Quetelet, Adolphe
Quetelet, Adolphe
Organization of data collection
Lambert Adolphe Jacques Quetelet (1796-1874), best known for his contributions to statistics, was born in the Belgian city of Ghent. When he was seven his father died, and Quetelet, on finishing secondary school at the age of 17, was forced to earn his own living. He accepted a post as teacher of mathematics in a secondary school at Ghent, but his true inclination at the time was toward the arts, not the sciences. For a time he was an apprentice in a painter’s studio, and he later produced several canvases of his own, which were well received. He wrote poetry of some distinction and collaborated on an opera with his old school friend Germinal Dandelin. Only through the influence of Jean Guillaume Gamier, a professor of mathematics at the newly created University of Ghent, was Quetelet finally persuaded to turn from his artistic endeavors to the full-time study of mathematics (although he continued to dabble in poetry until about the age of thirty). His doctoral dissertation, in which he announced the discovery of a new curve, la focale, was the first to be presented at the university (on July 24, 1819), and was widely acclaimed as an original contribution to analytic geometry. As a result, at age 23 Quetelet found himself called to Brussels to occupy the chair of elementary mathematics at the Athenaeum. Only a few months later, early in 1820, he was further honored by being elected to membership in the Academie Royale des Sciences et des Belles-Lettres de Bruxelles.
The rapid pace set in the first part of Quetelet’s scientific career never slackened; his productivity over the next fifty years was phenomenal. The record of his activities during the ten or so years after his arrival at Brussels well illustrates his prodigious capacity for work: Immediately after he assumed the position at the Athenaeum, he began publishing a vast array of essays, mostly in mathematics and in physics; they appeared initially in the Nouveaux mémoires of the academy and later in Correspondances mathématiques et physiques, a journal he founded in 1825 and edited (for the first two years together with Gamier) until its dissolution in 1839. For a time this was the foremost journal of its kind in Europe, attracting contributions from the most eminent scientists on the Continent. In 1824 Quetelet added to his duties the task of delivering a series of public lectures at the Brussels Museum, first in geometry, probabilities, physics, and astronomy and later in the history of the sciences. There, as at the Athenaeum, he quickly became renowned as a great teacher, and his lectures were always crowded, by regular students and auditors and by eminent scientists who came from all over Europe to hear him. He continued these lectures until 1834, when the museum was absorbed by the University of Brussels. Offered a chair in mathematics at the new university, he declined in order to devote himself to his many researches. However, the public lectures were resumed in 1836, at the Military School at Brussels, founded two years earlier.
During this same period Quetelet published several elementary works in natural science and in mathematics, designed to expose these fields to a wide popular audience. Astronomie élémentaire, published in 1826, was soon followed by Astronomie populaire (1827a). (Several biographers—notably Reichesberg [1896] and Hankins [1908]—asserted that the latter work immediately achieved the “distinction,” accorded some earlier publications in astronomy, of being placed on the Index librorum prohibitorum. Lottin [1912, pp. 34-37] proved this to be a myth.) In 1827 Quetelet also published a summary of his course in physics at the museum, entitled Positions de ’physique, ou résumé d’un cours de physique générale (1827fa). Robert Wallace, in the preface to his English translation of the work in 1835, signaled its importance as follows: “No other work in the English language contains such an extensive and succinct account of the different branches of physics, or exhibits such a general knowledge of the whole field in so small a compass.”
The following year, 1828, saw the publication of Instructions populaires sur le calcul des probabilities, which Quetelet identified as a résumé of the introductory lectures to his courses in physics and astronomy at the museum. This work marked Quetelet’s shift from exclusive concentration on mathematics and the natural sciences to the study of statistics and, eventually, to the investigation of social phenomena.
Interestingly enough, Quetelet considered none of these works his main preoccupation or his main accomplishment in the ten years from 1823 to 1832. What concerned him most during this time was the project of establishing an observatory at Brussels. It is still unknown how Quetelet came to adopt this as a prime objective. What is certain, however, is that his activities directed toward establishing the observatory brought about, quite fortuitously, the major change of orientation in his scientific career. Upon accepting Quetelet’s proposal for an observatory, the minister of education promptly sent him to Paris to acquaint himself with the latest astronomical techniques and instruments. There he was warmly received by the astronomers Francois Arago and Alexis Bouvard and was introduced by Bouvard to the coterie of French intellectuals gathered around the illustrious mathematicians Poisson, Laplace, and Jean Baptiste Fourier. These men had for some time been engaged in laying the foundations of modern probability theory, and several of them had analyzed empirical social data in their work.
It was instruction from these mathematicians, particularly Laplace, together with the stimulation of continual informal contact with their group at the Ecole Polytechnique, that aroused in Quetelet the keen interest in statistical research and theory, based on the theory of probabilities, that was to become the focus of all his scientific work. In later reminiscences he said that after he had become acquainted with the statistical ideas of his French masters, he immediately thought of applying them to the measurement of the human body, a topic he had become curious about when he was a painter. One direct effect of learning the theory of probabilities was to make Quetelet realize “the need to join to the study of celestial phenomena the study of terrestrial phenomena, which had not been possible until now….” The crucial impact of the Paris experience on his thinking is evident a few sentences later, where he said, “Thus, it was among the learned statisticians and economists of that time that I began my labors …” (1870).
After his return from Paris in 1823, the project of the observatory moved along by fits and starts, at first held up by difficulties over financing and by some disagreements between Quetelet and the architect and later interrupted by the Belgian revolution of 1830 (during which the half-finished observatory was used as a makeshift fortress and suffered some structural damage). Quetelet finally took up residence in the nearly completed observatory in 1832.
Organization of data collection
While the observatory was under construction, Quetelet’s interest in statistics, which had crystallized during his visit to Paris, coupled with his manifest abilities as an organizer led him to become more and more active in projects requiring the collection of empirical social data. When the Royal Statistics Commission was formed in 1826, he became correspondent for Brabant. (From 1814 to 1830 Belgium was under Dutch rule; thus, “Royal” in this case refers to the House of Orange.) Quetelet’s first publications covered quantitative information about Belgium which could be used for practical purposes, including mortality tables with special reference to actuarial problems of insurance. In 1827 he analyzed crime statistics, again with a practical eye to improving the administration of justice. In 1828 he edited a general statistical handbook on Belgium, which included a great deal of comparative material obtained from colleagues he had come to know during his stays in France and also in England. At his urging, a census of the population was taken in 1829, the results of which were published separately for Holland and Belgium after the revolution of 1830.
In 1841, largely through Quetelet’s efforts, the Commission Centrale de Statistique was organized, and this soon became the central agency for the collection of statistics in Belgium. Quetelet served as its president until his death, and under his direction it performed its functions with remarkable thoroughness and efficiency, setting a standard for similar organizations throughout Europe. In 1833 he was delegated official representative to the meeting of the British Association for the Advancement of Science and there played a key role in the formation of a statistical section. Dissatisfied with the narrow scope of the section, he urged its chairman, Babbage, to organize the Statistical Society of London. This was accomplished in 1834, and the society survives today as the Royal Statistical Society (having been renamed in 1877).
