The Abacus—Bead Calculator of the Orient
By “Awake!” correspondent in Taiwan
AT THE local store in Japan a woman has purchased a number of items. “How much, please?” she asks. The Japanese storekeeper picks up his abʹa·cus and with a quick tilt and sweep of the hand ‘clears’ it of previous calculations. Then, as fast as he can recite the individual prices, he adds them. The moment he has recited the last price he reads off the total. The woman pays the amount asked without question. To her the answer is as authoritative as that of a cash register.
A traveler in a Tokyo bank decides to change all his pocket money into yen. He has $53.67. The clerk picks up his abacus and, in less time than it would take to write down the figures to work it out, he has the answer. Looking around the well-equipped bank, the Westerner might well be puzzled. There are many modern business machines and typewriters. Nevertheless, about three fourths of the employees rely on the abacus for their calculations.
Yes, wherever one goes in Japan or China he is sure to see the Oriental version of this most ancient of calculating machines, the abacus, in constant use. When he sees the shopkeeper use it to add a few figures, he may tend to despise its real value. “Why not do it mentally rather than rely on his bead calculator?” he might think. At least that is what I thought when I first went to Japan and saw how dependent people seemed to be on their bead calculator.
However, when a person sees that clerks and bank tellers use the abacus for working out more complicated problems, he will no doubt respect it more. If he inquires about it, he might be told that the operator has not only calculated the problem in that short time but has double-checked by reversing the calculation to obtain the original figures. “Truly amazing!” he will think. All that with a wooden frame containing some beads?
From Ancient Times to Today
The abacus is one of the oldest counting devices known to man. It was used, for example, by the ancient Greeks and Romans. Since Roman numerals do not have a place-value system nor a zero concept, some sort of aid in calculating was essential. If you try to add the Roman numerals XCVIII and LXXXIX you will more fully appreciate the problem. An effort at multiplying those two numbers will further demonstrate the problem. The development of ‘Arabic’ numerals with their place-value system and zero concept diminished the need for the abacus in the West.
However, among the Chinese and Japanese the abacus found a welcome new home. But even in the West there is a simple form of abacus in use today that is familiar to many persons. Yes, you too may have started your knowledge of numbers with the aid of such an abacus-like instrument. It is the little set of horizontal bars with colored beads that is on many children’s playpens around the world.
The Chinese abacus is called a suan-pan, while the Japanese version is known as a soroban. The Oriental abacuses have vertical rods divided in two, with the beads above the crossbar being five times the value of the beads below the divider. Note that in the illustration the Chinese suan-pan has two beads above the crossbar or divider and five below. The modern Japanese soroban, on the other hand, has one bead above and four below the divider.
A basic difference between the Japanese and Chinese abacuses is the size and shape. The Japanese version uses smaller beads and usually has more rods. The Chinese abacus uses larger beads, and fewer rods. The Japanese abacus is therefore long and narrow, while the Chinese is not so long. The smaller construction of the Japanese instrument makes for faster manipulation while the larger construction of the Chinese abacus makes accidental moving of the beads less likely and also makes for easier reading. However, the tendency here in Taiwan nowadays is to switch to the Japanese style.
Learning the Basic Principles
I decided to learn the rudiments of operating an abacus. I bought a standard Japanese one, two and a half inches wide and twelve inches long (6 cm x 30 cm). It cost the equivalent of $2. On the dividing bar there is a little dot on certain rods. The operator selects one of these as the unit rod. The rod to the left is the tens rod, the next to the left is the hundreds and the third to the left is the thousands rod.
The value of the rods to the right decreases by tens so that they equal tenths, hundredths, thousandths and so on. It is thus a decimal system.
It was explained to me that the abacus is ‘cleared’ by a quick tilt toward yourself, so that the beads all slide to the bottom of the rods, or in the case of the upper beads, down to the divider. Then the upper beads are moved upward by a quick sweep along their lower edge with the index fingernail.
If you now push up one bead on the unit rod until it comes in contact with the crossbar or divider, you have set one on the abacus. Push up another two of these beads and you now have three of the lower beads in the upper position so that you have three set on the abacus.
