Why did China call "mathematics" "arithmetic" in ancient times?

Mathematics was called "arithmetic" in ancient China. Its earliest operating tool is called "plan", which is usually called "plan" or "plan". Actually, it's just some sticks or grass sticks or bamboo joints. If you put them on the ground or on the table, you can operate them according to certain rules.

However, it should be pointed out that in ancient times, planning can not only refer to arithmetic tools, but also refer to yarrow for planting. In other words, the tools originally used in ancient arithmetic and divination probably belong to the same type. In the eyes of the ancients, yarrow was sacred. Therefore, we can also infer that arithmetic may be mysterious at first. In fact, it is not only an arithmetic tool, but also a bag used by the ancients to hold calculation funds, and it is also regarded as a sacred object.

It is said that Qin Shihuang once threw a bag into the East China Sea. As a result, a fish was born in this bag!

Judging from the use of daily language, the ancients regarded the rules and methods of digital operation as a kind of "technique", so it was also called "arithmetic". The process of mathematical activities such as divination and fortune telling is regarded as an operation, so it is also called "accounting". Here, we can also see the primitive relationship between arithmetic and divination. Perhaps arithmetic evolved from divination, which is also very possible.

Hanshu gives a style of calculation and compilation:

Its algorithm uses bamboo, which is one minute in diameter and six inches long, and 27 1 block is made into six pieces, which is a grip.

This means that the counting chip is made of bamboo, with a diameter of one minute and a length of six inches. 27 1 counter chip forms a hexagonal prism, which is called the grip.

On the surface, the composition of this pair of calculations seems to be nothing strange. However, in the cultural atmosphere of the Han Dynasty, each of their articles has the concept of mathematics. Please look at the notes in Hanshu:

The diameter is like a dry yellow clock, but it looks like the length of Lin's clock. Its number is fifty in the Book of Changes, and its use is forty-nine, which is the image of Chengyang Liuliu and Liuzhou Liuliu.

In other words, the diameter of the computing chip is a point, which symbolizes one-ninth of the yellow bell, the first of the six laws in the twelve laws; It is six inches long, symbolizing the head of Lin Zhong, the pipe captain; And the number of one grip is 27 1, which comes from the sum of the big derivative number, dry strategy number and six numbers of the Book of Changes, that is, 49+2 16+6 = 27 1.

Xu Yue's Shu Shu Ji Yi and Sui Shu's Li Luzhi also have similar records, only comparing the calculation size with the mysterious numbers in the mathematical system, thus mystifying the calculation or arithmetic, just like Han Shu's Li Luzhi.

Another unique computing tool in ancient China was the abacus, and its earliest record was also found in Xu Yue's Notes on Numerology. Xu Yue wrote in the book "Abacus": "The four seasons control the belt, and the latitude and longitude are talented." In other words, the bead algorithm maintains and runs through the four seasons, and also fixes the talents of heaven, earth and people, just like the warp and weft of fabric. Later, Zhen Luan, an annotator of Numerology Notes, gave the practice of abacus at the bottom of this passage, that is, a wooden board was separated by three transverse partitions, the upper and lower partitions were used to hang movable abacus beads, and the middle partition was used to locate; Everyone has five beads, and one bead on the positioning plate is not the same color as the four beads below; The upper bead is equivalent to five units, and the lower four beads are equivalent to one unit each. Because the four beads move up and down, it stays throughout the four seasons; And because there are three partitions for beads to move between, it is said that it fixes three talents, just like the warp and weft of cloth. Judging from Zhen Luan's comments, although the structure of this abacus is similar to that of later generations, it has obvious mysterious tendency because it is attached to the concepts of four seasons and three talents.

In fact, similar to calculations and abacus, the structures of rulers, measuring tools and other instruments in ancient China also have various mysterious explanations. So it is not surprising that mathematics was called "arithmetic" in ancient times!