Ramble, Part 11: Paperwait
Jan. 13th, 2007 08:29 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowAt the end of the last Ramble, I raised the question of the reasons for the slowness of the West in adopting Hindu-Arabic numerals. There are three aspects to this that interest me; as usual, they're under the cut.
First, it needs to be noted that, although Hindu-Arabic notation had several advantages over Roman numerals, that was not the key point; the real competition came, not from any other written system, but from the abacus. (There were a couple of other devices for calculation around as well, but the abacus was the big one.) Although the time required to learn the computational algorithms of the abacus is nontrivial, once learned they are considerably faster than those required for Hindu-Arabic numerals. The abacus also matches several of the advantages of Hindu-Arabic numerals; it is positional in nature, and extension is obtained simply by using a larger abacus.
Nonetheless, the abacus had one major disadvantage relative to its new rival, and that is that the intermediate steps in any computation are ephemeral. Here, the error-checking capacities of Hindu-Arabic notation come into play, and this is an advantage (as I said before) in financial recordkeeping. However, to make use of this one needs cheap and plentiful writing material - and this Europe did not have, for a very long time. The Egyptians had papyrus and the Mesopotamians clay, both ready at hand in large quantities, but for centuries the most readily available writing medium in Europe was parchment - treated animal skin. This was inherently more expensive, so much so that it was a common practice to scrape the writing from used parchment so that it could be re-used. (I mentioned this before, in connection with Archimedes' letter to Eratosthenes.) The answer was, of course, paper, which had spread fairly rapidly from its Chinese home across Eurasia, but did not gain a foothold in Europe until sometime in the thirteenth century.
The key figure in the successful introduction of Hindu-Arabic numerals to Europe was one Leonardo of Pisa (1170?-1240?). Leonardo's father was a merchant, working the short North-South route between Italy and North Africa. Leonardo spent a good deal of his youth in Africa, where he observed the Arab merchants using their numerical notation, and became convinced of its superiority. He wrote a book, the Liber abaci, in which he outlined the use of Hindu-Arabic notation and applied it to a variety of problems both practical and speculative, including the computation of interest and currency-changing. The book was popular and widely imitated, and won him an audience with the Emperor Frederick II. The struggle between the traditional "abacists" and the "algorists" of Leonardo's party was not won overnight, but with the publication of the Liber abaci (and the coming of paper) the tide had turned.
Leonardo's role in this is not particularly well-known; he is more famous for one of the problems in his book, and under a different name. The problem dealt with the growth of a population of rabbits, under certain assumptions about their rate of maturation and breeding; the numbers generated by that problem are world-famous. You see, Leonardo's father was named Bonaccio, and thus he was often referred to as "the son of Bonaccio" - in the Pisan dialect, "fi'Bonacci"...
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First, it needs to be noted that, although Hindu-Arabic notation had several advantages over Roman numerals, that was not the key point; the real competition came, not from any other written system, but from the abacus. (There were a couple of other devices for calculation around as well, but the abacus was the big one.) Although the time required to learn the computational algorithms of the abacus is nontrivial, once learned they are considerably faster than those required for Hindu-Arabic numerals. The abacus also matches several of the advantages of Hindu-Arabic numerals; it is positional in nature, and extension is obtained simply by using a larger abacus.
Nonetheless, the abacus had one major disadvantage relative to its new rival, and that is that the intermediate steps in any computation are ephemeral. Here, the error-checking capacities of Hindu-Arabic notation come into play, and this is an advantage (as I said before) in financial recordkeeping. However, to make use of this one needs cheap and plentiful writing material - and this Europe did not have, for a very long time. The Egyptians had papyrus and the Mesopotamians clay, both ready at hand in large quantities, but for centuries the most readily available writing medium in Europe was parchment - treated animal skin. This was inherently more expensive, so much so that it was a common practice to scrape the writing from used parchment so that it could be re-used. (I mentioned this before, in connection with Archimedes' letter to Eratosthenes.) The answer was, of course, paper, which had spread fairly rapidly from its Chinese home across Eurasia, but did not gain a foothold in Europe until sometime in the thirteenth century.
The key figure in the successful introduction of Hindu-Arabic numerals to Europe was one Leonardo of Pisa (1170?-1240?). Leonardo's father was a merchant, working the short North-South route between Italy and North Africa. Leonardo spent a good deal of his youth in Africa, where he observed the Arab merchants using their numerical notation, and became convinced of its superiority. He wrote a book, the Liber abaci, in which he outlined the use of Hindu-Arabic notation and applied it to a variety of problems both practical and speculative, including the computation of interest and currency-changing. The book was popular and widely imitated, and won him an audience with the Emperor Frederick II. The struggle between the traditional "abacists" and the "algorists" of Leonardo's party was not won overnight, but with the publication of the Liber abaci (and the coming of paper) the tide had turned.
Leonardo's role in this is not particularly well-known; he is more famous for one of the problems in his book, and under a different name. The problem dealt with the growth of a population of rabbits, under certain assumptions about their rate of maturation and breeding; the numbers generated by that problem are world-famous. You see, Leonardo's father was named Bonaccio, and thus he was often referred to as "the son of Bonaccio" - in the Pisan dialect, "fi'Bonacci"...
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