Games, Game Space, Game Theory

Smooth and Striated, Go and Chess

The last two, “smooth” and “striated” space, detailed by Deleuze and Guattari in their work A Thousand Plateaus: Capitalism and Schizophrenia, are particularly interesting.

Is space equivalent to a void, like between the walls of a container? Is it an extension around a location? Is it the distance between objects? Does it have structure?

They coin these types of space in their discussion of the nature of “the State” and “the War Machine,” which they illustrate with two board games: Go and chess.

They write, “The ‘smooth’ space of Go, as against the ‘striated’ space of chess,” and declare that “chess is a game of the State.” In chess, pieces exhibit distinct intrinsic behaviors and move in almost formal ways. In Go, the pieces are anonymous; they influence through extrinsic factors, their relationships to each other, the topology and connectedness of neighbors. Deleuze and Guattari continue:

“Finally, the space is not at all the same: in chess, it is a question of arranging a closed space for oneself, thus of going from one point to another, of occupying the maximum number of squares with the minimum number of pieces. In Go, it is a question of arraying oneself in an open space, of holding space, of maintaining the possibility of springing up at any point: the movement is not from one point to another, but becomes perpetual, without aim or destination, without departure or arrival.” (Deleuze Guattari 352-353)

AI to reason about game-space

Reiterating, “the space is not at all the same.” While we usually think of games as collections of rules, if we think of them as embodying various types of “space,” then the reasoning used to play them (the predicting, strategizing, positioning, decisioning, etc.) should also reflect the qualities of those types of space.

The “smooth” space of Go, as against the “striated” space of chess…

(An animation of how a knight would traverse all the squares on a chessboard.)

And regardless of whether the players are humans or bots, this reasoning isn’t fungible between games. Assuming the human players are only experienced at their respective games, we wouldn’t expect a chess grandmaster to perform competitively against a 9-dan Go player at Go, and vice versa. They understand the dynamics of their craft uniquely and distinctly.

AI for a particular game-space

Similarly, the AI systems that garnered the highest profile AI-defeats-human headlines for chess and Go were also quite different. Deep Blue, which defeated Garry Kasparov in 1997, was an expert system, and AlphaGo that defeated Lee Sedol in 2016 used a neural network trained with modern deep learning techniques.

Even though today’s chess engines like Leela Chess Zero also use deep neural networks, we still wouldn’t expect chess models to perform well at Go out-of-the-box, unless explicitly trained to do so (like AlphaZero and MuZero). An AI trained on Terrace would be yet another story, as would Quoridor, and so on.

So an AI can reason through a game’s mechanics and game-space, which all appear intrinsically linked to each other.

Games and Game Space

I especially like board games in discussions of spatial AI because they’re familiar and accessible, and they represent different kinds of abstract space. Chess is a space of 64 squares, and while a physical chess game exists as a board and 32 pieces, they are constrained by the rules of the game.

Even the enormous-but-finite game-space of the 361-location Go board takes among the most advanced neural networks built to reason about.

Spatial AI is for the game players as well as the game designers.

Game Theory + Systems Theory

More than abstract notions of space, we can take a bit of inspiration from game theory – the mathematical methods for decision-making amidst competing incentives – and which is applicable not only to games, but business, economies, biology, etc.

And also systems theory, which provides frameworks to model the dynamics of complex systems.

(Systems flow diagrams from Thinking in Systems: A Primer by Donella Meadows.)

While these fields have been tailored for problems of strategic planning, they aren’t easily applicable to the kinds of decisions spatial designers face.