 Several problems with this kind of program make themselves felt immediately. Consider, for example, a spacetime representing the final state of the complete gravitational collapse of a spherically symmetric body resulting in a black hole. (See  section 3  below for a description of black holes in general, and  Figure 4  for a representation of a body collapsing to form a black hole.) In this spacetime, any timelike path entering the black hole will necessarily be extendible for only a finite amount of proper time—it then “runs into the singularity” at the center of the black hole. In its usual presentation, however, there are no obvious points missing from the spacetime at all. By any standard measure, as a manifold in its own right it is as complete as the Cartesian plane, excepting only the existence of incomplete curves, no class of which indicates by itself a place in the manifold at which to add a point so as to make the paths in the class complete. Likewise, in our own spacetime every inextendible, past-directed timelike path is incomplete (and our spacetime is singular): they all run into the Big Bang. Insofar as there is no moment of time at which the Big Bang occurred (no moment of time at which time began, so to speak), there is no point to serve as the past endpoint of such a path. We can speak of the cosmic epoch, the time after the big bang. That makes it easy to imagine that cosmic time zero is some initial event. That, however, is an illusion of our labeling. Cosmic time “zero” is a label attached to no event. If instead we had labeled epochs with the logarithm of cosmic time, then the imaginary moment of the big bang would be assigned the label of minus infinity and its fictional character would be easier to accept. (One can make the point a little more precise: the global structure of our universe, as modeled by our best cosmological theories, is essentially the same as a well known mathematical space, either ℝ4 or 𝕊3 x ℝ, which are both complete and inextendible as manifolds independent of any spacetime metrical structure, in every reasonable sense of those terms.) 