The Number Devil: "The Fourth Night"–"The Sixth Night"

“True,” said the number devil, “but then you’ve got to deal with fractions, and fractions, if I’m not mistaken, are something you can’t abide. ‘If ⅓ of 33 bakers can make 89 pretzels in 2½ hours, then how many pretzels can 5¾ bakers make in 1½ hours?'"

By now he knew that whenever it happened there was something interesting coming up, something the number devil couldn’t easily explain. But the chain was flapping dangerously close to Robert’s head and had wound so tightly round the number devil that much of him had receded from view.

“It’s about time,” said the number devil, raising his stick, which now had several layers of nines entwined around it. Then he mumbled some gibberish to himself and the chains disappeared in a flash.

“It’s about time,” said the number devil, raising his stick, which now had several layers of nines entwined around it. Then he mumbled some gibberish to himself and the chains disappeared in a flash.

“Twenty-five,” said Robert, “is five times five, which makes its rutabaga five.”
“Keep it up, Robert, and you’ll be my apprentice someday. Rutabaga of thirty-six?”

“Right you are, but I’m afraid I can’t help you there. Taking the number any farther would mean running myself, or my calculator, into the ground.”
“Well, let’s try something a little less daunting.”

“Well, squares are wily beasties. Never trust a square. They may look innocent, but they can be full of tricks. Take this one, for instance.” And he carved a perfectly ordinary empty square into the sand.

“It’s not so bad as all that,” said the number devil. “But we don’t need to work it out. Just don’t go thinking that unreasonable numbers are a rarity. Quite the contrary. Take it from me, they’re like sand on the beach, more common even than the other kind.”

“Now you’re going too far,” said Robert in no uncertain terms. “I refuse to believe it. More than infinite? Nothing is more than infinite. That’s a lot of malarkey, that’s what it is.”

“Want me to prove it?” asked the number devil. “Want me to conjure up all the unreasonable numbers at once?”

Robert waited and waited for his visitor from the realm of numbers, but the number devil never came.

The heat was terrible. It was just the kind of thing he hated about dreams. On and on he trudged, thirsty, sweaty, with blisters all over his feet, until at last he made out a few trees in the distance.

It must be either a mirage or an oasis, he thought.

So on he hobbled until he came to the first palm. And there he heard a voice calling, a voice he was sure he knew.

“Come on up,” said the number devil. Marshaling all the strength he had left, Robert climbed to the top of the tree.

“Any plans for today?”
“Don’t you need to rest after your trek across the desert?”

“A cinch—” 12 = 1 + 1 + 10
“See what I mean? It always works. And now for something truly sensational. Add each triangle number to the one next to it and you won’t believe what you get.”

“Six times thirteen,” said Robert, “is seventy-eight. The twelfth triangle number!”
“See what triangle numbers are good for? And by the way, quadrangle numbers aren’t bad either.”

“The only what?” asked Robert.
“The only number devil. But I’m not. I’m one of many. Number Heaven, where I come from, is teeming with us. I’m not even one of the bosses. The bosses do nothing but sit and think. There are times when I don’t understand a thing.”

“You poor devil,” Robert said. “Here I thought you were so sure of yourself.”
“Why do you think they send me out at night? Because the bigwigs have things to do other than visiting apprentices like you.”

Next the number devil started running through the Bonacci numbers in a kind of singsong. The aria from a Bonacci opera, you might say.

“Fine, fine. Fine and dandy. But tell me, what are they good for, your Bonacci numbers?”
“You don’t think mathematics is for mathematicians only? Nature needs numbers too. Trees add. Fish subtract.”

But even as he spoke, new hordes of rabbits were being born and joining their brown and white kin romping over the potato field.

But even as he spoke, new hordes of rabbits were being born and joining their brown and white kin romping over the potato field.

The number devil went back his old friend Bonacci and their number-crunching cronies in Number Heaven.