Archive for History of Exact Sciences最新文献

This article observes and describes distinct stylistic registers that appear in the two main sections of Archimedes’ Quadrature of the Parabola. The correspondence between prose register and mathematical method indicates that in the mechanical propositions of the first section of Quadrature of the Parabola, as well as in several of his other treatises, Archimedes was purposefully deploying a unique style as a kind of rhetorical branding for his most innovative work. This Archimedean register may have been designed to be persuasive to a naturally resistant audience, or to draw mathematical theory into the world of daily experience without compromising its precision. Later authors who took inspiration from Archimedes also imitated his stylistic choices, and the Archimedean register became a signifier of mathematics that pushed the limits of conventional practice.

In this article, I examine how research on the foundations of quantum mechanics contributed to the development of quantum optics during the 1970s and 1980s. To this end, I draw on the scientific trajectories of two renowned physicists, John Clauser and Alain Aspect, both of whom were awarded the 2022 Nobel Prize in Physics for their experimental tests of Bell’s inequalities. These experiments, which rely on optical techniques, not only shed light on the debate between Bohr and Einstein on the interpretation of quantum mechanics, but also prompted Clauser and Aspect to conceive and carry out new experiments that directly addressed the quantum properties of light. I will explain the technical features of this shift, particularly Aspect’s source of entangled photons, which shows an instrumental continuity between his tests of Bell’s inequalities and his subsequent single-photon interference experiments.

In 2007, a trove of bamboo and wooden slips clandestinely smuggled out of China was sold to the Yuelu Academy of Hunan University by a Hong Kong cultural relics dealer. The following year, another small number of slips that later proved to belong to the same group were also donated to the Academy. These slips are believed to date from no later than 212 bce. Among the documents conveyed to the Yuelu Academy is a mathematical text, the 數 Shu (Mathematics), a character that appears on the verso of slip 01(0956) and generally regarded as the title of this work. The problems in the Shu can be divided into eleven distinctive types, namely: areas, fractions, military encampments, norms, grain conversions, proportional distributions, shao-guang ([method for] slightly [increasing] widths), volumes, excess and deficiency, right triangles (gou-gu), and taxation. The original collators of the Shu published photographs of a majority of the Shu slips along with transcriptions and notes concerning their contents in 2011; the rest appeared in 2022. In the course of the research presented here, each character on the Shu slips has been individually examined, special scribal marks have been identified, and their functions are explained. Also, each Chinese sentence has been carefully punctuated, resulting in a more readable version of the Chinese text. In what follows, the Shu is translated into English for the first time, with corresponding notes to help readers better understand the context of the Shu as well as many of the paleographic, philological, and various technical details necessary for a correct understanding of the translation. This work serves as a window into the evolution and development of Chinese mathematics during the pre-Qin and Qin periods, and thereby reflects the state of ancient Chinese mathematics at that time.

I show on the basis of unpublished sources how Hilbert’s conviction of the solvability of all mathematical problems originated from an engagement with Kant’s philosophy of mathematics. Furthermore, I consider other sense of the “solvability” or “decidability” of mathematical problems which Hilbert thought about later: decidability in finitely many steps, which is an issue Hilbert inherited from Kronecker, “finitistic decidability” which Hilbert develops by reflecting on Kronecker’s methodological strictures, and finally the decision-problem as raised by Behmann in the 1920s. I argue that these different preoccupations have different historical and biographical roots, and should also be kept conceptually distinct.

This article analyzes the fragments connected with Hipparchus' Star Catalogue (i.e., the fragment in the Codex Climaci Rescriptus, those in the so-called Aratus Latinus, and P.Aberd. 12) and compares them to the evidence provided by the Exegesis to the Phaenomena of Aratus and Eudoxus, the only work by Hipparchus that has reached us by direct tradition, to assess their value and what they can tell us about Hipparchus’ engagement with stars and star catalogues.

This paper translates and interprets a neglected and significant original text in Zhu Zaiyu’s 朱載堉 (1536–1611) calendar system. The invention and application of Guo Shoujing’s 郭守敬 (1231–1316) hushi geyuan 弧矢割圓 was a great change in the concept of constructing calendar system. In this text we argue that, by giving the relationship between xian-hu 弦弧 ratio and shi 矢, Zhu Zaiyu provided a new method of hu shi 弧矢新術 with higher accuracy than Guo Shoujing’s. Furthermore, we retrieved the construction of the new method of hu shi and discovered the crucial fact that Zhu Zaiyu created a new interpolation method. According to Zhu Zaiyu, a linear interpolation was used to modify the coefficient in each single step, then by repeating the steps, a high-order polynomial function could be constructed. Zhu Zaiyu’s interpolation was mechanical, and the polynomial function constructed by this method was categorized as the type of Newton interpolation, notably in modern terms. The critical purpose of ancient Chinese calendar compilers in interpolation was to construct higher order polynomial function; crucially, Zhu Zaiyu gave a general solution to this problem.

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.

This paper studies the development of intensity schemes within the framework of the old quantum theory. It investigates how these schemes emerged in a complex process involving empirical observation, data analysis and conceptual reconfiguration and became essential tools for predicting the intensities of multiplets in the absence of a well-formed quantum theory of radiation. By applying the concept of paper tools, the study shows how intensity schemes became theoretical representations allowing both the classification and interpretation of observations and the formulation of theoretical predictions. It thereby highlights the importance of representational tools and empirical regularities within the development of the old quantum theory.

This paper provides a comprehensive summary of Johannes Kepler's research during his first tenure at Benatky, from February to June 1600. For the first time, Kepler had unrestricted access to Tycho Brahe's precise Mars observations, enabling him to test and refine his theories of planetary motion. Kepler aimed to resolve inconsistencies in Tycho’s Mars model, particularly its failure to predict parallactic observations accurately. Over the four months, he developed innovative methods, such as combining observations to triangulate distances and employing Tycho’s model as a generator of reliable heliocentric longitudes. Despite numerous mathematical errors and theoretical missteps, Kepler laid the groundwork for the revolutionary ideas he would later present in Astronomia Nova. This paper highlights Kepler’s creative and exploratory approach, his use of Tycho’s data, and the significant progress he made in understanding Mars’ orbit, even as many of his early hypotheses were ultimately discarded.