Hans Magnus Enzensberger - The Number Devil: A Mathematical Adventure

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Contents

For Theresia

The First Night

Robert was tired of dreaming. I always come out looking dumb, he said to himself.

For example, he would dream of being swallowed by a big ugly fish, and even after it was over he could smell the fishs awful stench. Or hed be sliding down an endless slide, faster and faster, and no matter how many times he cried out Stop! or Help! on he went until finally he woke up drenched in sweat.

His dreams also played tricks on him whenever he wanted something really bad. Once he had his heart set on a racing bike with twenty-eight gears, and he dreamed that the bike was waiting for him in the basement. It was an unbelievably detailed dream: the bike had a purple metallic finish and was parked next to the wine cabinet. He even knew the sequence of the combination lock: 12345. He couldnt forget that now, could he? Well, in the middle of the night, still woozy with sleep, he staggered down to the basement in his pajamas, and what did he find next to the wine cabinet? A dead mouse. That was a low blow!

Eventually Robert came up with a way of dealing with the tricks his dreams played on him. The minute one started, he would think (without waking up), Its just another one of those yucky fish. I know just whats going to happen. Its going to gobble me up. But I also know its only a dream, because only in dreams can a fish swallow a person. Or hed think, Here I go sliding again, but theres nothing I can do about it. I cant stop, and Im not really sliding, anyway. And when the fantastic racing bike came back to haunt him, or a computer game he couldnt live withoutthere it was, right

next to the telephonehe knew it was just a hoax. He didnt even look at the bike; he turned away. But no matter what he did, the dreams kept coming back, and that troubled him.

And then suddenly one nightthere was the number devil!

Robert was thrilled to be free of the hungry fish and the endless slide. This time he dreamed of a meadow. The funny thing was that the grass grew so tall that it seemed to reach the sky, or at least over his head. And what did he see but a gigantic beetle glaring at him, a caterpillar perched on a blade of grass, and an elderly man the size of a grasshopper bobbing up and down on a spinach leaf and staring at him with bright and shining eyes.

Who are you? Robert asked.

The man responded in a surprisingly loud voice.

I am the number devil!

Robert was in no mood to put up with nonsense from a pip-squeak like that.

First of all, theres no such thing as a number devil.

Is that so? How can you be speaking to me if I dont exist?

And besides I hate everything that has to do with numbers.

And why is that, may I ask?

You sound as though you never went to school. Or maybe you are a teacher yourself?

If 2 pretzel makers can make 444 pretzels in 6 hours, how long does it take 5 pretzel makers to make 88 pretzels?

How dumb can you get! said Robert. A colossal waste of time if you ask me. So get going! Scram! Shoo!

But instead of doing as he was bidden, the number devil made an elegant leap and landed smack next to Robert, who was staging a sit-down strike in the tall grass.

Where does your pretzel tale come from? School, I bet.

Where else? said Robert. Mr. Bockelhes our teacher, a new teacherwell, hes always hungry, though hes got plenty of fat on him. Whenever he thinks were not looking because were so into the problems he gives us, he sneaks these pretzels out of his briefcase and wolfs them down.

I see, said the number devil with a wry smile. I have nothing against your Mr. Bockel, but that kind of problem has nothing whatever to do with what Im interested in. Do you want to know something? Most genuine mathematicians are bad at sums. Besides, they have no time to waste on them. Thats what pocket calculators are for. I assume you have one.

Sure, but were not allowed to use them in school.

What did Robert see but an elderly man the size of a grasshopper bobbing up and down on a spinach leaf and staring at him with bright and shining eyes.

I see, said the number devil. Thats all right. Theres nothing wrong with a little addition and subtraction. You never know when your battery will die on you. But mathematics, my boy, thats something else again!

Youre just trying to win me over, said Robert. I dont trust you. If you give me homework in my dream, Ill scream bloody murder. Thats child abuse!

If Id known you were going to be such a scaredy-cat, I wouldnt have entered your dream. All I want is to perk you up a little, and since Im off duty most nights, I thought Id spare you those endless slides youve been going down.

Gosh, thanks.

Im glad you understand.

But I hope you understand that I wont let you take me for a ride.

Suddenly the number devil leaped up out of the grass, a pip-squeak no more.

Thats no way to talk to a devil, he shouted, his eyes sparkling, and he trampled the grass until it was all flat.

Im sorry, Robert said meekly, though the whole thing was getting weirder and weirder. But if talking about numbers is as simple as talking about movies or bikes, why do they need their own devil?

Youve hit the nail on the head, my boy, the devil replied. The thing that makes numbers so devilish is precisely that they are simple. And you dont need a calculator to prove it. You need one thing and one thing only: one. With oneI am speaking of the numeral, of courseyou can do almost anything. If you are afraid of large numberslets say five million seven hundred and twenty-three thousand eight hundred and twelveall you have to do is start with

and go on until you come to five million etcetera. You cant tell me thats too complicated for you, can you? Any idiot can see that.

Right, said Robert.

And thats not all, the number devil added, picking up a walking stick with a silver knob and twirling it in front of Roberts nose. When you get to five million etcetera, you can go on. Indefinitely. Theres an infinite number of numbers.

Robert didnt quite know whether to believe him.

How can you be so sure? he asked. Have you ever tried?

Cant say I have, the devil answered. It would take too long, for one thing. And it makes no sense anyway. It would be a waste of time.

Robert didnt see why.

Either I can count to the end, in which case there is no such thing as infinity, or there is no end and I cant count to it.

Wrong! the number devil shouted, his mustache quivering, his eyes bulging, and his face turning red with rage.