The Geometry of System 3 Creative Thought: A Formal Equation for Creativity

Creativity is typically defined as the production of ideas or artifacts that are both novel and appropriate, yet there is still no simple formalism that specifies how generative, evaluative, integrative, and metacognitive processes combine over time to yield creative outcomes. This article proposes a compact “geometry” of creative cognition expressed by the equation E = (G R I M)^T, where E denotes Eureka-level creative effectiveness, G wide stochastic generation, R focused reflection and evaluation, I multimodal integration and iteration between intuitive and analytic codes, M metacontrol via implicit and explicit metacognition, and T temporal consistency across episodes. To make E empirically tractable, creative effectiveness is operationalized through novelty, usefulness, and diversity (NUD), which mirror evolutionary tactics of variation, selection, and maintenance of variation. The article maps each equation factor onto behavioral and neural indices, highlights the central role of metacontrol in balancing persistence and flexibility, and situates the framework within developmental, individual-difference, and evolutionary perspectives. It then derives implications for the assessment and training of creativity, emphasizing creative metacognition as a key leverage point, and extends the geometry to artificial architectures and human–AI co creation. The resulting formulation provides testable predictions about how measures of generation, evaluation, integration, metacognition, and practice should interact to shape NUD profiles over time, and offers a principled bridge between human and artificial creativity.