Monday, April 27, 2009

Geometry of Biological Time, Chapt 2.

Co-tidal map from NASA via Wikicommons. The points of intersection are the "phase singularities" where the tidal phase is undefined.

Slowly making my way through this book. Chapter 2 is about phase singularities -- places where the phase of some oscillation is undefined. The coolest example is the earth's tides. The surface of the earth is a sphere ("S2" in topology speak) and the tides are defined by a phase (S1). So for each point on earth at any given moment there's a tidal phase. But S2->S1 mappings (with certain continuity assumptions) must contain phase singularities -- there must be places where you can't define the phase. Above is a map from NASA showing these places as the intersections of the co-tidal lines. You can think of the tides as sloshing around those points where the sea level doesn't change.

The chapter is mostly about biological versions of such phase singularities. Detailed examples are given from fruit fly circadian rhythms, but the technical details of the experiments were overwhelming so I didn't fully follow and decided, perhaps unwisely, to plod forward without complete understanding.

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