The Thouless theory of quantum pumps establishes quantized transport per cycle and determines the conditions for that. When the description is shifted to a moving frame, transported and residing charges mix. That transformation is encoded in Galilean space and time, but underlying it is one of vector bundles that may be described in a number of ways, that may or may not rely on Bloch theory. In one of them, the transformation mixes strong and weak indices of a bundle on a 2-torus; in another one, a 3-torus is at center stage; in yet another one, and somewhat informal way, the transformation is related to a parodox that astonished seafarers of centuries past. (Joint work with T. Esslinger and F. Santi