Coordinate system specifies each spin of the pen on the hand or occasionally the arm by the region symbols representing regions which the spinning pen touches, like the Cartesian coordinate system in mathematics, which specifies each point in a plane.
To denote coordinate of spins of a trick, Pen Spinning Trick Directory introduces new symbols - (dash), / (slash), and ^ (caret) (Table 5) as well as region symbols, in which a and b represent arbitrary different regions.
And, parentheses ( ) in which some symbols may be put are used to show that those indicated regions of the hand are not very important or definite to notate. We must remember that it is never easy to describe in symbols the rather fuzzy motion of the pen, as this coordinate system is an artificial model just created to try to better understand pen spinning tricks.
TABLE Symbols for notating coordinates of spins
Coordinate system is expected to prevent the abuse of such notations as hybrid notation and facilitate description of some hard-to-classify tricks such as Spider Spin. With spin coordinates, for example, specific trick names like Inverse Shadow and Palmspin would not be necessary, instead they can be just notated as Top spin whose coordinates of spins are 1p^2p^3p, Hp, etc.
We can also follow the time course of spins during a trick by its coordinate of spins, which will be significant in analyzing mechanisms of tricks (introduced in the next step). In other words, keeping track of changes in spin coordinates result in more precise and implicative mechanism system.
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