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  

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:

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

'Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in
(John Derbyshire)

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

Hope this helps a little bit,



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