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Assigning
a computer to find all possible tricks is straightforward, as the tricks
are closely related to the concept of permutations. The number of
different tricks at a given word length is roughly proportional to the
factorial of the word length. (The.factorial function starts small and
grows really fast. For example, there is only one "trick" at
word length one but thousands at word length six.) There is no need to
stop at 491. Since there is no limit to the word length, there is no end
to the list of tricks. We now give a list of some tricks you can try.
3
balls: 4 2; 4 4 1 (This is probably the most elementary trick that is
not widely known. When run, i.e. 4 4 1 4 41 4 41, it resembles the box
pattern but yet is quite different. Note that the 1 throws go left and
right, though with a different ball each time.); 4 4 4 0; 5 3 1; 4 5 1 4
1; 6 3 1 6 1 3 1
4 balls: 5 3 (the half shower); 5 5 2; 5 5 51; 5 5 5 5 0; (Notice a pattern in these four tricks?)
Also
try 6 3 3; 6 4 5 1; 5 6 4 1; 6 6 3 ; 7 5 3 1; 7 3 4 5 ; and 5 6 6 1 5
1. This last one made a big show at the convention and was was used by
three competitors. 5 5 6 1 3 is interesting because you can run 5 6 1
as many times as you like before the 3 ends the trick and returns you
to the fountain. That is, 5 5 6 1 5 6 1 56 1 3 is also a valid trick.
Klimek calls 5 6 1 an excited state trick: it can't be done directly from the fountain, you throw a single 5 first. To start it cold, start with three in one hand and one in the other, and throw the first one from the hand with three in it. Another excited state trick is 6 6 1 6 1. Can you see how to "get into" it from the fountain?
The
diagram notation may help. 5 balls: 6 4; 6 6 3 (3s are hard. They're
so low you need to look down to see them, unlike 1s which are lower
but can be done blind.) ; 6 6 6 2; 6 6 6 6 1; 6 6 6 6 6 0 (seem
familiar?); 7 4 4; 7 7 3 3; 7 5 7 5 1; 7 7 7 3 1; 7 5 6 2; 8 5 5 2;
8 4 4 4; 8 8 4 4 1; 8 8 5 3 1; 9 5 5 5 1; 9 7 5 3 1; 1 0 5 5 5 5 0.
For the daring, 6 6 6 7 1 7 7 7 1 6 1 will provide hours of
amusement. Some excited state tricks are 7 7 1 (a 6 6 or a 7 5 will
get you started), 7 5 7 1 (the poor man's six ball half shower), and
7 7 7 1 7 1.
If
you're ready for tricks with six or more, work them out yourself, or
send for the computer program. (It has been posted on the juggler's
listserver.) You might also want to try the above as four or five
club tricks. At the 1990 LA convention, Jason Garfield tried to do a
head roll (head spin? What are these called, anyway?) with five
clubs. Since a head roll is a 3, he needed a five object pattern
with a 3 in it. After a boast and several misses on his own, (he
tried the 7 7 7 3 1 without our prompting) we told him about
the 6 6 3. He got it on the second or third try, and then did a neck
roll, a single spin butterfly throw, and a chin sweep each on the
first try.
In
summary, we have proposed a notation for juggling tricks that
involve differing throw heights. It simplifies the description of
these patterns. Also, if you're looking for new directions in your
juggling, don't get cross at the occult! Look to the numbers
instead, as the mathematical basis for this system leads to a large
class of new tricks at all levels of difficulty.
Correspondence is welcome. I prefer e-mail but also give my real address. Bruce Tiemann, Caltech, Pasadena, CA.
(Bruce
Tiemann has a B.S. in chemistry from Caltech and now works there
studying nonlinear optical materials. In addition to juggling numbers,
so to speak, his other
interests are amateur radio and building lasers.)
* This paper is dedicated to the memory of Bengt Magnusson. May he now find the peace he did not in his life. |
