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By Root 880 0

college. He got started, he would say, by not having a proper education. His father, rising from the bottom of the life insurance business to the level of vice president, moved the family almost yearly up and down the East Coast, and Winfree attended more than a dozen schools before finishing high school. He developed a feeling that the interesting things in the world had to do with biology and mathematics and a companion feeling that no standard combination of the two subjects did justice to what was interesting. So he decided not to take a standard approach. He took a five-year course in engineering physics at Cornell University, learning applied mathematics and a full range of hands-on laboratory styles. Prepared to be hired into the military-industrial complex, he got a doctorate in biology, striving to combine experiment with theory in new ways. He began at Johns Hopkins, left because of conflicts with the faculty, continued at Princeton, left because of conflicts with the faculty there, and finally was awarded a Princeton degree from a distance, when he was already teaching at the University of Chicago.

Winfree is a rare kind of thinker in the biological world, bringing a strong sense of geometry to his work on physiological problems. He began his exploration of biological dynamics in the early seventies by studying biological clocks—circadian rhythms. This was an area traditionally governed by a naturalist’s approach: this rhythm goes with that animal, and so forth. In Winfree’s view the problem of circadian rhythms should lend itself to a mathematical style of thinking. “I had a headful of nonlinear dynamics and realized that the problem could be thought of, and ought to be thought of, in those qualitative terms. Nobody had any idea what the mechanisms of biological clocks are. So you have two choices. You can wait until the biochemists figure out the mechanism of clocks and then try to derive some behavior from the known mechanisms, or you can start studying how clocks work in terms of complex systems theory and nonlinear and topological dynamics. Which I undertook to do.”

At one time he had a laboratory full of mosquitoes in cages. As any camper could guess, mosquitoes perk up around dusk each day. In a laboratory, with temperature and light kept constant to shield them from day and night, mosquitoes turn out to have an inner cycle of not twenty-four hours but twenty-three. Every twenty-three hours, they buzz around with particular intensity. What keeps them on track outdoors is the jolt of light they get each day; in effect, it resets their clock.

Winfree shined artificial light on his mosquitoes, in doses that he carefully regulated. These stimuli either advanced or delayed the next cycle, and he plotted the effect against the timing of the blast. Then, instead of trying to guess at the biochemistry involved, he looked at the problem topologically—that is, he looked at the qualitative shape of the data, instead of the quantitative details. He came to a startling conclusion: There was a singularity in the geometry, a point different from all the other points. Looking at the singularity, he predicted that one special, precisely timed burst of light would cause a complete breakdown of a mosquito’s biological clock, or any other biological clock.

The prediction was surprising, but Winfree’s experiments bore it out. “You go to a mosquito at midnight and give him a certain number of photons, and that particularly well-timed jolt turns off the mosquito’s clock. He’s an insomniac after that—he’ll doze, buzz for a while, all at random, and he’ll continue doing that for as long as you care to watch, or until you come along with another jolt. You’ve given him perpetual jet lag.” In the early seventies Winfree’s mathematical approach to circadian rhythms stirred little general interest, and it was hard to extend the laboratory technique to species that would object to sitting in little cages for months at a time.

Human jet lag and insomnia remain on the list of unsolved problems in biology. Both bring out the worst