Comment by xnorswap | Hacker News Reader

Comment by xnorswap | Hacker News Reader

I was taught the juggling notation site-swap around 25 years ago, and it's one of those things that sticks with you despite the fact that I don't have the coordination to juggle.

What really impressed me at the time was the ability to take something as complex and time-dependent as juggling and reduce it to a simple notion of numbers such as "53444", and that another juggler could take that string of numbers and produce a meaningful juggle from it. I seem to remember that even numbers implied a same-hand throw and sticking to odd numbers would mean only cross-hand throws, but my memory is a bit foggy on the details.

That a seemingly complex juggle could be reduced by abstraction to just a couple of numbers was mind-blowing ( To be fair, I was ~12 at the time. ).

In addition there was software which could then take any such string and reproduce the juggle, and that was even cooler. I definitely spent the next few weeks playing around with different patterns in that software. One of the other fascinating things was trying to plug random numbers in, they'd seldom come out as anything particularly interesting. You'd end up with a lot of patterns where balls were same-hand juggled to different heights.

I learned quickly that I was less interested by the juggling and more interested in the mathematics which let you reduce it down to a small sequence, and that random data rarely holds genuinely interesting patterns even if they first appear so.

Site-swap notation is in terms of "beats". The number is how many beats will elapse for that throw before it lands. The beats alternate hands, so any odd number means that ball is scheduled to land in the opposite hand. The standard cascade is 333, meaning each ball thrown will land three beats later, and in the opposite hand.

The constraint on a useful site-swap number is this: you can't have two balls scheduled to land on the same beat, which would mean arriving at the same hand at the same time. Or more generally a ball can't land when that hand is otherwise occupied.

Advanced jugglers can do that stuff physically (catch simultaneously or in an occupied hand), but it's not the purest version of juggling. More generally, advanced jugglers can do many positional and timing variations including simultaneous catches or throws, that aren't covered by the standard basic site-swap notation. There are extensions to the notation, like using parentheses around two numbers to show two throws occuring at the same time, and if the numbers are different they will land at different times.

> Advanced jugglers can do that stuff physically (catch simultaneously or in an occupied hand)

aka "multiplex".

The mathematics of siteswap are fascinating. The linked article points to the canonical Internet source for siteswap information: http://www.siteswap.org/

There you will find many articles on the subject and several varieties of the software you described to visualize or verify patterns.

I've fond memories of getting very deep in finding new siteswaps, through the night and into dawn, many nights across Europe in 2008. I'd keep a notebook going and email friends back home once a week or so, just with a dot point list of numbers.

Siteswap notation is really cool. At the same time, it's important to also realize that it's a distillation of juggling that deliberately sacrifices capturing much of the performance information inherent in actually throwing balls in the air to impress an audience.

Very much like how sheet music doesn't capture the nuance and expressiveness of a performance. It's a useful tool, but being able to read sheet music does not a musician make.

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