## What is an Abacus and why was it invented?

It is presumed today, that in ancient times the need for mechanical calculating devices was felt due to

- 1Lack of numerical notation system in early times for counting. As a result, pebbles, shells, bones, knots on strings and human fingers were used as counting devices. As trade increased, the need for counting large inventory of goods sold or bought, also increased.
- 2Scarcity of writing materials.

Initially, a very small stone was used to represent one object and number of objects was ascertained by counting the number of stones. The word calculate, in fact comes from Latin word calculus which means small stone. Slowly, people realized that this method can be used to count up to small numbers as bigger number required gathering large number of stones.

This led to principle of number base. At first, stones of different sizes were assigned different order of units. It was only a matter of time, before the concept evolved to arranging stones in columns marked on a surface and assigning them order of units, leading to the concept of a counting board.

Increased trade requirements led to the invention of various types of portable counting devices. So, abacus originated primarily as a counting board for large numbers. For this reason, It was also called a counting frame.

It is the view of the historians, that the first abacus consisted of a shallow tray filled with fine sand or dust and numbers were recorded and erased with a finger. It is also thought that the word abacus, might have come from the Greek word "**abax**", meaning a reckoning table covered with dust. Abax itself is derived from Semitic word for “dust,” *abq**.*

### Who first invented the abacus and How old is the Abacus?

It is thought that this simple apparatus originated in Babylon about 4,400 years ago. Some evidence of its use in ancient times in Mesopotamia, Egypt, Persia, Greece, China, Rome, Japan, India and Korea have been found.

Written records from Greek Historian Herodotus (480 - 425 BC) are the oldest surviving documents in history that refers to the use of Abacus. Use of abacus by Egyptians is also referred to, in these records.

Oldest physical counting board was discovered in the Greek island of Salamis in 1846. It dates back to 300 BC and is now kept in the Epigraphical Museum in Athens. It was made from a white marble of dimensions 149 cm x 75 cm x 4.5 cm. It had two sets of horizontal parallel lines engraved (5 lines in the upper area and 11 lines in lower area). Both the sets of lines are divided into half by a perpendicular line.

The third, sixth and ninth line of the 11 line set, is marked with a cross at the intersection.

As the number system evolved and Hindu - Arabic numerals came into use, abacus was adapted for place value counting. With the passage of time, it evolved into a calculating tool used for carrying out basic arithmetic calculations.

Hence we may define Abacus as a counting and calculating device used from ancient times, that performs basic arithmetic functions by manually sliding counters on rods or grooves. In modern times we may call it as a simple instrument for carrying out rapid arithmetic calculations. Person who uses an Abacus is called an **Abacist**.

### Different Types of Abacus in Earlier Times

Three types of Abacus evolved in the earlier times - Dust, Line and Grooved abacus.

- 1
**Dust Abacus**was in the form of a board covered with fine sand or dust. On this board, lines were drawn, which represented different place values. Numbers were indicated by various lines or symbols across the lines. - 2
**Line Abacus**- Ruled boards were used and pebbles or counters were placed across lines to represent numbers. Its use in Egypt, Greece, Rome and India is documented. Various forms of line abacus were in use in Europe till 17^{th}Century. - 3
**Grooved Abacus**was used by the Romans. In this type, various grooves were carved on the board. Counters were moved up and down on these grooves to do the calculations. It had upper and lower grooves. In each of the upper grooves only one counter was laid, while four counters were used for lower grooves. Chinese 6th century documents have reference to the grooved-abacus.

All the above types of abacuses were in use in Rome at some time or the other.

## Abacus in Recent Times

From the grooved form, fourth type of instrument evolved, which had beads moving on the rods fixed on frames. This is called as the **rod or bead abacus** and allows calculations to be made at much faster speed. In the 19th and 20th century, it was still used in Japan, China, the Middle East, Russia and other parts of the world.

A modern abacus is made of wood or plastic, consisting of a rectangular frame with at least nine vertical rods strung with movable beads. The number of vertical bars and beads on each bar varies with location and culture, but the basic function of the abacus remains the same.

Abacus with twenty one bamboo rods is the most common form in Japan. Instruments with thirty-one, twenty-seven, seventeen and thirteen rods are also used.

