Wilhelm Lexis: The normal length of life as an expression of the "nature of things"

Population

Volumn 58, Issue 3, 2003, Pages 303-322

  Véron, Jacques ^a   Rohrbasser, Jean Marc ^a  

^a INSTITUT NATIONAL D'ÉTUDES DÉMOGRAPHIQUES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; LIFE TABLE; MORTALITY; POPULATION DYNAMICS;

LEXIS;

EID: 22144464214     PISSN: 16342941     EISSN: None     Source Type: Journal    
DOI: 10.2307/3246676     Document Type: Article

References (57)

1. Lexis (1837-1914) studied law, mathematics, and natural science. After teaching mathematics at the Bonn lyceum (high school), he served as Extraordinary Professor of Political Economy at the University of Strasbourg, and Professor of Geography, Ethnography, and Statistics at Dorpat (now Tartu, Estonia). In 1878, he held the Chair of Political Economy at the University of Freiburg int Breisgau (Grand Duchy of Baden). In 1889, he became Vice-President of the International Statistical Institute and, in 1895, the head of the first Department of Actuarial Science at the University of Göttingen.
2. W. Lexis, "Sur la durée normale de la vie humaine et sur la théorie de la stabilité des rapports statistiques", Annales de démographie internationale, 1878, II, Paris, pp. 447-62.
3. Väinö Kannisto has applied Lexis's method to recent data: "Mode and dispersion of the length of life", Population: An English Selection, 13-1, 2001, pp. 159-72.
4. Statistique de la France, second series, vol. IV, part 1, "Mouvement de la population pendant l'année 1854," Strasbourg, Berger-Levrault, 1857, p. xliii.
5. MF", Le Moniteur des Assurances, 84, 15 September 1875, pp. 346-348.
6. 20 - (40 - 20)7/10 = 42 - 14 = 28 years.
7. "Qu[e]telet's remarkable research has taught us the interesting fact that individuals belonging to a given nationality are more or less exact copies of a model of given proportions [...]" (Lexis, 1878, p. 447).
8. Adolphe Quetelet, Anthropométrie ou mesure des différentes facultés de l'homme, Brussels, Muquardt, 1871, p. 5.
9. Quetelet, 1871, p. 10.
10. Adolphe Quetelet, Sur l'homme et le développement de ses facultés ou essai de physique sociale, Paris, Bachelier, 1835; reprint Fayard, Paris, 1991, p. 31.
11. As Quetelet noted in the Bulletin of the Central Statistical Commission of the Kingdom of Belgium - a commission of which he was currently chairman - this distance makes it possible to develop a science of collective phenomena: "[...] by losing sight of individuals, one can unravel, through the social phenomena that dominate the masses, a set of laws that one determines with extreme precision. The initial obstacle was the belief in man's free will; one knew that his will is an elusive cause, located outside the scope of any law; from this, it was concluded that the effects of that cause would thus be impossible to determine; but one overlooked the fact that man's will ceases to act beyond certain limits where science begins, and that the effects, which appeared to be so powerful - such as those that people have always thought to be present at the birth of things - could be judged practically non-existent if they are examined from a collective viewpoint. Experience indeed soon proved to the most lucid observers that individual wills neutralize one another amid general wills." Bulletin de la Commission centrale de statistique, Kingdom of Belgium, Ministry of the Interior, vol. VIII, Brussels, 1860, pp. 433-34.
12. Quetelet, 1835, p. 37 (author's italics).
13. Adolphe Quetelet, Du sytème social et des lois qui le régissent, Paris, Guillaumin, 1848, book 1, section 1, chapter 2, pp. 13-14.
14. In his Anthropométrie..., Quetelet (1871, p. 22) reasserts the value of multiplying the observations of a given type: "If I had a hundred different persons measure the Apollo Belvedere, and if I then carefully computed the average of the hundred numbers denoting the size of the head, or of the eyes, or of the mouth, etc., I could with all these averages reconstruct the primitive type. This would be impossible only in the absence of a general type, whose existence everything points to here".
15. Quetelet, 1835, p. 44.
16. Michel Armatte, "Théorie des erreurs, moyenne, et loi 'normale'", in Jacqueline Feldman, Gérard Lagneau, and Benjamin Matalon (eds), Moyenne, milieu, centre. Histoires et usages, Paris, EHESS, 1991, pp. 67 and 68.
17. e siècle", in Jacqueline Feldman et al., op. cit., p. 93.
18. Lexis, 1878, p. 450.
19. In Zur Theorie der Massenerscheinungen in der menschlichen Gesellschaft, published in Freiburg im Breisgau in 1877, Lexis had already used the metaphor of the game of boules, specifying a distance to the target "of about 70 feet", to state that the bowls were distributed on the near side and far side of the target in accordance with mathematical error theory, the dispersion being determined by the player's skill. Note that this distance of 70 feet recalls a life span of 70 years.
