A.V. Khalyavkin

We can indirectly estimate an opportunity to live up to age, which essentially exceeds a canonical centenary boundary. The regularities of statistics of mortality allow making it. The Gompertz law connects the force of mortality M(X) in some cohort with its current age X by means of formula M(X)=M*exp[aX]. Here the parameter ‘M’ is a characteristic force of mortality and the kinetic parameter ‘a’ characterize the rate of aging. Let us consider extreme age (Xe) as the age when M(X)=1 per year. That is to say that the life expectancy at this age must be approximately only one year. For this reason Xe(a,M)=(1/a)*ln(1/M). It is underestimated estimation for Xe because the force of mortality at advanced age grows more slowly than exponent of the Gompertz law. The second regularity of mortality statistics connects characteristic force of mortality ‘M‘ of some cohort with its kinetic parameter ‘a’ (rate of aging) by means of formula lnM=lnB-a*T. Here the parameter ‘B’ is a characteristic force of mortality when a=0 (hypothetical case of full non-senescence) and parameter ‘T’ is a characteristic species-specific age. That is to say that the relationship between of extreme age and the rate of aging parameter ‘a’ is Xe(a)=T+(1/a)*ln(1/B). We know that for human beings B~0.05 per year and T~70 years. As ln(1/0.05)=3 the rough formula for extreme age evaluation is Xe(a)~70+3/a. As parameter ‘a’ for contemporary developed countries is around 0.1 per year and more an underestimated extreme age for these countries must be around 100 years. We know that for underdeveloped populations (especially for previous centuries) parameter ‘a’ was around 0.03-0.06 per year. It means that the appropriate extreme age should be approximately 120-170 years. So the empirical laws of mortality are compatible with a real possibility of super-longevity. Unfortunately, this rather rare but potentially possible super-longevity is combined with low life expectancy because of high value of parameter М. The artificial combination of low values both for ‘М’, and for ‘а’ will allow increasing both life expectancy and records of super-longevity.

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