The Abacus, Unplugged

Someone asked for more info about how an abacus ticks. I’m on it.The thing about an abacus is that unlike many tools, it’s *always* unplugged!

Abacus. | feck_aRt_post

Wikipedia tells us that an abacus (counting frame) is a calculating tool–in these times, a bamboo frame with beads sliding on wires.  In times past, beans, stones, or metals were used.  The abacus is still widely used by merchants, traders, and clerks.  Many abaci are beautifully crafted and wonderful to look at and touch.  They are also easily reversible for lefties–just flip it over.

The abacus is not just for adding, subtracting, multiplying, and dividing.  You can use it for square and cube roots, logarithms, linear equations, vector norms, and more.

These countries used/use abaci–
Mesopotamia, Egypt, Persia, Iran, Greece, Rome, China, India, Japan, Korea, Native America, and Russia.  In Japan, the abacus is called a soroban  (算盤, そろばん, counting tray), and was imported from China around 1600.

Why use an abacus?
The abacus is highly prized in areas of the world that don’t have steady electricity. Many, many people can compute on it faster than you could use a calculator.  It’s also a fine tool for the visually impaired. As an arithmetic teaching tool, it has been of immense value. In fact,—20 most important tools ranks the abacus as the second most important tool of all time.  (The first is the knife.)

The wikipedia entry has a few tutorial links, and I’m sure the web in general has a lot of them. The one I liked best is from Totton Heffelfinger and Gary Flom—Abacus: Mystery of the Bead.

From their tutorial–

Dividing the upper and lower portion of the soroban is a horizontal bar called a beam or reckoning bar.

On a modern-day soroban, 1 bead sits above the beam and 4 beads sit below. (The Chinese use 2 beads above and 5 below.) The beads above the beam are often called heaven beads and each has a value of 5. The beads below are often called earth beads and each has a value of 1.

The value zero is represented when no beads touch the beam.  To represent a number you move beads to touch the beam, either from above or from below.  Starting from the units column, or rod, a bead moved to touch the beam from below equals 1.  A bead in that same rod moved down from above to touch the beam equals 5.   So if, in the “units” rod, one beam from above and three from below touched the beam, the value shown would be 5 +3, or 8.

Setting numbers on a soroban
Use only the thumb and index fingers to manipulate beads on a soroban. The thumb moves the earth beads up toward the beam. The index finger moves everything else (all earth beads down away from the beam and all heaven beads up & down).

moving earth beads down

moving heaven beads up

moving heaven beads down

Clearing a soroban
You want to start with an empty or cleared soroban. Lay the soroban flat on a table, then tilt the frame horizontally toward you. Gravity pulls all the beads down. Now the earth beads have been cleared away from the beam.Lay the soroban back onto the table and steady it  in your left hand. Using the nail side of the right index finger, make a sweeping motion from left to right between the top of the beam and the bottom of the heaven beads. clearing the heaven beads.

This moves the heaven beads up away from the beam. When none of the rods shows any value, this is a cleared frame: zero.

A process of thoughtlessness
In competent hands, a soroban is a very powerful calculating tool. Much of its speed is attributed to the concept of mechanization. The idea is to minimize mental work as much as possible and to perform the task of adding and subtracting beads mechanically, without thought or hesitation—to develop a process of thoughtlessness.

For more on complementary numbers, cultivating thoughtlessness, adding, subtracting, the order of the rod, and finger movements, see Totton Heffelfinger and Gary Flom, Abacus: Mystery of the Bead.

David Bernazzani’s Soroban-Abacus Handbook (PDF)