Thursday, August 16, 2012

The Abacus

After mentioning Fibonacci's work, the Liber Abacus, it occurred to me that the place of the abacus in history deserved a little attention.

The Salamis Tablet, 300 BCE
Like the etymology for book, the word "abacus" does not start out to "mean" a frame with wires and beads. The word "abacus" first enters print in the English language in 1387. The Latin word from which it is lifted refers to a sandboard, a counting board covered in sand that allows you to draw with your finger. Latin took the word from the Greek abax, abakos, a board covered with sand for the purpose of drawing figures and calculating. At some point, the sand was replaced with counters of wood or stone that were moved from column to column for calculations, and the board itself was designed to facilitate calculations

In 1846, on the island of Salamis, a white marble counting board was discovered. The Salamis Tablet has been studied extensively, and one scholar has made a video of its proper use.

But when did abacus come to refer to the wooden frame with beads on wires? A reconstruction of a 1st century Roman abacus shows a board with grooves to keep the round beads in line. Visually, it resembles the abacus with which we are familiar. Gerbert of Aurillac (c.946-1003), one of the most influential scientific minds of his era, pushed the use of the abacus as a method of calculating much more swiftly than when using Roman numerals. He was able to promote its use even more when he became Pope Sylvester II.

The abacus in the form we think of it seems to come from China in the 2nd century BCE. Called a suanpán ("counting tray"), it was built with rods that held beads, 2 on an upper deck and 5 on a lower. Now called the "2/5 abacus," the two decks allowed the user to use larger numbers without adding 1+1+1+1, etc. Other versions had different numbers of rods, and different numbers of beads on them.

Abacus showing 87,654,321
Visually, it is very much like the Roman abacus mentioned above. Commerce between Rome and China was not unknown, but a direct influence cannot be proven. Still, the wooden-framed Chinese suanpán was so much like the Roman abacus that it was natural that the West would use the same name for the new device. In fact, no one type of the many objects used for calculating universally replaced the others. Counting boards of clay or wax were used well past the Middle Ages. In fact, until just after 2000, some accounting schools in China required proficiency in using the bead abacus.

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