Academic journal article Population

Wilhelm Lexis: The Normal Length of Life as an Expression of the "Nature of Things"

Academic journal article Population

Wilhelm Lexis: The Normal Length of Life as an Expression of the "Nature of Things"

Article excerpt

At the first International Congress of Demography held in Paris in 1878, the German statistician Wilhelm Lexis(1) gave a paper in French entitled "On the normal length of human life and on the theory of the stability of statistical ratios"(2). In the words of Jacques Bertillon, Lexis's treatment of the subject displayed "a consummate mathematical science [that] sheds light [on] demographic studies". In this paper, Lexis claims that "the concept of normal lifetime [has] its significance in the nature of things".

For Lexis, everyone should live the same length of time - the normal length of life - but some of us are prevented from doing so by particular circumstances. It is therefore possible to distinguish "normal" deaths, which occur at the normal age of death or are randomly distributed around that age, from premature deaths of adults and, a fortiori, deaths of children.

Lexis's concept of the length of life can be understood as a synthesis of two elements: first, Quetelet's contributions to sociology via the notion of "l'homme moyen" or "average man"; second, the law of normal distribution of errors formulated by Laplace and Gauss(3).

I. Mortality: mere statistical regularity or law of nature?

By computing a series of probabilities of dying, a pattern of mortality can be identified. But the question arises - and has been the subject of a recurrent debate in the history of demographic thought - of whether this pattern is a construct of the human intellect or, on the contrary, is part of the very nature of things. In his writings on the length of human life, Lexis favoured a statistical approach capable of bringing to light the orderly progression of mortality, but he saw that order as pertaining to the laws of nature.

While the conception held by Lexis had been the most common in the eighteenth century, it was not so in the nineteenth century. For example, in the 1854 volume of Statistique de la France on population trends, the "law of mortality" was characterized only by a series of numbers without any higher order being mentioned:

"Looking at the general table [...], one observes [...] that one-sixth of all children die in their first year; one-fifth do not reach the age of 2, onefourth the age of 3, and one-third the age of 12. One-half remain at age 38, one-third at age 59, one-fourth at age 65, one-fifth at age 69, and onesixth at age 72.

This survival expresses the law of mortality [...]."(4)

Lexis proceeds from an entirely different perspective. His research on mortality is conducted using the concept of the average, but an average that is not merely the summary of a set of data values. For him, it is the expression of a natural law of mortality.

II. A single model of man

Lexis lays claim quite explicitly to the intellectual heritage of Adolphe Quetelet(7). For him, as for the Belgian astronomer, the social body exhibits an essential unity, guaranteed by the laws of nature. The investigations of mortality are an application of the conceptual model developed by Quetelet.

1. Quetelet: harmony and stability of laws

In his Anthropométrie (1871), Adolphe Quetelet sets out his vision of social phenomena very clearly:

"Individual man has generally been studied with care, but little thought has been given to examining the social body to which he belongs, and whose different properties are not only of great importance, but should elicit the keenest attention by virtue of the remarkable laws presiding over their unity."(8)

Quetelet sees the unity of the individual and the social body as a sign of the existence of unchanging and consistent laws of nature:

"The more one studies the works of creation, the more one has to admire the laws that ensure their harmony and stability. These laws, which regulate the functioning of worlds and assign to each its movement and rank, are no less wondrous in regard to the tiniest specks of dust scattered over their surface. …

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