Nash Meets Heisenberg. Indeterminacy, Equilibria, and the Planck Constants of Social Interaction

Observed Two of the most productive mathematical frameworks of the twentieth century have grown in parallel for eighty years without speaking to each other: game theory andquantum mechanics. Both describe agents navigating spaces of possibility under irreducible constraints. Both produce stable configurations from the interplay of opposing pressures. Both harbour quantities that cannot be simultaneously sharp. Proposed This paper proposes that the formal structure of Gradient Indeterminacy (I-G) --- originally developed to derive quantum mechanics from geometric principles --- can be applied to strategic spaces. Pairs of variables such as pressure and flexibility, or aggressiveness and cooperativeness, obey constraints of the form | A| | B| V DS, where DS is a social quantisation constant --- the analogue of for human interaction. Nash equilibria are reinterpreted as states of minimal strategic indeterminacy, analogous to coherent states in quantum mechanics. Critical social transitions --- marketcrashes, revolutions, technological disruptions --- are reinterpreted as drain vortices in strategic space. Speculative And Dunbar's number (N 150, the observed limit on stable human relationships emerges from the saturation of a social indeterminacy relation.