Cascade (juggling)

An illustration of the three-ball reverse cascade.

The reverse cascade, or outside cascade,[16] is a juggling pattern in which the props follow the same path as the cascade, but with time going backwards, hence the 'reverse'. One throws every ball with, "an outward instead of an inward scoop," and throws, "every ball over the incoming ball rather than under it."[17]

The pattern is performed with an odd number of props. As in the cascade, props are thrown from alternating hands and each prop is caught in the opposite hand from which it was thrown. The key difference between a regular cascade and the reverse cascade (from a juggler's point of view) is that one throws each object over rather than under the others, i.e., outside rather than inside.

While in a cascade objects are caught on the outside of the pattern (on the far left and right) and thrown from closer to the middle of the pattern, causing each ball to pass under the ball previously thrown, in a reverse cascade objects are caught near the middle of the pattern and thrown from the outside, causing each ball to pass above the ball previously thrown. Thus from the juggler's perspective the left hand moves in a clockwise motion, and the right hand in a counterclockwise motion.

The reverse cascade is generally considered to be more difficult to perform than the cascade, with a difficulty rating of 4 rather than 2 out of 10.[1] The reverse cascade is, "perhaps the simplest," of, "several possible patterns that can be juggled with crossed arms."[18]

Path traveled by balls in the tennis and reverse tennis patterns.

Many tricks or patterns are generated from mixing cascade and reverse cascade throws. For example, for tennis (siteswap: 3[4]) one ball is thrown over (reverse) while the other two are thrown under (inside). One juggles, "a cascade with two balls while the 'tennis' ball is thrown [back and forth] over the top."[19]

Reverse tennis is where one ball is thrown inside while the other two are thrown over.

Chops is a juggling pattern based on the cascade, performed with 3 objects that involves a semicircular carry performed with either one or both hands (Single Chops/Double Chops). Chops can be performed continuously, by one or both hands, or in single instances.

The distinctive carry occurs at the moment of catch; rather than returning the ball into the cascade pattern the juggler carries the ball in his/her hand in a downward-pointing semicircle over the ball just thrown by the other hand, in the case of single chops, or over the other hand, in the case of double chops. At the end of the semicircular movement the carried ball is tossed virtually straight up to be caught by the other hand. The hand used to carry then quickly returns to its original position to catch the ball that was thrown by the other hand.

This pattern is of medium difficulty since very fast and controlled arm movements are necessary, though with practice, the pattern can actually be performed in a slow-looking motion.

Named variants include the "overhead cascade"[20][21] and a virtually infinite number of cascade patterns such as 522, 720, 900, 72222, and so on (see article on Siteswap notation).[22]

An illustration of Shannon's juggling theorem for the cascade juggling pattern

Cascade ladder suggested by Shannon's formula

Claude Shannon, builder of the first juggling robot, developed a juggling theorem, relating the time balls spend in the air and in the hands: (F+D)H=(V+D)N, where F = time a ball spends in the air, D = time a ball spends in a hand/time a hand is full, V = time a hand is vacant, N = number of balls, and H = number of hands.[9] For example, a hand's and a ball's perspectives in the two-hand (H) three-ball (N) cascade pattern:

      1st 2nd 3rd
hand: D--VD—VD--V
ball: D--F--D--F--
      R     L

(F+D)H=(V+D)N

(3+3)2=(1+3)3

6×2=4×3

12=12