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Abaci GalleryAbacus, Suan Pan, Tschu Pan, Schoty, Soroban
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This is one of the newest galleries at ISRM, and was inspired by a donation of abaci from a couple of donors. As the ISRM curator, I have focused on logarithmic based calculating devices, also fondly known as slide rules, over the past 10 years, and have basically ignored other historic 'mechanical' calculators and methods. This was mostly because of lack of time and resources, but as I have come to learn about, and appreciate, the manufacturing art and long history of abaci in various cultures. I have become a great fan of 'bead math' or 'counting beads' and am just learning the intracacies of their use (and usefulness). I would never have believed that one could do square roots on them, along with multiplication and division, even though most people used them purely for addition and subtraction. As I acquired artifacts for the gallery, I was puzzled with many Japanese sorobans had upwards of 21 digits, or columns of beads. After all, the United States national debt is in the trillions which is 1012 and only needs 14 digits, counting two decimal points, to display. A good friend of mine, Jiro Higuchi in Japan, explained: "In Japan sorobans are still being manufactured for education. The reason why there are so many digits up to 27 is that, when the calculation of multiplication and division is carried out, the right part and the left part of soroban are used separately. (I am sorry I cannot do multiplication nor division by using soroban, but only addition and substraction) Sometimes they use the left part of soroban to store the result tentatively.". I now understand the significance of the dots on the bridge of sorobans. I was also surprised, when I started receiving these, at how small most are. The modern era (Showa) sorobans are approximately the same size as slide rules making them very portable, even for the pocket. If you are a regular visitor to ISRM you will have noticed the other new gallery on 'slide rule calculators' which was inspired by the 40th anniversary of the introduction of the HP-35 electronic slide rule, or scientific calculator. Within 5 years, the slide rule industry was out of business. What I did not stop to realize was that the abacus industry also was displaced by the basic electronic four-function calculator, creating significant changes in that part of Japanese manufacturing. I hope to learn more about this as together, we build this gallery. I hope you enjoy sharing the journey with me! As I do with the other galleries, I wish to get donations of abacus from users from different countries so that we can place a name and history with them. Please enjoy this gallery . Michael Konshak, ISRM Curator. |
Abacus is a Latin word meaning sand tray, that has its origins in the Greek words abax or abakon (meaning "table" or "tablet") which in turn, possibly originated from the Semitic word abq, meaning "sand"
Specimens for this gallery, currently under construction, are being acquired through selective purchases and donations by Friends of the Museum. As this gallery is being constructed, one of the best references for the history and use of Abaci is Totten Heffelfinger's website out of Toronto, Canada. Other references, images and texts are provided Wickipedia and other sources. |
Instructions on Calculating with Beads
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An Introduction to the Abacus
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Click Here to go to Abaci Ephemera
Historical and Modern Photos of people and locations showing an Abacus. Soroban, Schoty or Suan Pan. |
The Chinese Abacus was an early aid for mathematical computations. Its only value is that it aids the memory of the human performing the calculation. A skilled abacus operator can work on addition and subtraction problems at the speed of a person equipped with a hand calculator (multiplication and division are slower). The abacus is often wrongly attributed to China. In fact, the oldest surviving abacus was used in 300 B.C. by the Babylonians. The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.
Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a place holder. The zero was probably introduced to the Chinese in the Tang Dynasty (618-907 AD) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians. A publication of a French mathematical congress held in 1902 stated that the soroban replaced the use of bamboo rods at the end of the 16th century. According to Sal Restivo in Mathematics in Society and History: Sociological Inquiries (pp. 55-56) Chinese mathematics was in decline as Japanese interests were developing. "The scholar Mori Shigeyoshi [early to mid 17th century] who flourished in this period is Japan's first 'mathematician'. He is, according to legend, supposed to have traveled to China and returned with a knowledge of Chinese mathematical achievements and the suan-pan, a Chinese abacus. There is no historical basis for this story. The suan-pan was probably introduced to Japan much earlier. In any case, Mori was apparently a skilled manipulator of the suan-pan, known as the soroban in Japan . He taught the soroban arithmetic to many pupils, and may have written a text on the soroban, now lost." Two of Shigeyoshi's students wrote extant works which discussed the use of the soroban. Both wrote about square and cube root calculations and one of them also works on areas and volumes. Suanpan arithmetic was still being taught in school in Hong Kong as recently as the late 1960s, and in Republic of China into the 1990s. However, when hand held calculators became readily available, school children's willingness to learn the use of the suanpan decreased dramatically. In the early days of hand held calculators, news of suanpan operators beating electronic calculators in arithmetic competitions in both speed and accuracy often appeared in the media. Early electronic calculators could only handle 8 to 10 significant digits, whereas suanpans can be built to virtually limitless precision. But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the suanpan could never compute higher functions, such as those in trigonometry, faster than a calculator. Nowadays, as calculators have become more affordable, suanpans are not commonly used in Hong Kong or Taiwan, but many parents still send their children to private tutors or school- and government- sponsored after school activities to learn bead arithmetic as a learning aid and a stepping stone to faster and more accurate mental arithmetic, or as a matter of cultural preservation. Speed competitions are still held. Suanpans are still being used elsewhere in China and in Japan, as well as in some few places in Canada and the United States. In mainland China, formerly accountants and financial personnel had to pass certain graded examinations in bead arithmetic before they were qualified. Starting from about 2002 or 2004, this requirement has been entirely replaced by computer accounting.
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A Brief History of "Counting Beads" |
1899 Photo of Salamis Tablet c300B.C. | The Salamis Tablet was an early counting device (also known as a "counting board") dating from around 300 B.C. that was discovered on the island of Salamis in 1846. A precursor to the abacus, it is thought that it represents a Babylonian means of performing mathematical calculations common in the ancient world. Pebbles (calculus) were placed at various locations and could be moved as calculations were performed. The marble tablet itself has dimensions of approximately 150x75x4.5 cm Originally thought to be a gaming board, the slab of white marble is currently at the National Museum of Epigraphy, in Athens. As with an abacus, pebbles represent small numbers (generally between zero and four) and a system of lines serves to group them by powers of ten. A pebble between the lines represents a five. On this board, physical markers (indicators) were placed on the various rows or columns that represented different values. The indicators were not physically attached to the board. On the tablet Greek numbers are represented. |
Abacus using Pebbles in grooves | No actual specimens of the true Roman counting board are known to exist, but historic language in texts, the most reliable and conservative guardian of a past culture, has preserved the fact of the unattached counters. so faithfully, in fact, that we can discern this more clearly than if we possessed an actual counting board. What the Greeks called psephoi, the Romans called calculi. The Latin word calx means 'pebble' or 'gravel stone'; calculi are thus little stones (used as counters)." |
