Mathematical Psychology: Geometry, Mapping and Dynamics in Emotion Space

这项资助将支持首席研究员，一位数学教授，在为期一年的长期跨学科研究项目中与两位共同PI合作，两位共同PI都是PI所在大学心理学院的教授。具体来说：(1)PI将在社会心理学方面进行深入的研究和培训，特别关注当前的人类情感具体化理论。(2) PI将开发个人和群体“情感空间”的数学模型，并将监督计算机辅助工具的开发，以利用拓扑、几何和动力学技术绘制和探索这些模型。(3)项目负责人、联合项目负责人和其他合作者（包括心理学专业的研究生和本科生、计算机科学专业的教师和学生，可能还包括心理学学院的临床教师）将使用这些模型和工具来开发新的实验方案，收集数据，并完善模型和工具。这项研究的出发点是心理学家弗里茨·海德（Fritz Heider）和阿尔伯特·米霍特（Albert Michotte）在半个多世纪前的观察，他们发现，即使是一个非常模糊的几何刺激（圆圈和三角形以高度受限的方式沿直线或平面运动的粗糙动画），也会在很多观察者中产生一种引人注目的、高度多样化的情感体验。尽管动画技术取得了巨大的进步，但直到最近，心理学家和认知科学家才开始对Heider-Michotte现象进行积极的探索；即使是这些最近的探索在数学建模方面也做得很少，这是这项拨款所解决的一个疏忽。这项拨款构成了一个更大的项目的关键部分，即探索人类情感的心理物理、发展、进化和文化基础。由于其明显的简单几何性质，Heider-Michotte现象为PI（一位精通拓扑和几何的数学家）提供了一个方便且非常有趣的切入点。该IGMS项目由MPS多学科活动办公室（OMA）和数学科学司（DMS）联合支持。

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).