  On looking at the literature associated with string theory one finds
statements that a sequence of matrix algebras converges to the 2-sphere (or to
other spaces). There is often careful bookkeeping with lengths, which suggests
that one is dealing with ``quantum metric spaces''. We show how to make these
ideas precise by means of Berezin quantization using coherent states. We work
in the general setting of integral coadjoint orbits for compact Lie groups.
