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The Mathematics of Society: Variation and Error in Quetelet's Statistics

Published online by Cambridge University Press:  05 January 2009

Theodore M. Porter
Affiliation:
Corcoran Department of History, Randall Hall, University of Virginia, Charlottesville, VA 22903, USA.

Extract

“Let us apply to the political and moral sciences the method founded upon observation and upon calculus, the method which has served us so well in the natural sciences.” The social sciences have known no truer follower of Laplace's dictum than Adolphe Quetelet. His mécanique sociale, later physique sociale, was conceived as the social analogue to Laplace's mecanique celeste, and embodied the results of an unswerving commitment not only to the presumed method of celestial physics, but even to its concepts and vocabulary. It is too weak to say that Quetelet's goal was the transmission of the achievements of celestial physics into the social sphere. He aspired to nothing less than imitation.

Type
Research Article
Copyright
Copyright © British Society for the History of Science 1985

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References

This work was supported by a graduate fellowship from Princeton University, an Andrew Mellon postdoctoral instructorship at the California Institute of Technology, and the Zentrum für interdisziplinäre Forschung der Universität Bielefeld. I am grateful for comments and criticisms received on earlier versions of the manuscript from Diane Campbell, I. B. Cohen, Lorraine Daston, C. C. Gillispie, Ian Hacking, Donald MacKenzie, John Servos, Stephen Stigler, Geoffrey Sutton, and Norton Wise.

The following abbreviations will be used: NMB: Nouveaux mémoires de l'académic royale des sciences et belles-lettres de Bruxelles (after 1840, de Belgique); AO: Annuaire de l'observatoire de Bruxelles; BCC: Bulletin de la commission centrale de statistique (of Belgium).

Translations from works cited in French are my own.

1 de Laplace, Pierre Simon, Philisophical Essay on Probabilities, 2d ed., New York, 1917, pp. 107–8.Google Scholar

2 Quetelet, , “Notice sur Pierre-Joseph Braemt,” Annuaire de l'académie royale des sciences et belles-lettres de Belgique, 23 (1867), 108120, p. 108.Google Scholar The colleague of whom this was written was born just a few months after Quetelet in the same Belgian city, Ghent.

3 Quetelet, , Histoire des sciences mathématiques chez les Belges, Bruxelles, 1864, p. 312.Google Scholar

4 Cannon, Susan Faye, “Humboldtian Science,” in Science in Culture: The Early Victorian Period, New York, 1978.Google Scholar On Quetelet's scientific ambitions, see Quetelet, , Sciences mathématiques et physiques chez. les Belges au commencement du XIXe siècle, Brussels, 1866, p. 9Google Scholar; Histoire (n. 3), pp. 375–6Google Scholar; Physique sociale, ou essai surle développement des facultés de l'homme, 2 vols., Brussels, 1869, t. 2, 446 ff.Google Scholar

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9 Quetelet, , “Notice scientifique,” written for his own book, Sur l'homme (n. 49), and published in AO, 7 (1840), 230247, p. 230.Google Scholar

10 Typical is the Annuaire presenté au gouvernement par le bureau des longitudes, Paris. 1807 et seq.Google Scholar, published annually, which contained population figures for France and the world, tables of mortality, and the like. See also papers by Dupin, Demonferrand, Civiale, Double, Bienaymé, Mercier, Moreau de Jonnès, and Poisson, in Comptes rendus hebdomadaires des séances de l'académie des sciences (1835 et seq.)Google Scholar

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12 On thé tradition of Statistik see John, Vincenz, Geschichte der Statistik, Bd. 1, Stuttgart, 1884Google Scholar, and, in relation to Quetelet, Hankins, Frank H., Adolphe Quetelet as Statistician, New York, 1908, ch. 2.Google Scholar

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15 On French official statistics see Coleman, Death (n. 14); Marie-Noelle Bourguet's thesis at the Université de Reims (1983); and, more generally Koren, John, ed., The History of Statistics (1918), repr. New York, 1970.Google Scholar

16 “Introduction,” Bulletin de la societé française de statistique universelle, t. 1 (18301831), p. 33.Google Scholar

17 For example, Lucas, , “Influence morale de l'instruction et de la civilisation en général sur la diminution des délits et des crimes,” Bulletin universal des sciences et de l'industrie, 6ème section, Bulletin des sciences géographiques, t. 15 (1828), 105117Google Scholar, and a number of other papers in the same journal. On Britain see Cullen, Michael, The Statistical Movement in Early Victorian Britain: The Foundations of Empirical Social Research, Sussex 1975.Google Scholar

