  Is the geometry of space a macroscopic manifestation of an underlying
microscopic statistical structure? Is geometrodynamics - the theory of gravity
- derivable from general principles of inductive inference? Tentative answers
are suggested by a model of geometrodynamics based on the statistical concepts
of entropy, information geometry, and entropic dynamics. The model shows
remarkable similarities with the 3+1 formulation of general relativity. For
example, the dynamical degrees of freedom are those that specify the conformal
geometry of space; there is a gauge symmetry under 3d diffeomorphisms; there is
no reference to an external time; and the theory is time reversible. There is,
in adition, a gauge symmetry under scale transformations. I conjecture that
under a suitable choice of gauge one can recover the usual notion of a
relativistic space-time.
