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A Mathematical Challenge to Obesity

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FIGHTING OBESITY Carson Chow at a supermarket. Dr. Chow, a mathematician, has found that a food glut is behind America’s weight problem.

Carson C. Chow deploys mathematics to solve the everyday problems of real life. As an investigator at the National Institute of Diabetes and Digestive and Kidney Diseases, he tries to figure out why 1 in 3 Americans are obese.

We spoke at the recent annual meeting of the American Association for the Advancement of Science, where Dr. Chow, 49, gave a presentation on “Illuminating the Obesity Epidemic With Mathematics,” and then later by telephone; a condensed and edited version of the interviews follows.

You are an M.I.T.-trained mathematician and physicist. How did you come to work on obesity?

In 2004, while on the faculty of the math department at the University of Pittsburgh, I married. My wife is a Johns Hopkins ophthalmologist, and she would not move. So I began looking for work in the Beltway area. Through the grapevine, I heard that the N.I.D.D.K., a branch of the National Institutes of Health, was building up its mathematics laboratory to study obesity. At the time, I knew almost nothing of obesity.

I didn’t even know what a calorie was. I quickly read every scientific paper I could get my hands on.

I could see the facts on the epidemic were quite astounding. Between 1975 and 2005, the average weight of Americans had increased by about 20 pounds. Since the 1970s, the national obesity rate had jumped from around 20 percent to over 30 percent.

The interesting question posed to me when I was hired was, “Why is this happening?”

Why would mathematics have the answer?

Because to do this experimentally would take years. You could find out much more quickly if you did the math.

Now, prior to my coming on staff, the institute had hired a mathematical physiologist, Kevin Hall. Kevin developed a model that could predict how your body composition changed in response to what you ate. He created a math model of a human being and then plugged in all the variables — height, weight, food intake, exercise. The model could predict what a person will weigh, given their body size and what they take in.

However, the model was complicated: hundreds of equations. Kevin and I began working together to boil it down to one simple equation. That’s what applied mathematicians do. We make things simple. Once we had it, the slimmed-down equation proved to be a useful platform for answering a host of questions.

What new information did your equation render?

That the conventional wisdom of 3,500 calories less is what it takes to lose a pound of weight is wrong. The body changes as you lose. Interestingly, we also found that the fatter you get, the easier it is to gain weight. An extra 10 calories a day puts more weight onto an obese person than on a thinner one.

Also, there’s a time constant that’s an important factor in weight loss. That’s because if you reduce your caloric intake, after a while, your body reaches equilibrium. It actually takes about three years for a dieter to reach their new “steady state.” Our model predicts that if you eat 100 calories fewer a day, in three years you will, on average, lose 10 pounds — if you don’t cheat.

Another finding: Huge variations in your daily food intake will not cause variations in weight, as long as your average food intake over a year is about the same. This is because a person’s body will respond slowly to the food intake.

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