Surely You're Joking, Mr. Feynman! (26 page)

After that, I tried to do those things. I memorized a few logs, and began to notice things. For instance, if somebody says, “What is 28 squared?” you notice that the square root of 2 is 1.4, and 28 is 20 times 1.4, so the square of 28 must be around 400 times 2, or 800.

If somebody comes along and wants to divide 1 by 1.73, you can tell them immediately that it’s .577, because you notice that 1.73 is nearly the square root of 3, so 1/1.73 must be one-third of the square root of 3. And if it’s ‘/1.75, that’s equal to the inverse of 7/4, and you’ve memorized the repeating decimals for sevenths: .571428.

I had a lot of fun trying to do arithmetic fast, by tricks, with Hans. It was very rare that I’d see something he didn’t see and beat him to the answer, and he’d laugh his hearty laugh when I’d get one. He was nearly always able to get the answer to any problem within a percent. It was easy for him–every number was near something he knew.

One day I was feeling my oats. It was lunch time in the technical area, and I don’t know how I got the idea, but I announced, “I can work out in sixty seconds the answer to any problem that anybody can state in ten seconds, to 10 percent!”

People started giving me problems they thought were difficult, such as integrating a function like 1/(1 + x ), which hardly changed over the range they gave me. The hardest one somebody gave me was the binomial coefficient of x^10 in (1 + x)^20; I got that just in time.

They were all giving me problems and I was feeling great, when Paul Olum walked by in the hall. Paul had worked with me for a while at Princeton before coming out to Los Alamos, and he was always cleverer than I was. For instance, one day I was absent-mindedly playing with one of those measuring tapes that snap back into your hand when you push a button. The tape would always slap over and hit my hand, and it hurt a little bit. “Geez!” I exclaimed. “What a _dope_ I am. I keep playing with this thing, and it hurts me every time.”

He said, “You don’t hold it right,” and took the damn thing, pulled out the tape, pushed the button, and it came right back. No hurt.

“Wow! How do you _do_ that?” I exclaimed.

“Figure it out!”

For the next two weeks I’m walking all around Princeton, snapping this tape back until my hand is absolutely raw Finally I can’t take it any longer. “Paul! I give up! How the hell do you hold it so it doesn’t hurt?”

“Who says it doesn’t hurt? It hurts me too!”

I felt so stupid. He had gotten me to go around and hurt my hand for two weeks!

So Paul is walking past the lunch place and these guys are all excited. “Hey, Paul!” they call out. “Feynman’s terrific! We give him a problem that can be stated in ten seconds, and in a minute he gets the answer to 10 percent. Why don’t you give him one?”

Without hardly stopping, he says, “The tangent of 10 to the 100th.”

I was sunk: you have to divide by pi to 100 decimal places! It was hopeless.

One time I boasted, “I can do by other methods any integral anybody else needs contour integration to do.”

So Paul puts up this tremendous damn integral he had obtained by starting out with a complex function that he knew the answer to, taking out the real part of it and leaving only the complex part. He had unwrapped it so it was _only_ possible by contour integration! He was always deflating me like that. He was a very smart fellow.

The first time I was in Brazil I was eating a noon meal at I don’t know what time–I was always in the restaurants at the wrong time–and I was the only customer in the place. I was eating rice with steak (which I loved), and there were about four waiters standing around.

A Japanese man came into the restaurant. I had seen him before, wandering around; he was trying to sell abacuses. He started to talk to the waiters, and challenged them: He said he could add numbers faster than any of them could do.

The waiters didn’t want to lose face, so they said, “Yeah, yeah. Why don’t you go over and challenge the customer over there?”

The man came over. I protested, “But I don’t speak Portuguese well!”

The waiters laughed. “The numbers are easy,” they said.

They brought me a pencil and paper.

The man asked a waiter to call out some numbers to add. He beat me hollow, because while I was writing the numbers down, he was already adding them as he went along.

I suggested that the waiter write down two identical lists of numbers and hand them to us at the same time. It didn’t make much difference. He still beat me by quite a bit.

However, the man got a little bit excited: he wanted to prove himself some more. “_Multiplicao!_” he said.

Somebody wrote down a problem. He beat me again, but not by much, because I’m pretty good at products.

The man then made a mistake: he proposed we go on to division. What he didn’t realize was, the harder the problem, the better chance I had.

We both did a long division problem. It was a tie.

