  The directed landscape is a prominent model of random geometry which is
believed to be the universal scaling limit of all planar random geometries in
the Kardar-Parisi-Zhang universality class. It comes equipped with a few
different natural simple curves associated to it, such as geodesics and
interfaces. Given such a curve, one might wonder whether the geometry off this
curve determines the entire landscape, or if in fact, there is non-trivial
extra information actually present "on" the curve. In this paper, we show that
the former is true for an interface in the directed landscape, while the latter
is true for a geodesic instead. Further, as is used in the proof of the first
assertion above, we show that the set of times where any geodesic intersects an
interface a.s. has dimension zero.
