Summary When dealing with philosophical questions such as the choice of a world system or the substance of heaven, some sixteenth-century astronomers, including Tycho Brahe and Christophe Rothmann, devised more accurate experimental setups so that they could refine their celestial observations. With this desire to listen to nature arose new questions, in particular that of atmospheric refractions, the understanding and resolution of which became decisive to guarantee the best accuracy. However, to solve such practical problems, it was necessary to consider (...) their philosophical and theological background, as well as the knowledge of optics inherited from the medieval period. We examine this heritage and its transmissions through the works of Peter Ramus's assistants, especially Jean Pena and Friedrich Risner. From this first survey, we try to analyse the lively debate on atmospheric refractions in the late sixteenth and early seventeenth centuries by exploring the argumentative structure, the philosophical background, and the epistemological grounds of the discourse of authors such as Tycho Brahe, Christoph Rothmann, and Johannes Kepler. (shrink)

Descartes’s most extensive discussion of the law of refraction and the shape of the anaclastic lens is contained in Rule 8 of "Rules for the Direction of the Mind". Few reconstructions of Descartes’s discovery of the law of refraction take Rule 8 as their basis. In Rule 8, Descartes denies that the law of refraction can be discovered by purely mathematical means, and he requires that the law of refraction be deduced from physical principles about natural (...) power or force, the nature of the action of light, and the behavior of light rays in a variety of transparent media. For over a century, however, there has been broad agreement that Descartes discovered the law of refraction by purely mathematical means, and that he only later provided the relevant physical rationale (via comparisons or analogies) in Dioptrics II. I execute each step in Descartes’s proposed deduction of the law of refraction and the shape of the anaclastic lens in Rule 8 and concretely show how Descartes could have discovered the law of refraction and the shape of the anaclastic by its means. Rule 8, I argue, reflects Descartes’s actual path to the discovery of the law of refraction and the shape of the anaclastic lens. (shrink)

Homer in general, and Helen in particular, were of great interest to the lyric poets. This article examines ways in which major fragments of Alcaeus, Ibycus, and Sappho select and combine aspects of the Iliadic Helen in order to pursue various poetic agendas, providing diverse perspectives on the complex issues of Helen's choice, agency, beauty, and eroticism. Since Helen, like Pandora, is a kalon kakon, it proves impossible to praise or blame her unambiguously.

A Volume in Cognition, Equity & Society: International Perspectives formally known as International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology The diversity of research in mathematics education has been addressed as both, a problem and a strength. When manifested through adherence to different intellectual roots and theoretical orientations, diversions constitute 'refractions' of mathematics education. The collection and analysis of empirical data in a study (...) are by necessity refracted through the specific analytical lens employed, as well as the aim of the study itself. Refractions can also refer to looking at old phenomena through new lenses. The chapters in this book are refracted through philosophical, political, mathematical and personal lenses by distinguished authors in the field, addressing issues about the elusive experience of doing mathematics, purification of texts, refractions, mathematics and ethnomathematics, political messages in textbook tasks, mathematics education policy debate, the political in mathematics education research, philosophy and mathematics, meanings and representations, identity of mathematical modeling, and dilemmas in the teaching of calculus. An ancient Sanskrit adage states that Knowledge is something that grows when shared, but shrinks when hoarded. Academics engaged in the generation of new Knowledge are blessed with both the time and the freedom to engage in pursuits that allow for intellectual pleasure. As a phenomenon of the Zeitgeist many have succumbed to the increased corporatization of academic work, engaging in activities for monetary and self advancement purposes. Are there any real intellectuals left in academia, a l Adorno, Bourdieu, Chomsky, Foucault, among others? This Festschrift is dedicated to academics that don't bother with self promotion or aggrandizement of themselves or their ideas in simplistic terms. (shrink)

