Where is the origin of abacus?

The abacus is a traditional calculation tool in China, which evolved from the calculation that was commonly used as early as the Spring and Autumn Period. It is not only an important invention in ancient China, but also a widely used calculation tool before Arabic numerals appeared. China is the hometown of abacus. Today, computers have been widely used. The ancient abacus has not been abandoned, but it is still favored by many people because of its advantages such as convenience and accuracy. Therefore, people often compare the invention of the abacus with four great inventions of ancient china, and think that the abacus is also a great contribution of the Chinese nation to mankind. However, when did China start to have an abacus? Since the Qing dynasty, many mathematicians have studied this problem, and Japanese scholars have also invested a lot of energy in it. However, due to the lack of sufficient evidence, the origin of abacus is still controversial today.

Mathematicians in Qing Dynasty, such as Mei Qizhao, believed that abacus originated in the Eastern Han Dynasty and the Southern and Northern Dynasties in China. It is based on the fact that Xu Yue, a mathematician in the Eastern Han Dynasty, once wrote a book "The Legacy of Numerology", in which 14 kinds of algorithms were recorded, and the 13th kind was called "abacus calculation", and he said, "abacus calculation, controlling four seasons, and three talents in latitude and longitude." Later, Zhen Luan, a mathematician in the Northern Zhou Dynasty, commented on this passage: "Stereotype is divided into three parts, the upper and lower parts are divided into two parts, and the middle part is divided into fixed positions. There are five beads in each position, and the upper bead is different from the lower four beads. The upper bead with different colors is five, and the lower four beads are one. To the next four beads, so' cloud belt at four o' clock. Its beads swim among the three parties, so the cloud' latitude and longitude three talents' is also. " These characters are considered to be the earliest records of abacus calculation in China. However, some scholars in modern times believe that the abacus described in the Book of Numerology is at best a counting tool or a simple calculation board that can only be used for addition and subtraction, which is not the same as the abacus that appeared later.

scholars in Qing dynasty, such as Qian da-ting, thought that abacus appeared in the middle of yuan dynasty and was widely used in the late yuan dynasty and early Ming dynasty. It is based on the fact that Tao Zongyi in the Yuan Dynasty quoted a proverb at that time to describe slaves in the twenty-ninth volume "Well Pearl" of "The Record of Dropping out of Farming in the South Village": "When a servant is a servant, he will beat the pearls when he first comes, but he will not dial them automatically; A little longer, the abacus beads, the words will move; For a long time, the Buddha's top beads, words all day long, although the dial does not move. " Later generations called this "three-bead drama language." Comparing a veteran handmaiden to an abacus bead, you can stir it, which shows that abacus was very popular among the people at that time. At the end of the Song Dynasty and the beginning of the Yuan Dynasty, Liu Yin also wrote a five-character quatrain titled Abacus in the book "Collected Works of Mr. Jingmu": "If you don't do business, don't stop the cake's song. How hard is it to raise funds? " This is also a strong proof that abacus appeared in the Yuan Dynasty. In addition, in the section "Pang Jutu Misplaced Future Debts" in Yuan Qu Xuan, it was also mentioned that "I went to the abacus and dialed my age". By the Ming Dynasty, the specifications and dimensions of making an abacus had been included in the Luban Mujing compiled during Yongle period: "Abacus type: one foot and two inches long, four inches and two minutes big. Box six points thick, nine points big, ... Two sons on the line, one inch; Five cents under the line, three inches and one point. Length and size, look at the child and do it. " In addition, Xu Xinlu's Arithmetic of Calculating Beads, Cheng Dawei's Unified Theory of Direct Arithmetic, Ke Shangqian's General Track of Mathematics, Zhu Zaiyu's New Theory of Arithmetic, etc. have appeared, so there is no doubt that abacus has been widely used in Ming Dynasty.

With the discovery of new historical materials, some experts believe that abacus should have originated in the Tang Dynasty and was popular in the Song Dynasty. It is based on the fact that in the famous painting "The Riverside Scene at Qingming Festival" in the Song Dynasty, there was a drugstore with an abacus on the front counter. After the abacus experts in China and Japan enlarged the picture, it was confirmed that the object in the painting was a serial abacus similar to the abacus used in modern times. Moreover, in 1921, a wooden abacus bead was unearthed in Julu County, Hebei Province, China. Although it has been submerged by water and soil for 8 years, it can still be seen that it is drum-shaped with holes in the middle, which is no different from modern abacus beads.

In addition, people who hold this view also believe that there is a nine-file abacus diagram in the textbook of Mongolian studies in the early Yuan Dynasty. Since it was already a training content in the early Yuan Dynasty, it can be seen that the abacus was an ordinary thing at that time, and its appearance can at least be pushed up to the Song Dynasty. Besides, Liu Yin, who wrote the poem Abacus, was also from the late Song Dynasty and the early Yuan Dynasty. His poems are more accurate than descriptions of things in the Yuan Dynasty. Similarly, Tao Zongyi's "three-bead drama" shows that there is an abacus in Yuan proverbs, which also reflects that "the law prevailed in Song Dynasty".

However, if we think that the abacus originated in the Song Dynasty, there seems to be some doubt. Because from the shape point of view, the abacus in the Song Dynasty has been relatively mature, and there is no awkwardness or roughness that new things often have. Therefore, many mathematicians believe that the birth of abacus can be pushed up to the Tang Dynasty. Because of the constant wars in the Five Dynasties and Ten Kingdoms period before the Song Dynasty, the development of science and technology culture was relatively slow, so it is unlikely that the abacus was born at this time. The Tang Dynasty is a prosperous time in China's history, and its economy and culture are developed, so it is necessary to have new calculation tools. Therefore, it is very possible that the abacus was invented in the Tang Dynasty.