The Varieties of Phaseless Experience: In which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways

In Chapter 1 we dwelt on the notion of smooth maps from one space to another. In Chapter 2 it emerged that certain kinds of mapping involving circles cannot be contrived smoothly. As an application we saw that certain kinds of experimentally observed continuity and smoothness involving measures that are periodic in space or time inescapably imply an unobserved (but observable) discontinuity. A phase singularity is one way to resolve this crisis of continuity implicit in the observation of nonzero winding number.