tag:blogger.com,1999:blog-10614348.post6995914904864063024..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: How infinite primes could correspond to quantum states and space-time surfaces?Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-10614348.post-50246409897018621192010-03-26T06:38:30.708-07:002010-03-26T06:38:30.708-07:00I'm no theoretical physicist or geometrician b...I'm no theoretical physicist or geometrician but could these thoughts coincide with E8 X E8 theory. Just food for thought.Anonymoushttps://www.blogger.com/profile/00457809645666524714noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-54536598432355508712010-01-31T20:12:53.610-08:002010-01-31T20:12:53.610-08:00I suppose reductionism itself is one of those if n...I suppose reductionism itself is one of those if not the "generally accepted axiom" you mention. To a curious mind that does not entail message to stop thinking about Riemann hypothesis but rather a challenge to think beyond and not bound by reductionistic axiomatics, yet not abandoning analytical mode of thought either.<br /><br /> Riemann hypothesis, zeta function or distribution of primes can be said to be fenomenological and empirical reality that is true wihtout proving (Gödelian themes arise here very naturally) and area of number theory into which lot of physics reduces to, but the difficulty or impossibility of a formal mathematical proof of Riemann hypothesis - inside generally accepted axioms - also suggests and challenges that it could be thought about in terms other than generally accepted axioms, in a way that is not limited to reductionism itself. <br /><br />IIRC it was Einstein that said that a problem cannot be solved at the same level of thought that created the problem in the first place, or something similar.<br />Seeking guidance from non-reductionistic schools of thought like Buddhism the notion of co-dependence could be hypothesized to be a functioning thinking strategy - "If this arises, that arises; if this ceases, that ceases" was what Buddha had to say about causality. Also often complexities just tend to confuse when truth is very simple - and beautifull.<br /><br />I don't know if the question about fundamental reciprocical codependence between infinite primes and their properties and natural primes and their distribution has any merit, as a strategy to solve the problem of proving Riemann hypothesis or in any other way, all I can say is that the question rises quite naturally... :)Santeri Satamahttps://www.blogger.com/profile/03186892016891445179noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-83320790097163382512010-01-22T21:09:27.070-08:002010-01-22T21:09:27.070-08:00"Ring" has probably some additional mean..."Ring" has probably some additional meaning hidden from me so that I cannot answer. In any case hyper-octonoinic infinite primes have enormous expressive power and could allow to express the entire mathematics of quantum theory as long as one remains in the real of algebraic numbers.<br /><br />Those infinite primes which correspond to free many fermion and boson states can be constructed straightforwardly. Those which correspond to bound states are not so straightforward to construct and might be analogous to finite primes which must be simply discovered.<br /><br />Rieman Zeta has interpretation as thermodynamical partition function in the bosonic sector of quantum field theory for which free bosonic many particle states correspond to infinite primes. Also the fermionic analog of Rieman Zeta follows as fermionic partition function and has a close relation to Rieman Zeta.<br /><br />About Riemann hypothesis I cannot say anything. Maybe it is also something irreducible to generally accepted axioms.Matti Pitkänenhttps://www.blogger.com/profile/13512912323574611883noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-24345884631667563232010-01-22T14:18:43.439-08:002010-01-22T14:18:43.439-08:00As above
so below,
reads the Hermetic Emerald tab...As above<br />so below,<br /><br />reads the Hermetic Emerald tablet. Could these hyperoctonionic infinite primes be the missing part of "The Ring", not a mere reductionistic product of natural primes but The inner structure&being of natural primes and their distribution? Could it be shown that the Riemans Hypothesis and zeta funtion is (co)dependent from qualities of infinite primes?<br /><br />Is a TOE without solution to Riemans hypothesis a real TOE with sole and soil and soul and Sol or just a finger pointing at the moon, so and so and just for the show? Sormet sanoo soo-soo-soo, kengän kannat koo-koo-koo... oom ;) :PSanteri Satamahttps://www.blogger.com/profile/03186892016891445179noreply@blogger.com