  We discuss how concepts such as geodesic length and the volume of space-time
can appear in 2d topological gravity. We then construct a detailed mapping
between the reduced Hermitian matrix model and 2d topological gravity at genus
zero. This leads to a complete solution of the counting problem for planar
graphs with vertices of even coordination number. The connection between
multi-critical matrix models and multi-critical topological gravity at genus
zero is studied in some detail.
