THE ABACUS

by

Gina Simmons

Gulf Coast Community College

April 2000

 

        In a society of computers and spreadsheet programs, it is difficult to remember a time when calculations were not done with the aid of a machine. In this new millennium, even the simple calculator is becoming an archaic tool. If we were to go back in time, to a moment when mathematicians of yesteryear were busy configuring, we would probably find them holding---the Abacus.

        To American society, the abacus may seem a simplistic tool for calculating, easily replaced by a calculator or an adding machine.  However, in many Asian countries the abacus is used by shopkeepers, merchants and accountants and considered more reliable than mechanical devices. Contrary to popular belief, the abacus is not a calculator; it is actually an aid for keeping track of several calculations already made.

        There is some dispute as to the meaning of the word Abacus and were it is derived. According to Encyclopaedia Britannica, it was “probably derived through its Greek form ‘abakos’, from a Semitic word such as the Hebrew ‘ibec’ [meaning] ‘to wipe the dust’ or the noun abaq meaning ‘dust’” (7). However, Karl Menninger in his book, Number Words and Number Symbols-A Cultural History of Numbers disagrees. He feels the word actually came from the Greek word “abax’ meaning “stemless cup’ or from the Romans who had ornate display tables which were called “Abacus” (301).

        Before calculating devices, computations were either done in the head, on fingers, or by tallying. These sums were then noted in the sand or on flat surfaces covered with sand. The earliest evidence of permanent notation was recovered in1854 near Babylon, called the Senkereh Tablet which dates back to 2300-1600 BC. There are marks on it made by a wedge shaped instrument and is thought to have been used for keeping track of calculations. (Pullman, 2).

        As counting evolved to “reckoning”, which literally means, “to compute” stones and pebbles were used to keep track of groups. Most reckoning was done on counting boards held in hand; some were small tables with parallel lines carved into them. Like the abacus the parallel lines represented numerical values but values were changeable and the counters were removable and could be repositioned.

        The earliest known counting board used by ancient Babylonians was discovered in 1899. Aptly named, The Salamis Tablet was found on the island of Salamis. It is made of marble, which helped it to survive the erosion of time, and dates back to 300 B.C. The tablet is marked at the top with a group of five small parallel lines chiseled onto the stone. Further down, towards the lower end of the tablet, are eleven longer parallel lines, a straight line runs down the center of the lower group. On the sides and bottom of the tablet are several Greek numerical and monetary denominational symbols. “These symbols for numerical values testify that the tablet was actually used for computations, very likely in governmental financial offices…” (Menninger, 299). It is believed that the use of the abacus spread from the Greeks to the Romans.

        Roman artwork dating back to the 1st Century A.D. depicts the use of the abacus to compute estate values in Roman society. It was also discovered that the Romans used a miniature version, known as a hand abacus, for smaller computations; only two such abaci still exist today. This abacus, unlike the Salamis Tablet, had eight vertically parallel grooves, which were called “alveoli”. Within the grooves were small permanent counters known as “claviculi”, which means, “little nails”. The claviculi were moved up and down the groove much like the modern abacus.

       
The use of the abacus spread with the growth of the Roman Empire and its influence on other cultures; the spread of Christianity carried it further. It traveled as far as Europe but did not really become standard and eventually died out. Contrarily, the abacus moved as far East as China where it is called a “suapan”. The word “suan” means “to calculate” and the Chinese written character for this, when broken down, literally means “…two hands holding a reckoning board of bamboo.” (Menninger, 310). Historical records show its arrival somewhere around the 12th Century and becoming standard by the 13th Century.

        Unlike the Roman hand abacus wooden beads were strung on wire or strings. Pictured at the beginning of this report is a Chinese suapan. In the upper deck two beads are present on each rod, each bead represents a value of five.  A horizontal beam divides the upper deck from the lower deck. The beads in the lower deck have a value of one. Like the tallying sticks, the user would raise, toward the beam, up to five beads in the lower deck. If the value is larger than five, he would then slide the four back into place and move to the upper deck lowering one bead toward the beam to represent a unit of five. Likewise, the user would count up to nine on the first row then lower two beads from the first column in the upper deck to represent ten and carry over to the next column the remaining values. So, to make the value 538 the user would move, on the first column, one bead down in the upper section and three beads up in the lower section. He would the move to the second row and place three beads up in the lower section. Then move to the third row and move down one bead from the upper section. If a decimal was needed the user would divide the abacus vertically using the columns to the right for fractional numbers, then skipping a row which would hold the decimal place and using all columns to the left for whole number values. Louis Fernandes has developed a web site, known as The Art of Calculating with Beads, dedicated to the abacus. One can learn anything from the history and construction to the interactive teaching of abacus technique.

