**Devlin, Keith**
Take a look at the guy in the photo. According to the Centers for
Disease Control and Prevention, he is overweight. They base this
classification on a number called the body mass index, or BMI. Also
overweight, according to this CDC endorsed metric, are athletes and
movie stars Kobe Bryant, George Clooney, Matt Damon, Johnny Depp, Brad
Pitt, Will Smith, and Denzel Washington. Tom Cruise scored even worse,
being classified as downright obese, as was Arnold Shwarzenegger when he
was a world champion body-builder. With definitions like that, no
wonder Americans think of themselves as having an overweightness
epidemic. (Using the CDC's BMI measure, 66 percent of adults in the
United States are considered overweight or obese.)

Yes, it's that time of year again, when I go for my annual physical. I
know the routine. My body mass index regularly comes out at around 25.1,
putting me just into the "overweight category," and the doctor sends me
a fact sheet telling me I need to lose weight, exercise more, and watch
my diet. Notwithstanding that fact that the person *he has just examined*
has a waist of 32 inches, rides a bicycle in the California mountains
between 120 and 160 miles a week, competes regularly in competitive
bicycle events up to 120 miles, does regular upper-body work, has a
resting pulse of 59 beats per minute, blood pressure generally below
120/80, healthy cholesterol levels, and eats so much broccoli I would
not be surprised to wake up one morning to find it sprouting out of my
ears. (Yes, that's me in the - recent - photo. No, I'm not a "fitness
junkie". And I am certainly not a professional athlete. I'm just a
fairly ordinary guy who was lucky to be born with good genes and who
likes being outdoors on my bike when the weather is nice, and I have a
competitive streak that makes me want to race every now and then. A not
atypical Californian academic, in fact.)

Why do we have this annual BMI charade? Why would otherwise
well-educated medical professionals ignore the evidence of their own
eyes? Because the BMI is one of those all-powerful magic entities: a *number*. And not just any number, but one that is generated by a *mathematical formula.* So it has to be taken seriously, right?

Sadly, despite that fact that completion of a calculus course is a
necessary prerequisite for entry into medical school, the medical
profession often seems no less susceptible than the general population
to a misplaced faith in anything that looks mathematical, and at times
displays unbelievable naivety when it comes to numbers.

(Actually, my own physician is smarter than that. I chose him because he
is every bit as compulsive an outdoorsy, activities person as I am, and
he seems to know that the BMI routine we go through is meaningless,
though the system apparently requires that he play along and send me the
"You need to lose weight and exercise more" letter, despite our having
spent a substantial part of the consultation discussing our respective
outdoors activities.)

So what is the BMI? A quick web search on "BMI" or "body mass index"
will return hundreds of sites, many of which offer calculators to
determine your BMI. All you do is feed in your height and your weight,
and out comes that magic number. Many of the sites also give you a
helpful guide so you can interpret the results. For instance, the CDC website gives these ranges:

below 18.5 = Underweight
18.5 to 24.9 = Ideal

25.0 to 29.9 = Overweight

30.0 and above = Obese

(Tom Cruise, with a height of 5'7" and weight of 201 lbs, has a body
mass index of 31.5, while the younger Schwarzenegger, at just over six
feet tall and about 235 pounds, had a BMI over 31. The figures I quote
for athletes and movie stars are from data available on the web, and I
believe they are accurate, or were when the information was entered.)

Some sites even tell you how this mystical number is calculated:

BMI = weight in pounds/(height in inches x height in inches) x 703

Hmmm. No mention of waist-size here? Or rump? That's odd. Isn't the
amount of body fat you carry related to the size belt you need to wear
or how baggy is the seat of the jeans the belt holds up?

And what about the stuff inside the body? One thing all those
"overweight" and "obese" athletes and movie stars have in common is that
they have very little fat and a lot of muscle, and possibly also
stronger, healthier bones. Now, a quick web-search reveals that mean
density figures for these three body component materials are: fat 0.9
gm/ml, muscle 1.06 gm/ml, and bone 1.85. In other words, the less fat
you have, and the more your body weight is made up of muscle and bone,
the greater the numerator in that formula, and the higher your BMI. In
other words, if you are a fit, healthy individual with little body fat
but strong bones and lots of muscle, the CDC (and other medical
authorities) will classify you as overweight. Note the absurdity of the
whole approach. If I actually did take my physician's BMI-triggered,
form-letter advice and exercise more, I would put on even more muscle
and lose even more of what little body fat I have, and my BMI would
increase! With a medical profession like that, who needs high
cholesterol as an enemy?

Admittedly, those same authorities also say that a male waistline of 40
inches and a female waistline of 35 inches are where "overweight"
begins. But this of course is totally inconsistent with their claim that
the BMI is a reliable indicator of excess body fat. In contrast, it is
consistent with my observation that it is the density of the stuff
inside the body that is key, not the body weight. If you ignore that
wide variation in densities, then of course you will end up classifying
people with 32 inch waists as overweight. Yet this blatant inconsistency
does not seem to cause anyone to pause and ask if there is not
something just a little odd going on here. Isn't it time to inject some
science into this part of medical practice?

