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05 March 2004

Counting with pebbles

by Forrest M. Mims III

Imagine a world without those wonderful pocket calculators we all take for granted.

Let's say that you live on a desert Island with a few palm trees and a beach lined with shells. After tourists discover your island, you need a way to keep track of your sales of shell necklaces.

You don't own a calculator, and the tourists left their calculators at home. How can you add up your sales?

Simple. First, use your index finger to form a row of half a dozen or so parallel grooves in a small patch of smooth sand.

Next, place nine small pebbles in each groove so that they form parallel rows. The rows of pebbles should be lined up to form a rectangle.

You have just built a sophisticated number machine that can add and subtract without the need for electricity. You have built an abacus.

Your abacus is very easy to use.

Say you want to add the 11 sales you made yesterday to the 13 you made today.

First, enter the number 11 in your abacus by moving the top pebble in one column along its groove by a finger width or so. Then move the top pebble in the next column to the right the same direction and distance along its groove.

Your neat array of pebbles is no longer a rectangle. Instead, a pebble in one row is moved upward slightly and a pebble in the row to the right has also been moved up.

Your abacus indicates the number 11.

Now you want to add 13 to the 12 you have entered on your abacus.

Push a second pebble up under the first 1 in 11. Then push three pebbles up under the second 1 in 11.

Now your abacus has 2 displaced pebbles in one row and 4 displaced pebbles in the next row to the right.

This means the number 24 is now displayed on your abacus. In other words, 11 + 13 = 24.

You subtract numbers on your abacus the same way as you add. You just do it backwards.

For example, let's say 3 customers returned the shell necklaces you sold them. Just push three of the pebbles down in the right row. Now your abacus indicates 21.

Your abacus uses no electricity, yet it stores your calculation until a wave washes it away.

It can add faster than a digital calculator. That's because the abacus displays its result immediately after you move the pebbles. A calculator requires that you press the equal key to see the answer.

There was a time when children learned basic arithmetic with an abacus. If I was in charge of all the schools, I would bring this teaching method back. Our kids would learn to understand simple arithmetic faster than any other method.

Forrest M. Mims III and his science are featured online at http://www.forrestmims.org/.

This feature was originally published in Forrest Mims's weekly science column in the Seguin Gazette-Enterprise, Seguin, Texas. The column is written for a general audience.