tag:blogger.com,1999:blog-10614348.post163796849712476561..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: Motives and infinite primesMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-10614348.post-72846751529786628092011-05-26T11:38:09.391-07:002011-05-26T11:38:09.391-07:00I don't know exactly how I would interpret tho...I don't know exactly how I would interpret those words of yours, concerning my post. <br /><br />Look here. Something happen.<br />http://www.neverendingbooks.org/index.php/the-birthday-of-the-primesknots-analogy.htmlUllahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-15854460557001055562011-05-22T19:51:35.038-07:002011-05-22T19:51:35.038-07:00I have often thought of writing a post about blog ...I have often thought of writing a post about blog culture. The sad fact is that the attention of most bloggers -Peter Woit is basic example- is directed to stupidities written by big names. The last example are the commentaries articles about the claimed connection of inflationary multiverse and quantum measurement theory: it is simply total rubbish. <br /><br />But should one waste time to this kind of rubbish? Every professional knows that it is rubbish and there is no danger than this rubbish could spoil the life of a layman. <br /><br />The blog culture tends to give a very weird view about theoretical physics: as if all of us were some kind of swindlers. There are also people doing excellent work instead of narcissistic fighting for the attention of media. The problem is that understanding of this kind of work would require also the blogger to work hardly. It is much easier to write about trash by big names and it makes also the blogger to feel himself intelligent and certainly guarantees maximum number of readers.Matti Pitkanenhttp://tgd.wippiespace.com/public_html/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-23350799840858716442011-05-22T19:38:48.387-07:002011-05-22T19:38:48.387-07:00What Nima and others are developing is a new mann...What Nima and others are developing is a new manner to calculate scattering amplitudes in N=4 SUSYs which as such are not physical since only gauge bosons and superpartners are in spectrum. This probably will have applications also in less symmetric situation. The ability to calculate will eventually have very far reaching implications.<br /><br />What is perhaps even more important than calculational technology is the identification of Yangian symmetry which in zero energy ontology of TGD leads to really powerful vision about generalization of S-matrix, the basic prediction of QFT. Zero energy states span the symmetry algebra of S-matrix. , It is hard to imagine a deeper realization of symmetries of the theory than identification of quantum states as infinitesimal generators of symmetries. If one wants to get visual grasp of this think of the diagram of E_8 Lie algebra which became familiar to us during the short period of time when media raised Lisi to the status of next Einstein. Generalize this by making it infinite-dimensional.<br /><br /><br />A further important theoretical outcome is the discovery that motives, extremely abstract structures due to Grotendienck- certainly one the strangest persons in mathematics- seem to relate to physics. <br />This comes from residue calculus to which the calculation of amplitudes residues and this is integration: very roughly performing infinite sums.<br /><br />Motivic cohomology - cohomology is about integrals - could be also seen as an attempt to give meaning for integration of forms also in p-adic realm in a number theoretically universal manner: p-adic integration is one of the basic challenges of TGD and can be carried out in terms of Fourier/harmonic analysis making sense for symmetric spaces and their padic variants. Therefore the connection with number theoretical universality of physics- the basic element of TGD - is suggestive already in the mathematical structure of existing theories.<br /> <br />The really astonishing outcome of my attempt to understand the basic ideas of motivic cohomology was that the correspondence of infinite primes with rational functions and polynomials leads to a generalization of homology and cohomology theories to their non-Abelian variants by replacing boundary and coboundary operations with non-Abelian modifications mapping group elements to elements of commutator group, whose mapping to zero gives counterparts of ordinary homology and cohomology. This non-abelialinization is to my best knowledge something completely new. The realization of this picture leads also to braids appearing as basic structural elements of quantum TGD. This would mean also unification of homology and cohomology with braid and knot theories.<br /><br />Therefore TGD is more and more contributing also to the development of new mathematics by inspiring new mathematical insight just as quantum physics as inspired ideas in topological quantum field theories. And as one can guess, colleagues continue to remain silent hoping that there could still be small probability that TGD might be wrong. Extremely silly but this is what Big Science is!Matti Pitkanenhttp://tgd.wippiespace.com/public_html/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-8829528336771896212011-05-22T11:28:49.153-07:002011-05-22T11:28:49.153-07:00http://zone-reflex.blogspot.com/2011/05/castle-is-...http://zone-reflex.blogspot.com/2011/05/castle-is-crushing-down.html<br />:)Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-34260459866729400322011-05-22T08:33:48.731-07:002011-05-22T08:33:48.731-07:00Look at this new talk of Arkani-Hamed,from 2.5.
h...Look at this new talk of Arkani-Hamed,from 2.5. <br />http://online.itp.ucsb.edu/online/bblunch/arkanihamed/<br /><br />A general formula for Feynmans. Strong and weak forces.Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.com