Encyclopedia > Abacus

Article Content

Abacus

An abacus is a counting frame, typically wooden with balls sliding on wires. It was first used before the adoption of the ten-digit Arabic numeral system and is still widely used by small merchants in China.

The Roman abacus contains seven long and seven shorter rods or bars, the former having four perforated beads running on them and the latter one. This figure of a Roman abacus is taken from an ancient monument:

The bar marked 1 indicates units, X tens, and so on up to millions. The beads on the shorter bars denote fives,--five units, five tens, etc. The rod O and corresponding short rod are for marking ounces; and the short quarter rods for fractions of an ounce. Computations are made with it by means of balls of bone or ivory running on slender bamboo rods, similar to the simpler board, fitted up with beads strung on wires, which has been employed in teaching the rudiments of arithmetic in English schools.

The suanpan (算盤 or 筭盤 suan4 pan2) of the Chinese closely resembles the Roman abacus in its construction and use.

The Chinese abacus is usually around eight inches tall and it comes in various width depending on 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. The beads are usually round and made of hard wood. 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. The beads are counted by moving them up or down towards the beam. Chinese abacus does more than just counting. Unlike the simple counting board used in elementary schools, very efficient Suan4-Pan2 techniques were developed to do multiplication, division, addition, subtraction, square root and cubic root at high speed. The beads and rods were often lubricated to ensure speed. When all five beads in the lower deck are moved up, they are reset to the original position, and one bead in the top deck is moved down as a carry. When both beads in the upper deck are moved down, they are reset and a bead on the adjacent rod on the left is moved up as a carry. The result of the computation is read off from the beads clustered near the separator beam between the upper and lower deck. In a sense, the abacus works as a 5-2-5-2-5-2... 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, he simply adds another abacus to the left of the row. In theory, the abacus can be expanded infinitely.

As recently as the late 1960s, abacus arithmetics were still being taught in school (e.g. in Hong Kong). When hand held calculators became popular, nobody wanted to learn how to operate an abacus any more. In the early days of handheld calculators, news about abacus operators beating electronic calculator in arithmetics competitions in both speed and accuracy often appeared in the media. The main reason being that early calculators were often plagued by rounding and overflow errors. (Most handheld calculators can only handle 8 to 10 significant digits, the abacus is virtually limitless in precision.) Inexperienced operators might contribute to the loss too. But when calculators' functionality improved, everyone knew that the abacus could never compute complex functions (e.g. trignometry) faster than a calculator. The older generation (those who were born before the early 1950s) still used it for a while, but electronic calculators gradually displaced abacus in Hong Kong over the past four decades. As calculators became more affordable, abacus is hardly seen in Hong Kong nowadays. However, abacuses are still being used in China and Japan. The slide rules also suffered a similar demise.

The Suan4-Pan2 is closely tied to the Chinese "Hua1 Ma3" numbering system.

The Japanese eliminated one bead each from the upper and lower deck in each column of the Chinese abacus, because these beads are redundent. That makes the Japanese soroban (十露盤) more like the Roman abacus. The soroban is about 3 inches tall. The beans on a soroban are usually double cone shape.

Many sources also mentioned use of abacus in ancient Mayan culture. The Mesoamerican abacus is closely tied to the base-20 Mayan numerals system.