Now move down the upper bead (which is five times the value of the beads below the divider), and you have added five. This means you have five above the divider and three below the divider bar for a total of eight. If you now want to add on another three, you do not have enough beads left on the units rod, so you have to spill over to the left to the tens rod. You do not think 8 + 3 = 11, but think along the lines of 3 = 10 − 7. You remove seven by sliding the five up and two of the unit beads down. Then add one ten, (that is, you move up one bead on the rod to the left of the unit rod) and the result will be eleven, as in the illustration. Of course, there are many ways of explaining how to work out these rules of movement, but in actual practice they become automatic.
When you have larger numbers, how do you proceed? You just start at the left or highest column involved in your calculation and work from left to right. Thus if you have 548 and wish to add 637, you will first put 548 on your calculator. Then add the 6 to the 5. You follow the rule or pattern 6 = 10 − 4 by removing the 5 on the hundreds rod and adding a 1 on the same rod (−5 + 1 = −4) then add one of the thousands beads on the rod to the left. You then proceed to add the three to the four, the seven to the eight and your abacus will appear as in the illustration. Can you read the answer? It is 1,185.
Because you thus work from left to right, you can start your calculation as soon as you know the first digit. In mental or written arithmetic you work from the units or right hand side of the problem. The abacus has an advantage.
Putting My Knowledge to Work
I learned to add and subtract, and later, when I had the need for more addition, I decided to put my knowledge to work. The results were disappointing at times and encouraging at others. I decided to find out why.
Study of a booklet on the technique showed me that I had no system and that I was not using my fingers in the proper manner. I learned that with the Japanese abacus you should use only the index finger and thumb and that you must follow a special order in moving the beads if you want accuracy and speed. With the Chinese abacus, use of an additional finger is recommended due to its larger construction.
With a little study and practice my accuracy improved so that a recent visiting friend from overseas was surprised to see me, a Westerner, using my little Oriental bead calculator for not only addition and subtraction but also multiplication and division. Of course, I am by no means a skilled operator and thus am very slow by Japanese or Chinese standards, but it certainly saves much work for someone who would otherwise have to rely on writing the figures in columns and laboriously adding them.
Advantages, Disadvantages
A distinct advantage of the abacus is that maintenance costs are also in line with the low initial cost. Recently my abacus was getting so sticky that I was having trouble operating it. I resigned myself to having to buy a new one. When I went to buy one I mentioned my problem. “That’s all right,” the proprietor said. “We have a maintenance kit.” I bought one for less than twenty cents. It consisted of bristles protruding from the top of a plastic case that looked like a saltshaker. The case contained French chalk. Holes between the bristles let some chalk come through when the brush is used to scrub the beads. A few brushings and my abacus was like new, with the little beads clicking back and forth in easy sliding motions again. Somewhat different from maintaining an electric calculator!
There are, of course, a number of disadvantages to be encountered. One of these is the fact that there is no record of the steps involved in the calculation. Only the answer is available when the calculation is completed. Also, to obtain any degree of skill much practice is involved. Because I do not have that practice and rarely do involved calculations, I often have difficulty with multiplication and division when there are a number of digits involved in the multiplier or divisor.
The Oriental abacus has a lot going for it even in this electronic age. All Japanese and Chinese children learn to operate one in grade school. There are also numerous schools to prepare students to take examinations conducted regularly in Japan. There are three main grades to be attained, and if a person is qualified as a first-grade operator he or she has a much better opportunity of gaining a good office position. This is true even though the company may have the latest calculating machines.
The training that use of the abacus gives the mind is another factor in its popularity. Mental training is such that one abacus operator, Mr. Yoshio Kojima, is recorded as having given correct answers to fifty division problems, each containing five to seven digits in its dividend and divisor, in the time of one minute, 18.4 seconds. Then in 13.6 seconds he added ten numbers of ten digits each. All this without his abacus, paper or other aid! It is said that such men do this by working the problem mentally on an imaginary abacus!
While the abacus in China and Japan is giving some ground to the more sophisticated machines, it still has a firm position in the Oriental business world. Regardless of its future, this business tool of the East and educational toy of the West holds a unique place in man’s progress with mathematics. I am one Westerner who truly appreciates the bead calculator of the Orient.
[Picture on page 18]
A Chinese abacus set at eleven
[Picture on page 19]
A Japanese abacus set at the number 1,185