 The most obvious option is to define a spacetime as singular if and only if it contains incomplete, inextendible timelike geodesics, i.e., paths representing the possible trajectories of inertial observers, those in free-fall. This criterion, however, seems too permissive, in that it would count as non-singular some spacetimes whose geometry seems otherwise pathological. For example, Geroch (1968c) describes a spacetime that is geodesically complete and yet possesses an incomplete timelike path of bounded total acceleration—that is to say, an inextendible path in spacetime traversable by a rocket with a finite amount of fuel, along which an observer could experience only a finite amount of proper time. Surely the intrepid astronaut in such a rocket, who would never age beyond a certain point, but who also would never necessarily die or cease to exist, would have just cause to complain that something was singular about this spacetime. 