Adolphe Quetelet

Chapter 1 · An Observatory, and a Trip to Paris

Where the method came from

1796 – 1828 · Ghent · Brussels · Paris

Adolphe Quetelet was born at Ghent in 1796. He wrote poetry, painted, taught mathematics at a school, and in 1819 took the first doctorate in science awarded by the new University of Ghent, on conic sections.

His ambition was an observatory. Belgium — then part of the Netherlands — had none, and Quetelet spent years lobbying for one, on the argument that a nation without astronomical facilities was not a serious nation. He got the money in 1826.

In 1823 he was sent to Paris to learn how such an institution is run. He came back with instruments and with something more consequential: an education in the mathematics of measurement.

Every astronomical observation is slightly wrong. Measure the same star's position twenty times and you get twenty answers, and the question of what to do with them had produced a substantial body of theory — Laplace, Legendre, Gauss. The answers scatter around the true value in a shape that is regular and predictable: most measurements close to the truth, fewer further out, symmetrically on both sides.

Quetelet learned it as a working technique for an astronomer. What he did with it was not what his teachers had in mind.

Why this matters

The mathematics of measurement error was developed for stars, and its transfer to human beings is one of the most consequential moves in the history of social science.

An astronomer's training, about to be pointed somewhere unexpected. What would you ask him?

Ask Quetelet

• “Why did Belgium need an observatory?”
• “What did you learn in Paris about measurement?”
• “Why do repeated measurements of the same thing disagree?”
• “What shape do the disagreements take?”
• “Did you go to Paris expecting to change subject?”

Chapter 2 · Five Thousand Scottish Soldiers

The same curve, with nothing being measured

1830s · Brussels

The Edinburgh Medical and Surgical Journal had published the chest circumferences of 5,738 Scottish soldiers, gathered for the purpose of ordering uniforms. Quetelet plotted them.

The result stopped him. The measurements fell into exactly the shape that measurement errors fall into: most near the middle, fewer at each extreme, symmetric. He did the same with the heights of a hundred thousand French conscripts and got it again.

Here is why that is startling rather than obvious. When twenty astronomers measure one star, there IS a true value, and the scatter is the failure of the instruments to find it. When you measure five thousand different men's chests, there is no true value. Each man simply has the chest he has. The scatter is not error; it is the men.

And yet the shape is the same.

Quetelet drew the boldest available conclusion. If the measurements behave exactly as if there were a true value and errors around it, then perhaps there is something like a true value: a type, of which the individuals are imperfect executions. He wrote that if nature had aimed at producing one man and had produced five thousand attempts, the results would look precisely like this.

That sentence contains everything good and everything dangerous in his work.

Why this matters

The same pattern arising where nothing is being measured is a real and striking fact — and the explanation Quetelet reached for was not the right one.

A curve that should not have been there. What would you ask him?

Ask Quetelet

• “What did the Scottish soldiers' measurements show?”
• “Why is it surprising to find an error curve where there is no error?”
• “Is variation between people the same kind of thing as error?”
• “What did you mean about nature aiming at one man?”
• “What else did you measure to check it?”

Chapter 3 · The Average Man

1835, and the objection he could not answer

1835 – 1850s · Brussels · Paris

In 1835 Quetelet published Sur l'homme et le développement de ses facultés, essai de physique sociale — on man and the development of his faculties, an essay in social physics. Its central figure is l'homme moyen, the average man.

The average man has the average height, the average weight, the average propensity to marry, to be born in a particular month, to commit a crime. He is not a person. He is, Quetelet says, the type about which a population is arranged, and departures from him are to be treated the way an astronomer treats errors: as noise around a true figure.

It was enormously influential. It made the population, rather than the individual, an object of study, and it gave the social sciences a programme. Florence Nightingale admired it deeply and applied its methods to army mortality; Herschel reviewed it favourably; governments across Europe took it up.

The objection came quickly and it is fatal. Cournot pointed out that an average of individuals need correspond to no possible individual: take the average of the sides of a set of right triangles and you get a triangle that is not right-angled. The average man may be impossible. Averaging the heights and the weights and the propensities of a population produces a set of numbers that no human being need ever have satisfied simultaneously.

Quetelet never met the objection properly. He restated the average man, hedged it, and continued.

The modern version of the argument is exactly the same and is still live: an average is a summary, not a person, and a policy designed for the average person may fit nobody at all.

Why this matters

An average is a summary of a group and not a description of a member, and the confusion between the two is still being made every day.

A type that may correspond to nobody. What would you ask him?

Ask Quetelet

• “Who is the average man?”
• “Cournot said your average man might be impossible. Was he right?”
• “What does an average actually tell you about one person?”
• “Why treat individual differences as errors?”
• “What did Florence Nightingale take from you?”

