Taken from “Surely You're Joking, Mr.
Feynman!” Adventures of a Curious Character by Richard Phillips Feynman as told to Ralph Leighton edited by
Edward Hutchings
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—funny
numbers! 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. E. 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.