This bothered the hell out of the Japanese man, because he was apparently very well trained on the abacus, and here he was almost beaten by this customer in a restaurant.

“_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.”

So now I had to convert all that Spanish into Portuguese! I found a Portuguese graduate student at Cornell, and twice a week he gave me lessons, so I was able to alter what I had learned. On the plane to Brazil I started out sitting next to a guy from Colombia who spoke only Spanish: so I wouldn’t talk to him because I didn’t want to get confused again. But sitting in front of me were two guys who were talking Portuguese. I had never heard _real_ Portuguese; I had only had this teacher who had talked very slowly and clearly. So here are these two guys talking a blue streak, _brrrrrrr-a-ta brrrrrrr-a-ta_, and I can’t even hear the word for “I,” or the word for “the,” or anything.

Finally, when we made a refueling stop in Trinidad, I went up to the two fellas and said very slowly in Portuguese, or what I thought was Portuguese, “Excuse me . . . can you understand . . . what I am saying to you now?”

“_Pues não, porque não?_”–” Sure, why not?” they replied.

So I explained as best I could that I had been learning Portuguese for some months now, but I had never heard it spoken in conversation, and I was listening to them on the airplane, but couldn’t understand a word they were saying.

“Oh,” they said with a laugh, “_Nao e Portugues! E Ladäo! Judeo!_” What they were speaking was to Portuguese as Yiddish is to German, so you can imagine a guy who’s been studying German sitting behind two guys talking Yiddish, trying to figure out what’s the matter. It’s obviously German, but it doesn’t work. He must not have learned German very well.

When we got back on the plane, they pointed out another man who did speak Portuguese, so I sat next to him. He had been studying neurosurgery in Maryland, so it was very easy to talk with him–as long as it was about _cirugia neural, o cerebreu_, and other such “complicated” things. The long words are actually quite easy to translate into Portuguese because the only difference is their endings: “-tion” in English is “-çao” in Portuguese; “-ly” is “-mente,” and so on. But when he looked out the window and said something simple, I was lost: I couldn’t decipher “the sky is blue.”

I got off the plane in Recife (the Brazilian government was going to pay the part from Recife to Rio) and was met by the father-in-law of Cesar Lattes, who was the director of the Center for Physical Research in Rio, his wife, and another man. As the men were off getting my luggage, the lady started talking to me in Portuguese: “You speak Portuguese? How nice! How was it that you learned Portuguese?”

I replied slowly, with great effort. “First, I started to learn Spanish. . . then I discovered I was going to Brazil.

Now I wanted to say, “So, I learned Portuguese,” but I couldn’t think of the word for “so.” I knew how to make BIG words, though, so I finished the sentence like this: “_CONSEQUENTEMENTE, apprendi Portugues!_”

When the two men came back with the baggage, she said, “Oh, he speaks Portuguese! And with such wonderful words: _CONSEQUENTEMENTE!_”

Then an announcement came over the loudspeaker. The flight to Rio was canceled, and there wouldn’t be another one till next Tuesday–and I had to be in Rio on Monday, at the latest.

I got all upset. “Maybe there’s a cargo plane. I’ll travel in a cargo plane,” I said.

“Professor!” they said, “It’s really quite nice here in Recife. We’ll show you around. Why don’t you relax–you’re in _Brazil_.”

That evening I went for a walk in town, and came upon a small crowd of people standing around a great big rectangular hole in the road–it had been dug for sewer pipes, or something–and there, sitting exactly in the hole, was a car. It was marvelous: it fitted absolutely perfectly, with its roof level with the road. The workmen hadn’t bothered to put up any signs at the end of the day, and the guy had simply driven into it. I noticed a difference: When _we’d_ dig a hole, there’d be all kinds of detour signs and flashing lights to protect us. There, they dig the hole, and when they’re finished for the day, they just leave.

Anyway, Recife _was_ a nice town, and I _did_ wait until next Tuesday to fly to Rio.

When I got to Rio I met Cesar Lattes. The national TV network wanted to make some pictures of our meeting, so they started filming, but without any sound. The cameramen said, “Act as if you’re talking. Say something–anything.”

So Lattes asked me, “Have you found a sleeping dictionary yet?”

That night, Brazilian TV audiences saw the director of the Center for Physical Research welcome the Visiting Professor from the United States, but little did they know that the subject of their conversation was finding a girl to spend the night with!