When it was time to do a senior thesis—at Princeton everyone is required to do one—I wanted to pick something about geometry in nature, although I didn't know exactly what. My adviser, Fred Almgren, who was famous for studying the geometry of soap bubbles, suggested a problem about DNA geometry. Could we understand, for instance, what it might be about DNA that allows it to unwind itself without getting tangled? Given that it's so long, you'd think maybe it would get tangled occasionally and that this would be deadly if it happened in the cell. What keeps it from doing that? By working on this project I got to learn about DNA, and wrote a senior thesis about its geometry. I collaborated with a biochemist to propose a new structure of something called chromatin, which is a mixture of DNA and proteins that makes up our chromosomes. It's the next level of structure after the double helix. We know that the double helix gets wound around little spools of protein called nucleosomes, but no one knows how the nucleosomes themselves become arranged like beads on a string or how that structure is wound up to make chromosomes. My biochemical adviser and I ended up publishing a paper in the Proceedings of the National Academy of Sciences, and it was very exhilarating. I was now doing research in mathematical biology, so even though I wasn't a doctor, I was using math in biology about real stuff, about chromosomes.

That was when I realized that I wanted to be an applied mathematician doing mathematical biology. I went to England and studied at Cambridge on a Marshall scholarship and was completely bored with the traditional program—the stuff that G. H. Hardy describes in his book, A Mathematician's Apology, known as "the Mathematical Tripos." Cambridge has had the same kind of course since Newton, and I was bored with it. One day I found myself wandering into a book store across the street, where I picked up a book with the unlikely title, The Geometry of Biological Time. I say unlikely because I had subtitled my own senior thesis, "An Essay in Geometric Biology." I thought I had made up this phrase—geometric biology, the juxtaposition of geometry and biology, shape and life—and here was somebody using practically the same title. So who was this guy, Arthur T. Winfree?

I started reading the book, and thought he was nuts; he looked like a crackpot. I didn't know if I should believe that he was serious because the titles of his chapters have puns in them, he has data from his own mother about her menstrual cycle over many years, and it's all about the cycles of living things. At the time Winfree, who just died on November 5, 2002, was not someone who was really on the map. He was a professor of biology at Purdue. I glanced at the book, put it back on the shelf, and found myself coming back a few days later and read some more, and eventually bought it. Partly because I was so lonesome in England, suffering from culture shock, and partly because this book was so entrancing to me, I started reading and underlining it every day, and fell in love with the vision of living things with many cyclic processes, from cell division to heartbeat to rhythms in the brain, jet lag and sleep rhythms, all described by a single mathematics. This is what Winfree was proposing in his book, and it really is what got me started in the direction of studying synchrony.

We see fantastic examples of synchrony in the natural world all around us. To give a few examples, there were persistent reports when the first Western travelers went to southeast Asia, back to the time of Sir Francis Drake in the 1500s, of spectacular scenes along riverbanks, where thousands upon thousands of fireflies in the trees would all light up and go off simultaneously. These kinds of reports kept coming back to the West, and were published in scientific journals, and people who hadn't seen it couldn't believe it. Scientists said that this is a case of human misperception, that we're seeing patterns that don't exist, or that it's an optical illusion. How could the fireflies, which are not very intelligent creatures, manage to coordinate their flashings in such a spectacular and vast way?

One theory was that there might be a leader. It sounds ridiculous, because why would there be one special firefly? We don't believe that there is a leader any more, or that there might be atmospheric conditions that cause synchrony, like if a lightning bolt startled every one of them, and made them start flashing at the same time, which would cause them to stay together. Synchrony occurs on nights that are perfectly clear. It was only in the 1960s that a biologist named John Buck, from the National Institutes of Health, and his colleagues started to figure out what was really going on, which is that the fireflies are self-organizing. They manage to get in step every night of the year and flash in perfect time for hours upon end with no leader or prompting from the environment, through what is essentially a very mysterious process of emergence. This is a phrase that we hear all the time, but this is emergence in the natural world.

The thinking now is that individual fireflies are able not only to emit flashes but also to respond to the flashes of others—they adjust their own timers. To demonstrate this, Buck and his wife, Elisabeth, who was with him on this trip to Thailand in the mid-'60s, collected bags full of male fireflies, brought them back to their hotel room in Bangkok, and released them in the darkened room. They found that the fireflies were flitting around and crawling on the ceiling and walls, and that gradually little pockets of two and then three and four fireflies would be flashing in sync. Later lab experiments showed that by flashing an artificial light at a firefly you could speed up its rhythm, you could slow it down, make it flash a little later than it would otherwise. The point is that each firefly sends a signal that causes another firefly to speed up or slow down in just the right way so that they end up inevitably coming into sync, no matter how they started.

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