### Resurgence of Abacus Learning

However, the awareness of the importance of Abacus and Mental Arithmetic was rekindled once again in the late 1980's and early 1990's especially after the reports of the First and Second International Comparative Studies of Mathematics Achievement conducted by the International Association for the Evaluation of Educational Achievement (IEA) were published. In both studies, the performance of the students from the Eastern countries was found to be consistently higher than the Western counterparts.

Consequently, Abacus education has again gained a lot of prominence & importance and is now considered as an essential skill development education for children with large number of benefits.

### What are the main techniques of Abacus Learning?

**Use of Abacus**: In this technique, we use an abacus to perform most arithmetic operations such as addition, subtraction, multiplication, division, square root and cubic root, etc.**Visualization**: Instead of manipulating a physical abacus, in this technique, calculations are done mentally with an imaged abacus, and such calculation method is the so-called ‘‘*abacus-based mental calculation (AMC)*“. AMC is an efficient calculation strategy that can be mastered by children through Abacus training.

## What is the History of the Abacus?

### Oriental Abacus

Old Chinese books on Mathematics do not carry any reference to Abacus. Hence, no definite information about the origin of Oriental Abacus exists. First reliable reference is found in a book * Mathematical Treatises by the Ancients*, compiled at the beginning of the third century by Hsu Yo. The book was annotated in the sixth century by Chen Luan.

In the notes added by Chen Luan, he describes the device as having three sections and talks about function and construction of each section. We get some idea of its usage from a verse in Hsu Yo’s poetical description of the board. The verse is figurative and subject to interpretations.

As per one of the popular interpretations of the verse, it was used in calculations related to astronomy, calendar, land surveys and human daily life affairs.

From the description in the above texts, Oriental abacus appears to be similar in concept to the Roman grooved Abacus. The only difference is that in the Roman version, the counters were moved along the grooves, making them much slower in operation.

In the book by Hsu Yo, various other reckoning devices and boards are mentioned. Some used different colours of counters, light color for numbers between 1 to 5 and dark color for numbers 6 to 9. Some had different spatial arrangements.

Various reckoning devices mentioned in the book were in use, until phased out by more advanced and useful versions, due to steady developments.

### Oriental Abacus inspired by Roman Abacus

Some other reasons which suggest that Oriental Abacus was inspired by the Roman one are:

- 1Chinese is written in vertical columns from up to down. If they are forced to write in a horizontal line they will do so from right to left. However the numbers on abacus are worked in reverse direction. It is difficult to imagine that they will invent something opposite to their normal flow.
- 2Their numerical notation system as described above, was unsuitable for calculation. Suanpan, in its current form, was not developed till the twelfth century. Hence, they faced difficulty in fast calculations for larger numbers.
- 3So it is more likely, that having been introduced to Roman system, they continued using it and even developed it to be a very efficient calculating device. So much so, they continued using it even after being introduced to Hindu - Arabic numeral system.

Prof. Yamazaki and Prof. Suzuki of Nihon University cited the following evidence in their works in support of the above theory:

- 1Both had one five units counter and four one unit counters.
- 2The method of operation of ancient Chinese abacus was the same as Roman method. In this method, multiplication was done by repeated addition and division by repetitive subtraction and counting these repetitions.
- 3Both Roman numerals and Chinese pictorial representation showed traces of Reckoning by 5’s. In Roman numerals, four is IV and six is VI.
- 4Trade relations existed between the two countries. Chinese documents have description of two routes known as silk roads between the two countries.

### Why Abacus Thrived in the East

We have noted so far that Abacus or similar devices were in use in all the ancient civilizations in some form or the other. Eastern civilizations (China and Japan) continued to use it, where it developed into an efficient calculating machine. Similar developments did not take place in the West. Let us look at some of the probable reasons.

- 1Differences in numerical nomenclature and calculation systems
**-**Numerical nomenclature and systems of calculations were significantly different between the east and the west. In Orient, the numbers were named and set from left to right on the calculating boards in use. Denominations decreased from left to right with highest denomination being on the extreme left and lowest on extreme right. Thus abacus was ideally suited for use with Chinese method of naming and using numbers on the board. This compatibility resulted in vast improvement and development to modern form. - 2In ancient China and Japan, reckoning devices called Chancku and Zeichiku, respectively were used. These devices were used not only for basic arithmetic operations, but were also able to solve quadratic, cubic and simultaneous operations. During these times, however, there was little need for rapid calculations. Hence, abacus while in use, was not developed as much till the twelfth-century.
- 3With the rise of commerce and industry during the rule of Ming Dynasty (1368 - 1636 AD), use and development of abacus increased manifold.
- 4Abundance of bamboo as ideal raw material in Orient resulted in a highly efficient low cost device.
- 5Number of counters in the heaven area were increased to two to take care of the weight and currency systems in place. Two beads are also more suited to Chinese method of multiplications and division by the use of special division table. This method of division was in use there.