Time to take a look at that BMI formula and ask where it came from. I've
already noted that it ignores waistline, rump-size, and the different
densities of fat, muscle, and bone. Next question: Why does it
mysteriously *square* the height? What possible *scientific*
reason could there be to square someone's height for heaven's sake?
(Multiplying height by girth at least has some rationale, as it would
give an indication of total body volume, but it would put girth into the
denominator in the formula, which is not what you want.) But height
squared? Beats me.

Then there is that mysterious number 703. Most websites simply state it
as if it were some physical constant. A few make the helpful remark that
it is a "conversion factor." But I could not find a single source that
explains what exactly it is converting. It did not take long to figure
it out, however. The origins of the BMI, of which more later, goes back
to a Belgian mathematician. The original formula would thus have been in
metric units, say

BMI = weight in kilograms/(height in meters x height in meters)

To give an equivalent formula in lbs and inches, you need to solve the following equation for C

1lb/(1in x 1in) x C = 0.4536kg/(0.0254m x 0.0254m)

which gives C = 703 (to the nearest whole number).

Well that at least explains the 703. Sort of. But given that the formula
is self-evidently just a kludge, why not round it to 700. Stating it as
703 gives an air of accuracy the formula cannot possibly merit, and
suggests that the folks who promote this piece of numerological nonsense
either have no real understanding of numbers or they want to blind us
by what they think we will accept as science.

Another question: Why is the original metric formula expressed in terms
of kilograms and meters? Why not grams and centimeters? Or some other
units? Well, given the scientific absurdity of dividing someone's weight
by the square of their height it really doesn't matter what the units
are. I suspect the ones chosen were so that the resulting number comes
out between 1 and 100, and thus looks reassuringly like a percentage.
I'm beginning to suspect my "blind-us-with-science" conspiracy theory
may be right after all.

So which clown first dreamt up this formula and why? Well, it was
actually no clown at all, but one of the smartest mathematicians in
history: the Belgian polymath Lambert Adolphe Jacques Quetelet (1796 -
1874). Quetelet received a doctorate in mathematics from the University
of Ghent in 1819, and went on to do world class work in mathematics,
astronomy, statistics, and sociology. Indeed, he was one of the founders
of both these last two disciplines, being arguably the first person to
use statistical methods to draw conclusions about societies.

It is to Quetelet that we can trace back that important figure in
twentieth century society, the "average man." (You know, the one with
2.4 children.) He (Quetelet, not the average man) realized that the most
efficient way to organize society, allocate resources, etc. was to
count and measure the population, using statistical methods to determine
the (appropriate) "averages". He looked for mathematical formulas that
would correlate, *numerically,* with those "average citizens."

(Elementary) statistics being the highly simplistic (but extremely
powerful) tool that it is, it is generally not difficult to find simple
formulas that correlate pretty well with society's averages. You just
play around with a few variables until you find a formula that fits. If
you can provide a scientific rationale for the formula, so much the
better, and you are justified in having more confidence in your ability
to use the formula predictively. But it is generally enough that your
formula is empirically representative. *Provided* that all you are
doing is trying to draw conclusions about society as a whole, that is.
Quetelet knew what he was doing. Many since then, including, it appears,
the CDC, do not.

The absurdity of using statistical formulas to make *any* claim
about a single individual is made clear by the old joke about the man
who had his head in the refrigerator and his feet in the fire: on
average he felt fine!

Yet the CDC says, on its website,

"BMI is a reliable indicator of body fatness for people."

Nonsense. It is off-the-charts unreliable for me and for millions of
people like me. True, a few sentences later, the CDC - doubtless at the
insistence of their lawyers - says

"However, BMI is not a diagnostic tool."

You're telling me! Come on guys, either the BMI is, as you claim, "a
reliable indicator of body fatness", in which case you can so use it,
or, as you also admit, it cannot be used to diagnose excess body fat.
Which is it to be?

The CDC's answer becomes clear as we read on. Lest we note the
disclaimer that the BMI cannot be used to diagnose excess body fat and
demand a more reliable procedure, they immediately go on to mask their
legal get-out by claiming,

"Calculating BMI is one of the best methods for population assessment of
overweight and obesity. Because calculation requires only height and
weight, it is inexpensive and easy to use for clinicians and for the
general public. The use of BMI allows people to compare their own weight
status to that of the general population."

I'll say it again. This statement is completely false; there are several

*much*
better methods - some of which the CDC actually lists on its website!
The only part of this second statement that I see as having any validity
is the very telling admission that the BMI method is inexpensive and
easy to use.

