Cultural imagery and statistical models of the force of mortality: Addison, Gompertz and Pearson

We describe selected artistic and statistical depictions of the force of mortality (hazard or mortality rate), which is a concept that has long preoccupied actuaries, demographers and statisticians. We provide a more graphic form for the force-of-mortality function that makes the relationship between its constituents more explicit. The 'Bridge of human life' in Addison's allegorical essay of 1711 provides a particularly vivid image, with the forces depicted as external. The model that was used by Gompertz in 1825 appears to treat the forces as internal. In his 1897 essay Pearson mathematically modernized 'the medieval conception of the relation between Death and Chance' by decomposing the full mortality curve into five distributions along the age axis, the results of five 'marksmen' aiming at the human mass crossing this bridge. We describe Addison's imagery, comment briefly on Gompertz's law and the origin of the term 'force of mortality', describe the background for Pearson's essay, as well as his imagery and statistical model, and give the bridge of life a modern form, illustrating it via statistical animation.