How did East Asians do math before the adoption of arabic numerals, which are universally used today?
October 14, 2004 7:16 PM Subscribe
How did East Asians do math before the adoption of arabic numerals, which are universally used today? Were there a variety of local systems? When did the switchovers happen? [more inside]
Here in Korea, language is written down in the the Korean alphabet, hangeul (with some Chinese-derived hanja mixed in), and Japan and China and countries in South East Asia have their own scripts, of course. But what about numbers? We know from history that Europe adopted arabic numerals to do math, and approximately when, but when did Asia start using them, and what was used before that? Here in Korea, you occasionally see (usually on bar tabs, to count the number of beers, in my experience, not surprisingly perhaps) a way of writing down numbers that resembles a more complicated version of our own 4 uprights and a diagonal to denote groups of five, but that certainly wouldn't be enough to do any real math.
Any math historians out there?
Here in Korea, language is written down in the the Korean alphabet, hangeul (with some Chinese-derived hanja mixed in), and Japan and China and countries in South East Asia have their own scripts, of course. But what about numbers? We know from history that Europe adopted arabic numerals to do math, and approximately when, but when did Asia start using them, and what was used before that? Here in Korea, you occasionally see (usually on bar tabs, to count the number of beers, in my experience, not surprisingly perhaps) a way of writing down numbers that resembles a more complicated version of our own 4 uprights and a diagonal to denote groups of five, but that certainly wouldn't be enough to do any real math.
Any math historians out there?
Not sure what you're looking for but China was doing positional notation at 400 BCE or earlier. They didnt have the algebraic numbers we have today but that didnt hinder anything since they have their own numbers.
Thats certainly enough to do "real math" but there's something else: When we think of mathematics today we think algebra but not too long ago, mathematics meant geometry. You can demonstrate and derive all sorts of complex propositions using geometric arguments. In fact, Newton's Principia, containing his discoveries about the gravitational force, is a book of proofs by geometry.
posted by vacapinta at 8:19 PM on October 14, 2004
Thats certainly enough to do "real math" but there's something else: When we think of mathematics today we think algebra but not too long ago, mathematics meant geometry. You can demonstrate and derive all sorts of complex propositions using geometric arguments. In fact, Newton's Principia, containing his discoveries about the gravitational force, is a book of proofs by geometry.
posted by vacapinta at 8:19 PM on October 14, 2004
This article basically answers your questions. The Chinese had a rod system that worked on the same principle as ours. Their problem was they had to write out the rod positions in a very detailed manner to record their work. They still were basically able to do the same calculations as the Hindu-Arabic methods allowed, it was just laborious to keep doing it their old way. And everyone else uses the Hindu-Arabic method so I'm sure that was a heavy influence. Correct me if my reading comprehension was off, I am not a math person.
posted by geoff. at 9:40 PM on October 14, 2004
posted by geoff. at 9:40 PM on October 14, 2004
But if you're looking for a date, I bet they were using the Arabic system by at the very latest the Opium Wars. At that point they were so intertwined with the Western world they must have been aware of Western numbering (from accounting for trade) it would have been foolish not to adopot it.
It could have come much earlier but I would just be totally guessing at that point.
posted by geoff. at 9:43 PM on October 14, 2004
It could have come much earlier but I would just be totally guessing at that point.
posted by geoff. at 9:43 PM on October 14, 2004
Anyone interested in this subject should get hold of a copy of The Universal History of Numbers by Georges Ifrah. It's exhaustive to the point of clearly being the product of a near obsessive. My copy is at home, however, so I can't help with the question immediately.
vacapinta - I was under the, possibly mistaken, impression that Newton originally used calculus to derive the proofs in Principia then re-cast them in rather tortuous geometrical terms. He did this because he was unconvinced that the philosophical foundation of calculus (specifically, the use of infinitely small entities, without a good definition of what exactly infinitely small means) was shaky and would cast doubt on his conclusions.
posted by thatwhichfalls at 10:41 PM on October 14, 2004
vacapinta - I was under the, possibly mistaken, impression that Newton originally used calculus to derive the proofs in Principia then re-cast them in rather tortuous geometrical terms. He did this because he was unconvinced that the philosophical foundation of calculus (specifically, the use of infinitely small entities, without a good definition of what exactly infinitely small means) was shaky and would cast doubt on his conclusions.
posted by thatwhichfalls at 10:41 PM on October 14, 2004
Response by poster: I think you missed my point, kinda, vacapinta. I was asking more about the language of numbers, if that makes sense, than about doing mathematics per se. My undergraduate degree was in mathematics, so I understand what you were getting at, though. Thanks for the links.