In his work in statistics, as in the natural sciences, Quetelet placed great emphasis on the need for uniformity in methods of data collection and tabulation and in the presentation of results. His principal goal, in all his organizational endeavors, was to see this realized in practice. In 1851 Quetelet proposed to a group of scientists gathered at the Universal Exposition in London a plan for international cooperation in the collection of statistical information. The idea was heartily approved, and progress on it was so rapid that in 1853 the first International Statistical Congress was held at Brussels. At the initial session of the congress Quetelet was chosen president, and he naturally devoted his opening address to the importance of uniform procedures and terminology in official statistical publications. During the next twenty-five years the congress was enormously effective in spurring the development of official statistics in Europe, establishing permanent lines of communication between statisticians, and improving comparability. Internal dissension and controversy weakened the congress during the 1870s and eventually led to its collapse in 1880. By that time, however, Quetelet’s original proposition that there must be some international organization to maintain uniformity and promote cooperation in the collection and analysis of official statistics had been so fully accepted that it was only a matter of five years before a new organization, the International Statistical Institute, was established to continue the work of the congress.
To round out this picture of Quetelet’s successes as an organizer, we need only mention the preeminent role he played in the Academie Royale des Sciences et des Belles-Lettres. When he was chosen a member in 1820, the academy was near to closing down, with only about half a dozen superannuated members attending its sessions and virtually no publications to its name. Quetelet brought new life and vigor into the association, quickly assuming the major responsibility for its activities, recruiting into its ranks many of his young scientific colleagues, and fortifying its publications with his own numerous scientific writings. He was made director for the years 1832 and 1833, and in 1834 he was elected perpetual secretary, an office he occupied for the next forty years, during which time he was considered “the guiding spirit of the academy.”
Social research and theory
The two memoirs which form the basis for all of Quetelet’s subsequent investigations of social phenomena appeared in 1831. By then he had decided that he wanted to isolate, from the general pool of statistical data, a special set dealing with human beings. He first published a memoir entitled Recherches sur la loi de la croissance de I’homme (1831a), which utilized a large number of measurements of people’s physical dimensions. A few months later he published statistics on crime, under the title Recherches sur le penchant au crime aux differens ages (1831b). While the emphasis in these publications is on what we would call the life cycle, both of them also include many multivariate tabulations, such as differences in the age-specific crime rates for men and women separately, for various countries, and for different social groups. (As noted by Hankins [1908, p. 55] and by Lottin [1912, pp. 128-138], the core idea contained in the second memoir—the constancy in the “budget” of crimes from year to year in each age group—can be traced back to a memoir read to the academy on December 6, 1828, and published early in 1829. Thus, Quetelet was probably right in claiming priority for the idea [1835; see p. 96 in 1842 edition] over A. M. Guerry, who published it under the title “Statistique comparee de l’etat de l’instruction et du nombre des crimes” [1832].)
In 1833 Quetelet published a third memoir giving developmental data on weight (1833a). By this time he had formed the idea of a social physics, and in 1835 he combined his earlier memoirs into a book entitled Sur I’homme et le developpement de ses facultes, with the subtitle Physique sociale (see 1835). Quetelet republished this work in an augmented version, with the titles reversed, in 1869. To prevent confusion, the first edition is usually referred to as Sur I’homme, the second as Physique sociale. Included in the later edition, and one of its highlights, is a long essay by the English astronomer John Herschel: it had first been published in the Edinburgh Review (1850) as a review article on Quetelet’s Letters …on the Theory of Probabilities and other work by Quetelet, and since it was highly favorable, Quetelet made it the introduction to his Physique sociale. To the constancy in crime rates noted earlier, this work added demonstrations of regularities in the number of suicides from year to year and in the rate of marriage for each sex and age cohort. Although Quetelet was convinced that many other regularities existed, these three—in crimes, suicides, and rates of marriage—were the only regularities in man’s “moral” characteristics (i.e., those involving a choice of action) actually demonstrated in his writings. Thus, with the publication of Sur I’homme, all of Quetelet’s basic ideas became available to a broader public.
Basic principles
It was in writings published in the 1830s that Quetelet established the theoretical foundations of his work in moral statistics or, to use the modern term, sociology. First there was the idea that social phenomena in general are extremely regular and that the empirical regularities can be discovered through the application of statistical techniques. Furthermore, these regularities have causes: Quetelet considered his averages to be “of the order of physical facts,” thus establishing the link between physical laws and social laws. But rather than attach a theological interpretation to these regularities—as Sussmilch and others had done a century earlier, finding in them evidence of a divine order—Quetelet attributed them to social conditions at different times and in different places [see the biography ofSussmilch]. This conclusion had two consequences: It gave rise to a large number of ethical problems, casting doubt on man’s free will and thus, for example, on individual responsibility for crime; and in practical terms it provided a basis for arguing that meliorative legislation can alter social conditions so as to lower crime rates or rates of suicide.
On the methodological side, two key principles were set forth very early in Quetelet’s work. The first states that “Causes are proportional to the effects produced by them” (1831b, p. 7). This is easy to accept when it comes to man’s physical characteristics; it is the assumption that allows us to conclude, for example, that one man is “twice as strong” as another (the cause) simply because we observe that he can lift an object that is twice as heavy (the effect). Quetelet proposed that a scientific study of man’s moral and intellectual qualities is possible only if this principle can be applied to them as well. (The role this principle played in Quetelet’s theories is discussed below.) The second key principle advanced by Quetelet is that large numbers are necessary in order to reach any reliable conclusions—an idea that can be traced to the influence of Laplace (1812), Fourier (1826), and Poisson (1837). The interweaving of these principles with the theoretical ideas summarized above is illustrated in the following:
It seems to me that that which relates to the human species, considered en masse, is of the order of physical facts; the greater the number of individuals, the more the influence of the individual will is effaced, being replaced by the series of general facts that depend on the general causes according to which society exists and maintains itself. These are the causes we seek to grasp, and when we do know them, we shall be able to ascertain their effects in social matters, just as we ascertain effects from causes in the physical sciences. (1831b, pp. 80-81)
Quetelet was greatly concerned that the methods he adopted for studying man in all his aspects be as “scientific” as those used in any of the physical sciences. His solution to this problem was to develop a methodology that would allow full application of the theory of probabilities. For in striking contrast to his contemporary Auguste Comte, Quetelet believed that the use of mathematics is not only the sine qua non of any exact science but the measure of its worth. “The more advanced the sciences have become,” he said, “the more they have tended to enter the domain of mathematics, which is a sort of center toward which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation” (1828, p. 230).
Pattern of work
Before proceeding to a more detailed exposition of Quetelet’s work in moral statistics, we should note his method of publication. Quetelet’s literary background and the fact that his humanist friends remained an important reference group for him help to explain the manner in which he published his works. When he had new data or had developed a new technique or idea, he first announced his discovery in brief notes, usually in the reports of the academy or in Correspondances and sometimes in French or English journals. Once such notes had appeared, he would elaborate the same material into longer articles and give his data social and philosophical interpretations. He would finally combine these articles into books which he hoped would have a general appeal. He obviously felt very strongly that empirical findings should be interpreted as much as possible and made interesting to readers with broad social and humanistic concerns.
Quetelet further extended his influence through the voluminous correspondence he maintained with scientists, statesmen, and men of letters throughout Europe and America. Liliane Wellens-De Donder has identified approximately 2,500 correspondents, including such names as Gauss; Ampere; Faraday; Alexander von Humboldt; James A. Garfield, then a U.S. congressman, who solicited Quetelet’s advice on means of improving the census; Joseph Henry; Lemuel Shattuck; Charles Wheatstone; Louis Ren6 Villerme; and Goethe, who befriended Quetelet when the latter visited Germany in 1829 (see Wellens-De Donder 1964).
