A conjecture on demographic mortality at high ages

TL;DR

This paper introduces a mathematical model called Arbitrary Oscillator (ArbO) to simulate demographic mortality curves, proposing that as lifespan increases, real mortality patterns will align with the ArbO distribution, offering insights into aging limits.

Contribution

The paper formalizes and analyzes the ArbO model's distribution, applying it to demographic data and predicting future mortality trends based on critical event limits.

Findings

The ArbO distribution fits historical mortality data reasonably well.

Demographic mortality curves tend to resemble the ArbO distribution as longevity improves.

There is a potential absolute limit on human lifespan related to critical event accumulation.

Abstract

The study considers the model of an abstract organism, called Arbitrary Oscillator (ArbO), which is capable of making decisions at each timed step. These decisions are 'critical' since, randomly, their outcome can be 'fatal' for ArbO, thus bringing its life cycle to an end. If we impose limits on the total number of critical decisions using a fixed parameter TC (Total Cases), we can treat the statistical distribution of fatal events over a large number of ArbOs using statistical mechanics methods. This results in a mathematically definable asymmetric 'bell' distribution, which can be compared with demographic mortality curves (dx curves), with an appropriate choice of time scale (one step = five years). Our conjecture assumes that, as demographic longevity improves, i.e., with the lengthening of lifespan, the actual demographic curves will increasingly match the mathematical distribution curve of our ArbO. The statistical distribution of the ArbO was introduced by the author in a previous paper and is here recalled and formalized analytically and its characteristics are detailed. The above said conjecture is based on two case studies: mortality in the United States from 1900 to 2017 and mortality in Italy from 1974 to 2019. The conjecture, applied to both case studies, appears reasonable. Tables and comparison figures are provided to support this. Also, an attempt to predict demographic mortality behavior and limitations for the years to come is provided. Finally, the more general theme of the nature of human aging can also be related to our conjecture, since it can highlight the presence of an absolute limit on the number of 'critical' events (the TC parameter). As 'critical' events accumulate over time by aging, approaching the final limit value, the probability of death will tend toward one.