Toward mathematical modeling of big History processes

Korotayev, Andrey Vitalievich
D.Sc. in History, Leading Research Fellow, Head of the Laboratory for Monitoring the Risks of Socio-Political Destabilization, HSE University, Leading Research Fellow, Division of Oriental History, RAS Institute of Oriental Studies, Professor, Department of Global Studies, MSU, Moscow, Russia
akorotaev@hse.ru


Abstract
Our quantitative analysis allows us to assume the existence of fairly strict global macroevolutionary patterns (describing the evolution of complexity on our planet over the past few billion years, including human history), which can be surprisingly accurately described by extremely simple mathematical functions. The calculations suggest the following: the fact that the rate of increase in global complexity (dn / dt) and the population of the Earth (N) until the early 1970s grew according to the same law (xt = C/2027–t), is by no means an accident, but a manifestation of a fairly deep pattern. It turns out that in the social phase of the Universal and global history, the hyperbolic growth in the rate of increase in global complexity and the hyperbolic growth in the population of the Earth turn out to be two closely related sides of a single process. This, by the way, makes us expect that the global demographic transition and the cessation of the hyperbolic growth of the Earth's population will be accompanied by a radical change in the patterns of growth in global complexity and technological development, which naturally move away more and more from hyperbolic to a fundamentally different model, which is still waiting to be studied.

Keywords: cliodynamics, big history, mathematical modeling, singularity, phase transitions, global evolution, macroevolution