October 30, 2016
What do criminal records tell us about Adam Smith and the Industrial Revolution?
Emily Skarbek
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This raises a question that has been bugging me for years: Why is body mass index defined as the ratio of body mass to the square of your height, and not the cube?
@Andy Wood
Take a look. The BMI is simpler to calculate in your head, though, which probably accounts for its appeal.
Body mass increases roughly as the cube of body length, and tooth surface as the square of face length...
"As the square...?" Horses have rows and columns of teeth?
Why didn't this happen with other animals?
I thought amount eaten increases more slowly than body mass with increasing size.
You may be thinking of Kleiber's Law...
But, since they already screwed up the fact that the chewing surface for a horse is directly proportional to the length of its mouth, not the square of that length, we can forgive the fact that the amount that it eats is proportional to the 9/4 power of the body length, not the cube of that length.
In fact, your recollection solves a problem raised by my noticing that chewing surface is not proportional to the square of mouth length. Since the exponential ratio 9/4 : 1 is almost the same as 3 : 2, the empirically observed proportions of body length to mouth length are maintained. So it's only the analytical explanation that is mistaken, not the measurements.