Bringing Culture to the Physicists

Nina Byers, a professor at UCLA, became in charge of the physics colloquium sometime in the early seventies. The colloquia are normally a place where physicists from other universities come and talk pure technical stuff. But partly as a result of the atmosphere of that particular period of time, she got the idea that the physicists needed more culture, so she thought she would arrange something along those lines: Since Los Angeles is near Mexico, she would have a colloquium on the mathematics and astronomy of the Mayans—the old civilization of Mexico.

(Remember my attitude to culture: This kind of thing would have driven me crazy if it were in my university!)

She started looking for a professor to lecture on the subject, and couldn’t find anybody at UCLA who was quite an expert. She telephoned various places and still couldn’t find anybody.

Then she remembered Professor Otto Neugebauer, of Brown University, the great expert on Babylonian mathematics [2]. She telephoned him in Rhode Island and asked if he knew someone on the West Coast who could lecture on Mayan mathematics and astronomy.

“Yes,” he said. “I do. He’s not a professional anthropologist or a historian; he’s an amateur. But he certainly knows a lot about it. His name is Richard Feynman.”

She nearly died! She’s trying to bring some culture to the physicists, and the only way to do it is to get a physicist!

The only reason I knew anything about Mayan mathematics was that I was getting exhausted on my honeymoon in Mexico with my second wife, Mary Lou. She was greatly interested in •art history, particularly that of Mexico. So we went to Mexico for our honeymoon and we climbed up pyramids and down pyramids; she had me following her all over the place. She showed me many interesting things, such as certain relationships in the designs of various figures, but after a few days (and nights) of going up and down in hot and steamy jungles, I was exhausted.

In some little Guatemalan town in the middle of nowhere we went into a museum that had a case displaying a manuscript full of strange symbols, pictures, and bars and dots. It was a copy (made by a man named Villacorta) of the Dresden Codex, an original book made by the Mayans found in a museum in Dresden. I knew the bars and dots were numbers. My father had taken me to the New York World’s Fair when I was a little kid, and there they had reconstructed a Mayan temple. I remembered him telling me how the Mayans had invented the zero and had done many interesting things.

The museum had copies of the codex for sale, so I bought one. On each page at the left was the codex copy, and on the right a description and partial translation in Spanish.

I love puzzles and codes, so when I saw the bars and dots, I thought, “I’m gonna have some fun!” I covered up the Spanish with a piece of yellow paper and began playing this game of deciphering the Mayan bars and dots, sitting in the hotel room, while my wife climbed up and down the pyramids all day.

I quickly figured out that a bar was equal to five dots, what the symbol for zero was, and so on. It took me a little longer to figure out that the bars and dots always carried at twenty the first time, but they carried at eighteen the second time (making cycles of 360). I also worked out all kinds of things about various faces: they had surely meant certain days and weeks.

After we got back home I continued to work on it. Altogether, it’s a lot of fun to try to decipher something like that, because when you start out you don’t know anything—you have no clue to go by. But then you notice certain numbers that appear often, and add up to other numbers, and so on.

There was one place in the codex where the number 584 was very prominent. This 584 was divided into periods of 236, 90, 250, and 8. Another prominent number was 2920, or 584 x 5 (also 365 x 8). There was a table of multiples of 2920 up to 13 x 2920, then there were multiples of 13 x 2920 for a while, and then—funnynumbers! They were errors, as far as I could tell. Only many years later did I figure out what they were.

Because figures denoting days were associated with this 584 which was divided up so peculiarly, I figured if it wasn’t some mythical period of some sort, it might be something astronomical, Finally I went down to the astronomy library and looked it up, and found that 583.92 days is the period of Venus as it appears from the earth. Then the 236, 90, 250, 8 became apparent: it must be the phases that Venus goes through. It’s a morning star, then it can’t be seen (it’s on the far side of the sun); then it’s an evening star, and finally it disappears again (it’s between the earth and the sun). The 90 and the 8 are different because Venus moves more slowly through the sky when it is on the far side of the sun compared to when it passes between the earth and the sun. The difference between the 236 and the 250 might indicate a difference between the eastern and western horizons in Maya land.

