Causal Diagram
Causal Diagram: This visualization is very similar to that of a Siteswap Diagram, but here, the arrows in the diagram point to the hand/throw that is caused by the object. Like "this throw must be made so the hand is free to catch"
Description
The causal diagram has a direct relation to the Siteswap Diagram, but the arrows have a different meaning. In a siteswap diagram, arrows represent the siteswap number. In a causal diagram, arrows point to the throw that frees the same hand for the next catch.
As a result, the number represented by an arrow is the siteswap number minus the number of beats until the same hand throws again.
This can make the graph appear counter-intuitive (especially if one expects the arrows to represent siteswap numbers directly):
- arrows for zips point to the left, i.e. are pointing back in time (because the throw to free the hand actually happens before the zip)
- "zero", i.e. empty hands go even further back in time
- flips produce an arrow pointing back to themselves, reflecting that nothing forces the flip and it can be replaced by a hold
Disadvantages of Causal Diagrams
- counter-intuitive at first glance
- harder to see where an object ends up (some things are only obvious in a siteswap diagram)
Advantages of Causal Diagrams
- shorter arrows make the resulting diagrams much less cluttered
- less overlapping arrows make it easier to validate 3 or more person patterns
- directly show which throw triggers (and maybe causes) a bad throw happening in the pattern. Often the obvious bad throw that ends the pattern is caused one throw or several backwards in the causal chain of throws.
Examples
2-Hand 3 Ball Cascade
The siteswap diagram, in which the arrows represent the siteswap number, looks like this:
In the causal diagram, the arrows point to the previous beat on the same hand. As this example has two hands, the arrows are always shifted by two beats:
As you can see, the diagram becomes much less crowded. The more complex the diagram, the more helpful this becomes.
531 – Example with a Zip
One counter-intuitive feature is, that causal arrows can point backwards in time if zips are involved.
Note that the 3 is magic in this pattern, which you can easily see in the siteswap diagram, but not anymore in the causal diagram.
And as causal diagram:
While arrows pointing back in time *seem* counter-intuitive, it actually makes sense: As a zip arrives one beat after it was thrown, the hand has to be freed on the beat before the zip. So the zip "causes" the throw one beat earlier. You have to make that throw, else you cannot do you zip!
522 - Example with Flips
Here, the 3 and 1 cause each other. As a consequence, if you don't do one of the throws, you can (and must) also not do the other. In other words: you can just hold (or flip):
Again, what you see here in the diagram is that flips cause themselves - or in other words, you can do a flip or you can just leave that be and hold the club until it's this hand's turn again
