  The existence of a thermodynamic description of horizons indicates that
spacetime has a microstructure. While the "fundamental" degrees of freedom
remain elusive, quantizing Einstein's gravity provides some clues about their
properties. A quantum AdS black hole possesses an equispaced mass spectrum,
independent of Newton's constant, $G$, when its horizon radius is large
compared to the AdS length. Moreover, the black hole's thermodynamics in this
limit is inextricably connected with its thermodynamics in the opposite
(Schwarzschild) limit by a duality of the Bose partition function. $G$, absent
in the mass spectrum, reemerges in the thermodynamic description through the
Schwarzschild limit, which should be viewed as a natural "ground state". It
seems that the Hawking-Page phase transition separates fundamental,
"particle-like" degrees of freedom from effective, "geometric" ones.