I discovered another table nearby that had periods of 11,959 days. This turned out to be a table for predicting lunar eclipses. Still another table had multiples of 91 in descending order. I never did figure that one out (nor has anyone else).

When I had worked out as much as I could, I finally decided to look at the Spanish commentary to see how much I was able to figure out. It was complete nonsense. This symbol was Saturn, this symbol was a god—it didn’t make the slightest bit of sense. So I didn’t have to have covered the commentary; I wouldn’t have learned anything from it anyway.

After that I began to read a lot about the Mayans, and found that the great man in this business was Eric Thompson, some of whose books I now have.

When Nina Byers called me up I realized that I had lost my copy of the Dresden Codex. (I had lent it to Mrs. H. P Robertson, who had found a Mayan codex in an old trunk of an antique dealer in Paris. She had brought it back to Pasadena for me to look at—I still remember driving home with it on the front seat of my car, thinking, “I’ve gotta be careful driving: I’ve got the new codex”—but as soon as I looked at it carefully, I could see immediately that it was a complete fake. After a little bit of work I could find where each picture in the new codex had come from in the Dresden Codex. So I lent her my book to show her, and I eventually forgot she had it.) So the librarians at UCLA worked very hard to find another copy of Villacorta’s rendition of the Dresden Codex, and lent it to me.

I did all the calculations all over again, and in fact I got a little bit further than I did before: I figured out that those “funny numbers” which I thought before were errors were really integer multiples of something closer to the correct period (583.923)—the Mayans had realized that 584 wasn’t exactly right! [3]

After the colloquium at UCLA Professor Byers presented me with some beautiful color reproductions of the Dresden Codex. A few months later Caltech wanted me to give the same lecture to the public in Pasadena. Robert Rowan, a real estate man, lent me some very valuable stone carvings of Mayan gods and ceramic figures for the Caltech lecture, It was probably highly illegal to take something like that out of Mexico, and they were so valuable that we hired security guards to protect them.

A few days before the Caltech lecture there was a big splurge in the New York Times, which reported that a new codex had been discovered. There were only three codices (two of which are hard to get anything out of) known to exist at the time-hundreds of thousands had been burned by Spanish priests as “works of the Devil.” My cousin was working for the AP, so she got me a glossy picture copy of what the New York Times had published and I made a slide of it to include in my talk.

This new codex was a fake. In my lecture I pointed out that the numbers were in the style of the Madrid codex, but were 236, 90, 250, 8—rather a coincidence! Out of the hundred thousand books originally made we get another fragment, and it has the same thing on it as the other fragments! It was obviously, again, one of these put-together things which had nothing original in it.

These people who copy things never have the courage to make up something really different. If you find something that is really new, it’s got to have something different. A real hoax would be to take something like the period of Mars, invent a mythology to go with it, and then draw pictures associated with this mythology with numbers appropriate to Mars—not in an obvious fashion; rather, have tables of multiples of the period with some mysterious “errors,” and so on. The numbers should have to be worked out a little bit. Then people would say, “Geez! This has to do with Mars!” In addition, there should be a number of things in it that are not understandable, and are not exactly like what has been seen before. That would make a good fake.

I got a big kick out of giving my talk on “Deciphering Mayan Hieroglyphics.” There I was, being something I’m not, again. People filed into the auditorium past these glass cases, admiring the color reproductions of the Dresden Codex and the authentic Mayan artifacts watched over by an armed guard in uniform; they heard a two-hour lecture on Mayan mathematics and astronomy from an amateur expert in the field (who even told them how to spot a fake codex), and then they went out, admiring the cases again. Murray Gell-Mann countered in the following weeks by giving a beautiful set of six lectures concerning the linguistic relations of all the languages of the world.

