Thursday, July 05, 2007

On al-Khwarizmi and the diffusion of ideas

In the last few years, I’ve been fascinated by how ideas that originate in one place diffuse and reach other cultures, and how these receiving cultures shape them in their own distinctive ways. Recently, I found these paragraphs that explain how the numbers we use today – commonly called Arabic numerals – and take for granted made their way in the 8th century from India to the brilliant mathematician Musa al-Khwarizmi, originally an Uzbek but resident at the time in Baghdad. It was through Musa al-Khwarizmi’s treatise On the Calculation of Hindu Numerals that the Europeans got to know of this system of representing numbers (which is why they called it Arabic numerals). Because of its advantages over the cumbersome, alphabetic Roman numeral system, Italian merchants like Fibonacci preferred it:
“Traditional systems had used different letters of the alphabet to represent numbers or cumbersome Roman numerals, and the new system was far superior, for it allowed people to multiply and divide easily and check their work. The merchant Leonardo Fibonacci of Pisa, who had learned about Arabic numerals in Tunis, wrote a treatise rejecting the abacus in favor of the Arab method of reckoning, and as a result, the system of Hindu-Arabic numeration caught on quickly in Central Italy. By the fourteenth century, Italian merchants and bankers had abandoned the abacus and were doing their calculations using pen and paper, in much the same way we do today.”
Musa al-Khwarizmi also pioneered the field of algebra (root al-jabr). The paragraph below explains, how the alphabet x came to represent the unknown in all of mathematics:
“Al-Khwarizmi had used the Arabic word for "thing" (shay) to refer to the quantity sought, the unknown. When al-Khwarizmi's work was translated in Spain, the Arabic word shay was transcribed as xay, since the letter x was pronounced as sh in Spain. In time this word was abbreviated as x, the universal algebraic symbol for the unknown.”
And here’s how word ‘algorithm’ came into being:
Robert of Chester's translation of al-Khwarzmi's treatise on algebra opens with the words dixit Algorithmi, "Algorithmi says." In time, the mathematician's epithet of his Central Asian origin, al-Khwarizmi, came in the West to denote first the new process of reckoning with Hindu-Arabic numerals, algorithmus, and then the entire step-by-step process of solving mathematical problems, algorithm.”
The picture above of Musa al-Khwarzmi is from this Wikipedia website, and, interestingly, is a commemorative stamp issued by the Soviet Union in 1983.

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