# Soroban

A modern soroban. Note that the user has manipulated the "five" and "one" beads to represent the number 1234567890

The soroban (算盤, そろばん?, counting tray) is an abacus developed in Japan. It is derived from the Chinese suanpan, imported to Japan in the 14th century.[1][nb 1] Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocket electronic calculators.

## Construction

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

The soroban is composed of an odd number of columns or rods, each having beads: one bead having a value of five, called go-dama (五玉, ごだま?, "five-bead") and four beads each having a value of one, called ichi-dama (一玉, いちだま?, "one-bead"). Each set of beads of each rod is divided by a bar known as a reckoning bar. The number and size of beads in each rod make a standard-sized 13-rod soroban much less bulky than a standard-sized suanpan of similar expressive power.

The number of rods in a soroban is always odd and never less than nine. Basic models usually have thirteen rods, but the number of rods on practical or standard models often increases to 21, 23, 27 or even 31, thus allowing calculation of more digits or representations of several different numbers at the same time. Each rod represents a digit, and a larger number of rods allows the representation of more digits, either in singular form or during operations.

The beads and rods are made of a variety of different materials. Most soroban made in Japan are made of wood and have 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 normally made of wood, although the beads of some soroban, especially those made outside Japan, can be marble, stone, or even plastic. The cost of a soroban can increase depending on the materials.

One unique feature that sets the soroban apart 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.

## Usage

### Representation of numbers

The soroban uses a decimal system, where each of the rods can represent a single digit from 0 to 9. By moving beads towards the reckoning bar, they are put in the "on" position; i.e., they assume value. For the "five bead" this means it is moved downwards, while "one beads" are moved upwards. In this manner, all digits from 0 to 9 can be represented by different configurations of beads, as shown below:

 0 1 2 3 4 5 6 7 8 9

These digits can subsequently be used to represent multiple-digit numbers. This is done in the same way as in Western, decimal notation: the rightmost digit represents units, the one to the left of it represents tens, etc. The number 8036, for instance, is represented by the following configuration:

 8 0 3 6

The soroban user is free to choose which rod is used for the units; typically this will be one of the rods marked with a dot (see the 6 in the example above). Any digits to the right of the units represent decimals: tenths, hundredths, etc. In order to change 8036 into 80.36, for instance, the user places the digits in such a way that the 0 falls on a rod marked with a dot:

 8 0. 3 6

### Methods of operation

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

There are many methods to perform both multiplication and division on a soroban, 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. These methods were chosen for efficiency and speed in calculation.

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

## Modern use

A dual soroban-calculator, SHARP ELSI MATE EL-8048, produced from 1979

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

The soroban is taught in primary schools as a part of lessons in mathematics because the decimal number system can be demonstrated visually. When teaching the soroban, teachers give song-like instructions. Primary school students often bring two soroban to class, one with the modern configuration and the one having the older configuration of one heavenly bead and five earth beads.

People who become proficient in use of soroban almost automatically become adept at mental calculation, known as anzan (暗算?, "blind calculation") in Japanese. As a part of soroban instruction, intermediate students are asked to do calculation mentally by visualizing the soroban (or any other abacus) and working out the problem without trying to figure out the answer beforehand. This is one reason why, despite the advent of handheld calculators, some parents send their children to private tutors to learn the soroban.

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

## Brief history

The soroban's physical resemblance is derived from the suanpan but the number of beads is identical to 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 around the 14th century.[1][nb 1] 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 Kōwa, 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. In 1891, Irie Garyū further removed one earth bead, forming the modern configuration of one heavenly bead and four earth beads.[4] This configuration was later reintroduced in 1930 and became popular in the 1940s.

Also, when the suanpan was imported to Japan, it came along with its division table. The method of 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's present form was reintroduced 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, first suggested by mathematician Momokawa Chubei in 1645,[5] and therefore had to compete with the division table during the latter's heyday.

## Comparison with the electric 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 basis for scoring in the contest was 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.[6]

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

The breakdown of results is as follows:

• Five additions problems for each heat, each problem consisting of 50 three- to six-digit numbers. The soroban won in two successive 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 heats; 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.

## Notes

1. ^ a b Some sources give a date of introduction of around 1600.[2]

## Footnotes

1. ^ a b Gullberg 1997, p. 169
2. ^ Fernandes 2013
3. ^ Kojima, Takashi (1954). The Japanese Abacus: its Use and Theory. Tokyo: Charles E. Tuttle. ISBN 0-8048-0278-5.
4. ^ Frédéric, Louis (2005). "Japan encyclopedia". translated by Käthe Roth. Harvard University Press. pp. 303, 903.
5. ^ Smith, David Eugene; Mikami, Yoshio (1914). "Chapter III: The Development of the Soroban.". A History of Japanese Mathematics. The Open Court Publishing. pp. 43–44. Free digital copy available at Questia.
6. ^ Stoddard, Edward (1994). Speed Mathematics Simplified. Dover. p. 12.

## References

• Kojima, Takashi (1963). Advanced Abacus: Japanese Theory and Practice. Tokyo: Charles E. Tuttle.