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No. 29: Sep-Oct 1993

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Temptations Of Numerology

"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:

  1. The proton-to-electron mass ratio is almost exactly 6pi5 ;
  2. The sum of the masses of the basic octet pio, pi+, k+, k-, ko, k-baro is 3.14006 times the proton mass;
  3. The sum of the masses of the baryon octet is very close to pi2 times the proton mass; and
  4. The reciprocal of the fine structure constant, 137.03604 is close to 4-pi3 +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.)

From Science Frontiers #29, SEP-OCT 1983. 1983-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:


  • "A sourcebook of unexplained phenomena is therefore a valuable addition to a collection of scientific literature. William R. Corliss has provided this in the past with his source books of scientific anomalies in several subjects, and now he has provided it for astronomy. He has done an excellent job of collecting and editing a large amount of material, taken in part from scientific journals and in part from scientific reporting in the popular or semi-scientific press." -- "The Mysterious Universe: A Handbook of Astronomical Anomalies", reviwed by Thomas Gold, Cornell University, in Icarus, vol.41, 1980

  • "An interesting, systematic presentation of unusual weather [..] This book is recommended for a general audience" --"Corliss, William R., Tornados, Dark Days, Anomalous Precipitation, and Related Weather Phenomena, Sourcebook Project, 1983.", revieweed in Choice, September 1983
  • "..the science is necessarily somewhat speculative, but Corliss's symthesis is based on reputable sources." -- "Corliss, William R. (Compiler). Lightning, Auroras, Nocturnal Lights, and Related Luminous Phenomena" reviwed by Joseph M. Moran, Univ. of Wisconsin in Science Books and Films, Sep/Oct 1983

  • "Before opening the book, I set certain standards that a volume which treads into dangerous grounds grounds like this must meet. The author scrupulously met, or even exceeded those standards. Each phenomenon is exhaustively documented, with references to scientific journals [..] and extensive quotations" -- "Book Review: The moon and planets: a catalog of astronomical anomalies", The Sourcebook Project, 1985., Corliss, W. R., Journal of the Royal Astronomical Society of Canada, Vol. 81, no. 1 (1987), p. 24., 02/1987