Cultural Imagery and Statistical Models of the Force of Mortality: Addison, Gompertz and Pearson
Bibliographic record
Abstract
Summary 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".