  We consider maximal almost disjoint families of block subspaces of countable
vector spaces, focusing on questions of their size and definability. We prove
that the minimum infinite cardinality of such a family cannot be decided in ZFC
and that the "spectrum" of cardinalities of mad families of subspaces can be
made arbitrarily large, in analogy to results for mad families on $\omega$ . We
apply the author's local Ramsey theory for vector spaces to give partial
results concerning their definability.
