Quetelet, the average man and medical knowledge

Abstracts

Analizo, a partir de dos libros de Adolphe Quetelet, su teoría del 'hombre medio' o que permite asociar la normalidad biológica y social a la frecuencia de aparición de determinadas características poblacionales. Los libros son:Sur l'homme et le développement de ses facultés yDu systeme social et des lois qui le régissent. Ambos muestran que las ideas de Quetelet están atravesadas por estrategias explicativas próximas a la física y a la astronomía, y también por estrategias discursivas próximas a la teología y a la religión. La estabilidad de la media por oposición a la dispersión de las características y hechos individuales servirá de fundamento para el uso de las estadísticas en las ciencias sociales y en la medicina.

Adolphe Quetelet (1796-1874); hombre medio; tipo ideal; media estadística; medicina


Using two books by Adolphe Quetelet, I analyze his theory of the 'average man', which associates biological and social normality with the frequency with which certain characteristics appear in a population. The books are Sur l'homme et le développement de ses facultés and Du systeme social et des lois qui le régissent. Both reveal that Quetelet's ideas are permeated by explanatory strategies drawn from physics and astronomy, and also by discursive strategies drawn from theology and religion. The stability of the mean as opposed to the dispersion of individual characteristics and events provided the basis for the use of statistics in social sciences and medicine.

Adolphe Quetelet (1796-1874); average man; ideal type; statistical average; medicine


Comparison with normal values and deviations or variations from normality is a resource used on a daily basis in medicine in the study of various health-disease processes. Normal values and deviations define what is considered to be a healthy cholesterol level, as well as appropriate blood pressure, the desirable height-weight ratio known as Body Mass Index (BMI), or the quantity of white blood cells in the blood indicative of disease. The explanatory strategy that allows those values to be defined as ideal is based on the frequency and regularity with which they appear in the population overall.

The distribution of values such as BMI or cholesterol levels in the population follows a bell curve pattern, in which the mean values are the most frequent, while higher and lower values, in other words those that are furthest away from the mean, are more infrequent and rare. However, the observation of that statistical regularity, verifying that a greater number of individuals in a given population possess, for example, a particular height-weight ratio, does not immediately authorize us to convert that average into a norm or model to be followed and desired by all. The move whereby values that appear more frequently become 'normative', defining a parameter of differentiation between normal averages and pathological deviations, continues to be one of the greatest epistemological challenges of medical discourse today.

Thus, although it can be said that certain deviations from the mean indicate pathology, the explanatory strategy that defines the precise moment when a pathological process begins, for an infinite variety of markers, is not simple to understand. Why should a BMI between 18 and 25 be considered normal whereas values lower than 18 or higher than 25 indicate a pathological state or a risk?

Adolphe Quetelet (1796-1874), a Belgian astronomist who created what we now call the BMI, was the first to articulate the now long-standing belief that biological and social normality is associated with how frequently certain characteristics appear in the population (Rabinow, 2006; Desrosières, 2008), while abnormality or pathological processes are deviations from the average or statistical frequency. As Canguilhem (1990, p.122)CANGUILHEM, Georges. Le normal et le pathologique. Paris: PUF. 1990. argues, "the interesting thing about Quetelet's concept is that in his notion of the average, statistical frequency and the norm are seen as identical, because an average that determines deviations which become increasingly rare the larger they become constitutes, in reality, a norm".1 1 In this and other citations of texts from non-English languages, a free translation has been provided.

Two texts by Quetelet will be analyzed in this article: Sur l'homme et le développement de ses facultés (On man and the development of his faculties), published in 1835, and Du systeme social et des lois qui le régissent (On the social system and the laws that govern it), published thirteen years later (1848). Both texts show that Quetelet's ideas about the average man are imbued both by explanatory strategies taken from classical science disciplines such as physics and astronomy and by discursive strategies drawn from theology and religious arguments.

The average man

The idea of the average man developed by Quetelet both resembles and departs from the set of statistical patterns which we still habitually use nowadays, above all in medical discourse. This average man is the result of the articulation of a series of physical, moral and intellectual causes that remain constant at certain historical moments and in certain geographical locations (Quetelet, 1991QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.), so that there different 'typical men' or patterns for different societies. However, Quetelet saw this apparent variability of types as evidence of a unique certainty: the existence of complete regularity and constancy in the repetition of the most diverse social phenomena. Quetelet set out to explain the regularity he observed, not just in physical features such as height, weight, or chest size (he doggedly devoted himself to recording soldiers' chest measurements), but also in behaviors such as crime, murders, suicide, and madness, among other things.

Quetelet seemed obsessed with determining the laws that govern this regularity of social and biological facts as precisely as astronomers could determine the laws governing the movement of the stars. As Hacking states (1995, p.158), "Quetelet was fond of numbers and happy to jump to conclusions. It is astonishing how profoundly Quetelet's jumping to conclusions affected the twentieth-century conceptual scheme of truths and possibilities to which we still subscribe".2 2 All citations from Ian Hacking were sourced from The taming of chance, Cambridge, Cambridge University Press, 1990. Among these truths is the conviction that the most frequent characteristics of a population should be considered normal and desirable, whereas deviations constitute pathologies.

