From Randomness to Recursion: A Geometric Theory of Free Will in an Indeterministic World

This paper develops the Recursive Informational Curvature (RIC) theory as a unifying framework for understanding free will, agency, and consciousness in an indeterministic universe. While classical libertarian models often fall into the trap of arbitrariness, and compatibilist theories reduce agency to constraint-bound predictability, RIC introduces a novel alternative: freedom as the recursive stabilization of symbolic curvature within a high-dimensional informational manifold. Formally defined by the equation \(\:\mathcal{K}\)(t)=α⋅λ(t)−β⋅∇S(t), RIC links recursive gain and symbolic entropy to volitional collapse, identifying the threshold conditions under which intentional action emerges. The model reconceptualizes the Principle of Alternative Possibilities not as metaphysical bifurcation but as a condition of recursive viability. Applied across biological systems, RIC explains gradient agency, from basal cognition to symbolic introspection, by measuring an organism’s recursive capacity for symbolic coherence under entropy pressure. Philosophically, RIC reframes the self as a recursive attractor, time as a generated manifold of informational curvature, and freedom as a topological achievement. It integrates and extends elements from process philosophy, phenomenology, and systems neuroscience into a cohesive model that is formal, scalable, and testable. The result is a new geometry of mind in which consciousness is curved, agency is recursive, and freedom is the architecture of intentional collapse. RIC offers a theoretical advance and a potential paradigm shift in how volition, identity, and meaning are scientifically and philosophically understood.