Mathematical Psychology: Geometry, Mapping and Dynamics in Emotion Space

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This grant will support the Principal Investigator, a Professor of Mathematics, during one year of a longer-term, already on-going interdisciplinary research project in collaboration with two co-PIs, both Professors in the School of Psychology at the PI's home institution. Specifically: (1) The PI will undertake intensive study and training in social psychology, with particular attention to current theories of embodied human emotions. (2) The PI will develop mathematical models of individual and group ``emotionspaces'', and will supervise the development of computer-aided tools to map and explore these models using techniques from topology, geometry, and dynamics. (3) The PI, co-PIs, and other collaborators (including graduate and undergraduate students in Psychology, faculty and students in Computer Science, and in time probably clinical faculty in the School of Psychology) will use these models and tools to develop new experimental protocols, gather data, and refine the models and tools.The starting point of this investigation is the observation by the psychologists Fritz Heider and Albert Michotte, over half a century ago, that even a very degraded geometric stimulus (crude animations of circles and triangles moving, in highly constrained ways, along a line or in a plane) produces in very many observers a compelling experience of highly varied emotions. Despite tremendous advances in animation technology, it has only been comparatively recently that psychologists and cognitive scientists have begun a vigorous exploration of the Heider-Michotte Phenomenon; even these recent explorations have done little in the way of mathematical modeling, an oversight which is addressed by this grant. The larger project of which this grant forms a key part is an exploration of the psychophysical, developmental, evolutionary and cultural bases of human emotions. Because of its apparently simple geometrical nature, the Heider-Michotte phenomenon provides a convenient, and very intriguing, entry point into this project for the PI, a mathematician with expertise in topology and geometry.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).