Shells and Pebbles

Adolphe Quetelet: a statistical method for all

Statistics form the methodological basis of a large variety of disciplines, from humanities to the natural sciences.1 These statistical methods have their roots in nineteenth-century statistical thinking. Statistical thinking in the nineteenth century could mean different things for different thinkers. We recognise three main trends.2 First, the practitioners of state sciences, who were called statisticians, used descriptive and textual methods to organise state affairs efficiently. This form of statistical thinking was about bureaucracy, and resembled the collecting and ordering of facts, which led to statistics being seen as a historical discipline.3 A second version of statistical thinking, also related to state affairs, did make use of numbers and numerical data. From the end of the seventeenth century onwards, we recognise “political arithmetic” as defined by William Petty, where averages and estimations were used such that a complete census was no longer necessary.4 Lastly, and in line with the second trend, the numerical state science, methods developed by mathematicians and astronomers, such as error margin calculations and probability theory, were used to study social and societal data. This approach was developed at the beginning of the nineteenth century by Pierre Simon Laplace, but no one embraced this approach as enthusiastically as the Belgian Lambert Adolphe Quetelet.

This blogpost describes Quetelet’s attempt to form a discipline that would study the statistical regularities found within the data of a large range of subjects. While this did not succeed as Quetelet had envisioned, his statistical approach was adopted by a large range of disciplines. To his own surprise, Quetelet found such regularities in many different types of data, such as crime or suicide rates and birth ratios, as well as in the average height and weight of men. He used the method of least squares to show that all the data followed a normal distribution, and concluded that this implied the existence of “statistical laws.”

As a case study I will use Quetelet’s research into plant sciences, botany, where he studied the relationship between temperature and the growth and development of plants using statistical methods. Over the course of the nineteenth century, botany went through a number of transformations, which included an increasing emphasis on quantitative data and, in extension, statistical methods. Whilst in the late eighteenth and early nineteenth centuries, botany enjoyed immense popularity among amateur naturalists, by the end of the nineteenth century, this situation had changed drastically. Botany had become more of a specialised and laboratory-oriented discipline, and this made it less accessible to amateurs. I will show how Quetelet’s attempt to use statistical methods to study many different topics might not have had the result he wanted, which was to create a discipline or research field in its own right, but that it did result in the spread of statistics to a range disciplines. This case can tell us more about how disciplines and disciplinary boundaries were formed and maintained in the nineteenth century.5

Adolphe Quetelet was born in Ghent in 1796, where he graduated with a degree in mathematics in 1819.6 Still, Quetelet was not interested in solely mathematics.7 Together with Jean-Guillaume Garnier, he established and edited the journal Correspondance mathématique et physique (1825-1839), in which scholars could publish results from observations and ongoing research in physics and maths. These tables of observations could be used by other scientists. For this to work, Quetelet established rules and procedures for doing observations which were also published in his journal, as well as instructions on how to use observational instruments. The journal provided Quetelet with an international network of scholars whose research all focused on observations. On top of this, Quetelet lobbied for the construction of an observatory in Brussels, especially after Belgium’s independence in 1830, a project for which he visited the Paris observatory, where he met Laplace, and which resulted in the opening of the Brussels observatory in 1834. Quetelet worked at the observatory as secretary and conducted many observations from there, including botanical observation in the garden of the observatory. These activities, the journal and the observatory, illustrate Quetelet’s scientific ambition: he argued for the use of the same set of methods for the collection, ordering, and analysing of different kinds of observational data.

Royal Observatory of Belgium (Royal Observatory of Belgium (oma.be)

Observation practices have shaped the foundations of the modern sciences and humanities, providing the basis for arguments, evidence, or inspiration to scholars throughout all disciplines. Practices of observation in knowledge production cover many aspects, such as experiences, interpretations, instrumentations, and data practices. As Lorraine Daston and Elizabeth Lunbeck have argued: “Observation is the most pervasive and fundamental practice of all modern sciences, both natural and human.”8 Yet the nature, role, and practice of observation changed over time, and have always been highly dependent on their historical and social context, specifically their disciplinary context. By studying how scholars dealt with observational data, we can get a better understanding of the disciplinary contexts of these scholars and their practices.

