On 28 Oct 2013, at 12:31, Richard Ruquist wrote:


Bruno Marchal via googlegroups.com
4:53 AM (2 hours ago)



to everything-list

On 27 Oct 2013, at 23:26, Richard Ruquist wrote:

It is derived from PA both the universes and the Metaverse.


How?

Richard: I say how in the abstract of the second paper. The Calabi- Yau compact manifolds are numerable based on observed monotonic variation of the fine structure constant across the visible universe.

The fact that something is enumerable does not entail that you can derive it from PA, nor that it is a necessary part of physics.





>It seems also that you believe in a computable universe, but that cannot be the case if our

>(generalized) brain is computable.

Richard: That does not make sense.


If my brain is Turing emulable, and if I am in some state S, whatever will happen to me is determined by *all* computations going through the state S (or equivalent). Our first person indeterminacy domain is an infinite and non computable set of computations. The indeterminacy domain is not computable because we cannot recognize our 1p in 3p- computations (like the one done by the UD). Please take a look at the detailed explanation in the sane04 paper. You need only the first seven steps of the UDA, which does not presuppose any special knowledge. It gives to any fundamental physics some non computable features. Keep in mind that the computable is somehow strictly included in the provable (by universal machine) strictly included in truth. Computable is Turing equivalent with sigma_1 provable, but arithmetical truth is given by the union of all sigma_i, for i = 0, 1, 2, 3, ... (this needs a bit of theoretical computer science).

Note that we cannot derive the existence of matter in arithmetic, but we can, and with comp we must (by UDA) derive the machine's belief in matter. machines lives in arithmetic, but matter lives in the machines' dream which "cohere enough" (to be short). If it happens that the machines dream do *not* cohere enough to percolate into physical realities, then comp is wrong.

By the UDA, and classical logic, you get the physical certainty, by the true sigma_1 arithmetical sentences (the UD-accessible states), which are provable (true in all consistent extensions) and consistent (such accessible consistent extensions have to exist). That's basically, for all p sigma_1 (= "ExP(x") for some P decidable arithmetical formula) beweisbar('p') & ~beweisbar('~p') & p. The operator for that, let us write it "[]", provides a quantum logic, by the application of "[]<>p". This gives a quantization of arithmetic due to the fact, introspectively deducible by all universal machines, that we cannot really know who we are and which computations and universal numbers sustain us. Below our substitution level, things *have* to become a bit fuzzy, non clonable, non computable, indeterminate.

In fact this answers a question asked by Wheeler, and on which Gödel said only that the question makes no sense and is even indecent! The question was "would there be a relationship between incompleteness and Heisenberg uncertainties?"

There is no direct derivation of Heisenberg uncertainty from incompleteness, as that would be indecent indeed, but assuming comp and understanding the FPI, you can intuit why the fuzziness has to emerge from inside the digital/arithmetic, below or at our substitution level, and the math of self-reference gives a quick way to get the propositional logic of that "universal physics" (deducible by all correct computationalist UMs).

And there is the Solovay gifts, which are theorems which show that incompleteness split those logics,. That is useful for distinguishing the true part of that physics from the part that the machine can (still introspectively) deduces. Some intensional nuances, like the "[]" above, inherit the split, some like the Bp & p does not, and facts of that type can help to delineate the quanta from the qualia, but also the terrestrial (temporal) from the divine (atemporal).

Assuming comp, elementary machine's theology and physics becomes elementary arithmetic, relativized by the universal machine's point of view. It makes physics invariant for the choice of the universal system chosen to describe the phi_i, the W_i, etc.

Comp suggests to extend Everett on the universal quantum wave on arithmetic and the universal machines dreams. The wavy aspect being explained by the self-embedding in arithmetic. Comp entails a sort of self-diffraction.

No problem trying to get the fundamental physics from observation, and indeed that will help for the comparison. The approach here keep the 1/p 3/p distinctions all along, and in that sense proposes a new formulation, and ways to consider, the mind-body problem (in which I am interested and is the main motivation for interviewing the antic, the contemporaries and the universal numbers :)


Bruno


http://iridia.ulb.ac.be/~marchal/



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