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A Free Offer, a Call to Teachers, and the Invention of Juggling Notations

BY ARTHUR LEWBEL

THE OFFER: In response to popular demand, if you send me a self-addressed, stamped (sufficient postage for 7 ounces) 10 x 13" or larger manila envelope, 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 articles 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.

A CALL TO TEACHERS: Some teachers have expressed interest in incorporating juggling into their physics, math and other curriculums. I would very much like to hear from any teachers who have done so, and will use this forum to share the results.

JUGGLING NOTATIONS: The most useful contribution of academic analyses for jugglers so far is site swap notation and its extensions, which has lead to the creation of a new genre of juggling patterns. A full description of site swap notation is in the Summer 1991 Juggler's World article, "A Notation for Juggling Tricks. A LOT of Juggling Tricks," by Bruce Tiemann (Boppo) and the late Bengt Magnusson.

Site swap notation consists of a diagram showing the paths of balls among hands

over time, and a string of numbers that concisely describe the diagram. Other contributors to the development of site swap theory include Jack Boyce, Allen Knutson, Ed Carstens, and jugglers on the computer network.

An extension to site swap notation that deals with simultaneous and multiplex throws and catches is Carstens multihand notation (MHN). MHN is described in Ed's 1992 unpublished paper, "The Mathematics of Juggling," and in his computer program "Jugglepro," which was recently reviewed in both Juggler's World and Kaskade.

Jugglepro is available from Ed at Rolla, MO. Other juggling simulation software, some of which incorporate site swaps, include "the Juggler" by Bruce Love, "JUG - The Juggling Simulator" by David Greenberg, "The Juggling Video Task" by Anthony A. M. van Santvoord, "Juggle!" by Michael Kramer, "The 3 Ball Juggler" by John Gallant, and the site swap pattern generator by Jack Boyce.

The potential usefulness of a juggling notation for describing, remembering and inventing juggling tricks must have been obvious for a long time, especially before the advent of video. For example, sometime around 1972 Steve Mills saw Ron Lubman perform a 3 ball trick that was so intriguing that he dragged out a Super-8 movie camera to film it. By studying the film, Steve learned the trick, and improved it by continually reversing its direction. The result was the creation of Mills Mess. With cheap, convenient video, this process of learning from and improving recorded tricks is now commonplace and has contributed substantially to the current explosion in variety of juggling moves.

In searching through old juggling publications (a very pleasant pastime) the earliest published juggling notation I found is by Dave Storer, "A Written Notation for Describing Ball Juggling Tricks," In the IJA Newsletter (the publication that preceded Juggler's World), MarchApril 1978, vol. 30, # 2, p.7. Storer's notation is nothing like site swap. It is basically an analogy of music notation for juggling. Another music or dance style notation is proposed by B.W Stone in The Juggler's Handbook, published in 1983 by Spiritwood Publishers in Minneapolis. Richard Dingman's 1984 self-published book, "Patterns," also contains a rudimentary non-site swap-related notation for club passing patterns.

The second oldest notation I found was a short article by Jeff Walker in the January 1982 Juggler's World. I'll come back to this one later.

Where did site swap notation originate? The first published reference to site swaps is in Tiemann and Magnusson's article "The Physics of Juggling," in "The Physics Teacher," 1989 pp. 584-588. They credit Paul Klimak with inventing it first, and say they reinvented it a short time later. They also mention the article by Charlie Simpson, "Juggling on Paper," in Juggler's World, Winter 1986, p. 31. This article contains the diagram that shows the paths of balls over time, and uses it to invent a few tricks that would now be called site swaps.