Fjordman will begin a small series of essays next week with a focus on mathematics and mathematical astronomy. Below are some excerpts from his brief introductory post at the Brussels Journal:
I heard the claim from one European reader that “The Arab world invented the zero, and it’s been downhill ever since.” This is false, but unfortunately not an uncommon mistake. Our numeral system dates back to India during the post-Roman era, but it came to Europe via the medieval Middle East which is why these numbers are called “Arabic” numbers in many European languages. Yet even Muslims admit that they imported these numerals from India. Calling them “Arabic” numerals is this therefore deeply misleading. “Hindu-Arabic” number system could be accepted, but the preferred term should be “Indian numerals.”
The question nevertheless remains why Indians dropped their own multiplicative system and introduced the place-value system, including a symbol for zero. We currently don’t know for sure. Victor J. Katz elaborates in his fine A History of Mathematic, Second Edition:
“It has been suggested, however, that the true origins of the system in India may be found in the Chinese counting board. Counting boards were portable. Certainly, Chinese traders who visited India brought them along. In fact, since southeast Asia is the border between Hindu culture and Chinese influence, it may well have been the area in which the interchange took place. Perhaps what happened was that the Indians were impressed with the idea of using only nine symbols, but they took for their symbols the ones they had already been using. They then improved the Chinese system of counting rods by using exactly the same symbols for each place value rather than alternating two types of symbols in the various places. And because they needed to be able to write numbers in some form, rather than just have them on the counting board, they were forced to use a symbol, the dot and later the circle, to represent the blank column of the counting board. If this theory is correct, it is somewhat ironic that Indian scientists then returned the favor and brought this new system back to China early in the eighth century.”
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Some Sanskrit works were introduced to Europe via Arabic translations. One Latin manuscript begins with the words “Dixit Algorismi,” or “al-Khwarizmi says.” The word “algorismi,” through some misunderstandings became a term referring to various arithmetic operations and the source of the word algorithm. “Zero” derives from sifr, Latinized into “zephirum.” The word sifr itself was an Arabic translation of Sanskrit sunya, meaning “empty.” The English word “sine” comes from a series of mistranslations of the Sanskrit jya-ardha (chord-half). Aryabhata frequently abbreviated this term to jya or jiva. When some Hindu works were translated into Arabic, this word was transcribed phonetically into jiba. But since Arabic is a consonantal alphabet usually written without added short vowels, later writers interpreted the consonants jb as jaib, which means bosom or breast. When an Arabic work of trigonometry was translated into Latin, the translator used the equivalent Latin word sinus, which also meant bosom. This Latin word has become our modern English “sine.”
Leonardo of Pisa (ca. 1170-1240), often known as Fibonacci (son of Bonaccio), was an Italian and the first great Western mathematician after the decline of ancient Greek science. The son of a merchant from the city of Pisa with contacts in North Africa, Leonardo himself travelled much in the region. He is most famous for his masterpiece the Liber abbaci or Book of Calculation. The word abbaci (from abacus) does not refer to a computing device but to calculation in general. The first edition appeared in 1202, and a revised one was published in 1228. This work enjoyed a wide European readership and contained rules for computing with the new Indian numerals. The examples were often inspired by examples from Arabic-language treatises, but filtered through Leonardo’s creative and original genius. Indian numerals faced powerful opposition for generations but were gradually adopted during the Renaissance period, especially by Italian merchants. Their practical advantages compared to the more cumbersome Roman numerals were simply too great to ignore, although Roman numerals are still used for certain limited purposes in the West in the twenty-first century.
Read the rest at the Brussels Journal.