When Quetelet (1848, p.18)QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848. analyzed the average height of men in a given population, he said that "the average height of man is an element that has nothing accidental about it. It is the product of fixed causes that assign him a given size. We should not treat height in men like the height of buildings in a city, which varies according to the tastes of the time and the whims of those who built them". If we take the height of houses in a country and classify them by size, we will not find any regularity, but if, on the other hand, we measure the height of the inhabitants of that country we see very precise consistency and regularity. In the latter case, the numbers will present as if they were the result of various measurements of the same person with imprecise instruments, which would explain the deviations.

Quetelet based his argument on the measuring methods of astronomy, to which he was accustomed. In astronomy, in order to determine the trajectory or orbit of a celestial body, various more or less approximate measurements are taken, and the average value of those measurements with different instruments is defined as the real trajectory of the celestial bodies. When there are no precise, reliable instruments to determine the exact trajectory, the consistent elements of the different measurements are identified and used to discount errors due to lack of precision in the various measurements. In this way, errors due to imprecise measurement tend to cancel each other out, and the resulting average defines the real trajectory of celestial orbits.

The same measurement principle could be applied to various human proportions, such as height, for example. And this was one of Quetelet's main arguments: that natural laws, biological laws and social laws were identical. In all three cases, the so-called law of error allows diverse facts to be unified.

Constant causes and accidental causes

Quetelet transferred that logic and analysis methodology to human affairs, whether biological and physical or moral and social. Thus, he argued, population measurements presented a variety of values, among which the largest number corresponded to the average type (both ideal and real) of that population, and deviations - which were rarer the further away they were from the mean, and more frequent the closer they were to the mean - tended to cancel one another out, making possible the consistency and permanence of the average type of that population over time. This occurred as often, in Quetelet's view, as if we measured the average man's height at various different times and with different, unreliable instruments. After a great deal of measurements we could determine that the deviations showing a greater height balance out those that indicate a lesser height, and those measurements that remain the same indicate the average man's real height (Quetelet, 1848, p.18QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

However, Quetelet was not interested in this or that individual but in defining population characteristics. "One might ask whether a population has a type of man, a man who represents that population in terms of height, in relation to which all other men in the nation may be considered greater or lesser deviations. The numbers one obtains on measuring such men will be grouped around the average just like the numbers that would be obtained if that average man were to be measured numerous times with more or less imprecise methods (Quetelet, 1991, p.9QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.). Similarly, comparison of the average types of various populations allows us to define precisely the proportions of the average man as a parameter for defining normality and deviations in humanity as a whole. "Quetelet defines the 'average man' as the human type in relation to which deviation becomes rarer the greater it is" (Canguilhem, 1990, p.123CANGUILHEM, Georges. Le normal et le pathologique. Paris: PUF. 1990.; emphasis in the original).

In order to determine consistency of occurrence - that is, to determine the existence - of fixed values like height, weight, strength or BMI, for a group of individuals of the same age who live in a given population, Quetelet argued that we must take a population perspective: "In speaking of the individual it must be understood that we are not attempting to speak of this or that man in particular; we must turn to the general impression that remains after having considered a great number of people separately" (Quetelet, 1991, p.12QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.).

The science Quetelet set out to develop had an extremely ambitious goal: to study man in three dimensions, physical, moral and social, and in various degrees of aggregation, from the individual to populations, and finally to humanity as a whole. Each of these combinations would give rise to a new order (Quetelet called it "a new body") that would need to be explored. "The studies must begin with man considered as an individual; then we will go to the next level up, where, ignoring the particularities that characterize him, we will only perceive the outline of the people to which he belongs. Thirdly, we will attempt to discover the links between peoples that constitute humanity as a whole" (Quetelet, 1848, p.IVQUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). However, we soon see that this triple analytic perspective tended to disappear across his work as he focused on a population perspective, privileged both in his 1835 and 1848 works.

Quetelet concluded, on the basis of quantitative studies and on observation of empirical data, that every year there were the exact same number of crimes, suicides, marriages and births in a given population. Analyzing army statistics, he concluded that, year after year, soldiers' weight, height and chest measurements were the same. He observed that the number of mentally deranged people confined in asylums remained astonishingly consistent, and that the types of crimes and sentences passed remained regular, according to registry office data and psychiatric records. The only way of explaining these constants that appealed so much to Quetelet was to analyze each of these facts not on an individual basis but from a population perspective. It wasn't a question of understanding why a certain type of crime occurred and not another, or why an individual was a particular height or weight. Quetelet sought to explain the repetition of phenomena whose consistency seemed to indicate some common force capable of maintaining that equilibrium, the action of laws as regular as those that govern the stars or gravity.

Above all, we must stop thinking of man in isolation and treat him as merely a fraction of the species. Removing his individuality we will eliminate all that is accidental, and particularities will be erased. ... This is how we will study the laws concerning the human species, because if we examine them close up it becomes impossible to find them and we get stuck on individual particularities, which are infinite (Quetelet, 1991, p.31).

To explain this population perspective, Quetelet used figurative descriptions, such as an immense circumference drawn around a plane. He said that when we get up close, we only see a part, made up of a series of points that look disordered and disconnected to us; these points only constitute a particular form when we observe the whole. To understand the laws that govern 'social physics' we have to ignore peculiarities and anomalies, leave out singularities. For Quetelet, from a population perspective, the role of the average man was analogous to that of a center of gravity for bodies. He was the mean around which all social phenomena oscillated, a fictitious being who showed the average results obtained based on the set of physical and moral qualities of the individuals who made up a given society. "By grouping individuals of the same age and sex and presenting the average of their particular constants, one obtains the constants I attribute to that fictitious being I call 'the average man' of a given people" (Quetelet, 1848, p.14QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.; emphasis in the original).