Roman Abacus. Bronze Replica by Joern Luetjen, Germany | A Roman hand abacus replica, owned by Professor Joern Luetjen's Abacus-OnLine-Museum. 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. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals. Instead of running on wires as in the Chinese and Japanese models, the beads of Roman model run in grooves, presumably making arithmetic calculations much slower. Both the Roman abacus and the Chinese suanpan have been used since ancient times. With one bead above and four below the bar, the systematic configuration of the Roman abacus is coincident to the modern Japanese Soroban, although the soroban is historically derived from the suanpan. |
Along The River by Zhang Zeduan, Saun Pan in Herbal Shop | In the famous long scroll Along the River During the Qingming Festival painted by Zhang Zeduan (1085-1145 AD) during the Song Dynasty (960-1297 AD), a suanpan is supposedly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's. However, the identification of the object as an abacus is a matter of some debate. |
Along The River by Zhang Zeduan Displayed at Ching Ming Festival |
The European Table Abacus (Circa 1299) | The European table abacus or reckoning table became standardized to some extent by this time. The pebbles previously used as counters were replaced by specially minted coin-like objects that were cast, thrown, or pushed on the abacus table. They were called jetons from jeter (to throw) in France, and werpgeld for "thrown money" in Holland. In the wood block shown on the left a wood block from Margarita Philosophica, 1508 by Gregor Reisch (1368-1644), shows a table abacus. |
A Baqua circular abacus (1368-1644) | A woman presents a Bagua (the Eight Diagrams) abacus of the Ming Dynasty (1368-1644) in Huizhou County, east China's Anhui Province July 17, 2006. This 50 digit abacus is approximately 30cm (11.8 inches) in diameter and allows the operator to shift the decimal point in either direction. |
Chinese Shop Owner Using Suan Pan | The Chinese Abacus or "Suan Pan" is largely unchanged since early records reaching back to ~500 B.C. The notation is bi-quinary: an upper deck selecting the 0-5 or 6-10 range, and the lower deck representing (in unary notation) 0-5 or 6-10. The beads are moved to add or subtract, and when all beads in a deck are up a carry to the next position is made. Multiplication and division are carried py repetetive addition and subtraction. Divison on an abacus was described in Latin by Bishop Gerbert of Navarro, Spain, who later, in AD. 999, become Pope Sylvester II. Known as the suànpán, (suànpán, lit. "Counting tray"), the Chinese abacus, is typically 20 cm (8 in) tall and comes in various widths depending on the operator. 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 for both decimal and hexadecimal computation. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. If you move them toward the beam, you count their value. If you move away, you don't count their value. The suanpan 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. Suanpans can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed. There are currently schools teaching students how to use it. |
Frozen Fish Market, St. Petersburg | |
Japanese Student Using Soroban, c1930 Japanese "Merchant Making Accounts" on Soroban by Artist Hokusai who is one of the main artists of the EDO school, known as "paintings of the floating world". He is also known for the diversity of names used throughout his professional career, Shunro, Sori, Kako, Taito, Gakyonjin, Iitsu and Manji. |
A Japanese abacus called "Soroban". The Japanese equivalent for 'reading, writing and arithmetic' is yomi, kaki, soroban. The soroban is supposedly more 'efficient', using only one and four beads, but requires different fingering. There are a wide variety in the number of digits or rods available on a Soroban (like the 1/4 37 digit shown above), which keep the same height but extend the length. The standard is 15 digits. The Roman Abacus used a similar configuration, somewhat matching the represenation by Roman numerals. The modern Showa era Japanese soraban, post 1930, are generally much smaller in width than the Chinese Suan Pan and Russian Schoty making them more portable as hand-held calculators. The date range of a soroban can be inferred due to the number of beads it contains (Google translates the Japanese word for 'beads' as 'pearls'). The Itsutsudama type Soroban was manufactured in Japan before 1850 and included a 2/5 bead combination (2 beads on the upper deck (Heavan) and 5 beads on the lower deck (Earth). The Japanese formally changed to a Mutsudama type Soroban in the early Meiji Period (1868-1912) which removed one of the '5' beads in heavan. Finally the modern Yotsudama style Soroban reduced the Earth beads to 4 in 1935 which was during the Showa period 1926-1989. This was because one 5-bead and four 1-beads were