reprinted from The Wall Street Journal
Weight Loss Is Harder Than Rocket Science
The equation behind body-mass index is simpler than the math used in space flight, but measuring human bodies is a tricky business
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Credit: Tomasz Walenta
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By Eugenia Cheng
January 30, 2020, 9:54 a.m. EST
We all have different ways to judge whether or not we need to lose weight. Some of us are always happy the way we are; some worry that our clothes are getting too tight or notice changes in the mirror; and others, especially doctors, pay attention to body-mass index or BMI.
BMI is given by a straightforward mathematical formula: weight (technically mass) divided by height squared, where weight is in kilograms and height in meters. The idea is that taller people should naturally weigh more, so we need some sort of ratio between weight and height. But why is height squared?
Mathematically, areas increase according to length squared, but volumes according to length cubed. A 12-inch pizza isn’t twice the size of a 6-inch pizza, but four times the size, whereas a 12-inch watermelon would be about eight times the volume of a 6-inch one.
Humans are three-dimensional, not flat like pizzas, but the formula for BMI seems to treat us as two-dimensional objects. One mathematical interpretation of the formula is that as humans get taller, their measurements should not scale up in all directions. Perhaps we expect tall people to be wider but not thicker from front to back.
The idea behind BMI was proposed in 1832 by the statistician Adolphe Quetelet, who wasn’t trying to define a healthy weight but to model a bell curve or normal distribution of human body sizes. He studied heights and weights and observed that weight tended to increase not according to the cube of height but with its square. The Quetelet index was renamed the body-mass index in 1972 by physiologist Ancel Keys, but it still wasn’t meant to measure the health of individuals, only to show trends among populations.
One reason the BMI model runs into problems when applied to individuals is because it doesn’t take body composition into account. It uses the crude measure of weight without distinguishing between muscle and fat, even though excess fat is much more likely to be detrimental to health than large amounts of muscle. Measuring fat composition directly comes with its own problems, however, so BMI is used as a simpler model.
The variations in our individual biology are always going to make it hard to model anything about humans precisely. It is sometimes said that “losing weight isn’t rocket science”—a field that is popularly invoked to indicate extreme difficulty. It’s true that rocket science involves much more complicated formulas than the one for BMI. But rocket science is arguably simpler than weight loss, in the sense that it involves less unpredictability and variation. We control how rockets are made, and they don’t change their material composition over time.
That is why the relationship between math and physics is generally much closer than the relationship between math and biology. But mathematical models are still helpful even when caveats and exceptions are needed. Just because an idea is expressed mathematically doesn’t mean it’s always right; but equally, just because a mathematical model isn’t always right doesn’t mean it’s completely wrong. The point of a mathematical model is to produce a theoretical version of a real-life situation, which sometimes involves trading precision for simplicity. It’s easy to dismiss BMI out of hand because of its flaws, but it’s more productive for us to use math appropriately, in full awareness of both its shortcomings and its many benefits.
