Сурелы Ыоуре Joking, Mr. Феынман: Adventures of a Curious Character   ::   Feynman Richard Phillips

So when I got to MIT there was a dance, and one of the seniors had his girlfriend there, and she knew a lot of puzzles, and he was telling her that I was pretty good at them. So during the dance she came over to me and said, “They say you’re a smart guy, so here’s one for you: A man has eight cords of wood to chop …”

And I said, “He starts by chopping every other one in three parts,” because I had heard that one.

Then she’d go away and come back with another one, and I’d always know it.

This went on for quite a while, and finally, near the end of the dance, she came over, looking as if she was going to get me for sure this time, and she said, “A mother and daughter are traveling to Europe …”

“The daughter got the bubonic plague.”

She collapsed! That was hardly enough clues to get the answer to that one: It was the long story about how a mother and daughter stop at a hotel and stay in separate rooms, and the next day the mother goes to the daughter’s room and there’s nobody there, or somebody else is there, and she says, “Where’s my daughter?” and the hotel keeper says, “What daughter?” and the register’s got only the mother’s name, and so on, and so on, and there’s a big mystery as to what happened. The answer is, the daughter got bubonic plague, and the hotel, not wanting to have to close up, spirits the daughter away, cleans up the room, and erases all evidence of her having been there. It was a long tale, but I had heard it, so when the girl started out with, “A mother and daughter are traveling to Europe,” I knew one thing that started that way, so I took a flying guess, and got it.

We had a thing at high school called the algebra team, which consisted of five kids, and we would travel to different schools as a team and have competitions. We would sit in one row of seats and the other team would sit in another row. A teacher, who was running the contest, would take out an envelope, and on the envelope it says “forty-five seconds.” She opens it up, writes the problem on the blackboard, and says, “Go!”—so you really have more than forty-five seconds because while she’s writing you can think. Now the game was this: You have a piece of paper, and on it you can write anything, you can do anything. The only thing that counted was the answer. If the answer was “six books,” you’d have to write “6,” and put a big circle around it. If what was in the circle was right, you won; if it wasn’t, you lost.

One thing was for sure: It was practically impossible to do the problem in any conventional, straightforward way, like putting “A is the number of red books, B is the number of blue books,” grind, grind, grind, until you get “six books.” That would take you fifty seconds, because the people who set up the timings on these problems had made them all a trifle short. So you had to think, “Is there a way to see it?” Sometimes you could see it in a flash, and sometimes you’d have to invent another way to do it and then do the algebra as fast as you could. It was wonderful practice, and I got better and better, and I eventually got to be the head of the team. So I learned to do algebra very quickly, and it came in handy in college. When we had a problem in calculus, I was very quick to see where it was going and to do the algebra—fast.

Another thing I did in high school was to invent problems and theorems. I mean, if I were doing any mathematical thing at all, I would find some practical example for which it would be useful. I invented a set of right-triangle problems. But instead of giving the lengths of two of the sides to find the third, I gave the difference of the two sides. A typical example was: There’s a flagpole, and there’s a rope that comes down from the top. When you hold the rope straight down, it’s three feet longer than the pole, and when you pull the rope out tight, it’s five feet from the base of the pole. How high is the pole?

I developed some equations for solving problems like that, and as a result I noticed some connection—perhaps it was sin 2  + cos 2  = 1 —that reminded me of trigonometry. Now, a few years earlier, perhaps when I was eleven or twelve, I had read a book on trigonometry that I had checked out from the library, but the book was by now long gone. I remembered only that trigonometry had something to do with relations between sines and cosines. So I began to work out all the relations by drawing triangles, and each one I proved by myself. I also calculated the sine, cosine, and tangent of every five degrees, starting with the sine of five degrees as given, by addition and half-angle formulas that I had worked out.

A few years later, when we studied trigonometry in school, I still had my notes and I saw that my demonstrations were often different from those in the book. Sometimes, for a thing where I didn’t notice a simple way to do it, I went all over the place till I got it. Other times, my way was most clever—the standard demonstration in the book was much more complicated! So sometimes I had ‘em heat, and sometimes it was the other way around.

While I was doing all this trigonometry, I didn’t like the symbols for sine, cosine, tangent, and so on. To me, “sin f” looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign.

Now the inverse sine was the same sigma, but left-to-right reflected so that it started with the horizontal line with the value underneath, and then the sigma. That was the inverse sine, NOT sink f—that was crazy! They had that in books! To me, sini meant i/sine, the reciprocal. So my symbols were better.

I didn’t like f(x)—that looked to me like f times x. I also didn’t like dy/dx—you have a tendency to cancel the d’s—so I made a different sign, something like an & sign. For logarithms it was a big L extended to the right, with the thing you take the log of inside, and so on.

I thought my symbols were just as good, if not better, than the regular symbols—it doesn’t make any difference what symbols you use—but I discovered later that it does make a difference. Once when I was explaining something to another kid in high school, without thinking I started to make these symbols, and he said, “What the hell are those?” I realized then that if I’m going to talk to anybody else, I’ll have to use the standard symbols, so I eventually gave up my own symbols.