Alex's Adventures in Numberland - Alex Bellos [33]
Pythagoras has a dual and contradictory legacy: his mathematics and his anti-mathematics. Maybe, in fact, as some academics now suggest, the only ideas that can be correctly attributed to him are the mystical ones. Pythagorean esotericism has been a constant presence in Western thought since antiquity, but was especially in vogue during the Renaissance, thanks to the rediscovery of a poem of ‘self-help’ maxims written around the fourth century bc called The Golden Verses of Pythagoras. The Pythagorean Brotherhood was the model for many occult secret societies and influenced the creation of freemasonry, a fraternal organization with elaborate rituals that is believed to have almost half a million members in the UK alone. Pythagoras also inspired the ‘founding mother’ of Western numerology, Mrs L. Dow Balliett, an Atlantic City housewife who wrote the book The Philosophy of Numbers in 1908. ‘Pythagoras said the Heavens and Earth vibrate to the single numbers or digits of numbers,’ she wrote, and she proposed a system of fortune-telling in which each letter of the alphabet corresponded with a number from 1 to 9. By adding up the numbers of the letters in a name, she asserted, personality traits could be divined. I tested this idea on myself. ‘Alex’ is 1 + 3 + 5 + 6 = 15. I completed the process by adding the two digits of the answer, getting 1 + 5 = 6. This gives me a name vibration of six, which means that I ‘should always be dressed with care and precision; be fond of dainty effects and colors, lifting yourcolors of orange, scarlet and heliotrope into their lighter shades, yet always keeping their true tones’. My gems are topaz, diamond, onyx and jasper, while my mineral is borax, and my flowers are tuberose, laurel and chrysanthemum. My odour is japonica.
Numerology, of course, is now an established dish on the buffet of modern mysticism, with no shortage of gurus willing to advise on lottery numbers or speculate on the portent of a prospective date. It sounds like harmless fun – and I enjoyed my conversation with Jerome Carter immensely – yet giving numbers spiritual significance can also have sinister consequences. In 1987, for example, the military government in Burma issued new banknotes with a face value divisible by nine – for the sole reason that nine was the ruling general’s favourite number. The new notes helped precipitate an economic crisis, which led to an uprising on 8 August 1988 – the eighth of the eighth of ’88. (Eight was the anti-dictatorship movement’s favourite number.) The protest was violently put down, however, on 18 September: in the ninth month, on a day divisible by nine.
Pythagoras’s Theorem states that for any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Its words are imprinted in my brain like an old nursery rhyme or Christmas carol; the phrase is nostalgic and comforting independently of its meaning.
The hypotenuse is the side opposite the right angle, and a right angle is a quarter turn. The theorem is the smash hit of basic geometry, the first truly thought-provoking mathematical concept we are taught at school. What I find exciting about it is how it reveals a deep connection between numbers and space. Not all triangles are right-angled, but when they are, the squares of two of the sides must equal the square of the third. Likewise, the theorem holds in the other direction too. Take any three numbers. If the square of two of them equals the square of the third then you can construct