Mathematical Psychology: Geometry, Mapping and Dynamics in Emotion Space

数学心理学：情感空间中的几何、映射和动力学

• 批准号: 0308894
• 负责人: Lee Rudolph
• 金额: $ 9.99万
• 依托单位: Clark University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-03-01 至 2005-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0308894&HistoricalAwards=false
• 关键词: Mathematical; Psychology; Geometry; Mapping; Dynamics

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).

这笔赠款将支持首席研究员、数学系教授，与两名合作的私人投资机构合作，在一个较长期的、已经在进行的跨学科研究项目中的一年内，这两人都是私人投资机构所在机构心理学院的教授。具体地说：(1)社会心理学将进行密集的学习和培训，特别关注当前体现人类情感的理论。(2)PI将开发个人和群体“情绪空间”的数学模型，并将监督计算机辅助工具的开发，以使用拓扑学、几何学和动力学的技术绘制和探索这些模型。(3)PI、共同PI和其他合作者(包括心理学研究生和本科生、计算机科学教员和学生，将来可能还包括心理学院的临床教员)将使用这些模型和工具来开发新的实验方案、收集数据并改进模型和工具。这项研究的起点是心理学家弗里茨·海德和阿尔伯特·米霍特在半个多世纪前观察到的，即使是一个非常退化的几何刺激(圆圈和三角形以高度受限的方式、沿着一条线或在一个平面上移动的粗略动画)也会在非常多的观察者中产生一种令人信服的各种情绪体验。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海德-米霍特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，这项拨款解决了这一疏忽。这笔赠款构成其关键部分的更大项目是探索人类情感的心理物理、发展、进化和文化基础。由于其明显简单的几何性质，海德-米霍特现象为PI提供了一个方便且非常有趣的入口点，PI是一位在拓扑和几何方面有专长的数学家。这个IGMS项目由MPS多学科活动办公室(OMA)和数学科学部(DMS)联合支持。