  We link the thermodynamics of colloidal suspensions to the statistics of
regular and random packings. Random close packing has defied a rigorous
definition yet, in three dimensions, there is near universal agreement on the
volume fraction at which it occurs. We conjecture that the common value of
phi_rcp, approximately 0.64, arises from a divergence in the rate at which
accessible states disappear. We relate this rate to the equation of state for a
hard sphere fluid on a metastable, non-crystalline branch.
