Numerology, or What Pythagoras Wrought, by Underwood Dudley, Mathematical Association of America, Washington DC, 1997

Here’s a book that might go on the New Age shelves by mistake.

Who’d have thought that a book about numerology could be such fun? Woody Dudley makes it so. He looks at Pythagoras’ original speculations about the mystical powers of numbers, gematria (giving letters numerical values), the number of the Beast, triangular and pyramidal numbers and Pyramid Power, biorhythms, and how modern numerology (properly numeromancy) was virtually invented by Mrs L. Dow Balliett (Josephine, later Sarah Joanna, probably changed to improve its number power) of Atlantic City, New Jersey, about a hundred years ago.

Among the diversions are Shakespeare’s numbers, biblical numbers and rithmomachy, a once-popular board-game, like chess but with numbered pieces whose moves and power depend on not only their own numbers but those of the pieces they are attacking and the distance between them. (He gives enough information that you could make a set and play the game, which looks much more difficult than chess, but would be ideal for senior maths students.)

Another is “number forms” the patterns that perhaps one in 30 males and one in 15 females carry in their heads, on which numbers are consistently arranged, throughout their lives. Such people may think nothing of them and assume that everyone has one.

Two of the book’s useful contributions are the Law of Small Numbers and the Law of Round Numbers: there aren’t enough small numbers or round numbers to meet the many demands made of them. So if you go data-mining for small numbers or rounded-off large numbers and then look for correspondences between them, you’ll find some.

I’m sorry to learn that everybody’s favourite number,

1 + 1
1 + 1
1 + …
= 1.618… or phi,

wasn’t used to design the Parthenon or the Great Pyramid, isn’t generally chosen as the most pleasing proportion for rectangles (1.83 is), doesn’t divide our bodies at the navel (men’s are higher), and apparently wasn’t even called the Golden Section until 1835. It’s still a lovely number to play with, but Dudley shows that many of its mysterious properties also derive from the Law of Small Numbers.

He doesn’t mention our own premier number-cruncher (and muncher, and mixer-upperer), Captain Bruce Cathie, and his invention of “Harmonics” (multiply by 10n, where n is any whole number he pleases) and the grid of great circles he devised/discovered by which UFOs are powered and navigated. Perhaps the puddle is bigger and/or the frog smaller than we imagine.

Dudley never mocks the numerologists, but debunks them with charm and grace and sympathy for their (our) human plight of looking for meaning where there may be none.

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