World games

I will consider for the purpose of philosophizing about space and time world games which have spatial relations through a world and temporal relations through gameplay of some kind. Of particular interest is the kinematics of units, which can move in certain patterns in the world. I will start with considering combinatorial game theory in particular. In combinatorics, spatial relations can be modeled by graphs and time can be modeled by partial orders. Conway's game of life can be considered a zero-player combinatorial game, the spatial relations are basically a king's graph where each position is related vertically, horizontally, and diagonally. Checkers has its own sort of graph, defined by the movements of units backwards and forwards.

Chess is a separate concept because of the different kinds of motions of its units. This makes one wonder what the space of the world of chess means. Perhaps the most sensible thing, in general is that the spatial relations are the union of the knight's graph and the queen's graph. This is a diameter two graph, which means that no matter what unit you are using there are places that cannot be reached. This means the chess space at least preserves some sense locality which wouldn't be there if its union graph was diameter one.

Then there are a variety of subgraphs of these graph that determine the kinematics of different units. The minor piece graphs the bishop graph, the knight's graph, and the bishop graphs are all perfect. The bishop graphs are defined for different square colors, and the knight's graph is also bipartite. The bishop graphs need to be defined for a subset of the total space, because they cannot change colors. The rook graph is diameter two, which is shared by the queen's graph since it is a supergraph, as well the graph of the whole space, etc. The king's graph is also defined for the king. All of these are different graphs that describe the movement of different units. There are many different variants of chess as well.

Generally the most popular of these games tend to be board games where the world is simply the board and units move around it. War games are another interesting case, where the games tend to have a world map. The world map can have rivers, roads, mountains, forests, plains, and other concepts analogous to these concepts of real world geography. Likewise, units tend to come in a variety of forms, which can be moved around in these world which is a concept of space. Analogous concepts occur in turn-based and real time strategy games, which have spatial maps that units can move around in. A separate concept, something like an action game, tends to have only one main unit but they still tend to have some spatial world they take place in.