The Value of the Abacus

The abacus today is often associated with cultures of the East. It is not uncommon to find oneself in a Chinese shop (even in a local Chinatown) and find the proprietors calculating a sale using a modern abacus.

What most people don't realize, however, is that the abacus truly did not come from just a single culture, but in truth possesses a long and unique history, coming in many different forms from many different nations throughout world history, from the Egyptians to the Greeks and Romans to the Native Americans prior to Western influence.

The abaci (that is the plural of abacus) are not exactly identical in any of these cultures, of course. For as many phases mathematics has gone through during the history of its development, mankind has found clever ways of calculating. Past abaci have come in the form of stones, sticks, grooved surfaces and any number of complex mechanical methods of performing mathematical tasks.

Today's Abacus

Modern abaci - the ones one would find in an antique store or novelty shop - have become rather standardized, which makes them rather simple to explain.

An abacus is divided into two portions, a "lower" portion and a narrower "upper" portion separated by a dividing beam. In each of these portions there are several series' of beads which can be moved up or down (although as abaci are meant to be used lying flat, the beads in reality move "side to side"). The columns of beads in the bottom portion number five, while the top portion contains columns of only two (as can be seen in the image accompanying this article).

The bottom beads are all meant to represent values of 1 and the top beads represent values of 5. The individual columns, however, represent powers of ten. This all provides simple algorithmic methods of performing basic calculations.

To hopefully make this easier:

To represent the number 472 on an abacus, we would simply use the three rightmost columns (the first column representing the "ones," the second representing the "tens" and the third representing the "hundreds." So in the first column we would simply slide two of the lower beads toward the dividing beam, representing the 2. In the second column we would similarly slide two of the lower beads toward the beam as well as one of the top beads, giving us 2 +5 = 7. In the third column we would simply move four of the lower beads up and then we would be done.

These are the most absolutely basic principles of representing numbers on an abacus, and as the reader can hopefully see already, the more columns of beads a particular abacus possesses, the larger the number which can be represented (and it is also possible to begin the "ones" column further to the left in order to allow columns of decimalization).

Abacus Functions

Of course, if all an abacus was good for was to represent numbers visually, it would really be rather useless, as it would be easier simply to write the number down. Fortunately, these handy little devices are much more useful than that, and can be used to solve almost any standard arithmetical problem, from simple addition and subtraction to multiplication, division, and even finding the square and cubic roots of numbers!

Simply using the above explanation of representing numbers on an abacus, the most basic of these should be somewhat self explanatory. To add or subtract one number from another (no matter how large the number), all one needs to do is add or subtract beads, beginning from one column and moving to the next (and, just like writing these problems on paper, numbers over ten can be "carried" from one column to another).

Things certainly get more complicated as problems move into more advanced multiplication and division, but in the end the abacus continues to remain one of the most intuitive methods of mathematical problem solving the world has ever seen (prior to the advent of the "adding machine" and modern calculators and computers, of course).

Abaci today are, to most people, little more than clever and amusing devices, but there is a sense in which using them allows a person a unique insight into the science of numbers and mathematics, and therefore may prove beneficial to anyone with a mathematical interest.

There are many abaci for sale on the internet, whether used or antique on Ebay or new from many other online vendors, and there are certainly still shops which sell them as well. They make fantastic gifts and beautiful, unique, and very pragmatic sources of decoration, as well.

References:

"Abacus: The Art of Calculating with Beads."

Ball, W.W. Rouse. "A Short Account of the History of Mathematics." 1893. Dover.

An Example of a Roman Abacus

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