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No. 32: Mar-Apr 1984

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What makes a calculating prodigy?

The above title is also that of a new book by Steven Smith. Naturally, the book is full of anecdotes about the phenomenal accomplishments of calculating prodigies, both unlettered children and such famous scientists and mathematicians as Euler, Gauss, and A.C. Aitken. The latter

"...had the uncanny power of mentally computing, to a long string of decimals, the values of e and e163 When asked (by his children) to multiply 987...1 by 123...9, he remarked afterwards: 'I saw in a flash that 987...1 multiplied by 81 equals 80 000 000 001, and so I multiplied 123...9 by this, a simple matter, and divided the answer by 81.'"

But what, asks Smith, led Aitken to 81? To this question, which is the heart of the mystery, he commendably admits he has no reply. And the same deep mystery confronts us even after all has been said about the sur, as distinct from the underlying, structure of the processing.

At the unlettered end of the spectrum of mental calculators, the

"...ignorant vagabond, Henri Mondeux, who at the age of 14 years, before the French Academy of Sciences, was able promptly to state two squares differing by 133."

Of course, some mental feats of calculation can be done consciously employing various shortcuts and mathematical tricks. The really fantastic performances, however, are accomplished unconsciously. No one knows how, even the calculators themselves.

(Cohen, John; "What Makes a Calculating Prodigy?" New Scientist, 100:819, 1983.)

From Science Frontiers #32, MAR-APR 1984. 1984-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:

Quotes

  • "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