The hope of finding a new outlook on the world, new methods of cognition and prediction of course of historical processes, may be connected with the theory of self-organization of complex systems, called also synergetics, as a new interdisciplinary field of research. Synergetics facilitates our understanding of evolutionary pathways of the complex social and human systems, the causes of evolutionary crises, the threats of catastrophes, the reliability of forecasts and the principle limits of predictability in ecology, sociology, economy, geo-policy. Synergetics provides us with the knowledge of constructive principles of co-evolution of complex social systems, co-evolution of countries and geopolitical regions being at different stages of development, integration of the East and the West, the North and the South. Due to the growth of population on the Earth in blow-up regime, the general and local instability of development is increasing. The social world seems to go towards a unity, a sustainable commonwealth through a pulsation rather than monotonously. It goes via alternation of disintegration, even if partial, and getting more powerful integration of structures. There is a pathway of multiple reduction of temporal and material expenses, path of a resonant excitation of a desirable and - that is not less important - feasible in a given social system structure. In the case of right topology of integration of geopolitical structures, an arising whole organization can accelerate its tempo of evolution.