Probably Quetelet’s most famous correspondence was with the princes Ernest and Albert of Saxe-Coburg and Gotha, whom he tutored in mathematics beginning in 1836, at the request of their uncle, Leopold I, king of the Belgians. Although the princes left Belgium to attend school in Germany shortly after they began studying under Quetelet, the lessons continued for many years by correspondence. Quetelet’s second major work on moral statistics, Letters Addressed to H.R.H. the Grand Duke of Saxe-Coburg and Gotha, on the Theory of Probabilities, as Applied to the Moral and Political Sciences (1846), shows his side of the correspondence. (The title refers only to Ernest, who as reigning duke was head of the house of Coburg.) Du systeme social et des lois qui le regissent (1848), was dedicated to Albert, with whom Quetelet had established an especially close friendship. Quetelet’s profound influence on Albert’s thinking is clearly shown in the keynote address Albert delivered to the fourth meeting of the International Statistical Congress in London, on July 16, 1860 (see Schoen 1938).
The average man
Quetelet’s conceptualization of social reality is dominated by his notion of the average man, or homme moyen. In his preface to Du systeme social, he himself identified this as his central concept and traced its development through his writings (1848, pp. vii-ix). In Sur Thomme, he said, he had developed the idea that the characteristics of the average man can be presented only by giving the mean and the upper and lower limits of variation from that mean. In the Lettres he had shown that “regarding the height of men of one nation, the individual values group themselves symmetrically around the mean according to …the law of accidental causes” (p. viii); and further, that for a nation the average man “is actually the type or the standard and that other men differ from him, by more or by less, only through the influence of accidental causes, whose effects become calculable when the number of trials is sufficiently large …. In this new work,” Quetelet continued, “I show that the law of accidental causes is a general law, which applies to individuals as well as to peoples and which governs our moral and intellectual qualities just as it does our physical qualities. Thus, what is regarded as accidental ceases to be so when observations are extended to a considerable number of cases” (p. ix). It is no wonder, then, that discussions of Quetelet’s theories and researches on society invariably take as a starting point his concept of the homme moyen.
His first approach to the concept was through the measurement of physical characteristics of man, in particular height and weight (1831a). He conceived of the average height of a group of individuals of like age as the mean around which the heights of all persons of that age “oscillate,” although just how this oscillation takes place Quetelet could not say. He did suggest, even in this first exposition of the concept, that similar means and oscillations might be observed if moral and intellectual, not just physical, qualities of men were studied.
In his essay Recherches sur le penchant au crime, the term homme moyen appears for the first time. There, also, we find the first statement of the idea that if one were to determine the homme moyen for a nation, he would represent the type for that nation; and if he were determined for all mankind, he would represent the type for the entire human species.
The next advance in the development of the concept came in a memoir published in 1844, in which Quetelet first took note of the fact that his observations were symmetrically distributed about the mean—in almost exactly the pattern to be anticipated (prévu) from the binomial and normal distributions—and went on to speculate about the likelihood that all physical characteristics might be distributed in the same way. By applying the theory of probabilities, he was then able to derive a theoretical frequency distribution for height, weight, or chest circumference that coincided remarkably with the empirical distributions in his data for various groups.
An interesting result obtained by applying this method, also first published in the memoir of 1844, was Quetelet’s discovery of draft evasion in the French army. By noting the discrepancy between the distribution of height of 100,000 French conscripts and his prediction (i.e., the theoretical distribution calculated by assuming a probable error of 49 millimeters), he came to the conclusion that some 2,000 men had escaped service by somehow shortening themselves to just below the minimum height. Thus, quite by accident, Quetelet emerged with the first practical, although perhaps somewhat trivial, application of his statistical techniques.
In his discussions of the average man, Quetelet had up to this time limited himself to calculating the means and distributions of only a few physical characteristics. The task he now set for himself was to extend the concept to all of man’s physical traits (thus forming the basis for what he called “social physics”) and, thence, to all moral and intellectual qualities as well (“moral statistics”). Furthermore, he planned to apply the concept to collectivities of all sizes, ranging from the small group to the whole of mankind, and expected that it would hold equally well for any time in human history. Quetelet had suggested these extensions in earlier works, but the grand generalization did not emerge in its final form until the publication of Dmsysteme social. In the first pages Quetelet announced his theme: “There is a general law which governs our universe …; it gives to everything that breathes an infinite variety…. That law, which science has long misunderstood and which has until now remained useless in practice, I shall call the law of accidental causes” (1848, p. 16). A few lines later he elaborated his over-all viewpoint:
…among organized beings all elements vary around a mean state, and …variations, which arise from accidental causes, are regulated with such harmony and precision that we can classify them in advance numerically and by order of magnitude, within their limits.
One part of the present work is devoted to demonstrating the law of accidental causes, both for physical man and for moral and intellectual man, considering him individually, as well as in the aggregate…. (P. 17)
Concept of causality
It is obvious that an explanation of what Quetelet meant by “accidental causes” and by “law” is critical for an understanding of his conception of the average man. Quetelet hypothesized that every mean he presented resulted from the operation of constant causes, while the variations about the mean were due to “perturbative” or “accidental” causes. “Constant causes,” he explained, “are those which act in a continuous manner, with the same intensity and in the same direction” ([1846] 1849, p. 107). Among the constant causes he named are sex, age, profession, geographical latitude, and economic and religious institutions. (As a category parallel to constant causes, Quetelet sometimes mentioned “variable causes,” which are those that “act in a continuous manner, with energies and intensities that change” [ibid.]. The seasons are cited as the type case, although Quetelet meant to include as variable causes all periodical phenomena.) “Accidental causes only manifest themselves fortuitously, and act indifferently in any direction” (ibid.). Quetelet frequently classed man’s free will as an accidental cause (although occasionally he claimed that it played no role at all), but insisted that its operation is constrained within very narrow limits. The essence of Quetelet’s theory is that, given sufficient data over time, the shape and extent of variations about the mean state which result from accidental causes can be “classified in advance” with a high degree of accuracy, through the application of the theory of probabilities of independent events.
Quetelet’s conception of “law” depended on whether he was talking about man’s physical attributes, his moral traits, or all human characteristics. Thus, in Dmsysteme social we find these three distinct uses of the term. In the early part of the book, he referred to a trend in a series of averages over time as a law: “If we knew what [man’s mean] height had been from one century to another, we would have a series of sizes which would express the law of development of humanity as regards height” (1848, p. 11). Later, in presenting the law of propensity to crime, he used the term to denote a regular pattern of correlations: “The propensity to crime increases quite rapidly toward adulthood; it reaches a maximum and then decreases until the very end of life. This law appears to be constant, and varies only with respect to the magnitude of the maximum and the time of life when it occurs” (p. 86). (By way of contrast, his law of propensity to suicide posits a direct variation with age “until the most advanced age” [p. 88].)
It is important to note in this connection that Quetelet went far beyond such simple two-variable correlations in his studies of man. Numerous three-variable and four-variable tables appear throughout his work (see esp. 1835, vol. 2). In one case, for example, he presented a table that shows the relationship of mean weight to age, sex, and occupation (ibid., p. 91); similar tables show the breakdown of crimes in various groups by sex and level of education (p. 297), by age and sex (p. 302), and by age, sex, and the type of court in which the crime was tried (p. 308). These remarkable anticipations of modern techniques went largely unnoticed by Quetelet’s contemporaries, and only in recent times have social scientists rediscovered and fully explored the possibilities of multivariate analysis—a striking discontinuity in the history of empirical social research that surely deserves further study and explanation.
