Archive for History of Exact Sciences最新文献

{"title":"Some remarks on Husserl’s Doppelvortrag","authors":"Davide Emilio Quadrellaro","doi":"10.1007/s00407-026-00367-x","DOIUrl":"10.1007/s00407-026-00367-x","url":null,"abstract":"<div><p>We provide an interpretation of Husserl’s 1901 <i>Doppelvortrag</i> in Göttingen from the viewpoint of the modernist transformation of mathematics. We emphasise the dialectical aspects of the <i>Doppelvortrag</i>, and especially the underlying conflict between <i>abstraction</i> and <i>intuition</i>, which often resurfaces in Husserl’s philosophy. We focus on three key aspects: (1) the relation between Husserl’s idea of pure logic and Hilbert’s axiomatic method; (2) the concept of <i>Definitheit</i> and the early developments of model theory; (3) the nature of imaginary numbers and their justification in arithmetic and algebra. We stress that, in contrast to Hilbert’s Completeness Axiom from his <i>Grundlagen</i>, Husserl viewed the <i>Definitheit</i> as a statement requiring a proof, and he believed that one could be provided in the cases of arithmetic and geometry.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-026-00367-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147938143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How did Zu Chongzhi calculate (pi =355/113)?: a reconstruction of an ancient Chinese algorithm for fractional approximation","authors":"Wei Chen,&nbsp;Anjing Qu","doi":"10.1007/s00407-026-00365-z","DOIUrl":"10.1007/s00407-026-00365-z","url":null,"abstract":"<div><p>In the early fifth century AD, ancient Chinese calendar-makers developed an algorithm for calculating astronomical constants, which functioned efficiently for deriving precise fractional approximations and is mathematically equivalent to the continued fraction algorithm. A series of highly accurate fractions could be easily obtained by repeatedly applying this algorithm, which suggested that these highly accurate fractions did not appear randomly or coincidentally in ancient Chinese mathematics or calendar systems; however, was established using a systematic method. Based on historical and mathematical analysis, it is highly probable that Zu Chongzhi 祖冲之 (429–500) derived his famous approximation of <span>(pi )</span>(<span>(pi =355/113)</span>, as known as the Zu ratio 祖率) using this algorithm.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kepler’s early applications of the distance law: manuscript evidence and the emergence of a universal physical principle","authors":"Christián C. Carman","doi":"10.1007/s00407-026-00370-2","DOIUrl":"10.1007/s00407-026-00370-2","url":null,"abstract":"<div><p>This paper examines Kepler’s earliest applications of the distance law in a group of manuscripts from 1601 to 1602. It argues that these texts reveal not merely a technical innovation but a methodological transformation: Kepler assumed that a physically grounded hypothesis must hold across the entire celestial system. The study reconstructs several early extensions of the law—to the Earth, to lunar theory, and to the relation between terrestrial eccentricity and the length of the year—showing how rapidly he treated the principle as universally valid. It also offers a systematic presentation of these manuscript episodes and proposes refinements to the chronology of Pulkovo XIV.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction: Planetary first and last visibility in ancient astronomy: a cross-cultural comparison","authors":"Zhenhua Wang,&nbsp;Ruilin Zhang,&nbsp;Quan Tang","doi":"10.1007/s00407-026-00368-w","DOIUrl":"10.1007/s00407-026-00368-w","url":null,"abstract":"","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Peacock’s principle as a conservative strategy","authors":"Iulian D. Toader","doi":"10.1007/s00407-026-00366-y","DOIUrl":"10.1007/s00407-026-00366-y","url":null,"abstract":"<div><p>The view that Peacock’s principle of permanence has been invalidated by Hamilton’s introduction of non-commutative algebras has always seemed rather odd, in light of Peacock’s favorable reception of quaternions and the endorsement of his principle by Hamilton. But the view is not just odd; it is incorrect. In order to show this, I critically analyze Peacock’s attempts to reject possible exceptions to his principle, like the factorial function and an infinite series due to Euler. Then I argue that the principle of permanence is best understood as an expression of a conservative strategy, philosophically grounded in Hume’s conception of the laws of reasoning, which advocates their preservation to the furthest extent possible, thus allowing exceptions, i.e., violations of these laws. On this reading, non-commutative multiplication does not invalidate Peacock’s principle, if the reasons for violating commutativity outweigh the reasons for its preservation. Finally, I show that Hamilton followed a conservative strategy of precisely this sort when he developed his quaternionic calculus.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-026-00366-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Ptolemy’s improvement of the parameters of the latitude models for the superior planets","authors":"Gonzalo L. Recio,&nbsp;Christián C. Carman","doi":"10.1007/s00407-026-00364-0","DOIUrl":"10.1007/s00407-026-00364-0","url":null,"abstract":"<div><p>In <i>Almagest</i> XIII, Ptolemy explains his latitude theories for the superior and inferior planets. There he provides, among other things, the values for the inclinations of the planets eccentres and epicycles. The methods and observations Ptolemy uses to calculate the values of these inclinations are highly problematic and are one of the main reasons for the predictive difficulties of the models. This is because they yield a final value for the inclinations of the eccentre and epicycle which are, in many cases, grossly incorrect. The latitude models for the superior planets in the <i>Planetary Hypotheses</i> signify a definitive improvement in the sense that they provide very accurate inclinations for both the eccentre and the epicycle. The main purpose of the paper is to present a simple and plausible explanation of how Ptolemy could have arrived at the accurate values he provides in the <i>Planetary Hypotheses</i>. As we will show, the method we propose is consistent with Ptolemy’s general methodology when facing similar problems. Also, and crucially, we will show that they relate to the work he had done in the <i>Almagest</i> on the latitude tables. Finally, we will show that in the years he was probably starting to work in his post-<i>Almagest</i> modifications, he had at his disposal potential observations which were very well suited to our method.