> On 6 Aug 2020, at 14:06, Philip Thrift <[email protected]> wrote: > > > > What is really going on here is that a language of hypergraphs (not well > specified) is what is assumed to be defined. All of fundamental physics is to > be rewritten in this language, replacing the others. > > > https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/ > > By the way, when it comes to mathematics, even the setup that we have is > interesting. Calculus has been built to work in ordinary continuous spaces > (manifolds that locally approximate Euclidean space). But what we have here > is something different: in the limit of an infinitely large hypergraph, it’s > like a continuous space, but ordinary calculus doesn’t work on it (not least > because it isn’t necessarily integer-dimensional). So to really talk about it > well, we have to invent something that’s kind of a generalization of > calculus, that’s for example capable of dealing with curvature in > fractional-dimensional space. (Probably the closest current mathematics to > this is what’s been coming out of the very active field of geometric group > theory.)
If Mechanism is assumed, there is no choice: the laws of physics are given by the laws of self-reference, and they are invariant for the choice of the ontological theory, or first principles. It is a way to explain the impact of incompleteness on physics: the laws of physics are “machine” or “theory” independent. This does not mean that some choice cannot help in the derivation process, but that should be clearly made “temporarily”, and that choice must be either discarded or justifies, from the view of any universal system, run by any universal machinery. Indeed the physical reality emerges from the statistical interference based on *all* computations. Bruno > > @philipthrift > > On Thursday, August 6, 2020 at 6:54:33 AM UTC-5 Lawrence Crowell wrote: > In reading the first of these I run into the usual sense or difficulty with > Wolfram of understanding how to compute or calculate things. > > This does get into HoTT (homotopy type theory) which I see as a sort of > quantum of homotopy or index that represents the obstruction to > diffeomorphisms on paths. A hole or "horn you can't pull the reins over" that > prevents any diffeomorphism that moves a curve past the hole or horn, defines > a first fundamental form π_1(M) = ℤ. The HoTT is a binary set of paths that > wrap around the obstruction and those which do not. In a quantum mechanical > form this can be a form of quantum bit. > > The role of topology with quantum mechanics is not fully understood. An > elementary particle is really a set of quantum states or numbers, and these > may have topological definition. The charge, spin, etc are topological > quantum numbers, and the Cheshire Cat experiments illustrate how these are in > a form of entanglement. Elementary particles are really not that different > from quasiparticles in condensed matter physics' > > LC > > On Wednesday, August 5, 2020 at 1:17:48 PM UTC-5 [email protected] > <applewebdata://87978C6F-012E-4197-8472-2E099BF727E7> wrote: > > (HyPE = Hypergraph Programming Engine ?) > https://www.wolframphysics.org/bulletins/2020/08/a-candidate-geometrical-formalism-for-the-foundations-of-mathematics-and-physics/ > > <https://www.wolframphysics.org/bulletins/2020/08/a-candidate-geometrical-formalism-for-the-foundations-of-mathematics-and-physics/> > Formal Correspondences between Homotopy Type Theory and the Wolfram Model > > > cf. > https://writings.stephenwolfram.com/2020/07/a-burst-of-physics-progress-at-the-2020-wolfram-summer-school/ > > <https://writings.stephenwolfram.com/2020/07/a-burst-of-physics-progress-at-the-2020-wolfram-summer-school/> > @philipthrift > > > > > > -- > 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/475075a2-c912-4532-af6a-13843a37808an%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/475075a2-c912-4532-af6a-13843a37808an%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/5CC16595-6DDC-4799-A627-10B918A77EFF%40ulb.ac.be.