Found Out in Paris

I gave a series of lectures in physics that the Addison-Wesley Company made into a book, and one time at lunch we were discussing what the cover of the book should look like, I thought that since the lectures were a combination of the real world and mathematics, it would be a good idea to have a picture of a drum, and on top of it some mathematical diagrams—circles and lines for the nodes of the oscillating drumheads, which were discussed in the book.

The book came out with a plain, red cover, but for some reason, in the preface, there’s a picture of me playing a drum. I think they put it in there to satisfy this idea they got that “the author wants a drum somewhere.” Anyway, everybody wonders why that picture of me playing drums is in the preface of the Feynman Lectures, because it doesn’t have any diagrams on it, or any other things which would make it clear. (It’s true that I like drumming, but that’s another story.)

At Los Alamos things were pretty tense from all the work, and there wasn’t any way to amuse yourself: there weren’t any movies, or anything like that. But I discovered some drums that the boys’ school, which had been there previously, had collected: Los Alamos was in the middle of New Mexico, where there are lots of Indian villages. So I amused myself—sometimes alone, sometimes with another guy—just making noise, playing on these drums. I didn’t know any particular rhythm, but the rhythms of the Indians were rather simple, the drums were good, and I had fun.

Sometimes I would take the drums with me into the woods at some distance, so I wouldn’t disturb anybody, and would beat them with a stick, and sing. I remember one night walking around a tree, looking at the moon, and beating the drum, making believe I was an Indian.

One day a guy came up to me and said, “Around Thanksgiving you weren’t out in the woods beating a drum, were you?”

“Yes, I was,” I said.

“Oh! Then my wife was right!” Then he told me this story:

One night he heard some drum music in the distance, and went upstairs to the other guy in the duplex house that they lived in, and the other guy heard it too. Remember, all these guys were from the East. They didn’t know anything about Indians, and they were very interested: the Indians must have been having some kind of ceremony, or something exciting, and the two men decided to go out to see what it was.

As they walked along, the music got louder as they came nearer, and they began to get nervous. They realized that the Indians probably had scouts out watching so that nobody would disturb their ceremony. So they got down on their bellies and crawled along the trail until the sound was just over the next hill, apparently. They crawled up over the hill and discovered to their surprise that it was only one Indian, doing the ceremony all by himself—dancing around a tree, beating the drum with a stick, chanting. The two guys backed away from him slowly, because they didn’t want to disturb him: He was probably setting up some kind of spell, or something.

They told their wives what they saw, and the wives said, “Oh, it must have been Feynman—he likes to beat drums.”

“Don’t be ridiculous!” the men said. “Even Feynman wouldn’t be that crazy!”

So the next week they set about trying to figure out who the Indian was. There were Indians from the nearby reservation working at Los Alamos, so they asked one Indian, who was a technician in the technical area, who it could be. The Indian asked around, but none of the other Indians knew who it might be, except there was one Indian whom nobody could talk to. He was an Indian who knew his race: He had two big braids down his back and held his head high; whenever he walked anywhere he walked with dignity, alone; and nobody could talk to him. You would be afraid to go up to him and ask him anything; he had too much dignity. He was a furnace man. So nobody ever had the nerve to ask this Indian, and they decided it must have been him. (I was pleased to find that they had discovered such a typical Indian, such a wonderful Indian, that I might have been. It was quite an honor to be mistaken for this man.)

So the fella who’d been talking to me was just checking at the last minute—husbands always like to prove their wives wrong—and he found out, as husbands often do, that his wife was quite right.

I got pretty good at playing the drums, and would play them when we had parties. I didn’t know what I was doing; I just made rhythms—and I got a reputation: Everybody at Los Alamos knew I liked to play drums.

When the war was over, and we were going back to “civilization,” the people there at Los Alamos teased me that I wouldn’t be able to play drums any more because they made too much noise. And since I was trying to become a dignified professor in Ithaca, I sold the drum that I had bought sometime during my stay at Los Alamos.

The following summer I went back out to New Mexico to work on some report, and when I saw the drums again, I couldn’t stand it. I bought myself another drum, and thought, “I’ll just bring it back with me this time so I can look at it.”

