> On 7 Jun 2020, at 13:25, Lawrence Crowell <[email protected]> > wrote: > > On Saturday, June 6, 2020 at 5:25:23 PM UTC-5, Philip Thrift wrote: > > As for Hossenfelder's fav quantum mechanics semantics, she has stated many > times on her blog, it's superdeterminism. > > https://arxiv.org/abs/1912.06462 <https://arxiv.org/abs/1912.06462> > > "A superdeterministic theory is one which violates the assumption of > Statistical Independence (that distributions of hidden variables are > independent of measurement settings). Intuition suggests that Statistical > Independence is an essential ingredient of any theory of science (never mind > physics), and for this reason Superdeterminism is typically discarded swiftly > in any discussion of quantum foundations. The purpose of this paper is to > explain why the existing objections to Superdeterminism are based on > experience with classical physics and linear systems, but that this > experience misleads us. Superdeterminism is a promising approach not only to > solve the measurement problem, but also to understand the apparent > nonlocality of quantum physics. Most importantly, we will discuss how it may > be possible to test this hypothesis in an (almost) model independent way." > > @philipthrift > > > Superdeterminism is just a form of hidden variable theory. This invariant set > theory of Palmer and Hossenfelder as a means of connecting nonlinearity with > QM is interesting. The approach with Cantor sets connects with > incomputability.
The Mandelbrot Set (its complement) has been shown indecidable, but in a vary peculiar theory of computability, which has not so many relation with Turing. It is “computability in a ring”. In the Turing theory, it is an open problem if he complement of the rational-complex Mandelbrot set is undecidable. That is a conjecture in my long thesis. Penrose has come up with a similar (less precise) hypothesis. > I prefer a more standard definition of incomputability than what P&H appeal > to. This works invariant set theory does imply a violation of statistical > independence, but it does so as a hidden variable. > > The complement of a fractal set is undecidable. The complement of some fractal set have been shown undecidable in a theory of computability on a ring. This has been shown by Blum, Smale and Shub, if I remember well. > A fractal set is recursively enumerable, which means we can compute it in a > finite automata up to some point, and “in principle” a Turing machine that > runs eternally could compute the whole thing. Yes, but it uses only the potential infinite. We get all element in the enumeration after a finite time (except that here we use computability on a ring, which is not so easy to compare with Turing computability). > The complement of this is not computable. The complement of a recursive set > is recursive, but the complement of a recursively enumerable set is not > recursively enumerable and is incomputable. You mean “ … is not necessarily recursively enumerable”. Of course a complement of a recursively enumerable set can be recursively enumerable. That is always the case with recursive set. > The invariant set in this superdeterminism is a form of Cantor set or related > to a fractal. The results of Matiyasevich showed that p-adic sets have no > global solution method, where p-adic sets are equivalent to Diophantine > equations. I would be interested in a precise statement of this, and some link to a proof. What has a p-adic set? Set of what? Cantor sets are related to self-reference in many ways. For example through the topological semantic of G and S4Grz, but also through the “fuzzification” of Gödel or Löb theorem, like in a paper by Grim. > This means that dynamical maps from one point to another on the Cantor set > are not given by the same quotient group and in general there is no single > decidable system for such maps. In effect this means it is not observable. What is the relation between observable and decidable? If you study my papers, this is the most difficult thing to do. It is possible, and necessary, though, by the fact intensional variant of G and G*, which makes the logic of the observable/predictibvle obeying a quite different logic than G (indeed, a quantum logic). > > So, while superdeterminism violates statistical independence this is all a > nonlocal hidden variable and thus unobservable. In ways this is where I > depart from Hossenfelder and Palmer, where Palmer uses a different concept of > incomputability, based on the idea of Smale et al on the need to compute a > fractal an infinite amount. I thought you did this. > I appeal to the complement of a fractal, a fractal being a recursively > enumerable set Set of what? > and computable in a standard sense, but where the complement is not > computable. The complement of a creative set (the set-definition of a universal machine, due to Emil Post, and done before Church and Turing) is always non recursively enumerable. The complement of any set of all theorems of an axiomatic rich enough to prove the axiom of RA is automatically non recursively enumerable. Thanks to the work of Myhill, we know that a theory is Turing complete (Turing universal) iff and only the complement in N of the set of (Gödel number of) its theorem is constructively not recursively enumerable. A set S of numbers is constructively not recursively enumerable, or called also productive, means that for any W_i subset of S, you can find some x in S, but not in W_i.. That x serves as counter-example of the recursive enumerability of S. You can extend the extension of S in the constructive transfinite, by reiterating this trasnfinitely (on the recursive ordinals, or beyond). A Recursively enumerable set with a productive complement is called creative, by Emil Post, and is the set theoretical definition of Turing universality, by a result of Myhill. > The fractal emerges from QM in a singular perturbation series and the > complement comes with the dual of a convex set with measure L^p is L^q with > 1/p + 1/q = 1. I fail to see what are the elements of the sets you are talking. The standard notion of computability concerns set of natural numbers (or of things encodable into finite numbers, like strings (the computer science one!), words, formula, etc. Bruno > > 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/affd7fd8-26f9-4cca-983c-aa038a542739o%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/affd7fd8-26f9-4cca-983c-aa038a542739o%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/D7E82826-967F-4E7C-B1F8-92060C39DE4D%40ulb.ac.be.
