Sunday, May 11, 2014

Bringing Culture to the Physicists

from Surely You're Joking, Mr. Feynman

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 [1].  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 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 while longer to figure out that 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 of the 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 the 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! [2]

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 Madrix 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 do 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 "error," and so on.  The numbers should have to be worked out a bit.  Then people would say, "Geez!  This had 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 reproduction of the Dresden Codex and the authentic Mayan artifacts watched over by an armed guard in uniform; they heard the 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.


[1] When I was a young professor at Cornell, Professor Neugebauer had come one year to give a sequence of lectures, call the Messenger Lectures, on Babylonian mathematics.  They were wonderful.  Oppenheimer lectured the next year.  I remember thinking to myself, "Wouldn't it be nice to come, someday, and be able to give a lecture like that!"  Some years later, when I was refusing invitations to lecture in various places, I was invited to give the Messenger Lectures at Cornell.  Of course I couldn't refuse, because I had put that in my mind, so I accepted an invitation to go over to Bob Wilson's house for a weekend and we discussed various ideas.  The result was a series of lectures call "The Character of Physical Law."

[2]  While I was studying this table of corrections for the period of Venus, I discovered a rare exaggeration by Mr. Thompson.  He wrote that by looking at the table, you can deduce how the Mayans calculated the correct period of Venus -- use this number four times and that difference once and you get an accuracy of one day in 4000 years, which is really quite remarkable, especially since the Mayans observed for only a few hundred years.  Thompson happened to pick a combination which fit what he thought was the right period for Venus, 583.92.  But when you put in a more exact figure, something like 583.923, you find the Mayans were off by more.  Of course, by choosing a different combination you can get the numbers in the table to give you 583.923 with the same remarkable accuracy!

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