In his Oppenheimer lecture entitled “Gravity is cool, or, why our universe is as hospitable as it is”, Freeman Dyson discusses how time has two faces: the quick violent face and the slow gentle face, the face of the destroyer and the face of the preserver (Dyson 2000). He entirely attributes these two faces to gravity and the ease with which gravitational energy can change irreversibly into other forms of energy. The simplest system exhibiting these two faces is that of three gravitating bodies; for most configurations, the slow gentle face is the norm, while for a very important subset, violence is the order of the day.