Archive for History of Exact Sciences最新文献

In ancient China, astronomers attempted to correct mean geocentric longitude of the inner planets using planetary “Expansion–Contraction Difference” (yingsuo cha 盈縮差) to obtain the true geocentric longitude. They used the “Limit Degree” (xiandu 限度) as the independent variable for the “Expansion–Contraction Difference”. Although this idea was relatively ideal and operationally simple, the algorithm of the “Expansion–Contraction Difference” designed by ancient Chinese astronomers had significant flaws in terms of its actual computational effectiveness for calculating the position of the inner planets. The reason for this flaw is that, based on its intended purpose, the “Expansion–Contraction Difference” should be a three-variable function, including the planetary equation of center, the solar equation of center and the phase angle of the planet, and each variable has different independent variables. However, ancient Chinese astronomers attempted to simplify this complex three-variable function into a single-variable function, and such simplification was unsuccessful. Further research indicates that the starting point of the expansion phase in the “Table of Expansion–Contraction Difference” (Yingsuo Li 盈縮曆) for the inner planets in ancient Chinese astronomical systems did not accurately depict the position of the planetary perihelion. Adjusting the starting point based on the longitude can improve the accuracy to some extent. Although the special coefficients of “double it for Venus, triple it for Mercury” can enhance the accuracy of calculations on the position of the inner planets, the result is not as ideal as expected. This study highlights that within the framework of ancient Chinese planetary theory, the algorithm of the “Expansion–Contraction Difference” for the inner planets possessed inherent and irreparable flaws, resulting in significant errors in the calculation of the apparent position of the inner planets.

During the Renaissance, several scholars worked to revive the contents and methods developed by the ancient Greek mathematicians. They began their research by studying the Latin editions of the Greek classics. The problem of Apollonius is a significant case study that sheds light on the recovery and re-appropriation of the solution methods employed by Greek mathematics. In this article, I will explore both the manuscript sources and the printed editions used by the Urbino School (Federico Commandino and Guidobaldo del Monte) to solve the problem of Apollonius.

Although rarely appreciated, the collaboration that brought Felix Klein and Sophus Lie together in 1869 had mainly to do with their common interests in the new field of line geometry. As mathematicians, Klein and Lie identified with the latest currents in geometry. Not long before, Klein’s mentor Julius Plücker launched the study of first- and second-degree line complexes, which provided much inspiration for Klein and Lie, though both were busy exploring a broad range of problems and theories. Klein used invariant theory and other algebraic methods to study the properties of line complexes, whereas Lie set his eyes on those aspects related to analysis and differential equations. Much later, historians and mathematicians came to treat the collaboration between Klein and Lie as a famous early chapter in the history of transformation groups, a development often identified with Klein’s “Erlangen Program” from 1872. The present detailed account of their joint work and mutual interests provides a very different picture of their early research, which had relatively little to do with group theory. This essay shows how the geometrical interests of Klein and Lie reflected contemporary trends by focusing on the central importance of quartic surfaces in line geometry.

The general recognition of the existence of atoms and molecules occurred only at the beginning of the twentieth century. Many researchers contributed to this, but the ultimate proof of the molecular nature of matter that convinced even the last sceptics was the confirmation of Albert Einstein’s statistical-fluctuation theory of Brownian motion, a part of his comprehension of interdisciplinary atomism, by Jean Perrin’s experiments on colloidal gamboge particles. Einstein noticed a difference between the values of Avogadro’s constant derived from Perrin’s experiments and Planck’s calculation from black-body radiation. Einstein assumed the incorrectly evaluated size of the gamboge spherules to be a culprit of the difference and asked Perrin to check the assumption with additional experiments and using the viscosity formula introduced in his own dissertation. The result was a discrepancy that neither Einstein nor Perrin settled any further. In this communication, based on the survey of developments in colloid and polymer science and their comparison with relevant experiments, an explanation of the dilemma is given that now, after more than a century, proves Einstein correct. The comparison was de facto possible during his lifetime.

