>Because the exact relationship ends up predicting the existence of throws that go backwards in time. When I give my talk I get the audience to make this prediction, and then I show how it can, in fact, be done (in some interpretation). I then show that balls traveling backwards in time are the same as anti-balls traveling forward in time, and it's a lot of fun.

I don't get it.

Let's try to help you - here's a revised version of what I said:

1. The exact relationship between the number used to represent a throw is complicated.

2. When you use the relationship, you end up predicting that some throws have to go backwards in time.

3. SiteSwap predicts the existence of juggling tricks that use these "Time-Traveling" throws.

4. The juggling tricks can, in fact be done.

5. We interpret a ball going backwards in time as an anti-ball going forwards in time.

So, which bit don't you get? Ask, and I shall expand.

Could you link us to something explaining the number & the throw? (BTW I saw your talk as a kid, though before I knew any real maths. Very fun!)

I've just submitted link to a gentle, but thorough explanation of "Vanilla" SiteSwaps:

http://news.ycombinator.com/item?id=4947536

I don't imagine it will get any upvotes, but it's a place to put some of the more detailed discussion, if anyone wants it.

In short, we juggle to a fixed rhythm with the hands taking it in turns. For a given throw, the number is when that ball will next be thrown. Time between throws is made up of "Flight Time" and "Dwell Time".

Under reasonable, simplifying assumptions, the Dwell Time is always one beat, so the time of flight is always one less than the number describing the throw.

And thank you! Nice to know you remember it being fun.

Looks like it's been edited with your suggestion.

It has removed the bit about a 4 being in the air twice as long as a 2, yes, but has not included the bit where I say the exact relationship is complicated.