  I make three conceptual points regarding multigrid methods for computing
propagators in lattice gauge theory: 1) The class of operators handled by the
algorithm must be stable under coarsening. 2) Problems related by symmetry
should have solution methods related by symmetry. 3) It is crucial to
distinguish the vector space $V$ from its dual space $V^*$. All the existing
algorithms violate one or more of these principles.
