  We review the construction of monsters in classical general relativity.
Monsters have finite ADM mass and surface area, but potentially unbounded
entropy. From the curved space perspective they are objects with large proper
volume that can be glued on to an asymptotically flat space. At no point is the
curvature or energy density required to be large in Planck units, and quantum
gravitational effects are, in the conventional effective field theory
framework, small everywhere. Since they can have more entropy than a black hole
of equal mass, monsters are problematic for certain interpretations of black
hole entropy and the AdS/CFT duality.
  In the second part of the paper we review recent developments in the
foundations of statistical mechanics which make use of properties of
high-dimensional (Hilbert) spaces. These results primarily depend on kinematics
-- essentially, the geometry of Hilbert space -- and are relatively insensitive
to dynamics. We discuss how this approach might be adopted as a basis for the
statistical mechanics of gravity. Interestingly, monsters and other highly
entropic configurations play an important role.
