  This paper addresses the question: how should N n-dimensional subspaces of
m-dimensional Euclidean space be arranged so that they are as far apart as
possible? The results of extensive computations for modest values of N, n, m
are described, as well as a reformulation of the problem that was suggested by
these computations. The reformulation gives a way to describe n-dimensional
subspaces of m-space as points on a sphere in dimension (m-1)(m+2)/2, which
provides a (usually) lower-dimensional representation than the Pluecker
embedding, and leads to a proof that many of the new packings are optimal. The
results have applications to the graphical display of multi-dimensional data
via Asimov's "Grand Tour" method.
