Causal Diagrams

I wrote a computer program that implements one particular kind of juggling notation known as causal diagramming (introduced to me by a juggler named Martin Frost). This notation can be handy for doodling around trying to find new multiperson passing patterns. (Actually, I started writing the program. Its still rickety and unfinished, and will probably always remain so - it was more an experiment in QuickDraw GX programming than anything else.)

 

The program implements a kind of active graph paper, allowing you to draw only "legal" throws, and constraining your diagrams in appropriate ways (such as preventing you from drawing throws that go back in time, for a start).

 

Fig. 1 shows the diagram for a juggler doing a basic three-object pattern (called a cascade), and will serve to show both how the notation works and how juggling works. First the diagram: Time marches off inexorably to the right, divided into nice, even steps (called counts} . A juggler is represented through time as a row of Ls and Rs, representing the jugglers left and right hands, alternately throwing things. A thrown object is represented by an arrow from the hand that throws it to the hand that catches it. The pattern wraps around at the dotted lines, and repeats endlessly - or until someone drops something. (The program always shows two re­peating cycles like this.) Note that the arrows (throws) form an unbroken line traveling through time from left to right, and that each hand has exactly one "input" and one "output."

 

Contrary to what you might think at first glance, the overall path the arrows make doesn't directly trace the path of an individual club. If it did, this would just be a diagram of throwing one club back and forth between two hands. (That's a necessary prerequisite to juggling, but is definitely not juggling.) Instead, each throw displaces a club that is always assumed to be held, waiting, in the receiving hand. Think of the juggler as holding a club in each hand, while the third is in the air. The incoming club displaces the club that's already there, forcing the juggler to throw it elsewhere. In a cascade, the displaced club is thrown back to the opposite hand, where it in turn displaces the club that's there, which goes back to the first hand, displacing the club that's there, and so on, ad infinitum. (Note that although I'm saying "club" here, all these principles apply equally well to balls or rings or rubber chick­ens.) So the chain of throws is really a conceptual one, not a material one; it's a chain of cause and effect through time.

 

Diagrams of Passing

Fig. 2 shows two jugglers passing with each other (the repeated cycle was cropped for space reasons). Note that they juggle in time with each other, like musicians keeping a beat. (When juggling with clubs, you actually hear the beat, when the clubs slap into the jugglers' hands.) Both jugglers throw a club to each other at the same time, both from the right hand (though it could just as well be the left). Throwing a club to another juggler "breaks" the juggler's continuous line of throws, but the other juggler's club arrives in the nick of time, knitting the pattern back together. This is a requirement: any club thrown to another juggler must be replaced by an incoming one. Otherwise, juggling can't continue; the juggler just stops, a club in each hand, waiting. (Actually, there are common situations that force a juggler to "stall" like that for a count or two, but we'll limit ourselves to the non­stalling patterns here.)

 

Because of the close timing, both jugglers must agree on the pattern before starting. The pattern in Fig. 2 is called a four-count because there's a pass every four counts. (Another name for this pattern is every other, referring to the fact that every other right hand throw is a pass.) The four-count is a very common pattern, and for most club jugglers this is the default, "idling" pattern. Since there's so much time between passes, it's possible to do lots of fancy free-form tricks (affectionately known as "throwing trash") in the midst of the pattern. Of course, "so much time" isn't really much time at all: a club juggle is roughly 160 counts per minute, so there's just over a second between the passes in a four-count.

 

These diagrams show nothing about spatial relationships, by the way. The usual situation has the jugglers facing each other 6 or 8 feet apart, but the same patterns .can be done standing side by side, back to back, or even with one juggler standing on the other's shoulders. These diagrams show only the "connectedness" of the pattern through time, and in fact you can draw patterns that work fine on paper but are difficult to actually do because of mid-air collisions.