> On 7 Mar 2020, at 00:25, Lawrence Crowell <[email protected]> > wrote: > > 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 > <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.
… to Turing computability. Right. But the paper here define a special λ-calculus based on ZFC. It is unclear if this does not computer more. The author claims that his approach is not leading to hype or super-computation, but after a glance I would say that it is an invitation to descriptive set theory, which allows distincts way to conceive notions of computations on the real numbers. So, it does not address or criticise the usual CT. > In fact it is similar to Assembly language. It might be that some of these > problems could be looked at according to λ-calculus. .. and ZFC. In fact, the axiom of choice can be proven to have no incidence of the elementary theory of computations, but the axiom of choice (the C in ZFC) does say something about how to interpret their results. Bruno > > 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 > <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] > <mailto:[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 > > <https://groups.google.com/d/msgid/everything-list/bbe488a7-ceb5-4955-b4b3-1a6faaf3032d%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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/06E3925A-EC5F-4C66-85E5-2D3503F2903A%40ulb.ac.be.
