46-4,p31

Academic Juggler

A Messy History and Other Academic Notes

BY ARTHUR LEWBEL

This column investigates the history of Mills mess. Before this messy tale, some news notes:

The MIT juggling club in Cambridge, Massachusetts is now twenty years old! It is the oldest juggling club (though not the oldest juggling school) in continuous operation in North America, and possibly the world. I and some friends started the MIT juggling club in 1975, inspired by a combination of John Grimaldi's juggling club which met at Trinity church off Wall Street in New York City, and the MIT unicycle club that was started by Andy Rubel in 1974. By 1976 MIT was one of only four juggling clubs listed in the IJA Newsletter, the publication that preceded Jugglers World. The others were Grimaldi's New York club, the Pioneer Valley juggling association in Amherst, Massachusetts, and the MacArthur Park jugglers in Los Angeles. After 20 years, the MIT club is still going strong, and still meeting on Sunday afternoons (in the Lobby of building 10 at MIT, or outdoors by the Student center).

In other Academic juggling news, the cover story of the June-July 1994 issue of the American Mathematical Monthly (vol. 101, #6, pp. 507519) is "Juggling Drops and Descents," by lJAers Joe Buhler, David Eisenbud (another Brandeis professor like mysel), Ron Graham, and Colin Wright.

Colin is one of the inventors of site swap notation, which is the real subject of the article. See Tiemann and Magnussen in the Summer 1991 Jugglers World for an introduction to site swaps. The terms "drops" and "descents" that appear in the title are puns, having specialized meanings in the mathematical group theory used in the article. The main result they derive is that the number of different site swap patterns for b or fewer balls which are exactly n numbers long equals b raised to the power n. While simple to state, this result is surprisingly difficult to prove.

In response to popular demand, my offer from the last Academic Juggler still stands. Send me a self addressed, stamped (with sufficient postage for 8 ounces), 10 by 13 inch or larger manila envelope and I will mail it back to you filled with 40 pages of the math and science of juggling, including a bibliography of over 50 references on the subject and copies of some particularly useful articles. Past Academic Juggler columns are included. The address is below. When you write, please include a letter about yourself telling why you are interested in the material. Also, if you find or write any academic references to juggling that are not included in the bibliography, or if you use this material in some other way, please let me know.

I claimed in the last Academic Juggler that in the early 1970s Steve Mills learned a Ron Lubman three ball trick that he then convened into what is now known as Mills Mess. After that article came out Ron Graham called me to say that it was he who had given Steve the initial idea. Ron Graham is a former IJA president, a world famous mathematician, a coauthor of the Drops and Descents paper described above, and the Guinness book world record holder for the largest number ever used in a published mathematics proof.

So what is the true story of Mills Mess? Apparently Graham experimented with many patterns that crossed hands or changed direction in the Mess way, some of which were likely to be close to the current Mess: Steve studied Ron's patterns, and other jugglers as well, including films of Vaudeville jugglers. From this stew, the Mess emerged.

Ron and Steve juggled at the YMCA in Morristown, N.J., when the mess was created, but the name "Mills Mess" was given to this trick some years later on the West coast by Ed Jackman, Barrett Felker, and / or Norm Johnson. No one seems to know exactly when the trick was invented or named, but I saw Steve show it, without a name, at John Grimaldi's New York City Juggling Club in 1974.

After seeing the Mess this first time, I went home and tried to learn it. Later, when I saw Steve again and showed him the trick. He said, "I don't know what you're doing." I had unintentionally invented a different messy trick, and had to start over learning the real Mess.

One reason for the popularity of Mills Mess is that, while relatively easy to learn, it looks dazzlingly complicated, and is almost impossible to describe in words. This hasn't stopped people from trying. For example, many descriptions of the trick have

appeared in rec.juggling on the Internet (see the IJA news in the Fall 1994 Jugglers World for information about Juggling on the internet.

The first written attempt to describe Mills Mess that I have found is by Dave Walden, a former MIT juggler and one time president of the MIT Juggling Club, in the March-April 1977 issue of The IJA Newsletter. Dave's write up egins:

A THREE BALL TRICK. At the 1976 convention Steve Mills was teaching a relatively complex three ball trick to many of the conventioneers, many of whom seemed to be having trouble understanding what he was saying. Apparently, this same trick has been the subject of much instruction at previous conventions. I think I've got it now, and a written description follows...

I won't repeat Dave's description here. The Mills Mess really should be seen to be learned.

The Steve Mills and family authorized spelling of the trick is "Mills Mess," rather than Mill's, Mills' or Mills's mess. I won't accept responsibility for the anguish this may cause among punctuation purists.

According to Bob Nickerson, "Jugglers are not efficiency experts. They're always saying:. There's got to be a harder way to do this." Nickerson's claim definitely applies to Mills Mess, where in addition to the four and five ball Mills Mess, some jugglers do Mills Messed site swaps. One can also see site swaps and any number of balls done the Mills Mess way on Ed Carsten's computer program "JugglePro."

Mills Mess has inspired many other alliterative, eponymous juggling tricks, the most famous being Eric's Extension, Burke's Barrage, and Rubenstein's Revenge. Each adds more confusion or difficulty to the original Mess.

Like America with Columbus, the question of who found the Mess first can never be known for sure. Mills Mess may have been discovered and forgotten many times before Steve found it and made it famous. Do you suppose these women from the Hassan tomb could have been working on a juggling mess?

The Academic Juggler is an occasional feature of Jugglers World, and is devoted to all kinds of formal analyses of juggling. You can write to me at Arthur Lewbel, Lexington, MA.