Phase Singularities (Screwy Results of Circular Logic)

Abstract

A phase singularity is a point at which phase is ambiguous and near which phase takes on all values. My purpose in this chapter is to give examples by somewhat idealized description of phase singularities observed in several experimental systems. In some cases, the phase singularity is at this writing (viz., in 1978: see below and in Chapter 10 for 1999 updates) only inferred and not yet demonstrated. Some cases of purely hypothetical and trivial nature are also thrown in to help clarify the principles that I take to be involved in the more interesting biological examples. Much is glossed over here that should disturb a thoughtful person acquainted with the physiology of any one of these systems. These details are dealt with in Chapter 10 and in the Bestiary (Chapters 11–23).

... beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

Aurelius Augustinus, Bishop of Hippo