Season 11 Episode 4

In this episode, Elwyn and James explore siteswap notation for juggling, a system that converts certain integer sequences into juggling patterns.

Watch on YouTube

Further Reading

Siteswap

You can find out more about siteswap on websites like this one (from 1993!).

If you prefer a Wikipedia summary over the 90s internet, see Siteswap | Wikipedia.

Lots of the animations online are made with the Juggling Lab software, which uses siteswap notation. This software has lots of parameters beyond the simple siteswap that we talked about in the OOMC episode. To give you a sense of the range of behaviour possible, here’s a funny YouTube video of people making incomprehensible juggling routines with Juggling Lab.

Colin Wright

Colin Wright is one of the people credited with inventing siteswap notation. Colin is well-known for his entertaining sessions on the Mathematics of Juggling. You can find one on YouTube at Math Encounters -- Five Balls, Two Hands: The Patterns of Juggling -- Colin Wright (Presentation) | National Museum of Mathematics | YouTube
 

Joel David Hamkins

One of the other people credited with inventing siteswap notation is Joel David Hamkins. Since then, Joel has become one of the most well-known Philosophy researchers in the world. Joel runs a blog with the subtitle “Mathematics and Philosophy of the Infinite” where he’s written about set theory, infinite chess, surreal numbers, and lots more. I’ve linked to the “Math for kids” section because that seems like the most approachable, but note that Joel also writes about his cutting-edge philosophy research.

Claude Shannon

Claude Shannon didn’t invent siteswap notation, but he did invent information theory, which is probably more important in the modern world! He made contributions to cryptography and to our understanding of entropy, and he worked on very early attempts at artificial intelligence. It's weird to think that the word "bit" in computer science was invented by a specific person, but that was one of his.

He was also really into juggling. He spent a lot of time building a juggling robot. He has a Juggling Theorem! I was reminded of Claude Shannon’s love of juggling by a recent episode of Tim Harford’s podcast Cautionary Tales. The key question for Tim is whether spending time on the juggling robot was a good idea or not...

If you’d prefer to read something instead of watching a video or listening to a podcast, try this article on a juggling website.