The swanpan (算盤 or 筭盤 Pinyin: suan4 pan2) of the Chinese dates from the Yuan Dynasty (1271-1368) was when the Mongols ruled China. It was a period of cultural enlightenment. The Mongols replaced the Han Chinese bureaucrats and all important central and regional posts within China were monopolized by Mongols, who also preferred employing non-Chinese from other parts of the Mongol domain--Central Asia, the Middle East, and even Europe to fill positions for which no Mongol could be found. Scientific education, literacy, and public works flourished under Mongols.

The Chinese abacus is typically around 20 cm (8 inches) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom for both decimal and hexadecimal computation. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. The abacus can be reset to the starting position instantly by a quick jerk along the horizontal axis to spin all the beads away from the horizontal beam at the center.

Chinese abaci can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient swanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed.

See also: counting rods

Origins

The earliest mention of an abacus in Chinese literature was in 190 CE in a book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue in that year.

Another reference to an abacus in China occurred at the latest during the Song Dynasty (960-1297), when Zhang Zeduan painted his Riverside Scenes at Qingming Festival. In this famous long scroll, an abacus is clearly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).

Its similarity to the Roman abacus suggests that that was the ultimate source, and this was possible, since there were direct trade relations between the classical world and China, and Mongol traders along the Silk Route were a bridge between East and West. It could even have been introduced by the Roman soldiers captured by the Persians and sold to the Chinese emperor as engineers. Most were later ransomed, but many found China much to their liking. In 166 CE, a trade convoy sent out by Emperor Antoninus Pius reached the Chinese capital Luoyang in and was greeted by Eastern Han Dynasty Emperor Huan. This was recorded in Hou Hanshu (History of the Later Han).

An opposing view suggests that no connection exists between the two abaci. The similarity between the two designs was merely a product of convergent evolution and the natural outcome from counting with five fingers in one hand and using the other hand for place holders.

Recently there are studies showing Chinese abaci were perfected by combination of its three former ancestors (precursors) [abaci with rod], [Taiyi, Liangyi, Sancai, from Taoism/Daojia].

It is thought that the evolution of the Chinese abacus design could be traced back to Chinese counting rods. Chinese counting rods operated on a decimal system and lacked the concept of a zero as a place holder. The zero was probably introduced to the Chinese in the Tang Dynasty (618-907) when trade mission along the Indian Ocean and the Middle East would have provided direct contact with India and Islam allowing them to acquire the concept of Zero and the decimal point from Indian and Islamic merchants and mathematicians.

Another argument for independent development is that the Chinese abacus is suited for hexidecimal and decimal numeral systems, whereas the Roman abacus used only the Roman numerals.

There is still disagreement on the origin of the Chinese abacus. See Discussion

Beads

There are two types of beads on the abacus, those in the lower deck, below the separator beam, and those in the upper deck above it. The ones in the lower deck are sometimes called earth beads, and carry a value of 1 in their column. The ones in the upper deck are sometimes called heaven beads. The columns are much like the places in arabic numerals: one of the columns, usually the rightmost, represents the ones place; to the left it are the tens, hundreds, thousands place, and so on, and if there are any columns to the right of it, they are the tenths place, hundredths place, and so on.

At the end of a decimal calculation on a Chinese abacus, it is never the case that all five beads in the lower deck are moved up; in this case, the five beads are pushed back down and one carry bead in the top deck takes their place. Similarly, if two beads in the top deck are pushed down, they are pushed back up, and one carry bead in the lower deck of the next column to the left is moved up. In hexadecimal calculation, all seven beads on each column are used. The result of the computation is read off from the beads clustered near the separator beam between the upper and lower deck.

The earth beads and heaven beads are usually not used in addition and subtraction. They are essential (compulsory) in some of the multiplication methods [2 amongst 3 methods requires them] and Division method [special division table, Quichu, 1 amongst 3 methods]. There are cases when the intermediate result (in multiplication and division) is large than 15 (fifteen), the lower of the upper bead is moved halfway to represent ten [xuanchu, suspended]. Thus the same rod can represent up to 19 (compulsory as intermediate steps in tradition Chinese abacus multiplication and division).

The mnemonics/readings of the Chinese division method [Quichu] origins from the use bamboo sticks [Chousuan], which is one of the reasons that many believe the evolution of Chinese Abacus [Sunpan] is independent of the Roman Abacus.

This Chinese division method [i.e. with division table] was not when the Japanese changed their abacus to 1 upper bead and 4 lower beads in about 1920's. So, without a clear knowledge of division table, the trial of history, many have the wrong perception that Chinese abacus was from Roman Grooved Abacus.

The beads and rods are often lubricated to ensure quick, smooth motion.

Decimal system

Like the Roman abacus, this device works as a bi-quinary based number system in which carries and shiftings are similar to the decimal number system. Since each rod represents a digit in a decimal number, the computation capacity of the abacus is only limited by the number of rods on the abacus. When a mathematician runs out of rods, another abacus can be added to the left of the first. In theory, the abacus can be expanded indefinitely in this way.

Hexadecimal system

Traditional Chinese weighing units was a hexadecimal system. One jin (斤) equals sixteen liang (兩). Abaci were commonly used in market place to calculate with these hexadecimal units. When all the beads in the Chinese abacus are used, each column can be used to represent numbers between 0 to 15 (two 5s and five 1s.) Computation in decimal and hexadecimal is very similar except one extra bead from both the upper and lower deck are used.

Modern decline in use

Abacus arithmetic was still being taught in school in Hong Kong as recently as the late 1960s, and in Taiwan into the 1990s. However, when handheld calculators became readily available, schoolchildren's willingness to learn the use of the abacus decreased dramatically. In the early days of handheld calculators, news of abacus operators beating electronic calculators in arithmetic competitions in both speed and accuracy often appeared in the media. Early electronic calculators could only handle 8 to 10 significant digits, whereas abaci can be built to virtually limitless precision. But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the abacus could never compute higher functions – such as those in trigonometry – faster than a calculator. Nowadays, as calculators have become more affordable, the abacus is hardly seen in Hong Kong. Abaci are, however, still being used elsewhere in China and in Japan. Though abaci are not commonly used in Hong Kong and Taiwan, many parents still send their children to private tutors to learn bead arithmetic as a learning aid and a stepping stone to faster and more accurate mental arithmetic.

In mainland China, formerly accountants and financial personnel had to pass certain graded examinations in bead arithmetic before they were qualified. Starting from about 2003 or 2004, this requirement has been entirely replaced by computer accounting.

Miscellanea

The swanpan is closely tied to the Chinese "Hua1 Ma3" numbering system.