Thus the average man is the term of comparison that allows us to determine the physical and moral qualities that are desirable for individuals who make up a given society. Quetelet declared in his 1835 work that the average man is a fiction, an être fictif. But that thesis should be treated with caution in light of the average man's role in the explanatory structure presented by Quetelet. Claiming that the average man is a fiction merely means that we will not find a man with a score that corresponds exactly to the population average, for example, a man with 2.2 children. But for Quetelet, that average man was as objective a reality as the law of gravity; he was no more and no less than the measurement around which all social phenomena revolved, a framework that allows us to identify the regularity and constancy of social phenomena and at the same time the deviations, accidents and errors.

As Halbawachs (1912, p.158)HALBAWACHS, Maurice. La théorie de l'homme moyen: essai sur Quetelet et la statistique morale. Paris: Alcan. 1912. puts it, "for Quetelet, the frequency of a characteristic is not, in and of itself, the sign that it is normal. It is not more frequent because it is normal; rather, it is normal, de facto and de jure, because it is the most frequent". He immediately adds that this characteristic, repeated in the majority of the population, would be considered by Quetelet as the closest to its true nature. To understand why the most frequently-seen characteristics define the average man, we have to differentiate between two types of causality: constant causes, which tend to maintain the same proportion of phenomena or characteristics, and accidental causes, which produce variations that lead to the existence of less probable or frequent phenomena or particular, individual characteristics - that is, to greater or lesser deviations from the average.

It is this constant cause that is expressed in the normal curve. This is why it is not possible to apply to the idea of the average to any and all circumstances. Desrosières (2002, p.5)DESROSIÈRES, Alain. Adolphe Quetelet. Courrier des statistiques, Paris, n.104, p.2-8. 2002.stresses that there is a condition that restricts its use: namely, that calculation of the average of quantities involving characteristics or different beings can only be justified if the distribution of those measurements follows the law of probability; in other words, a normal curve. Only the presence of the bell curve justifies the hypothetical existence of a constant cause operating behind the diversity observed in actual beings. Thus, Quetelet believed it was necessary to differentiate a true average, which involved a constant cause and followed a normal curve, from false averages, like the one obtained if we unify facts whose distribution is not normal, such as a binomial distribution. Quetelet's examples were: "the average distribution of the height of the buildings in a city or the average life-expectancy for the population of children born in the same year" (Desrosières, 2002, p.6DESROSIÈRES, Alain. Adolphe Quetelet. Courrier des statistiques, Paris, n.104, p.2-8. 2002.). According to Quetelet, it was necessary to ignore such false averages and to focus on those that showed the regularity and constancy of physical phenomena, such as soldiers' height, or social phenomena, such as the regularity with which crimes are committed.

According to Sánchez Carrión (2000, p.59)SÁNCHEZ CARRIÓN, Juan. Sociología, orden social y modelización estadística: Quetelet y el hombre medio. Empiria - Revista de Metodología de Ciencias Sociales, Madrid, n.3, p.49-72. 2000., Quetelet was the first person to express the regularity of social and physical phenomena using the average, showing that individual dispersion followed a normal distribution:

It was precisely that kind of average, derived from a normal distribution, that interested Quetelet, and he called it simply 'an average', as opposed to averages with non-normal distribution, which he termed 'arithmetical averages'. The interest of the former is that they allow one to discover real objects underlying the diversity of singular averages which are used for calculations (for example, the true position of a star in astronomy), as opposed to the other, arithmetical averages, which are merely numbers devoid of meaning (for example, the average height of the buildings on a street). Using the type of averages that permit the discovery of truths that are impossible to capture without statistics, Quetelet constructed his idea of the 'average man' as the normative synthesis of all singular men.

Thus, the fictitious character initially attributed by Quetelet to the average man should not limit the explanatory potential of this figure, which was so real that it constituted a goal to be achieved and became the measurement of all human variation. To say that the average man is a fictitious being is simply to acknowledge the impossibility of an individual resulting exclusively from the action of constant causes, in other words a being not subject to the influence of accidental causes. Something similar can be observed in the movement of bodies when we think of physical laws. "Contrary to what is usually affirmed, the law of inertia does not originate in the experience of common sense. We never witness rectilinear movement. It is really an attempt to explain what is on the basis of what is not, of what never occurs, and even of what can never be" (Koyré, 1980, p.195KOYRÉ, Alexandre. Galileo y la ley de inercia. Estudios Galileanos. Madrid: Siglo XXI. p.149-278. 1980.). This is also true of the average man: the absolute impossibility of a population that is not subject to accidents, deviations or errors. The fact that the average man is not found in day-to-day experience is, on the contrary, the condition of his existence as an instance of intelligibility, on the basis of which actual individuals can be thought of in terms of constants and deviations.

However, Quetelet was not satisfied with this argument and, years later, in his 1848 work, he declared instead that: "it seems we have direct proof that not only is the average man not impossible, as we came to believe [in 1835], but he is necessary. I find this a priori demonstration that a Type or Model man exists very important for the topic we are studying, since it allows us to give the theory of Man the firm bases it lacked" (Quetelet, 1848, p.46QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). Thus, for him, this average man who appeared as a model or type in relation to which physical characteristics and human qualities were defined as normal or as deviations, was not merely a metaphysical postulate but also a real, necessary being - a goal to be reached.

