"Too much innocent energy is being spent on the search for numerical coincidences with physical quantities. Would that this Pythagorean energy were spent more profitably."

Following this admonition, John Maddox conceded that numerology, on rare occasions, has provided useful insights. Musings about Bode's Law are not complete wastes of time; and Prout's hypothesis that the masses of the elements would be found to be integral multiples of the mass of the hydrogen atom was not far off the mark.

Certainly an entertainment factor exists, too, for Maddox cannot resist printing a curious little contribution by Peter Stanbury, entitled "The Alleged Ubiquity of pi." Stanbury has discovered a large number of relations between the masses of the fundamental particles that are closely related to pi. Four representative examples follow:

The proton-to-electron mass ratio is almost exactly 6pi^{5} ;

The sum of the masses of the basic octet pi^{o}, pi^{+}, k^{+}, k^{-}, k^{o}, k-bar^{o} is 3.14006 times the proton mass;

The sum of the masses of the baryon octet is very close to pi^{2} times the proton mass; and

The reciprocal of the fine structure constant, 137.03604 is close to 4-pi^{3} +pi ^{2} + pi , or 137.03630.

There are many more such relationships. Further, the ratios 1.0345 and 1.1115 keep popping up more frequently than coincidence would seem to allow. What could these ratios be? At least pi has geometrical significance.

(Maddox, John; "The Temptations of Numerology," Nature, 304:11, 1983.)