considered sufficient to do all the calculations. When primary school textbooks were revised in 1935, the four-beaded Yotsudama Soroban became the standard. The older Meiji Era wooden Japanese soroban were designed like an open box with a closed back. Soroban of this generations, that were designed especially for merchants, had nearly every row of beads identified in beautiful carved kanji with digit markers. More modern Japanese abacus have digit markers only every 3 or 4 rows. The older frames were commonly made of oak while the beads were boxwood. These soroban were likely made exclusively with traditional Japanese hand tools instead of modern power tools. Tools such as the nokogiri (Japanese pull saw) and kana (block plane) may have been used to carefully cut and shape each wooden part and to create the delicate and expert joinery which have held the abacus together all these years. |
Abacus, Suan Pan, Schoty, and Soroban Gallery |
ISRM Japanese Soroban 1/5 beads 15 digits |
Japanese Soroban 1/5 beads 15 digits Brand: Marks: a name of small trading company in Osaka, "Norokatsu Ltd." The top mark is the logo. Material: Black painted wood frame, bare oak bar, wood rods and black painted beads Age: c1930 Beads: 1/5 (1 above, 5 below), 19mm dia Digits/Columns: 15 Size: 33 x 11 x 3.5cm Frame Construction: mitered mortise and tenon joints |
Japanese Soroban 1/4 beads 13 digits ISRM 19.02.21.07 |
Japanese Soroban 1/4 beads 13 digits Brand: TBD Material: Black wood frame, bare oak bar, wood rods and wood beads Age: c1950 Beads: 1/4 (1 above, 4 below), 19mm dia Digits/Columns: 13 Size: TBD Frame Construction: All wood. Gift of Gregory and Joy Playle of Alexandria, Virginia. It was a gift from their father. |
Japanese Soroban 1/4 beads 15 digits ISRM 17.05.22.01 |
Japanese Soroban 1/4 beads 15 digits Brand: TBD Material: Black plastic frame, bare oak bar, wood rods and white beads Age: c1960 Beads: 1/5 (1 above, 4 below), 19mm dia Digits/Columns: 15 Size: ? x ? x 3.5cm Frame Construction: Molded plastic. Gift of Pam Eaton |
Lotus Flower Suan Pan 2/5 beads 15 digits ISRM |
Chinese Suan Pan - Lotus Flower 2/5 beads 15 digits Brand: Lotus Flower, People's Republic of China Material: Black painted wood frame, wood rods and black painted beads Age: Unknown Beads: 2/5 (2 above, 5 below) Digits/Columns: 13 Size: 25 x 11.8 x 2.3cm Frame Construction: mitered butt joints, brass corner reinforcements nailed to frame. Donated by Joel Haertling of Boulder, Colorado, after he saw the ISRM exhibit. |
Joel Haertling is the Film Program Coordinator for the Boulder Public Library Cinema Program. Joel Haertling has self-produced 23 films in 8mm and 16mm, alongside performing soundtracks for and/or acting in various Stan Brakhage films. Super 8mm films by Joel Haertling was released in Zurich in 1994, excerpts from his Boyd Rice Documentary were published by Mute Film (UK) in 1995, and others have been broadcast on cable in San Francisco, New York, Denver, Zurich (CH), and Boulder channels 8, 19, and 28. Joel began publishing the Zamizdat Trade Journal, a guide to self-published experimental music, in 1984 and continued with it for over a decade while writing for various other publications on the side. He has played the french horn in orchestra, and has created visuals for raves and live shows, He authored the Charles A. Haertlsing Architect A.I.A. web site. The latter is a dedication to his father. |
Nanjo & Co. - Chinese Suan Pan 2/5 beads 13 digits ISRM |
Nanjo & Co. - Chinese Suan Pan 2/5 beads 13 digits Brand: Nanjo & Co. Ltd. Nihonbashi, Tokyo, Japan, Manufacturers of "Sun" brand Soroban Material: Black painted wood frame, bare oak bar, wood rods and black painted beads Age: c1970 Beads: 2/5 (2 above, 5 below), 18mm dia Digits/Columns: 13 Size: 29 x 13 x 2cm Frame Construction: mortise and tenon joints |
Wang Way. - Chinese Suan Pan 2/5 beads 9 digits ISRM 22.05.06.01 |
Wang Way. - Chinese Suan Pan 2/5 beads 9 digits Made by Wang Way Mfg. 157 weilin St. Sham Shui PO, Hong Kong Material: Black painted wood frame, bare oak bar, wood rods and black painted beads Age: c1970 Beads: 2/5 (2 above, 5 below), 15mm dia x 8mm thick Digits/Columns: 13 Size: 19 x 13 x 2cm Frame Construction: mitered joints with brass plates. |
REF Russian Shoty 10 or 4 beads, 10 digits |
Russian Shoty 10 or 4 beads, 10 digits Brand: Unknown Material: Oak wood frame, curved steel rods and oak beads Age: Unknown Beads: 10b x 9 + 4b x 1 Note the 4 beads digit is for 1/4 Kopecks) Digits/Columns: 10 Size: 240 x 165 mm (9.6x 6.6") Archive internet photo. |
Chinese (China) 2/5 x 13d, 25x11.8x2.3cm black painted wood frame, wood rods, donation by Joel Haerting
Chinese (japan) 2/5 x 13d, 29x13x2cm black painted wood frame, oak bar. ebay