The two uses of the term “law” illustrated above are similar in that they both refer in some way to a correlation—in one case between height and century, and in the other between age and the incidence of some social act. Quetelet’s third type of law, the “law of accidental causes,” is quite another thing; it is simply the assertion that every human trait is normally distributed about a mean and that the larger the number of observations, the more closely the empirical distribution will coincide with the theoretical probability distribution. In sum, the word “law” is used alternatively to refer to a trend in a series of specific empirical findings, an empirical generalization, and an assertion (or, in effect, a theory) that a certain type of regularity exists in all human phenomena.
Measurement
Perhaps one reason Quetelet had trouble maintaining a single conception of “law” is that the types of measures he used to substantiate laws were few in number and inadequate to his purpose. Limiting himself to the manipulation of data gathered from available official statistical publications, he was forced to improvise new and different techniques for physical and moral qualities and so emerged with different kinds of laws, according to the type of phenomenon in question. It comes as something of a surprise to realize that in all Quetelet’s research on man, for example, he actually used only three kinds of measurements. (He did suggest some others but never applied them to his data or attempted to collect the data that would make them applicable. Lazarsfeld’s 1961 essay analyzes the kinds of measures that are mentioned in Physique sociale in the light of modern ideas on quantification.)
First, he determined the empirical distribution of some human trait in a group and computed the mean—which he then identified as a characteristic of the average man for the group. He repeatedly asserted that similar distributions and means could be found for moral and intellectual characteristics, presented some rough hypothetical curves, but never performed any such calculations using a set of empirical observations. A second type of measurement involved counting the number of certain social events, such as crimes or marriages, that occurred during a series of years among particular groups; the average of these yearly counts was taken to be the probable number of such events that would occur in each group during the next year. As a third type of measurement Quetelet used rates—the number of crimes or other events in each age group, divided by the number of persons in that group. Quetelet regarded the results as the respective probabilities of committing a crime at various ages; he called these probabilities the propensity to crime—the penchant au crime or, alternatively, the tendance au crime—at each age. (At one point in Du systéme social [1848, p. 93] he proposed substituting the word possibilité for penchant, but he reverted to the use of penchant throughout the later text.) Although Quetelet said again and again that his concern was with groups, not with individuals, there are many instances where he clearly uses the penchant au crime derived by this method to refer to a characteristic of each member of a given age group.
Apparent and real propensities
Quetelet developed the concept of penchant in order to overcome the methodological and theoretical problems he encountered in trying to found a science that would deal with all aspects of man. As long as he restricted himself to physical characteristics there was no problem; the technique for obtaining individual measurements was obvious, and moreover, plentiful data of this sort had already been collected by many agencies and was available for analysis. Once he moved on to moral and intellectual traits, however, the only data available were rates (of crime, or suicide, or marriage) for different populations. To parallel his analysis of physical characteristics, Quetelet would have needed measurements taken on each individual in a group over a period of time, and so far no one had collected such data. Occasionally, in the more speculative portions of his writings, Quetelet was able to suggest how such individual measurements might be made: to measure a scholar’s productivity, for example, he thought of counting the number of publications the man produced.
Unfortunately, he never applied such ideas in his statistical work. Instead, he made do with the data at his disposal by establishing the critical distinction between “apparent propensities” and “real propensities.” Apparent propensities are those that can be calculated as outlined above, using the population rates found in official statistical publications. The information needed is only the number of acts (crimes, suicides, marriages), the age of each actor, and the total population, distributed according to age. The real propensity is what causes the observable regularity to appear; and this propensity, Quetelet claimed, cannot be ascertained from direct observation. It can be known only by its effects.
The following passage illustrates how Quetelet related the two types of propensities. Commenting on computations of the probability of marriage for certain city dwellers, he said:
This probability may be considered as giving, in cities, the measure of the apparent tendency to marriage of a Belgian aged 25 to 30. I say apparent tendency intentionally, to avoid confusion with the real tendency, which may be quite different. One man may have, throughout his life, a real tendency to marry without ever marrying; another, on the contrary, carried along by fortuitous circumstances, may marry without having the least propensity to marriage. The distinction is essential. (1848, p. 77)
The cue to the way Quetelet visualized the relation between apparent tendencies and real tendencies lies in his repeated statement that “causes are proportional to effects.” Thus, if one thinks of the apparent tendencies as being caused by the underlying real tendencies, “the error that may result from substituting the value of the one for the other can be calculated directly by the theory of probabilities” (ibid., p. 78).
Rather than solve the problem, this does no more than identify it. Quetelet’s difficulty arose from the fact that he never clearly separated the problem into its two components. One is the question that continues to be of interest today: how may manifest data be related to latent dispositions? The other is the methodological problem of whether measurement techniques analogous to those applied to individual physical traits could be developed for moral and intellectual characteristics as well.
On the theoretical side, Quetelet failed to recognize that his dispositional concept of penchant could just as reasonably be applied in the study of physical attributes as in the study of moral or intellectual traits. One can, for example, conceive of studying the “tendency to obesity” in a population, which would parallel, in the physical, Quetelet’s notion of a penchant au crime. On the methodological side, he failed to realize that some of the techniques he himself suggested for measuring individual personality or intelligence were exact counterparts to his “direct” measurements of physical traits. Especially surprising—in view of his extensive use of crime statistics—is the fact that the idea of analyzing, for example, “repeated offenders,” completely eluded him. This would have provided him with quantitative individual “measures” of criminal behavior, corresponding to measures of size or weight. It seems likely that these shortcomings in Quetelet’s work were due, not to sheer lack of insight, but, at least in part, to the inadequacies of the data available at the time. It is only benefit of hindsight that allows us to identify such gaps, and one cannot gainsay Quetelet’s merit in having made the first attempt to handle what remain to this day crucial problems in the analysis of empirical social phenomena.
After Quetelet
In 1855 Quetelet suffered a stroke, from which he never totally recovered. He résuméd his work very soon afterward but never again produced any new ideas. His publications from then on, although numerous, were largely compendia of prior essays or summaries of new researches which supported his earlier ideas. His son Ernest virtually took over the running of the observatory after 1855. Quetelet died on February 17, 1874, and as Hankins put it, “was buried with honors befitting one of the earth’s nobility.” A statue of him, funded by popular subscription, was unveiled at Brussels in 1880.
Quetelet’s concern with the distribution of human characteristics was destined for an interesting future. His basic idea was that certain social processes (corresponding to his interplay of causes) would explain the final distribution of certain observable data. This notion has been amply justified by modern mathematical models regarding the distribution of, for example, income, words, or city sizes. But Quetelet concentrated exclusively on the binomial and normal (Gaussian) distributions, which presuppose the independence of the events studied. Today many other distributions are known, based on more complicated processes; especially in the social sciences, “contagious events,” which depend upon each other, are in the center of interest. Quetelet remained unaware of alternative mathematical possibilities. Nonetheless, his basic idea was not only correct but probably influenced directly writers who had begun to broaden this whole field, such as Poisson and Lexis.
In general, however, Quetelet’s contemporaries focused their attention primarily on his concept of the average man and his proposition that social phenomena reproduce themselves with extreme regularity. For different reasons these ideas quickly became the subject of the most vigorous and widespread debate among nineteenth-century statisticians, philosophers, and social scientists, while most of Quetelet’s other ideas remained largely unnoticed.
