The Body Mass Index (BMI) has lots of critics, but is still widely used by dieters and health care providers; discovered in 1832 this ratio was supposed to be part of the most objective analysis of human society and behaviour possible.

### Average Men and Normal Curves

Next time someone thinks they’re being funny by asking you to name a famous Belgian, respond with Lambert Adolphe Jacques Quetelet. This Belgian astronomer and mathematician developed a theory about weight and height that was eventually reformulated as the ‘Body Mass Index’ and is still used by doctors and dieters today – sometimes referred to by its older name: the Quetelet Index. Adolphe Quetelet wasn’t particularly interested in measuring obesity or promoting diets, but was on a quest to discover ‘*l’homme moyen*’, that is the ‘average man’ described statistically.

Why would an astronomer care about the ‘average man’? Because discovering the average is, according to Quetelet, the only way an astronomer or mathematician can properly study human society. His ambition was to find the underlying mathematical laws that govern human lives using the same techniques astronomers used to figure out the movements of planets and stars.

The laws that concern man, and those that govern social development, have always had a special attraction for the philosopher, and perhaps most especially for those who have directed their attention to the system of the universe. Accustomed to considering the laws of the material world, and struck with the admirable harmony that reigns there, they can not be persuaded that similar laws do not exist in the animate world.

In other words, once a mathematical eye was turned to human society, remarkable patterns could be found. Some things we take for granted, such as the fact that the ratio of men and women remains roughly constant in a population. But Quetelet also discovered surprising facts, for example that the number of crimes committed in Belgium appeared to be stable and consistent over time. The fact that human behaviour – such as committing a crime – could be mathematically predicted suggested that even ‘free will’ was governed by fundamental, discoverable equations.

## Are people as predictable as planets?

At the centre of the study of *l’homme moyen* was a mathematical tool used by astronomers: mathematician Gauss's curve of errors – a bell shaped distribution thought to illustrate the range of errors one would expect to see when making astronomical observations. The Gaussian curve suggested that errors would cluster around the ‘true’ reading (most people or instruments would get close to the correct answer) while incorrect answers trail off as you get to measurements much higher or lower than the true figure. The graph predicts that even when it’s very hard to take an accurate reading, if you make enough observations and then average them you should get close to the ‘right’ answer – and the more observations you get, the more accurate your average will be.

What Quetelet did was to take this graph and its mathematical underpinnings and apply them to human society. It seemed impossible to discover the laws of society by studying every member of a community individually, but what mathematicians and social scientists could do was take thousands, tens of thousands, of measurements and then find the average. Just as the average reading is close to truth in astronomy, so it would be close to the truth in the human sciences, from criminology to medicine.

To paraphrase the historian of statistics Theodore (Ted) Porter: as astronomers might not study every individual atom which makes up a planet or a star, but instead do their calculations as if the mass of the celestial body was concentrated at its centre, so astronomers of humanity could concentrate on the fate of ‘average man’ and so predict the movement of a whole society.

## How much would the earth’s population weigh?

Quetelet calculated a model of the average relationship between human height and weight by comparing many measurements of new-borns, children and adults (including a set of records of Cambridge university undergraduates he got from the inventor of the term ‘scientist’, William Whewell). From these data he claimed there was a natural law of body mass: aside from growth spurts weight increases in relation to the square of the height of a person. He then calculated that the entire population of the earth weighed the same as a pool of water one third of an acre in area and 100 meters deep!

This height-weight ratio was not designed to test an individual’s obesity – Quetelet was far more interested in populations than individuals, but you can figure out how far any individual deviates from this average by dividing their weight in by the square of their height (try it here; 18-25 is usually considered ‘normal’). It was not until the twentieth century that the measurement began to be used widely, particularly by insurance companies who recorded weights and heights of clients to judge their risk of illness. In 1972 American physiologist and nutritionist Ancel Keys and colleagues published a review of studies showing that, according to thousands of measurements, Quetelet’s index was an accurate description of ‘normal’ human growth. From here the index became known as the BMI, and was more routinely used to judge if a patient ‘deviated’ too far from some average measurement.

While there are plenty of criticisms of the BMI as a measure of health, it remains popular. Perhaps one reason is its simplicity – it’s easy to measure height and weight, compared to more complicated systems of health assessment using fat callipers or running machines. Another is that the principle behind it remains mathematically ‘true’…for a population. Whether it has any relevance for a specific individual is another matter.

guardian.co.uk © Guardian News and Media Limited 2010

image: © Helga Weber

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