  I propose a general, covariant way of defining when one region is "deeper in
the bulk" than another. This definition is formulated outside of an event
horizon (or in the absence thereof) in generic geometries; it may be applied to
both points and surfaces, and may be used to compare the depth of bulk points
or surfaces relative to a particular boundary subregion or relative to the
entire boundary. Using the recently proposed "lightcone cut" formalism, the
comparative depth between two bulk points can be determined from the
singularity structure of Lorentzian correlators in the dual field theory. I
prove that, by this definition, causal wedges of progressively larger regions
probe monotonically deeper in the bulk. The definition furthermore matches
expectations in pure AdS and in static AdS black holes with isotropic spatial
slices, where a well-defined holographic coordinate exists. In terms of
holographic RG flow, this new definition of bulk depth makes contact with
coarse-graining over both large distances and long time scales.