A normative model

In this way, Quetelet constructed a typological model of analysis that has remained largely unaltered to this day. The average man, in the precise moment of enunciation, became normative. He would serve as a parameter, a comparison for defining the values considered desirable for each society in particular, but also for humanity as a whole. It would be in reference to the average man as an ideal type that the correctness or deviation of the most varied of human characteristics would be determined, whether physical or moral, such as height, weight, body proportions, number of crimes, suicides, mental illnesses or physical abnormalities that characterize the individuals of every society. ForQuetelet (1991, p.505)QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.:

the average man's constitution serves as a type for our species. Each people has its own particular constitution, which is determined by the influence of climate and habits, and which deviates more or less from that of the average man who characterizes the country. Every individual has his own particular constitution which depends on his organization and nature. Consequently, we have an interest in discovering each one of those elements that concerns us individually and a general interest in discovering the elements that are relative to the average man, who is the type to which we must ceaselessly refer.

There is another reason why Quetelet established the average man as a universal parameter of measurement. He represented not only that which is discovered by the frequency with which human proportions or behaviors are repeated, but also a model of both physical and moral beauty and perfection to which all should aspire, and which civilized societies increasingly came to resemble. For this reason, Quetelet (1991, p.502)QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991. affirmed that "if the average man were perfectly determined and defined, we could consider him the type (or model) of beauty, and, on the contrary, everything that instead of resembling his proportions or his way of being departed from them, would constitute deformities or diseases". To such a degree that whatever was presented as radically different from the average man, not just from the point of view of proportion and form but in all the various dimensions of humanity, should be considered not just as diseased but as monstrous. Thus, the greater the distance between an individual and the average man, the more such an individual departed from humanity and approached that intermediate state between man and animal known as monstrosity.

On the opposite extreme to monstrosity, the height of humanity was seen in those individuals Quetelet termed 'great men': geniuses, artists, and notable statesmen. All of them shared the same characteristic: they were the ones who most resembled the average man, since "an individual who incorporated, in a given era, all the qualities of the average man, would also represent everything that is great, good and beautiful" (Quetelet, 1991, p.510)QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.. He acknowledged that even though approximations might exist, there was no absolute similarity between great men and the ideal type of perfection of beauty represented by the average man. For even great men, such as Socrates, for example, might lack certain characteristics, such as beauty or perfect proportions. Thus, although the model represented by the average man in all his physical, moral and intellectual capacities was considered impossible to attain in certain eras and possible in others, Quetelet declared definitively that there were individuals and peoples who came close to the ideal type and others who were far from it.

Diversity is what defines humankind. Therefore, according to Quetelet, there ought to be a theoretical and methodological strategy that would allow him to respect the normative or typological nature of the average man without ignoring the diversity that characterizes individuals and peoples. "It is impossible in a given whole, such as in a particular group of people with a common type, not to find individuals who more or less represent that type. There are those who represent it to a lesser extent, less clearly, more confusedly, and there are those who represent it more clearly, and less confusedly. Thus it is possible to establish a demarcation line among all individuals in the same group of people" (Quetelet, 1991, p.511QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.); among those who are closer to the average man and those who are further away. That demarcation line is what allows us to differentiate normality from disease, or normality from monstrosity when the deviation is extreme.

In fact, Quetelet insisted that for every physical or moral characteristic it was possible not only to define the exact average represented by the type (the average man) but the level of dispersion (Doval, 2004DOVAL, Hernán. La "distribución normal" de Gauss y el "hombre tipo" de Quetelet. Revista Argentina de Cardiología, Buenos Aires, v.72, n.3, p.239-242. 2004.) or the limits of variability that might be considered acceptable, both above and below the average. Whatever fell within those acceptable limits of variability could be considered normal and what fell outside those limits should be considered pathological or indicated a tendency (penchant) towards a pathological or abnormal state. The demarcation of those limits would be set by the frequency with which a given parameter, such as height, appeared in the population being studied, establishing a normal margin of variability among the most frequent deviations, both above and below the average.

According to Quetelet, the level of dispersion was dependent on various simple mathematical calculations that, in every particular case, would give the maximum and minimum acceptable measurements, whether of height, weight, head-body proportion, crimes, births or madness. In order to understand how these parameters for normality and deviation worked, we have to analyze the role of the average man in the field of medical knowledge. We shall see that the ideal type was used as the basis for defining parameters of health and normality for such phenomena as heart rate, blood pressure or the ideal height-weight ratio.

The average man and medical knowledge

Quetelet pioneered a new, mathematical way of understanding the relationship between height and weight (Sánchez Carrión, 1999SÁNCHEZ CARRIÓN, Juan. Quetelet y la sociología. Reis - Revista española de investigaciones sociológicas, Madrid, n.87, p.291-303. 1999.), which would give rise to what we now call the BMI. "Quetelet's index, also called the BMI, is calculated as the ratio between body mass (in kilograms) to height squared, and is widely used in current epidemiological studies" (Gugelmin, Santos, 2006, p.1865GUGELMIN, Silvia; SANTOS, Ricardo Ventura. Uso do Índice de Massa Corporal na avaliação do estado nutricional de adultos indígenas Xavante, Terra Indígena Sangradouro - Volta Grande, Mato Grosso. Cadernos de Saúde Pública, Rio de Janeiro, v.22, n.9, p.1865-1872. 2006.). Quetelet established for the first time the ideal ratio of height to weight, and also defined the limits between what was considered a normal height/weight ratio and what should be considered pathological. Thus, he set out to establish the acceptable margin of variability or level of dispersion, either on the high end (which today would be a BMI>25) or the low end (which today would be a BMI<18) of the mean, identified as the ideal proportion (BMI=21). The way the acceptable margins of variability and the boundaries that separate them from pathological deviation are defined is essential for understanding the strategic role of statistical averages in the field of medical knowledge from 1835 to the present.