The debate over the homme moyen was set off by Quetelet’s suggestion that the means of various traits could be combined to form one paradigmatic human being, who would represent the “type” for a group, a city, a nation, or even for all of mankind. Typical of the early criticism was that of Cournot (1843), who reasoned from a mathematical analogy: just as the averages of the sides of many right triangles do not form a right triangle, so the averages of physical traits would certainly not be compatible. Combining them would not, as Quetelet claimed, produce a “type for human beauty” or a “type for physical perfection,” but a monstrosity. Quetelet’s insistence that the average man be considered no more than a “fictitious being” was taken as simply an evasion of the issue; his attempts to reply directly to Cournot proved unconvincing. (A recent essay by Guilbaud discusses the Cournot problem as it relates to current statistical concepts like that of “aggregation”; Guilbaud 1952.)
Quetelet’s inability to refute Cournot’s criticism encouraged others to publish similar attacks until, in 1876, Bertillon issued what is usually considered the definitive statement, which pretty well put an end to the debate. Here the criticism was applied not only to Quetelet’s notion of combining average physical characteristics but also to his ideas about moral and intellectual traits. Surely, Bertillon said, Quetelet was mistaken in believing that his average man would represent the ideal of moral virtue or intellectual perfection. Such a man would, on the contrary, be the personification of mediocrity or, to use Bertillon’s apt phrase, the type de la vulgarite (p. 311). Thereafter the average man was generally viewed as a concept not worth taking seriously, although sporadic attempts have been made to revive it. (The latest is that of Maurice Frechet, who suggests that Quetelet’s homme moyen could be “rehabilitated” as the concept of the homme typique; by defining the homme typique as a particular individual in the group—whose traits taken as a whole come closest to the average—Frechet manages to avoid most of the criticisms leveled against Quetelet’s concept; Frechet 1955.)
A second and even more widespread controversy centered on the question of what implications ought to be drawn from the startling regularities Quetelet had demonstrated in his studies of social phenomena. Did Quetelet’s proposition that “society prepares the crime and the guilty person is only the instrument by which it is executed” (1835, p. 108 in 1842 edition) imply that human beings have no free will at all? Quetelet’s philosophical speculations on the subject certainly left room for this interpretation. The result was a heated and long-lasting debate between those who supported Quetelet’s “deterministic” explanation of social regularities and those who argued that only by taking the individual as the starting point for analysis could one arrive at an explanation of human behavior. Free will, the latter group contended, must be considered a prime determinant of action, not classed as a practically negligible “accidental cause.” (One by-product of the debate was the formation of a “German school” of moral statisticians, headed by Moritz Wilhelm Drobisch, one of Quetelet’s most vehement opponents; see Drobisch 1867.) The over-all result of the controversy was not so much to refute Quetelet’s ideas as to argue them into oblivion. In P. E. Fahlbeck’s opinion (1900), its most important effect was that until the end of the nineteenth century statisticians were so involved in discussing the implications of Quetelet’s propositions that they made little effort to confirm empirically the nature and extent of the regularities Quetelet had discovered. (A detailed discussion of the controversy over Quetelet’s determinism and over the concept of the average man appears in Lottin 1912, pp. 413-458.)
Only in recent years has Quetelet’s sociological work begun to receive due recognition. His conviction that a scientific study of social life must be based on the application of quantitative methods and mathematical techniques anticipated what has become the guiding principle of modern social research. Some of the specific methods he employed and advocated—e.g., the substitution of one-time observation of a population for repeated observations of the individual, and his early attempts at multivariate analysis—are as important today as they were new in his time. The same may be said of his efforts to transform statistics from the mere clerical task of collecting important facts about the state (hence the term “statistics”) to an exact method of observation, measurement, tabulation, and comparison of results, which would serve as the scaffolding upon which he could erect his science of moral statistics. On these grounds alone it is difficult to dispute Sarton’s description of Sur Vhomme as “one of the greatest books of the nineteenth century” ([1935] 1962, p. 229); or, for that matter, his choice of Quetelet over Comte as the “founder of sociology.”
David Landau and Paul F. Lazarsfeld
[For the historical context of Quetelet’s work, seeSociology, article onTHE EARLY HISTORY OF SOCIAL RESEARCH, and the biographies ofGauss; For the historical context of Quetelet Laplace; For the historical context of Quetelet Poisson; for discussion of the subsequent development of Quetelet’s ideas, seeGovernment STATISTICS; Sociology, article onTHE FIELD; Statistics, Descriptive, article onLOCATION AND DISPERSION; and the biographies ofBertillon; Galton; Gini, Niceforo; Pearson].
WORKS BY QUETELET
(1826) 1834 Astronomie élémentaire. 3d ed., rev. & corrected. Brussels: Tircher.
(1827a) 1832 Astronomie populaire. 2d ed., rev. Brussels: Remy.
(1827b) 1834 Positions de physique, ou résumé d’un cours de physique génerale. 2d ed. Brussels: Tircher. → An English translation was published by Sinclair
in 1835, as Facts, Laws and Phenomena of Natural Philosophy: Or, Summary of a Course of General Physics.
1828 Instructions populaires sur le calcul des probabilites. Brussels: Tarlier. → Translation of extract in the text was provided by David Landau. An English translation of the entire work was published by Weale in 1849, as Popular Instructions on the Calculation of Probabilities, with appended notes by Richard Beamish.
1831a Recherches sur la loi de la croissance de Vhomme. Brussels: Hayez. → A 32-page pamphlet. Also published in Volume 7 of the Nouveaux mémories of the Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique.
(1831b) 1833 Recherches sur le penchant au crime aux differens ages. 2d ed. Brussels: Hayez. → An 87-page pamphlet. Translations of extracts in the text were provided by David Landau. Also published in Volume 7 of the Nouveaux mémories of the Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique.
1833a Recherches sur le poids de Vhomme aux differens ages. Brussels: Hayez. → A 44-page pamphlet. Also published as part of Volume 7 of the Nouveaux mémories of the Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique.
1833b Lettre à M. Villermé, sur la possibilité de mesurer l’influence des causes qui modifient les éléments sociaux. Annales d’hygiéne publique et de médecine legate 1st Series 9:309 only.
(1835) 1869 Physique sociale: Ou, essai sur le développement des facultes de Vhomme. 2 vols. Brussels: Mu-quardt. → First published as Sur Vhomme et le de-veloppement de ses facultés: Physique sociale. An English translation was published by Chambers in 1842 as A Treatise on Man and the Development of His Faculties.
1844 Sur l’appréciation des documents statistiques, et en particulier sur l’appreciation des moyennes. Belgium, Commission Centrale de Statistique, Bulletin 2:205-286.
(1846) 1849 Letters Addressed to H.R.H. the Grand Duke of Saxe-Coburg and Gotha, on the Theory of Probabilities, as Applied to the Moral and Political Sciences. London: Layton. → First published in French.
1848 Du systéme social et des lois qui le régissent. Paris: Guillaumin. → Translations of extracts in the text were provided by David Landau.
1870 Des lois concernant le développement de l’homme. Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Bulletin 2d Series 29:669-680. → Translations of extracts in the text were provided by David Landau.
SUPPLEMENTARY BIBLIOGRAPHY
Bertillon, Adolphe 1876 La theorie des moyennes en statistique. Journal de la Societe de Statistique de Paris 17:265-271, 286-308.
