Once we get used to describing data structures like sets or Conway games with this kind of notation, we can start ringing changes with them. Here's Conway's games:
And, here are two new generalizations of games.
- GG ::= { GG* [| GG*]* }
- GH(i) ::= {i GH(j <> i)* | GH(j<>i)* i}
And, of course, they compose
- GGH(i) ::= {i GGH(j<>i)* [| GGH(j<>i)*]* i}
The first variant, GG, has a geometric interpretation. In the Conway form, G, we are looking at points of the real line. The variant GG may be interpreted as a simplex, the different components giving limits of barycentric components.
You know, it really hit me, today, how large the question of where people come from. It takes people to make people!