Using my soroban one day, I found a mistake in my checkbook log. The soroban is the Japanese abacus, and it’s as much technology as I need for math.
I took calculus and physics in college, applying sines and cosines and more to learn the slopes of curves, but most of my math now involves adding and subtracting numbers in my checkbook. For years, I used my calculator for my checkbook log, but I realized when our granddaughter needed help with math homework that I had nearly forgotten how to add and subtract on paper, carrying numbers to the next column, and I had to stop and relearn before I could teach. I did relearn, though, and when my calculator quit, I switched to paper and pen.
My Alaska brother-in-law gave me the soroban that had lain hidden in his mother’s closet since his Air Force days. I struggled at first to learn soroban operations, but once I did, I could quickly add and subtract.
The calculator or computer demand no more effort than pushing the proper number buttons. I can mindlessly add numbers on a calculator and never be aware of whether they’re correct, but the soroban requires an engaged brain. The soroban has a horizontal beam separating five single counters below the beam whose total equals that of one counter above the beam. The columns of counters represent units of 10. The right column is the smallest unit. If adding whole numbers, the right column is the ones position — the counters below represent ones, and the counter above the beam is five. The counters below the beam in the second column from the right are tens and the counter above is 50. The third column is hundreds and 500 and so on. To add or subtract money, you make the right two columns the tenths and hundredths places for the cents.
Counters are moved toward the beam, below up and above down, to engage numbers. If a single counter is moved up in the first column, it represents one; if a single counter is moved up in the third column, it represents 100. A five counter moved down in the fourth column represents 5,000. If this is hard to visualize, you can draw it on paper or use coins or pebbles to make a version of an old-style abacus.
The abacus started as a board covered with dust, later with wax, on which lines were drawn and marks representing numbers made. It was followed by a board marked with lines upon which were placed loose counters in the form of small discs of metal, bone, glass or other material and then by a table on which the counters were fastened by means of grooves. The modern abacus is a framework holding horizontal rods that hold the counters. This abacus allows portability; my soroban is pocket-size.
The abacus was known in Mediterranean countries around 450 B.C., and references to it are found in Roman literature. The Romans got the abacus from the Etruscans. “Abacus” is Latin for “table”; “calculus” is Latin for pebble; plurals are “abaci” and “calculi.” The modern Chinese abacus, called the suan-pan, was used as early as the 12th century. It has two fives above the beam. The Russian abacus is the s’choty; Armenian, choreb; and Turkish, coulba.
Europeans in the middle ages used a line abacus, a table ruled with horizontal lines representing successive powers of ten, each space representing half the value of the line immediately above it. The line abacus was used well into the 18th century; “to abacus” was the equivalent of “to compute.” Mexicans and Peruvians had abaci when the Spaniards arrived.
Ancient number scripts were simply labels to record abacus results rather than pure representations of numbers that are manipulated; in other words, numbers were mere symbols for the counters and were not added or multiplied on paper.
Computing discs in Britain were called counters; in Latin they were called projectiles, because they were thrown or cast upon the counting board. In France they were called jetons and in Germany, Rechenpfennig or Zahlpfennig.
My Japanese soroban has a black wooden frame and 13 columns of dark brown counters. The number of columns varies in sorobans; more columns, of course, permit calculation of larger numbers.
I knew I understood addition on my soroban when I added 123,456,789 nine times and arrived at the correct sum of 1,111,111,101. I even found a mistake in the book, which lists each multiple of 123,456,789. The abacus is about as quick as the calculator for basic functions and it’s not as quick as the computer that automatically totals your bills, but it’s good exercise for the brain and a satisfying use of the fingers, which need more manipulation than simple clicking of a mouse.
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