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PYTHAGOREANISM IN EDO From ARAI Hakuseki to SAKUMA Shôzan

PYTHAGOREANISM IN EDO From ARAI Hakuseki to SAKUMA Shôzan. Chikara SASAKI 佐佐木 力. Introduction. Pythagoreanism and the Study of Mathematics in Early Modern Japan.

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PYTHAGOREANISM IN EDO From ARAI Hakuseki to SAKUMA Shôzan

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  1. PYTHAGOREANISM IN EDOFrom ARAI Hakuseki to SAKUMA Shôzan Chikara SASAKI 佐佐木 力

  2. Introduction. Pythagoreanism and the Study of Mathematics in Early Modern Japan • Joseph Needham李約瑟 (1900—1995) (Science and Civilisation in China, vol.1: “Introductory Orientations”，1954)： “ While the Pythagorean School flourished (-600 t0 -300) the Scholars and divines in China were developing the I Ching (Book of Changes) into a universal repository of concepts which included tables of antinomies (Yin and Yang) and cosmic numerology; all this was systematized in the Han.” (p．228)．Mikami Yoshio三上義夫 (1875-1950), “Japanese Mathematics from the Viewpoint of Cultural History ” (1922)．

  3. 1. NEO-CONFUCIANISM AS “TOKUGAWA IDEOLOGY” IN THE 17TH CENTURY AND ARAI HAKUSEK’S POLICY OF MONEY MAKINC • Fujiwara Seika 藤原惺窩 (1561-1619) • Hayashi Razan 林羅山 (1583-1657) • Nakae Nakae 中江藤樹(1608-1648) • Yamazaki Ansai 山畸闇齋 (1619-1682) • Arai Hakuseki 新井白石(1657-1725) • Takebe Katahiro 建部賢弘(1664-1739)

  4. 2. NEO-CONFUCIAN RATIONALISTS MIURA BAIEN AND KAIHO SEIRYô • Miura Baien三浦梅園 (1723-1789) • Kaiho Seiryô 海保青陵 (1755-1817)

  5. 3. THE NEO-CONFUCIANIST WHO CONVERTED TO A WESTERN PYTHAGOREAN: SAKUMA SHôZAN • Sakuma Shôzan 佐久間象山(1811-1864) • Katsu Kaishû勝海舟(1823-1899)

  6. 4. FROM TENZAN ALGEBRA TO WESTERN ARITHMETIC: YANAGAWA SHUNSAN’S YôSAN YôHô OF l857 • Yanagawa Shunsan 柳河春三 (1832-1870) • Arai Hakuseki (1657-1725) = 新井白石『白石建議四』 (1713) A Proposal in 1713:

  7. Small numbers are visible numbers which appear in abacus and which can be known through counting, while large numbers are numbers of which great arithmetic exists between the heaven and the earth even though they cannot be seen in abacus. Hence, those who are familiar with arithmetic can count small numbers, while large numbers can be recognized only by those who understand principles (li) and they are hard to be handled even by those who know the theory of them. For example, although the science of calendrical numbers became exact and pricise in recent years, errors necessarily appear in the long run. (Complete Works, vol. 6, p. 192.)

  8. Kaiho Seiryô (1755-1817) = 海保青陵 『養蘆談』 Doubt things until doubts are entirely solved. To have a doubt is a virtue. The heaven is full of arithmetical uses.

  9. Sakuma Shôzan (18ll-1864) = 佐久間象山『省諐錄』(1854) All learning is cumulative. It is not something that one comes to realize in a morning or an evening. Effective maritime defense is in itself a great field of study. Since no one has yet thoroughly studied its fundamentals, it is not easy to learn rapidly its essential points. […] Mathematics is the basis for all learning. In the Western world after this science was discovered military tactics advanced greatly, far outstripping that of former times. (Collected Works, vol. 1, p. 9.)

  10. Katsu Kaishû 勝海舟 (Nagasaki) to Shôzan on May 6, 1856 Among the disciplines, two astronomers of us understood “stuurkunst” or the art of navigation in mathematical sciences. Naturally, since their mathematics is not ultimately different from ours, those who are good at mathematics quickly understand it. People who not good at mathematics as I feel quite difficult for the disciplines through it. Recently we recognize this thing almost. As we feel difficult about it, we are not happy. What you said about “shôshôjutsu” (“wiskunde”) is quite correct.

  11. Sakuma Shôzan to Kaishû on July 10, 1856: Concerning the method of mathematics, after all, since there is no difference between ours and the Western, it is true that those who are good at our mathematics become quickly familiar with theirs. Nevertheless, problems and their technics in Western countries are all useful, while mathematicians in our country are usually concerned with useless things. Further, as mathematics in our country have been originated in the Chinese method, mathematicians tackle circle problems through squares, based on kôko (句股Pythagorean theorem), when discussing the circle principles of the art of tetsujutsu 綴術. To the contrary, Western trigonometry treats square problems through circles. Confusion scholars in the Qing dynasty such as Dai Dongyuan戴東原, Jiao Xun焦循, and Ruan Yuan阮元 insisted that there is no difference between Chinese Western mathematics. But, I cannot agree with them. In my opinion, whereas Chinese mathematics treats circles through squares, Western mathematics challenges squares through circles. How do you think of this? I would like to ask you, if you have high opinion.

  12. Thanks for your attention!

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