Adolphe Quetelet: Big Mistakes of a Brilliant Statistician

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Who was Adolphe Quetelet? Why is he famous, and what was one of his biggest scientific mistakes?

Adolphe Quetelet (Quételet) was a Belgian mathematician who developed the idea of the “average human” (l’homme moyen) through the use of “means”—golden averages that represented the ideal human form. He lived from 1796 to 1874.

We’ll cover Adolphe Quetelet’s mistake in assuming that all phenomena can be charted on a bell curve and we’ll look at how we understand the world differently today.

The Mistakes of Adolphe Quételet

At first, Adolphe Quetelet’s inquiries were limited to human beings’ physical characteristics—height, weight, newborn weight, chest size—but before long, he began to seek averages in the social realm by studying human habits and morals. Adolphe Quetelet developed bell curves to describe humans’ deviance—literally—from both physical and moral norms.

Although Adolphe Quetelet’s ideas were influential in his historical moment, there were skeptics. Augustin Cournot, a fellow mathematician and philosopher, pointed out that social averages would necessarily depend on exactly whom and what attribute was being studied. An obvious example is human diet: If you were trying to determine the amount of seafood an average human consumes, you might get vastly different measurements if you were surveying inland populations versus coastal ones, or populations whose cultural traditions included a seafood-heavy diet.

The Limits of the Bell Curve 

Why was Adolphe Quetelet’s use of the bell curve so off? The classic bell curve—which is also called the “Gaussian distribution” after German mathematician Carl Friedrich Gauss—is an accurate description of Mediocristan phenomena, but it is dangerously misleading when it comes to Extremistan.

Consider human height, an eminently Mediocristan phenomenon. With every increase or decrease in height relative to the average, the odds of a person being that tall or short decline. For example, the odds that a person (man or woman) is three inches taller than the average is 1 in 6.3; 7 inches taller, 1 in 44; 11 inches taller, 1 in 740; 14 inches taller, 1 in 32,000.

It’s important to note that the odds not only decline as the height number gets further and further away from the average, but they decline at an accelerating rate. For example, the odds of someone being 7’1” are 1 in 3.5 million, but the odds of someone being just four inches taller are 1 in 1 billion, and the odds of someone being four inches taller than that are 1 in 780 billion! Adolphe Quetelet was right about the data of physical characteristics forming the shape of a bell curve.

Now consider an Extremistan phenomenon like wealth. In Europe, the probability that someone has a net worth higher than 1 million euros is 1 in 62.5; higher than 2 million euros, 1 in 250; higher than 4 million, 1 in 1,000; higher than 8 million, 1 in 4,000; and higher than 16 million, 1 in 16,000. The odds decrease at a constant, rather than accelerating, rate, indicating that their distribution doesn’t conform to a bell curve. With characteristics like these, bell curves don’t describe the world accurately: This was Adolphe Quetelet’s mistake.

(Note: The European wealth statistics cited above aren’t precise, but they illustrate the central point: that wealth is scalable and does not look like a bell curve.)

The upshot is that in Extremistan, as the name suggests, extreme events have much better odds of occurring than in Mediocristan. Simply put, the bell curve does not apply.

This type of mistake wasn’t Adolphe Quetelet’s alone. In our contemporary moment, the most egregious misuse of bell curves can be found among economists and financial-industry analysts. Most economists, including many Nobel Prize–winners, treat financial markets as though they hail from Mediocristan when, in fact, they’re from Extremistan.

A stunning example of economists’ misinterpretation of the market came in 1998, with the collapse of Long-Term Capital Management (LCTM), a hedge fund that included among its founding partners two Nobel Prize–winners, Myron Scholes and Robert C. Merton (Robert K. Merton’s son). Scholes and Merton won their Nobel Prize for a theory of stock option pricing; the theory, however, was based on a Gaussian model of the market that excluded the possibility of Black Swans.

When markets were disrupted by the Asian financial crisis of 1997 and the Russian financial crisis of 1998—a one-two punch of Black Swans—Scholes and Merton’s theory was revealed for the fantasy it was. The twin crises resulted in a crushing $4.6 billion loss for LCTM in fewer than four months. The firm had to be bailed out by a consortium of private banks, at the behest of the Federal Reserve. 

The problem is that economists’ models, like Adolphe Quetelet’s, are thoroughly Platonified: self-consistent, but bearing almost no resemblance to reality. Economists are like philosopher John Locke’s madmen: they reason “correctly from erroneous premises.”

Adolphe Quetelet: Big Mistakes of a Brilliant Statistician

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Amanda Penn

Amanda Penn is a writer and reading specialist. She’s published dozens of articles and book reviews spanning a wide range of topics, including health, relationships, psychology, science, and much more. Amanda was a Fulbright Scholar and has taught in schools in the US and South Africa. Amanda received her Master's Degree in Education from the University of Pennsylvania.

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