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Planetary first and last visibility in ancient astronomy: a cross-cultural comparison","authors":"Zhenhua Wang,&nbsp;Ruilin Zhang,&nbsp;Quan Tang","doi":"10.1007/s00407-026-00361-3","DOIUrl":"10.1007/s00407-026-00361-3","url":null,"abstract":"<div><p>The prediction of planetary First/Last Visibility features prominently in the observational records and calendrical computations of many ancient cultures, although the ways in which these events were conceptualised and operationalised differ substantially. Focusing on the First/Last Visibility of the five classical planets (Venus, Jupiter, Mercury, Mars, and Saturn), this article reviews and compares the relevant textual evidence and computational procedures in Babylonian, Greek, Arabic, Indian, and Chinese traditions. A cross-cultural analysis shows that these visibility events were widely recognised as salient nodes within planetary synodic cycles across the traditions examined. Babylonian sources, however, tend to treat them as observationally significant without articulating a single, explicit and general criterion for judgement. In Greek and Arabic astronomy, shaped by geometric modelling, visibility was commonly handled through dedicated procedures adjunct to core positional computation, with careful attention to geographic latitude, seasonal geometry, and planetary ecliptic latitude. By contrast, Indian and Chinese approaches, largely procedure-based and algorithmic, typically treated First/Last Visibility as special cases within broader planetary computations and often did not incorporate planetary ecliptic latitude as an explicit parameter. Nevertheless, with the partial exception of the Babylonian material, the traditions surveyed most consistently relied on the Sun–planet separation—usually ecliptic elongation, and in some cases separation expressed in equatorial coordinates—to decide visibility. Comparison with modern visibility theory and our numerical simulations further indicates that elongation-based criteria are strongly conditioned by geographic latitude and seasonal observing geometry. Although such criteria are not highly precise, they are practical and intelligible, and in many historical contexts they were adequate for the predictive needs of working astronomers and calendar-makers. By clarifying both shared assumptions and systematic divergences in these traditions, this study contributes a comparative framework for understanding how visibility phenomena were incorporated into ancient astronomical theory and practice.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating illusion: Panofsky and others on perspective","authors":"J. V. Field","doi":"10.1007/s00407-026-00358-y","DOIUrl":"10.1007/s00407-026-00358-y","url":null,"abstract":"<div><p>In 1927, the eminent art historian Erwin Panofsky published an article about linear perspective, the history of its use in paintings, the principles underlying constructions and whether perspective could be regarded as a ‘symbolic form’, that is, as a subject in itself. Today his article, which is still widely read among historians of art, seems inadequate in several ways, notably in its treatment of what would now be regarded as the relevant mathematics and optics, and some matters of history of art; moreover, to today’s readers the article also raises questions not only about how the treatment of history of the sciences has developed in the last century but also about what we would now consider an acceptable approach to writing on perspective, a subject that does not wholly belong to either history of science or to history of art.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-026-00358-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mayer’s theory of gas condensation (1937–1970): phase transitions and mathematical reasoning","authors":"Martin Niss","doi":"10.1007/s00407-026-00359-x","DOIUrl":"10.1007/s00407-026-00359-x","url":null,"abstract":"<div><p>We study the origins and reception of the statistical mechanical theory of gas condensation put forward by the American scientist Joseph E. Mayer in 1937. Promising the first single and unified treatment of the gas and liquid phases of molecule assemblies on a solid theoretical footing, the theory was praised by Mayer’s contemporaries as a breakthrough. Mayer’s mathematical reasoning was, however, soon the subject of much debate, and while some of his peers accepted his reasoning, others questioned its validity on various grounds. With the intermission of World War II, it was first in the 1950s that the valid parts of the reasoning could be separated from the questionable ones, which meant that most physicists dropped the theory as a research object. The paper addresses Mayer’s mathematical reasoning and its reception, as well as the impact of the theory on physics. The theory helped put the problem of a statistical mechanical theory of phase transitions on physicists’ agenda as well as highlight the importance of mathematical sound reasoning in this area.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-026-00359-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The rapid arrival of Josiah Willard Gibbs’s Elementary Principles in Statistical Mechanics in European university libraries","authors":"Hector Giacomini","doi":"10.1007/s00407-026-00362-2","DOIUrl":"10.1007/s00407-026-00362-2","url":null,"abstract":"<div><p>This note offers an overview of how Josiah Willard Gibbs’s <i>Elementary Principles in Statistical Mechanics</i>, published simultaneously in London and New York in 1902, spread through European university libraries. Information gathered through direct contacts with numerous academic libraries reveals an unexpectedly rapid material diffusion beginning on April 1, 1902. This early propagation can be explained by several channels: presentation copies sent by Yale University to leading universities, personal mailings by Gibbs himself to prominent scientists, and the distribution of copies by the American publisher to major scientific journals.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}