Quetelet himself studied the statistical regularities he found in different types of numerical data across disciplines, whether they concerned weather phenomena, birth rates, or the lengths and weights of French soldiers.9 Quetelet saw these regularities as statistical laws, and his insight that these could be found in different areas was to him an important moral victory for the statistician in a chaotic and everchanging society. These statistical methods were demonstrated in his most well-known work Sur l’Homme et le développement de ses facultés (1835), which he himself referred to as Essai de physique sociale.10 Social physics was the overarching discipline Quetelet aimed at: a discipline to study how statistical laws had an impact on humans and nature, in the same way as physical laws had.

In Sur l’Homme, Quetelet presented his ideas for the studying of regularities based on statistical laws. These regularties could be found everywhere, in nature and in society. While Quetelet admitted that the consequences of such societal laws were of a different nature than the natural laws, his analogies between social physics and physics (celestial mechanics in particular) were intentional and thorough: Quetelet saw both disciplines as two parts of the same whole, because they were both committed to observations and studying what he called “periodical phenomena”.11

Quetelet attempted to study these periodical phenomena on a large, international scale. To be able to achieve this he had to create some guidelines: comparing and analysing observations required a similar approach to conducting them. For this reason, Quetelet wrote a handbook called Instructions pour l’observation des phénomènes périodiques (1842), from which the quote above are the opening lines. This handbook contained mostly lists and tables of matters which Quetelet deemed worthy of observing at an international scale. These were divided into three categories: meteorology and earth sciences (“physique du globe”), the plant kingdom, and the animal kingdom. For the plant kingdom, Quetelet dictated that it would be interesting to observe certain phenomena annually, while others should be observed daily. He explained what kind of instruments should be used and how the observations should be noted down. Observers were asked to send their data to the Brussels observatory, where Quetelet collected and analysed them.

Quetelet’s Instruction pour l’observation des phénomènes périodiques (1842) (Instructions pour l’observation des phénomènes périodiques : Quetelet, Lambert Adolphe Jacques, 1796-1874)

In this way, Quetelet organised an international network of observers.12 One of his correspondents was a former student of his and is most interesting for my case study: Charles Morren. Morren corresponded with Quetelet since 1826.He sent him letters including observations of comets or of his microscopy work.13 From 1832 onwards, Morren also sent botanical observations to Quetelet.

Morren’s botanical observations were clearly of a different nature than his previous work: where in his earlier letters he was mostly descriptive and collecting textual data, when he observed plants, he committed to numerical data. In February 1841, for instance, Morren wrote that he would like to contribute to the collection of all statistics on the Belgian flora. To do this, he had ordered his observations in a table, where he had noted down the numbers of a certain plant he had observed each month. This table he turned into a diagram, in which he explained that the diagram showed how big the relationship was between the number of flowering plants and the month. This approach shows Morren’s statistical methods: he used the data he had to make a best fitting graph. This very closely resembled Quetelet’s approach of how to observe and analyse such periodical phenomena.

It is no surprise that Morren’s botanical observations differed from his earlier, physical observations: Morren studied maths and natural philosophy at Ghent University, where he was supposed to become an instructor of geology, zoology, and anatomy in 1832, but in that year the faculty of science at Ghent University closed. Instead, Morren got a job at an influential industrial school in Ghent, where he taught physics, before becoming a professor of botany at the University of Liège. Seven years later, the chair of agriculture was added to his appointment. At Liège, Morren opened a botanical museum and rearranged the botanical gardens. In other words, Morren had become a botanist. During these years, Morren continued to use Quetelet’s approach, employing quantitative and statistical methods to observe plants.