Buckle, Henry Thomas (1857-1861) 1913 The History of Civilization in England. 2d ed. 2 vols. New York: Hearst.
Correspondances mathématiques et physiques. → Published from 1825 to 1839.
Cournot, Antoine Augustin 1843 Exposition de la theorie des chances et des probabilités. Paris: Hach-ette. → See especially pages 213-214. Discours [prononcés aux funérailles de Quetelet], by N. de Keyser et al. 1874 Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Bulletin 2d Series 37:248-266.
Drobisch, Moritz W. 1867 Die moralische Statistik und die menschliche Willensfreiheit. Leipzig: Voss.
Durkheim, Émile (1897) 1951 Suicide: A Study in Sociology. Glencoe, 111.: Free Press. → First published in French. See pages 300-306 for a discussion of Quetelet’s concept of the “average man.”
Fahlbeck, Pontus E. 1900 La régularité dans les choses humaines ou les types statistiques et leurs variations. Journal de la Societe de Statistique de Paris 41:188-201.
[Fourier, Jean Baptistei 1826 Mémoire sur les résultats moyens deduits d’un grand nombre d’observations. Volume 3, pages ix-xxxi in Seine (Dept.), Recherches statistiques sur la ville de Paris et le departement de la Seine. Paris: Imprimerie Royale.
Frechet, Maurice 1955 Rehabilitation de la notion statistique de l’homme moyen. Pages 310-341 in Maurice Frechet, Les mathématiques et le concret. Paris: Presses Universitaires de France.
Galton, Francis (1869) 1952 Hereditary Genius: An Inquiry Into Its Laws and Consequences. New York: Horizon Press. → See the Appendix for a discussion of some of the mathematical aspects of the “average man.” A paperback edition was published in 1962 by World.
Gillispie, C. C. 1963 Intellectual Factors in the Background of Analysis by Probabilities. Pages 431-453 in Symposium on the History of Science, Oxford, 1961, Scientific Change: Historical Studies in the Intellectual, Social, and Technical Conditions for Scientific Discovery and Technical Invention, From Antiquity to the Present. New York: Basic Books.
Gini, Corrado 1914a L’uomo medio. Giornale degli economisti e rivista di statistica 3d Series 48:1-24.
Gini, Corrado 1914b Sull’utilita delle rappresentazioni grafiche. Giornale degli economisti e rivista di statistica 3d Series 48:148-155.
Guerry, Andre Michel 1832 Statistique comparee de l’etat de l’instruction et du nombre des crimes. Revue encyclopedique 55:414-424.
Guilbaud, Georges Th. (1952) 1966 Theories of the General Interest and the Logical Problem of Aggregation. Pages 262-307 in Paul F. Lazarsfeld and Neil W. Henry (editors), Readings in Mathematical Social Science. Chicago: Science Research Associates. → See especially pages 271-292. First published in French in Volume 5 of Économie appliquée.
Halbwachs, Maurice 1912 La theorie de l’homme moyen: Essai sur Quetelet et la statistique morale. Paris: Alcan.
Hankins, Frank H. 1908 Adolphe Quetelet as Statistician. New York: Longmans.
[herschel, John F. W.] 1850 [Review of] Letters…. Edinburgh Review 92:1-57.
Knapp, Georg F. 1871 Bericht über die Schriften Quetelet’s zur Socialstatistik und Anthropologie. Jahr-biicher fur Nationalökonomie und Statistik 17:167-174, 342-358, 427-445.
Knapp, Georg F. 1872 A. Quetelet als Théorétiker. Jahr-bucher filr Nationalökonomie und Statistik 18:89-124.
Laplace, Pierre Simon De (1812) 1820 Theorie ana-lytique des probabilites. 3d ed., rev. Paris: Courcier.
Lazarsfeld, Paul F. 1961 Notes on the History of Quantification in Sociology: Trends, Sources and Problems. Isis 52:277-333.
Lottin, Joseph 1912 Quetelet, statisticien et sociologue. Paris: Alcan; Louvain: Institut Superieur de Philosophic.
Mailly, Nicolas É. 1875a Essai sur la vie et les ouv-rages de Lambert-Adolphe-Jacques Quetelet. Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Annuaire 41:109-297.
Mailly, Nicolas É. 1875b Eulogy on Quetelet. Smithsonian Institution, Annual Report [1874]: 169-183. → Abstract of “Notice sur Adolphe Quetelet,“first published in Series 2, Volume 38 of the Bulletin of the Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique.
Poisson, Simeon Denis 1837 Recherch.es sur la probability des jugements en matiere criminelle et en matiére civile, précédées des regies générales du calcul des probabilites. Paris: Bachelier.
Reichesberg, Naum 1896 Der berühmte Statistiker, Adolf Quetelet, sein Leben und sein Wirken: Eine biographische Skizze. Zeitschrift für schweizerische Statistik 32:418-460.
Sarton, George (1935) 1962 Quetelet (1796-1874). Pages 229-242 in George Sarton, Sarton on the History of Science. Edited by Dorothy Stimson. Cambridge, Mass.: Harvard Univ. Press.
Schoen, Harriet H. 1938 Prince Albert and the Application of Statistics to the Problems of Government. Osiris 5:276-318.
Wellens-de Donder, Liliane 1964 La correspondance d’Adolphe Quetelet. Archives et bibliothéques de Belgique 35:49-66.
Wolowski, L. 1874 Éloge de Quetelet. Journal de la Société de Statistique de Paris 15:118-126.
Quetelet, Lambert-Adolphe-Jacques
QUETELET, LAMBERT-ADOLPHE-JACQUES
(b. Ghent, Belgium, 22 February 1796; d. Brussels, Belgium, 17 February 1874)
statistics.
Adolphe Quetelet was the son of Franςois-Augustin-Jacques-Henri Quetelet and Anne-Franςoise Vandervelde. After graduating from the lyeee in Ghent he spent a year as a teacher in Oudenaarde. In 1815 he was appointed professor of mathematics at the Collège of Ghent. He wrote an opera, together with his friend G. P. Dandelin (better known for a theorem on conics); he also published poems and essays. Quetelet was the first to receive a doctorate (1819) from the newly established University of Ghent, with a dissertation on geometry. The same year he was appointed professor of mathématiques élémentaires at the Athénée of Brussels. In 1820 he was elected a member of the Académie Royale des Sciences et Belles-Lettres of Brussels. During the next years he worked in geometry. His papers were published by the Academy and in the periodical Correspondance mathématique et physique which he founded and coedited with J. G. Garnier, a professor at Ghent who had guided Quetelet’s first steps in higher mathematics. From 1824 Quetelet taught higher mathematics at the Athénée and physics and astronomy at the Museée, which later became the Université Libre. His wife, whom he married in 1825, was a daughter of the French physician Curtet and a niece of the chemist van Mons; she bore him a son and a daughter. In 1826 he published popular books on astronomy and on probability.
From 1820 Quetelet had proposed founding an observatory, and in 1823 the government sent him to Paris to gain experience in practical astronomy. Here he met famous scientists. His increasing interest in probability was possibly due to the influence of Laplace and Fourier. In 1827 he went to England to buy astronomical instRūments and to visit universities and observatories. The following year he was appointed astronomer at the Brussels Royal Observatory, which was not completed until 1833. Meanwhile he traveled extensively. In 1834 he was elected permanent secretary of the Brussels Academy.
