On Wed, Dec 12, 2012 at 11:46 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > On 12 Dec 2012, at 16:27, Richard Ruquist wrote: > > On Tue, Dec 11, 2012 at 10:08 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > <snip> > > > This means literally that if the theory below (A, B, C, ... J) is correct A, > B, C ..., J have to be theorem in arithmetic (and some definition *in* > arithmetic). > Agreed > > Here from Davies 2005 is what I consider to be appropriate ST axioms: > http://xa.yimg.com/kq/groups/1292538/1342351251/name/0602420v1.pdf > " > A. The universes are described by quantum mechanics. > B. Space has an integer number of dimensions. There is one dimension of > time. > C. Spacetime has a causal structure described by pseudo-Riemannian geometry. > D. There exists a universe-generating mechanism subject to some form > of transcendent physical law. > E. Physics involves an optimization principle (e.g. an action > principle) leading to well defined laws, at least at relatively low > energy. > F.The multiverse and its constituent universes are described by mathematics. > G.The mathematical operations involve computable functions and standard > logic. > H.There are well-defined “states of the world” that have properties > which may be specified mathematically. > I. The basic physical laws, and the underlying principle/s from which > they derive, are independent of the states. > J. At least one universe contains observers, whose observations > include sets of rational numbers that are related to the (more > general) mathematical objects describing the universe by a specific > and restricted projection rule, which is also mathematical. > > I do not claim the ability to defend all these axioms or even > understand them all for that matter. But I think a little more needs > to be said about A. > > Quantum theory must be based on complex variables and not real numbers > or quaternions for example. Again from Davies 2005 "In addition, one > can consider describing states in a space defined over different > fields, such as the reals (Stueckelberg, 1960) or the quaternions > (Adler, 1995) rather than > the complex numbers. These alternative schemes possess distinctly > different properties. For example, if entanglement is defined in terms > of rebits rather than qubits, then states that are separable in the > former case may not be separable in the latter (Caves, Fuchs and > Rungta (2001) “Entanglement of formation of an arbitrary state of two > rebits,” Found. of Physics Letts. 14, 199.,2001). And as I recently > learned, in quantum information theory, "Negative quantum entropy can > be traced back to “conditional” density matrices which admit > eigenvalues larger than unity" for quantum entangled systems > (http://arxiv.org/pdf/quant-ph/9610005v1.pdf). > > It is not clear that your simple arithmetic axioms can derive complex > variables, > > > UDA is a proof that IF ctm is correct, then, if complex variable are > unavoidable, this has to be justified in term of machine's psychology, that > is in term of number relative selmf-reference. Same for all other axioms.
My point is that universes based on real numbers and/or quaternions, etc., are perhaps also unavoidable. Is that so?...part of the infinities of infinities? > > You can see this as a poisonous gift of computer science. With comp the > fundamental science has to backtrack to Plato if not Pythagorus, in some > way. The physical universes are projections made by dreaming numbers, to put > things shortly. My prejudice is that the projection from dreams of the mind is to a unique physical universe rather than every possible one. Is CTM capable of such a projection even if it is not Occam? > > Yet it works up to now. We already have evidences that comp (CTM) will lead > to the axioms A. But may be it will take a billions years to get the Higgs > boson (in case it exists). If so, the billions of years, I prefer to start with the ST axioms and some experimental properties, like of BEC and physical constants, and like you see what their consequences are. > > My point is technical: IF comp is correct, then physics is not the > fundamental science. Physics is reducible to arithmetic, like today > biochemistry can be said reducible to physics. I have no problem with physics being reducible. But I question if some aspects of physics like dimension is reducible to arithmetic. > > > > > and if they can then the resulting universes seem not to > have unique properties especially concerning entanglement, which is an > essential feature of my approach to resolving the paradox between MWI > and SWI. BTW I consider MWI to apply to the mental realm and SWI to > apply to the physical realm in a mind/brain duality with the two > realms being connected by BEC entanglement. > > > I really love BEC, as they help to make concrete the quantum topological > computer of Friedman and Kitaev. I like condensed matter physics a lot. It > explains how some part of the quantum reality are literally quantum > universal dovetailer already. I think that the primes numbers in arithmetic > constitutes already a quantum universal dovetailer. > But even this cannot be used to get the TOE. If we want both quanta and > qualia, we have to derive physics from self-reference, The late Chris Lofting derived quantum theory from the 1s and 0s of the I Ching using self-reference. >as it is the only > place where we can use the distinction between truth and belief in a > sufficiently clear way to get a theory of qualia extending the theory of > quanta (sharable qualia). This is over my head but that's OK. >It is also the only to solve the mind-body problem > as formulated in the CTM. Could you mention (again) how the mind/body problem is formulated in CTM? > > > > > > I am not sure why you single out Peano Arithmetic in your paper. Logician > > use Peano Arithmetic like biologist use the bacterium Escherichia Coli, as a > > good represent of a very simple Löbian theory. > > > I singled out PA because that was the limit of what I knew of Godel's > math at the time that I wrote that paper two years ago. > > > OK. But Gödel's theorem applies to *all* effective extensions of PA, in a > large sense of "extension". It applies to ZF, and virtually to all > arithmetically sound machines with enough beliefs (which means not so much). > Agreed. I guess I really used PA because I could then characterize the Calabi-Yau cubic lattice manifold as a sound machine since every compact manifold therein is distinct from astronomical observations of variations of the fine structure constant. Would such a lattice constitute a sound machine? > > > > Gödel used Principia Mathematica, and then a theory like PA can be shown > > essentially undecidable: adding axioms does not change incompleteness. That > > is why it applies to us, as far as we are correct. It does not apply to > > everyday reasoning, as this use a non monotonical theory, with a notion of > > updating our beliefs. > > > Not all undecidable theory are essentially undecidable. Group theory is > > undecidable, but abelian group theory is decidable. Does that rule out abelian group theory for our purposes? > > > Bruno > > > > At the time that I wrote that paper, I considered to step from Godel's > incompleteness of consistent discrete real number systems to > consciousness to be a 'leap of faith'. Since becoming a little > familiar with your CTM, I have not been able to discern if you make > the same leap or not. Can you help me here? > > > I think that's the right direction. Consciousness is an unconscious, > instinctive, automatic, bet in our own consistency. It seems that your use of the word bet is equivalent to making a conjecture, that is, an educated guess?? >It is a built in > implicit metaknowledge. In the knower logic (S4) it becomes the dual of Kt, > that is ~K~t, which is Dt v t.(because Kp is Bp & p). It is trivial, for > the knower, thanks to the "t", yet Dy remains true but non provable. > > Do you know modal logic? No. I do not even know string theory. I am like a systems engineer for string theory. Not even that much for logic, my weakest subject. >here Dp = ~B~p. or <>p = ~ ~p. D = Diamond, B = > Box. > t = true, f = false (the propositional constants). > "Bp" is the modal box of the particular modal logic G, and corresponds to > Beweisbar ('p') in Gödel 1931, by results of Gödel, Löb and Solovay (and > others). It means provable (by PA, or PM, or ZF, etc.). > > Bruno > > > > > > > Richard > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.