  Motivated by Leinster-Cobbold measures of biodiversity, the notion of the
spread of a finite metric space is introduced. This is related to Leinster's
magnitude of a metric space. Spread is generalized to infinite metric spaces
equipped with a measure and is calculated for spheres and straight lines. For
Riemannian manifolds the spread is related to the volume and total scalar
curvature. A notion of scale-dependent dimension is introduced and seen,
numerically, to be close to the Hausdorff dimension for approximations to
certain fractals.
