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Re:Juggling by numbers: How notation revealed new tricks by ColinWright on Thursday December 20, 2012 @11:47AM (#4948584)
I can't find anywhere that it says the number is how high it goes. It says clearly:

    > These sequences encoded the number of beats of each
    > throw, which is related to their height and the hand
    > to which the throw is made.
It doesn't say that a "4" is twice as high as a "2" (although an earlier draft did - I managed to get that fixed).

When you throw a ball, the number is how many beats later the ball will next be thrown. Simplifying, some of that is in the air, and one beat (or so) is in the hand, so the flight time is one less than the number shown. That would mean that a "5" is in the air for four beats, and thus will go 4 times higher than a "3", which is in the air for two beats, or half the time.

The truth is more complicated, because your hands aren't full for half the time (which is the one beat assumption above), and the dwell time (percentage time your hand is full) actually varies (although is usually around 65% to 70%).

For the numbers to be used it's the beat time that matters, and you can throw higher by slowing the beat, but that still leaves a "3" as a "3" and that doesn't convert it into a "4".

All these details are covered in the gentle introduction, but this specific question is dealt with in even more detail in the "Technical Notes" section:

http://www.solipsys.co.uk/new/SiteSwap.html#technotes

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