Allocating on the basis of need is a distinguishing principle in publicly funded health care systems. Resources ought to be directed to patients, or the health program, where the need is considered greatest. In Sweden support of this principle can be found in health care legislation. Today however some domains of what appear to be health care needs are excluded from the responsibilities of the publicly funded health care system. Corrections of eye disorders known as refractive errors is one such (...) domain. In this article the moral legitimacy of this exception is explored. Individuals with refractive errors need spectacles, contact lenses or refractive surgery to do all kinds of thing, including participating in everyday activities, managing certain jobs, and accomplishing various goals in life. The relief of correctable visual impairments fits well into the category of what we typically consider a health care need. The study of refractive errors does belong to the field of medical science, interventions to correct such errors can be performed by medical means, and the skills of registered health care professionals are required when it comes to correcting refractive error. As visual impairments caused by other conditions than refractive errors are treated and funded within the public health care system in Sweden this is an inconsistency that needs to be addressed. (shrink)

Thirty years after the demise of the Soviet bloc, there still persists a rhetoric of differentiation and a discursive polarisation between the Western and the non-Western educational thinking and practices. This rhetoric overshadows a potential similarity, or homogeneity, between the dominant and several marginalised contexts. Regional, local and personal variations are prematurely attributed to fundamental, if often poorly argued, cultural differences. We seek to introduce and to preliminarily summarise the existing understandings of refraction in education and social research. Sporadically (...) used but seldom defined, the refraction metaphor appears to feature: (a) a multiplicity of viewpoints as an incentive for social research, (b) non-relativistic, scientific progress as an end value for understanding social reality, (c) a balanced approach towards homogeneity and heterogeneity in social research, and (d) a substantially historical orientation towards analysing homogeneity and heterogeneity. Education in the former socialist European countries demonstrates how heterogeneity is rhetorically overstated and how variations can be more adequately addressed by analysing refractions. (shrink)

Johannes Kepler dedicated much of his work to discover a law for the refraction of light. Unfortunately, he formulated an incorrect law. Nevertheless, it was useful for anticipating the behavior of light in some specific conditions. Some believe that Kepler did not have the elements to formulate the law that was later accepted by the scientific community, that is, the Snell–Descartes law. However, in this paper, we propose a model that agrees with Kepler’s heuristics and that is also successful (...) in anticipating the behavior of light when it passes through a surface that separates two media with different optical densities. This model adopts strategies that were recommended by Kepler in two types of analogies. The obstacles that led to the failure of the two types of analogies are presented in the article, and we argue that the model proposed here could overcome these specific obstacles. Finally, we show how the proposed model could be articulated with Kepler’s metaphysics of light. (shrink)

Despite many points of divergence, social scientists and social theorists seem united by one primary concern: to identify what it is people are doing. The thought that this might count as not only a viable but centrally important concern is grounded in a scepticism about the ability of societies’ ordinary members to reliably correctly identify their own and others’ actions. In this scepticism, such social scientists and social theorists usually situate themselves in opposition to ethnomethodologists and Peter Winch. This scepticism (...) is grounded in a belief that ordinary or competent members of societies are unreliable authorities on the identity of their own and others’ actions because they are subject to systems of sociological refraction. The idea being that ordinary members of society are systematically misled as to the identity of their actions and those of their peers because they — or their perceptions of actions — are subject to the refractive properties of ideology, or folk theories of action, and so on. In this paper, I subject to analysis this core commitment of much social science and social theory. (shrink)

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 Tractatus Opticus 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 Tractatus Opticus II and First Draught, 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 De Corpore 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 De Corpore 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 Tractatus Opticus 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. (shrink)

Throughout his career, Wes Sharrock has, following in the footsteps of Ludwig Wittgenstein, Peter Winch and Harold Garfinkel, sought to argue against accounts of the identity of an action which are the products of a social theory, a specific methodology or what Garfinkel termed formal analysis. In contrast, much of contemporary social science and social theory is grounded in a belief that ordinary or competent members of societies are unreliable authorities on the identity of their own and others’ actions because (...) they are subject to systems of sociological refraction. The idea being that ordinary members of society are systematically misled as to the identity of their actions and those of their peers because they—or their perceptions of actions—are subject to the refractive properties of (for example) ideology, or folk theories of action, and so on. In this paper, I subject to analysis this core commitment of much social science and social theory. (shrink)

