Alex's Adventures in Numberland - Alex Bellos [67]
When Akira Haraguchi recited 100,000 digits of pi by heart, he used a mnemonic technique, assigning syllables to each number from 0 to 9 and then translating pi’s decimals into words, which in turn formed sentences. The first fifteen digits sounded like: ‘the wife and children have gone abroad; the husband is not scared.’ Using words to remember the digits in pi this way is used by schoolchildren in cultures all over the world, but usually this is done not by assigning syllables, but by creating a phrase in which the number of letters in each word represents each consecutive digit in the decimal expansion of pi. A well-known English one is credited to the astrophysicist Sir James Jeans: How I need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard. ‘How’ has 3 letters, ‘I’ has 1, ‘need’ has 4, and so on.
Among numbers, only pi has inspired this type of fandom. No one wants to memorize the square root of two, which is just as challenging. Pi is also the only number to have inspired its own literary subgenre. Constrained writing is a technique in which some condition is adopted that imposes a pattern or forbids certain things in the text. Entire poems – or ‘piems’ – have been written under the constraint that the number of letters per word is determined by pi, usually with the convention that a 0 in the expansion requires a ten-letter word. The most ambitious piem is the Cadaeic Cadenza by Mike Keith, which follows pi for 3835 digits. It begins as a pastiche of Edgar Allan Poe:
One; A poem
A Raven
Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap – the weirdest tap!
An ominous vibrating sound disturbing my chamber’s antedoor. ‘This,’ I whispered quietly, ‘I ignore.’
Keith says that writing with a difficult constraint is an exercise both in discipline and discovery. Since the digits in pi are random, the constraint is, he said, ‘like bringing order out of chaos’. When I asked him ‘Why pi?’ he replied that pi was ‘a metaphor for all things infinite, or inscrutable, or unpredictable, or full of endless wonder’.
Pi has gone by this name only since 1706, when the Welshman William Jones introduced the symbol p in his book, the snappily titled A New Introduction to the Mathematics, for the Use of some Friends who have neither Leisure, Convenience, nor, perhaps, Patience, to search into so many different Authors, and turn over so many tedious Volumes, as is unavoidably required to make but tolerable progress in the Mathematics. The Greek letter, which was probably an abbreviation for the word periphery, did not immediately catch on, howeve, becoming standard notation for pi only 30 years later when Leonhard Euler adopted it.
Euler was the most prolific mathematician of all time (he published 886 books), and he is possibly the one who contributed most to an understanding of pi. It was his improved formulae for pi that enabled the eighteenth-and nineteenth-century digit-hunters to peel back more and more decimal places. In the beginning of the twentieth century the Indian mathematician Srinivasa Ramanujan devised many more Euler-style infinite series for pi.
Ramanujan was a largely self-taught mathematician who worked as a clerk in Madras before writing a letter to Cambridge university professor G.H. Hardy. Hardy was flabbergasted to see that Ramanujan had rediscovered results that had taken centuries to achieve, and invited him to England, where the men collaborated before Ramanujan died aged 32. His work showed an extraordinary intuition about the properties of numbers, including pi, and his most famous formula is the following: