On Saturday, April 11, 2020 at 2:15:48 PM UTC-5, Bruno Marchal wrote: > > > On 11 Apr 2020, at 19:24, John Clark <johnk...@gmail.com <javascript:>> > wrote: > > In the April 10 2020 issue of the Journal Science the best evidence yet > for the existence of a quasiparticle called a "Anyon" is presented. Anyon's > are important because when 2 Anyon's loop around each other their quantum > state is altered and so that brading can be used to encode information. > Such brading would be far less susceptible to quantum decoherence than > other ways of encoding information, and decoherence is the only reason we > don't have practical and scalable Quantum Computers right now. > > > > I agree. I guess you mean braiding, like the space time description of two > particles going around each other, or around a third one, leading to a > braid (in 3d space). > > Nonabelian anyons have a braid group structure.
LC > It is why I except braiding from the projections obtained in arithmetic > from the quantization. Braids and links, and knots are simple topological > structure, but provides semantic for quantum logics, quantum computations, > but also the computations as “seen from inside arithmetic” by universal > machine/number/words/finite)-beings. > > The the fractional Hall effect, the “quantum field” of the condensed > matter, are “shortcut” to Deutsch's quantum Turing universality. > > There are also extraordinary relations between Artin’s group of braids (a > generalisation of the permutation group), Temperly-Lieb Algebra (and > decoupling theory) and self-distributive algebra, related to the theory of > high cardinal in Zermelo-Fraenkel set theory. A left-self-distibutive > algebra is a set D with a a law * such that or all x, y, z: > > x*(y*z) = (x*y)*(x*z) > > For example, if G is a multiplicative group, the law x * y = xyx^(-1), > conjugacy, makes (G, *) into a left-self-distributive algebra. Another > typical exemple is a Ring, (or a Module) with a mean law: (x * y) = > (x+y)/2, as you can easily verify, or more generally (x*y) = (1 - r)x + ry, > with r in R. Such structure plays a transversal role from the “logic of > space” to the logic of some models of “powerful" Turing machine. > > I recall that among the five (actually eight) mains variant of provability > imposed by incompleteness, > > P > []p > []p & p > []p & <>t > []p & <>t & p > > > on p partially computable (provable when true, sigma_1, obeying p -> []p), > the observable is given by the three last one, which are five, as the two > last one splits along G and G* (which I hope you all have an idea go the > importance in self-reference, but ask if you have missed this). > > Now, they are all graded, by the fact that you have variant brought by > replacing []p by [][]p,or []…[]p, with n boxes, written []^n p? > <>^m t can replace <>t, and from those numbers comes the braiding, and > normally the “illusion” of space, in self-introspecting universal machine. > But here, that is not yet proven, and relies on conjecture in mathematical > logic, set theory, etc. Anyon are cool, anyway! (Not easy mathematics > though) > > Bruno > > > > > > > > Fractional statistics in anyon collisions > <https://science.sciencemag.org/content/368/6487/173.full> > > John K Clark > > -- > 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 everyth...@googlegroups.com <javascript:>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv1zZ-hmtiDkCMe3noR%3DFYC%3DavhGxgr28%2BCj1iP-g6W75g%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv1zZ-hmtiDkCMe3noR%3DFYC%3DavhGxgr28%2BCj1iP-g6W75g%40mail.gmail.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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/7677e37c-6643-41b0-a87b-f4455230a13b%40googlegroups.com.
