Mike Beversluis

Thursday, January 26, 2006

And yet Deion Sanders is nowhere mentioned


From this article also known as Prime Time:

Riemann found that certain complex numbers, when plugged into the zeta function, produce the result zero. The few zeros he could calculate lay on a vertical line in the complex plane, and he guessed that, except for a few well-understood cases, all the infinity of zeros should lie exactly on this line.

What does this have to do with the primes? If you plot how many primes exist below a given number (see Diagram above), what you get is a smooth curve with small wiggles added, —that is, the 1/ln(x) rule, plus deviations.

According to Michael Berry of Bristol University, you can think of that pattern of deviations as a wave. Just like a sound wave, it is made up of many frequencies. "And what are the frequencies?" asks Berry. "They're the Riemann zeros. The zeros are harmonies in the music of the primes."

Berry isn't speaking in metaphors. "I've tried to play this music by putting a few thousand primes into my computer," he says "but it's just a horrible cacophony. You'd actually need billions or trillions—someone with a more powerful machine should do it."

There are a few directions I could go here, but behind door number one is the fact that every number theorist I have ever met or known was borderline insane. Furthermore, a few had spent time South of the Border. There is just something about the study whole numbers (and whole numbers only) that self-selects the unbalanced. (Pi springs to mind) The take-home message is that genius is best appreciated from a safe distance.

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