  Using the tools of noncommutative geometry we calculate the distances between
the points of a lattice on which the usual discretized Dirac operator has been
defined. We find that these distances do not have the expected behaviour,
revealing that from the metric point of view the lattice does not look at all
as a set of points sitting on the continuum manifold. We thus have an
additional criterion for the choice of the discretization of the Dirac
operator.
