around looking for patterns in chaotic systems, and so he pursued a pattern involving joining up four points with six lines, all red or all blue, in a tube of many dimensions. This pattern is repeated many times in an all-blue cube, but Graham changed the color of individual edges, trying to avoid the pattern in just one color. His aim was to see if avoidance of the pattern in blue would force it to pop up in red. This doesn't happen in three, four, or even five dimensions. The number of dimensions