Soroban

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Should not be confused with the Japanese rock band Soroban.
A soroban. Note that the user's hand seen here seem to appear that the user is left-handed as most users would operate the soroban with the right.
A soroban. Note that the user's hand seen here seem to appear that the user is left-handed as most users would operate the soroban with the right.

The soroban (算盤, そろばん? counting tray) is an abacus developed in Japan. It is derived from the suanpan, imported from China to Japan through Korea around 1600.[1] [2] Like the suanpan, the soroban is still used in Japan today, even with the proliferation, practicality, and affordability of pocket electronic calculators.

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[edit] Construction

A suanpan (top) and a soroban (bottom). The two abaci seen here are of standard size and have thirteen rods each.
A suanpan (top) and a soroban (bottom). The two abaci seen here are of standard size and have thirteen rods each.

It is composed of an odd number of columns or rods, each having five beads: one bead valuing at five (called a heavenly bead) and four beads valuing at one (called an earth bead). Each set of beads of each rod is divided by a bar known as a reckoning bar. The number of beads in each rod make a standard-sized 13-rod soroban much less bulky than a standard-sized suanpan of similar size and length.

The number of rods in a soroban is always odd and it can never have less than nine rods. The most basic models usually have thirteen rods, but the number of rods on practical or standard models usually increase to 21, 23, 27 or even 31, thus allowing calculation for more digits or representations of several different numbers at the same time. Each rod represents a digit and the increasing number of rods can equate the number of digits either in singular form or during an operation.

The beads and/or the rods are made of a variety of different materials. Most soroban made in Japan are mostly made of wood with either wood, metal, rattan, or bamboo rods for the beads to slide on. The beads themselves are usually biconal (shaped like a double-cone). They are usually made of wood, although those of some soroban, especially those made outside Japan, can be either marble, stone, or even plastic and the cost of each soroban can increase depending on the materials.

One unique feature that sets the soroban from its Chinese cousin is a dot marking every third rod in a soroban. These are unit rods and any one of them is designated to denote the last digit of the whole number part of the calculation answer. Any number that is represented on rods to the right of this designated rod is part of the decimal part of the answer, unless the number is part of a division or multiplication calculation. Unit rods to the left of the designated one also aid in place value by denoting the groups in the number (such as thousands, millions, etc.). Suanpan usually do not have this feature.

[edit] Methods of operation

The methods of addition and subtraction in a soroban are basically the same as operating on a suanpan, with basic adding and subtracting and making use of a complementary number to add or subtract ten in carrying over.

For the soroban, there are many methods for both multiplication and division, especially Chinese methods that came with the importation of the suanpan. The authority in Japan on the soroban, the Japan Abacus Committee, has recommended so-called standard methods for both multiplication and division which require only the use of the multiplication table to solve. These methods were chosen for efficiency and speed in calculating.

Because the soroban is developed through the reduction of beads from seven, to six, and then to the present five, these methods can be used on the suanpan as well as soroban produced before the 1930s, which have five "earth" beads and one "heavenly" bead.

[edit] Modern usage

Despite the popularity of calculators, the soroban is very much in use today. Even today, the Japanese Chamber of Commerce and Industry has been conducting examinations for soroban users to obtain licenses.[3] There are six levels of mastery, starting from sixth-grade (which ranks as very skilled) all the way up to first-grade (for those who completely master the soroban's use). Those obtaining at least a third-grade license are qualified to work in public corporations.

The use of the soroban is taught in primary schools as a part of lessons in mathematics because the decimal numerical system can be demonstrated visually. When teaching the soroban, a song-like instruction is given by the teacher. Often, primary school students may bring along with them two sorobans, one with modern configuration and the one having the older configuration of one heavenly bead and five earth beads.

Experts on using the soroban have also been known to use mental calculation, also known in Japanese as anzan (暗算? "blind calculation") or ànsuàn in Mandarin Chinese. They do this by visualizing the soroban (or any other abacus) on one's head and work out the problem without trying to figure out the answer beforehand. This is why despite the advent of handheld calculators, some parents send their children to private tutors to learn using the soroban as proficiency in soroban calculation can be easily converted to mental arithmetic at a highly advanced level.