Quetelet dedicated part of his 1835 book to analyzing the relationship of the average man to medical knowledge. That section is entitled "On the average man considered according to his relationship with natural and medical science" (1991, p.499-514). In it, he claimed that his theory of the average man was merely aimed at broadening the use of a strategy that medicine was already applying in a routine way - albeit with little reflection and in an almost intuitive manner - to include physical, moral and intellectual aspects. "Consideration of the average man is so important in medicine that it is virtually impossible to judge the state of an individual without referring to a fictitious being, observed as being the normal state, which is, fundamentally, the same thing we are considering here" (Quetelet, 1991, p.503QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.). He remarked that when a doctor examines a patient, he may say that his pulse is very rapid or his breathing very agitated. But in saying this, he is presuming two things: on the one hand, that there is a normal value in relation to which a given characteristic is judged to be excessive, and on the other, that this deviation from the limits of normality represents a danger to health.

Every doctor knows intuitively from personal experience with countless patients what that deviation means and the danger it represents. The research Quetelet was proposing aimed to establish the precise constants for weight, height and all the possible physical characteristics that characterize the average man, as well as "the limits that those values may reach" (Quetelet, 1991, p.502), without being prejudicial. This data would help, although it could never substitute for, medical experience. For Quetelet, there was only one legitimate way to substitute for that clinical experience: each patient could keep permanent track of his respiration rate or heart rate or the variations in his height-weight ratio. However, patients were not usually capable of keeping track of such things. "Since in the majority of cases, the patient cannot present any satisfactory observation about his person, the doctor will be forced to refer to a common scale and compare him with the average man" (Quetelet, 1991, p.504QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.).

It is possible to identify the use of average population values with the way medicine uses those constants nowadays. However, Quetelet would add that such immediate reference to the average man could have serious consequences in the health care field "since general laws relative to masses are essentially false when they are applied immediately to individuals: which does not mean that they should not be consulted" (Quetelet, 1991, p.505QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.).

In 1848, Quetelet's concern that medicine make careful use of the average man was not so marked. He insisted, fundamentally, on the need to establish mathematical formulas to identify the constants of size, weight, height, respiration and pulse rate. Thus, bearing in mind some accidental characteristics of populations (such as age, sex, or the community to which one belongs) and grouping them accordingly, one could establish reference values and more or less fixed limits of normality to use as parameters for comparison in medical examinations.

He wrote that for a long time, observing how doctors checked their patients' pulse, he believed it was well known what the normal heart rate was, "but I was disconcerted when I myself checked the pulse of elderly and young people and came up with numbers that were the opposite of what appears in treatises on physiology. ... This is an example of the use of averages and the usefulness of calculation methods in the science of mankind" (Quetelet, 1848, p.48QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). Based on observations of numerous individuals of different ages, heights and weights, he arrived at the following conclusion: "The heart rate should be inversely related to the square root of height; using 1.68m as the average height, the heart rate will be 70" (Quetelet, 1848, p.49QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

Similarly, he set out to find the exact calculation that would allow him to establish the ideal proportion of height to weight. "According to the numerous studies done on the correlation of height and weight in adult men, I believe I may conclude that: the ideal weights are proportional to height squared" (Quetelet, 1848, p.43QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

Thus, those facts that medical observation could deduce from clinical experience, or that each one of us could deduce with the naked eye by observing, for example, a significant imbalance between height and weight, were governed, according to Quetelet, by laws that should be written with mathematical characters. Therefore, even though intuitive understanding of averages might exist outside science, it is science that allows us to endow that unconscious knowledge with more precision. "For that understanding to be complete, the limits (of normality) need to be considered. The average and the two limits within which all individual values are contained are not as vague as common knowledge believes them to be, they are well-determined quantities that observation allows us to discover with the most perfect exactitude" (Quetelet, 1848, p.41QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

It is true that when we analyze a given population we can deduce certain constants, such as height, intuitively. However, according to Quetelet, those constants that we vaguely deduce by mere observation can only be precisely determined with the aid of science. What happens is that simply identifying constants does not help us understand the average man in all his complexity.

It is necessary also to know the limits between which those heights may vary. When the following three elements are known: average height, maximum height and minimum height, the law of accidental variations allows us to calculate how the population is divided with respect to height. This law is repeated in regard to weight, strength and all the physical qualities of mankind. Therefore it is possible to calculate how a population is distributed with regard to weight, height or strength (Quetelet, 1848, p.49).