20. The term "accidental" expresses, in the case of young children, the occurrence of an event that brings life to a premature end; in the case of the normal group of deaths, the same term describes a random dispersion around a central value.
21. Lexis, 1878, p. 451.
22. Lexis, 1877, p. 45. (Translator's note: quotation translated into English from the authors' French rendering of the original German.)
23. Lexis, 1877, pp. 48-9.
24. "The figures are reduced to a cohort of 500 births [...]" (Lexis, 1878, p. 451).
25. Implying that the total number of normal deaths is 200.
26. 72.5 ± 7.5.
27. This is Laplace's integral. For a description of the statistical analysis of accidental errors, see, for example, Émile Borel, Traité du calcul des probabilités et de ses applications, vol. 1, fascicle II, R. Deltheil, "Erreurs et moindres carrés", Paris, 1930.
28. Or probable deviation.
29. Cf. note 24.
30. Lexis, 1877, p. 63.
31. The Bertillon family distinguished itself in France in the second half of the nineteenth century. Louis-Adolphe Bertillon, a physician, took a special interest in hygiene and the statistics of the causes of death; his son Jacques, also a physician, was a founder of the International Statistical Institute. His fields of interest were population decline and alcoholism (cf. Jacques and Michel Dupâdquier, Histoire de la démographie, Paris, Perrin, 1985, pp. 401-406). Louis-Adolphe was the son-in-law of Achille Guillard, who introduced the term "demography" in his Éléments de statistique humaine or démographie comparée..., Paris, Guillaumin, 1855.
32. Bertillon in Annales de démographie internationale, 1878, p. 461.
33. This argument had been expounded by Christiaan Huygens in 1669, in his correspondence with his brother Lodewijk. The Huygens brothers also discuss this comparison between averages and probability.
34. "[...] the physiological conditions of our species naturally include a certain normal length of life [...]" (Lexis, 1878, p. 450).
35. Bertillon in Annales de démographie internationale, 1878, p. 461.
36. Bertillon in Annales de démographie internationale, 1878, p. 461.
37. Luigi Perozzo was at that time an engineer at the Italian Statistical Office. He is known for the stereogram, a spatial representation of the dynamics of a population.
38. Luigi Perozzo, "Distribuzione dei morti per età", Annali di Statistica, 2nd series, vol. 5, 1879, pp. 75-93.
39. "[...] possono dubitare se la verificazione della legge sia dovuta all'artificiale produzione delle cifre a cui si applica od esprime un vero fatto naturale", (Perozzo, 1879, p. 77).
40. The first letter is addressed to "Louis" Bodio, with a request that he forward it to Luigi Perozzo; the second is addressed directly to Perozzo.
41. "I thank you ['Louis' Perozzo] for your positive reaction, in your interesting study, to my theory or rather my hypothesis." (Lexis in Annali di Statistica, 1879, p. 81).
42. Lexis in Annali di Statistica, 1879, p. 81.
43. "[...] since 55% of deaths belong to classes 0-15, there remain only 45% to be divided between premature [deaths] and the normal group. In Norway, for example, three-quarters of children born alive survive beyond age fifteen, and that is why the normal group is far larger there than in Italy." (Lexis in Annali di Statistica, 1879, p. 82).
44. Luigi Bodio, at the time, was Director General of Statistics of the Kingdom of Italy. He had attended the session of 9 July 1878, in which Lexis had presented his concept of the normal lifetime.
45. Lexis attended this session of 14 April.
46. Luigi Bodio, "Quelques renseignements sur les conditions hygiéniques et sanitaires de l'Italie", in Bulletin de l'Institut international de statistique, vol. II, part 1, 1887, pp. 264-84.
47. A liberal economist, Pierre Émile Levasseur (1828-1911) was Professor at the Collège de France and Administrator of the institution, a member of the Institut de France, and President of the Société de Statistique de Paris. His works include a multi-volume Histoire des classes ouvrières en France (History of the Working Classes in France) (1859-67).
48. The first volume was published in 1889.
49. Levasseur, La Population française, 1891, book II, chapter 13, p. 178.
50. Levasseur speaks of a "disk" (disque) rather than a "bowl" (boule) as Lexis does.
51. Hence chance plays a role.
52. Levasseur, 1891, book II, chapter 13, pp. 178-9.
53. Vilfredo Pareto (1848-1923) succeeded Léon Walras to the Chair of Political Economy at the University of Lausanne. He contributed to the "neo-classical revolution" in economics.
54. Vilfredo Pareto, Cours d'économie politique, vol 1, 1896, and vol 2, 1897, new edition by G. H. Bousquet and G. Busino, Geneva, Droz, 1964.
55. Pareto makes several references to Levasseur's work.
56. "Mr. Lexis has produced an important theory, of which we shall say a few words" (Pareto's, 1896, § 158, p. 77).
57. Pareto's name does not appear in the list of those attending the 1878 Congress: cf. Annales de démographie internationale, 1878, pp. 303-6.