  The null-surface formulation of general relativity -- recently introduced --
provides novel tools for describing the gravitational field, as well as a fresh
physical way of viewing it. The new formulation provides ``local'' observables
corresponding to the coordinates of points --- which constitute the spacetime
manifold --- in a {\em geometrically defined chart\/}, as well as non-local
observables corresponding to lightcone cuts and lightcones. In the quantum
theory, the spacetime point observables become operators and the spacetime
manifold itself becomes ``quantized'', or ``fuzzy''. This novel view may shed
light on some of the interpretational problems of a quantum theory of gravity.
Indeed, as we discuss briefly, the null-surface formulation of general
relativity provides (local) geometrical quantities --- the spacetime point
observables --- which are candidates for the long-sought physical operators of
the quantum theory.
