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Chapter 15 - Numbers Lesson: An Attempt to Teach Mathematical Innocence After the Crash

The old man was pleased with such a request; he cleared his throat and began to speak.

"Twenty or thirty years ago, my story would have been very popular, but these days, no one seems interested..."

"There you go again!" cried Hair-lip, irritated. "Stop this strange talk and speak intelligibly. What does 'interested' mean? You speak like a child who hasn't learned to speak."

"Leave him alone," Edwin warned him. "Or he'll get angry and won't speak at all. Ignore the strange bits. We'll understand some of what he's telling us."

The old man had already begun to mutter about the disrespect of elders and the regression of all human beings to barbarism after they have fallen from the heights of civilization to this primitive state; Ho-Ho encouraged him to speak, saying, "Tell us the story, Grandpa."

And the story began.

"There were a great many people in those days. San Francisco alone had four million..."

"What millions?" Edwin interrupted.

Grandpa looked at him sympathetically and said, "I know you can't count past ten, so I'll tell you. Hold up both of your hands. You have ten fingers on them. Okay, now I'll take this grain of sand. You hold it, Ho-Ho." He placed the grain of sand in the boy's palm and continued, "Now this grain of sand represents Edwin's ten fingers. "I will add another grain of sand, which means I add ten more fingers, then a third, then a fourth, then a fifth, until the number of grains of sand equals the number of Edwin's ten fingers. This equals what I will call a hundred. Remember this word: a hundred. Now, I will put this pebble in Hair-lip's hand, and it represents ten grains of sand or ten tens of fingers or a hundred fingers. I put in ten pebbles, and it represents a thousand fingers. I take an oyster shell, and it represents ten pebbles or a hundred grains of sand or a thousand fingers…" And so with much effort and much repetition, he tried to form in their minds a rudimentary conception of numbers. As the quantities increased, he would ask the boys to hold different quantities in their hands. When representing larger quantities, he would place symbols on a piece of driftwood, and he had some difficulty finding these symbols; He had to use teeth extracted from skulls to represent millions, and crab shells to represent billions. He stopped there, however, as the boys began to show signs of exhaustion.

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