If we examine the space of all possible chess games we should be able to map out all games a really played look at how they are distributed in the game space (what are the dimensions of a game space, though?). It is possible that these games cluster in different ways and we could then term these clusters “styles” of play. We at least have a naive understanding of what this would mean.
But what about the distribution of these clusters overall in a game space – are they equally distributed? Are they parts of mega clusters that describe “human play”, clusters that orient around some local optimum? And if so, do we now have tools to examine other mega clusters around other optima?
Is there a connection to non-ergodicity here? A flawed image: game style as collections of non-ergodic paths (how could paths be non-ergodic?) in a broader space? No. But there is something here – a question about why we traverse probabilities in certain ways, why we cluster, the role of human nature and cognition.The science fiction theme of cognitive clusters so far a part that they cannot connect. Styles that are truly, and necessarily alien.
How would we answer a question about how games are distributed in a game space? Surely this has been done. Strategies?