12:03 PM

Communal Value Systems and Mathematics

A few months ago I translated and broke down the method of square root extraction in the Japanese mathematical textbook the Jinkouki. One of my supervisors was greatly disappointed in their method, which she described as a 'hack job', because it appears to use guess work at times and the Chinese, whose mathematics the Japanese are known to have read and studied, had much more precise formulaic techniques. The method of the Japanese though, be it somewhat inefficient and messy, does work and obtain correct results. Is it fair that contemporary western mathematicians such as my supervisor look at these old methods with such disgust?

In mathematics, when two methods produce the same results, do we really have a right to say that one is a 'hack job' and inferior to the other? Does the Japanese method only seem inferior because we are coming from the western paradigm, and would it be the case that their method would be superior if we were to consider and adopt the communal value system of Edo Japan? Do westerners really have the right to say that their methods are better and the accurate way to do things, or is it just personal opinion and our own communal value systems that influence us to think this way. My mind is brought back to contemporary debates between constructivists and formalists. Mathematics is able to be pretty well described by both of these, and it seems to be more a matter of personal opinion than transcendental fact as to which is better because both seem to express the same truths in different ways. I wonder if we ought to treat the mathematics of the Japanese with more respect, because it is just a different way of achieving the same results we attain through western mathematics today.

2:32 PM

Why we shouldn't ignore East-Asian mathematical traditions

Well I felt inspired by my friend over at http://phrenicphilosophy.blogspot.com/ to actually put my blog to some use. There is probably some interesting things I can post on here along with some rants.

Those who know me know that I've been learning a bit of Japanese this year, because my Masters thesis is on mathematics in Japan in the Edo period. I've been looking at Korean these past few days also because I'm considering teaching English in South Korea next year. Korean has a very interesting and intuitive alphabet, and after learning Japanese it's much easier to pick up. Their pronunciation is a bit harder though. I find it interesting how different the Korean and Japanese languages are, especially given how many Koreans immigrated to Japan in this early years (the Yayoi people in around 300 BCE for example). I had assumed some of their spoken language would have made its way into Japanese, but from what I gather this doesn't seem so.

I think I'd like to become reasonably proficient in Japanese and Korean so that I can research the mathematical influence the Yayoi had on Japan. I find the mathematics of cultures in Asia so fascinating, and I don't think history of mathematics can be complete until we study it, because if we want to claim that mathematics is universal and cross-cultural we need to actually study the history and philosophy of mathematics of countries like Japan and Korea. I know a fair bit about mathematics in old Japan now, but I have no clue of what went on in Korea other than that they used counting rods which were probably got from China. But did they use Chinese mathematical texts like the Japanese did? I just don't know, and I feel I should know because I'm supposed to be a Historian and Philosopher of Mathematics. I know Koreans do use some Chinese in their language, and the alphabet they use now was only introduced in 1443, so did they use Chinese characters solely before then?

I kinda feel any good historian of mathematics should know about Asian mathematical tradition, but the fact is most historians knowledge is limited to a bit about China. Historians seem to assume that mathematics in Korea and Japan isn't worth studying because "It's all just copied from the Chinese", but my research into Edo mathematics has proved this is most certainly not the case. Japanese mathematics diverged from Chinese and became something unique to Japanese culture during 1600 and 1868, and historians ought to know this. I can only wonder at what amazing stuff there is in the history of Korean mathematics that I don't know about.