However, Morren’s disciplinary development started to have an influence on how he appreciated Quetelet’s approach. In 1842, Morren wrote Quetelet a critical letter in which he stated that Quetelet’s focus on certain isolated or separated observations was lacking, and that Quetelet ran the risk of being unable to obtain an overarching perspective of the phenomena which he was studying.14 Morren wrote that he not only planned to study the flowering of a certain plant, but also the smells, colours, and the environment in which the plant was growing. This would give him a better view on the phenomenon of flowering, which for him was an important criterion for proper plant science.

Morren started to feel strongly for a different approach and to make that clear he coined a new term for his own work: in 1849 he referred to his work as “phenology”.15 This was explicitly different to what Quetelet was doing. Morren argued that “[l]’ensemble de ces phénomènes constitue évidemment pour la nature végétale la manifestation de la vie réglée par le temps. On a nommé cet ensemble, dans ces derniers temps, les phénomènes periodiques. Le mot nous paraît trop vague, parce qu’il est trop général.”16 Quetelet never adopted the term “phenology”.17

Morren’s criticism of Quetelet is exemplary for how other scientists and scholars reacted to Quetelet’s proposition. The botanical physiologist Julius Sachs, for instance, argued that Quetelet’s research into the relationship between temperature and the growth of plants was not precise enough and with that, that Quetelet’s data were not precise enough.18 Jules Émile Planchon criticised Quetelet’s focus on averages, since extreme values have huge consequences for plants, so averages would never be able to tell a scientist what they need to know: a year with a very warm summer and cold winter would have the same average temperature as a mild year, while this would mean something completely different for the plants.19 In other words, Quetelet’s approach was not deemed specific enough by these botanical scientists.

This illustrates historical developments concerning discipline formation. Botanical scientists had contrary ideas to Quetelet about what kinds of data should be collected, based on which criteria, and these choices determined what they saw as standards for their discipline. In this they differed from Quetelet: Quetelet wanted to create an overarching approach that could be applied to any observations from any discipline. Quetelet had determined which matters should be observed, but these phenomena were part of many different disciplines. For example, Quetelet’s opus on the Belgian climate consisted of seven parts: 1) Solar radiation and air and ground temperatures (1845), 2) Direction, intensity, duration and character of the wind (1848), 3) The electricity of the air (1849), 4) Atmospheric pressure and waves (1851), 5) Rains, hails and snow (1852), 6) The hygrometer (1854), 7) The state of the heavens in general (1857).20 This did not always match with developments within the disciplines themselves, as we have seen in the case of botany: Quetelet’s approach was not deemed specific enough, and with that did not meet the disciplinary standards. In this we see a tension between disciplinary boundaries and a unification of the sciences.

The tension signalled above shows that it is worthwhile to dive a bit deeper into these disciplinary boundaries and how they work. Our case study demonstrates how disciplinary standards, which take care of bounding off the discipline, were defined and upheld by the scientists within the discipline themselves: Sachs, Planchon, and Morren criticised Quetelet’s approach. This The emerging and maintaining of disciplinary standards is an active process, which I have called “disciplinary activity”, based on a term introduced by historian Libby Schweber.21 Quetelet was also involved in disciplinary activity: he tried to establish a social physics discipline, where studying periodical phenomena using statistical methods was the central aim. However, his activity was seen as too general.

Similar criticism was also given during the series of statistical congresses which Quetelet had organised. The idea behind this congress series was to create statistical central bureaus in different European cities from which data could be collected and analysed using the same approach. Quetelet organised these congresses and was president of the first episode, held in 1853 in Brussels. There were nine congresses in total, between 1853 and 1876: after Quetelet’s death in 1874, the series was stopped, and even though a permanent international committee was established in 1873, this was also disbanded in 1878.22 The biggest problem for the participants of these congresses was that there was no clear idea for which topics should be discussed during these congresses. The result was that during the congresses organised in different countries, lots of different topics were discussed, depending on the interests and preferences of the national organising committees. Because of this, there was no unity between the different congresses and the approach remained, again, too general.

