History of Numbers
Date: 09/04/97 at 20:54:16 From: Lesa Subject: History Of Numbers My Algebra 2 teacher asked us to do a report on the history of numbers. What was the first number? Who discovered it/invented it? When and where? Please help.
Date: 09/15/97 at 10:52:41 From: Doctor Guy Subject: Re: History Of Numbers This is actually a fascinating question, which recently has been answered. Most older books on the history of math and numbers say that at some point (they are vague on when) somebody made a connection between the number of fingers on a hand and the number of cows or sheep, and figured out the concept of "number." See Boyer & Merzbach, "A History of Mathematics" (Wiley & Sons, 1968, 1989, 1989) for example, or O. Neugebauer, "The Exact Sciences in Antiquity." But in the past ten years or so, truly marvelous results have been obtained by one Denise Schmandt-Bessarat, doing research into interesting "tokens" found all over the Middle East. Her book, which is not too hard to understand, is called "Before Writing." She also published at least one article in Scientific American magazine. The gist of what she said is that mathematics (or numbers and the writing thereof) came before writing itself. In the Fertile Crescent of southwest Asia, where farming may have developed first, people had surpluses of wheat, or barley, or beans, or wine, or oil, or beer, or various other things like that. Containers of them would be stored in central locations (whether voluntarily or not, I cannot tell), or else someone would owe someone else some of these (or live cows, chickens, goats, sheep, etc.), and records were made. The form that these records took is most curious: people would make little "tokens" out of clay and then fire the tokens in hot fires so that they would not fall apart, exactly as people today make pottery and "fire" it in kilns. In fact, Schmandt-Bessarat claims these tokens were the very first clay objects to be intentionally fired! If I gave you two baskets of wheat to keep for me, then you would give me two tokens that stood for the two baskets. Remember, though, numbers per se hadn't been invented yet. Each style and shape of token stood for a different type of item. In order that these tokens would not disappear, various things were tried; sometimes they were tied to strings, but that didn't work well. Eventually they were put into clay "envelopes" and stored; some of these envelopes were found. The only problem was, once you put something in a clay envelope, you couldn't see what was inside unless you broke the "envelopes," which would have people's "seals" embedded in them to prevent fraud. After a few thousand years, someone got the bright idea that before you put the tokens inside the clay envelope, you should press each one into the wet clay of the envelope. Then people could tell exactly what the contents were inside. Then someone else got another bright idea: instead of pressing 9 tokens for "sheep" and 8 tokens for "bottles of oil" on the outside, and so on, which could get pretty crowded, they invented a shorthand: press "sheep" one time, then 9 little marks; one "oil" and 8 little marks. This was a big step! Later, they invented some shortcuts for the numbers. Then a few thousand years later, someone else got an even brighter idea: why put the tokens inside the envelope at all? We have everything we need on the outside of the envelope! Thus, the Mesopotamians invented cuneiform writing on slabs of wet clay, meaning that they took reeds (like from bamboo) and pushed the ends of the bamboo sticks carefully into the clay to mean different things, including numbers. According to this same author, Egyptian writing and numerals were invented a bit later, all at once, as a conscious decision of some committee, rather than "growing" naturally as cuneiform did. Clearly the Maya developed mathematics and writing completely on their own; nobody from Europe or Asia influenced them in the slightest. I highly recommend her book. It has lots of pictures. -Doctor Guy, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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