I wonder if Japan and Korea, or Thailand and Cambodia (or...) simply piggybacked on the Chinese system or not. I note that there is a special unit in Korean for 10,000 as there is in Chinese, and that Korean uses number words both indigenous and Chinese in different situations (ie in English 'one, two, three' can be either 'hana, dul, set' or 'il, ee, sam') when speaking (although they're written 1, 2, 3 in both cases).
The part that interests me is when and how these started being written with arabic numerals, and what was used before.
If I understand correctly, vacapinta's link tells us how the numbers were spoken (?) (which was not what I was looking for), but geoff.'s link does indeed show us how the numbers were written.
Anyone? Thanks for the answers, but I'm maybe even more at sea than I was!
posted by stavrosthewonderchicken at 10:43 PM on October 14, 2004
I wonder if Japan and Korea, or Thailand and Cambodia (or...) simply piggybacked on the Chinese system or not. I note that there is a special unit in Korean for 10,000 as there is in Chinese, and that Korean uses number words both indigenous and Chinese in different situations (ie in English 'one, two, three' can be either 'hana, dul, set' or 'il, ee, sam') when speaking (although they're written 1, 2, 3 in both cases).
The part that interests me is when and how these started being written with arabic numerals, and what was used before.
If I understand correctly, vacapinta's link tells us how the numbers were spoken (?) (which was not what I was looking for), but geoff.'s link does indeed show us how the numbers were written.
Anyone? Thanks for the answers, but I'm maybe even more at sea than I was!
posted by stavrosthewonderchicken at 10:43 PM on October 14, 2004
Aryabhatta, an Indian scientist and astronomer "invented" the zero. Sorry I can't remember where I read it, but the Indians were using logarithms around the time Rome was being built, if not earlier. Our digits look slightly different from Arabic digits, but I believe that the similarities between the two might be because of the short distance between the two regions.
posted by riffola at 10:45 PM on October 14, 2004
posted by riffola at 10:45 PM on October 14, 2004
I should add that I know India doesn't qualify as East Asia, but I just wanted to add that to sort of show what was happening in the subcontinent.
posted by riffola at 10:49 PM on October 14, 2004
posted by riffola at 10:49 PM on October 14, 2004
Response by poster: Any glyph system should work. As long as they can work out a null value like zero, which doubles as a placeholder. Like someone wrote above, a lot of math is derived straight from geometry. What base you are using is important too I guess. Base-10 seems to be popular.
Not to be overly ungracious, but have I expressed myself so badly in my question and subsequent elaborations that you think this might actually be an answer to my question?
posted by stavrosthewonderchicken at 4:26 AM on October 15, 2004
Not to be overly ungracious, but have I expressed myself so badly in my question and subsequent elaborations that you think this might actually be an answer to my question?
posted by stavrosthewonderchicken at 4:26 AM on October 15, 2004
Response by poster: I'm sorry for that last comment, because I have realized that my original question was actually a piece of shit, a question that vacapinta tried to answer as did skallas, valiantly, but which actually wasn't actually the question that I wanted to ask.
What I meant to ask was 'how did they write down the numbers?', which is well preliminary to asking 'how did they do teh mattth, urrrr?' and considerably simpler.
I am an idiot, it seems.
Still, if anyone has any ideas, I'd like to hear 'em. Even though I'm an idiot amd everything.
posted by stavrosthewonderchicken at 5:08 AM on October 15, 2004
What I meant to ask was 'how did they write down the numbers?', which is well preliminary to asking 'how did they do teh mattth, urrrr?' and considerably simpler.
I am an idiot, it seems.
Still, if anyone has any ideas, I'd like to hear 'em. Even though I'm an idiot amd everything.
posted by stavrosthewonderchicken at 5:08 AM on October 15, 2004
Hi Stav, at the risk of misunderstanding your question as well let me add the following. The Chinese always used a base 10 counting system but they wrote out the numbers using rods and bars (as indicated by geoff's very interesting link).
