Chinese abacus

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Chinese abacus or suanpan (the number represented in the picture is 6,302,715,408)

The suanpan (Simplified Chinese: 算盘; Traditional Chinese: 算盤; pinyin: suànpán) of the Chinese dates from the Han Dynasty (202 BCE - 184 CE).

However, it rose to prominence during the Yuan Dynasty (1271 CE - 1368 CE).

The Chinese abacus 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 suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed.

See also: counting rods

1 Origins
2 Beads
3 Decimal system
4 Hexadecimal system
5 Modern decline in use
6 Miscellanea
7 External links

[edit] Origins

The earliest mention of an abacus in Chinese literature was in a 190 CE book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue in that year. However, the exact design of this abacus is not known.

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

The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, as there is some evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Japanese) has 4 plus 1 bead per decimal place, the standard Chinese abacus has 5 plus 2, allowing less challenging arithmetic algorithms, and also allowing use with a hexadecimal numeral system. Instead of running on wires as in the Chinese and Japanese models, the beads of Roman model runs in groves, presumably making arithmetic calculations much slower.

Another possible source of the Chinese abacus is Chinese counting rods, which operated with a decimal system but 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 travel in 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.

[edit] 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]. When the intermediate result (in multiplication and division) is larger 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] has its origin in 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 in use when the Japanese changed their abacus to 1 upper bead and 4 lower beads in about the 1920's.

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

[edit] Decimal system

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.

[edit] 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.

[edit] Modern decline in use

Abacus arithmetic was still being taught in school in Hong Kong as recently as the late 1960s, and in Republic of China 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, abaci are not commonly used in Hong Kong or Taiwan, but many parents still send their children to private tutors or school- and government- sponsored afterschool activities to learn bead arithmetic as a learning aid and a stepping stone to faster and more accurate mental arithmetic, or as a matter of cultural preservation. Speed competitions are still held. Abaci are still being used elsewhere in China and in Japan.

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.