  We propose a connection between self-similar, focusing dynamics in nonlinear
partial differential equations (PDEs) and macroscopic dynamic features of the
glass transition. In particular, we explore the divergence of the appropriate
relaxation times in the case of hard spheres as the limit of random close
packing is approached. We illustrate the analogy in the critical case, and
suggest a ``normal form'' that can capture the onset of dynamic self-similarity
in both phenomena.
