**The phenomenological
theory of world population growth**

**by**

Paper from Physics-Uspekhi 39(1) 57-71 (1996). Copyright S.P.Kapitza

Contents1. Introduction2. World population as a system3. Mathematical model for population growth4. Population limit and the number of people who ever lived5. Population growth and the model6. The demographic transition and population stabilisation7. Transformation of growth with time8. Stability of growth and development9. Influence of the enviroment10. Conclusions11. ReferencesAbstract:Of all global problems world population growth is the most significant. Demographic data describe this process in a concise and quantitative way in its past and present. Analyzing this development it is possible by applying the concepts of systems analysis and synergetics, to work out a mathematical motel for a phenomenological description of the global demographic process and to project its trends into the future. Assuming self-similarity as the dynamic principle of development, growth can be described practically over the whole of human history, assuming the growth rate to be proportional to the square of the number of people. The large parameter of the theory and the effective size of a coherent population group is of the order of 10^{5}and the microscopic parameter of the phenomenology is the human lifespan. The demographic ttransition - a transition to a stabilised world population of some 14 billion in the foreseeable future - is a systemic singularity and is determined by the inherent pattern of growth of an open system, rather than by the lack of resources. The development of a quantitative non-linear theory of the world population is of interest for interdisciplinary research in anthropology and demography, history and sociology, for population genetics and epidemiology, for studies in evolution of humankind and the origin of man. The model also provides insight into the stability of growth and the present predicament of humankind, and provides a setting for discussing the main global problems.

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