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The Geometry of Biological Time
Dealing with dynamics of processes that repeat themselves regularly, this revised and updated edition extends the thread from 1980 to the present day, concentrating on areas of interest where there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities introduced in the original book. In particular the work on excitability in cell membranes will be thoroughly updated as will the references throughout the book.
Hardcover
First published January 1, 1980
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Displaying 1 - 3 of 3 reviews
August 9, 2015
This is a huge undertaking by Art, and ultimately a reference work for your areas of interest rather than something to be read cover to cover. Having said that, the first 4 chapters or so are excellent summaries that fit 'chronobiology' (most famously the circadian rhythm) into a broader context among maths and engineering fields. It has to be said that Winfree has done a brilliant job elevating the work of geneticists et al. into that history, in no small part through a great number of his own publications (similarly those of Albert Goldbeter). The updated footnotes from its 2nd edition are full of the folk knowledge that would otherwise have been lost with his passing, though in an ideal world this would all have been edited to appear more integrated into the text. A really unique and valuable work, which I look forward to owning and rummaging through on rainy days.
October 5, 2015
Fast read
July 22, 2025
Insightful, but dated
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.
Blog review.
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.
Blog review.
Displaying 1 - 3 of 3 reviews