The Mathematical Formula of Consciousness: A Synchrony-Based Model for a Unified Psychology

Abstract

This article proposes a unifying neuro-mathematical model that conceptualizes consciousness as a negotiation process between the natural synchronous tendency of neural oscillators (Kuramoto model) and informational dissonances originating from the environment (which modulate frequencies ω) and the internal state (which modulates coupling strengths K). The stable synchrony within the "rich club" of the neural network constitutes the "Self," while consciousness emerges as the dynamic interaction between this coherent pattern and incoming asynchronies.

The model mathematically derives the Weber-Fechner Law [ω(I) = log(I)] as an inevitable consequence of the operational limitations of neural oscillators, thereby explaining the dimensional structure of qualia. We demonstrate the unifying power of the framework by mechanically reinterpreting fundamental findings from behaviorism (reinforcement as reduction of volitional dissonance), cognitivism (object permanence as maintenance of frequency patterns), and Gestalt (perceptual closure as a phase transition towards coherence).

This formulation establishes the foundation for a unified psychology with consistent ontology, epistemology, and methodology, offering both a solution to the "hard problem" of consciousness and experimentally testable predictions.