Topologization in Psychological Modeling: From Two-Dimensional Analysis to the Third Dimension in Psychometrics

This article contributes to the ongoing debate on topological explanations by developing the concept of topologization in psychological modeling. Referring to mathematical topology—particularly the notions of dimensionality and projection—it proposes a new interpretation of psychological constructs that goes beyond classical two-dimensional representations. The article addresses the issue of topologization in psychological modeling, indicating that many existing models—traditionally analyzed in two-dimensional spaces—may in fact possess a hidden three-dimensional structure. Based on conceptual, methodological, and psychometric analyses, the author shows that the transition to three-dimensional modeling allows for a more complete representation of the studied psychological constructs. The example of Antonina Gurycka’s model of upbringing errors serves as an illustration of a situation in which the emergence of an additional dimension results from interpretative inconsistencies in the center of the circular model. The article discusses the limitations of classical statistical methods, such as factor analysis, and proposes alternative analytical approaches—including support vector machines with RBF kernel (from the field of artificial intelligence) and topological data analysis (TDA). These methods enable the detection of the depth and structural complexity of psychological models, thereby challenging existing assumptions in psychometrics and psychological diagnosis. The conclusion indicates how topologization may influence the future of psychological theory, measurement methods, and therapeutic interpretation.