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Re: [PrimeNumbers] Re: Prime numbers in math.

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  • Martin Aaronson
    Mark ­ Thanks for your very interesting reaction to my question about ³Convergence². The answers such as yours, and I have received several, have a life of
    Message 1 of 9 , Jun 22, 2010
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      Mark ­ Thanks for your very interesting reaction to my question about
      ³Convergence². The answers such as yours, and I have received several, have
      a life of their own, far removed from the original intent. It is amazing how
      the world relates to and is influenced by the concept of prime numbers. Your
      interest is appreciated. Marty

      From: Mark <mark.underwood@...>
      Date: Tue, 22 Jun 2010 18:08:27 -0000
      To: <peter_boos@yahoogroups.com>
      Subject: [PrimeNumbers] Re: Prime numbers in math.

      --- In primenumbers@yahoogroups.com <mailto:primenumbers%40yahoogroups.com>
      , "Peter_Boos" <peter_boos@...>
      > what we observe in nature we call physics.
      > what we see in physics, follows the rules of math.
      > Above here i wrote down relation to the outside world and math.
      > What i am curious of, prime numbers certainly have a clear formulation
      and follow their own order in math. not really related to our visual
      perception, but there is a clear definition prime numbers are no random
      numbers. Since prime numbers have their use to us.
      > And they contain special properties, in math in general.
      > How does this reflect backwards in physics, or nature ?
      > has anyone observed prime numbers, in physics, or nature ?.

      A few years ago I received a book as a gift: The Music of the Primes by
      Marcus du Sautoy.

      Below is an an excerpt from page 285-286 which you might find


      The power of the analogy between the Riemann zeros and quantum physics
      is twofold. First, it tells us where we should be looking for a solution
      to the Riemann Hypothesis. And second, as Keating had now proved, it can
      predict other properties of Riemann's landscape. ... Even if the
      physicists can't come up with a physical model that generates zeros,
      mathematicians admit that it could well be a physicist who finally
      proves the Riemann Hypothesis. ....

      The physicists believe that the reason Riemann's zeros will be in a
      straight line is that they will turn out to be frequencies of some
      mathematical drum. A zero off the line would correspond to an imaginary
      frequency which was prohibited by the theory. It was not the first time
      that such an argument had been used to answer a problem. Keating, Berry
      and other physicists learnt as students about a classical problem in
      hydrodynamics whose solution depends on similar reasoning. The problem
      concerns a spinning ball of fluid held together by the mutual
      gravitational interactions of the particles inside it. For example, a
      star is a ball of spinning gas kept together by its own gravity. The
      question is, what happens to the spinning ball of fluid if you give it a
      small kick? Will the fluid wobble briefly and remain intact, or will the
      small kick destroy the ball completely? The answer depends on showing
      why certain imaginary numbers lie in a straight line. If they do, the
      spinning ball of fluid will remain intact. The reason why these
      imaginary numbers do indeed line up is related very closely to the
      quantum physicists' ideas about proving the Riemann Hypothesis. Who
      discovered this solution? Who used the mathematics of vibrations to
      force these imaginary numbers onto a straight line? No other than
      Bernhard Riemann.

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