Today, a witch doctor practices computer
arithmetic. The University of Houston's College of
Engineering presents this series about the machines
that make our civilization run, and the people
whose ingenuity created them.

The scene is a remote
Ethiopian village in 1940. A Farmer offers his herd
of 34 goats for sale. One goat is worth, say $7.
The villagers don't know how to multiply, so they
call in a shaman. They ask him to set a fair price
for the whole herd.

The shaman digs two rows of small holes in the hard
dry earth. He reaches into his sack of pebbles and
goes to work. He puts 34 stones in the first hole
on the left -- one for each goat. He puts half
that, or 17, in the next -- half 17, or 8, in the
next -- and so on. He keeps dividing by two and
dropping the remainder, until the sixth hole has
only one stone in it.

Now he goes to the other row. He puts 7 stones --
the value of one goat -- in the first hole. He puts
twice that, or 14 stones in the next hole, and so
on. Now his deliberations begin.

He goes down the left-hand side, seeing whether the
holes are good or evil. An even number of stones
makes the hole evil. An odd number makes it good.
Two holes are good. The holes next to them, in the
right row, contain 14 stones and 224 stones. He
adds those numbers together. The result is the fair
market value of the herd. It's $238.

You and I know about multiplication. So we multiply
the number of sheep, by the value of a sheep -- 7
times 34. When we do that, we get $238. But that's
just what the shaman got! So what in the world was
all the business with the holes? And would he get
the right answer with different numbers?

We try it with other numbers. It works every time.
So we turn to a mathematician. He says it's not at
all obvious. He puzzles for a long time. Finally he
sees it. This Ethiopian shaman has created a
remarkable algorithm.

All that business with the holes identifies the
numbers in their binary form. That lets the shaman
reduce multiplication to simple addition. He's
multiplied just the way a digital computer does.
Where did his method come from? How long have his
forbears carried this rote tradition?

An anonymous genius lurks somewhere in the haze of
his history. So we look at our own multiplication
and realize that we too use ritual to find what 7
times 34 is. It makes no more sense to most people
who use it than the shaman's holes. Our
multiplication algorithm was also given us by an
anonymous genius. He is also lost in rote
tradition.

So how do we and that Ethiopian shaman differ? Very
little, I reckon. Very little indeed. Of course, I
wouldn't be surprised if he makes fewer mistakes
than we do.

I'm John Lienhard at the University of Houston,
where we're interested in the way inventive minds
work.

(Theme music)

Currie, W.S., Binary in the Stone Age.
Geophysics: The Leading Edge of
Exploration, March, 1985, pp. 50-52.

The shaman's multiplication of 7 x 34:

row #1 row #2 the calculation
34 stones (evil) 7 evil 0
17 (good) 14 good 14
8 (evil) 28 evil 0
4 (evil) 56 evil 0
2 (evil) 112 evil o
1 (good) 224 good 224
________
238 = 7 x 34

The Engines of Our Ingenuity is
Copyright © 1988-1997 by John H.
Lienhard.

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