L'invention de la table de mortalite, de Graunt a Wargentin, 1662-1766 (review)

Tables of mortality—exhibiting the numbers of persons out of a given number born or living at a particular age who live to attain successive higher ages, and the number of those who die in the intervals—have long been a basic tool used by biostatisticians and actuarians to calculate life expectancy and contingency. However, Jacques Dupâquier, a distinguished historian of early modern European demography, points out that this basic statistical tool is itself a historical artifact: it was forged and refined by a series of mathematicians over the seventeenth and eighteenth centuries, with two periods of creativity clustered around 1670 and 1740. Dupâquier argues that with few exceptions it was mathematicians and astronomers who discovered the mortality table, which deserves to be considered one of the crowning achievements of the scientific revolution. While historians of science have long pointed to a mathematization of knowledge in the seventeenth and eighteenth centuries, too often they have singled out the invention of the calculus and its application to physics and have neglected the important simultaneous development of political arithmetic and the application of calculus and probability to the human and social sciences. In this slim and carefully edited volume Dupâquier presents a well-documented history of the early modern invention of the mortality table, and a review of the often discontinuous and chaotic progression of the statistical and mathematical refinements animating the progress of demography in the seventeenth and eighteenth centuries.

Dupâquier is not the first to navigate the little-traveled waters of the history of statistics. English readers will probably be familiar with the recent work of Lorraine Daston on classical probability theory of the eighteenth century, ¹ and the biometrician and statistician Karl Pearson wrote a solid volume on this matter in the 1920s. ² A recent work on William Farr by John Eyler has traced the importance of vital statistics as an animating agent in the public health reforms of the late nineteenth century. ³ But Dupâquier has filled an important lacuna in the history of statistics and demography by emphasizing how much ground was gained in the early modern period, both by internal mathematical developments and by a mental change toward viewing death as a proper subject of human and mathematical investigation, and not the concern of God alone. The major players in Dupâquier’s history are not new: John Graunt, William Petty, the Huygens brothers, Gottfried Leibniz, and Edmund Halley represent the seventeenth century, while Willem Kersseboom, Nicolas Stryuck, Antoine Deparcieux, Leonard Euler, and Pierre Wargentin are the stars of the eighteenth.

What is it that explains why the birth pangs of the mortality table lasted for more than a century? Dupâquier points out that while the mathematical formulae were worked out by a series of competent and bright mathematicians, many of them better known for their accomplishments in other varied scientific fields, the communication of mathematical discoveries did not proceed smoothly. For example, the Huygens brothers and Leibniz wrote important papers on the matter, but did not publish their writings (the Huygens brothers seem not to have understood the importance of their discovery of the difference between average age and mean age—it had to be rediscovered by Deparcieux seventy-seven years later). Moreover, language continued to present barriers; it took four decades before Graunt’s seminal work was available to French mathematicians in a partial translation.

But principally, these men were hampered by a lack of reliable data. Only in Sweden and in Finland, and then only in the eighteenth century, were careful records kept on the distribution of the population by ages and by deaths. Hence, these early modern mathematicians were forced to draw their conclusions on thin records—at first those of London and Breslau, and then only on limited groups of peoples: subscribers to annuities, investors in tontines, or members of monastic houses...