Многочисленные спекуляции по поводу максимальной продолжительности жизни человека связаны не только с незнанием истинной причины
старения, но и с неправомерной экстраполяцией
демографических данных при использовании закона Гомперца. Однако этот закон, хотя и учитывает
биологическую компоненту - потерю жизнеспособности, проектирует ее на популяцию, то есть не
выводит формулу старения организма. Если исходить из принципа, предложенного Гомперцем, то
математическая модель старения организма должна отражать корреспондирующее с ростом смертности экспоненциальное падение жизнеспособности. Анализ такой модели позволяет понять, почему продолжительность жизни не подчиняется закону нормального распределения. Предложенная
формула, с учетом нормального распределения
резерва жизнеспособности, что обусловливает
продолжительность жизни, позволяет оценить границу максимальной продолжительности жизни.
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.
Численні спекуляції з приводу максимальної тривалості життя людини пов'язані не тільки з
незнанням справжньої причини старіння, а й з неправомірною екстраполяцією демографічних даних при
використанні закону Гомперца. Однак цей закон, хоча і враховує біологічну компоненту - втрату життєздатності, однак проектує її на популяцію, тобто не виводить формулу старіння організму. Якщо виходити з
принципу, запропонованого Гомперцом, то математична модель старіння організму повинна відображати
кореспондуюче з ростом смертності експоненціальне падіння життєздатності. Аналіз такої моделі дозволяє зрозуміти, чому тривалість життя не підкоряється закону нормального розподілу. Запропонована формула, з урахуванням нормального розподілу резерву життєздатності, що обумовлює тривалість життя,
дозволяє оцінити межу максимальної тривалості життя.
