Hey Ayi,

What’s the deal with the abacus? Why do so many Chinese people still use them, and how do you do calculations?

Signed

Bean Counter

Dear Bean Counter,

Like virtually everything else of use in our disposable modern culture, the abacus was invented in China. The Aztecs independently invented a type of abacus circa 1000 AD, but while the ancient South American calculating devices are found only in musty museums, you can see a suanpan (calculating board) in use in many department stores in Beijing and on the desks of bookkeepers all over the People’s Republic.

The earliest known use of the abacus was around 500 BC in China. Calculating devices using pebbles or other moveable counters were also found in ancient Rome, Greece and Egypt. The Japanese copied the Middle Kingdom’s abacus in about 1600 AD. In the shuzi shidai (digital age), the abacus is still commonly used in the Middle East, and in Southeast and East Asia.

A standard Chinese abacus consists of a frame divided by a middle bar into an upper and lower deck, with eight parallel rods running from top to bottom. Each rod has five beads on the lower deck and two beads on the upper deck. For calculations, each bead on a given wire on the lower deck has the same value: either ten or some multiple or submultiple of ten. The beads on the upper deck have a value of five each. The design of the Chinese abacus in use today has not changed since the sixteenth century, but other countries use slightly different versions. The Japanese insisted on fiddling with the written script they copied from us and they fiddled with the abacus too: a Japanese abacus has four beads on the lower deck and one on the upper. Other combinations of beads are used in different countries.

Calculations on a Chinese abacus are performed by placing the abacus flat on a table or one’s lap and manipulating the beads with the fingers of one hand. You need nimble fingers to do it fast. Beads in the lower deck are moved up with the thumb and down with the index finger, with the middle or index finger used on the upper deck. Beads are counted by moving them towards the middle bar. The right-most rod is usually the ones column; to its the left is the tens column next to which is the hundreds rod, and so on. After five beads are counted in the lower deck, the result is 'carried' to the upper deck; after both beads in the upper deck are counted, the result (10) is then carried to the left-most adjacent rod. Decimals can be counted by choosing a space between two rows to designate the decimal point. All the rods to the right of that space then represent fractional portions.

Addition and subtraction are easy on the abacus. To do the sum 30+12, first move three beads on the lower second (tens) rod up to the middle bar, leaving the first rod unchanged; this is 30. Then move one bead on the lower second rod and two beads on the first lower rod up to the bar. You now have four tens beads and two ones beads at the bar: the answer is 42. Multiplication and division require more complex bead movement but are based on the same simple principle.

Despite the current abundance of Casio and Sharpee electronic calculators in the Middle Kingdom, many Chinese people are still attached to their abacuses. Every taxi driver in Beijing can tell you about the competitions held between geeks on electronic calculators and geeks on abacuses. A proficient abacus geek can do complex calculations faster than a rival keying in the same sums on a calculator. The abacus can be used for even square and cube roots.

Grade Four pupils in Chinese elementary schools are still taught how to use the abacus, although many of the little emperors - who could play Nintendo games before they could speak - object to the old-fashioned lessons. The abacus is also a required skill to qualify as an accountant in China. This is one of the biggest headaches for modern accounting students. Their abacus education often starts with the memorization of mnemonic rhymes that are soulless enough to cause a poet to have a heart attack, but are nonetheless useful in getting the abacus user up to working speed.