By Dave Johnson

The following article by veteran juggler Dave Johnson appears in his recreational column in "develop," a journal published for Macintosh programmers. We're reprinting it here in hopes that you'll enjoy sharing Daves thoughts about juggling and notation, as he explains these to a mostly non-juggling audience.

-Martin Frost

 

I've been juggling seriously since the summer of 1979, in college, when I saw a performance of the Pickle Family Circus in a park one gorgeous Saturday afternoon. I already knew how to juggle three balls - shakily - but that was the day I really discovered juggling. I had never seen clubs juggled up close and in person before, and in particular I had never seen jugglers throw things back and forth between each other (called passing). The Pickle Family did lots of both.

 

I was stunned. I was bowled over. I was frozen in my seat, gaping and incredulous. I couldn't believe that what I was seeing was possible. I had to learn to do that.

Fortuitously, the circus offered workshops in various circus arts, including juggling, so I immediately signed up. The following morning I learned the basics of passing balls, forced my roommate to learn to juggle three balls so that I'd have someone to try it out with, and embarked on a long and fruitful juggling binge. The fire that was lit that day burned white hot for over five years, and will remain fitfully smoldering as long as I can still lift my arms, close my fingers, and count to three.

 

My favorite kind of juggling nowadays is getting together with other jugglers and passing clubs. We arrange ourselves in various formations about the floor, start juggling all together, and throw the juggling clubs back and forth between each other in varied and complex - but mostly predetermined - ways.

 

Analyzing Passing Patterns

Which brings me to the main topic of this column: how multiperson juggling patterns work, and how to write them down on paper. I'm going dangerously far out on a limb here, assuming that it will be interesting to you, even though it has precious little to do with programming computers, and even though you're probably not a juggler. This particular limb is propped up a little by the very high proportion of computer people, mathematicians, engineers, and other scientists among jugglers. (There have been long-winded and unresolved discussions about why this should be so, but whatever the reason, its a fact.)   Its also been my observation (at Apple at our weekly juggle, and at the Worldwide Developers Conference) that computer people, in their endearing analytical way, often stand around for a long time trying to figure out the patterns.

 

Once you understand the rules of how the objects interleave and the jugglers interconnect, you can search for new patterns on paper, whether or not you know how to juggle. It's like a puzzle, or like a mathematical game. Its even conceivable (though just barely) that a knowledge of juggling patterns could be useful to you. I saw a citation on the rec.juggling Internet newsgroup a while back for a paper called "Juggling Networks," published in the proceedings of a conference on parallel and distributed computing. From the abstract: These constructions are based on a metaphor involving teams of jugglers whose throwing, catching, and passing patterns result in intricate permutations of the balls. This metaphor affords a convenient visualization of time-division-multiplex activities that should be of value in devising networks for a variety of switching tasks.

 

There have been several mathematical papers that deal with juggling in one way or another, and even so eminent a personage as Claude Shannon, the father of information theory, was an amateur juggler and was interested in the permutations and combinations in juggling patterns. He wrote a paper called "The Scientific Aspects of Juggling" (in Claude Elwood Shannon, Collected Papers, IEEE Press, 1993), and I heard that when he appeared at a juggling convention he drew thunderous applause from the assembled jugglers (another indication of how many jugglers are science types).

 

Passing

Club passing is by far my favorite kind of juggling. The jollies I get from it are all over the map; it's deeply satisfying for me on many, many levels. Part of it is social, of course. Like sex, it's just more fun with others. And a big part of it is the cooperation, being a part of this complicated group pattern that's built and maintained by everyone together. I suspect it's a lot like jamming with a band in that sense: we all agree on a framework - 12-bar blues in E or a seven-club four-count with triples, as the case may be - and then go for it, the members either struggling to keep up or embellishing wildly, according to their level of skill. Sometimes we'll hit a "groove," a day and a pattern and a distribution of people that just feels right, the beat solid, the hands sure of their grip.

 

Club passing can feel like being part of some giant, whirling, clockwork contraption, with everything ticking and clacking along. Talk about being a cog in the machine! The spinning clubs form this sort of living, writhing, flying tangle with its own weird existence, a kind of "energy net" connecting the jugglers involved. The old saw "what goes around comes around" has a particularly pointed truth in club passing: if one juggler throws a pass badly - say without quite enough spin, or a little off target - it causes the receiving juggler some, well, discomfort. That discomfort often manifests itself in another bad pass, causing the next receiver to struggle, and so on. It's often actually visible; you can see the disturbance making the rounds, until it either gets smoothed out by jugglers who manage to keep their cool, or amplifies itself so badly that the whole pattern comes crashing down around the jugglers' heads. (Interestingly, the disturbance often travels independently of the clubs themselves, in different directions and at different speeds, like a wave passing through water.) And passing clubs fosters - requires, actually - a sort of heightened awareness of the other people involved. Often a quick, nearly imperceptible motion on the part of one juggler, a tiny hesitation, or the beginning of a wrong throw, corrected almost before it happens, causes another juggler to react reflexively. Typically both burst out laughing, mostly because it's unbelievable that such a tiny signal is transmitted at all.

 

And then there's the patterns game: a significant portion of the time spent "juggling" is really spent standing around, fiddling with the clubs, and trying to come up with new formations, new ways to arrange ourselves and the clubs in space and time so that everything fits together. The landscape of possible patterns is vast and complex, but also highly structured in mysterious ways. Like other iterative systems (computers, economies) the ­ underlying rules are relatively simple but the results can be very complex and widely variable. It's a kind of combinatorics and is, I think, actually covered by the mathematics of group theory.