“Surely You’re Joking, Mr. Feynman”: Adventures of a Curious Character

“Raios cubicos!” he says, with a vengeance. Cube roots! He wants to do cube roots by arithmetic! It’s hard to find a more difficult fundamental problem in arithmetic. It must have been his topnotch exercise in abacus-land.

He writes a number on some paper—any old number—and I still remember it: 1729.03. He starts working on it, mumbling and grumbling: “Mmmmmmagmmmmbrrr ”—he’s working like a demon! He’s poring away, doing this cube root.

Meanwhile I’m just sitting there.

One of the waiters says, “What are you doing?”

I point to my head. “Thinking!” I say. I write down 12 on the paper. After a little while I’ve got 12.002.

The man with the abacus wipes the sweat off his forehead: “Twelve!” he says.

“Oh, no!” I say. “More digits! More digits!” I know that in taking a cube root by arithmetic, each new digit is even more work than the one before. It’s a hard job.

He buries himself again, grunting, “Rrrrgrrrrmmmmmm …”

while I add on two more digits. He finally lifts his head to say, “12.0!”

The waiters are all excited and happy. They tell the man, “Look! He does it only by thinking, and you need an abacus! He’s got more digits!”

He was completely washed out, and left, humiliated. The waiters congratulated each other.

How did the customer beat the abacus? The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12. The excess, 1.03, is only one part in nearly 2000, and I had learned in calculus that for small fractions, the cube root’s excess is one-third of the number’s excess. So all I had to do is find the fraction 1/1728, and multiply by 4 (divide by 3 and multiply by 12). So I was able to pull out a whole lot of digits that way.

A few weeks later the man came into the cocktail lounge of the hotel I was staying at. He recognized me and came over. “Tell me,” he said, “how were you able to do that cube-root problem so fast?”

I started to explain that it was an approximate method, and had to do with the percentage of error. “Suppose you had given me 28. Now, the cube root of 27 is 3..

He picks up his abacus: zzzzzzzzzzzzzzz–

“Oh yes,” he says.

I realized something: he doesn’t know numbers. With the abacus, you don’t have to memorize a lot of arithmetic combinations; all you have to do is learn how to push the little beads up and down. You don’t have to memorize 9 + 7 = 16; you just know that when you add 9 you push a ten’s bead up and pull a one’s bead down. So we’re slower at basic arithmetic, but we know numbers.

Furthermore, the whole idea of an approximate method was beyond him, even though a cube root often cannot be computed exactly by any method. So I never could teach him how I did cube roots or explain how lucky I was that he happened to choose 1729.03.

O Americano, Outra Vez!

One time I picked up a hitchhiker who told me how interesting South America was, and that I ought to go there. I complained that the language is different, but he said just go ahead and learn it—it’s no big problem. So I thought, that’s a good idea: I’ll go to South America.

Cornell had some foreign language classes which followed a method used during the war, in which small groups of about ten students and one native speaker speak only the foreign language-nothing else. Since I was a rather young-looking professor there at Cornell, I decided to take the class as if I were a regular student. And since I didn’t know yet where I was going to end up in South America, I decided to take Spanish, because the great majority of the countries there speak Spanish.

So when it was time to register for the class, we were standing outside, ready to go into the classroom, when this pneumatic blonde came along. You know how once in a while you get this feeling, WOW? She looked terrific. I said to myself, “Maybe she’s going to be in the Spanish class—that’ll be great!” But no, she walked into the Portuguese class. So I figured, What the hell—I might as well learn Portuguese.

I started walking right after her when this Anglo-Saxon attitude that I have said, “No, that’s not a good reason to decide which language to speak.” So I went back and signed up for the Spanish class, to my utter regret.

Some time later I was at a Physics Society meeting in New York, and I found myself sitting next to Jaime Tiomno, from Brazil, and he asked, “What are you going to do next summer?”

“I’m thinking of visiting South America.”

“Oh! Why don’t you come to Brazil? I’ll get a position for you at the Center for Physical Research.”