Chess, which exists predominantly in two dimensions, is one of the world's most difficult games. Three-dimensional chess is an invitation to insanity. But human relationships, even of the simplest order, are like a kind of four-dimensional chess, a game whose pieces and positions change subtly and inexorably between moves, whose players stare dumbly while their powerful positions deteriorate into hopeless predicaments and while improbable combinations suddenly become inevitable. To make matters worse, some games are open to any number of players, and all sides are expected to win.