On 12/12/2012 7:27 AM, Richard Ruquist wrote:

On Tue, Dec 11, 2012 at 10:08 AM, Bruno Marchal<marc...@ulb.ac.be> wrote:## Advertising

On 10 Dec 2012, at 19:03, Richard Ruquist wrote:On Mon, Dec 10, 2012 at 11:42 AM, Bruno Marchal<marc...@ulb.ac.be> wrote:Richard, On 10 Dec 2012, at 16:17, Richard Ruquist wrote:Roger Bruno, How is consciousness related to god? It seems like the beginning of an infinite god regression.God = Truth (Plato). OK? With the CTM, arithmetical truth is enough (and a tiny provable part is enough for the ontology). I would say that consciousness is a form of knowledge. Knowledge intersects belief and truth. (It is a private undefinable notion, with CTM). The knower in you is the "inner God", which is God restricted by the universal window of your brain/body. I don't know if God (truth) is conscious, but without God (truth) I doubt I could be conscious, even if most of the content of my consciousness is wrong (except on the indubitable fixed point, and perhaops the sharablke oart of math, arithmetic, perhaps). I have no certainties, and that is why I use the arithmetical translation of Plotinus in such conversation, with God = Arithmetical Truth Believable = (sigma_1) provable = universal (Löbian) machine Knowable = the same, but true (unlike proved) = the inner god = the universal soul intelligible matter = the same as 'believable", but together with consistence sensible matter = the same as intelligible matter, but as true That gives eight modalities, as they divided by incompleteness (except God and the Soul). If Gödel's incompleteness theorem was wrong, all those modalities would collapse. Despite the modalities extension is the same set of arithmetical propositions, the machine cannot knows that, and this change drastically the logic of the modalities. Roughly speaking, "God" obeys classical logic, the "Universal Soul" obeys intuitionist logic, and the two matters obeys (different) quantum logics, perhaps even linear (with some luck!)Bruno, thanks. That helps alot. In case you have not already guessed I am trying to marry CTM, string theory and monadology/Indra'sJewels, in order to improve my paper on incompletenes/consciousness: http://vixra.org/pdf/1101.0044v1.pdfThis will work only if you derived the axioms of string theory from arithmetic, unless your theory contradicts the comp or CTM theory.First of all, your request seems to contradict the definition of axiom to claim that they should be derived from arithmetic (meaning CTM I suppose). 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

`This bespeaks a confusion. Axioms are mathematical assumptions. You don't have to defend`

`them; you assume them and build a model on them. Then you see if your model is consistent`

`with the know facts (if not, too bad) and does it successfully predict some new facts (if`

`so, great!).`

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.

`I don't see how you can rule out quaternions, or even octonions, since they include`

`complex numbers.`

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).

`This is not so esoteric. It's just accounting. There's no negative money, but you still`

`have negative entries in your bank account. If you have two systems and to calculate the`

`total entropy you get some number. Then if you learn that one of them is entangled with`

`the other and is perfectly correlated with it, you have to subtract off that duplicated`

`entropy.`

It is not clear that your simple arithmetic axioms can derive complex variables,

`They don't even entail real numbers. But just as computers can deal with real numbers as`

`approximations, so they can approximate complex, quaternion, octonion, and other number`

`systems. And they do this finitely.`

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 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.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.

`Bruno, is there an general, meta-mathematical theory about what axioms will produce a`

`decidable theory and which will not?`

Brent

BrunoAt 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? Thanks, Richard

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