On Friday, March 6, 2020 at 5:57:34 AM UTC-6, Philip Thrift wrote: > > > > While programming/computing in (hypothetical) infinite domains is > interesting ... > > *Computing in Cantor’s Paradise With λ_ZFC* > https://jeapostrophe.github.io/home/static/toronto-2012flops.pdf > > how any of this relates *in any way* to physical reality (the *stuff of > nature *that is *actually around us* in the universe, vs. just some > theoretical, mathematical concoction someone may come up with) is dubious. > > (Things like consciousness is another thing, or subject: It may be > "beyond" Turing, bit in a way that has nothing to do with "super" or > "hyper" Turing or Cantor or Godel.) > > @philipthrift >
λ-calculus is equivalent to Turing computation. In fact it is similar to Assembly language. It might be that some of these problems could be looked at according to λ-calculus. LC > > On Friday, March 6, 2020 at 5:40:08 AM UTC-6, Lawrence Crowell wrote: >> >> Szangolies [ J. Szangolies, "Epistemic Horizons and the Foundations of >> Quantum Mechanics," 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. >> >> If we think of all physics as a form of convex sets of states, then there >> are dualisms of measures p and q that obey 1/p + 1/q = 1. For quantum >> mechanics this is p = ½ as an L^2 measure theory. It then has a >> corresponding q = ½ measure system that I think is spacetime physics. A >> straight probability system has p = 1, sum of probabilities as unity, and >> the corresponding q → ∞ has no measure or distribution system. This is any >> deterministic system, think completely localized, that can be a Turing >> machine, Conway's <i>Game of life</i> or classical mechanics. A quantum >> measurement is a transition between p = ½ for QM and ∞ for classicality or >> 1 for classical probability on a fundamental level. >> >> What separates these different convex sets are these topological >> obstructions, such as the indices given by the Kirwan polytope. The >> distinction between entanglements is also given by these topological >> indices or obstructions. How these determine a measurement outcome, or the >> ontology of an element of a decoherent sets is not decidable. This is where >> Gödel’s theorem enters in. A quantum measurement is a way that quantum >> information or qubits encode other qubits as Gödel numbers. >> >> The prospect spacetime, or the entropy of spacetime via event horizon >> areas, is a condensate or large N-entanglement of quantum states then >> implies there is a connection between quantum computation and information >> accessible in spacetime configurations. These configurations may either be >> the Bekenstein bound S = kA/4ℓ_p^2, or quantum modified version S = >> kA/4ℓ_p^2 + quantum corrections. Then the quantum processing or quantum >> Church-Turing thesis is I think equivalent to the information processing of >> spacetime as black holes and maybe entire cosmologies. >> >> These are exciting developments. >> >> LC >> >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/bbe488a7-ceb5-4955-b4b3-1a6faaf3032d%40googlegroups.com.
