★★★☆☆ Insightful, but dated

The Geometry of Biological Time

Arthur T Winfree

I read Arthur T. Winfree's The Geometry of Biological Time when I was a Biochemistry grad student. It was already clear to me that I was more mathematically inclined than most of my fellow students and profs, and this book (which was new then) was spoken of as one that applied sophisticated mathematics to biology.

It does that, but at the end I felt let down. Here's the basic idea. Living things often proceed through cycles. Winfree is most concerned with the daily cycles that most animals have, that are synchronized with the light of the sun, but his ideas also apply, for instance, to the cell cycle (which was only beginning to be understood at that time). How does geometry come into this?

Consider a two-dimensional plane that has a point we identify as its center. Picture all the points that are exactly 1 unit of distance (any unit you want) from the center. These points called the unit circle, or the unit 1-sphere, S^1, constitute a one dimensional space that wraps in on itself. (Why 1? Although we pictured a plane to construct it, when we move on S^1 we can move backward and forward along only one direction. Forward or backward only -- no sideways, no up or down.)

Winfree's insight is that any aspect of a living thing that cycles can be thought of as a point moving around the unit circle. And all things that occupy the unit circle share mathematical properties by virtue of its geometry. Of course he goes further than this -- it's an entire book! But that's where it begins.

This was a valuable insight in 1980, since almost nothing was known about the biochemical mechanisms of daily rhythms, and the technologies to find out more about mechanisms were only beginning to be developed. Therefore, a way of thinking about the rhythms that didn't depend on nuts and bolts could get somewhere.

That is the strength and the weaknesses of Winfree's approach. Because it was independent of mechanism, it had almost nothing to say about mechanism. That bothered me as a 25-year-old student. I felt that I had put in a lot of mind-breakingly difficult mental effort to understand his ideas and arrived nowhere. Now, forty years later, knowing the nuts and bolts in detail, it feels even more so.

Still, the mind-breakingly hard mental effort was its own reward.

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