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.) @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 cloud...@gmail.com wrote: > >> >> (HyPE = Hypergraph Programming Engine ?) >> >> >> 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/ >> >> @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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/475075a2-c912-4532-af6a-13843a37808an%40googlegroups.com.
