No. 111: May-Jun 1997
Where? "Everywhere, of course," is the answer of any anomalist worth his or her salt. Especially, though, something strange in going on with prime numbers.
In an homage to the revered mathematician P. Erdos, who died September 20, 1996, D. Mackenzie mentioned a theory Erdos published in 1940 with M. Kac. This theory states that a plot of the number of prime factors of very large numbers forms a bell curve -- almost as if these numbers were "choosing" their prime factors at random. Alluding to a assertion Einstein is said to have made, Erdos commented:
"God may not play dice with the universe, but something strange is going on with the prime numbers."
(Mackenzie, Dana; "Homage to an Itinerant Master," Science, 275:759, 1997.)
Cross reference. The distribution of prime numbers is more than strange, see the plot in SF#42/332.
What do prime numbers have to do with the real world? Are math and natural science really separate, unlinked disciplines?
Pythagoras, 2,500 years ago, decided that: "All is number." He may be right. A strange connection seems to exist between prime numbers and quantum physics. On one side of the chasm that supposedly separates math from physics, we have the prime numbers and the Riemann zeta function, which provides information on how prime numbers are distributed among the other integers. On the "physics" side of the chasm, we have the behavior of complex atomic systems. The chasm seems bridged when one compares the energy levels of an excited heavy nucleus with the distribution of the zeros of the zeta function. Why should this correspondence exist? B. Cipra exclaimed:
"Just why number theory and quantum chaos should be soul mates is a mystery for the gods to unveil."
(Cipra, Barry; "Prime Formula Weds Number Theory and Quantum Physics," Science, 274:2104, 1996.)
Comment. God, well known to be a geometer, evidently also dabbled in prime numbers!