I've been thinking. Classical mechanics essentially occurs in the category of manifolds, with every problem having a finite dimensional symplectic manifold or tensor field on a 4-manifold as a solution. On the other hand, quantum mechanics takes place in the category of (generally infinite dimensional) rigged Hilbert spaces of distributions on manifolds. Could a solution to the meme problem arise from constructing the appropriate functors between these categories, i.e finding a way to write problems in smooth manifold theory as equivalent problems in distributional analysis?