The earliest representatives of abacus culture in historic relic are the 90 cyan-yellow ceramic balls discovered and excavated by archaeological workers when they were excavating an ancient tomb of Western Zhou Dynasty in March of 1976. As authentication showed that these ceramic balls of Western Zhou Dynasty were the earliest abacus beads with a history of 3,000 years.
The earliest work with “abacus” in it is a book written by Xu Yue of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures, where “abacus” was recorded as one of the 14 methods of calculation, saying that “The Chinese bead abacus (so called suanpan) has a rectangular wooden frame with thin rods across it. On each rod are placed seven glass or wooden beads: five (the number of fingers of a human) below the strip of wood, that divides the frame into two unequal parts, and two above it (the number of hands)” (Yu Ningwang, Chinese Abacus Calculation, Tianjin Science and Technology Press, Editor of 1990, Page 111). So the Supplementary Notes on the Art of Figures had become the earliest representative of abacus culture in abacus works.
The earliest famous painting with “abacus” in it is the scroll Along the River During the Qingming Festival attributed to Song Dynasty artist Zhang Zeduan, with an abacus of 15 rods on the desk of an herbal medicine shop of Officer Zhao. So this painting had become the representative of abacus culture with the most historic research value in painting.
From rod calculus to abacus calculation, there’re two inspects including calculation tool (hardware) and calculation method (software, pithy formula, and formula in verse). In Chinese history, there’re varieties of calculation tools and methods, only in Supplementary Notes on the Art of Figures 14 kinds were recorded. There’re still other abacuses out of China, such as Roman abacus (divided into two parts of above and below, and in each part abacus can be recorded as one digit as it reaches the top, which was hard to identify) and the horizontal abacus with 10 beads along the rods (in Russia, Northern Europe, etc.), which has a wide difference with Chinese abacus, but only Chinese abacus has been widely used over the world through years.
Obviously, abacus calculation is evolved from rod calculus. In the Laozi (Tao Te Ching) there were words saying that, “A good counter needs no rod calculator”, which can proof that rods, as a kind of calculator, are rather popular, since that rod calculus was recorded to be mature in the Spring and Autumn Period. The characters “Suan (Calculate)” and “Chou (Rods)” were first found on the books of Spring and Autumn Period, such as the Etiquette and Ceremonial, Sun Tzu, Laozi, Book of Law, Guanzi, Xunzi, etc. No track of the two characters can be found on bones and tortoises or on ancient bonze projects. Rod calculus involving numbers larger than 1, 2 and 3 were earliest founded on the money (knife money and spade money) in Warring States Period.
In rod calculus, the one rod above is regarded as 5, the one below is as 1, same as the beads in abacus. Since in multiplication and division of rod calculus, the figure of some digits may equal to 10 or greater than 10, abacus was improved into structure with 2 beads above and 5 below.
Since the birth of formular in verse, the existed defect of rod calculus became more obvious, reflected in the contradiction between the quickness of verse formula and the slowness of sliding rods. In consideration of facility, people created a much advanced tool which is called “abacus”. From the reserved works it is recorded that the revolution of rod calculus was not beginning with revolution of tool but the simplification of rod calculus, and the revolution of tool finally led to the birth of abacus.
Abacus stood out in the fully-developed history, and got unified by the end of the 1915s’, which became to change all the way until the popularity of computers.
Abacus wall of the museum
Walnut Abacus of Maiji Mountain, Gansu Province,China