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Posted by Mark on June 25, 2003 02:19:48 UTC

I just read a book entitled Prime Obsession. In one chapter, it explains how the statistical distribution of the zeros of the Riemann zeta function echoes the statistical distribution of the eigenvalues of some types of random matrices.

These random matrices are the same ones used in quantum theory to mathematically model atomic energy states.

The Euler product equation states that this sum:

zeta(s) = 1 + 1/2^s + 1/3^s + 1/4^s + 1/5^s + 1/6^s + 1/7^s + ... 1/n^s (all natural numbers out to infinity)

is equal to this product:

(1 + 2^s)^-1 x (1 + 3^s)^-1 x (1 + 5^s) x (1 + 7^s)^-1 x (1 + 11^s) x ... (1 + p^s)^-1 (all prime numbers out to infinity)

So the zeta function is intimately entwined with prime numbers, and at the same time mysteriously tied to atomic behavior.

What the heck does quantum physics have to do with number theory? Apparently there is a fundamental connection between prime numbers and the universe.

~~~We can't DO anything with the knowledge of black holes, or the edge of the universe, or where the universe began~~~

Just as with number theory, Riemannian space and differential geometry are abstract concepts born and nurtured within the human genius. General Relativity was built on a lot of what G.F.B. Riemann "thought up". Einstein saw the connection between the abstract and the physical and triumphantly bridged the gap. With his resulting equations, Schwarschild finds a solution describing a paricular geometric configuration whereby all geodesics return to a mutual origin (blackhole).

...All of this accomplished with pencil (or chalk) and paper (or chalkboard) ... decades later an astronomer looks up and notices a star orbiting something invisible! Amazing!

~~~We'll NEVER EVER be near enough to a black hole to probe it - but that's not the point - is it?~~~

Never say never mah dear ... just messin'

~~~It's conquering the fear of the unknown and radically changing the way we see reality.~~~

May I humbly offer a correction? It's not fear of the unknown, it's pure curiosity. We don't study mathematics/science out of fear...

~~~But it, like poetry, is dead and cold to those who choose not to understand it.~~~


~~~It's a shadow of a glimmer of what God must see - and control.~~~

Back to the prime numbers, I just wanted to offer a quick semi-educated opinion (hey I'm not Richard or Bruce but I do read a lot). I think that the GUT (Grand Unified Theory) will be based on number theory (the "purest" branch of mathematics). I always thought it fascinating when the number pi unexpectdly crops up, or when e or phi (golden ratio) pop their heads up. But to see prime numbers arise in areas as fundamental to science as quantum physics is more than amazing, it's beauty!

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