Chapter 4 · The Budget of the Scaffold

Crimes counted, and a claim about society

1830s – 1860s · Brussels · Europe

Quetelet's second claim was about steadiness, and it disturbed people more than the first.

France had begun publishing judicial statistics in 1827, and Quetelet worked through them. The number of murders each year was almost constant. So was the number committed with a knife, with a firearm, by strangling. So were the numbers of marriages, of suicides, of letters posted without an address.

His conclusion, put with some relish: there is a budget which is paid with a frightful regularity, that of prisons, chains and the scaffold. Society prepares the crime and the guilty person is only the instrument.

He argued that no account resting on individual choice can explain this. Each murder is a decision by a particular person in particular circumstances; there is no committee ensuring the annual total. If the total is nonetheless stable to within a percent or two, then something operates at the level of the population that does not operate at the level of the person — and that something is what a science of society would study. He called the enterprise social physics.

The objection is the free-will one and it was made immediately: if the numbers are fixed in advance, in what sense is a murderer choosing? Quetelet's answer was that individual freedom is entirely compatible with aggregate regularity, which is right, but he was not always careful to say so, and the fatalistic reading was widely taken up.

He also built the machinery to do it properly. He advised on the Belgian census of 1846, which asked what people actually were rather than what they claimed, and organised the first International Statistical Congress in 1853 so that countries' figures could be compared at all.

Why this matters

The stability of social numbers year on year is a genuine fact that needs explaining, and the argument about what it implies for individual choice is not over.

A regularity that looks like fate and is not. What would you ask him?

Ask Quetelet

• “Why is the number of murders each year so steady?”
• “Does that mean the murderer had no choice?”
• “What did you mean by 'society prepares the crime'?”
• “Why did the statistical congress need to exist?”
• “What makes a census question a good one?”

Chapter 5 · What Galton Did Next

A curve handed on

1855 – 1874, and after · Brussels · London

Quetelet had a stroke in 1855 which limited his work considerably, though he continued to direct the observatory and to organise until his death in 1874.

His afterlife is more complicated than his life. Two things descended from him and they went in opposite directions.

The first is the whole modern apparatus of social measurement. Censuses conducted on a plan, comparable across countries, repeated on a schedule; the study of populations by their distributions; public health statistics; the body-mass index, which is his and is still used and still argued about. Florence Nightingale's mortality work, and through it the sanitary reform of the British Army, is direct Quetelet.

The second is Francis Galton. Galton read Quetelet, took the curve, and asked a question Quetelet had not: what if the deviations are not errors at all, but the interesting thing? If human qualities vary and the variation is inherited, then variation is the raw material of improvement — and Galton founded eugenics on that thought.

Quetelet cannot be held responsible for what a later man did with his curve, and it is not a small distance: Quetelet's average man is a type to be described, not a target to be bred towards. But the intellectual route from the one to the other is short, and it runs through the idea that a population has a proper form from which individuals deviate.

The honest summary is that the counting was a genuine advance, the average man was an error that has never entirely gone away, and the question of what an average is a fact ABOUT remains one of the most consequential in the sciences.

Why this matters

A method can be an advance and still carry a mistake that later hands turn into something worse.

A curve that went in two directions after him. What would you ask him?

Ask Quetelet

• “What did Galton do with your curve?”
• “Is a deviation from the average a defect?”
• “How responsible is a thinker for what is built on their work?”
• “What is your index of weight against height actually for?”
• “Which of your claims would you now withdraw?”

What Quetelet changed

Quetelet turned the mathematics of measurement error onto human populations and founded the statistical study of society. Censuses conducted on a plan, comparable internationally and repeated on a schedule, are his machinery, and the first International Statistical Congress of 1853 was his. His demonstration that social numbers are steady from year to year established that populations have regularities requiring explanation — the founding claim of social science. His index of weight against the square of height is still used daily.

A debate that continues

The average man was attacked by Cournot in his own lifetime on the ground that an average of individuals may correspond to no possible individual, and Quetelet never answered the objection properly. His treatment of individual variation as error rather than as the phenomenon itself was the mistake that Francis Galton inverted and built eugenics upon — a direction Quetelet did not intend but whose intellectual route from his work is short.

Keep exploring — ask Quetelet

• “Is an average a fact about a group or a description of a member?”
• “Can a population be regular while every individual in it chooses freely?”
• “Is variation the noise around a type, or the thing itself?”

Related lives

• Florence Nightingale — The Lady with the Lamp
• Carl Friedrich Gauss — Few, But Ripe
• William Playfair — Whatever The Eye Takes In

Related themes

Averages and spread · Social statistics · Measurement and error