The article offers a general account of the genesis of the absolute differential calculus (ADC), paying special attention to its links with the history of differential geometry. In relatively recent times, several historians have described the development of the ADC as a direct outgrowth either of the theory of algebraic and differential invariants or as a product of analytical investigations, thus minimizing the role of Riemann’s geometry in the process leading to its discovery. Our principal aim consists in challenging this historiographical tenet and analyzing the intimate connection between the development of Riemannian geometry and the birth of tensor calculus.

Several artists, artisans, and mathematicians described fascinating solid bodies in the fifteenth and sixteenth centuries. The knowledge they developed on the subject was so progressive that it is considered a milestone in the history of polyhedra. In the first part of this study we analyze, from a chronological and comparative perspective, the consistent studies developed between 1460 and 1583 on those that came to be recognized as Archimedean Solids. The authors who engaged in such studies were Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Augustin Hirschvogel, an Anonymous Author who accomplished remarkable studies between 1538 and 1556, Wentzel Jamnitzer, Daniele Barbaro, Lorenz Stöer, Rafael Bombelli, and Simon Stevin. In the second part, we discuss how the revolutionary method of describing solid bodies with planar nets contributed to the rediscovery of the Archimedean Solids. We also present our interpretation of some of the studies by the Anonymous Author and our conclusions on his identity and influence on other authors.

This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics, a role that has not been taken into account in the standard histories. Radiation was perceived by the main protagonists of matrix and wave mechanics as a central lacuna in these emerging theories and continued to contribute to the theoretical development and conceptual clarification of quantum mechanics. Studying the interplay between quantum mechanics and radiation, the paper provides an account of (a) how quantum mechanics was able to connect to its empirical basis in spectroscopy and (b) how Schrödinger’s equivalence proof emerged from his explorative calculations on the emission of radiation.

The development of the statistical theory of turbulence mainly take places between 1920 and 1940, in a context where emerging theories in fluid mechanics are striving to provide results closer to experimentation and applicable to practical fluid problems. The secondary literature on the history of fluid mechanics has often emphasized the importance of the contributions of Prandtl, Taylor, and von Kármán to the closure problem of Reynolds equations for a turbulent fluid confined by walls and to the statistical description of an isotropic and homogeneous turbulent flow. During the same period, a new theory of turbulence also surfaces in France. This theory is formulated by a group of researchers led by Philippe Wehrlé (1890–1965), the director of the French National Meteorological Office (Office national météorologique, ONM), and Georges Dedebant (1902–1965), the head of ONM’s Scientific Service. Their objective is to mathematically formalize the turbulence, taking into account the atmospheric turbulence and using a theory of random functions defined from experimental concepts. However, this French theory of turbulence gradually loses international recognition after World War II. After introducing the key figures and the fundamental components of their theory, the article explores various scientific factors why their contribution was increasingly forgotten after the Second World War.

David Fabricius, a Reformed pastor in Ostfriesland, was highly regarded by Kepler as an exceptional observer, second only to Tycho Brahe. From 1596 to 1609, Fabricius engaged in extensive correspondence, exchanging numerous letters with Brahe and subsequently with Kepler. These communications also provided values for direct observations on meridian altitudes of planets and stars, as well as elongations between a planet and a star or between two stars. We provide a detailed summary of Fabricius’s observations and compare them with the prediction of twenty-first-century models. The analysis indicates that under specific conditions, his observations exhibit sub-arcminute deviations in relation to those calculated from modern theories. Our findings preliminarily indicate that Fabricius’ astronomical observational abilities were comparable to, an occasionally superior to, those of Brahe himself. We provide machine-readable tables of his observations.

The investigation of condensed matter transformations hinges on the precision of free-energy calculations. This article charts the evolution of molecular simulations, tracing their development from the techniques of the early 1960s, through the emergence of free-energy calculations toward the end of the decade, and leading to the advent of umbrella sampling in 1977. The discussion explores the inherent challenges and limitations of early simulational endeavors, such as the struggle with accurate phase-space sampling and the need for innovative solutions like importance sampling and multistage sampling methods. Taken together, the initial hurdles and subsequent adoption of advanced techniques exemplify the leap from analytical methods to effective computational strategies that enabled more reliable simulations. Further analysis of this narrative reveals the methodological breakthroughs as well as the setbacks that transformed the theoretical and practical understanding of condensed matter phenomena. A follow-up study will examine the shifts in free-energy calculations from the late 1970s into the 1980s.