PurposeThis study investigated the impact of age and myopia on visual form perception among Chinese school-age children.MethodsThis cross-sectional study included 1,074 students with a mean age of 12.1 ± 4.7 years. The mean spherical equivalence refraction of the participants was −1.45 ± 2.07 D. All participants underwent distance visual acuity, refraction measurement and local and global visual form perception test including orientation, parallelism, collinearity, holes and color discrimination tasks.ResultsThe reaction times of emmetropes were slower than those of myopic (...) and high myopic groups on both local and global discrimination tasks. A reduction in reaction times was found with increasing age on both local and global discrimination tasks. Age was significantly associated with both local and global visual perception performance after adjusting for gender, visual acuity and SER.ConclusionsThis study revealed that both local and global visual perception improve with age among Chinese children and that myopes seem to have better visual perception than emmetropes. (shrink)

In 1626, René Descartes and Claude Mydorge worked closely together on the problem of refraction, apparently discovering what is now known as the sine law of refraction. They constructed a plano-hyperbolic lens in order to test out the truth of this mathematical relationship. In 1637, Descartes finally published the sine method of determining refractions in his Dioptrique, which also demonstrated, on the basis of this relationship, that the hyperbola and ellipse were anaclastic lines (that is, that a lens (...) with their profile would refract rays perfectly to a single point) without mentioning Mydorge. Mydorge himself wrote a short manuscript on the subject of refraction and lenses, which is found in a copy among Mersenne’s papers. Scholars have usually assumed that this treatise was written as Mydorge and Descartes worked together in 1626. However, other evidence shows that only the first part of the treatise records the two men’s early collaboration. Subsequently, Mydorge and Descartes completed their arguments separately, Descartes with the help of Isaac Beeckman. (shrink)

Let AC be a ray coming from the medium DC into the medium CE, and let the density of the former to the latter be as d to e. It is asked, how should the ray ACB be directed so that it is the easiest path of all, or that (AC x d) + (CB x e) is a minimum. Let DC = l, and EC = m. It is given also that FG = f, and let AD = FC (...) = x, CG = EB = f – x. Therefore, AC = √(l2 + x2) and CB = √(m2 + f2 +x2 – 2fx). 2 It will then be the case that d√(l2 + x2) + e√(m2 + f2 + x2 – 2fx is equal to a minimum. Therefore, through my method of tangents it is the case that: (2dx/(√(l2 +x2)(AC))) + ((2ex -2ef)/ (√(m2 +f2 +x2 +2fx)(BC))) = 0. That is, it will be the case that AC/BC = dx/e(f-x). Now if we suppose that AC and BC are equal, it will be the case that f – x is to x, as d to e. Therefore, if a circle, with its center at C, is described by the ray CA or CB, AD or “x,” – the sine of the angle of incidence – will be to BE or “f – x,” – the sine of the angle of refraction – as e, the density of the medium of refraction, will be to d, the density of the medium of incidence, that is, the sines of the angles will be in reciprocal relation to the mediums or densities. (shrink)

Keats’ misgivings about science unweaving the rainbow and robbing Nature of its mystery were shared by many of contemporaries, and successive generations have been compelled to ask how this rapidly escalating knowledge of the universe would affect their understanding of themselves and the world they lived in. This is the concern of most of the essays in these two volumes: how are we to live with science and the issues scientific discoveries and propositions raise? And how has this relationship with (...) science been explored and expressed in literary works? Yet even before science became such a challenge to the imagination, an awareness of how people interact with the natural world – in terms of sickness and health, medicine, mathematics – had already been a literary subject, also reflected in a number of articles in Restoring the Mystery of the Rainbow: Literature’s Refraction of Science. In the twentieth century doubt became a crucial component of science as well as literature, and the relativism and uncertainty of quantum physics have proved fruitful to a wide range of dramatist, poets and novelists as many articles indicate. A systematic desire for objective criteria, verifiability, and conceptual frameworks has also increased the importance of methodology and of criticism: the many approaches adopted by the contributors to these volumes further point to the refraction of science in literature. (shrink)

Personal narratives in which medical students and clinicians reflect on their education and practice, or recipients of health care reflect on their journey though the system can provide valuable insights which can usefully be shared. In this paper, a medical student describes the effect of a humanities-based student-selected component on her understanding of anatomy and dissection, and a junior doctor in Iraq learns some painful lessons about medicine and society during a night shift in the casualty department.

This article explores the dialogical engagement between text and interpreter, which is shaped by the particular socio-cultural location of African American readers/hearers. It identifies some of the key issues that help to shape an African American socio-cultural context and explores their implications for biblical interpretation.