Saturday, February 26, 2005

Numb3rs

In to-day's Not-Even-Wrong I learned that M-theory God Ed Witten has followed his brother's Matt Witten's example and is now a TV writer(;-)! The TV series Numb3rs is very ambitious project. The basic goal is to fight against the anti-intellectualism, which has got wings during Bush's era and attack the stereotype about mathematician as a kind of super book-keeper and super-calculator with zero real life intelligence. A TV series in which mathematician's solve crimes is an ingenious choice since detectives must be real-life-intelligent even if they are mathematicians. The team coworks with real mathematicians in Caltech (as you see they look very hippie like) since the goal is to be as autenthic as possible. Even the formulas on blackboard must be sensible so that even mathematician can enjoy the series without fear of sudden strong visceral reactions. Ed Witten got a manuscript to read and proposed an episode in which a rogue mathematician proves Riemann Hypothesis to destroy internet security. My interest is keen since I have proposed a proof, or more cautiously A Strategy for a Proof of Riemann Hypothesis, which has been published in Acta Math. Univ. Comeniae, vol. 72. . I have proposed also a TGD inspired conjecture about the zeros of Zeta. The postulate is that real number based physics of matter and various p-adic physics (one for each prime p) describing correlates of cognition are obtained by algebraic continuation from rational number based physics. This translates to the mathematics the idea that cognitive representations are mimicries of reality and cognitive representation and reality meet each other in a finite number of rational points. This is just what happens in the numerical modelling of the real world since we can represent only rationals using even the best computers. This vision leads to concrete conjectures about the number theoretical anatomy of the zeros of Riemann Zeta which appear in a fundamental role in quantum TGD. The conformal weights of the so called super-canonical algebra creating physical states are suitable combinations of zeros of Zeta. The conjecture is following: for any zero z=1/2+iy of Zeta at critical line the numbers p^(iy) are algebraic numbers for every prime p. Therefore any number q^(iy) is an algebraic number for any rational number q. This assumption guarantees that the expansion of Zeta makes sense also in various p-adic senses for z=n+1/2+iy. A related conjecture is that ratios of logarithms of rationals are rationals: this hypothesis could in principle be tested numerically by looking whether ratios of this kind have periodic expansions in powers of any chosen integer n>1. I would be happy if I had even a slight gut feeling about how the "Strategy for a Proof of Riemann Hypothesis" might relate to Internet safety. Here I meet the boundaries of my narrow mathematical education. So, at this moment it seems that I will not be a notable risk for Internet safety. A word warning is however in order: TGD will certainly become a safety risk for M-theory: sooner or later;-)! Matti Pitkanen

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