Knotted Minds: Knot Theory as a Framework for Modeling Psychological Dynamics

This paper explores a novel synthesis between knot theory and psychology, proposing that recurring mental processes can be interpreted through topological structures. Building on Kurt Lewin’s early topological psychology and subsequent dynamical approaches to cognition, we suggest that concepts from knot theory, such as knots, links, braids and their invariants, provide a useful structural language for describing persistent patterns of thought, conflict and identity. We introduce key ideas from knot theory and illustrate how they may be mapped onto psychological phenomena including rumination loops, traumatic entanglements, goal conflicts, and multi-process behavioural dynamics. The framework is then situated within several established psychological perspectives, including cognitive-behavioural theory, psychodynamic models, and contemporary research on neural dynamics. Finally, we outline potential empirical directions inspired by modern topological data analysis (TDA), suggesting how recurrent trajectories in behavioural or neural time-series data might reveal underlying topological structures. By extending Lewin’s classical life-space diagrams into dynamic trajectories that may form loops, links and braids, this framework provides a new conceptual lens for understanding the structure and persistence of complex psychological phenomena.