By: Joe Hruban
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| A Russian Abacus at the Ashmolean Museum, Oxford |
The Abacus was an advantageous tool to use to count numbers and do simple operations. It helped count, add, subtract, and a little bit of multiplication and division. It assisted the user in calculations and was used by many different cultures. This gave it many different forms as well. However, the history of its development begins in Sumer.
The Abacus first originated in Ancient Sumer sometime in the mid 2000s B.C. It is possible that the Babylonians used it to make calculations, however it is not for certain. We start to gain a little more certainty of the abacus when we get to Egypt. The Greeks mentioned that Egyptian used counters or pebbles to help with calculations or just counting. The Persians begin to use the abacus after this, yet, it isn’t until the Geeks that we actually have proof that the abacus was used. With the Greeks, tables with some sort of counters in them have been discovered. The Romans adopt this from the Greeks. The Chinese and Russians also used the abacus and made further changes to it. W. W. Rouse Ball (1912) states that “this instrument was in use among nations so widely separated as the Etruscans, Greeks, Egyptians, Hindoos, Chinese, and Mexicans,” to show the popularity and vast spread of this instrument. This expansive distribution of the abacus leads to its development and modifications.
The abacus went through many changes and modifications as it progressed from place to place. It first started out as a wooden board with grooves cut into it. These grooves were made to hold pebbles or counters of some kind. A variation of this form was a table covered with sand with grooves in it that were made by someone’s fingers. However, it was the same concept. To represent a number, one would look at the grooves and the pebbles to understand place and value, respectively. The number of pebbles or counters in the first groove signified the value of the one’s place. The number of pebbles in the second groove represented the value of the ten’s place, and so on. Once you reach ten in any of the grooves, you clear that groove and put one pebble in the following groove. One must keep in mind that whichever groove was considered the first groove depended on which way the culture that was using it read; in other words, left to right or right to left. This model of the abacus was just the template for another form, the swan-pan.
The swan-pan was a form of the abacus where there were parallel wires within a wooden frame. This is the form that we know today when we think of an abacus. The swan-pan of the Greeks and Romans did not have a top to the frame. This was so they could place or remove their counters on the wires. They created two margins on their abaci: one with four counters and one with twelve counters. This signified the addition of fractions with denominators of four or twelve. Their abaci were made to represent numbers of up to one-hundred million. Although this abacus suited the needs of the Greeks and Romans, the Russians decided to modify it further.
The Russians made some changes to the abacus as well to suit their needs. They elongated the wires and put nine or ten beads on each wire and closed the frame. This eliminated the need to add or remove beads from each wire and since the wires were longer, all they had to do was slide the desired beads up or down to represent the number they needed. Gerbert added to this by coloring the beads different colors and by marking them one through nine. This made using the instrument more organized and slightly quicker. The Chinese saw further developments that could be made.
The Chinese and Japanese made a slightly different model. There model had a top row with two beads on each wire and a bottom row with five beads on each wire. To represent a number, one would slide the beads up towards the divider. The two beads above the divider represent a value of five (in decimal notation) so if one would want to represent the number seven, the beads in the top row would be one up and one down and the beads in the bottom row would be two up and three down. This made performing the operations of addition, subtraction, multiplication, and division, much faster. Ball (1912) stated “I am told that an expert Japanese can, by the aid of a swan-pan, add numbers as rapidly as they can be read out to him.” The abacus was a great aid to the Japanese as well as many other civilizations.
The abacus helped civilizations in making calculations until the invention of the conventional calculator. It went through many changes with each civilization that used it but benefitted all. The fact that the idea of it stayed relatively concrete throughout every civilization it was a part of further solidifies its notion of an effective tool.
Bibliography
Ball, W. W. R. (1912). A Short Account of The History of Mathematics. London, England: Macmillan & Co., Ltd. 123-126.
