§ The Zen of juggling three balls
- Hold one ball in the left hand
A, two in the right hand
B, C. This initial configuration is denoted
B from the right hand to the left hand. This configuration is denoted by
[A;B←;C] where the
B← is in the middle since it is in-flight, and has
←since that's the direction its travelling.
- When the ball
B is close enough to the left hand that it can be caught, throw ball
A. Thus the configuration is now
- Now catch ball
B, which makes the configuration
- With the right hand, throw
C (to anticipate catching
A). This makes the configuration
- Now catch the ball
A, which makes the configuration
- See that this is a relabelling of the state right after the initial state. Loop back!
§ The Zen
- The key idea is to think of it as (1) "throw (B)" (2) "throw (A), catch (B)", (3) "throw (C), catch (A)", and so on.
- The cadence starts with a "throw", and then settles into "throw, catch", "throw catch", "throw, catch", ...
- This cadence allows us to actually succeed in the act of juggling. It fuses the hard parts of actually freeing a hand and accurately catching the ball. One can then focus attention on the other side and solve the same problem again.