Greek angles from Babylonian numbers

Models of planetary motion as observed from Earth must account for two principal anomalies: the nonuniform speed of the planet as it circles the zodiac, and the correlation of the planet’s position with the position of the Sun. In the context of the geometrical models used by the Greeks, the practical difficulty is to somehow isolate the motion of the epicycle center on the deferent from the motion of the planet on its epicycle. One way to isolate the motion of the epicycle center is to determine the longitude and time of oppositions of the planet with the mean Sun. A Greek astronomer might have realized that the predictions of mean oppositions by Babylonian models could serve as useful proxies for real empirical observations. It is shown that a Greek astronomer with a reasonable understanding of Babylonian System A models for the outer planets and the Sun–Moon could have used those models to estimate approximate values for the eccentricity e and longitude of apogee A required for geometrical models. The same method would work for the inner planets if conjunctions were observable, but they are not, and the variation of the observable synodic events—first and last morning and evening visibilities—is dominated more by the motion of the planet in latitude than the nonuniform motion of the epicycle center.     

A New Role for the Hippopede of Eudoxus

The geometry of the alternative reconstruction of Eudoxan planetary theory is studied. It is shown that in this framework the hippopede acquires an analytical role, consolidating the theorys geometrical underpinnings. This removes the main point of incompatibility between the alternative reconstruction and Simpliciuss account of Eudoxan planetary astronomy. The analysis also suggests a compass and straight-edge procedure for drawing a point by point outline of the retrograde loop created by any given arrangement of the three inner spheres. (Received March 20, 2001)     

A Study of Babylonian Observations of Planets Near Normal Stars

The present paper is an attempt to describe the observational practices behind a large and homogeneous body of Babylonian observation reports involving planets and certain bright stars near the ecliptic (Normal Stars). The reports in question are the only precise positional observations of planets in the Babylonian texts, and while we do not know their original purpose, they may have had a part in the development of predictive models for planetary phenomena in the second half of the first millennium B.C. The paper is organized according to the following topics: (I) Sections 1–3 review the format of the observations and the texts in which they are found; (II) Sections 4–6 discuss the composition of the Normal Star list; (III) Sections 7–8 concern the orientation of the reported celestial directions from star to planet; (IV) Sect. 9 concerns the relationship between the reported distances and the actual angular distances between planet and star; and (V) Sect. 10 discusses the reports of planetary stations, which are the most common reports giving precise locations of planets when they are not near their closest approach to stars, and draws some brief general conclusions about the utility of the Babylonian observations for estimating planetary longitudes and calibrating models in antiquity.I wish to thank Lis Brack-Bernsen, John Britton, Peter Huber, Hermann Hunger, Teije de Jong, Norbert Roughton, John Steele, and Noel Swerdlow for comments on drafts of the paper, for access to work before publication, and for help in various forms.     

The Keplerian and mean motions. A geometrical study

Summary The point of reference to which the mean motion of the planets against Keplerian motion can optimally be applied and the behavior of its astronomical functions are analysed mathematically. To the results of our problem, which was solved by the first and second laws of Kepler, virtually all models of planetary motions seem to be related.     

Galileo and Descartes on Copernicanism and the cause of the tides

Galileo and Descartes were on the front lines of the defense of Copernicanism against theological objections that took on special importance during the seventeenth century. Galileo attempted to overcome opposition to Copernicanism within the Catholic Church by offering a demonstration of this theory that appeals to the fact that the double motion of the earth is necessary as a cause of the tides. It turns out, however, that the details of Galileo's tidal theory compromise his demonstration. Far from attempting to provide a demonstration of the earth's motion, Descartes ultimately argued that his system is compatible with the determination of the Church that the earth is at rest. Nonetheless, Descartes's account of the cause of the tides creates difficulty for this argument.     