From 1832 Quetelet lived at the observatory. His research there was more meteorological and geophysical than astronomical, with an emphasis on statistics. He had turned to statistics as early as 1825, and until 1835 he wrote a considerable number of papers on social statistics. In that year he published Sur l’homme et le devéloppement de ses facultés, essai d’une physique sociale, which made him famous throughout Europe. Subsequently a great part of his activity consisted in organizing international cooperation in astronomy, meteorology, geophysics, and statistics. His work after 1855 was impaired by the consequences of a stroke he had suffered in that year.
Quetelet was an honorary member of a great many learned societies and received many decorations. His funeral was a gathering of princes and famous scientists, and his memory was honored by a monument, unveiled in Brussels in 1880.
By his contemporaries his personality has been described as gay, charming, enthusiastic, and gifted with wide intellectual interests. Though he exerted a tremendous influence in his lifetime, his fame hardly survived him. His work has not been republished since his death.
The word “Statistik” first printed in 1672, meant Staatswissenschaft or, rather, a science concerning the states. It was cultivated at the German universities, where it consisted of more or less systematically collecting “state curiosities” rather than quantitative material. The actual predecessor of modern statistics was the English school of political arithmetic; the first effort to describe society numerically was made by Graunt in 1661. This school, however, which included Malthus, suffered from a lack of statistical material. In 1700 Napoleon, influenced by Laplace and fond of numerical data, established the Bureau de Statistique. In 1801 the first general censuses were held in France and England. Statistics became a fashionable subject, but nobody knew what kind of data to collect or how to organize the material. Nothing was done to justify Fourier’s plea:
“Statistics will not make any progress until it is trusted to those who have created profound mathematical theories.”
With Quetelet’s work of 1835 a new era in statistics began. It presented a new technique of statistics or, rather, the first technique at all. The material was thoughtfully elaborated, arranged according to certain preestablished principles, and made comparable. There were not very many statistical figures in the book, but each figure reported made sense. For every number, Quetelet tried to find the determining influences, its natural causes, and the perturbations caused by man. The work gave a description of the average man as both a static and a dynamic phenomenon.
This work was a tremendous achievement, but Quetelet had aimed at a much higher goal; social physics, as the subtitle of his work said; the same title under which, since 1825, Comte had taught what he later called sociology. Terms and analogies borrowed from mechanics played a great part in Quetelet’s theoretical exposition. To find the laws that govern the social body, said Quetelet, one has to do what one does in physics: to observe a large number of cases and then take averages. Quetelet’s average man became a slogan in nineteenth-century discussions on social science. The use of mathematics and physics in social sciences was praised, although none of the parties to the discussions knew what it should really mean.
The above statement also applied to Quetelet himself. There is not much more mathematics contained in his work than the vague idea that the reliability of an average increases with the size of the population—and even this idea was not understood by many of his contemporaries. It is evident that Quetelet knew more about mathematical statistics, but he never thought to apply it in his social statistics. Neither did he make significance tests, although as early as 1840 they came into use in medical statistics. He often urged that one should consider not only the average but also the deviation in order to know whether the latter is accidental or not, but he never followed up this suggestion. He always judged intuitively whether a statistical figure was constant or variable under different conditions.
In more theoretical work about 1845, Quetelet approached mathematical statistics more closely. For the first time he mentioned the normal distribution, or, rather, a binomial distribution of a high degree. As an example, he explained the error distribution by the theory of elementary errors. Possibly he made this discovery independently of Thomas Young, G. Hagen, and Bessel. In any case it was clearly Quetelet’s own achievement to unveil the normal distribution of the heights of a population of soldiers. The normal distribution, not only as a law of observation errors but also as a genuine natural law, was indeed an important discovery, although Quetelet’s examples were not convincing.
Quetelet’s impact on nineteenth-century thinking can in a certain sense be compared with Descartes’s in the seventeenth century. He certainly gave science new aims and tools, although his philosophy was rather pedestrian and his thinking in somewhat sophisticated matters was rather confused. There was a strong emotional component in Quetelet’s influence. In fact, he became famous for a passage, quoted again and again from Sur l’homme, in which he draws his conclusions from the statistics of the French criminal courts from 1826 to 1831:
The constancy with which the same crimes repeat themselves every year with the same frequency and provoke the same punishment in the same ratios, is one of the most curious facts we learn from the statistics of the courts; I have stressed it in several papers; I have repeated every year: There is an account paid with a terrifying regularity; that of the prisons, the galleys, and the scaffolds. This one must be reduced. And every year the numbers have confirmed my prevision in a way that I can even say: there is a tribute man pays more regularly than those owed to nature or to the Treasury; the tribute paid to crime! Sad condition of human race! We can tell beforehand how many will stain their hands with the blood of their fellow-creatures, how many will be forgers, how many poisoners, almost as one can foretell the number of births and deaths.
Society contains the germs of all the crimes that will be committed, as well as the conditions under which can develop. It is society that, in a sense, prepares the ground for them, and the criminal is the instrument ….
This observation, which seems discouraging at first sight, is comforting at closer view, since it shows the possibility of improving people by modifying their institutions, their habits, their education, and all that influences their behaviour. This is in principle nothing but an extension of the law well-known to philosophers: as long as the causes are unchanged, one has to expect the same effects.
H. T. Buckie, in England, and Adolph Wagner, in Germany, were Quetelet’s most fervent supporters in social science. Florence Nightingale considered his work a new Bible.
BIBLIOGRAPHY
I. Original Works. Quetelet’s writings include Sur l’homme et le developpment de ses facultés, essai d’une physique sociale (Paris, 1835); “Sur l’appreciation des documents statistique …,” in Bulletin de la Commission de Statistiquc (de Belgique) (1845), 205–286; Lettres a S. A. R. le due reégnant de Saxe-Cobourg et de Gotha(Brussels, 1846); and Du systeme social et des his qui le regissent (Paris, 1848).
II. Secondary Literature. On Quetelet and his works, see Hans Freudenthal, “De eerste ontmoeting tussen de wiskunde en de sociale wetenschappen,” in Verhandelingen van de k, vlaamse academie voor wetenschappen, letteren en schone kunsten van België, 28 , no. 88 (1966); Maurice Halbwachs, La theéorie de l’homme moyen (Paris, 1912); F. H. Hankins, Adolphe Quetelet as Statistician (New York, 1908); G. F. Knapp, “Bericht uber die Schriften Quetelets zur Sociaistatistik und Anthropologie,” in Jahrb$#x00FC;cher f$#x00FC;r Nationalökonomie und Statistik, 17 (1871), 106–174, 342, 358; J. Lottin, Quetelet statisticien et sociologue (Paris, 1912); and E. Mailly. Essai sur la vie et les outrages de L.-A-J.Quetelet (Brussels, 1875).
