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.