Henry Dresser and Victorian Ornithology: Birds,Books and Business

The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. Part I of this paper contains a discussion of how, for Kepler, the circle also functions in geometry to select the basic polygons, in music to select the basic harmonies, and in astrology to select the basic aspects. In Part II, the discussion centres on the question of how the replacement of circular planetary orbits by elliptical orbits in the Astronomia Nova of 1609 affected Kepler's metaphysical commitment to celestial circularity that was made manifest in the derivation of planetary radii in the Mysterium Cosmographicum of 1596. The answer is found in the new and much more accurate derivation of both the planetary radii and their eccentricities in the Harmonice Mundi of 1619. It is the relationship of the diurnal movements of single planets at aphelion and perihelion to specific musical consonances that provides the first step. Then, in the second step, these ratios are ‘tempered’ so that all six planets can provide a heavenly choir. The third and final step employs the ‘mean period’, which is obtained directly from the tempered ratios given by musical theory and diurnal (not annual) motion, in the 3/2 power law to calculate the planetary radii and eccentricities with amazing accuracy. Thus the ellipse is necessary to supply the variation in angular velocities that contain the Creator's archetypal celestial circularity.     

Epicycles,eccentrics, and ellipses: The predictive capabilities of Copernican planetary models

A theoretical analysis of the potential accuracy of early modern planetary models employing compound circles suggests that fairly simple extensions of those models can be sufficiently accurate to meet the demands of Tycho Brahe's observations in both ecliptic longitude and latitude. Some of these extensions, such as the substitution of the true sun for the mean sun, had already been taken by Kepler before he abandoned circular models. Other extensions, involving one or two extra epicycles, were well within the mathematical capabilities of sixteenth-century and seventeenth-century astronomers. Hence neither the failure of astronomers before Kepler to correct errors in planetary positions nor Kepler's decision to abandon circular models was a consequence of inherent limitations in those models.     

Testing galaxy formation and dark matter with low surface brightness galaxies

Galaxies are the basic structural element of the universe; galaxy formation theory seeks to explain how these structures came to be. I trace some of the foundational ideas in galaxy formation, with emphasis on the need for non-baryonic cold dark matter. Many elements of early theory did not survive contact with observations of low surface brightness galaxies, leading to the need for auxiliary hypotheses like feedback. The failure points often trace to the surprising predictive successes of an alternative to dark matter, the Modified Newtonian Dynamics (MOND). While dark matter models are flexible in accommodating observations, they do not provide the predictive capacity of MOND. If the universe is made of cold dark matter, why does MOND get any predictions right?     

基于图论的六挡自动变速器的方案分析

基于图论知识,发展一套系统化的设计理论,用于自动变速器的设计研究。根据行星齿轮系的基本特性及理论,列出应用于六挡自动变速器的三排行星齿轮系目录,即齿轮系与其对应图画间具有一对一的对应关系,再利用约束条件删除不符的图画。并根据基于图论的基本回路的方法,对方案进行运动分析。该方法较传统方法方便、直观,有效利用电脑实现程序化,可发展为系统化的理论,是研究自动变速器的有利工具。     

Re-situating fieldwork and re-narrating disciplinary history in global mega-geomorphology

In 1985, more than thirty geomorphologists, planetary scientists, and remote sensing specialists gathered at a conference center in Oracle, Arizona, to discuss an emerging area of research that they called “mega-geomorphology.” Building on a conference of the same name held in London in 1981, they argued that new techniques of remote sensing and insights emerging from the study of extraterrestrial planets had created opportunities for geomorphology to broaden its spatial and temporal scope. This new approach was, however, neither unproblematic nor uncontested. In the discussions around mega-geomorphology that took place in the mid-1980s, the perceived conflict between the use of remote-sensing techniques to observe phenomena on vast spatial scales, on one hand, and the disciplinary centrality of fieldwork and field experience to geomorphology, on the other, was a recurrent theme. In response, mega-geomorphologists attempted to re-situate fieldwork and re-narrate disciplinary histories in such a way as to make remote sensing and planetary science not only compatible with geomorphological traditions but also means of revitalizing them. Only partially successful, these attempts reveal that the process of adopting a planetary perspective in geomorphology, as in other earth sciences, was neither straightforward nor inevitable. They also show how the field and fieldwork could remain central to geomorphology while also being extensively revised in light of new technical possibilities and theoretical frameworks.     

