On the Statistical Law of Life

In this paper we derive a statistical law of Life. It governs the probability of death (or complementary of survival) of the living organisms. We have deduced such a law coupling the widely used Weibull (1951) statistics, developed for describing the distribution of the strength of solids, with the “universal” model for ontogenetic growth only recently proposed by West and co-authors (2001). The main idea presented in this paper is that cracks can propagate in solids and cause their failure as sick cells in living organisms can cause their death. Making a rough analogy, living organisms are found to behave as “growing” mechanical components under cyclic, i.e., fatigue, loadings and composed by a dynamic evolutionary material that, as an ineluctable fate, deteriorates. The implications on biological scaling laws are discussed. As an example of application, we apply such a statistical law to large data collections on human deaths due to cancer of various types recorded in Italy: a relevant agreement is observed. Introduction: Weibull’s and West et al.’s approaches Weibull Statistics (Weibull, 1951) describes the statistical distribution for the strength of solids. Weibull derives the cumulative probability of failure for a structure of volume V and subjected to a uniaxial local stress f P ( ) x σ , a function of the position vector x , as ( )               − − = ∫ 3