  Motivation for the study of spacetime noncommutativity comes primarily from
its possible use in investigations of (Planck-scale) spacetime fuzziness, but
most work focuses on S-matrix/field-theory observables and still very little
has been established for geometric observables. We argue that it might be
useful to exploit the "pregeometric" formulation of spacetime noncommutativity,
which in particular describes the coordinates of the Moyal plane in terms of
the phase-space coordinates of a point particle "living" in a
auxiliary/fictitious spacetime ($\{x_1,x_2\}_{Moyal} \equiv
\{q,p\}_{particle}$). This leads us straightforwardly to a distance operator
for the Moyal plane, and allows us to expose some limitations of a previous
attempt to describe the "area of a disc" in the Moyal plane. We also observe
that from our pregeometric perspective it is rather natural to contemplate a
spacetime whose pregeometric picture is based on the phase-space coordinates
(fields) of a string. The fact that such "stringspaces" essentially provide
spacetime points with extendedness is relevant for the fuzziness of geometric
spacetime observables in ways that we preliminarily characterize through an
analysis of the distance observable on a two-dimensional stringspace and
through the observation that by implementing the
Amati-Ciafaloni-Veneziano/Gross-Mende uncertainty relation in the phase space
of the pregeometric string one could have stringspaces with a novel type of
fuzzy coordinates.