The system was a place-value system but it lacked a zero which meant it could sometimes be ambiguous (e.g. 60000 looked like 6). The zero did eventually arrive from India in the eighth century (probably in the pack of some Buddhist pilgrim) and was represented by a circle. I'm not certain when the Chinese adopted the Western number shapes, I would presume around the time of the first Portuguese missions when the Jesuits became very influential in the court.
The Thais, incidentally, use a related counting system to the Chinese (neung=yi, song=er, sam=san, si=si etc.) but learnt to write their numbers from the Cambodians who use an Eastern derivative of Indian numerals.
posted by lagado at 6:09 AM on October 15, 2004
The system was a place-value system but it lacked a zero which meant it could sometimes be ambiguous (e.g. 60000 looked like 6). The zero did eventually arrive from India in the eighth century (probably in the pack of some Buddhist pilgrim) and was represented by a circle. I'm not certain when the Chinese adopted the Western number shapes, I would presume around the time of the first Portuguese missions when the Jesuits became very influential in the court.
The Thais, incidentally, use a related counting system to the Chinese (neung=yi, song=er, sam=san, si=si etc.) but learnt to write their numbers from the Cambodians who use an Eastern derivative of Indian numerals.
posted by lagado at 6:09 AM on October 15, 2004
I can address Japanese numbering, at least a little. Japan had no writing system before the introduction of Chinese. I have no idea if they had any sort of simple numbering system before that for keeping books, but when they were exposed to Chinese, they adopted the Chinese writing system as a whole, and that included all the kanji/hanja/hanzi used for numbers (which is base-ten, but bundles large numbers by the 10,000 rather than the 1,000). It was only later that the Japanese adapted the Chinese writing system for actually expressing the Japanese language itself.
While there were (and are) indigenous words ("yamato-kotoba") for numbers before that, these have been supplanted to some extent by Chinese-derived words, though it's pretty much a mishmash, with indigenous number words used in some contexts, Sinofied number words used in others, and weird exceptions here and there--Sinofied numbers are used for the days of the month except for the 1st through 10th and the 20th.
Incidentally, the Japanese use the five-stroke character for "correct" as an equivalent to the western four bars and a slash. You see this on bar tabs all the time.
posted by adamrice at 8:03 AM on October 15, 2004
While there were (and are) indigenous words ("yamato-kotoba") for numbers before that, these have been supplanted to some extent by Chinese-derived words, though it's pretty much a mishmash, with indigenous number words used in some contexts, Sinofied number words used in others, and weird exceptions here and there--Sinofied numbers are used for the days of the month except for the 1st through 10th and the 20th.
Incidentally, the Japanese use the five-stroke character for "correct" as an equivalent to the western four bars and a slash. You see this on bar tabs all the time.
posted by adamrice at 8:03 AM on October 15, 2004
Read the book thatwhichfalls recommends -- when I had to read that book for a publicity campaign, I went briefly insane, but I vaguely remember something about the number systems of around the world. It'd explain everything.
posted by Katemonkey at 1:55 PM on October 15, 2004
posted by Katemonkey at 1:55 PM on October 15, 2004
Response by poster: Well, I was kinda hoping for an answer that didn't involve 'read this book' because for various reasons, I can't really do books here unless they're soft copy. Thanks for the answers though...
posted by stavrosthewonderchicken at 7:17 PM on October 15, 2004
posted by stavrosthewonderchicken at 7:17 PM on October 15, 2004
Maybe the links from the Wikipedia article on numeral systems might help?
(two traditional Chinese systems, Japanese, Thai).
The first article also mentions a Chinese system for armies and provisions which used prime numbers, maybe in a similar way to Godel numbers.
posted by plep at 8:31 AM on October 17, 2004
(two traditional Chinese systems, Japanese, Thai).
The first article also mentions a Chinese system for armies and provisions which used prime numbers, maybe in a similar way to Godel numbers.
posted by plep at 8:31 AM on October 17, 2004
This thread is closed to new comments.
posted by jdroth at 7:40 PM on October 14, 2004