Yoshida Mitsuyoshi

Yoshida Mitsuyoshi ( Japanese 吉田 光 由 ; * 1598 ; † 1672 ), also Yoshida Kōyū (the Sino-Japanese reading of his name), was a Japanese mathematician of the Edo period . He wrote the widespread arithmetic book Jinkōki ( 塵 劫 記 ), which gained great influence both on subsequent authors and on mathematics teaching.

Life

Yoshida was the son of a doctor and came from Saga, a suburb of Kyoto . His relationship to the wealthy Suminokura merchant family enabled him to receive extensive training and gave the mathematically gifted Yoshida access to Chinese mathematics books such as the Sanpō Tōsō ( Chinese  算法 统 宗 , Pinyin Suànfă tŏngzóng ), which he would later fall back on for his own work.

Yoshida reckoned with the Japanese abacus ( Soroban ) .

The economic upswing after the political turmoil of the Azuchi-Momoyama period and the unification of the country under the Tokugawa - shogunate was accompanied by an increased need for mathematical calculations, which were hampered by imperfect process and a complicated monetary system. Constant conversions between the gold currency Edos , the silver currency Kyōtos and Osakas and various copper currencies as well as between the various measures and weights were necessary. The Japanese abacus , the so-called Soroban , became increasingly important as an aid in such calculations . However, introductions to its use and the most important calculation methods were still in short supply.

Yoshida tried to close this gap with his arithmetic book Jinkōki in 1627 - similar to a century earlier European arithmetic masters like Adam Ries . In addition to the mathematical procedures required on a daily basis, it also contained numerous tasks with a mental exercise character, for which Yoshida partly fell back on Chinese models such as the Sanpō Tōsō . He revised his work several times until the end of 1641 and tried to make his own obvious through innovations such as colored illustrations, different colors for positive numbers (red) and negative numbers (black) and finally the “still to be solved problems”, a collection of twelve unsolved tasks to outdo numerous imitators.

After 1641 Yoshida turned to river engineering projects, it is controversial whether he actually wrote a book from 1643 attributed to him. He was relatively certainly involved in two calendar works, the Wakan Hennen Gōunzen from 1645 and the Koreki Binran from 1648. Yoshida Mitsuyoshi died in 1672.

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Representation of binomial coefficients in Jinkōki , 1641

Yoshida's most famous work, the Jinkōki , appeared between 1627 and 1641 in at least six, sometimes quite different, editions. Until the European-oriented school reforms at the beginning of the Meiji period , it was used in the Terakoya schools, among others . The Jinkōki belongs to breitenwirksamsten range of traditional Japanese mathematics (和算, Wasan ), which in contrast to the more scientifically oriented experts mathematics of about Seki school (after Seki Takakazu ) and ritually significant Sangaku -other was intended for domestic use. The numerous drawings it contains, probably designed by the author, also contributed to the practical use of the work. He did without a mathematical notation in the current sense, all tasks are described in words and with a view to the calculation with the help of Soroban.

The current editions of the Jinkōki in detail:

• 1627: Everyday calculations and the areas and volumes of selected bodies are described in four volumes with a total of 26 chapters.
• 1629: In addition to the content of the first edition, five volumes with a total of 48 chapters present calculations with large numbers and some exercises with a game-theoretical character.
• 1631: The three volumes with a total of 48 chapters also contain colored illustrations and colored positive and negative numbers to protect against imitators.
• 1634: This edition consists of four small-format volumes with a total of 48 chapters, but the content differs significantly from the previous and later editions.
• June 1641: In three volumes with a total of 50 chapters, the contents of the previous editions are presented comprehensively and largely self-contained. The first volume contains an introduction to Soroban's arithmetic as well as exercises on rice prices, currency exchange, interest calculation and purchasing goods. The second volume contains tasks that are of particular interest to individual professional groups such as traders, farmers, craftsmen or land overseers, such as calculating the area of ​​rice fields or the grain tax. The third volume consists of tasks suitable to impress math amateurs, such as exponential growth, square and cube roots.
• November 1641: This edition, possibly intended as a supplement to the edition from June of the same year, contains, in addition to further tasks on surfaces and volumes of solid bodies, also the twelve “problems to be solved”.

Yoshida's book was just one of many arithmetic books written in Japan in the first half of the 17th century. However, it evidently gained a great deal of influence both on subsequent authors, whom its author claimed to be imitators and black copiers, as well as on mathematics lessons. A hundred years after Yoshida's death, hardly any book appeared without “problems to be solved”, some of which were up to 200 in number. By 1913, over 300 arithmetic books had been published that had the term Jinkōki in their name. Only with the school reforms of the Meiji period from 1872 and the associated preference for western mathematics (Yosan) did Yoshida lose its importance. He became better known again in the late 1990s through new editions of his work in English and modern Japanese.

expenditure

• Osamu Takenouchi et al. (Ed.): Jinkōki . Wasan Institute, Tokyo 2000 (the English edition contains the June 1641 edition and parts of the November 1641 edition as facsimile and in English translation, extensive notes and explanations; Japanese edition ISBN 4-87639-120-3 ).

literature

• Walther L. Fischer: The Jinko-ki by Mitsuyoshi Yoshida (1627). The most famous Japanese arithmetic book of the Edo period (=  work reports and reprints . No. 2 ). University of Erlangen-Nuremberg, Nuremberg 1996.
• David Eugene Smith , Yoshio Mikami : A History of Japanese Mathematics . Open Court Publishing, Chicago 1914 ( full online version at Internet Archive ).

Web link

Commons : Yoshida Mitsuyoshi  - album with pictures, videos and audio files

Japanese name: As is common in Japan, the family name comes before the first name in this article . So Yoshida is the family name, Mitsuyoshi the first name.

This version was added to the list of articles worth reading on May 2, 2007 .