Focusing between Mathematics and Physics. A Longterm History of Caustics from the 17th to the 20th Century

专注于数学和物理之间。

• 批准号: 419007942
• 负责人: Professor Dr. Tilman Sauer
• 金额: --
• 依托单位: Arbeitsgruppe Geschichte der Mathematik und der Naturwissenschaften
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/419007942?language=en
• 关键词: Focusing; between; Mathematics; Physics.; Longterm

This project is about the history of caustic curves and surfaces as a looking glass for a historical understanding of the complex and evolving interactions between mathematics and physics from a long-term perspective. Caustics, defined as the high concentration of light rays along curves or surfaces, are common in everyday life, but are also a key pattern to understand less evident phenomena like gravitational lensing. Ever since the 17th century, the phenomenon of caustics has been a challenging problem on different levels. Its mathematical understanding required sophisticated and changing geometric and analytical frameworks, from precalculus ray geometry to 20th century catastrophe theory. It is also intimately linked to contrasting and contradictory physical theories of light, situated between corpuscular and wave theoretical conceptions. And its empirical investigation called for different experimental constellations from glass spheres and burning mirrors to gravitational lensing by galaxies and black holes. Nowadays, caustic phenomena have also a transdisciplinary dimension, since the same mathematical theory has applications in a variety of knowledge areas, ranging from biology to sociology and economics. Despite its relevance in many fields, the topic of caustic curves and surfaces and the contexts of their investigation and conceptualization has hardly been treated in the historical literature. The analysis of such boundary objects and their development offer an excellent challenge for a historical understanding of the vexing relations between mathematics and physics in their specific historical contexts and situated practices. Aiming at filling a gap in the historical literature in this respect, it is a goal of the project to develop a general historical-philosophical framework for dealing with this kind of objects at the interplay between conceptual constructions, mathematical descriptions, and experimental practices. Last but not least, the project intends to be relevant in the field of didactics of mathematics and physics as well, specifically by focusing on the introduction of mathematical and physical concepts through their concrete historical contexts.

该项目是关于焦散曲线和曲面的历史，作为从长期角度历史性地理解数学和物理之间复杂且不断发展的相互作用的镜子。焦散，定义为光线沿着沿着曲线或表面的高度集中，在日常生活中很常见，但也是理解引力透镜等不太明显的现象的关键模式。自世纪以来，焦散线现象一直是一个在不同层面上具有挑战性的问题。它的数学理解需要复杂多变的几何和分析框架，从前微积分射线几何到世纪的突变理论。它也与光的对比和矛盾的物理理论密切相关，位于微粒和波动理论概念之间。它的实证研究需要不同的实验星座，从玻璃球和燃烧的镜子到星系和黑洞的引力透镜。如今，苛性现象也具有跨学科的维度，因为相同的数学理论在各种知识领域都有应用，从生物学到社会学和经济学。尽管它在许多领域的相关性，焦散曲线和曲面的主题和他们的调查和概念化的背景下几乎没有在历史文献中处理。对这些边界对象及其发展的分析，为历史性地理解数学和物理在其特定历史背景和情境实践中的令人烦恼的关系提供了一个极好的挑战。为了填补这方面的历史文献中的空白，该项目的一个目标是开发一个一般的历史哲学框架，用于在概念构建，数学描述和实验实践之间的相互作用中处理这类对象。最后但并非最不重要的是，该项目打算在数学和物理教学领域相关，特别是通过其具体的历史背景下，通过数学和物理概念的介绍。