| Abstract | The ‘mathematical imaginary’ at work in psychology is central to the contingent history of the discipline, but is also responsible for considerable confusion and ambiguity around the ontological assumptions of psychological theories and models. Rather than reject the mathematical altogether, this article argues for an alternative form of mathematical description in psychology through the use of topology. Drawing on DeLanda’s topological account of the virtual, the relationship between psychology and ontology is progressively questioned in relation to memory. Henri Bergson’s conception of duration and the pure past is juxtaposed with the topological psychology of Kurt Lewin and its notion of life space as a manifold with n-dimensions. Using a diagrammatic strategy developed by Mullarkey, an actualist account of the virtual is used to hold these distinct bodies of work together. Psychological events may be given a ‘thick description’ through the identification of topological relations and invariants. The interplay between the actual entities that are afforded in experience can be seen to be virtualized as planes of irreality. A topological approach to psychology offers the opportunity of replacing the taxonomy of essences common to the discipline with a dynamic account of invariance through homeomorphism.
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