  Following the general principles of noncommutative geometry, it is possible
to define a metric on the space of pure states of the noncommutative algebra
generated by the coordinates. This metric generalizes the usual Riemannian one.
We investigate some general properties of this metric in the finite commutative
case which corresponds to a metric on a finite set, and also give some examples
of computations in both commutative and noncommutative cases.
