# Re: The Riemann Zeta Pythagorean TOE

Le 16-avr.-06, à 06:08, danny mayes a écrit :

> Could you expound on this a little more?  Both the MWI through a "wavy
> approach to numbers", and the point about primes are possibly new
> concepts to me.  Or maybe you're talking about things I am familiar
> with
> in an unfamiliar way.  I'm not sure...

I guess you know Euler has found a sort of of direct relationship
between the primes and the natural numbers. See my 29 mars post in this
2a285967d769a5c0/747d84038129a26f#747d84038129a26f

This gives Euler Zeta function, which is defined for s  bigger than
one. Riemann extended it in the complex plane, and you can already
interpret the real and imaginary parts of (some transformation of zeta
having the same zero) as linear combination of sinusoidal wavy
functions (up to some logarithmic rescaling). More generally you can
approximate typical arithmetical functions by sort of fourier transform
(in a base build from the complex roots of unity).
Voronin theorem says that zeta can approximate any analytical functions
(verifying some conditions), and it is an open problem to know if zeta
can approximate itself in this way. But apparently it has been shown
that this problem is equivalent to Riemann hypothesis.
Now if Voronin theorem can be applied on zeta itself, it gives to zeta,
and then to the primes distribution through Euler, some
self-referential abilities showing that the behavior of zeta on some
vertical line in the Riemann strip could simulate some information
preserving transformation of arbitrary solution of Schroedinger
equation (I am not yet sure of that).
The zero of zeta would correspond to a spectra related to some
"observation" of a very complex quantum object, and with enough
universality, it could describe a quantum computer, if not directly a
sort of universal topological quantum field theory (a modular functor,
I can give references later). This makes it possible to shift the MWI
of the SWE to zeta's behavior on some vertical line. Empirically the
zero seems to describe a quantum chaos with some classical regime which
could mean that the primes could describe a selection function as well!
No many-worlders ask for that, I know, but then numbers behave so
strangely, that I am forced to recognize the plausibility of some
bohmian interpretation of number theory, at this stage.
Nothing rigorous here, to be sure. Logically, at first sight, zeta
should not be universal but sub-universal, but that could be enough
locally, from the first person points of views.
This would also entails that zeta (and other function of the Dirichlet
family) would have some amazing computational speeding up ability.

I hope to be able to say more the day I will find and read the papers
by Bohr (Harald, not Niels) and Bagchi referred in Wolfram's MathWorld:
http://mathworld.wolfram.com/VoroninUniversalityTheorem.html

For the non-mathematicians who are interested, Marc Geddes is right,
the book

'Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in
Mathematics'
(John Derbyshire)
http://www.amazon.com/gp/product/0309085497/

is very readable and provides a good trade-off rigor/depth.

Hope this helps a little bit,

Bruno

http://iridia.ulb.ac.be/~marchal/

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