Hans Freudenthal
Quetelet, Adolphe
QUETELET, ADOLPHE
(1796–1874)
Born in Ghent, Belgium, mathematician and demographer Adolphe Quetelet earned a doctorate in mathematics at the age of twenty-three and was elected, one year later, to the Académie royale des sciences et belles-lettres. The Belgian academy became the central place from which Quetelet directed most of his activities for the rest of his life. He worked in a variety of disciplines such as astronomy, meteorology, physical geography, development psychology, demography, and statistics. Quetelet's work was profoundly influenced by early probability theory. From astronomer and mathematician Pierre-Simon Laplace (1749–1827), Quetelet learned that measurement errors are normally distributed around the true value; this information allowed him to detect systematic errors in early social science data. His notion of l'homme moyen also stems from Laplace's theory. However, Quetelet was never exclusively preoccupied by averages, and whenever possible he presented complete distributions. One of his contributions to demography is his presentation of age-specific rates for vital events or for other phenomena (e.g., crime), and his construction of time series. In fact, the materials brought together in his Physique Sociale (1835) mark the beginning of the statistical study of the life cycle. Quetelet's interpretation of population distributions of social characteristics announced the advent of sociology as a new science, according to which the entity called "society" could be studied and analyzed with objective methods. In contrast to philosopher Auguste Comte (1798–1857), Quetelet never developed a general plan for this new discipline, but his influence on sociology remained strong throughout the nineteenth century, as is evidenced in the work of French sociologist Émile Durkheim (1858–1917).
Quetelet's contribution to demography started in the 1820s. Together with E. Smits, he noted, like several others before him (e.g., French military engineer Sébastien Vauban [1633–1707] and German demographer Johann Peter Süssmilch [1707–1767]) that the numbers and age distributions of vital events in the Low Countries showed a remarkable degree of stability over time. In Physique Sociale, Quetelet argued that only major disturbances were capable of producing temporary distortions. By contrast, les causes constantes would re-establish the dominant pattern. This is a view similar to that of the homeostatic demographic regime of the economist T. R. Malthus.
Quetelet's other contributions to demography deal respectively with census taking and life table construction. These two areas were intimately related since no direct measurement of probabilities of dying (i.e., the qx-function of a life table) was available at that time. Hence, like all other investigators before him, Quetelet depended on the stationarity assumption that permitted the linkage of ved age structures to the Lx-function (numbers of person-years lived in an age interval). Quetelet explicitly discussed the properties of stationary populations, and showed that the hypothesis of constant mortality could be relaxed. In fact, he was on the way to showing that there is a neutral pattern of mortality decline (i.e., a reduction in age-specific death rates which does not alter the shape of the population age distribution). (For the proof, see A. J. Coale, 1972: 33–36.) Quetelet was never able to develop a model for a stable population with a constant growth rate different from zero. He also failed to recognize the significance of the logistic curve developed by one of his younger colleagues, Belgian mathematician and demographer Pierre-François Verhulst (1804–1849). In actual practice, Quetelet remained a master of comparative statics rather than of social dynamics.
Quetelet did not comment on the numerous social developments in Belgium, which began in the 1860s. After suffering a stroke in 1855, his scientific innovativeness ended. However, until his death in 1874, Quetelet continued to inspire statistical applications in other many fields, and to promote international comparability of statistical information. In the words of mathematician Alain Desrosières, "Quetelet was the orchestra conductor of nineteenth century statistics" (Derosières, p. 95).
See also: Demography, History of; Life Tables; Population Thought, History of; Verhulst, Pierre-Franç ois.
bibliography
selected works by adolphe quetelet.
Quetelet, Adolphe. 1835. Sur l'homme et le développement de ses facultés ou essai de physique sociale. Paris: Editions Bachelier. English transl.: A Treatise on Man and the Development of His Faculties. Edinburgh: Chambers, 1842.
——. 1848. Du système social et des lois qui le régissent. Paris: Guillaumin et Cie.
——1849. "Nouvelles tables de mortalité pour la Belgique." Bulletin de la Commission Centrale de Statistique 4: 1–22.
selected works about adolphe quetelet.
Académie Royale de la Belgique. 1997. Actualité et universalité de la pensée scientifique d'Adolphe Quetelet. Classe des Sciences, Actes du Colloque 24–25.10.96, Brussels, Belgium.
Coale, Ansley J. 1972. The Growth and Structure of Human Populations–A Mathematical Investigation. Princeton, NJ: Princeton University Press.
Desrosières, A. 1993. La politique des grands nombres–Histoire de la raison statistique. Paris: Editions La Decouverte. English edition: The Politics of Large Numbers: A History of Statistical Reasoning. Cambridge, MA: Harvard University Press. 1998.
Lesthaeghe, R. 2001. "Quetelet, Adolphe (1796–1874)." In Encyclopedia of the Social and Behavioural Sciences. Oxford: Elsevier Science Ltd.
Ron Lesthaeghe
Lambert Adolphe Jacques Quételet
Lambert Adolphe Jacques Quételet
The Belgian statistician and astronomer Lambert Adolphe Jacques Quételet (1796-1874) is considered the founder of modern statistics and demography.
Adolphe Quételet was born in Ghent on Feb. 22, 1796. When he finished secondary school at the age of 17, he took a job teaching mathematics in a secondary school. A professor of mathematics at the newly established University of Ghent influenced Quételet to study mathematics. In 1819 he received his doctorate in mathematics with a dissertation in which he claimed to have discovered a new curve. The work was heralded as an important contribution to analytic geometry.
That year Quételet was appointed to the chair of elementary mathematics at the Athenaeum, and shortly thereafter he was elected to membership in the Royal Academy of Sciences and Belles-lettres of Brussels. He wrote numerous essays in mathematics and physics, founded and edited a journal, delivered lectures on science in the Brussels Museum, and published introductory works in mathematics and natural science. In 1828 he became the first director of the Royal Observatory, a position held until his death on Feb. 17, 1874, in Brussels.
In Paris gathering technical knowledge for the building of the observatory, Quételet met a number of leading French scientists and mathematicians who were actively engaged in laying the foundations of modern probability theory. Although they were working in the natural sciences and mathematics, in the course of their studies some of them had occasion to analyze empirical social phenomena. What fascinated Quételet was the possibility of using statistics as an instrument to deal with social problems.
Quételet believed that statistical theory and research could be used to determine whether human actions occur with the expected regularity. If so, it would indicate that there are social laws which are as knowable as are the laws which govern the movements of the heavenly bodies. He thought that there were such social laws. He thus developed his famous notion of the "average man."
Quételet's concept of the average man was intended to be a construct of the mind or a model which would enable social "scientists" to express the differences among individuals in terms of their departure from the norm. This theory led to his "theory of oscillation." According to this hypothesis, as social contacts increase and racial groups intermarry, differences between men will decrease in intensity through a process of social and cultural oscillation, resulting in an ever-increasing balance and, eventually, international equilibrium and world peace. Thus, as Quételet saw it, the task of the academic and scientific communities in the immediate future was to develop a new social science, based on empirical observation and the use of statistics. This new science of "social physics" would discover the laws of society upon which human happiness depends. Quételet's subsequent works represent an attempt to formulate this new field of social physics.
To accomplish this goal, it was necessary to refine the techniques used in the collection of statistical data, since Quételet believed that through the analysis of such data empirical regularities or laws could be discovered. He was a moving force behind many of the governmental agencies and professional organizations involved in the gathering of statistical data, and he exerted an international influence on this area. His application of quantitative methods and mathematical techniques has been judged as anticipatory of the guiding principle of contemporary social science, especially his efforts to change statistics from a mere clerical function into an exact science of observation, measurement, and comparison of results.
Further Reading
Several of Quételet's major works are available in English translation. The best study in English of his significance is Frank H. Hankins, Adolphe Quételet as Statistician (1908), which includes a biographical sketch. See also George Sarton, Sarton on the History of Science, edited by Dorothy Stimson (1962), for the reasons why Sarton considers Quételet rather than Auguste Comte as the "founder of sociology, " and Quételet's work On Man and the Development of His Faculties as "one of the greatest books of the nineteenth century." □