The Statistical Theory of Global Population Growth

Abstract

Of all global problems world population growth is the most significant. The growth of the number of people expresses the sum outcome of all economic, social and cultural activities that comprise human history. Demographic data in a concise and quantitative way describe this process in the past and present. By applying the concepts of nonlinear dynamics and synergetics, it is possible to work out a mathematical model for a phenomenological description of the global demographic process and project its trends into the future. Assuming self-similarity as the dynamic principle of development, growth can be described over practically the whole of human history, with a growth rate proportional to the square of the number of people. This is due to a collective interaction, responsible for the growth of human numbers, as the result of the informational nature of development. The large parameter of the theory and the effective size of a coherent population group is of the order of 105. As the microscopic parameter of the phenomenology, the human life span is introduced into the theory. Estimates of the beginning of human development 4-5 million years ago and of the total number of people who have ever lived since then ≈ 100 billion are made. In the framework of the model, large scale cycles defined by history and anthropology are shown to follow an exponential pattern of growth, culminating in the demographic transition, a veritable revolution when population growth is to stabilize at 10 to 12 billion.

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which … describe observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.

John von Neumann