The soroban is also the basis for two kinds of abaci developed for the use of blind people in their calculations. One is the toggle-type abacus wherein flip switches are used instead of beads. The second is the Cramner abacus which has circular beads, longer rods, and a leather backcover so the beads would not slide around when in use.

[edit] Brief history

Although it is still debated, the soroban's modern construction has a similarity to that of the Roman abacus, which had four beads below and one at the top.

Most historians on the soroban agree that it has its roots on the suanpan's importation to Japan via the Korean peninsula in the 15th century. When the suanpan first became native to Japan as the soroban (with its beads modified for ease of use), it had two heavenly beads and five earth beads. But the soroban was not widely used until the 17th century, although it was in use by Japanese merchants since its introduction. Once the soroban became popularly known, several Japanese mathematicians, including Seki Kowa, studied it extensively. These studies became evident on the improvements on the soroban itself and the operations used on it.

In the construction of the soroban itself, the number of beads had begun to decrease, especially at a time when the basis for Japanese currency was shifted from hexadecimal to decimal. In around 1850, one heavenly bead was removed from the suanpan configuration of two heavenly beads and five earth beads. This new Japanese configuration existed concurrently with the suanpan until the start of the Meiji era, after which the suanpan fell completely out of use. Later in 1930, one earth bead was further removed, forming the modern configuration of one heavenly bead and four earth beads. This configuration became popular in the 1940s. Meanwhile, the soroban's Meiji-era form still survives in Korea today as the supan.

A modern representation of the now obsolete division table.
A modern representation of the now obsolete division table.

Also, when the suanpan was imported to Japan, it came along with it its division table. The method using the table was called kyūkihō (九帰法? "nine returning method") in Japanese, while the table itself was called the hassan (八算? "eight calculation"). The division table used along with the suanpan was more popular because of the original hexadecimal configuration of Japanese currency. But because using the division table was complicated and it should be remembered along with the multiplication table, it soon fell out in 1935 (soon after the soroban took its present form in 1930), with a so-called standard method replacing the use of the division table. This standard method of division, recommended today by the Japan Abacus Committee, was in fact an old method which used counting rods and therefore had to compete with the division table during the latter's heyday.

[edit] Soroban vs. calculator

On November 12, 1946, a contest was held in Tokyo between the Japanese soroban, used by Kiyoshi Matsuzaki, and an electric calculator, operated by US Army Private Thomas Nathan Wood. The bases for scoring in the contest were speed and accuracy of results in all four basic arithmetic operations and a problem which combines all four. The soroban won 4 to 1 with the electric calculator prevailing in multiplication.

About the event, the Nippon Times newspaper reported that "Civilization... tottered" that day because of the event, while the Stars and Stripes newspaper remarked the soroban's "decisive" victory as an event in which "the machine age took a step backward...."

The breakdown of results are as follows:

  • Five additions problems for each heat, each problem consisting of 50 three- to six-digit numbers. The soroban won in two succeeding heats.
  • Five subtraction problems for each heat, each problem having six- to eight-digit minuends and subtrahends. The soroban won in the first and third heads; the second heat was a no contest.
  • Five multiplication problems, each problem having five- to 12-digit factors. The calculator won in the first and third heats; the soroban won on the second.
  • Five division problems, each problem having five- to 12-digit dividends and divisors. The soroban won in the first and third heats; the calculator won on the second.
  • A composite problem which the soroban answered correctly and won on this round. It consisted of:
    • An addition problem involving 30 six-digit numbers
    • Three subtraction problems, each with two six-digit numbers
    • Three multiplication problems, each with two figures containing a total of five to twelve digits
    • Three division problems, each with two figures containing a total of five to twelve digits

Even with the improvement of technology involving calculators, this event has yet to be replicated officially.

[edit] See also

[edit] References

  1. ^ abacus
  2. ^ The Abacus: A Brief History
  3. ^ Kojima (1954); see below

[edit] External links