Cultural Characteristics of Chinese Abacus

Guo Shirong

Vice President of Chinese Abacus and Mental Arithmetic Association (CAMAA);

Professor at the Institute of History of Science and Technology, Inner Mongolia Normal University

The UNESCO Intergovernmental Committee for the Safeguarding of Intangible Cultural Heritage holds that: “Abacus is not only a symbol of Chinese cultural identity, but also a practical tool. This computing technique has been passed down through generations and integrated into many aspects of daily life. It has multiple socio-cultural functions, providing the world with an alternative knowledge system.” This is not only an important basis for the UNESCO to recognize abacus as an intangible cultural heritage of mankind, but also a summarization of the main characteristics of Chinese abacus culture.

In this report, six major characteristics of Chinese abacus culture, i.e., scientificity, uniqueness, sociality, continuity, internationality and symbolism, are elaborated in details.

I. Scientificity

Abacus is an important part of ancient Chinese mathematics, with scientificity as its first cultural characteristic. The scientificity of abacus lies in the formation of a complete abacus knowledge system. This system includes the scientific design of abacus, related mathematical theories, algorithms and formulas, and many other aspects such as the description and recording of abacus operation, demonstration and calculation process.

The invention of abacus not only absorbs the scientific component of traditional counting rods, but also features a new creation. The core of the abacus knowledge system is the mathematical principle and algorithm supporting abacus operation. Abacus has the basic operation functions including addition, subtraction, multiplication, division, evolution and power, which can solve all calculation problems encountered in ancient mathematics, including various application problems. This is the scientific basis that counting rods can be replaced in Ming Dynasty. The key to solve calculation problems is algorithm. The design of abacus algorithm and formula is one of the important manifestations of abacus science.

II. Continuity

Since the advent of abacus, it has been continuously developed without interruption, with new algorithms constantly improving and developing, and showing the characteristic of continuity. The origin of abacus is still an open question. The word “abacus” first appeared in the Annotations on Mathematical Techniques at the end of Han Dynasty, referring to “a calculator with beads as a computing element”. The Xie Chawei Mathematical Techniques, a mathematical works at the end of Five Dynasties, includes the contents related to abacus. At that time, counting rods prevailed, while abacus was mainly used among the general public. In the paintings, poems and literary works in Song and Yuan Dynasties, abacus appeared from time to time. From the paintings, we can see that street vendors sold abacuses and store tellers used them. In literary works, abacus had become a word in poetry and opera works, and was included in children’s books. All these indicate that abacus had a high degree of popularity among the general public, and it not only had become a fully-accepted and widely-used calculation tool in the society, but also was quite common for the ordinary people. The mathematical works in Song and Yuan Dynasties, such as Yang Hui Algorithm and Enlightenment of Mathematics, include some abacus contents expressed in the language of counting, and there also appeared other abacus works such as the Beads Collection and the Abacus Collection.

At the end of Yuan Dynasty, the mathematical tradition changed greatly, and mathematical works including both abacus and counting began to appear. In late Ming Dynasty, the big and small traditions of mathematics changed, with abacus replacing counting and becoming the big tradition. Counting began to exit from the historical stage gradually, while a large number of abacus works began to appear. During Ming and Qing Dynasties, several series of abacus works were developed and formed respectively, centered on the Arithmetic Law, Detailed Algorithm and Tongling Algorithm. In the reform of the school system at the end of Qing Dynasty, abacus was officially included in the curriculum system of mathematics education, and abacus was taught in primary and secondary schools, opening a new era of abacus education and abacus reform. In the 20th century, abacus became a necessary skill for financial personnel. With the popularization and convenience of modern electronic computing tools, abacus was replaced. However, the “combination of three calculation methods”, which had been tested since the 1950s and 1960s, eventually developed into the abacus and mental arithmetic, and abacus began to play a new role in another form.

III. Uniqueness

The uniqueness of the so-called abacus means that abacus is an independent invention of the Chinese people, and is unmatched in terms of function, effect and influence by all other similar computing tools in the world, that is, Chinese abacus is unique in the world.

