Archive for History of Exact Sciences最新文献

In this article, we report the discovery of a new type of astronomical almanac by Joseph Ibn Waqār (Córdoba, fourteenth century) that begins at second station for each of the planets and may have been intended to serve as a template for planetary positions beginning at any dated second station. For background, we discuss the Ptolemaic tradition of treating stations and retrograde motions as well as two tables in Arabic zijes for the anomalistic cycles of the planets in which the planets stay at first and second stations for a period of time (in contrast to the Ptolemaic tradition). Finally, we consider some medieval astrological texts where stations or retrograde motions are invoked.

We examine one of the well-known mathematical works of Abraham bar Ḥiyya: Ḥibbur ha-Meshiḥah ve-ha-Tishboret, written between 1116 and 1145, which is one of the first extant mathematical manuscripts in Hebrew. In the secondary literature about this work, two main theses have been presented: the first is that one Urtext exists; the second is that two recensions were written—a shorter, more practical one, and a longer, more scientific one. Critically comparing the eight known copies of the Ḥibbur, we show that contrary to these two theses, one should adopt a fluid model of textual transmission for the various manuscripts of the Ḥibbur, because neither of these two theses can account fully for the changes among the various manuscripts. We hence offer to concentrate on the typology of the variations among the various manuscripts, dealing with macro-changes (such as omissions or additions of proofs, additional appendices or a reorganization of the text itself), and micro-changes (such as textual and pictorial variants).

By 1933, the class of generally accepted elementary particles comprised the electron, the photon, the proton as well as newcomers in the shape of the neutron, the positron, and the neutrino. During the following decade, a new and poorly understood particle, the mesotron or meson, was added to the list. By paying close attention to the names of these and other particles and to the sometimes controversial proposals of names, a novel perspective on this well-researched line of development is offered. Part of the study investigates the circumstances around the coining of “positron” as an alternative to “positive electron.” Another and central part is concerned with the many names associated with the discovery of what in the late 1930s was generally called the “mesotron” but eventually became known as the “meson” and later again the muon and pion. The naming of particles in the period up to the early 1950s was more than just a matter of agreeing on convenient terms, it also reflected different conceptions of the particles and in some cases the uncertainty regarding their nature and relations to existing theories. Was the particle discovered in the cosmic rays the same as the one responsible for the nuclear forces? While two different names might just be synonymous referents, they might also refer to widely different conceptual images.

The Jeffreys–Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, the paradox was central to the Bayesian testing methodology developed by Sir Harold Jeffreys in the late 1930s. Jeffreys showed that the evidence for a point-null hypothesis ({mathcal {H}}_0) scales with (sqrt{n}) and repeatedly argued that it would, therefore, be mistaken to set a threshold for rejecting ({mathcal {H}}_0) at a constant multiple of the standard error. Here, we summarize Jeffreys’s early work on the paradox and clarify his reasons for including the (sqrt{n}) term. The prior distribution is seen to play a crucial role; by implicitly correcting for selection, small parameter values are identified as relatively surprising under ({mathcal {H}}_1). We highlight the general nature of the paradox by presenting both a fully frequentist and a fully Bayesian version. We also demonstrate that the paradox does not depend on assigning prior mass to a point hypothesis, as is commonly believed.

In a 1936 manuscript submitted to the Physical Review, Albert Einstein and Nathan Rosen famously claimed that gravitational waves do not exist. It has generally been assumed that there was a conceptual error underlying this fallacious claim. It will be shown, through a detailed study of the extant referee report, that this claim was probably only the result of a calculational error, the accidental use of a pathological coordinate transformation.

In this paper, we try to understand what considerations and possible sources of inspiration Desargues used to formulate his concepts of involution and transversal, and to state the related theorems that are at the basis of his Brouillon project. To this end, we trace some clues which are found scattered throughout his works, we connect them together in the light of his experience and knowledge in the field of perspective, and we investigate what were his motivations within Mersenne’s academy. As a result of our research, we can safely say that were his great geometrical insight and his projective vision of space which, guided by some classical theorems, led him to these completely new concepts in the panorama of the geometry of that time that were destined to remain misunderstood for about two centuries.

In 1927, Paul Dirac first explicitly introduced the idea that electrodynamical processes can be evaluated by decomposing them into virtual (modern terminology), energy non-conserving subprocesses. This mode of reasoning structured a lot of the perturbative evaluations of quantum electrodynamics during the 1930s. Although the physical picture connected to Feynman diagrams is no longer based on energy non-conserving transitions but on off-shell particles, emission and absorption subprocesses still remain their fundamental constituents. This article will access the introduction and the initial reception of this picture of subsequent transitions (PST) by conceiving of concepts, models, and their representations as tools for the practitioners. I will argue for a multi-factorial explanation of Dirac’s initial, verbally explicit introduction: the mathematical representation he had developed was highly suggestive and already partly conceptualized; Dirac was philosophical flexible enough to talk about transitions when no actual transitions, according to the general interpretation of quantum mechanics of the time, occurred; and, importantly, Dirac eventually used the verbal exposition in the same paper in which he introduced it. The direct impact of PST on the conception of quantum electrodynamical processes will be exemplified by its reflection in diagrammatical representations. The study of the diverging ontological commitments towards PST immediately after its introduction opens up the prehistory of a philosophical debate that stretches out into the present: the dispute about the representational and ontological status of the physical picture connected to the evaluation of the perturbative series of QED and QFT.

Aristarchus’s De magnitudinis et distantiis solis et lunae was translated into Latin and printed by Federico Commandino in 1572. All subsequent editions of Aristarchus’ treatise, published by John Wallis (1688), Fortia d’ Urban (1823) and Thomas Heath (1913), followed Commandino’s work. In this article, through a philological approach to the geometric diagrams, I tracked down one of the Greek sources used by Commandino for preparing his Latin version. Commandino pays particular attention to drawing figures. This article sheds light on the interaction between mathematical skills and the drawing of geometric diagrams implemented in his Latin edition of Aristarchus’ book.