        The movement of the abacus did not stop in China, it continued to spread into Korea and on into Japan, where it is named the “Soroban”. It appeared in Japan around the 16th Century. Mastery of the soroban in Japan, as well as the suapan in China, is taught at the youngest levels of schoolchildren. One can even find a school Online, which not only sells sorobans but teaches the art of the technique as well. (Soroban) The Japanese soroban is much like the Chinese suapan, except it holds a total of six beads on each of its “keta” meaning “row” or “wire”. Each keta has a horizontal beam, known as a ‘crosspiece’. The crosspiece divides the soroban into an upper deck, known as heaven and a lower deck, known as earth. The bead in heaven is worth a unit of five and the beads in earth are units of one. Like the suapan, work the soroban starting from the far right keta and moving across to the left.

        Russia also has its own version of the abacus, called a “Scet”. Unlike the other abaci, it is set horizontally, moving the beads from left to right rather than up and down. It is from Russia that the abacus made its way back to the west. After Napoleon’s invasion, the Russian army captured one of his lieutenants, Poncelet.  Having witnessed the use of the abacus while in captivity, Poncelet , brought the abacus back to France where it again spread throughout Europe and finally moved into America. “Thus it may well be said that the Roman hand abacus has come down to us by way of a long detour through Asia.” (Menninger, 315)

        Recent discoveries have shown that the abacus was actually introduced into the Americas even earlier. The Mesoamerican abacus, also known as the Aztec or Nepohualtzitzin abacus date back to 900-1000 A. D. It is constructed much like the Chinese abacus except that maize was strung on string in rows of 7 by columns of 13.These numbers are extremely important to the MesoAmerican culture. Seven is multiplied by the sum of two other sacred numbers, 9 and 13 which equals 819. This is the number of days in a Mayan cycle. The number 13 also refers to the number of days in a calendar year. In the Aztec culture, the number 13 symbolizes the thirteen levels of heaven. There are thirteen birds, which serve as patrons of the daylight hours and thirteen different gods who accompany each day. Thirteen is also the total number of members on the Aztec Supreme Council.

        Today, the abacus is relied upon in the merchant dealings of many Asian countries. In a contest held in Tokyo, Japan on Novemeber11,1946, an abacus expert named Kiyoshi Malsuzaki went up against a private Thomas Nathan Wood using an American office machine and won. A week later in a similar contest in New York, a Chinese university student competed against a payroll operator with an adding machine. The abacus again won by 8 seconds. (Yosino, vi). Because the computations are still figured in the mind with an abacus, the student remains sharp on his mathematical skills.

        Whether adding, subtracting, multiplying or dividing, the abacus has the capability of keeping track of every equation just as well as the calculator. As simplistic as it may seem, the abacus is actually a more efficient and reliable tool. With its long history, it has continually proven its value to estate owners, merchants and school children. Yet, as reliable as it is, it is only as good as its user.

 

 

References
 

“Abacus.” The New Encyclopedia Britannica:Micropedia. 1987.

“An Abacus”. What is?.com Online. Tech Target. America Online. 3 March 00

Chinese Abacus. Online. America Online. 29 March 00

            Available at: http://www.qi-journal.com/abacus.html.

Fernandes, Luis. The Abacus: The Art of Calculating With Beads.  Math History      

            Online. 17 March 00.

Loy, Jim. The Abacus. Online. Dogpile. 10 March 00

Menninger, Karl. Number Words and Number Symbols: A Cultural History of Numbers

            Cambridge: MIT, 1969.

Pullman, J. M. The History of the Abacus. New York: Praeger, 1968.

Tomoe Soroban. Online. America Online. 10 March 00

            Available at: http://www.soroban.com/index 2.html

Yoshino, Y. The Japanese Abacus Explained. New York: Dover, 1963.