JUGGLER'S WORKSHOP

 

 More Site Swaps for Passing

BY MARTIN FROST

 

Last time I described how to figure out where and when to throw a lone double, triple or quad in any passing pattern. We'll start this time with a clarification of the general rule for such special throws and then cover a new related topic. But first remember that any special sequence of throws such as a double or a double-triple changes the order of the clubs in a pattern and hence is known as a site swap because the sites of some clubs have been swapped.

 

The Rule for a Lone Special High Throw

First, I want to remind you of the rule for making a lone special high throw in a passing pattern, as explained in the last issue. Then I'll make a slight correction. Remember that a double or higher throw in a pattern skips past one or more hands whose throws are omitted as a result. I said:

 

At any time, in any pattern, you can add N extra spins to a throw (for N=1,2,3...) by skipping past N hands in the pattern when you make that throw.

 

This rule is valid for any pattern in which only singles are being passed. In fact, it is valid for any special throw which only skips hands that would have thrown singles. If, however, you skip past a hand that would have thrown a double, you have to add two spins, not just one; to skip past a triple, you add three spins; and so forth.

 

The reason for this is simple. The special throw has to take as long to arrive at the final destination as the sequence of omitted throws would have taken. So the special throw has as many spins as all the omitted throws put together, including the omitted normal throw of the special club itself: Since we assume that all throws spin at the same speed, we can sum their spins instead of summing their flight times. It's the total time that needs to remain unchanged.

 

Here is the correct general rule for all patterns, even those that normally contain doubles or higher throws:

 

At any time, in any pattern, you can bypass any number of hands in the pat­tern by throwing a club with as many spins as all the throws thus suppressed would have had together.

 

The throws omitted are consecutive throws in the pattern, each of which would have led to the next. The club of the first throw in the sequence omitted is the only club actually thrown. It is thrown directly to the hand that the last throw in the se­quence would have gone to, with as many spins as all of the throws in the sequence added together.

 

You can see that if all throws in the base pattern are singles, you just count up the number of hands skipped and add that many spins to the special club. That gives the original rule that we gave (add N spins), which does hold for a pattern of singles.

 

Causal Diagrams

An easy way to figure out what sequence of throws will be replaced with a high throw is to notate the pattern in a causal diagram. Fig. I shows the causal diagram for the 6-club 3-ct. Each arrow represents a throw. This causal notation not only dis­plays the sequence of throws that each jug­gler has to execute in a pattern, but it shows which clubs force other clubs to be thrown. That's exactly the information we need in order to figure out the possible special throws that we can make. In partic­ular, we'll call a line of connected arrows a causal line because it shows a sequence of throws with each one forcing the next one, as you read from left to right.

 

Each row represents the throws for one juggler. Consecutive letters on each row represent alternating right and left hand throws. An incoming arrow represents an incoming club (a catch), and an outgoing arrow is an outgoing club (a throw). Each "P" represents a Pass in the regular pattern and each "5" a self. When we diagram a site swap variation of some regular pattern, we leave the p's and 5's in place so that you can spot the base rhythm of the pattern. But to read a causal diagram, all you need is to follow the arrows.

 

In order to make this type of diagram easy to read, we don't bother showing the relative time of each throw and its imme­diately subsequent catch. Reading from left to right, you might think that the catch was made before the throw (which would result in two objects being in the hand briefly), but this is not the intent. A throw is made, as usual, just before each catch, unless the hand was empty to begin with.

 

In patterns where the juggler's right and left hands alternate throwing, we just alternate between hands on one row in the diagram. That makes the diagram a bit smaller and easier to read for most uses. We'll generally start these diagrams with the right hand, at least on the top row. When a person's right and left hands are throwing at the same time, we would sep­arate the hands onto two rows.

 

Here's an important feature of causal diagrams. Any regular pattern of 0 objects and H hands will have O-H causal lines flowing through the whole diagram. This O-H is the number of objects that cannot be held in the hands if each hand is lim­ited to one object. So O-H is just the number of objects normally in the air (ig­noring what happens during the brief pe­riods of the exchanges).

 

Possible Site Swaps from a Causal Line

You can find all the possible special throws for a given hand and moment by just looking ahead at the causal line that goes through that hand at that moment. You can omit two or more consecutive throws in a causal line and replace them with a throw from the beginning to the end of that segment. The number of spins of the special throw is the sum of the spins of the throws in that segment.