MM STD Tutorial Part 5

Here's the main point again from MM STD 04:

• When we move from one state to another we draw an arrow and say whether the exchange was an inside exchange or an outside exchange. We then put a circle or a bar on the arrow to show whether it's an inside or an outside exchange.

Also recall the diagram we had for the right-hand throw False Shower with underneath throws ...

You are further supposed now to have drawn the diagrams for the following patterns ...

1. the left-throw False Shower with underneath throws,
2. the left-throw False Shower with above throws,
3. the right-throw False Shower with above throws,
4. the cascade,
5. the reverse cascade,
6. the right-throw Half Shower.

At left, the left-throw False Shower with underarm throws,

At right, the left-throw False Shower with above throws,

At left, the right-throw False Shower with above throws,

At right, the cascade,

At left, the reverse cascade,

At right, the right-throw Half Shower.

How do these fit together?

Suppose you're in the middle of juggling some pattern and you find yourself in the state Ur. Remember, this means that your arms are uncrossed, and your right hand is about to do an exchange. What can we do now?

Looking at the diagrams above there are four things we've done so far from this situation. These are ...

1. An inside throw to Ul
2. An outside throw to Ul
3. An outside throw to Ll
4. An outside throw to Rl

Notice that in each case the state we go to has a left throw next. Of course, this has to be the case because the hands always alternate. We can go to the state Ul in two different ways, one is with an inside exchange, the other is with an outside exchange. The other options are to move to an arms crossed position, either right on top or left on top, but in each case we have do do an outside throw. We can lump all this together in a single, two-dimensional diagram, as shown here.

In fact, let's put in all the states, and all the arrows we've seen so far. Notice that we've been lazy and put both the I and the O on a single arrow between the Ur and Ul states, rather than having two arrows in each of the directions. It saves clutter.

The basic idea now is that you can wander around on this diagram, doing an exchange every time you follow an arrow. If you follow an arrow marked with a I then you have to do an inside exchange, and if you follow an arrow marked with a O you have to do an outside exchange. Of course, if the arrow has both a I and a O then you can do either type of exchange.

This isn't the whole story. For one thing the diagram isn't yet complete. We also need to see how to use it to analyse patterns and invent new ones.

Next ...

MM STD 06

Quotation from Tim Berners-Lee