> On 10 Mar 2020, at 23:27, Lawrence Crowell <[email protected]> > wrote: > > On Tuesday, March 10, 2020 at 7:50:32 AM UTC-5, Bruno Marchal wrote: > >> On 10 Mar 2020, at 01:52, Lawrence Crowell <[email protected] >> <javascript:>> wrote: >> >> On Monday, March 9, 2020 at 6:42:41 AM UTC-5, Bruno Marchal wrote: >> >>> On 6 Mar 2020, at 12:40, Lawrence Crowell <[email protected] <>> >>> wrote: >>> >>> Szangolies [ J. Szangolies, "Epistemic Horizons and the Foundations of >>> Quantum Mechanics," https://arxiv.org/abs/1805.10668 >>> <https://arxiv.org/abs/1805.10668> ] works a form of the Cantor >>> diagonalization for quantum measurements. As yet a full up form of the CHSH >>> or Bell inequality violation result is waiting. There are exciting >>> possibilities for connections between quantum mechanics, in particular the >>> subject of quantum decoherence and measurement, and Gödel’s theorem. >> >> The Digital Mechanist thesis enforces that physics is derivable from Gödel’s >> and Löbs’ theorem, and indeed we find quantum logic exactly were expected. >> >> All computations are executed/emulated, in the mathematical sense of the >> Logicians, in arithmetic. The physical appearances have to be justified by >> the calculus of the 1p (plural) indeterminacy in arithmetic. >> >> There is a natural, canonical “many-wold” interpretation of arithmetic, >> developed by the “majority of universal numbers in arithmetic. >> >> >> >> I will have to write more if possible. I am not sure that all of physics is >> derived from Gödel’s theorem. > > > That might not be the case, but it has to be so when we assume the digital > mechanist hypothesis? Of course it is not a direct derivation from Gödel, but > from all nuances that incompleteness impose to the provability notion. > Incompleteness gives sense to the Theatetus-like variant of the rational > opinion/belief, namely: > > TRUTH (p, God, the One, …) > BELIEF ([]p, provability, Incompleteness forbids to see this as a knowledge) > KNOWLEDGE ([]p & p, true belief, the soul, the first person, the owner of > consciousness) > > And the “two matters”: > > INTELLIGIBLE MATTER ([]p & <>t) (with p restricted to sigma_1 propositions, > the partial computable one) > SENSIBLE MATTER ([]p & <>t & p) (idem) > > The soul provides an intuitionist logic, the two matters and the soul > provides quantum logics when p is restricted on the partial computable > (sigma_1) propositions (the true and the false one, which makes things more > complex). > > See may papers for more on this. This needs some understanding of the > existence of all computations in the models of arithmetic). > > > > > > >> I see is as more that from classical to quantum mechanics there is a sort of >> forcing, to borrow from set theory, to extend a model with undecidable >> propositions. Where this undecidable matter enters in is with the problem of >> measurement and decoherence. > > With mechanism, physics must become a study of the relative computational > histories statistics. > > >> >> As for an earlier comment, Turing's model is in a grey zone between >> mathematics often seen as pure and with physics. The tape and reader, >> appearing a bit like a sort of cart on a track, is a model of a physical >> system. That system is a computer. > > A computer is universal implemented in the physical reality, but with > mechanism, the physical reality is what emerge statistically from the first > person points of view of the computer executed in the arithmetical reality > (or in any reality related to any universal machine). I use numbers only > because most people are familiar with them. > > I sum up 40 years of work, in a taboo domain, and all this is build on not so > well known, or understood, theorem in mathematical logic, so ask any > question, and maybe read also the papers. The first thing to understand is > the incompatibility between (very weak form of) Digital Mechanism and (very > weak form of ) Materialism or Physicalism. > > Bruno > > > > I am not sure that all physics comes from this.
I can explain that if we assume Mechanism, (Indexical Digital Mechanism, i.e, roughly ,The "yes Doctor” assumption (YD), + the Church-Turing (or Post-Kleene) thesis (CT). YD is the assumption that there is a substitution level such that we can survive with an artificial brain/body (in a large sense of that expression) CT is the thesis that the intuitively computable functions from N to N are the functions computable by the combinators (or the Turing machine, or the Lisp programs, or the quantum computer, or the game of life, etc. All those thesis are equivalent. With this thesis, whatever you add in the ontology will be a trouble, as you will have to justify its influence in the selection of the computational histories in the arithmetical reality (which we need to just enunciate the Church-Turing thesis). > My intent is more limited in showing that Gödel's theorem results in > epistemic horizons or limitation on knowledge any observer can have. That is coherent with the fact that incompleteness justifies all the variants of “opinion/belief” by showing that, with p partial computable proposition (sigma_1) 1) it is true that p is equivalent with []p, and with []p & p (Theatetus), and with []p & <>t, and with []p & <>t & p. The true logic of provability (the modal logic G1* (the G*of Solovay with the interpretation in arithmetic restricted to the sigma_1 sentence, that’s the Universal dovetailer in arithmetic) proves those propositional equivalence. Yet, 2) G, the provable logic by th any self-referentially correct machine, does not prove those equivalence, only a few of them. The universal machine knows that she is universal, so she can prove p -> []p (she proves her own sigma_1 completeness), but she can still not prove []p -> p. Obviously she would prove []f -> f, and thus ~[]f, and thus <>t (her consistency!) contradicting Gödel’s second theorem. So we have 5 variants, which are actually 8, as 3 of those self-reference modal logics splits in two along the difference between G and G*. p []p []p & p []p & <>t []p & <>t & p The three last one provides close but distinct quantum logics, and depending which one is closer to the observable/inferable logic of observation will measure a sort of degree of “idealism”. If they all violate the logic inferred from Nature, that becomes an experimental evidence that either Mechanism is false (or we are in a simulation made for failing us, but that is a bit too much conspiratorial for me!, it is just that this cannot be excluded logically. > This then in general is a basis for uncertainty principle and limits with > observing qubits with black holes. The problem with my approach, and mechanism, is that there is only way to find out, which is too extract all physical notions from the universal machine introspection, so that we can compare. And here, there is a lot of work to do, because the mathematical problem are huge. It is already a miracle that this “theology” is decidable at the propositional level, but it can been shown highly undecidable at the first order level (and the contrary would have been quite astonishing). So, we have not yet space (although the shadow of braids, and inserting projective algebra hides in the graded variants of the material modes: []^n p & <>^m t (m > n), and their quantisation ([]<>p). Finkelstein gives indices that the “right quantum logic” will gives not just (Everett) quantum mechanics (and the Gleason measure) but also General Relativity. But that can take a millennium, double so when the guy just saying that we can already listen to the machine (and that’s what Gödel, Löb, Visser, ..; Solovay did) is not much listen too. > I am not sure this encompasses the entirety of physical principles. This means you have not meditate enough on the “Universal Dovetailer Paradox”, or “Argument”. Wit mechanism, the physical has tp be given by a measure on all computations/histories going through our states. I have believed that this would easily leads to far too much histories, and be quickly refuted, but the math shows only a sort of quantum weirdness, so Digital Mechanism is not yet refuted. > It does not for instance tell us why dynamics involves the time derivative of > momentum or second order differentiation of position. I guess that information will be obtained by group theory, at some point. To get the measure right, the core of the physical reality has to be a very rich “symmetrical” object, and NOT Turing universal. To get the derivative and the integral right will need time, space and patience. Just reminding the mind body problem, or taking it out of below the rug requires a lot of patience and energy. BTW, energy remains a bit of a mystery too, with mechanism (and probably without too). 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