Are we 2-D? BMI!

Once again, a rash of media articles about obesity in the United States has broken out. And once again, the obesity statistics are defined in terms of BMI. Here is an example, from forbes.com:

To determine which cities were the most obese, we looked at 2006 data on body mass index, or BMI, collected by the Centers for Disease Control’s Behavioral Risk Factor Surveillance System, which conducts phone interviews with residents of metropolitan areas about health issues, including obesity, diabetes and exercise.

In this case, participants report their height and weight, which survey analysts use to calculate a BMI. Those with a BMI between 18.5 and 24.9 are considered at a healthy weight, those with a BMI between 25 and 29.9 are considered overweight, and those with a BMI of 30 or higher are considered obese. About 32% of the nation is obese, according to the Centers for Disease Control; Memphis ranked above the national average at 34%

Never mind that the city that ranked third in obesity, Nashville, turned up among the 25 “fittest” (as opposed to “fattest”) in a different survey, this one by Men’s Fitness (and, as far as I can tell, not based on BMI). I am not interested in the results, only in the use of BMI. And, what’s more, after entering “obesity BMI” in a Yahoo news search, not one of the first ten articles that I clicked on included an actual definition of BMI.

The BMI, or body-mass index, is defined very simply as a person’s weight (in kilograms) divided by height (in meters) squared. Thus, since I weigh 66 kg (145 lb.) and stand 1.71 m (about 5 ft 7½ in), my BMI is 66÷1.71² ≈ 22.5.

Now anyone with any familiarity with physical science will recognize a quantity defined as force (such as weight) divided by length squared (or area) as representing pressure or stress. For example, for people of different sizes but with similar body proportions, the area of any portion of their body surface – for example, the portion that is in contact with a chair on which they may be sitting – will be proportional to the square of the height. If the chair bears a person’s full weight, then the average pressure on the chair’s seat, equal to the weight divided by the contact area, will be proportional to that person’s BMI.

It is precisely for this purpose – the design of office chairs – that the quantity now known as BMI was invented by the nineteenth-century Belgian mathematician Adolphe Quetelet.

But human bodies are three-dimensional, not two-dimensional. For people of different stature but similar geometric proportions, the body volume is proportional to the cube, not the square, of the height. And if the proportions of the various constituents of body mass (bone, muscle, fat etc.) are similar, then the weight is proportional to the volume, and consequently to the cube of the height. Consequently, what people who are geometrically and physiologically similar have in common is the weight divided by the height cubed, not squared.

What this means is that people with the same build will have a higher BMI if they are taller and a lower BMI if they are shorter. It has already been noted that very tall people who are quite fit — for example, professional basketball players — have BMI values that would rank them as overweight. Thus, an NBA guard who is two meters (about 6 ft 7 in) tall and who has the same build as I do would weigh 66×(2.0÷1.71)³ ≈ 106 kg (232 lbs) and his BMI would be 26.4, in the “overweight” range.

It has also been remarked that in populations that, on the average, are significantly shorter than European (or European-descended) ones, a lower overweight threshold is necessary. For Southeast Asians, for example, it’s 23 (as in this document from Singapore). Were the body types the same, this would be consistent with average height being about 8% less. In fact, the average adult height in China, for example, is 6–7% less than the average of white Americans. But the body types are in fact different (for example, the waist-hip ratio of Chinese men is 0.87 while that of white Americans is 0.98, as given here).

I have no doubt that if an index were defined on the basis of weight divided by height cubed, the discrepancies would become negligible.

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Better late than never?

Bernard Kouchner is one of the few people in public life whom I have long admired, whether as a principled humanitarian (he was the founder of Médecins Sans Frontières but left it on a matter of principle) or as a practical politician (he was France’s Minister of Health in several left-wing governments and is now, without compromising his leftist politics, Foreign Minister in a right-wing government). And so, when he said last week that he was “very happy” about the prospects of the Annapolis Conference for peace in the Middle East, I felt at least mildly encouraged.

For seven years I have lived with the embarrassment of having written an essay, “Thoughts on the 2000 Election,” in which I wrote, among other things, that “a Bush – that is, a Republican – administration would have another advantage over Gore: it would not be burdened with the pro-Israel bias of the Democratic Party due (at least in part) to its heavy Jewish influence” and that “the highly effective Israel lobby would [not] altogether lose its clout in a Bush administration…” [but] “such an administration would have more freedom of action in imposing some tough choices on Israel.”

Of course I had no way of knowing that, in matters of international policy and security, the Bush administration would in fact become the Cheney rule, and that the paranoid neo-Nazi fantasy of the Zionist Occupation Government (“ZOG”) would become a reality, with many high-ranking officials (Wolfowitz, Perle, Abrams and their ilk) constituting, practically, a Washington cell of the Likud.

Now these people are gone, along with their enforcer Don Rumsfeld, and while Dick Cheney retains his constitutional position, his name is rarely heard outside of jokes. The Annapolis Conference represents the kind of initiative that I was so naively hoping for back in the year 2000.

The impression that I’ve been gathering from the media is that it’s too little, too late. And perhaps late is not better than never. Perhaps a fresh start in a new administration might have a better chance. But it never hurts to feel vindicated, even if very late.

Linguists and word-formation

A little while ago I received a message from the linguist Ben Zimmer (of the University of Pennsylvania and Oxford University Press) in regard to my post about localitarian. Ben, one of the people who publicized the “Word of the Year” locavore, commented that he not seen localitarian before, but he had come across locatarian.

That word immediately began to grate on me. One reason is that the obvious connection would be to the verb locate, and a locatarian would be someone who locates something or other. (It could be, for example, a location scout in the movie industry.) But another reason that a francophone reading it might associate it with the French locataire, which means ‘tenant’ or ‘renter.’ It’s what’s known as a false friend.

Anglophones who post on the Web often forget that it’s the World Wide Web, and that the English in which they write is likely to be read by millions of Web surfers for whom it is not the primary language. Of course I don’t expect such awareness from ordinary posters. But I do expect it from linguists. I know that this expectation is naive, since it is not borne out by the record.

The record, in fact, is mixed. When Noam Chomsky decided to use grammatical for ‘idiomatic’ he was being Humpty Dumpty (“a word means just what I choose it to mean”), knowingly and willfully redefining what is meant by grammar. But when Charles Ferguson introduced diglossia — a medical term — for a concept for which the far more canonical diglossy was already in use, he was just being sloppy. (I wrote about this in an essay.)

When William Safire (a “language maven” but not, academically, a linguist) chose to denote an ‘incorrect correction’ by the portmanteau incorrection (rather than the regularly formed miscorrection, since mis-, not in-, is the standard English prefix for ‘incorrect’), he was just trying to be clever, which is his shtick (remember “nattering nabobs of negativism”?). But when Mark Liberman, a prominent linguist (who has often been critical of Safire), propagates the usage on Language Log while ignoring the possibility that the word may be misread by francophones or other Romance-speakers (since French incorrection — along with its cognates — means ‘incorrectness’ or ‘discourtesy’), he is not furthering the cause advanced by much of the posting on Language Log: respect for linguists as the guardians of language. Quis custodiet ipsos custodes?