The Mathsticks of Early China

Article excerpt

The ancient Chinese devised an original system of calculating using counting rods

THE origins of numeration in China go back into the dim and distant past and since, as in many other countries, no-one knows precisely how it began, all sorts of legends and myths sprang up. An ancient book called Shi Ben ("The Book on Ancestries") tells how the legendary Yellow Emperor, regarded as the first emperor in China's history, ordered his subjects Xi He to observe the sun, Chang Yi to observe the moon . . . and Li Shou to invent arithmetic. The story of Li Shou became widely known, and people imagined that he discovered the concept of numbers by himself.

But to credit the concept of numbers to one man obviously does not accord with the historical facts; such a complex concept could not have been worked out single-handed, even by a genius. It is obvious that numbers gradually evolved throughout the long history of humanity in response to practical requirements.

Certain features in the evolution of Chinese numeration can be inferred from legends and myths, but more important clues can be drawn, and more accurate deductions can be made, from archaeological evidence.

Archaeologists discovered that some earthenware from the 7,000-year-old Yangshao Culture (excavated in Henan and Shanxi Provinces) bore specially inscribed signs and marks. Most of the marks were vertical lines, while others were Z-shaped. These vertical lines are believed to be the very earliest forms of numeration in ancient China.

After tens of thousands of years of primitive civilization, a society with a class structure evolved in China. This was the slave society of the Shang dynasty (circa sixteenth to eleventh centuries B.C.). It is clear from archaeological evidence that this culture was fairly well developed, producing bronze weapons, household utensils and sacrificial vessels. Around the fourteenth century B.C., the Shang Dynasty moved its capital to the neighbourhood of the present-day Xiaotun, near Anyang in Henan province. Culture and the economy took a further step forward, and a form of calendar appeared.

* The oracle bone script

In the course of the present century, a large collection of plastrons--the ventral part of tortoiseshells--and animal bones inscribed with characters have been excavated in the same area. Research has shown that the nobles of the Shang period worshipped the spirits of their ancestors. In their prayers they put questions to these spirits, inscribing the questions, the answers, and sometimes the subsequent verifications on the plastrons and on animal bones. The characters used in the inscriptions are generally known as "oracle bone script," and this is the earliest form of Chinese writing so far discovered, although isolated symbols have been found on Yangshao pottery.

Among the 5,000 characters used by the Shang people on the excavated oracle bones are the earliest known Chinese numerals. The oracle bones recorded how many prisoners were taken in war or how many of the enemy were killed, how many birds and animals the hunters caught and how many domestic animals were sacrificed to the spirits. Days were also numbered. Here are some examples:

"On the eighth day, namely the day of Xinhai, two thousand six hundred and fifty-six men were killed while crossing spears."

"Captured ten and six men."

"Ten dogs and five dogs."

"Ten cattle and five."

"Deer fifty and six."

"Five hundred four tens and seven days."

The largest number inscribed on the oracle bones is 30,000 and the smallest is one. Units, tens, hundreds, thousands and ten thousands each have a specific character to represent them.

Ancient inscriptions on bronze have also been found, in what is known as "bell vessel script" or "bronze script," and research shows that most of them date from the Zhou period (around the eleventh century to 221 B.C.). The numerals were written in a similar way to those on the oracle bones. …