18 Balbi, A. and Guerry, A. M., Statistique comparée de l'état de l'instruction et du nombre des crimes dans les divers arrondissements des académies et des cours de France, Paris, 1828Google Scholar, a set of charts; also Guerry, A. M., Essai sur la statistique morale de la France, Paris, 1833.Google Scholar Among the more sophisticated reactions was that of DeCandolle, Alphonse, “Considérations sur la statistique des délits,” Bibliothèque universelle des sciences, belles-lettres et arts, t. 104 (1830)Google Scholar, section de litterature, 159–186; and “De la statistique criminelle,” Ibid., t. 110 (1832), 23–59. Quetelet's explanation for why the correlation suggested by Guerry's tables was false appeared in “Recherches sur le penchant au crime aux differens ages,” NMB, 7 (1832), separate pagination, pp. 2644, 78.Google Scholar

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21 Quetelet papers in Bibliothèque royale de Belgique, folder 2561, letter of 18 Feb., 1846.

22 de Jonnès, Alexandre Moreau, Eléments de statistique, 2me ed., Paris, 1856, pp. 45, 132.Google Scholar

23 Poisson, Siméon-Denis, Recherches sur la probabilité des jugements, Paris, 1837.Google Scholar

24 “Prospectus,” Annales d'hygiène publique et de médecine légale, 1 (1828), p. vii.Google Scholar See also Perrot, Michelle, “Premiêres mesures des faits sociaux: les débuts de la statistique criminelle en France (1790–1830),” Pour une Histoire (n. 20), 125137.Google Scholar

25 Quetelet, , Popular Instructions on the Calculation of Probabilities, (Beamish, Richard, trans.), London, 1839, p. 108.Google Scholar French ed., 1828.

26 See Quetelet, “Aperçu” (n. 5); Histoire (n. 3), passim.; and various biographies in Sciences (n. 4).

27 Quetelet, , “Lettre à M. le Bourgmestre, 15 dec., 1831,” AO, t. 1 (1834), 284287Google Scholar; Mailly, Ed., “Essai sur la vie et les ouvrages de Lambert-Adolphe-Jacques Quetelet,” Ann. de l'acad. (n. 2), 41 (1875), 109297, pp. 186187Google Scholar; Lottin, Joseph, Quetelet: statisticien et sociologue, Paris, 1912.Google Scholar On Quetelet's politics and his ideas on revolution see Bartier, John, “Quetelet politique,” in Académie royale de Belgique, Adolphe Quetelet, 1796–1874 (Mémorial), 4 vols., Bruxelles 1974, t. 4, 2045Google Scholar; also Reichesberg, Naüm, “Der berühmte Statistiker Adolf Quetelet, sein Leben und sein Wirken: Ein Biografische Skizze,” Zeitschrift für schweizerische Statistik, 32 (1896), 418460.Google Scholar

28 Quetelet, , “Recherches sur la loi de la croissance de l'homme,” NMB, 7 (1832), separate pagination, p. 2.Google Scholar

29 Quetelet, , “Recherches sur le poids de l'homme aux differens ages,” NMB, 7 (1832), separate pagination, pp. 1112.Google Scholar

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31 Laplace, , Essay (n. 1), p. 108.Google Scholar

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33 Quetelet, , “penchant au crime” (n. 18), p. 80.Google Scholar

34 Quetelet, , “De l'influence de libre arbitre de l'homme sur les faits sociaux,” BCC, 3 (1847), 135155, p. 136.Google Scholar

35 Quetelet, , Du système social et des lois qui le régissent, Paris, 1848, p. 289.Google Scholar

36 For example, to Rehnisch, Eduard, “Zur Orientierung über die Untersuchungen und Ergebnisse der Moralstatistik,” Zeitschrift für Philosophie und philosophische Kritik, 68 (1876), 213264; 69 (1876), 43115.Google Scholar

37 Quetelet, , “Recherches statistiques sur le Royaume des Pays-Bas,” NMB, 5 (1829), 157, p. 28Google Scholar; Guerry, , Essai (n. 18), p. 11.Google Scholar

38 Quetelet, , “Sur la statistique morale et les principes qui doivent en former la base,” NMB, 21 (1848), separate pagination, p. 4.Google Scholar

39 Quetelet, , “libre arbitre” (n. 34), p. 136.Google Scholar

40 See, for example, Quetelet, , “Recherches” (n. 37), p. iiGoogle Scholar, a typical bit of rhetoric in which statistical research is applauded for ridding us “of the idea that events whose causes we cannot directly perceive are produced by chance.”

