Saturday, February 02, 2008

Games with games

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:
  • G ::= { G* | G* }
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!


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