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
>
>

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