41 Merz, J. T., “On the Statistical View of Nature,” in A History of European Thought in the Nineteenth Century, 4 vols., New York, 1965, vol. 2, 548626Google Scholar; also Porter, T. M., “A Statistical Survey of Gases: Maxwell's Social Physics,” Historical Studies in the Physical Sciences, 12 (1981), 77116CrossRefGoogle Scholar; idem., The Calculus of Liberalism: The Development of Statistical Thinking in the Social and Natural Sciences of the Nineteenth Century, PhD. dissertation, Princeton, 1981.Google Scholar

42 See Daston, Lorraine J., The Reasonable Calculus: Classical Probability Theory, 1650–1840, PhD. dissertation, Harvard, 1979, 443466.Google Scholar

43 Quetelet, , “penchant au crime” (n. 18), p. 4.Google Scholar

44 Quetelet, , Du système social (n. 35), p. 104.Google Scholar

45 Quoted in Shoen, Harriet H., “Prince Albert and the Application of Statistics to Problems of Government,” Osiris, 5 (1938), 276318, pp. 286–7.CrossRefGoogle Scholar

46 Quetelet, , “poids de l'homme (n. 29), p. 2.Google Scholar

47 Halbwachs, Maurice, La théorie de l'homme moyen: Essai sur Quetelet et la statistique morale, Paris, 1913, p. 6.Google Scholar

48 Cousin, Victor, Cours de philosophie: Introduction à l'histoire de la philosophie, Paris, 1828, 13me Lecon, pp. 36, 4243.Google Scholar

49 Quetelet, , Sur l'homme et le développement de ses facultés, ou essai de physique sociale, 2 vols., Bruxelles, 1836, t. 2Google Scholar; Cousin, , Cours (n. 48), Cours, 10me Lecon, pp. 67.Google Scholar

50 Quetclet, , Théorie des probabilitiés, Brussels 1853, p. 49Google Scholar; Du système social (n. 35), p. 197.Google Scholar

51 Quetelet, , Sur l'homme (n. 49), t. 1, p. 237.Google Scholar

52 Quetelet, , Du système social (n. 35), p. 110.Google Scholar

53 Quetelet, , “penchant au crime” (n. 18), p. 16.Google Scholar

54 Cousin, , Cours (n. 48), 8me Lecon, p. 10.Google Scholar

55 Hagen, G. H. L., Grundzüge der Wahrscheinlichkeits-Rechnung, Berlin, 1837.Google Scholar

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57 Fourier, , “Extrait d'un memoir sur la théorie analytique des assurances,” Annales de chimie et de physique, 10 (1819), 177189, p. 189.Google Scholar

58 Hilts, Victor L., “Statistics and Social Science,” in Giere, R. N., Westfall, R. S., eds., Foundations of Scientific Method: The Nineteenth Century, Bloomington, 1973, 206233.Google Scholar

59 Quetelet, , Lettres à S. A. R. le duc régnant de Saxe-Coburg eí Gotha sur la théorie des probabilités, appliquées aux sciences morales et politiques, Brussels, 1846Google Scholar, lettre XX; also Quetelet, , “Sur l'appréciation des documents statistiques, et en particulier sur l'appréciation des moyennes,” BCC, 2 (1844)Google Scholar. See also Gillispie, C. C., “Intellectual Factors in the Background of Analysis by Probabilities,” Crombie, A. C., ed., Scientific Change, New York, 1963, 431453Google Scholar; Buck, Peter, “From Celestial Mechanics to Social Physics: Discontinuity in the Development of the Sciences in the Early Nineteenth Century,” in Jahnke, H. N., Otte, M., eds., Epistemological and Social Problems of the Sciences in the Early Nineteenth Century, Dordrecht, 1981, 1933.CrossRefGoogle Scholar

60 Quetelet, , Anthropométrie, ou mesure des différentes facultés de l'homme, Brussels, 1871, p. 253.Google Scholar

61 The problem of homogeneity was often raised, e.g. by Say, J. B., “De l'objet et de l'utilité des statistiques,” Revue encyclopédique, 35 (1827), 529553, p. 548.Google Scholar The best-known critique of the coherence of the idea of l'homme moyen is Cournot, A. A., Exposition de la théorie des chances et des probabilités, Paris, 1843, p. 214.Google Scholar Stephen Stigler discusses these matters in “The Measurement of Uncertainty in Nineteenth-Century Social Science,” Heidelberger, Michael et al. , eds., Probability Since 1800: Interdisciplinary Studies of Scientific Development, Bielefeld, 1983, 131138.Google Scholar

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63 Quetelet, , Du système social (n. 35), p. 17.Google Scholar

64 Porter, , Calculus of Liberalism (n. 41).Google Scholar