To say that Chinese abacus is unique does not mean that only China has abacus. Historically, ancient Greece, ancient India and Russia had abacuses in different shapes and structures, but such abacuses were mainly teaching aids, and their scientific function development, design idea and scientific role cannot match Chinese abacus. In contrast, Chinese abacus has a prudent knowledge system, and it has been used in China and East Asia as an efficient mainstream computing tool for thousands of years, “providing the world with an alternative knowledge system” with strong oriental characteristics. This is not available in other abacuses. In addition, the social functions of other abacuses are extremely limited, while Chinese abacus has huge social impacts, and plays a very important role in the management of social affairs. It could be said that abacus is indispensable. This is an important manifestation of the uniqueness of Chinese abacus.

The origin of Chinese abacus has been the focus of the academic community. There were doubts about the independence of Chinese abacus, or arguments of the possibility that Chinese abacus originated in a foreign country. In this regard, Chinese abacus scholars have argued strongly on just grounds, presenting reasoned arguments to make scholars from all over the world to unanimously recognize that Chinese abacus is a calculation tool invented by the Chinese people, thus maintaining the independence of Chinese abacus.

IV. Sociality

Chinese abacus has multiple social and cultural functions, showing strong characteristic of sociality. Abacus is an indispensable part of Chinese social life. The abacus culture is integrated into all aspects of social life, completely rooted in the social life of Chinese people, and plays an extremely important social role.

Abacus is easy to be understood and mastered, and easy to popularize to the whole society. It is the scientific basis for its important social and cultural functions. Historically, among the members of Chinese society from ordinary people to senior state officials, including officials, managers, businessmen and technicians, the proportion of people who can use abacus is extremely high.

The widespread demand for abacus in the society is the basis for abacus to become a widely influential social culture. Abacus can be adapted to the computing needs of almost all aspects of the Chinese society. Where there is a need of calculation, abacus must be used, and abacus has become an indispensable calculation tool in Chinese society.

The sociality of abacus is also reflected in the familiarity of the whole society with it. Since Song Dynasty, abacus has been used as the materials in many literary and educational works, such as four forms of poetry, drama literature, note novels, paintings, children’s books, dialect slangs and social languages. Some abacus words have been well integrated into the social language, thus enriching the Chinese language. All these are the concrete manifestation of abacus’ deep popularity. Like daily necessity, abacus has been integrated into the life of the Chinese people.

V. Internationality

Abacus is both Chinese and international. The historical role and influence of Chinese abacus extends far beyond China. After the popularity of abacus in China, it began to spread to neighboring countries through the abacus works. The spread of abacus in East Asia and Southeast Asia, especially in South Korea, Japan, Vietnam, Thailand and Myanmar, has played a huge role in the development of mathematics in these countries, generating huge impacts. The works such as Yang Hui Algorithm, Enlightenment of Mathematics, Detailed Algorithm and Arithmetic Law had played a key role in the development of mathematics in Korea, Japan and other countries. In the 17th century, abacus works were spread to Europe, attracting a lot of attention. In the 19th century, many scholars in Britain, France, Germany, Russia and other countries studied the history of Chinese abacus and introduced Chinese abacus to readers, which has been continuing to this day. In the 20th century, abacus was introduced to the countries around the world as a suitable calculation tool, and various popular works on abacus were written in different languages. The Chinese all over the world are powerful spreaders of abacus. Wherever they go, they take abacus with them, and wherever there are Chinese, abacus is used. They also guide others to use abacus.

VI. Symbolism

Abacus “is a symbol of Chinese cultural identity”. Chinese abacus is one of the symbols of Chinese cultures and has important symbolic significance. “Whenever the abacus rings, enormous wealth flows through our fingers,” so abacus is also a symbol of wealth. Chinese abacus has the nature and influence of representing Chinese cultures.

(This is a speech delivered at the Eighth Seminar for Academic Exchanges on Abacus and Mental Arithmetic on April 12th, 2024.)