Tendencies of global development are increasingly determined by the “Challenges of History” under the global problems requiring from humanity coordinated and extraordinary measures to ensure their right to further existence. Stochasticity, nonlinearity of historical processes is manifested in the world polycentric development, diversification of its mechanisms, need to overcome its most serious and inefficient forms - destructive crises and confrontations. Superattractor which main feature is noosphere and aesthetosphefere synthesis should be the final result of multi aspect and contradictory processes of the modern world dynamics which lie at the heart of globalization. From the perspective of synergetics, one-sided cult of order is typical for noosphere thinking and synthesis of order and freedom (“chaos”) is considered to be harmonious for aesthetosphefere thinking.