Biological ageing determined by statistical constraints: a hypothesis on mortality

This article presents a conjecture, based on recent research carried out by the author, concerning
ageing and consequent demographic mortality. This conjecture hypothesizes that all human
populations will show a 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 model of cellular automata and a method based on Fermi
statistics. 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 le�
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 biologic ageing is seen in connection to our conjecture that predicts the presence of an
absolute limit (linked to the TC parameter) on the number of ‘critical’ events. As ‘critical’ events
accumulate over time by ageing, 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.
Key Words: Demographic Mortality, Cellular Automata, Statistical Mechanics, Ergodic Hypothesis,
Statistical Distributions, Demographic Life Tables, Biological Clock, Gompertz Law, Ageing, Fermi time,
Intrinsic Capacity.