  Recently it has been proposed that the Bekenstein-Hawking formula for the
entropy of spacetime horizons has a larger significance as the leading
contribution to the entanglement entropy of general spacetime regions, in the
underlying quantum theory [2]. This `spacetime entanglement conjecture' has a
holographic realization that equates the entropy formula evaluated on an
arbitrary space-like co-dimension two surface with the differential entropy of
a particular family of co-dimension two regions on the boundary. The
differential entropy can be thought of as a directional derivative of
entanglement entropy along a family of surfaces. This holographic relation was
first studied in [3] and extended in [4], and it has been proven to hold in
Einstein gravity for bulk surfaces with planar symmetry (as well as for certain
higher curvature theories) in [4]. In this essay, we review this proof and
provide explicit examples of how to build the appropriate family of boundary
intervals for a given bulk curve. Conversely, given a family of boundary
intervals, we provide a method for constructing the corresponding bulk curve in
terms of intersections of entanglement wedge boundaries. We work mainly in
three dimensions, and comment on how the constructions extend to higher
dimensions.
