The Abacus


Sergio Puche García


This page aims to combine the spreading of knowledge about the history of computing and calculating machines, and more specifically the abacus, with fun and direct contact with these devices. Although it is not possible to provide the reader of this page with a real abacus, it is possible to put at his disposal three virtual abacuses that are identical replicas in their operation to their analog counterparts. The user is invited and adviced to use these three small applications, which will provide a closer and more practical knowledge about the operational mechanisms of the different abacuses.

The three projects have been developed using the Scratch language and environment, which is mainly aimed at bringing the learning of programming to children and young people. However, Scratch is a perfectly valid language for anyone, novice or experts, with the desire to have fun programming small, entertaining and visual applications. The reader is invited to visit their website and take a look at the many interesting projects there stored and, if motivated enough, to also become an Scratcher: Scratch official website

Historical introduction

The first abacuses

The origins of the different instruments that we nowadays encompass under the concept of abacus lie in stone calculation techniques.

Since this method could only be used to count relatively small quantities (depending on the number of pebbles the user had on hand), a kind of plank now known as <<calculating board>> was invented. This utensil consisted of a board or table with different marks that indicated different numerical values. When depositing the pebbles on one or the other of these marks, they acquired some or other values. It is believed that these artifacts could have originated in Sumeria along with the first merchants, but the first abacus of this type conserved is the Tabla de Salamina, of Greek origins, which can be seen in the image below.

Tabla de Salamina

Later on, the Romans developed the first abacus of the kind which we know today, that is, a table with several beads or displaceable pieces embedded in it. This pocket abacus, which seems to have never been as popular among Romans as the <<calculating board>>, was metallic with various columns in which the beads were embedded. According to which column they belonged to, the accounts had one or another associated value, in general multiples of 10 (one column for the units, another for the tens, for the hundreds, etc.), except for the elements on the right side, that were used to perform accounts with the different types of Roman coins. This system, with multiple changes but maintaining the same essence, is what remains in the abacus used to date.

Ábaco romano

Three abacuses

The Chinese abacus or suanpan

During the Middle Ages, specifically around the 12th century, an abacus of displaceable embedded pieces was developed in China, possibly the oldest surviving one still in use until today. Its mechanism is very similar to that of the Roman abacus, so it is thought that it could have been created by drawing inspiration from it, perhaps through some commercial exchange between the two empires.

This abacus is composed of two parts, the upper one and the lower one, divided by a central wood. Each rod has five accounts at the bottom, with a value of 1, and two at the top, with an associated value of 5. These base values are then multiplied by the exponent of 10 associated with that column (1, 10, 100…). To add we must move the accounts towards the central part of the abacus, that is, raise the accounts of the lower part or lower those of the upper one.

Ábaco chino o suanpan

The Russian abacus or schoty

Something later is the Russian abacus or schoty, mentioned for the first time in 1658. Like the suanpan, the schoty can still be seen in some small Russian shops as a tool used to perform quick and reliable calculation. The Russian abacus, unlike the Chinese one, is operated in a vertical position, that is, moving the beads along the rod horizontally, specifically from left (starting position) to right to add a quantity, and vice versa to subtract it. It consists of several rows (usually eight or more) with ten accounts in each, except one that has only four and that was used to calculate the polushki, the smallest currency in the Russian monetary system, which equaled to a quarter of kopek. The rods under this row are those used to represent decimals.

The two central accounts of each rod are usually of a different color, usually black, compared to the rest that are white, which helps avoid confusion when operating. In addition, the rods are usually slightly curved to prevent involuntary movements.

Ábaco ruso o schoty

The Japanese abacus or soroban

The Japanese abacus or soroban is a derivation of the Chinese abacus, introduced in Japan around the year 1600, after the Japanese invasion of Korea. It seems that it shared the same structure as the Chinese suanpan until the middle of the 19th century, when it lost one of the two accounts at the top. During the first half of the 20th century, one of the pieces below was also suppressed, with which the soroban acquired its definitive shape. These changes eliminated the redundancies of the Chinese abacus, which might represent a number of different forms because each rod can add up to 15 units. That is why many authors consider the soroban as the abacus in its ultimate form, facilitating movements as fast and efficient as possible. In fact, the anecdote is known by which the champion of soroban Japanese was faced in a competition of rapid calculation to a soldier of the US Navy expert in the use of electromechanical calculators after the Second World War. The result was that the abacus master defeated the soldier and his calculator in both speed and accuracy.

The soroban is identical to the Chinese abacus in its operation and structure, except for the already commented detail that it has two less accounts on each rod, one above and one below. Therefore, each column of a Japanese abacus has four beads at the bottom, each with a value of 1, and one at the top with a value of 5, so that each rod can be user to count from 0 to 9, and to represent the numer 10 we would have to replenish the accounts of the current column to its initial position and instead move towards the center an account from the bottom part of the next column (to the left).

Ábaco japonés o soroban

About the author

These apps and webpage were by the student from the UPV Sergio Puche García for his final degree work under the tutelage of Professor Xavier Molero Prieto.