The Mathematician’s Obesity Fallacy
By Michael Moyer | May 15, 2012 | Comments10
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obesity man park benchAs I write, this interview with mathematician Carson C. Chow is the number-one most-emailed story on the New York Times Web site. Chow, a researcher at the National Institute of Diabetes and Digestive and Kidney Diseases, had no experience in the health sciences before he came to study the problem of why so many Americans are overweight. “I didn’t even know what a calorie was,” he says.
This kind of outsider’s perspective can be invaluable when attacking a problem as difficult and entrenched as the epidemic of obesity in the U.S. Chow relates the story of starting work at the institute—a division of the National Institutes of Health—and finding a mathematical model created by a colleague that could predict “how body composition changed in response to what you ate.” The problem, as Chow describes it, was that the model was complicated: “hundreds of equations,” he told the Times. “[We] began working together to boil it down to one simple equation. That’s what applied mathematicians do.”
And what did Chow’s simple model reveal about the nature and causes of obesity? Basically, that we eat too much. “The model shows that increase in food more than explains the increase in weight.” Food in, fat out. Simple enough to be captured in a single equation.
Unfortunately Chow’s outsider’s perspective on the obesity crisis isn’t really an outsider’s perspective at all: it is the physicist’s perspective. Physicists have a long history of marching into other sciences with grand plans of stripping complex phenomena down to the essentials with the hope of uncovering simple fundamental laws. Occasionally this works. More often, they tend to overlook the very biochemistry at the heart of the process in question.
Chow’s conclusion is not just obvious—it’s a tautology. Because for Chow, a calorie is just a unit of energy. Eat more calories than you burn, and the energy must go somewhere. That somewhere is fat cells. The conclusion is built into the assumptions.
But perhaps a calorie is not just a calorie. Perhaps, as some prominent researchers argue, the body processes calories from sugar in a fundamentally unique and harmful way. According to this hypothesis, we’re not getting fat because we’re eating more. We’re getting fat because of what we’re eating more of. The biochemistry that explains why this would happen is complex—certainly difficult to include in a computer model—but that doesn’t make it wrong.
Ultimately experiments will decide if this hypothesis is true, or if it is not true, or if it is true but just one part of a nuanced understanding of obesity that includes biochemistry, microbiology, neurobiology, politics, economics and much more. The obesity crisis isn’t rocket science. It’s complicated.
About the Author: Michael Moyer is the editor in charge of technology coverage at Scientific American. Follow on Twitter @mmoyr.
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In Their Prime: Mathematicians Come Closer to Solving Goldbach’s Weak Conjecture
A centuries-old conjecture is nearing its solution
By Davide Castelvecchi | May 11, 2012 | 3
One of the oldest unsolved problems in mathematics is also among the easiest to grasp. The weak Goldbach conjecture says that you can break up any odd number into the sum of, at most, three prime numbers (numbers that cannot be evenly divided by any other number except themselves or 1). For example:
35 = 19 + 13 + 3
77 = 53 + 13 + 11
Mathematician Terence Tao of the University of California, Los Angeles, has now inched toward a proof. He has shown that one can write odd numbers as sums of, at most, five primes—and he is hopeful about getting that down to three. Besides the sheer thrill of cracking a nut that has eluded some of the best minds in mathematics for nearly three centuries, Tao says, reaching that coveted goal might lead mathematicians to ideas useful in real life—for example, for encrypting sensitive data.
The weak Goldbach conjecture was proposed by 18th-century mathematician Christian Goldbach. It is the sibling of a statement concerning even numbers, named the strong Goldbach conjecture but actually made by his colleague, mathematician Leonhard Euler. The strong version says that every even number larger than 2 is the sum of two primes. As its name implies, the weak version would follow if the strong were true: to write an odd number as a sum of three primes, it would be sufficient to subtract 3 from it and apply the strong version to the resulting even number.
Mathematicians have checked the validity of both statements by computer for all numbers up to 19 digits, and they have never found an exception. Moreover, the larger the number, the more ways exist to split it into a sum of two other numbers—let alone three. So the odds of the statements being true become better for larger numbers. In fact, mathematicians have demonstrated that if any exceptions to the strong conjecture exist, they should become increasingly sparse as the number edges toward infinity. In the weak case, a classic theorem from the 1930s says that there are, at most, a finite number of exceptions to the conjecture. In other words, the weak Goldbach conjecture is true for “sufficiently large” numbers. Tao combined the computer-based results valid for small-enough numbers with the result that applies to large-enough numbers. By improving earlier calculations with “lots of little tweaks,” he says, he showed that he could bring the two ranges of validity to overlap—as long as he could use five primes.
Next, Tao hopes to extend his approach and show that three primes suffice in all cases. But that is not likely to help with the strong conjecture. The weak conjecture is incomparably easier, Tao says, because by splitting a number into a sum of three, “there are many, many more chances for you to get lucky and have all the numbers be prime.” Thus, a quarter of a millennium after Goldbach’s death, no one even has a strategy for how to solve his big challenge.
This article was published in print as “Goldbach’s Prime Numbers.”