is to see how the evolution of these works; this is what Pratt has figured out (in basic terms). Additionally, your repeated notion that if "any empirical difference between this arithmetical physics and the empirical physics, would refute, not Plotinus, but the present arithmetical interpretation" requires a means to connect or analytically continue into physical theory; "concrete 3D-time applications" are instances of the latter. By the way, the passages that I quoted previously from Stephen Wolfram where relating to that physical side and speak to limits on the content of individual Mechanisms; those are what I am considering in the bisimulation model of interactions. I am not advocating physicalism except as one side of a duality. I am against the idea that the physical (or the logical) is "all that exists" and the proof of sorts that I point to is the epiphenomena problem that both physical monism and mental/ideal monism have. Of course we need a neutral common ground to absorb both into but that is taken into account in terms of "in the limit of where all differences vanish". Forgive me here as I am sacrificing clarity for brevity. ** Additionally there is resent work that seems to strongly support my crazy idea of how we might solve the measurement problem in QM (which is my main motivation). [BM] So you do assume QM, even QM + collapse apparently. I don't assume anything in physics, given that the results is that physics is derivable from arithmetic, and *has to be derived* from arithmetic if we want obtain the qualia, and not just the quanta. [SPK] Yes, because I am coming from the opposite direction from you! I assume QM but not "collapse" per say as the metaphysical assumptions in "collapse" go against the Perfect Cosmological Principle. We see this in the preferred reference frame that any objective collapse model generates. What we need, I believe, is a model where we obtain what appears as a Collapse from a 1st person P.o.V. but is more like the Everett-Dewitt idea from the outside 3rd person view all the while understanding that there is no special "observer" that could perceive the latter except as an abstract notion. ** Please see: http://pages.stern.nyu.edu/~abranden/icig-05-27-08.pdf This is very much related to the work of Jean-Yves Girard in his "Geometry of Interaction". [BM] ? (The relation is either trivial, or is not obvious for me. Very technical paper(s). You should stick a bit more on the idea(s) instead of mentioning so much papers which seems to me both a bit 1004-like with respect to the topic). [SPK] That paper discusses the notion of correlations in games which is another way of looking at bisimulations between Mechanisms. From the abstract: "Correlations arise naturally in non-cooperative games, e.g., in the equivalence between undominated and optimal strategies in games with more than two players. But the non-cooperative assumption is that players do not coordinate their strategy choices, so where do these correlations come from? The epistemic view of games gives an answer. Under this view, the players’ hierarchies of beliefs (beliefs, beliefs about beliefs, . . . ) about the strategies played in the game are part of the description of a game. This gives a source of correlation: A player believes other players’ strategy choices are correlated, because he believes their hierarchies of beliefs are correlated. We refer to this kind of correlation as “intrinsic,” since it comes from variables—viz., the hierarchies of beliefs—that are part of the game. We compare the intrinsic route with the “extrinsic” route taken by Aumann [2, 1974], which adds signals to the original game." I hoped that you might get an intuition of what I am trying to work out by reading this paper... It seems to me that the notion of Belief that Brandenburger et al are using would be related to your B as in Bp&p. In my idea this manifests as simulations of simulations, etc. ** By the way, almost all of Girard's papers are inaccessible to me as I am not in a university. I know of his work from my study of Pratt's papers. Take a look here: http://iml.univ-mrs.fr/~girard/Articles.html from Girard's web page: http://iml.univ-mrs.fr/~girard/ Best, Bruno [SPK] Thanks for pointing me to that, now I have 2X reasons to learn to read French. :P I am still thinking on how to write up the interaction idea. It takes me time to translate pictures in my head to words on the screen. Kindest regards, Stephen -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. 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