This tells us something about the important elements necessary to constitute a discipline in the nineteenth century: a specific method is not sufficient, the topic of study also needs to be well-defined. This is in line with how sociologist and historian Rudolf Stichweh makes a distinction between premodern and modern disciplinary entities: before 1750 areas of study were determined on the basis of their method, and this changed between 1750 and 1850 towards a classification based on study object, according to Stichweh.23 In that sense, Quetelet’s attempt to create a discipline based on a method was not in sync with other developments in nineteenth-century academic disciplines.

Nevertheless, Quetelet’s statistical methods spread across many disciplines. In the present day, he is seen as an influential figure in modern scientific disciplines such as nutrition, criminology, and sociology.24 Indeed, this agrees with Quetelet’s own work: his aim was to employ the same method on many types of data to create a complete picture of man in nature and society. While not creating an overarching discipline, the spread of his methodological approach attests to Quetelet’s broad and non-disciplinary specific approach.

All in all, this historical case illustrates how disciplinary boundaries in the nineteenth century were actively discussed and, through that discussion activated, transgressed, and consolidated. In particular the correspondence between Morren and Quetelet illustrates how disciplinary boundaries played a role within research and how this was an active process. The fact that disciplinary boundaries were upheld actively does not mean that they were or are trivial: conducting research is determined by these standards for a great deal and scholars are consciously aware of this. Moreover, financial matters are divided and institutional decisions are made based on disciplinary boundaries, which also has very real consequences for the research that is conducted. This shows that it is all the more interesting to study the development of these disciplinary boundaries.

