The Geometry of Empathy: A Topological Approach to Affective Bias

Empathy is usually viewed as a spontaneous and morally neutral reaction to others’ suffering, yet recent developments in social neuroscience, Bayesian brain theory and political psychology point towards empathic responses as shaped by cognitive, ideological and physiological constraints. We introduce a topological framework redefining empathy as a geometrically constrained inference process that is structured, adaptive and modifiable. We situate empathy within a multidimensional perceptual space where topological deformations correspond to changes in moral valuation and social inclusion. The emergent, dynamic geometry of the context-sensitive affective surface is shaped by the interplay of three primary determinants: internalized ideological priors, physiological modulation and prosocial regulatory dispositions. Ideological structures like authoritarianism and social dominance orientation are treated as cognitive priors that curve the empathic manifold, biasing perceptual and moral judgments upstream of awareness. Physiological states, including stress reactivity, threat sensitivity and disgust responses, act as local warping functions that amplify or suppress the ideological curvatures through attentional modulation, creating topological gradients that selectively enhance or block empathic accessibility depending on internal arousal. In contrast, prosocial dispositions like dispositional empathy and cooperative tendencies function as smoothing operators that maintain surface continuity, enabling affective responsiveness across ideological divides. Overall, by characterizing ideological priors as curvatures, physiological variables as gain-modulating distortions and prosocial traits as continuity-preserving forces, we provide a mathematical structure for representing empathic variability. The result is a generative model that captures the structural transformation of empathy across individuals and contexts, offering tools for understanding political polarization, intergroup conflict, emotional rigidity and moral perception.