钟表匠的数学:以技术为基础的方法来研究Jost b rgi(1552-1632)的数学著作

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Damian Moosbrugger
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引用次数: 0

摘要

在本文中,我提出了一种新的方法来分析数学与技术之间的相互关系。它有可能在方法论上为数学历史领域以及当前背景下的计算技术研究做出贡献。基于数学作为一种偶然的人类实践的概念,我声称,与技术的实际接触不仅使新的领域、材料和问题受到数学审查,而且甚至可能从内部塑造数学。为了说明我的方法并证实我的论文,我提出了一个关于瑞士钟表和仪器制造商Jost b rgi(1552-1632)数学作品的历史案例研究。他除了是一个实践的工匠外,还留下了三篇数学论文。在他的时代,精细金属加工的进步,以钟表装置和测量仪器为例,不仅激励和指导了 rgi的数学研究。相反,我认为在实践中与这些技术装置的相互作用塑造了他的数学的内部结构和工作方式,也就是说,它的实体、论证、表示、证明和过程。仔细分析他的作品的某些方面,特别是他的正弦概念,他解释代数中多重解出现的方式,以及他在对数计算工具中对10的桥接的可视化描述,揭示了钟表匠的经验和实践知识与数学的潜在整合。因此,我认为他的数学著作描绘了一个钟表匠的数学。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A clockmaker’s mathematics: a technology-based approach to the mathematical works of Jost Bürgi (1552–1632)

In this article, I propose a new approach to analyze the interrelations between mathematics and technology. It has the potential to contribute methodologically to both the fields of history of mathematics as well as the study of computational technologies in the current context. Based on the conception of mathematics as a contingent human practice, I claim that the practical engagement with technology not only subjects new fields, materials, and problems to mathematical scrutiny but might even shape mathematics from within. To illustrate my approach and corroborate my thesis, I present a historical case study on the mathematical works of the Swiss clock- and instrument-maker Jost Bürgi (1552–1632). Besides being a practicing artisan, he left three mathematical treatises. The advancements in fine metal working at his time, exemplified in clockwork mechanisms and measuring instruments, not only motivated and directed Bürgi’s mathematical inquiries. Instead, I argue that the interaction with these technical apparatuses in practice has shaped the internal structure and workings of his mathematics, that is, its entities, justifications, presentations, proofs, and procedures. The close analysis of some aspects of his oeuvre, especially his notion(s) of the sine, his way of explaining the occurrence of multiple solutions in algebra, and his visual depiction of the bridging of ten in his logarithmic computational tool, reveals a potential integration of the experience and practical knowledge of a clockmaker into mathematics. I therefore make the point that his mathematical writings portray a clockmaker’s mathematics.

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来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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