 Another unusual kind of singularity characterized only recently characterized deserves mention here, because of its possible importance in cosmology. The physical processes that seem to eventuate in most known kinds of singular structure involve the unlimited clumping together of matter, as in collapse singularities associated with black holes, and the Big Bang and Big Crunch singularities of standard cosmological models. A big rip, contrarily, occurs when the expansion of matter increasingly accelerates without bound in a finite amount of proper time (Caldwell 2002; Caldwell et al. 2003; Chimento and Lazkov 2004; Dabrowski 2006; Fernández-Jambrina 2014). Rather than the volume of spacetime shrinking to zero, its volume increases without bound—spacetime literally tears itself apart, not even fundamental particles being able to maintain their structural unity and integrity (Chimento and Lazkoz 2004; Fernández-Jambrina 2014). Again, standard concepts and arguments about singularities characterized as incomplete paths do not seem easily applicable here. Although big rips do have incomplete paths associated with them as well as curvature pathology, they are of such radically different kinds as to prima facie warrant separate analysis. 