That year at Cornell I had a small apartment inside a bigger house. I had the drum in there, just to look at, but one day I couldn’t quite resist: I said, “Well, I’ll just be very quiet …”

I sat on a chair and put the drum between my legs and played it with my fingers a little bit: bup, bup, bup, buddle bup. Then a little bit louder—after all, it was tempting me! I got a little bit louder and BOOM!—the telephone rang.

“Hello?”

“This is your landlady. Are you beating drums down there?”

“Yes; I’m sor—”

“It sounds so good. I wonder if I could come down and listen to it more directly?”

So from that time on the landlady would always come down when I’d start to drum. That was freedom, all right. I had a very good time from then on, beating the drums.

Around that time I met a lady from the Belgian Congo who gave me some ethnological records. In those days, records like that were rare, with drum music from the Watusi and other tribes of Africa. I really admired the Watusi drummers very, very much, and I used to try to imitate them—not very accurately, but just to sound something like them—and I developed a larger number of rhythms as a result of that.

One time I was in the recreation hall, late at night, when there weren’t many people, and I picked up a wastebasket and started to beat the back end of it. Some guy from way downstairs came running all the way up and said, “Hey! You play drums!” It turned out he really knew how to play drums, and he taught me how to play bongos.

There was some guy in the music department who had a collection of African music, and I’d come to his house and play drums. He’d make recordings of me, and then at his parties, he had a game that he called “Africa or Ithaca?” in which he’d play some recordings of drum music, and the idea was to guess whether what you were hearing was manufactured in the continent of Africa, or locally. So I must have been fairly good at imitating African music by that time.

When I came to Caltech, I used to go down to the Sunset Strip a lot. One time there was a group of drummers led by a big fella from Nigeria called Ukonu, playing this wonderful drum music—just percussion—at one of the nightclubs. The second-in-command, who was especially nice to me, invited me to come up on the stage with them and play a little. So I got up there with the other guys and played along with them on the drums for a little while.

I asked the second guy if Ukonu ever gave lessons, and he said yes. So I used to go down to Ukonu’s place, near Century Boulevard (where the Watts riots later occurred) to get lessons in drumming. The lessons weren’t very efficient: he would stall around, talk to other people, and be interrupted by all kinds of things. But when they worked they were very exciting, and I learned a lot from him.

At dances near Ukonu’s place, there would be only a few whites, but it was much more relaxed than it is today. One time they had a drumming contest, and I didn’t do very well: They said my drumming was “too intellectual”; theirs was much more pulsing.

One day when I was at Caltech I got a very serious telephone call.

“Hello?”

“This is Mr. Trowbridge, Mahster of the Polytechnic School.” The Polytechnic School was a small, private school which was across the street diagonally from Caltech. Mr. Trowbridge continued in a very formal voice: “I have a friend of yours here, who would like to speak to you.”

“OK.”

“Hello, Dick!” It was Ukonu! It turned out the Master of the Polytechnic School was not as formal as he was making himself out to be, and had a great sense of humor. Ukonu was visiting the school to play for the kids, so he invited me to come over and be on the stage with him, and play along. So we played for the kids together: I played bongos (which I had in my office) against his big tumba drum.

Ukonu had a regular thing: He went to various schools and talked about the African drums and what they meant, and told about the music. He had a terrific personality and a grand smile; he was a very, very nice man. He was just sensational on the drums—he had records out—and was here studying medicine. He went back to Nigeria at the beginning of the war there—or before the war—and I don’t know what happened to him.

After Ukonu left I didn’t do very much drumming, except at parties once in a while, entertaining a little bit. One time I was at a dinner party at the Leightons’ house, and Bob’s son Ralph and a friend asked me if I wanted to drum. Thinking that they were asking me to do a solo, I said no. But then they started drumming on some little wooden tables, and I couldn’t resist: I grabbed a table too, and the three of us played on these little wooden tables, which made lots of interesting sounds.