BMI

If I have any readers (perhaps I should end the sentence right there) with medical training, perhaps they could explain something about the Body Mass Index to me.

My first love was engineering, before I betrayed the true faith and went into sales. As an engineering student, I was taught that because there are three dimensions, mass is a cubic function, written as (weight / length^3) = k. If you increase or reduce the size of an object while maintaining the same proportions, just blowing up the blueprint, its weight varies as the cube of the change- for example, if you double the length of an object, you also double its height and depth, so its weight is (2^3), or eight times as much. This applies to everything, even complicated devices, because each part follows the same law. It even applies to animals- the way scientists can estimate the weight of a dinosaur is to have a veterinarian examine the bones and tell a sculptor the kind of musculature it must have had, and between them they make a model of the dinosaur… knowing that flesh has about the density of water, they then dunk the model in a tank to get its water weight, and use the formula above to size it up correctly.

Now we come to the Body Mass Index. The formula for that, gotten off the CDC website, is (weight / height^2)(703) = BMI. Notice that this is a squared function, not a cubic! This formula would have the weight of two near-twins, identical in every possible way except height, vary by the square of their height, rather than the cube, as all other masses in the universe do. I can’t figure out what there is about the human body that would have it obey separate physical laws. I even tried charting the weights and BMI of famous people to try and understand.

Knowing that whichever function was correct, the cube or the square, inherent in the math is the fact that they will be closest to true in the smaller numbers, so I started charting at only five feet tall. Using the BMI formula, “normal” for 60” tall is from 94 ¾ lbs to 127 ½- that seemed reasonable to me, so I used that as the set point for the cubic formula as well. I then ran both formulae to 72” tall. The BMI formula gives the low end of normal for six feet tall as 136 ½ lbs… that’s what the late Don Knotts weighed at 5’6”- would Barney Fife have looked normal stretched out to six foot tall?? The "cube of the difference" formula makes the lighter side of normal at six foot tall to be 163 ¾ instead. I started looking for even taller famous people. Two-time MVP of the NFL, Indianapolis’ own Peyton Manning, at 6’5” and 230 lbs, has a BMI of 27.27- well into the “fat” category! But if you use the “cube of the difference” formula, “normal” for that height would be from 200 to 269 lbs. Shaquille O’Neal, at 7’2” and 325 lbs. has a BMI of 30.89- morbidly obese! But the cubic formula would have him right in the center of the normal range of 278 – 375 lbs… which is where most of the 7-footers in the NBA fall.

My conclusion: both theory and observed anecdotal evidence tell me that the BMI formula is fatally flawed, and that the taller you are above five foot, the greater the error will be. If there is a doctor reading this, would you please explain where the flaw in my thinking is?