Soroban
Encyclopedia
Abacus
The abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of...
developed in Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
. It is derived from the Chinese
Culture of China
Chinese culture is one of the world's oldest and most complex. The area in which the culture is dominant covers a large geographical region in eastern Asia with customs and traditions varying greatly between towns, cities and provinces...
suanpan, imported from China via Korea
Korea
Korea ) is an East Asian geographic region that is currently divided into two separate sovereign states — North Korea and South Korea. Located on the Korean Peninsula, Korea is bordered by the People's Republic of China to the northwest, Russia to the northeast, and is separated from Japan to the...
to Japan around 1600. Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocket electronic calculators.
Construction
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
Rattan
Rattan is the name for the roughly 600 species of palms in the tribe Calameae, native to tropical regions of Africa, Asia and Australasia.- Structure :...
, or bamboo
Bamboo
Bamboo is a group of perennial evergreens in the true grass family Poaceae, subfamily Bambusoideae, tribe Bambuseae. Giant bamboos are the largest members of the grass family....
rods for the beads to slide on. The beads themselves are usually biconal
Bicone
A bicone or dicone is the three-dimensional geometric shape swept by revolving an isosceles triangle around its edge of unequal length. Alternatively, one can view a bicone as the surface created by joining two identical right circular cones base-to-base....
(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
Marble
Marble is a metamorphic rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite.Geologists use the term "marble" to refer to metamorphosed limestone; however stonemasons use the term more broadly to encompass unmetamorphosed limestone.Marble is commonly used for...
, 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.
Methods of operation
The methods of additionAddition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
and subtraction
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
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
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
and division
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
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
Multiplication table
In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system....
. These methods were chosen for efficiency and speed in calculating.
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 "earth" beads and one "heavenly" bead.
Modern use
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. 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
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
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
Mental calculation
Mental calculation comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper. People use mental calculation when computing tools are not available, when it is faster than other means of calculation , or in a competition context...
, known as 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 to the Chinese suanpan, clearly indicates its origin. The number of beads, however, is similar to the Roman abacusRoman abacus
The Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of the previous Babylonian abacus. It was the first portable calculating device for engineers, merchants and presumably tax collectors...
, 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
Hexadecimal
In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
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. 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 it its division table. The method of using the table was called in Japanese, while the table itself was called the . The division table used along with the suanpan was more popular because of the original hexadecimal configuration of Japanese currency
Japanese currency
Japanese currency has a history covering the period from the 8th century to the present. After the traditional usage of rice as currency medium, Japan's currency was characterized by an early adoption of currency systems and designs from mainland China, before developing into an original system of...
. 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
Counting rods
Counting rods are small bars, typically 3–14 cm long, used by mathematicians for calculation in China, Japan, Korea, and Vietnam. They are placed either horizontally or vertically to represent any number and any fraction....
, first suggested by mathematician Momokawa Chubei in 1645, and therefore had to compete with the division table during the latter's heyday.
Soroban vs. 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 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, while the Stars and Stripes
Stars and Stripes (newspaper)
Stars and Stripes is a news source that operates from inside the United States Department of Defense but is editorially separate from it. The First Amendment protection which Stars and Stripes enjoys is safeguarded by Congress to whom an independent ombudsman, who serves the readers' interests,...
newspaper described the soroban's "decisive" victory as an event in which "the machine age
Machine Age
The Machine Age is a term associated mostly with the early 20th century, sometimes also including the late 19th century. An approximate dating would be about 1880 to 1945. Considered to be at a peak in the time between the first and second world wars, it forms a late part of the Industrial 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 contestNo contest (boxing)No contest is a technical term used in some combat sports to describe a fight that ends for reasons outside the fighters' hands.-Boxing:...
. - 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
Technology
Technology is the making, usage, and knowledge of tools, machines, techniques, crafts, systems or methods of organization in order to solve a problem or perform a specific function. It can also refer to the collection of such tools, machinery, and procedures. The word technology comes ;...
involving calculators, this event has yet to be replicated officially.