Abacus

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A historical sketch on the Abacus

“An Ukiyoe woodblock print of the Edo Period (1603-1867) shows a youth calculating on a soroban” From “The Abacus Today”, Mathematics in School, 4(5), 1975:19”

As a historical point of view, human being has been evolved for some reasons. In these sense, all materials in our daily life are easily adapted by those who are good at applying to brand new technologies. In mathematics, there is no exception to follow undeniable rules. Before accepting these rules, we might have been able to calculate simple things - which are included adding, subtracting, multiplying and dividing in a certain level - in our head. If not, we are still working on a certain level of simple calculation. Even though we could easily have done it in our own head, we certainly could not have done it as right way. For some reason, we tried to get a right answer with doing less working in progress.

“Nothing could be further from the truth. The abacus is at once one of the oldest, most enduring, and efficient products of the human mind. The Abacus has served mankind well, aiding him in commerce and invention. It is likely that the abacus was developed independently at different times in different civilizations; The Peruvian Indians, for instance, used a form of abacus for rapid calculation even before the arrival of the white man. The results of computation were recorded by knots tied in a cord.” (Haga, 1964:398) According to the Mathematical Association, we could get a brief historical archive on Abacus as below. “The principles of Abacus arithmetic were first developed in the Middle East over 5000 years ago by the Sumerian civilization. This civilization was probably the first to develop the subject of mathematics and their sexagesimal number system which is based on 60 is still with us in the way that we measure angles and time” (The Mathematical Association, 1981:2-3)

“A collection of various types of abacus is displayed at the Museum of Monetary History in the Fuji Bank’s head office in Tokyo” From “The Abacus Today”, Mathematics in School, 4(5), 1975:19
Through this practice, we could simply get a right answer through our own cognitive system. “In its earliest form the Abacus was probably a sand table with pebbles being used as counters. From this form it evolved to its modern design with beads moving on rods. This version dates from the Greek and Roman civilizations. The Abacus in its various forms continued to be used in Western Europe until the Middle Ages.” (The Mathematical Association, 1981:2-3)
“A clerk in the Hongkong and Shanghai Bank, From “The Abacus Today”, Mathematics in School, 4(5), 1975:19
In this situation, we may also need to get a sort of genius tools to aid our insufficient analytical system. In this sense, these days we take it for granted that we can easily add, subtract, multiply and divide numbers. It was pretty hard to see people those who use the Abacus for some reason. Especially, we could not figure out any institution to become well-trained technicians those who have a spectacular performance given by whom. It seems like the most heyday on Abacus is around 1960~90 just right before being computerized. Why has the abacus being popular at that time? We are already getting sick of the answer of this: the efficiency in some level.

Even if the spread of abacus focuses upon Asian Cultures, it is totally not. According to Haga(1964:398) “At one time the abacus was used in American schools to teach addition and subtraction. It has much to recommend it; it is pretty much cheap, fast, efficient, and versatile.” Furthermore, “one school in California, the abacus was introduced in all second and third grade classes as part of a project to improve speed and accuracy in the handling of numbers.” (Haga, 1964:398)

As we could easily assume, technologies do not dwell on the Abacus to improve speed and accuracy in handling of numbers. It was just one of the tons of advanced calculations in analytical system.

How it works

Tell me about Abacus: how to use it?

It consists with seven beads on each row. “Two of the beads are above the bar (upper beads) and five are below the bar (lower beads). The upper beads are worth “5” and the lower beads are worth “1”. Each row represents a decimal place. The right-hand row shows 1s (1 to 9) the second row 10s (10 to 90) and so on. To show a number beads are placed against the bar. “(Maxwell, 1981:3) Unlikely the Chinese Abacus, “the Japanese Abacus has only 1 upper and 4 lowers beads.” (Maxwell, 1981:3)

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It is because these two beads which are located in the most top and bottom is not needed at all in terms of double meaning. Even if the abacus needs to practice to calculate numbers, it is carried out a series of calculation in terms of “addition and subtraction, Simple and long multiplication, and simple and long division, and finding square and cube roots.” (Maxwell, 1981:3) I am not going to show how to calculate every single calculation, but it is obvious to need to a sort of train for that. If you want to get a sense of calculations on the abacus see the article.