We need to remember that accidental causes or variations refer to the set of elements that for one reason or another introduce some kind of deviation from the constant laws, which, free from those accidental alterations, would naturally tend towards the preservation of the average man's identity. However, Quetelet proposed and defended the hypothesis that those variations tend to neutralize one another as societies reach a greater level of perfection. At that point, he claimed, the maximum and minimum limits of variability would tend to approach one another and eventually cancel each other out. This hypothesis allowed Quetelet to insist on what would turn out to be the crux of his argument about the average man: that there is a tendency towards fixity and constancy in human proportions and that accidental deviations tend to cancel each other out. For him, "man's proportions are so fixed at any age that it is enough to have observed a small number of individuals, for the average to give us the ideal type" (Quetelet, 1848, p.34QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

Thus we arrive at the definition of two principles that Quetelet considered essential to understanding his theory of the average man. These principles, already present in his 1835 work, would be revisited in 1848. The first principle says: "The average man, the type of our species, is also the model of beauty" (Quetelet, 1848, p.38). The second principle states: "The margins of variation (higher or lower) are more restricted in a population the closer it gets to perfection" (Quetelet, 1848, p.38QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

Du systeme social et des lois qui le régissent (1848) is divided into three main parts: book 1, "On man"; book 2, "On societies"; and book 3, "On humanity." The second principle mentioned above constitutes the main theme of chapter III of book 3, titled "The limits between which elements relating to man vary, tend to approach one another" (Quetelet, 1848, p.252-257QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). In it, Quetelet referred once again to the constancy of type. He said that from time immemorial up to that moment, men had maintained the same type or model, repeated over generations. This meant that at different points in history, there could have been great differences of height or strength between men, but the average value had not varied over time, as a result of the compensation of accidental causes. He maintained that "everything points to the fact that, at least for physical qualities, the average man has not perceptibly varied, but also that the limits between which higher or lower variations occur, have come perceptibly closer" (Quetelet, 1848, p.532QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

The thesis Quetelet defended in this chapter concerns the triumphs of civilization not only in terms of physique but also on the moral and intellectual level. He believed that there were no longer any great differences between the poor and the rich in either extreme virtue or social depravation, nor in the intellectual privation and sublime intelligence that marked many ancient peoples, as seen, for example, in Homer's narratives. What existed was a tendency, as a result of the advances of civilization, for variability within the limits defining normality to become closer and closer to the average type, canceling out both good and bad extremes. This led to the need to know whether "it should be considered a good thing that the limits between which man may vary approach one another indefinitely" (Quetelet, 1848, p.255QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

The restriction of the margin of variability tended increasingly towards identification with the average man, which might lead to absolute equality. For Quetelet, this equality could only be negative, tending to take humanity back to the beginning, and discouraging innovation, creation, art and science. But, "if absolute equality must be considered an evil, it is nonetheless true that the mutual approach of the limits, up to a certain point, is a true privilege" (Quetelet, 1848, p.256QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). All that remained was to establish the limits between which restricted variation was desirable, and it was scientific knowledge that had to determine exactly what those limits were.

Leaving aside that extreme of absolute equality which is unattainable for human beings, Quetelet believed that in most civilized societies, the limits between which different human characteristics varied, particularly physical and biological characteristics like height-weight ratio, heart rate and respiration rate, tended to approach one another, and this was becoming possible thanks to the help of science. The development of medicine was stimulating the use of new technologies like surgery, vaccination, and the use of orthopedics, while hygiene measures allowed us to guarantee the normal development of all our functions. "The progress of medicine has diminished the severity of some diseases and prolonged the average life expectancy of man. However, we should not expect this average to keep going up indefinitely. Mortality responds to other rules than those that lead to advances in the art of healing" (Quetelet, 1848, p.260QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

Other social measures, such as the control of child labor, good nutrition, and reducing the number of hours in the workday, could contribute to narrowing the limits between which normality oscillates in a given society. The level of dispersion with regard to the average could reach its extreme in conditions of great social inequality and could approach the mean as a result of medical and social advances. Quetelet's faith in the civilizing process seems boundless: "Everywhere we see science narrowing the limits of those elements that are subject to variation (that respond to accidental causes)" (Quetelet, 1848, p.260QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

However, there was one illness that, unlike all the rest, was thought to be a product or an effect of the triumphs of civilization: mental derangement. Quetelet considered mental derangement to be an illness linked to the development of the intellectual faculties, so that the more these faculties grew, the more numerous and intense such pathologies became. Firstly, he thought it necessary to distinguish between two forms of mental derangement: idiocy and madness, the true form of derangement. While idiocy was directly linked to precarious living conditions, madness could affect more honorable and wiser men. The differences between the two are described by Quetelet, following Esquirol, as follows: "Idiocy is a state dependent on the soil and material influences, whereas madness is the product of society and of intellectual and moral influences. In the idiot, the causes have prevented the development of the organ (the brain) and consequently, the manifestation of intelligence. In madness, the brain is over-stimulated and its physiological capacity is exhausted" (Quetelet, 1991, p.389QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

Various statistical references backed Quetelet's thesis. He compared various countries in terms of the number of deranged people, idiots and madmen recorded in each, and their distribution. In the city, there were more madmen than idiots, while in the countryside the reverse occurred, and the number of idiots was higher. He compared the months with the greatest number of cases of mental illness and the months that saw the most cases of recovery, as well as the influence of age, season and type of work.

