It is stated that the process of human evolution on planet Earth has entered a permanent crisis mode. The Earth’s civilization is facing a growing set of challenges, threats of uncertainty, even in the very near future. These challenges are associated with the onset of the epoch of the Anthropocene, when human intervention in the bio-geo-sphere leads to its irreversible transformations, which with a high degree of probability may not be compatible with his own existence. On the other hand, on the horizon of the crisis evolution of mankind, a qualitatively new but still ghostly virtual entity appears, called artificial intelligence, which carries a potential threat of its enslavement, turning it into a new pet at best. In this context, a request is rapidly being formed for a new way (or mode) of integratively oriented polyocular thinking, a new conceptual optics that allows us to comprehend the current situation here and now, in order to build a variety of possible scenarios for future human coevolution, technology and the environment endowed with semiotic agency. Complexity thinking is evolutionary thinking together with complexity, thinking quantum-relativistic, mediating, procedural-temporal, thinking immersed in a non-equilibrium flow of becoming distinctions, along with the retention of the distinguishable and indistinguishable, as a kind of figure and background, text and context, self-organizing autopoietic system and structurally related environment. Thus, this mode of thinking becomes a recursive semiotically loaded contingent process in which the dialectic of necessity and randomness generates its qualitatively new states. Summing up, we can say that complexity acts as a kind of potentially active background, not fully manifested process, an infinite-dimensional quantum mechanical function, contact-meeting with which brings to life the appearance of a figure, a sign and its observer, referred to by us as a cross-border observer of network complexity.