Drawing on Wallerstein’s world systems theory and space-time as the basis of knowledge, this article demonstrates the ways in which we can use transformative space-time and our historical social system with the aim of reaching such a moment of complexity, turbulence or bifurcation. This article is divided into two parts; namely, the geopolitical spaces of capitalism and the complexity of time and space. The first part has to do with the global city which constitutes a constellation of complex urban spaces in the capitalist world-economy and their consequences in daily life. The second part refers to three cases of international turbulence. First of all, we present some crucial moments in the history of world oil in relation to the case of environmental complexity. Further, we include the aspect of illegal drugs industries in geographical spaces as a case of turbulence. Finally, in the last case, we associate the turbulence inside the international political system with the nuclear proliferation of weaponry in geographical spaces.