The example of a “tile world” in my post the other day was perhaps needlessly complicated. Let’s take a much simpler case — a world in which the inhabitants live within the surface of a cube.
These people don’t know they live in the surface of a cube, because they don’t think in three dimensions. When they cross the edge of the cube, going from one cube face to another, they don’t notice any change, because that edge is part of the surface of the cube.
Note that this world of a cube surface can be described as consisting of six plots of square land, with each plot of land adjoining four neighbors.
What makes life in this world strange is that at each corner of your plot of land you don’t have four neighbors, but rather only three. Since this world is a lot simpler than the sixty-plot world we were discussing the other day, it’s going to be a lot eisier to describe its strange properties.
More later.