### Why Abacus was not Similarly Successful in West

Line abacus was introduced in France in the Thirteenth-century and became quite popular. It was at one time used in households, businesses as well as in government offices till seventeenth-century. However, it failed to develop into an efficient rod abacus system in Europe. Some of the reasons are discussed below:

- 1Different countries in Europe used different numerical notations, such as duodecimal, sexagesimal, binary etc. Rod abacus cannot be used in an efficient manner on these systems.
- 2In Europe, however, with the introduction of Hindu - Arabic numerals, the development of instrumental arithmetic slowed down as they were more comfortable with graphic notations and abundant supply of writing materials further accelerated the decline.

### Abacus in Use in Different Countries in Recent Times

#### Chinese Abacus or Suan-Pan

The Chinese abacus has a horizontal bar which divides the frame into two parts, as shown above. The classic version of Chinese Abacus is called as the the “2/5 abacus", because two beads are placed in the upper section of the abacus and five beads in the bottom one. It is also known by the name * Suan-pan (arithmetic board) *in Mandarin language and

*in the Southern dialects of China.*

**Soo-Pan**It is thought to have been developed, in this form, around the 12th Century. However, it came into common use from the fourteenth century only.

Some of the important characteristics of the Suan-Pan are:

- In Suan-pan, the area above the horizontal bar, is called heaven, and consists of two beads per vertical rod. Each of these beads has a value of five.
- The lower area is called the earth. Each vertical rod in the earth area, contains five beads each, with each bead having a value of one.
- Each vertical rod represents a unit of ten. Calculation is done by moving beads toward or away from the horizontal divider.

#### Japanese Abacus or Soroban

While, abacus came into popular use in Japan in the seventeenth century only, it is thought to have been known to their traders at least from the fifteenth century. It has been studied very extensively by many Japanese mathematicians, including the renowned Seki Kowa (1640 - 1708).

These studies resulted in a series of improvements in the structure, form and operational methodology of the abacus.

Initially, the Japanese abacus, inline with the Chinese version had 2/5 structure. In the mid – 1800s, the 2/5 abacus was replaced by the 1/5 abacus with only one bead in the heaven area. And by the 1920s, the most widely used form of abacus was the Japanese – made *Soroban,* or 1/4 abacus.

This is also the modern version and resulted from further simplification of structure by omitting yet another bead, this time below the beam, leaving a total of four beads in the earth area.

- The numerical value of each bead depends on its location in the abacus. Each heaven-bead has a value of five times that of an earth bead below it and called as five units.
- Each rod represents columns of written numbers. Beads on the vertical rod farthest to the right have their values multiplied by one. On this rod, each earth bead is one and each heaven bead is five.
- Beads on the second rod from the right, however, have their value multiplied by 10. On this rod, each earth bead represents 10 and each heaven bead stands for 50. Beads on the third rod from the right have their value multiplied by 100, so that each earth bead represents 100 and each heaven bead stands for 500, and so on.

#### Russian Abacus

First reference of Russian abacus is found in an inventory book dated 1658. In Russia, it is called as Schoty and this abacus is still in use today, though no longer taught in schools now. The main features of Russian Abacus are:

- The rods in Schoty are in horizontal position, with ten beads on each rod and the beads are moved from right (home position) to left.
- Only one rod has four beads only and this rod acts a separator for the numbers and fractions. This row represents the four quarters of fraction.
- The rods are provided with curvature to prevent accidental sliding back of the beads to the home location.
- The design of Russian Abacus can be thought to resemble human hands put together with palms facing down. Two sets of four beads each and of same colour are on the outside, like fingers of both the hands. Two innermost beads are of same colour but different to outside beads, kind of representing thumbs.
- Row above the quarter row is the unit rod and each rod above represent 10s, 100s, 1000s and so on.