There is another problem with the manner in which the CDC and other
medical authorities explain the BMI. Notice that the interpretive ranges
into the categories underweight, ideal, etc. are given to one decimal
place, with equal signs. This suggests a level of precision in the
formula that cannot possibly be warranted. (Some sites give two decimal
places.) It would at least be more honest to give the ranges like this:

below 19 you are likely to be underweight
between 19 and 25 is the range generally viewed as ideal

between 25 and 30 suggests you may be overweight

if you are above 30 you are likely to be obese

This would not make the formula any less a piece of numerological junk,
but at least would indicate that the ranges are just rough guidelines.
The only possible reason for giving the ranges in the precise way the
CDC does is to try to mislead patients that there is something
scientific going on here. It's a classic example of "lying with
numbers."

So here is the beef (lean, of course). The BMI was formulated, *by a mathematician, not a medical physician,*
to provide a simple, easy-to-apply mathematical formula to give a
broad, society-level measure of weight issues. It has absolutely no
scientific or medical basis. It is based purely on a crude statistical
analysis. It measures a general society trend, it does not predict.
Since the majority of people today (and in Quetelet's time) lead fairly
sedentary lives, and are not particularly active, the formula tacitly
assumes low muscle mass and high relative fat content. It applies
moderately well when applied to such people because it was formulated by
focusing on them! Duh!

But this is not science - it's not even good statistics - and as a
result it should not be accepted medical practice, to be regularly
flouted as some magical mumbo jumbo and used as a basis for giving
advice to patients. (For heavens sake, even seven times Tour de France
winner Lance Armstrong's own Livestrong website provides a BMI
calculator, despite the fact that the boss himself, when he first became
a world champion cyclist - before chemotherapy for cancer took 20lbs
off him - found himself classified as "overweight" by the wretched
formula.)

As you might expect, once a piece of numerological nonsense is held up
for proper scrutiny, it doesn't take long before the whole house of
cards comes tumbling down. The surprising thing about the BMI is that it
has survived for so long (as a diagnostic for individual patients). As I
indicated earlier, I suspect that much of the appeal is that it is a
single number, easy to calculate, given an air of scientific authority
by a *mathematical formula*, and (just as my earlier quote from the
CDC makes clear) it is easier and quicker to base a diagnosis on a
number than on properly examining a patient. But at that point you have
stopped doing medicine and are just doing kindergarten arithmetic.

The good news is, at last there is hope of some sanity entering the
story. The science (the real science) is finally coming. For instance, a
study of 33,000 American adults, published recently in the American
Journal of Public Health (Vol 96, No.1, January 2006, 173-178), showed
that male life expectancy is greatest for BMIs of about 26 - overweight
under the CDC's rule, and equivalent to 24 lb extra for the typical man.
For women, the study found an optimum BMI of about 23.5, about 7 lbs
heavier than the CDC's standard.

The paper's author, Dr Jerome Gronniger, a government scientist,
concluded that, "I found that the current definitions of obesity and
overweight are imprecise predictors of mortality risk."

"Imprecise predictors"? Gronniger was clearly using "scientific
understatement." It was, after all, a scientific publication. Dr David
Haslam, the clinical director of Britain's National Obesity Forum was
more blatant in a statement he made to the Daily Telegraph newspaper:
"It's now widely accepted that the BMI is *useless* for assessing
the healthy weight of individuals." (My italics.) [In the UK, it's
almost impossible to be sued, and there is no massive lobby of medical
insurance companies looking for ways to avoid paying for your medical
treatment, so commentators tend to be more forthcoming.]

Of course, any mathematician surely knew what Haslam now confirms the
moment he or she took their first look at Quetelet's formula. It screams
"junk math".

Numbers are one of the most powerful tools we have to understand our
world and to improve our lives. But like all powerful tools, when used
irresponsibly, they can do more harm than good. Medical professionals
have enormous knowledge and experience that we all benefit from. I do
regularly go for my annual physical, and for the most part I listen to
my physician's advice. He knows a lot more than I do about the human
body and health issues. I trust him - for the most part. But when the
BMI comes up, we are definitely into territory where my expertise trumps
his, and I can recognize a piece of numerological nonsense when I see
it, and as a result I ignore that part of the proceedings. But if
trained medical practitioners, backed up by august professional
organizations such as a the CDC, are still so over-awed by such rubbish
(mathematics does that to people, I see it all the time) that they
continue to preach it as if it were gospel, then how can a patient with
less mathematical sophistication hope to resist this annual incantation.

Since the entire sorry saga of the BMI was started by a mathematician -
one of us - I think the onus is on us, as the world's experts on the
formulation and application of mathematical formulas, to start to
eradicate this nonsense and demand the responsible use of our product.

Heavens, next thing we know, some authority will be claiming that the
golden ratio is the aspect ratio of the rectangle most pleasing to the
human eye. Where will it all end?

After all that, I think I need a good long bike ride over the mountains to bring my blood pressure down.

Mathematician Keith Devlin (email:

devlin@stanford.edu) is the
Executive Director of the Human-Sciences
and Technologies Advanced Research Institute
(

H-STAR) at Stanford University and

The Math Guy on NPR's

Weekend Edition

Copyright ©2011 The Mathematical Association of America

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