The History of Mathematics: A Brief Course

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  1. JAPAN 51


2.1. Chinese influence and calculating devices. All the surviving Japanese

records date from the time after Japan had adopted the Chinese writing system.

Japanese mathematicians were for a time content to read the Chinese classics. In

701 the emperor Monbu established a university system in which the mathematical

part of the curriculum consisted of 10 Chinese classics. Some of these are no longer

known, but the Zhou Bi Suan Jing, Sun Zi Suan Jing, Jiu Zhang Suanshu, and Hai

Dao Suan Jing were among them. Japan was disunited for many centuries after

this early encounter with Chinese culture, and the mathematics that later grew

up was the result of a reintroduction in the sixteen and seventeenth centuries. In

this reintroduction, the two most important works were the Suan Fa Tong Zong

by Cheng Dawei, and the Suan Shu Chimeng of Zhu Shijie, both mentioned in

Chapter 2. The latter became part of the curriculum in Korea very soon after it was

written and was published in Japan in the mid-seventeenth century. The evidence

of Chinese influence is unmistakable in the mechanical methods of calculation used

for centuries—counting rods, counting boards, and the abacus, which played an

especially important role in Japan.

The Koreans adopted the Chinese counting rods and counting boards, which the

Japanese subsequently adopted from them. The abacus (suan pan) was invented

in China, probably in the fourteenth century, when methods of computing with

counting rods had become so efficient that the rods themselves were a hindrance to

the performance of the computation. Prom China the invention passed to Korea,

where it was known as the sanbob. Because it did not prove useful in Korean

business, it did not become widespread there. It passed on to Japan, where it is

known as the soroban, which may be related to the Japanese word for an orderly

table (soroiban). The Japanese made two important technical improvements in the

abacus: (1) they replaced the round beads by beads with sharp edges, which are

easier to manipulate; and (2) they eliminated the superfluous second 5-bead on

each string.

2.2. Japanese mathematicians and their works. A nineteenth-century Japan-

ese historian reported that the emperor Hideyoshi sent the scholar Mori Shigeyoshi

(Mori Kambei) to China to learn mathematics. According to the story, the Chi-

nese ignored the emissary because he was not of noble birth. When he returned to

Japan and reported this fact, the emperor conferred noble status on him and sent

him back. Unfortunately, his second visit to China coincided with Hideyoshi's un-

successful attempt to invade Korea, which made his emissary unwelcome in China.

Mori Shigeyoshi did not return to Japan until after the death of Hideyoshi, but when

he did return (in the early seventeenth century), he brought the abacus with him.

Whether this story is true or not, it is a fact that Mori Shigeyoshi was one of the

most influential early Japanese mathematicians. He wrote several treatises, all of

which have been lost, but his work led to a great flowering of mathematical activity

in seventeenth-century Japan, through the work of his students. This mathematics

was known as wasan, and written using two Chinese characters. The first is wa, a

word still used to denote Japanese-style work in arts and crafts, meaning literally

harmony. The second is san, meaning calculation, the same Chinese symbol that

respresents suan in the many Chinese classics mentioned above.^5 Murata (1994,

p. 105) notes that the primary concern in wasan was to obtain elegant results,

even when those results required very complicated calculations, and that "many

(^5) The modern Japanese word for mathematics is sugaku, meaning literally number study.

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