  1. This essay is based on the research which I completed as part of my PhD dissertation: Observing Disciplines. Data Practices In And Between Disciplines In The Nineteenth and Early Twentieth Centuries, (2022),University of Amsterdam. My PhD research was part of the NWO project “The Flow of Cognitive Goods: Towards a Post-disciplinary History of Knowledge” (2016-2020), together with Rens Bod, Jeroen van Dongen, Sjang ten Hagen, and Bart Karstens. This blogpost is an English translation of a piece I have been asked to submit to the Dutch Filosofie-Tijdschrift, to appear in November / December 2023, with the theme of unification of the sciences. ↩︎
  2. These three trends of nineteenth-century statistical thinking are referred to in various sources. For example: Porter, T.M. (1986) The Rise of Statistical Thinking 1820-1900. Princeton University Press, Princeton; Desrosières, A. (1998) The Politics of Large Numbers. A History of Statistical Reasoning. Translated by C. Naish, Harvard University Press; Prévost, J.G. & Beaud, J.P. (2012) Statistics, Public Debate and the State, 1800-1945. Studies for the International Society for Cultural History, Number 1, Pickering & Chatto; Stigler, S.M. (1986) The History of Statistics: The Measurement of Uncertainty before 1900. Harvard University Press; Stamhuis, I.H. (2008) “Introduction: The Statistical Mind in Modern Society. The Netherlands 1850-1940”, I.H. Stamhuis, P.M.M. Klep & J.G.S.J. van Maarseveen [eds] The Statistical Mind in Modern Society. The Netherlands 1850-1940. Volume I: Official Statistics, Social Progress and Modern Enterprise, Aksant, pp 11-41. ↩︎
  3. You can read more on descriptive statistics in: Echterhölter, A. (2016) “Data, Diplomacy, and Liberalism: August Ferdinand Lueder’s Critique of German Descriptive Statistics (c. 1810)”, Bulletin of the German Historical Institute, 59, pp 83-102; Hansen, J.D. (2015) Mapping the Germans: Statistical Science, Cartography, & the Visualization of the German Nation, 1848-1914. Oxford University Press. ↩︎
  4. Petty, W. (1690) Political Arithmetick, London, R. Clavel. See also: Stamhuis, I.H. (1989) ‘Cijfers en Aequaties’ en ‘Kennis der Staatskrachten’ Statistiek in Nederland in de negentiende eeuw. Dissertation, VU Amsterdam, Rodopi, p 36. ↩︎
  5. Much has been written about the history of disciplines and discipline formation. My presentation of this history is shaped mostly by Rudolf Stichweh’s sociological historical work: Stichweh, R. (1984) Zur Entstehung des modernen Systems wissenschaftlicher Disziplinen. Physik in Deutschland 1740-1890. Surhkamp Verlag, Berlin; and idem (1992), “The Sociology of Scientific Disciplines: On the Genesis and Stability of the Disciplinary Structure of Modern Science” in: Science in Context, 5(1), pp 3-15. It is also influenced by Michel Foucault’s view of disciplines as systems of control and training: Foucault, M. (1995) Discipline and Punish: The Birth of the Prison. Vintage Books, New York. These two authors are discussed concisely in the context of discipline formation and the rise of modernity by Johan Heilbron: Heilbron, J. (2004) “A Regime of Disciplines: Toward a Historical Sociology of Disciplinary Knowledge” in: C. Camic & H. Joas [eds] The Dialogical Turn: New Roles for Sociology in the Postdisciplinary Age. Rowan & Littlefield Publishers, Inc., Lanham, pp 23-42. ↩︎
  6. For a biography of Quetelet and an analysis of his research, see: Donnelly, K. (2015) Adolphe Quetelet, Social Physics, and the Average Men of Science, 1796-1874. University of Pittsburgh Press. ↩︎
  7. He also co-authored libretto’s and composed poetry. Donnelly (2015), p 100-101. ↩︎
  8. Daston, L. & Lunbeck, E. (2011) “Introduction. Observation Observed” in: L. Daston & E. Lunbeck [eds] Histories of Scientific Observation. The University of Chicago Press, pp 1-9, p 1. ↩︎
  9. This research resulted in our modern Body-Mass-Index (BMI) scale, also called the Quetelet Index. ↩︎
  10. Quetelet, A. (1835) Sur l’homme et le développement de ses facultés ou Essai de physique sociale. Paris, Bachelier, Imprimeur-Libraire. ↩︎
  11. Quetelet, A. (1842) Instructions pour l’observation des phénomènes périodiques. Brussels, Académie Royale de Bruxelles, p 1. ↩︎
  12. An interesting study of Quetelet’s observers can be found in: Donnelly, K. (2014) “The Other Average Man: Science Workers in Quetelet’s Belgium”, History of Science, 52(4), pp 401-428. ↩︎
  13. Their correspondence can be found in the archives of the Royal Academy of Belgium: Archives contemporaines, Papiers Quetelet, Correspondance Générale: lettres reçues et minutes de lettres expédiées, Morren (Charles). ↩︎
