The abacus is the oldest calculating tool still in everyday use. It has outlived the slide rule, the mechanical adding machine and the pocket calculator's LED screen. In 1946, in a public contest in Tokyo, one beat an electric calculator, and it was not close.
The oldest calculator
Before beads there were counting boards: a table ruled into columns, with pebbles moved between them. The Sumerians are thought to have used something like this between 2700 and 2300 BC. The Latin word for pebble, calculus, is where “calculate” comes from.
The oldest counting board that survives is the Salamis Tablet, a slab of white marble about 150 by 75 cm, found on the Greek island of Salamis in 1846 and dated to around 300 BC. It was first taken for a games board. It is now in the Epigraphical Museum in Athens. By the 1st century AD the Romans had a hand abacus small enough to carry, with beads sliding in grooves.
How beads become numbers
Each rod holds one digit: units on the right, then tens, then hundreds. Beads pushed towards the bar across the middle count; beads pushed away do not.
On a Japanese soroban, the single bead above the bar is worth five and each of the four below it is worth one. Every digit from 0 to 9 is some mix of those. Here is 1,946, the year of the Tokyo contest:
Adding when a rod runs out: 7 + 5
This is the part that makes the soroban fast. Suppose the units rod shows 7 (the upper bead and two lower beads) and you want to add 5. There is no second upper bead to push down. So you think of 5 as “10 take away 5”:
- Push up the upper bead on the units rod (take away 5). The rod now shows 2.
- Push up one lower bead on the tens rod (add 10).
- Read the answer: 1 ten and 2 units, 12.
Trained users do not think these steps through. Each pair of numbers becomes a single hand movement, much as a touch typist does not think about which finger hits which key. That is where the speed comes from.
Three famous designs
| Name | Where | Beads | Story |
|---|---|---|---|
| Suanpan | China | 2 above, 5 below | The earliest written mention usually cited is from 190 AD, though historians argue over whether it means a bead abacus. The standard form was fixed by the Ming dynasty. China's abacus tradition, zhusuan, was added to UNESCO's list of intangible cultural heritage in 2013. |
| Soroban | Japan | 1 above, 4 below | Came from China by the 16th century. The slimmer one-and-four layout became standard in the 1930s and 1940s. |
| Schoty | Russia | 10 per wire | No dividing bar; the fifth and sixth beads are a different colour to help the eye. The French mathematician Jean-Victor Poncelet, a prisoner of war in Russia after 1812, introduced it to France around 1820. It only lost ground in the USSR after cheap calculators arrived in 1974. |
The day the abacus won
Tokyo, 12 November 1946
At the Ernie Pyle Theater, Kiyoshi Matsuzaki, a champion soroban operator from the savings bureau of Japan's Ministry of Postal Administration, sat down against Private Thomas Nathan Wood of the US Army's 20th Finance Disbursing Section. Wood had won an arithmetic contest to be named the most expert operator of the electric calculator in Japan.
They met over five events: addition, subtraction, multiplication, division, and a composite problem using all four. In the first addition heat Matsuzaki finished in 1 minute 14.9 seconds. Wood took 2 minutes 0.2 seconds. The abacus won four events to one; the machine took only multiplication. The US forces newspaper Stars and Stripes did not dress it up: “The abacus victory was decisive.”
The result says less about beads versus electricity than about skill. A trained operator with an abacus was faster, for everyday arithmetic, than the electro-mechanical machines of the 1940s. It took the electronic calculator of the 1970s to change that for good.
The abacus in your head
Experienced soroban users can put the frame away and calculate by picturing the beads, a skill called mental abacus (anzan in Japanese). Research has looked at what is going on.
- A study by the psychologists Michael Frank and David Barner of children in Gujarat, India, found that users hold the imagined abacus in visual memory, three or four columns at a time. Repeating words aloud disrupted them only modestly, and simple finger-tapping disrupted them as much or more. Children without abacus training were thrown far more by the talking. The trained children were not reciting number facts; they were watching beads.
- A three-year randomised trial with 183 children in Vadodara, India, published in 2016, found clear gains in arithmetic for those taught mental abacus. It found no improvement in broader thinking skills or working memory.
- A one-year classroom trial in the US found no significant advantage in either maths or general ability.
So the fair summary is: mental abacus can make children very good at arithmetic when taught well and for long enough. It is not a general brain-training method, whatever some after-school programmes suggest.
Still in use
- In Japan. The Japan Chamber of Commerce and Industry still runs graded soroban exams, and a certificate at third grade or above has long been treated as a useful qualification by Japanese employers.
- For blind students. In 1962 Tim Cranmer, who worked for Kentucky's services for the blind, designed an abacus with a soft backing that stops the beads moving when touched, and raised dots to help find the place. The American Printing House for the Blind still makes the Cranmer abacus. It handles addition, subtraction, multiplication, division and roots.
- In classrooms everywhere, as the simplest way to show a child what “place value” means. The rod is the column.
Quick answers
How old is the abacus?
Counting boards go back to the Sumerians, around 2700 to 2300 BC. The oldest surviving one, the Salamis Tablet, dates from about 300 BC. Bead abacuses were in use in China by the Ming dynasty and probably much earlier.
What is the difference between a soroban and a suanpan?
The Chinese suanpan has two beads above the bar and five below. The Japanese soroban has one above and four below, which is all you need for the digits 0 to 9.
Is an abacus faster than a calculator?
For addition and subtraction, a trained operator can be faster than someone keying the same sums into a calculator. In 1946 a soroban champion beat an electric calculator four events to one in Tokyo.
Does learning the abacus make children smarter?
It can make them much better at arithmetic. A three-year trial in India found clear maths gains but no improvement in general thinking skills or memory.
Sources
- Wikipedia, “Abacus”; Wikipedia, “Soroban”; Wikipedia, “Suanpan”
- Wikipedia, “Salamis Tablet”; Computer History Museum, the Salamis Tablet
- UNESCO, Chinese Zhusuan (2013)
- Takashi Kojima, The Japanese Abacus: Its Use and Theory (Tuttle, 1954), account of the 1946 contest, reproduced here
- Michael C. Frank and David Barner, “Representing Exact Number Visually Using Mental Abacus”, Journal of Experimental Psychology: General.
- David Barner et al., “Learning Mathematics in a Visuospatial Format”, Child Development 87 (2016); summary by the British Psychological Society
- Journal of Numerical Cognition, US classroom trial of mental abacus
- Smithsonian NMAH, Cranmer abacus; National Federation of the Blind, Tim Cranmer obituary