＜概要＞Physicists say "Matrix algebras converge to the 2-sphere"

On looking at the literature of theoretical high-energy physics one finds statements that a sequence of matrix algebras converges to the 2-sphere (or to the torus, or to some other compact manifold). The definition of "convergence" is not given, but there is careful bookkeeping with lengths, which suggests to me that one is dealing with some kind of "quantum metric spaces". I will indicate how to make these ideas precise. This involves defining also a "quantum Gromov-Hausdorff distance". The technique for handling the 2-sphere will involve Berezin quantization.