# Appendix III - Juggling Notation

There are a variety of different methods for writing down juggling patterns on paper. Some systems just use strings of numbers to represent throws to different heights, others make use of diagrams to illustrate the pattern. Probably the most appropriate system from our point of view, and the one which I have used on this site, is called *Ladder Notation*.

A 3 object cascade represented using this method looks like this:

Time goes in the direction of the arrow, so to read this diagram start at the bottom and work up. The white and black circles represent throws and catches respectively, those on the left-hand leg of the ladder are made with the left hand and those on the right-hand leg by the right hand. The diagonal lines joining the circles represent the balls or clubs as they travel through the air from one hand to the other. The horizontal lines which form the rungs of the ladder denote equal time intervals.

To illustrate this idea, imagine throwing one ball back and forth between your hands, now the ladder looks like this:

(I have numbered the time intervals for easier reference, these numbers don't usually appear on ladder diagrams)

The ladder starts with a throw from the left hand to the right hand, it takes two intervals (let us call them seconds for convenience, although of course their actual length would depend on how high you threw the ball) to travel across, it is then caught and remains in the right hand for one second. This idea of holding the ball for a time before throwing it back is very important in juggling. If you look along the vertical bars of the ladder you will see that the spaces between the catches and the following throws are filled in with heavier lines than the periods between the throws and the following catches. This indicates that a ball is held in the hand for this time. Referring back to the first diagram of the cascade we see that the left hand is occupied for the second, fourth, sixth, and eighth intervals and empty during the first, third, fifth and seventh, the exact opposite is true of the right hand. Notice also that one or other of the hands always contains a ball, this happens when you juggle a cascade making each throw at the earliest possible time, i.e. when one ball reaches the halfway point between your hands you throw the next one. This halfway stage also corresponds to the moment at which the throws peak. For example look at the first right hand throw at the start of interval two, it can be seen by looking along the corresponding 'rung' that at the moment of release the previous throw from the left hand is half way across.

It is also possible to delay the throws a little and alter the timing of the cascade, wait until you actually see the ball start to descend before you make the next throw. Now the ladder diagram looks like this:

Now only one thing happens at a time - one hand makes a throw and then a catch, and only after it has finished does the other hand do the same. Whereas before the hands spent half the time empty and half the time full, now they are full most of the time. Because we now wait longer before each throw, the incoming ball is closer to the receiving hand when it throws, consequently it is empty for less time.

Note that the time intervals represented by the rungs of the ladder are arbitrary, the throws on the above diagram take 3 intervals each instead of 2 as before - this does not mean that they are in the air for longer, if the 2 patterns are juggled at the same height then the throws will be the same.