The idle ramblings of a Jack of some trades, Master of none

Jun 3, 2011


In 1236, Walter (Gautier) of Coincy wrote a vernacular poem for a largely non-literate audience. In it, he used the expression 'ciffres en augorisme' to mean a vacuous person. In other words, a zero. Clearly, if even an unlearned audience was meant to understand the reference, the cipher, or the Hindu-Arabic numeral, was already well-established in Europe.

Scientific, as opposed to mathematical, knowledge had already started flowing westwards in the preceding century. "After 1100, Euclid’s Elements gained increased prominence; in 1126 Adelard of Bath brought Al-Khwarizmi’s trigonometry to the West; in 1145 Robert of Chester translated Al-Khwarizmi’s Algebra; Ptolemy’s Almagest was translated from the Greek in 1160." [1]

How did the Europeans gain access to the concept of zero? As widely documented, the good news came from the East, via the Arabs.

I have read previously that Leonardo da Pisa (or Fibonacci)'s learned work Liber Abaci of 1202 was the main mechanism of transmission. Fibonacci had travelled extensively in North Africa training to become a merchant, had come in contact with Arabs there, and learned their sciences and mathematics.

Sefer ha-Mispar of Rabbi ben Ezra
As evidenced by Fibonacci, the main impetus to arithmetic appears to have been mercantile. The widespread use of the abacus had already introduced the notion of 'place value' to the Europeans, but they persisted in using Roman numerals in their documentation. Indeed, even innovators in business such as the English Exchequer and the Medici Bank decried the use of the new-fangled numerals. The Florentine guild of bankers required its members to “write openly and at length, using letters” — the fact that the ordinance had to be repeated three more times meant that by 1299, bankers in Florence had found it faster and more convenient to use the Hindu-Arabic numerals rather than write “at length” in the old script." [2]

I learn now, though, that an even earlier book had introduced the concept of zero to the Europeans.[3] The Spanish rabbi Abraham ben Ezra wrote about the Hindu-Arabic numerals in his book Sefer ha-Mispar (Book of Number) while visiting Verona in 1146. He used the first 9 letters of the Hebrew alphabet to represent the numbers 1 to 9, and made a small circle that he called galgal (Hebrew for 'wheel') for zero. (The Arabs used a dot.)

The Jews, of course, already had large trade networks across the Mediterranean and the Levant and deep into the Muslim lands. Their affinity for new ideas and business acumen meant that they had a long-standing advantage over their Gentile competitors. Indeed, as we have seen, the Christians were not loath to shoot themselves in the foot with proscriptions against new (or heathen) techniques.

It was not till the 15th century that the Church relented and allowed the use of the numerals. And they had the temerity all along to accuse of Jews of taking advantage of Christians and making money off the honest faithful. All I have to say is - pillocks.


1. Stephen E. Sachs, New Math: The‘Countinghouse Theory’and the Medieval Revival of Arithmetic (here)
2. Alexander Murray, Reason and Society in the Middle Ages (Oxford: Clarendon Press, 1978)
3. Paul Kriwaczek, Yiddish Civilisation: the Rise and Fall of a Forgotten Nation (London: Weidenfeld and Nicolson, 2005)


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