The treatment of observations in early astronomy

Communicated by Curtis Wilson     

Geminus and the concept of mean motion in Greco-Latin astronomy

Conclusion Geminus account of lunar motion in chapter 18 of hisIntroductio astronomiae is, in our view, an important contribution to Greco-Latin astronomy because, in attempting to reconstruct arithmetically (the parameters of) the Moon's motion in longitude, he undermines the task astronomers had hitherto set for themselves. This undermining of a commonly acknowledged view of the purpose of astronomy is articulated in a whole new set of questions concerning the nature and place of both observation and mathematical reasoning in the science of the heavens. Yet, one must not overlook the fact thatGeminus reconstruction also indicates resources for addressing these questions. Of these resources, the most powerful proved to be the idea that irregular motion could be quantified as a systematic departure from a mean motion, and the idea that observational data could be organized and structured by means of genetic arithmetical reconstructions.But, since we limit our attention to extant treatises and decline to speculate about works or parts of works that have not survived, we must say that it would takePtolemy to discern the new direction for astronomy thatGeminus opened up and to pursue it. In part, this involved straightening out the conflated conception of mean motion in chapter 18 — the qua arithmetic mean daily displacement can only be anapparent lunar motion in longitude and not one the Moonreally makes, but the same need not be true of the qua periodic mean daily displacement — and determining its proper relation to real and apparent planetary motion. Indeed,Ptolemy's genius lay, we think, in seeing that even though, in assimilating Babylonian astronomy, earlier and contemporary Greco-Latin writers betrayed a confused, inconsistent, and unsophisticated grasp of the proper role of arithmetic, geometry, and observation in astronomical argument [seeBowen 1994], the solution lay in a mathematical reconstruction of the observed celestial motions, in which mean motion played an essential role.     

A consideration of Babylonian astronomy within the historiography of science

This paper traces the reception of Babylonian astronomy into the history of science, beginning in early to mid twentieth century when cuneiform astronomical sources became available to the scholarly public. The dominant positivism in philosophy of science of this time influenced criteria employed in defining and demarcating science by historians, resulting in a persistently negative assessment of the nature of knowledge evidenced in cuneiform sources. Ancient Near Eastern astronomy (and astrology) was deemed pre- or non-scientific, and even taken to reflect a stage in the evolution of thought before the emergence of science (in ancient Greece). Two principal objections are examined: first, that the Near East produced merely practical as opposed to theoretical knowledge and, second, that astronomy was in the service of astrology and religion. As the notion of a universal scientific method has been dismantled by post-positivists and constructivists of the second half of the twentieth century, an interest in varieties of intellectual and cultural contexts for science has provided a new ground for the re-consideration of Babylonian astronomical texts as science developed here.     

Andalusian astronomy: al-Zîj al-Muqtabis of Ibn al-Kammâd

Communicated by J. North     

Transcendental philosophy and mathematical physics

This paper explores the relationship between Kant’s views on the metaphysical foundations of Newtonian mathematical physics and his more general transcendental philosophy articulated in the Critique of pure reason. I argue that the relationship between the two positions is very close indeed and, in particular, that taking this relationship seriously can shed new light on the structure of the transcendental deduction of the categories as expounded in the second edition of the Critique.     

Criticism of trepidation models and advocacy of uniform precession in medieval Latin astronomy

A characteristic hallmark of medieval astronomy is the replacement of Ptolemy’s linear precession with so-called models of trepidation, which were deemed necessary to account for divergences between parameters and data transmitted by Ptolemy and those found by later astronomers. Trepidation is commonly thought to have dominated European astronomy from the twelfth century to the Copernican Revolution, meeting its demise only in the last quarter of the sixteenth century thanks to the observational work of Tycho Brahe. The present article seeks to challenge this picture by surveying the extent to which Latin astronomers of the late Middle Ages expressed criticisms of trepidation models or rejected their validity in favour of linear precession. It argues that a readiness to abandon trepidation was more widespread prior to Brahe than hitherto realized and that it frequently came as the result of empirical considerations. This critical attitude towards trepidation reached an early culmination point with the work of Agostino Ricci (De motu octavae spherae, 1513), who demonstrated the theory’s redundancy with a penetrating analysis of the role of observational error in Ptolemy’s Almagest.     

Mogg’s celestial sphere (1813): the construction of polite astronomy

In this paper I discuss a cardboard dissected globe made in 1813 by Edward Mogg, a cartographer and map seller, to instruct children in the principles of astronomy. Since little is known about the maker or the specific object, I draw on evidence beyond the sphere itself to construct an account of how the object might have been used. In particular I address conversation as a key part of astronomical education and examine the way in which the cardboard plates of the sphere, the presentation slipcase and the accompanying booklet would have prepared young learners for polite astronomical discourse around large instruments in later life.     

A mathematical approach to cognitive processes

Summary A mathematical formalization of cognitive processes based on concepts previously given in Experientia¹ is presented. Cognitive processes are described as a set of exponentially decaying interaction probabilities determined by previous interactions between different elements and an association parameter, the inverse of the cognitive stability. The interactions occur in a cognitive string surrounded by a cognitive plasma which carries the contextual information. The complexity of a cognitive process is proportional to time.