On 12 Dec 2012, at 20:03, Richard Ruquist wrote:

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) iscorrect A,B, C ..., J have to be theorem in arithmetic (and some definition*in*arithmetic).Agreed

OK.

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 onedimension oftime.C. Spacetime has a causal structure described by pseudo-Riemanniangeometry.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 bymathematics.G.The mathematical operations involve computable functions andstandardlogic. 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 realnumbersor 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 distinctlydifferent properties. For example, if entanglement is defined intermsof 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 areunavoidable, this has to be justified in term of machine'spsychology, thatis in term of number relative selmf-reference. Same for all otheraxioms.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?

`Real numbers are unavoidable, and in my opinion, we will need the`

`octonions, and other non associative algebra. But it is too early to`

`introduce them. It will depends on the extension of the material`

`hypostases in the first order modal logical level.`

You can see this as a poisonous gift of computer science. With compthefundamental science has to backtrack to Plato if not Pythagorus, insomeway. The physical universes are projections made by dreamingnumbers, to putthings shortly.My prejudice is that the projection from dreams of the mind is to a unique physical universe rather than every possible one.

`On the contrary. It leads to many-dreams, and it is an open question`

`if this leads to a multiverse, or a multi-multiverse, or a multi-multi-`

`multiverse, etc.`

Is CTM capable of such a projection even if it is not Occam?

`CTM predicts it a priori. And it is OCCAM, in the sense that it is the`

`simplest conceptual theory (just addition and multiplication of non`

`negative integers).`

Yet it works up to now. We already have evidences that comp (CTM)will leadto the axioms A. But may be it will take a billions years to getthe Higgsboson (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.

`No problems with this. I try to put light on the mind body problem,`

`not on application.`

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.

`Read the UDA. If you get it, you will understand that all of physics`

`comes from arithmetic.`

and if they can then the resulting universes seem not tohave unique properties especially concerning entanglement, which isanessential 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 quantumtopologicalcomputer of Friedman and Kitaev. I like condensed matter physics alot. Itexplains how some part of the quantum reality are literally quantumuniversal dovetailer already. I think that the primes numbers inarithmeticconstitutes already a quantum universal dovetailer.But even this cannot be used to get the TOE. If we want bothquanta andqualia, 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 asufficiently clear way to get a theory of qualia extending thetheory ofquanta (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 inCTM?

`By UDA it takes the form of justifying the whole of physics from`

`numbers arithmetic.`

`It is done in the sense that the math equations are already given for`

`the logic of observation, which can be compared with the logic of the`

`physical propositions, and it fits, up to now. Those equation are`

`highly non trivial, so that fitting gives some eight to comp (alias`

`CTM, mechanism, ...).`

I am not sure why you single out Peano Arithmetic in your paper.Logicianuse Peano Arithmetic like biologist use the bacterium EscherichiaColi, as agood 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 ofPA, in alarge sense of "extension". It applies to ZF, and virtually to allarithmetically sound machines with enough beliefs (which means notso 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.

`OK. All what I say is that if we are machine, eventually you have to`

`justify strings without referring to observation. With comp we can use`

`the empiric world to test the theory, but not to find it. It has`

`become a form of treachery.`

Would such a lattice constitute a sound machine?

I don't know. You have to be more precise than above.

Gödel used Principia Mathematica, and then a theory like PA can beshownessentially undecidable: adding axioms does not changeincompleteness. Thatis why it applies to us, as far as we are correct. It does notapply toeveryday reasoning, as this use a non monotonical theory, with anotion ofupdating our beliefs.Not all undecidable theory are essentially undecidable. Grouptheory isundecidable, but abelian group theory is decidable.Does that rule out abelian group theory for our purposes?

For the ontological TOE, yes. But not as a tool among others. Bruno

BrunoAt the time that I wrote that paper, I considered to step fromGodel'sincompleteness 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 inimplicit metaknowledge. In the knower logic (S4) it becomes thedual of Kt,that is ~K~t, which is Dt v t.(because Kp is Bp & p). It istrivial, forthe 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, andcorresponds toBeweisbar ('p') in Gödel 1931, by results of Gödel, Löb and Solovay(andothers). It means provable (by PA, or PM, or ZF, etc.). Bruno Richard--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.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.

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