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The suanpan (), also spelled suan pan or souanpan) is an abacus of China origin. The earliest known written documentation of the Chinese abacus dates to the 2nd century BCE during the Han dynasty, and it was later described in a 190 CE book of the Eastern Han dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue. However, the exact design of this suanpan is not known.Peng Yoke Ho, page 71 Usually, a suanpan is about 20 cm (8 in) 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 on each rod in the bottom deck. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. The suanpan can be reset to the starting position instantly by a quick jerk around the horizontal axis to spin all the beads away from the horizontal beam at the center.
Suanpans 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.
The modern suanpan has 4+1 beads, colored beads to indicate position and a clear-all button. When the clear-all button is pressed, two mechanical levers push the top row beads to the top position and the bottom row beads to the bottom position, thus clearing all numbers to zero. This replaces clearing the beads by hand, or quickly rotating the suanpan around its horizontal center line to clear the beads by centrifugal force.
The long scroll Along the River During Qing Ming Festival painted by Zhang Zeduan (1085–1145) during the Song dynasty (960–1279) might contain a suanpan beside an account book and doctor's prescriptions on the counter of an apothecary. However, the identification of the object as an abacus is a matter of some debate.Martzloff, p. 216
Zhusuan was an abacus invented in China at the end of the 2nd century CE and reached its peak during the period from the 13th to the 16th century CE. In the 13th century, Guo Shoujing (郭守敬) used Zhusuan to calculate the length of each orbital year and found it to be 365.2425 days. In the 16th century, Zhu Zaiyu (朱載堉) calculated the musical Twelve-interval Equal Temperament using Zhusuan. And again in the 16th century, Wang Wensu (王文素) and Cheng Dawei (程大位) wrote respectively Principles of Algorithms and Suanfa tongzong, summarizing and refining the mathematical algorithms of Zhusuan, thus further boosting the popularity and promotion of Zhusuan. At the end of the 16th century, Zhusuan was introduced to neighboring countries and regions.
A 5+1 suanpan appeared in the Ming dynasty, an illustration in a 1573 book on suanpan showed a suanpan with one bead on top and five beads at the bottom.
The evident similarity of the Roman abacus to the Chinese one suggests that one may have inspired the other, as there is strong evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci could be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model and Chinese model (like most modern Japanese) has 4 plus 1 bead per decimal place, the old version of the Chinese suanpan has 5 plus 2, allowing less challenging arithmetic algorithms. Instead of running on wires as in the Chinese and Japanese models, the beads of Roman model run in grooves, presumably more reliable since the wires could be bent.
Another possible source of the suanpan is Chinese counting rods, which operated with a place value Decimal with empty spot as zero.
Although sinologist Nathan Sivin claimed that the abacus, with its limited flexibility, "was useless for the most advanced algebra", and suggested that "the convenience of the abacus" may have paradoxically stymied mathematical innovation from the 14th to 17th centuries, Roger Hart counters that the abacus in fact facilitated new developments during that time, such as Zhu Zaiyu's treatises on musical equal temperament, for which he used nine abacuses to calculate to twenty-five digits.
The suanpan is a 2:5 abacus: two heaven beads and five earth beads. If one compares the suanpan to the soroban which is a 1:4 abacus, one might think there are two "extra" beads in each column. In fact, to represent decimal numbers and add or subtract such numbers, one strictly needs only one upper bead and four lower beads on each column. Some "old" methods to multiply or divide decimal numbers use those extra beads like the "Extra Bead technique" or "Suspended Bead technique". The most mysterious and seemingly superfluous fifth lower bead, likely inherited from counting rods as suggested by the image above, was used to simplify and speed up addition and subtraction somewhat, as well as to decrease the chances of error. Its use was demonstrated, for example, in the first book devoted entirely to suanpan: Computational Methods with the Beads in a Tray ( Pánzhū Suànfǎ 盤珠算法) by Xú Xīnlǔ 徐心魯 (1573, Late Ming dynasty).
A simplify explanation on how to use the 5th beads is shown here.
The following two animations show the details of this particular usage:
In Shì yòng zhì (市用制), the unit of weight, the jīn (斤), was defined as 16 liǎng (兩), which made it necessary to perform calculations in hexadecimal. The Suanpan can accommodate up to 15 in each digit rod and when it becomes 16, the digit rod changes that will visualise the hexadecimal system.
This is the reason why the Japanese Soroban's 4 earth beads (when the value is 0) is one bead apart from the beam while the suanpan's 5 earth beads (when the value is 0) are 2 beads apart from its beam.
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The two most extreme beads, the bottommost earth bead and the topmost heaven bead, are usually not used in addition and subtraction. They are essential (compulsory) in some of the multiplication methods (two of three methods require them) and division method (special division table, Qiuchu 九歸, one amongst three methods). When the intermediate result (in multiplication and division) is larger than 15 (fifteen), the second (extra) upper bead is moved halfway to represent ten (xuanchu, suspended). Thus the same rod can represent up to 20 (compulsory as intermediate steps in traditional suanpan multiplication and division).
The mnemonics/readings of the Chinese division method Qiuchu has its origin in the use of bamboo sticks Chousuan, which is one of the reasons that many believe the evolution of suanpan 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 one upper bead and four lower beads in about the 1920s.
The suanpan's extra beads can be used for representing decimal numbers, adding or subtracting decimal numbers, caching carry operations, and base sixteen (hexadecimal) fractions.
Zhusuan is an important part of the traditional Chinese culture. Zhusuan has a far-reaching effect on various fields of Chinese society, like Chinese folk custom, language, literature, sculpture, architecture, etc., creating a Zhusuan-related cultural phenomenon. For example, ‘Iron Abacus’ (鐵算盤) refers to someone good at calculating; ‘Plus three equals plus five and minus two’ (三下五除二; +3 = +5 − 2) means quick and decisive; ‘3 times 7 equals 21’ indicates quick and rash; and in some places of China, there is a custom of telling children's fortune by placing various daily necessities before them on their first birthday and letting them choose one to predict their future lives. Among the items is an abacus, which symbolizes wisdom and wealth.
Suanpans are still widely used elsewhere in China and Japan, as well as in a few places in Canada and the United States. With its historical value, it has symbolized the traditional cultural identity. It contributes to the advancement of calculating techniques and intellectual development, which closely relate to the cultural-related industry like architecture and Tradition. With their operational simplicity and traditional habit, Suanpans are still generally in use in small-scale shops.
In mainland China, formerly accountants and financial personnel had to pass certain graded examinations in bead arithmetic before they were qualified. Starting from about 2002 or 2004, this requirement has been entirely replaced by computer accounting.
Modern usage
Suanpan arithmetic was still being taught in school in Hong Kong as recently as the late 1960s, and in China into the 1990s. In some less-developed industry, the suanpan (abacus) is still in use as a primary counting device and back-up calculating method. However, when handheld became readily available, school children's willingness to learn the use of the suanpan decreased dramatically. In the early days of handheld calculators, news of suanpan 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 suanpans can be built to virtually limitless precision. But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the suanpan could never compute higher functions – such as those in trigonometry – faster than a calculator. As digitalised calculators seemed to be more efficient and user-friendly, their functional capacities attract more technological-related and large scale industries in application. Nowadays, even though calculators have become more affordable and convenient, suanpans are still commonly used in China. Many parents still tend to send their children to private tutors or school- and government-sponsored after school 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.
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