Hi, I think I have already mentionned it (four years ago?) but I have another Theory of Everything sleeping somewhere in my brain and books. I made an allusion about it yesterday in my post to Peter D Jones, and I take this as an opportunity to say some more words on it. Hope it is not too technical. That theory is hardly original because it simply corresponds to the Polya-Hilbert conjecture in number theory. To sum it up, Euler discovered a rather cute relationship between the infinite sum of the inverse of natural numbers, with some exponents, and some infinite products related to the prime numbers. Precisely:

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Sum (n = 1 to infinity) 1/n^s = Product (on all primes) 1/(1-1/p^s). This is the well known zeta Riemann function. If you can read html: --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---

Or look at http://primes.utm.edu/notes/rh.html or here: http://www.maths.ex.ac.uk/~mwatkins/zeta/tutorial.htm The equivalence of that sum and product is actually equivalent with the fundamental theorem of arithmetic (which says that all numbers admit a unique decomposition in a product of primes numbers (not taking into account the factor order). Thanks to the work of Cauchy (complex analysis) Riemann realized that his zeta function zeta(s) defined a unique analytical function from C to C (C = the complex numbers), that is taking s as a variable on the C complex plane. Zeta(1), which is the harmonic series, still diverge but all other value of s, crazily enough, makes zeta converging. In particular zeta(-1) = -1/12. And this is a little bit crazy because it means that on the complex plane there is a sense to say that the infinite serie 1 + 2 + 3 + 4 + 5 + ... converge to minus 1/12. (When Ramanujan applied for a mathematician job in England, he just annonce that formula to show that he has some ability in computation stuff, and then he has been lucky enough that Hardy did understood it at once, knowing Riemann work). Now some computation can show that the behavior of the prime numbers, I mean the way they are distributed among natural numbers, is controlled by a set of zero of the Riemann zeta function. Actually that control is very fine once we assume those critical zero are all arranged on a line, and this is the famous Riemann hypothesis which fascinates so much mathematicians. The best introduction to that field (for those who remembers their high school math) is the dover book: H. M. Edwards, Riemann's Zeta Function, Dover Publications, 2001. It contains the original paper by Riemann. Now, all those zero could be justified being on a line in the case those zero would describe a spectrum of some quantum observable, and so this suggests a way to tackle that conjecture, and that way is attributed to Polya and Hilbert---from oral talks, see: http://www.dtc.umn.edu/~odlyzko/polya/index.html Now a logician can show that if you take the arithmetical formula having only the addition symbol (together with all other logical symbols except the multiplication) or, contrarily, only the multiplication symbol (and the logical one but no addition) well, in each case you can find a corresponding decidable and complete theory (with respect to truth for those set of formula). Put in another way, it is the mixing of addition and multiplication which is at the original of the richness of the relation between numbers. I have always suspected that the distribution of the prime numbers could encoded the logical mess coming from that mixing. In that case some "total" knowledge of the distribution of the primes would encode a necessarily non trivial part of the (incomplete, unaxiomatizable) arithmetical knowledge. The fact is that, thanks to an algorithm due mainly to Turing and refined by Odlyzko, there is a sort of experimental verification of the Polya-Hilbert conjecture. Indeed it looks like if the zeros of the zeta function describe a spectrum already introduced by quantum physicists when they have been confronted to very complex quantum system like big atom's nucleus: actually they introduce for such system just very big random matrices up the necessary condition of being unitary. It can be shown that such operator (interpreted in some way) describes a form of "quantum chaos". Such an "experimental" verification is of course very frustrating from the point of view of a mathematician who want to *prove* the Riemann hypothesis, but then it is a sort of delight for a pythagorean philosopher who want to extract physics from number theory. Actually, assuming comp and the 1-3 distinction, it would be enough to show that this "quantum chaos" (or some semi-classical regime which can be associated with it) is rich enough to simulate (even in a weak local sense) a universal dovetailer, for getting freely a universal quantum dovetailer from the prime numbers. I believe that an extraction of a universal dovetailer from the primes would also make the Riemann hypothesis undecidable in a very weak arithmetical theory (like Peano Arithmetic, or the weaker Robinson one), and that would be enough to prove the Riemann hypothesis (giving that if the Riemann Hypo is false then it is refutable in Peano Arithmetic (because PA can provably simulate the Turing-Odlyzko algorithm which search for zero out of the critical line). Such a theory is obviously compatible with what we could find by the "pure" interview of the lobian machine, and if it is true, should be identical. Such a Pythagorean TOE would give a more direct explanation of physics from numbers, as compared to the lobian interview which needs that godel encoding of propositions and machines, in term of numbers (many mathematicians hates such (intensional) use of numbers), but then such a theory would hide the 1-3 distinction in some "Everett like interpretation of prime number generated quantum chaos). Unfortunately I don't know well about quantum chaos. If someone knows about a proof of non-universality of quantum chaos .... Actually I got a proof of turing universality of classical chaos, and I got evidence of many universal facets of the zeta riemann conjecture, thanks to a work by Voronin: http://www.maths.ex.ac.uk/~mwatkins/zeta/voronin.htm The rest are conjectures; even more difficult than the lobian one ... Still I hope this post can help you to understand in a different way than my usual UDA/Lobian one, (or Hal Finney's universal absolute distribution, and other OM based toes) how realities could emerge from number theoretical relations. The advantage is that if it works, it would provide directly a universal *quantum* dovetailer. The lobian one leads only indirectly to it (if it leads to it at all). Bruno http://iridia.ulb.ac.be/~marchal/