Archive for History of Exact Sciences最新文献

{"title":"Einstein on involutions in projective geometry","authors":"Tilman Sauer,&nbsp;Tobias Schütz","doi":"10.1007/s00407-020-00270-z","DOIUrl":"10.1007/s00407-020-00270-z","url":null,"abstract":"<div><p>We discuss Einstein’s knowledge of projective geometry. We show that two pages of Einstein’s Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting with particular emphasis on the infinite point. We offer a conjecture as to the probable purpose of these geometric considerations.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 5","pages":"523 - 555"},"PeriodicalIF":0.5,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00270-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44262958","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":"A study of Babylonian planetary theory III. The planet Mercury","authors":"Teije de Jong","doi":"10.1007/s00407-020-00269-6","DOIUrl":"10.1007/s00407-020-00269-6","url":null,"abstract":"&lt;div&gt;&lt;p&gt;In this series of papers I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Papers I and II were devoted to system A theory of the outer planets and of the planet Venus. In this third and last paper I will study system A theory of the planet Mercury. Our knowledge of the Babylonian theory of Mercury is at present based on twelve &lt;i&gt;Ephemerides&lt;/i&gt; and seven &lt;i&gt;Procedure Texts&lt;/i&gt;. Three computational systems of Mercury are known, all of system A. System A&lt;sub&gt;1&lt;/sub&gt; is represented by nine &lt;i&gt;Ephemerides&lt;/i&gt; covering the years 190 BC to 100 BC and system A&lt;sub&gt;2&lt;/sub&gt; by two &lt;i&gt;Ephemerides&lt;/i&gt; covering the years 310 to 290 BC. System A&lt;sub&gt;3&lt;/sub&gt; is known from a &lt;i&gt;Procedure Text&lt;/i&gt; and from Text M, an &lt;i&gt;Ephemeris&lt;/i&gt; of the last evening visibility of Mercury for the years 424 to 403 BC. From an analysis of the Babylonian observations of Mercury preserved in the &lt;i&gt;Astronomical Diaries&lt;/i&gt; and &lt;i&gt;Planetary Texts&lt;/i&gt; we find: (1) that dates on which Mercury reaches its stationary points are not recorded, (2) that Normal Star observations on or near dates of first and last appearance of Mercury are rare (about once every twenty observations), and (3) that about one out of every seven pairs of first and last appearances is recorded as “omitted” when Mercury remains invisible due to a combination of the low inclination of its orbit to the horizon and the attenuation by atmospheric extinction. To be able to study the way in which the Babylonian scholars constructed their system A models of Mercury from the available observational material I have created a database of synthetic observations by computing the dates and zodiacal longitudes of all first and last appearances and of all stationary points of Mercury in Babylon between 450 and 50 BC. Of the data required for the construction of an ephemeris synodic time intervals Δt can be directly derived from observed dates but zodiacal longitudes and synodic arcs Δλ must be determined in some other way. Because for Mercury positions with respect to Normal Stars can only rarely be determined at its first or last appearance I propose that the Babylonian scholars used the relation Δλ = Δt −3;39,40, which follows from the period relations, to compute synodic arcs of Mercury from the observed synodic time intervals. An additional difficulty in the construction of System A step functions is that most amplitudes are larger than the associated zone lengths so that in the computation of the longitudes of the synodic phases of Mercury quite often two zone boundaries are crossed. This complication makes it difficult to understand how the Babylonian scholars managed to construct System A models for Mercury that fitted the observations so well because it requires an excessive amount of computational effort to find the best possible step function in a complicated trial and error fitting process with four or five free parameters. ","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 5","pages":"491 - 522"},"PeriodicalIF":0.5,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00269-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50444750","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":"The gravitational influence of Jupiter on the Ptolemaic value for the eccentricity of Saturn","authors":"Christián C. Carman","doi":"10.1007/s00407-020-00271-y","DOIUrl":"10.1007/s00407-020-00271-y","url":null,"abstract":"<div><p>The gravitational influence of Jupiter on Saturn produces, among other things, non-negligible changes in the eccentricity of Saturn that affect the magnitude of error of Ptolemaic astronomy. The value that Ptolemy obtained for the eccentricity of Saturn is a good approximation of the real eccentricity—including the perturbation of Jupiter—that Saturn had during the time of Ptolemy's planetary observations or a bit earlier. Therefore, it seems more probable that the observations used for obtaining the eccentricity of Saturn were done near Ptolemy’s time, and rather unlikely earlier than the first century AD. Even if this is not quite a demonstration that Ptolemy used observations of his own, my argument increases its probability and practically discards the idea that Ptolemy borrowed values or observations from astronomers further back than the first century AD, such as Hipparchus or the Babylonians.\u0000</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 4","pages":"439 - 454"},"PeriodicalIF":0.5,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00271-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50444810","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":"The development of the concept of uniform convergence in Karl Weierstrass’s lectures and publications between 1861 and 1886","authors":"Klaus Viertel","doi":"10.1007/s00407-020-00266-9","DOIUrl":"10.1007/s00407-020-00266-9","url":null,"abstract":"<div><p>The history of uniform convergence is typically focused on the contributions of Cauchy, Seidel, Stokes, and Björling. While the mathematical contributions of these individuals to the concept of uniform convergence have been much discussed, Weierstrass is considered to be the actual inventor of today’s concept. This view is often based on his well-known article from 1841. However, Weierstrass’s works on a rigorous foundation of analytic and elliptic functions date primarily from his lecture courses at the University of Berlin up to the mid-1880s. For the history of uniform convergence, these lectures open up an independent branch of development that is disconnected from the approaches of the previously mentioned authors; to my knowledge, Weierstraß never explicitly referred to Cauchy’s continuity theorem (1821 or 1853) or to Seidel’s or Stokes’s contributions (1847). In the present article, Weierstrass’s contributions to the development of uniform convergence will be discussed, mainly based on lecture notes made by Weierstrass’s students between 1861 and the mid-1880s. The emphasis is on the notation and the mathematical rigor of the introductions to the concept, leading to the proposal to re-date the famous 1841 article and thus Weierstrass’s first introduction of uniform convergence.