Mathematics of Juggling
Many years ago I received a t-shirt as a gift with the formula for juggling printed on it. The formula was from Claude Shannon, the builder of the first juggling robot, who developed a juggling theorem. There is a movie about Claud, The Bit Player that is worth watching.
Having juggled for many years prior to learning about the theorem, I immediately had an epiphany after receiving the shirt. I had noticed that more and more jugglers were experimenting with and teaching patterns that included asynchronous patterns. This was somewhat mind-blowing for me.
As an aside, it’s worth mentioning that Juggling communities that I have experienced are all about teaching and learning. We love to teach fellow jugglers new patterns and we all love to learn more tricks. In fact, if you want to learn to juggle, you can stop anyone juggling and they will teach you! I’ve taught countless people to juggle, if you ever see me, please ask to join in!
So the epiphany was, “This is how they did it!” After years and years of juggling being well understood, we suddenly had new patterns that never existed before. Here is a video explaining exactly that.
Shannon’s Juggling Theorem
(F+D)H=(V+D)N
F is the time a ball spends in the air (Flight)
D is the time a ball spends in a hand (Dwell), or equivalently, the time a hand spends with a ball in it
V is the time a hand spends empty (Vacant)
N is the number of balls
H is the number of hands
Claude E. Shannon‘s theorem
So what were they doing? They were inventing new patterns that people could first conceive on paper, using math, and then attempt to execute. Patterns with multiple drum beats if you will, some of the objects you juggled, moved at different timings than others! I had seen jugglers do it, and it was mind-blowing as I could not conceive of an asynchronous-looking pattern like that. Now that you know about the numbers, here is a great video showing some fun (and some difficult patterns!)
Get Juggling!
I love juggling and teaching juggling, and I hope it has been a lot of fun learning about the math of juggling and how that has developed a whole new world of juggling for all of the jugglers of the world. Now get juggling!