  14. Morren to Quetelet, 12 January 1842, Papiers Quetelet. Morren writes: “Quant à la réduction du programme, je suis plus embarrassé que jamais. (…) En restreignant les observations à des faits isolés, le grand but est manqué, (…) Si j’ai réussi, à Lyon, à Florence, à Naples etc. de faire sentir l’importance de ces travaux pour la physiologie, c’est en envisageant le phénomène de la périodicité dans son expression générale. A presque toute mon observation de floraisons j’avais indiqué les odeurs, à toutes les couleurs ; j’avais là des résultats très remarquables, mais en ne voulant que les floraisons seules et même celles de quelques fleurs que rien de précis ne déterminera et qui seront choisies d’après le caprice ou la paresse de l’observateur, vous pouvez être assuré que vous ôtez de votre conception tout ce qu’elle avait d’utile. Vos chers confrères n’ont pas compris où votre système menait.” ↩︎
  15. More about this historic episode can be found in: Demarée, G.R. & Chuine, I. (2006) “A Concise History of the Phenological Observations at the Royal Meteorological Institute of Belgium”, N.R. Dalezios & S. Tzortzios [eds] Proceedings volume III Phenology – Agroclimatology HAICTA 20-23 September 2006, Volos; Demarée, G.R. (2009) “The Phenological Observations and Networking of Adolphe Quetelet at the Royal Observatory of Brussels”, Italian Journal of Agrometeorology, 1, pp 22-24; and Demarée, G.R. & Rutishauser,T. (2010) “From ‘Periodical Observations’ to ‘Anthochronology’ and ‘Phenology’ – the scientific debate between Adolphe Quetelet and Charles Morren on the origin of the word ‘Phenology’”, International Journal of Biometeorology, 55, pp 753-761. ↩︎
  16. Morren, C. (1848) “Principes d’Horticulture” in: Annales de la Société royale d’agriculture et de botanique de Gand : journal d’horticulture et des sciences accessoires, 4, Ghent. Also cited in Demaré & Rutishauser (2010), p 758 as: “the returning phenomena for the plant kingdom constitutes the manifestation of life ruled by time. That collection of phenomena has recently been named ‘periodical phenomena’. The name seems to us too vague because it is too general.” ↩︎
  17. Phenology has become a scientific field of studies that still is practiced today. Interestingly, this modern phenology resembles Quetelet’s approach more than Morren’s: phenologists study the consequences of the climate and the weather on plants and areas. See for instance: Koch, E., Dittmann, E., Lipa, W., Menzel, A., Nekovar, J., Sparks, T.H., & van Vliet, A.J.H. (2009) “COST725 – establishing a European phenological data platform for climatological applications: major results”, Advances in Science and Research, 3, pp 119-122, which seems more ‘Queteletian’ than Morren’s definition did. ↩︎
  18. Sachs claimed Quetelet had collected “ungenauen Daten”. Sachs, J. (1860) “Physiologische Untersuchungen über die Abhängigkeit der Keimung von der Temperatur”, Jahrbucher für wissenschaftliche Botanik, bd 2, Berlin, pp 338-377, p 371. ↩︎
  19. Planchon, J.E. (1864) “De l’abus des moyennes thermométriques comme expression de la température dans ses rapports avec la végétation”, Bulletin du Congrès International d’Horticulture qui a été réuni à Bruxelles, les 24, 25 et 26 avril 1864, sous les auspices de la Fédération des Sociétés d’Horticulture de Belgique, en coïncidence avec l’exposition universelle d’horticulture, organisée par la société royale de flore. Ghent, C. Annoot-Braeckman, pp 70-72, p 71. Four years after the congress, Planchon would become internationally famous for ‘saving’ the French wine production from an exotic species of pest. For more on Planchon and his botanical science, see: Campbell, C. (2006) The Botanist and the Vintner: How Wine Was Saved for the World, Algonquin Books. ↩︎
  20. Quetelet, A. (1845-57) Sur le Climat de la Belgique. Académie Royale, Brussels. ↩︎
  21. Schweber, L. (2006) Disciplining Statistics: Demography and Vital Statistics in France and England, 1830-1885. Duke University Press, p 8. ↩︎
  22. Randeraad, N. (2011) “The International Statistical Congress (1853-1876): Knowledge Transfers and their Limits”, European History Quarterly, 41(1), pp 50-65, p 58. ↩︎
  23. Stichweh (1984), especially pp 15-16. ↩︎
  24. [1] Seifret Weigley, E. (1989) “Adolphe Quetelet (1796-1874): Pioneer Anthropometrist” in: Nutrition Today, 24(2), pp 12-16; Beirne, P. (1987) “Adolphe Quetelet and the Origins of Positivist Criminology” in: American Journal of Sociology, 92(5), pp 1140-1169; Eknoyan, G. (2008) “Adolphe Quetelet (1796-1874)-the average man and the indices of obesity” in: Nephrology Dialysis Transplantation, 23, pp 47-51; Faerstein, E. & Winkelstein, W. Jr. (2012) “Adolphe Quetelet: Statistician and More” in: Epidemiology, 23(5), pp 762-763; Mosselmans, B. (2005) “Adolphe Quetelet, the average man, and the development of economic methodology” in: The European Journal of the History of Economic Thought, 12(4), pp 565-582. ↩︎

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