  The Lin-Maldacena geometries are nonsingular gravity duals to degenerate
vacuum states of a family of field theories with SU(2|4) supersymmetry. In this
note, we show that at large N, where the number of vacuum states is large,
there is a natural `macroscopic' description of typical states, giving rise to
a set of coarse-grained geometries. For a given coarse-grained state, we can
associate an entropy related to the number of underlying microstates. We find a
simple formula for this entropy in terms of the data that specify the geometry.
We see that this entropy function is zero for the original microstate
geometries and maximized for a certain ``typical state'' geometry, which we
argue is the gravity dual to the zero-temperature limit of the thermal state of
the corresponding field theory. Finally, we note that the coarse-grained
geometries are singular if and only if the entropy function is non-zero.