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 4","pages":"455 - 490"},"PeriodicalIF":0.5,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00266-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50506818","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":"BM 76829: A small astronomical fragment with important implications for the Late Babylonian Astronomy and the Astronomical Book of Enoch","authors":"Jeanette C. Fincke,&nbsp;Wayne Horowitz,&nbsp;Eshbal Ratzon","doi":"10.1007/s00407-020-00268-7","DOIUrl":"10.1007/s00407-020-00268-7","url":null,"abstract":"<div><p>BM 76829, a fragment from the mid-section of a small tablet from Sippar in Late Babylonian script, preserves what remains of two new unparalleled pieces from the cuneiform astronomical repertoire relating to the zodiac. The text on the obverse assigns numerical values to sectors assigned to zodiacal signs, while the text on the reverse seems to relate zodiacal signs with specific days or intervals of days. The system used on the obverse also presents a new way of representing the concept of numerical ‘zero’ in cuneiform, and for the first time in cuneiform, a system for dividing the horizon into six arcs in the east and six arcs in the west akin to that used in the Astronomical Book of Enoch. Both the obverse and the reverse may describe the periodical courses of the sun and moon, in a similar way to what is found in astronomical texts from Qumran, thus adding to our knowledge of the scientific relationship between the two cultures.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 3","pages":"349 - 368"},"PeriodicalIF":0.5,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00268-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50501813","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":"Back to the roots of vector and tensor calculus: Heaviside versus Gibbs","authors":"Alessio Rocci","doi":"10.1007/s00407-020-00264-x","DOIUrl":"10.1007/s00407-020-00264-x","url":null,"abstract":"<div><p>In June 1888, Oliver Heaviside received by mail an officially unpublished pamphlet, which was written and printed by the American author Willard J. Gibbs around 1881–1884. This original document is preserved in the Dibner Library of the History of Science and Technology at the Smithsonian Institute in Washington DC. Heaviside studied Gibbs’s work very carefully and wrote some annotations in the margins of the booklet. He was a strong defender of Gibbs’s work on vector analysis against quaternionists, even if he criticised Gibbs’s notation system. The aim of our paper is to analyse Heaviside’s annotations and to investigate the role played by the American physicist in the development of Heaviside’s work.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 4","pages":"369 - 413"},"PeriodicalIF":0.5,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00264-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47448391","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 to: What Heinrich Hertz discovered about electric waves in 1887–1888","authors":"Jed Buchwald,&nbsp;Chen-Pang Yeang,&nbsp;Noah Stemeroff,&nbsp;Jenifer Barton,&nbsp;Quinn Harrington","doi":"10.1007/s00407-020-00267-8","DOIUrl":"10.1007/s00407-020-00267-8","url":null,"abstract":"","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 2","pages":"173 - 173"},"PeriodicalIF":0.5,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00267-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50446410","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":"Hobbes’s model of refraction and derivation of the sine law","authors":"Hao Dong","doi":"10.1007/s00407-020-00265-w","DOIUrl":"10.1007/s00407-020-00265-w","url":null,"abstract":"<div><p>This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical theory presented in <i>Tractatus Opticus I</i> constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in <i>Tractatus Opticus II</i> and <i>First Draught</i>, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in <i>De Corpore</i> Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in <i>De Corpore</i> does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of <i>Tractatus Opticus I</i>. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 3","pages":"323 - 348"},"PeriodicalIF":0.5,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00265-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42526867","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":"Operator calculus: the lost formulation of quantum mechanics","authors":"Gonzalo Gimeno,&nbsp;Mercedes Xipell,&nbsp;Marià Baig","doi":"10.1007/s00407-020-00262-z","DOIUrl":"10.1007/s00407-020-00262-z","url":null,"abstract":"<div><p>Traditionally, “the operator calculus of Born and Wiener” has been considered one of the four formulations of <i>quantum mechanics</i> that existed in 1926. The present paper reviews the operator calculus as applied by Max Born and Norbert Wiener during the last months of 1925 and the early months of 1926 and its connections with the rise of the new quantum theory. Despite the relevance of this operator calculus, Born–Wiener’s joint contribution to the topic is generally bypassed in historical accounts of quantum mechanics. In this study, we analyse the paper that epitomises the contribution, and we explain the main reasons for the apparent lack of interest in Born and Wiener’s work. We argue that they did not solve the main problem for which the tool was intended, that of linear motion, because of their reluctance to use Dirac delta functions.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 3","pages":"283 - 322"},"PeriodicalIF":0.5,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00262-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47165442","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":"Pipe flow: a gateway to turbulence","authors":"Michael Eckert","doi":"10.1007/s00407-020-00263-y","DOIUrl":"10.1007/s00407-020-00263-y","url":null,"abstract":"<div><p>Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly accepted formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 3","pages":"249 - 282"},"PeriodicalIF":0.5,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00263-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42320230","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}