+-- These are the same states --+
| |
| |
... -+-> Ur -o-> Ul -o-> Lr -+-> Ll -+-> Ur -o-> ...
4 2 4 2 4
If we assume that we start with a right hand throw then we
can ignore the second letter in each state. We know that we
have to throw with alternate hands, so we don't have to put
that in the states. Here's a new version, still with the
letters for the hands, but moved, and put in brackets ...
(r) (l) (r) (l) (r)
... -+-> U -o-> U -o-> L -+-> L -+-> U -o-> ...
4 2 4 2 4
What next? Suppose we throw the ball and then cross the
arms. It isn't really so much that we need to know which
arm is on top, it's more interesting to know whether the
throwing arm is going to cross ABOVE or BELOW the other arm.
This is a bit of a shift in thinking, but it does release us
completely from having to remember left and right. It lets
us think about the throwing hand/arm, rather than having to
think about absolute left or right. If we add this to our
pattern above, (remembering that we started with the right
hand,) we get something like this ...
(r) (l) (r) (l) (r)
... -+-> U -o-> U -o-> L -+-> L -+-> U -o-> ...
4 2 A 4 B 2 4
We perform the first "2" with the left hand, and then the
left arm crosses on top. We can think of that as doing the
throw and continuing the hand movement to cross above. In a
similar way, the following "4" ends with the throwing hand,
(the right) crossed below. We can now omit L, R and U
entirely from our description, giving us ...
... -+-> . -o-> . -o-> . -+-> . -+-> . -o-> ...
4 2 A 4 B 2 4
and we can rearrange this slightly to give this ...
... -+-> 4 -o-> 2A -o-> 4B -+-> 2 -+-> 4 -o-> ...What remains? Well, since SiteSwaps are usually thought of as having only inside exchanges, we can make it a convention that unless we say otherwise, every exchange is an inside exchange. What about outside exchanges?
Mike Day's convention is to put a bar over any outside throw.
This means the ordinary cascade is "3", the reverse
_ _
cascade is 3, the three ball half shower is 33 and the four
_
ball half shower is 53.
Using this idea we make almost our
last change to the notation. Our running example, the weave,
can now be written as ...
_ _
4 2 4 2
A B
No bar above a number means an inside exchange, a bar means
an outside exchange. No subscript on a number means the
hands finish uncrossed, an "A" means the throwing hand
finishes above the other arm, a "B" means the throwing hand
finishes below the other arm.
Our last remaining notational problem is having to place the bars above the numbers and the A's and B's below. We can "fix" this (at a cost of some readability) by putting "i" or "o" after _every_ number, and putting "A", "B" or "U" after every number, so the weave finally ends up as ...
4oU 2oA 4iB 2iU
This is, perhaps, slightly less readable than the version
with bars and subscripts, but it does allow us to put
everything in a single line. More, it is simply a way of
writing down what has so far been done on the diagram. You
will have to form your own opinion as to which you prefer,
but we'll use the last of these in our next lesson.
Go to Lesson 13
Back to Lesson 11
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