  The method of maximum entropy is used to model curved physical space in terms
of points defined with a finite resolution. Such a blurred space is
automatically endowed with a metric given by information geometry. The
corresponding space-time is such that the geometry of any embedded spacelike
surface is given by its information geometry. The dynamics of blurred space,
its geometrodynamics, is constructed by requiring that as space undergoes the
deformations associated with evolution in local time, it sweeps a
four-dimensional space-time. This reproduces Einstein's equations for vacuum
gravity. We conclude with brief comments on some of the peculiar properties of
blurred space: There is a minimum length and blurred points have a finite
volume. There is a relativistic "blur dilation". The volume of space is a
measure of its entropy.
