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.
I had also invented a set of symbols for the typewriter, like FORTRAN has to do, so I could type equations. I also fixed typewriters, with paper clips and rubber bands (the rubber bands didn’t break down like they do here in Los Angeles), but I wasn’t a professional repairman; I’d just fix them so they would work. But the whole problem of discovering what was the matter, and figuring out what you have to do to fix it—that was interesting to me, like a puzzle.
String Beans
I must have been seventeen or eighteen when I worked one summer in a hotel run by my aunt. I don’t know how much I got—twenty-two dollars a month, I think—and I alternated eleven hours one day and thirteen the next as a desk clerk or as a busboy in the restaurant. And during the afternoon, when you were desk clerk, you had to bring milk up to Mrs. D—, an invalid woman who never gave us a tip. That’s the way the world was: You worked long hours and got nothing for it, every day.
This was a resort hotel, by the beach, on the outskirts of New York City. The husbands would go to work in the city and leave the wives behind to play cards, so you would always have to get the bridge tables out. Then at night the guys would play poker, so you’d get the tables ready for them—clean out the ashtrays and so on. I was always up until late at night, like two o’clock, so it really was thirteen and eleven hours a day.
There were certain things I didn’t like, such as tipping. I thought we should be paid more, and not have to have any tips. But when I proposed that to the boss, I got nothing but laughter. She told everybody, “Richard doesn’t want his tips, hee, hee, hee; he doesn’t want his tips, ha, ha, ha.” The world is full of this kind of dumb smart-alec who doesn’t understand anything.
Anyway, at one stage there was a group of men who, when they’d come back from working in the city, would right away want ice for their drinks. Now the other guy working with me had really been a desk clerk. He was older than I was, and a lot more professional. One time he said to me, “Listen, we’re always bringing ice up to that guy Ungar and he never gives us a tip—not even ten cents. Next time, when they ask for ice, just don’t do a damn thing. Then they’ll call you back, and when they call you back, you say, ‘Oh, I’m sorry. I forgot. We’re all forgetful sometimes.’ ”
So I did it, and Ungar gave me fifteen cents! But now, when I think back on it, I realize that the other desk clerk, the professional, had really known what to do—tell the other guy to take the risk of getting into trouble. He put me to the job of training this fella to give tips. He never said anything; he made me do it!
I had to clean up tables in the dining room as a busboy. You pile all this stuff from the tables on to a tray at the side, and when it gets high enough you carry it into the kitchen. So you get a new tray, right? You should do it in two steps—take the old tray away, and put in a new one—but I thought, “I’m going to do it in one step.” So I tried to slide the new tray under, and pull the old tray out at the same time, and it slipped—BANG! All the stuff went on the floor. And then, naturally, the question was, “What were you doing? How did it fall?” Well, how could I explain that I was trying to invent a new way to handle trays?
Among the desserts there was some kind of coffee cake that came out very pretty on a doily, on a little plate. But if you would go in the back you’d see a man called the pantry man. His problem was to get the stuff ready for desserts. Now this man must have been a miner, or something—heavy built, with very stubby, rounded, thick fingers. He’d take this stack of doilies, which are manufactured by some sort of stamping process, all stuck together, and he’d take these stubby fingers and try to separate the doilies to put them on the plates. I always heard him say, “Damn deez doilies!” while he was doing this, and I remember thinking, “What a contrast—the person sitting at the table gets this nice cake on a doilied plate, while the pantry man back there with the stubby thumbs is saying, ‘Damn deez doilies!’ ” So that was the difference between the real world and what it looked like.
My first day on the job the pantry lady explained that she usually made a ham sandwich, or something, for the guy who was on the late shift. I said that I liked desserts, so if there was a dessert left over from supper, I’d like that. The next night I was on the late shift till 2:00 A.M. with these guys playing poker. I was sitting around with nothing to do, getting bored, when suddenly I remembered there was a dessert to eat. I went over to the icebox and opened it up, and there she’d left six desserts! There was a chocolate pudding, a piece of cake, some peach slices, some rice pudding, some jello—there was everything! So I sat there and ate the six desserts—it was sensational!
The next day she said to me, “I left a dessert for you.”
“It was wonderful,” I said, “absolutely wonderful!”
“But I left you six desserts because I didn’t know which one you liked the best.”
So from that time on she left six desserts. They weren’t always different, but there were always six desserts.
One time when I was desk clerk a girl left a book by the telephone at the desk while she went to eat dinner, so I looked at it. It was The Life of Leonardo, and I couldn’t resist: The girl let me borrow it and I read the whole thing.
I slept in a little room in the back of the hotel, and there was some stew about turning out the lights when you leave your room, which I couldn’t ever remember to do. Inspired by the Leonardo book, I made this gadget which consisted of a system of strings and weights—Coke bottles full of water—that would operate when I’d open the door, lighting the pull-chain light inside. You open the door, and things would go, and light the light; then you close the door behind you, and the light would go out. But my real accomplishment came later.