This question is just for fun and I apologise if it's too broad or off topic.
The Details:
As anyone who has played the Tony Hawk games can tell you, skateboarding - at least in part - can be scored using $\Bbb N$. Somewhat arbitrary points can be awarded for each successful trick in proportion to its perceived difficulty. These tricks can form sets. For example:
- $\square$ for flip tricks,
- $\bigcirc$ for grab tricks,
- $\triangle$ for grinds,
- $\updownarrow$ for flat ground tricks
The flip and grab tricks can be done with frontside $(+)$ or backside $(-)$ rotations in intervals of $180°$, multiplying the score of the trick by some factor. The grinds and the flat ground tricks are each done for a duration; the longer the duration, the higher the score; and the same is true for grab tricks
Skateboarding is sequence of combinations of tricks, such as
$$\text{frontside }180\text{ kickflip}\to 3\text{ second switch frontside fifty-fifty}\to 1\text{ second switch indy grab}.$$
It's also impossible to do certain trick combinations. For instance, you can't do a nollie out of a manual.
The Questions:
What kind of mathematics describes the set of all skateboarding combinations (and the point-scoring system)? Do any mathematical phenomena model the same mathematics?
Thoughts:
Surely there's at least one coherent answer since the Tony Hawk games exist.
I guessing a language in $\square\cup\bigcirc\cup\triangle\cup \updownarrow\cup (0, \infty)\cup\{\pm 180n°\mid n\in\Bbb N\}$ might suffice for the first question, with some function from the language to $\Bbb N$ for the scoring system.
The second question beats me.