Life and Death Statistical Constraints: a Conjecture on Mortality

This article presents a conjecture, based on recent research carried out by the author, concerning demographic mortality. This conjecture hypothesizes that all human populations will show a common demographic mortality trend as longevity increases. In particular, the demographic mortality curve will tend to converge towards a defined theoretical curve. This curve is calculated mathematically using an abstract cellular automaton model. This automaton (which we call the Arbitrary Oscillator) is constrained to end its life cycle upon reaching a maximum number of paths defined by a parameter TC (Total Counts). In the study, we highlight the mathematical properties of the curve and compare it with the trend of real mortality curves for various populations and for various historical periods. In doing so, we use the Life Tables generated by the demographic institutes of various countries. From this comparison, it appears that the conjecture may be reasonable and an attempt to predict demographic mortality behavior and limitations for the years to come is provided. From the mathematical properties of the theoretical distribution, constraints on the future development of mortality curves can also be deduced, should the conjecture be confirmed. In this case, the mortality curve cannot exceed a certain level of maximum peak height nor fall below a minimum width at half the height of the same peak. Another typical feature of real mortality distribution curves is that they are asymmetrical, with a tail of data to the left of the maximum peak. Using the explicit function, we show how this asymmetry can be interpreted as due to the sum of several discrete sub-components within the overall distribution. A discussion is held on the nature of these possible sub-components that appear at discrete age clusters. The availability of a mathematical description of the mortality distribution also allows us to compare the model with the experimental Gompertz law, finding confirmation of it except at high ages, where our model predicts a saturation. In this article, we also consider the possibility of extending these models to species other than humans by defining a species ‘time constant’. In the conclusions, the more general theme of the nature of human aging is seen in connection to our conjecture that predicts the presence of an absolute limit (the TC parameter) on the number of ‘critical’ events. As ‘critical’ events accumulate over time by aging, approaching the final limit value, the probability of death will tend toward one as a result of a sort of statistical “pressure”. Finally, we hypothesize a conceptual link between the TC parameter of the theoretical distribution and the Intrinsic Capacity (IC) parameter defined by the World Health Organisation.

The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.