The Mathematics of Obesity


” … 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.”

– Dr. Carson C. Chow, MIT mathematician

The New York Times Science section has a fairly interesting conversation with Dr. Carson Chow, an MIT-trained mathematician who works for the National Institutes of Health (NIH) National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK).  The article is titled A Mathematical Challenge to Obesity.  He’s worked with other researchers in applying a mathematical model to help describe and answer questions related to our national obesity epidemic. Several key findings are important to note in addition to the quote at the top of this page:

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.

Dr. Chow was hired to answer the question of what caused the obesity epidemic.  He suggests that food overproduction is the culprit.  And if we have too much food then we wind up eating too much food.  He also says that changing our weight takes a very long time.  He says:

Beginning in the 1970s, there was a change in national agricultural policy. Instead of the government paying farmers not to engage in full production, as was the practice, they were encouraged to grow as much food as they could. At the same time, technological changes and the “green revolution” made our farms much more productive. The price of food plummeted, while the number of calories available to the average American grew by about 1,000 a day.

Well, what do people do when there is extra food around? They eat it! This, of course, is a tremendously controversial idea. However, the model shows that increase in food more than explains the increase in weight.

Dr. Chow was asked about practical advice.  His answer:

One of the things the numbers have shown us is that weight change, up or down, takes a very, very long time. All diets work. But the reaction time is really slow: on the order of a year.

People don’t wait long enough to see what they are going to stabilize at. So if you drop weight and return to your old eating habits, the time it takes to crawl back to your old weight is something like three years. To help people understand this better, we’ve posted an interactive version of our model at People can plug in their information and learn how much they’ll need to reduce their intake and increase their activity to lose. It will also give them a rough sense of how much time it will take to reach the goal. Applied mathematics in action!

Dr. Chow’s final words regarding obesity may come as dreary news for people trying to lose weight and keep it off.  He says, “It’s so easy for someone to go out and eat 6,000 calories a day. There’s no magic bullet on this. You simply have to cut calories and be vigilant for the rest of your life.”

That is a very honest observation from a well-trained scientist.  Remember that the next time you see an ad for some sure-fire trendy diet or supplement.

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