Aspects of Aristotelian statics in Galileo's dynamics

This paper examines geometrical arguments from Galileo's Mechanics and Two New Sciences to discern the influence of the Aristotelian Mechanical Problems on Galileo's dynamics. A common scientific procedure is found in the Aristotelian author's treatment of the balance and lever and in Galileo's rules concerning motion along inclined planes. This scientific procedure is understood as a development of Eudoxan proportional reasoning, as it was used in Eudoxan astronomy rather than simply as it appears in Euclid's Elements. Topics treated include the significance of the circle in Galileo's demonstrations, the substitution of rectilinear elements for heterogeneous factors like weight and curvilinear distance, and the way in which elements of a motion are used to measure other elements of the same motion. The indirectness of Galileo's proofs, his conception of speed as relative and comparative, and the meaning of his concept of moment all come into clearer focus. Conclusions are drawn about Galilean idealization, and also about the contrast of literal versus figural modes of explanation in Galileo's science.     

On the necessary truth of the laws of classical mechanics

The idealization of primitive mechanical experience is shown to lead to four mutually related formulations of classical mechanics based on connections, action at a distance, stresses, and collisions. For a given structure of spacetime and a given characterization of mechanical systems, fundamental laws (including Newton's law of acceleration and d’Alembert's principle) are derived from a few general principles regarding the comprehensibility of motion. Special emphasis is placed on the “secular principle,” according to which the evolution of a system at the relevant time scale should not depend on finer details of the applied forces.     

Space-filling molecular models of oxiranes (epoxides)

Summary An oxirane unit was constructed from aluminium spheres to fit the popular CPK system of space-filling molecular models.The author thanks W. Arnold and F. Stehlin of the Institut für Organische Chemie for their careful machining of the aluminium models. Financial support by the Swiss National Science Foundation (project No. 2.837-0.80) is gratefully acknowledged.     

T. C. Chamberlin,Climate Change,and Cosmogony

This paper examines the life and work of T. C. Chamberlin, a prominent glacial geologist who developed an interest in interdisciplinary earth science. His work on the geological agency of the atmosphere informed his understanding of climate change and other terrestrial phenomena and led him to propose a new theory of the formation of the Earth and the solar system.Chamberlin's graduate seminar at the University of Chicago in 1896 contained all the themes that informed his research programme over the next three decades. These included the carbon dioxide theory of climate change in its relationship to diastrophism and oceanic circulation, the role of water vapour feedbacks in the climate system, and the relationship between multiple glaciations, the climate system, and the formation of the planet.     

Genera and species vs. laws of nature two epistemic frameworks and their respective ideal worlds

This paper seeks to exhibit and explain, by way of comparison, two ideal kinds of knowledge: knowledge based on classifications according to genera and species, as in Aristotelianism and common sense, and scientific knowledge based on the application of laws of nature. I will proceed by attempting (1) to determine the role that presuppositions play in knowledge in general by means of the distinction between content and form; (2) to describe and explain the main features of both ideal forms of knowledge; and, finally, (3) to analyze the relation between these two forms of knowledge as it is presented in Eddington's celebrated discussion of the “two tables”. I will be critical of the widespread view that modern science is the correct form of knowledge, and that common sense is merely an illusion.     

Unification, explanation, and the composition of causes in Newtonian mechanics

William Whewell's philosophy of scientific discovery is applied to the problem of understanding the nature of unification and explanation by the composition of causes in Newtonian mechanics. The essay attempts to demonstrate: (1) the sense in which ‘approximate’ laws (e.g. Kepler's laws of planetary motion) successfully refer to real physical systems rather than to (fictitious) idealizations of them; (2) why good theoretical constructs are not badly underdetermined by observation; and why, in particular, Newtonian forces are not conventional and (3) how empiricist arguments against the existence of component causes, and against the veracity of the fundamental laws, are flawed.