Aristotelian logic is based on the principle of non-contradiction. A proposition is either true or not true. To match this principle, a system must be plain, separable and it must meet the principle of the excluded middle. Such systems is said Cartesian. The Cartesian dichotomy stems from an often far too simplistic vision of our relationship to reality because if A is true, no-A must often be potentiated. The system (A, no-A) acquires the status of a duopoly (current & potential) whose monadic and unitary character must be considered. The third term, as an expression of intersession and mediation between both items, becomes then a constitutive element of the representation of the real. The analysis mainly based on category theory and on Grothendieck's bi-fibration of topoi shows that mediating functions are constitutive of duopoly. They only have meaning through an included middle; the "soul" of this middle is then a dynamic in complex plane. Here, the truth assumes the status of limits, while the lie misuses the status of a "neo-state" that, seen, in the context of complex entanglements, becomes a fallacious make up. Taking as reference the interpolation given by the Riemann zeta function in complex self-similar systems, we have termed "zeta management" the ability to manage the non-separable systems involving the included middle. We shall introduce the logic of the included middle which is fundamental for understanding the dynamics of complex systems (social systems, research ecosystems, control of crisis, etc). We will also show that it is the same methods which, transposed on the social field, are the basis of the dynamics of mediation (role of institutions in development mechanisms; role of Research in the acceptance of empirical uncertainty; role of the teaching for improving the citizen consciousness, etc.). Finally, we will preview how clan systems or unduly Cartesian educational trends, lead to restrain creativity and lead civilizations to decline for lacking adaptability.