Basing himself on the work of Falret, Quetelet defined certain constants that persisted over time in the case of France. Thus, he claimed that the level of frequency with which mental illness appears could be explained in different ways: in terms of the number of mentally ill, there were three times as many in women as in men; in terms of seasonal variation, the summer clearly affected women more; in terms of marital status, over a quarter of the men were single; in terms of age, mental illness developed between 30 and 40 in the case of men and between 40 and 50 in the case of women; in terms of pathology, melancholy predominated in women and homicidal tendencies in men (Quetelet, 1991, p.397QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). Lastly, he claimed that it was also possible to determine a certain constancy in relation to the pathologies and different life stages: "imbecility appears in infancy, mania in youth, melancholy in adults, and dementia in old age" (Quetelet, 1848, p.392QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

Final considerations

The two Quetelet texts analyzed in this article, Sur l'homme et le développement de ses facultés, published in 1835, and Du systeme social et des lois qui le régissent (1848), published thirteen years later, reveal a single concern that lasted over the years: to make explicit, with the help of mathematical instruments, the constancy and similarity with which the physical, moral and mental characteristics of man are repeated year after year. As I have attempted to show, it is possible to plan social and medical interventions that help reduce the margins distinguishing normality from abnormality: the upper and lower limits that characterize a given phenomenon in a given society can draw closer to one another. However, this margin of variability only makes sense if we think of it in relation to the average man. This figure, which is both fictitious and normative, allows us to speak of normality and deviations that are more or less acceptable. Thus, although the limits can vary, although the margins of normality can draw closer together, this in no way affects the constancy or the permanence of the average man, whose characteristics will remain historically unaltered.

The average man is imposed on us with such force that it is impossible to introduce any modifications. Not only are the physiological characteristics we may reach - such as respiration rate, heart rate, height or strength - defined in relation to the constant represented by the average man, but also social phenomena as diverse as the number of crimes, marriages, cases of mental illness, and suicides, are pre-established in such a way as to make it impossible for us to modify them.

Quetelet maintained the same certainty in 1835 and 1848:

We can tell in advance how many individuals will stain their hands with the blood of others, how many will be forgers, and how many poisoners, with as much precision as we can foretell the number of births and deaths that will occur in a society. Society contains within itself the seeds of all the crimes that will be committed, as well as the conditions that make them occur. It is society that causes its crimes, and the culprit is merely the instrument that performs them (Quetelet, 1991, p.35; 1848, p.315).

Crimes, like births, are the necessary result of social organization, so that if we attempt to modify these events it will not be by the individual action of this or that subject that such constants may be modified (Sánchez Carrión, 1999SÁNCHEZ CARRIÓN, Juan. Sociología, orden social y modelización estadística: Quetelet y el hombre medio. Empiria - Revista de Metodología de Ciencias Sociales, Madrid, n.3, p.49-72. 2000.; Rabinow, 2006RABINOW, Paul. Une France si moderne: naissance du social, 1800-1950. Paris: Buchet-Chastel. 2006.; Jorland, 2010JORLAND, Gerard. Une société a soigner: hygiène et salubrité publiques en France au XIX siècle. Paris: Gallimard. 2010.).

There is no room in this explanatory model for individual decisions; 'free will' is merely an obstacle to understanding the laws that govern biological and social constants. Quetelet was not claiming that each of our acts is pre-determined, nor was he denying individual freedom. His determinism was more complex. He argued that actions performed by free, individual choice in no way alter the constancy of social phenomena, since they will be compensated for by other actions of the opposite nature, leading to the permanence of the same social phenomena. It is useless for us to refuse to commit a crime; this act of liberty will be compensated by the reverse action, allowing the natural tendency to constancy and repetition to assert itself. At this point, it is worth returning to a question formulated by Halbawachs in 1912 (p.61)HALBAWACHS, Maurice. La théorie de l'homme moyen: essai sur Quetelet et la statistique morale. Paris: Alcan. 1912., in a critique of Quetelet: "Why consider the species as a type from which individuals only depart by accident (or due to accidental causes)? Why not think that this similarity is the result of the conflict of a certain number of organic tendencies that balance each other out?".

Because, for Quetelet, just as we cannot escape the law of gravity, we cannot escape the law of constant proportions that governs the average man. Both of them are laws of nature that, for Quetelet (1848, p.9QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.), are imposed by divine design: "I have no other objective in this study than to demonstrate that there are divine laws and principles of conservation in a world where so many others are determined to find permanent chaos". There are references to God and the divine throughout Quetelet's two texts. Religious thought is present from beginning to end of his studies; God is the great regulator who causes distances to be annulled and compensates for deviations from the average by guaranteeing permanence. It is he who, according to Quetelet, makes possible the admirable harmony we find in the universe, allowing man free exercise of his capacity for action, while at the same time limiting his actions with such wisdom that it is impossible to glimpse the immutable laws that govern the conservation of the world without the systematic study of 'social physics' (Quetelet, 1848, p.9QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.).

References to the divine as the origin of the principle of conservation that governs nature keep reappearing in the texts analyzed in this article. "All is foreseen, all is regulated: only our ignorance leads us to believe that everything is abandoned to whimsy or fate" (Quetelet, 1848, p.17QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). While at first glance we see differences here and there that seem to be accidental, when we analyze these situations, not on an individual level but on the basis of a large number of cases, it is clear that "what we considered an effect of random chance is submitted to fixed principles, and nothing escapes the laws imposed by divine omnipotence upon organized beings" (Quetelet, 1848, p.16QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). It is divine omnipotence that establishes that mysterious link that makes us necessarily parts of a whole, in which the average man appears as the great regulator, the model according to which deviations are defined and cancelled out. Again and again, Quetelet referred to "the fixed nature of proportions" as "proof of the astonishing wisdom of the creator's laws" (1848, p.37).

