Pre-European Japanese Math [and some Chinese math]
Eugene N. Miya
Stanford Math-CS library. I promised David Gast [UCLA] to get back to him.
After months of a hectic schedule, I had some chance to look for a few
pieces of reference material.
The topic came out of a discussion on E-W thinking, recent programs
on science history in both Japan and China. In the US one might be fortunate
to learn about the Roman numeral systems and I was also lucky to have
studied Babylonian arithmetic [base-60, etc.] It is much harder to
find contributions from the East. I was aware of Chinese solution of the
Pythagorian theorem, and one friend who is a Math prof at Stanford also
noted a Chinese version of Pascal's triangle.
Basically, I found a few entries in D.E. Smith's History of Mathematics.
Which noted the rise of algebra, geometry, and calculus in China (and later
migrating to Japan [I'll not bore you with details of who and how] following
similar developments in Europe and N Africa where algebra was developed.
Smith and other texts show the Japanese developed integral calculus
"yenri" [circle principle] (derived from the Chinese Li Yeh and
Tse-yua Hai-chang [from Smith]) using a Greek "Method of Exhaustion"
to find the area inside a circle. Various other formulae were shown
to be derived: circumfurance, methods of calculating pi, and other geomtric
relations, many of which were derived after European communications, a
few before.
Smith noted that 16th century Japanese math was very similar in awaken
to 13th century European math. China similarly had periods of a lack of
communications (noting China killed Jesuit priests teaching "the new math").
By the 1800s, the old Japanese math system "wasan" had largely been replaced.
I'm trying to locate references to wasan. I'm just curious for things
most mathematicians are interested in: number system base, symbology,
etc. I read they developed a thing for a short time called "tenzan algebra"
at the Seki school, but read nothing more than that.
As far as China goes, an excellent book entitled Chinese Mathematics:
A Concise History by Li Yan and Du Shiran published by Clarendon Press
(Oxford) is available 1987. It shows early Chinese math to be based
on a tally system similar in some ways to Roman and existing tally systems
(base five and 10) with a slightly different role for horizontal
bars or slashes like in existing tallies. By the 1800s the Chinese
mathematicians were using European operators ('=', '+", etc.) and 'x,' 'y,'
etc. Most historical reference is to the development of tools like the
Abacus (overshaowing lots of other stuff), dividers (from Europe for
geometry), and even simple computing engines.
I'll keep searching for wasan references as the number theory holds
some interest. The some of the more abstract reasoning is also of interest,
but the "300 year difference" probably kept math very practical like
Egypt. Development of arithmetic and multiplicative identities might be
interesting. I doubt they developed anything like hyperbolic or
spherical geometry. Some influence into astronomy was noted.
I probably won't post because it took months before I had time to even
research this. Seems somewhat interesting that two vartly different cultures
developed a base-10/5 number system when a society in between physically
develops a base-60 system.
Follow-ups to soc.culture.japan and discussion email to me as "who has
time to read s.c.j. anymore. I don't." I don't think these references are
specific enough to place in the FAQ.
--eugene miya, NASA Ames Research Center, eug...@orville.nas.nasa.gov
Resident Cynic, Rock of Ages Home for Retired Hackers
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