According to Bertrand Russell, reasonable arguments in science without using mathematical formulas (mathematical models) sometimes lead to false conclusions. Therefore, there is a justified desire to seek an explanation of biological phenomena by means of mathematical methods, used for a long time to describe the behavior of inanimate objects, physical and chemical processes. Biological processes are based on the same physical and chemical interactions. In particular, aging is a common phenomenon for nature. The aging of objects can be represented as the decay of the system that consists of timeless elements. This condition, unifying all aging objects of animate and inanimate nature, indicates the limit of structural organization – the elementary units that are not subjects to aging. This view is not accepted by biomedical approach. However, it corresponds with mathematical law and the formula proposed by Benjamin Gompertz in 19th century for describing the actual mortality charts. His mathematical model of aging considers an increase in the probability of dying to be the result of uniform and age-independent loss of vitality (life power). It is important to emphasize that Gompers’ formula is similar to the equations of a number of physical processes. However, in comparison with formulas of physics, these symbols show only mathematical relationship, but not actually calculated values. Nevertheless, Gompertz’ formula reflects a real plot showing the probability of death, defined as the ratio of deaths to the number of surviving within a certain age. The scientist was the first who noticed that this dependence can be expressed by an exponential function, and offered the coefficients for it. The most interesting in this formula is a coefficient – a factor reflecting the regular loss of vitality. During the creation of this law microscopic structure of the tissues and organs was not known and, in particular, the universal role of cells was shown later in the theory of the cell pathology by R. Virchow. However, even without this information, it was clear that loss of the vitality should be understood as the loss of material substrates – elementary structures providing certain vital functions. Numerous debates towards maximum human life expectancy are associated not only with the ignorance of the true cause of aging, but also with the unlawful extrapolation of demographic data when using the Gompertz’ law. If we proceed from the principle proposed by Gomperz, the mathematical model of organism’s aging should reflect exponential loss of viability corresponding to the increase in mortality. An analysis of such a model allows us to understand why life expectancy does not obey the law of normal distribution. The proposed formula, taking into account the normal distribution of the reserve of viability determining the life expectancy, allows us to estimate the limitations of maximum life expectancy. There is no doubt that each tissue system has its own reserve of life, which accounts for the uneven aging of various organs and tissues. It is especially important to know the reserve for tissue systems that determine their vital functions, in particular, the contractile function of the heart. This will allow to use a realistic assessment of the maximum life expectancy, and explain the reason for the so-called “sudden” death. When this ratio is found, “sudden” death will cease to be sudden and unpredictable, which seemed endothelial dystrophy, while the limiting level for this tissue system has been found. The ability to determine the maximum duration of human life, as it can now be done in relation to the viability of the cornea, stops speculation on topic of immortality or longevity records. Current paper is one of the first attempts to study a new mathematical concept of aging. It draws attention of exact sciences to this subject, whereby biomedical science will be able to overcome the dogmatic view of the aging of cells, which is the brake in gerontology.
Full text: PDF (Rus) 217K