Quetelet's god is not just a skillful calculator, an expert manipulator who makes us believe we are acting freely when we are merely responding to a pre-established order. He has also inculcated in our minds the existence of an ideal of beauty and harmony, a unique type for the whole species, which peoples approaching perfection will increasingly resemble. Quetelet's god is also an artist who has engraved the ideal aesthetic forms in us. "The creator, when he formed the type, must have engraved it in us and given us an intimate feeling for the proportion of forms" (Quetelet, 1848, p.39QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). We have such a clear feeling for the proportions of the human form that, without having studied it previously, we can rapidly discern the ideal type or deviations from it in a work of art, such as a sculpture, for example.

The god Quetelet described was a cautious one. "The supreme being has prudently set limits to our moral faculties (particularly free will), as he has done with our physical faculties (limited by the force of gravity), since he did not wish mankind to undermine his eternal laws" (Quetelet, 1848, p.79QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.). In all that happens, it is as if the various biological and social phenomena - suicide, crime, madness, or physiological characteristics - were subject to permanent laws of nature that impose their regularity and constancy. There is nothing we can do to change that regularity, because the effects of free will are restricted to narrow limits, playing the role of accidental causes whose effects neutralize and destroy each other.

In the explanatory structure imagined by Quetelet, God occupies a privileged place. He causes and legitimizes the ideal and normative figure of the average man. In this structure, God does not seem to occupy the secondary place attributed to him by Sánchez Carrión (1999)SÁNCHEZ CARRIÓN, Juan. Quetelet y la sociología. Reis - Revista española de investigaciones sociológicas, Madrid, n.87, p.291-303. 1999. but, on the contrary, appears to play a central role. If we exclude the hypothesis of a supreme being as the origin and cause of fixed proportions, all Quetelet's theoretical apparatus dissolves. Nothing explains why traits that appear more frequently in a population should be enough to demarcate the limits between normality and deviation. As Canguilhem (1990, p.200)CANGUILHEM, Georges. Le normal et le pathologique. Paris: PUF. 1990. states, it is certainly not true that "Quetelet presents the statistical average as the empirical foundation of the norm; on the contrary, the norm explicitly presents an ontological regularity that is expressed by the average". This should lead us to search for an explanation for human height in the will of God.

The frequency of occurrence of a given trait - such as height, for example - is meaningful for Quetelet because it allows us to point, in a given population, to the deviations that exist on both sides of the average man, thereby demarcating the level of dispersion, or the limits between which normality may vary. Limits which, as we saw, become ever closer as societies integrate the triumphs of civilization and move closer to the model or ideal type of beauty and normality created by God. Science and theology mix in Quetelet's discourse, to such a point that this ideal, fictitious being represents a supra-human type of validation, a normative reference that has remained unaltered over the centuries and subsequent cultural transformations. To the question posed at the beginning of this article about what authorizes us to transform frequency of occurrence of a given characteristic into a norm and a value to be attained, Quetelet's answer is: the supreme law that guarantees the constancy and repetition of that fictitious, ideal being, the average man.

References

  • CANGUILHEM, Georges. Le normal et le pathologique. Paris: PUF. 1990.
  • DESROSIÈRES, Alain. Pour une sociologie historique de la quantification: l'argument statistique. Paris: Mines. 2008.
  • DESROSIÈRES, Alain. Adolphe Quetelet. Courrier des statistiques, Paris, n.104, p.2-8. 2002.
  • DOVAL, Hernán. La "distribución normal" de Gauss y el "hombre tipo" de Quetelet. Revista Argentina de Cardiología, Buenos Aires, v.72, n.3, p.239-242. 2004.
  • GUGELMIN, Silvia; SANTOS, Ricardo Ventura. Uso do Índice de Massa Corporal na avaliação do estado nutricional de adultos indígenas Xavante, Terra Indígena Sangradouro - Volta Grande, Mato Grosso. Cadernos de Saúde Pública, Rio de Janeiro, v.22, n.9, p.1865-1872. 2006.
  • HACKING, Ian. La domesticación del azar. Barcelona: Gedisa. 1995.
  • HALBAWACHS, Maurice. La théorie de l'homme moyen: essai sur Quetelet et la statistique morale. Paris: Alcan. 1912.
  • JORLAND, Gerard. Une société a soigner: hygiène et salubrité publiques en France au XIX siècle. Paris: Gallimard. 2010.
  • KOYRÉ, Alexandre. Galileo y la ley de inercia. Estudios Galileanos. Madrid: Siglo XXI. p.149-278. 1980.
  • QUETELET, Adolphe. Sur l'homme et le développement de ses facultés. Paris: Fayard. 1.ed. 1835. 1991.
  • QUETELET, Adolphe. Du systeme social et des lois qui le régissent. Paris: Guillaumin. 1848.
  • RABINOW, Paul. Une France si moderne: naissance du social, 1800-1950. Paris: Buchet-Chastel. 2006.
  • SÁNCHEZ CARRIÓN, Juan. Sociología, orden social y modelización estadística: Quetelet y el hombre medio. Empiria - Revista de Metodología de Ciencias Sociales, Madrid, n.3, p.49-72. 2000.
  • SÁNCHEZ CARRIÓN, Juan. Quetelet y la sociología. Reis - Revista española de investigaciones sociológicas, Madrid, n.87, p.291-303. 1999.

  • 1
    In this and other citations of texts from non-English languages, a free translation has been provided.
  • 2
    All citations from Ian Hacking were sourced from The taming of chance, Cambridge, Cambridge University Press, 1990.

Publication Dates

  • Publication in this collection
    14 Aug 2013
  • Date of issue
    Jul-Sep 2013

History

  • Received
    Apr 2011
  • Accepted
    June 2011
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