title: [A model of the population growth of the Earth].
abstract: Of all global problems world population growth is the most significant one. World population drives all other global issues--of food and energy, resources and the environment. Although demographic data in a quantitative way does express the net result of our economic, social and cultural development, methods of demography can hardly suggest a more general, synergistic, approach to the study of long term growth. To describe this process in its past and project it into the foreseeable future a mathematical model is worked out. It treats the world population as an entity, seen as an open and evolving dynamic system. The approach is phenomenological and growth over very many generations is assumed to be self-similar. This invokes scaling and mathematically is expressed by a power law. Comparison with population data leads to a consistent description of growth by a hyperbolic growth curve valid from the Paleolithic up to the middle of this century. In terms of kinetics the growth rate is proportional to the square of the total number of people, rather than their number, as in the case of exponential growth. Thus nonlinear quadratic rate describes the sum outcome of all mechanisms that contribute to our growth and development in a collective interactive process. Taken without limits this pattern is divergent in the distant past and present, when it describes the population explosion. These singularities are cut off by introducing a characteristic time of 42 years,--the effective human life span--as the microscopic time constant in this phenomenology. The model gives an estimate of the beginning of human evolution congruent to 4.4 million years ago and of the total number of people who ever lived: congruent to 100 billion. In the scope of the model large scale cycles defined by history and anthropology are shown to be uniformly spaced in time on a logarithmic scale, expressing an inherent periodicity. On this scale, as we go into the past the rate of growth decreases when, finally in the early Paleolithic any appreciable change would take a million years to happen. As we approach the present this progression of cycles with the consequent compression of the time scale is now terminated by the demographic transition. This is seen as a singular epoch in all human development when the basic mode of world population growth is to change.(ABSTRACT TRUNCATED AT 400 WORDS)
mesh_terms: D003710:Demography; D004777:Environment; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical; D011158:Population Growth; D013597:Systems Analysis; D013997:Time Factors
vernacular_title: Model' rosta naseleniia Zemli.