A couple of weeks ago I claimed on rec.juggling that there’s no such juggling pattern as a three-ball synchronous half shower. I was contradicted by a long time rec.juggling regular named Luke Burrage. His exact words were:
You are so wrong it hurts. I’ve just tried it and managed to juggle a three ball synchronous half shower on my first attempt.
Just because you can’t make the numbers add up using siteswap doesn’t mean that the trick isn’t possible.
Well that’s quite an assertion to try to contradict, but I like a challenge so here follows an explanation of why there’s no such trick as a three-ball synchronous half shower. For the benefit of non-jugglers I’ll describe all of the jargon you need. It’s actually very simple.
- Siteswap is a system of notation for juggling patterns. I’m not going to describe it here since there’s no need for it when describing the patterns I’ll refer to.
- A pattern where one hand does all of the throwing and the other does all of the catching. The catching hand just passes the balls to the throwing hand after each catch. The balls follow a high arc from one hand to the other and a quick low pass back to the initial hand.
- Half Shower
- A pattern where the balls thrown from one hand always go higher than those from the other hand. The balls follow a high arc from one hand to the other and a lower arc back to the initial hand.
- Synchronous and Asynchronous
- Synchronous patterns have both hands throwing at the same time. Asynchronous patterns have the hands throwing one after the other in alternation.
That’s all of the juggling jargon you need to understand this post. If you got this far you should be able to understand my point.
Luke’s Three-Ball Synchronous Half Shower
Luke claimed that he could "juggle a three ball synchronous half shower on [his] first attempt." He wasn’t lying, he really did juggle a pattern that looks like a good candidate for the three-ball synchronous half shower. If I’m going to claim that it’s not one, I’m going to have to describe what he did.
Take two balls in the left hand, one in the right. Remember this is a synchronous pattern so both hands will throw at the same time. The left hand throws in a low arc to the right; the right hand throws in a higher arc to the left. That’s the gist of half shower. One low arc, one high. When the left-thrown ball lands in the right hand the right-thrown ball should be at the peak of its arc. We still have the last ball in the left hand. So make the same throws again. Low arc from left, high arc from right. This time when the second left-thrown ball lands in the right hand the first right-thrown ball will land in the left. Continue ad nauseum.
So what’s the deal? It’s a three-ball pattern, it’ synchronous, it has the distinctive high arc and low arc of a half shower. Why is this not a three-ball synchronous half-shower?
Why Luke’s Pattern Isn’t a Half Shower
Look at the descriptions of shower and half-shower patterns again. Shower: "The balls follow a high arc from one hand to the other and a quick low pass back to the initial hand." Half shower: "The balls follow a high arc from one hand to the other and a lower arc back to the initial hand." Now let me let you in on some elementary ballistics. A pass is still a parabola. It’s an arc, just like the low arc in the half shower. The descriptions I’ve given so far, the descriptions that most jugglers would recognise as distinguishing a half shower from a full shower, are meaningless. They do not distinguish. They are, in fact, qualitatively identical.
There is a qualitative difference between the shower and half shower in three-ball asynchronous and in all higher numbers. Maybe the people juggling the patterns don’t know what it is, but it’s there. In a three-ball asynchronous shower the low throw (the pass) is thrown and the next throw from the other hand is that passed ball. In the three-ball asynchronous half shower the low throw is thrown and the next throw from the other hand is a different ball. The same applies to higher numbers. In all cases the shower is identified as the pattern where the low throw is followed immediately by another throw of the same ball. The half shower always has another throw in between.
Look at Luke’s pattern again. The low throw is thrown again as (part of) the next throw. By the only definition that qualitatively distinguishes showers and half showers this pattern is a shower. It’s the three-ball synchronous shower.
Now to be fair I will acknowledge that many people will still prefer the high arc/low arc and high arc/pass descriptions of half shower and shower respectively to the other-ball-in-between and same-ball-thrown-again descriptions. And of course it usually doesn’t matter because this is the only case where they differ. I am consequently not likely to jump down someone’s throat for claiming that the three-ball synch shower and three-ball synch half shower are different. On the other hand I think I’ve made a good enough argument that the claim "You are so wrong it hurts" could be described as, at the very least, embarrassingly exaggerated.