The Two-Count

Fig. 3 shows another pattern that demonstrates some other important concepts. In this case, every right hand throw is a pass (which makes this pattern a two-count). Although the jugglers are juggling to the same beat, note that they are out of sync; one juggler's right hand throw is simultaneous with the other's left. Note also that each pass spends twice as long - two counts - in the air. In all the previous diagrams, the throws have been singles, meaning that the club spins around once during transit. The passes in Fig. 3 are doubles; since they're in the air twice as long, they have time to spin around twice before being caught. (The left hand throws are still singles.)

 

A warning about these multiple-spin throws: It's tempting, on paper, to make heavy use of long arrows (throws that spend lots of time in the air between jugglers). A little physics tells you, though, that the time in the air is propor­tional to the height of the throw squared.

 

So a double needs to be thrown four times the height of a single, and a triple must thrown nine times higher. A quadruple - a "quad" ­must be sixteen times the height of a single, and that's about as far as you can reasonably go with any sort of accuracy (or safety!). I generally stop at triples.

 

The Feed

Now take a look at Fig. 4 (again, cropped for space). This shows a three-person pattern called a feed. In this case one person (juggler 2) acts as the feeder and the others are feedees. The feeder is passing twice as often as the feedees; the feeder is doing a two-count, while the feedees are each doing a four-count, interleaved with each other in time. The feeder switches back and forth between the two feedees. This is another very common pattern, and can be added to indefinitely: juggler 3 could pass with a new juggler, juggler 4, on the first count, at the same time jugglers 1 and 2 are exchanging clubs. That makes juggler 3 a feeder as wen, feeding 2 and 4. And so on, ad infinitum.

 

Causal Diagram Notation

I think by now you can see how the patterns fit together. It's like building a network, where everything has to eventually connect up and balance out. Go ahead, give it a try. A favorite pattern of mine is a three-count, with a pass every third count; both left and right hands pass. How about a feed where the feedees do three-counts? How many three-count feedees can one feeder possibly handle? Try a ten-club feed (the feeder does two-count doubles, as in Fig. 3, and the feedees each do four-count doubles). Admire the attractive and tidy braids that result. Go wild.

 

There are some interesting and nonobvious things about this notation that are probably worth pointing out. You can tell how many clubs there are in a pattern by taking a vertical slice through the diagram anywhere, counting the throws you intersect, and adding two clubs per juggler. (Note that Fig. 3 is a seven-club pattern!) Also, if you start anywhere and follow the line of arrows around, wrapping back at the first dotted line, they always form closed paths, even­tually arriving back where they began. Some patterns form one long continuous cycle; they're knit from a single strand, like a sweater. All the examples here are like that. Other patterns form distinct "orbits," where there are two or more strands making up the pattern; the three-count is an example. Each strand is an independent line of cause and effect, really an independent subpattern, that has no effect on the other parts of the pattern. You can actually decompose such patterns into their constituent parts and juggle just one strand of the pattern at a time.

 

The fate of any particular club isn't obvious at all in these diagrams. You can trace it, if you like - a club leaves a hand two counts after it arrives - but it's a bit of a pain (hmm, that might make a good addition to the program). Of course, tracing the paths of individual clubs isn't of pri­mary interest to jugglers (though its fun some­times), in the same way that the path of an in­dividual dollar is rarely of interest to economists and the trials and tribulations of an individual electron don't concern circuit designers. In contrast, I'd bet that the paths of the individual clubs are of great interest to the folks who wrote the network paper cited earlier. This notation would probably be a poor choice for them.

 

The Real World

Finally; of course, the experience of juggling is nowhere to be found in these diagrams. "In contrast to their clean, orderly lines, passing clubs is a very physical thing, full of grimacing effort, plagued with fumbling and mistakes, and occasionally bone-whackingly painful. It's more like chopping wood than like doing math; it's more like pounding nails than like tying macrame, despite the nice braided look of the diagrams. But when things get cooking, when everyone is warmed up and throwing well, when the pattern grows and takes shape between our hands and fills the air with intricate, swirling, impossible motion, there's nothing else quite like it in the world.

 

Dave welcomes feedback on his musings. This is a preliminary draft of an article that will appear in Issue 22 (June 1995) of "develop, The Apple Technical journal."

 

If you have any comments or suggestions for jugglers Workshop, write to: Jugglers Workshop or call Martin Frost.