The following essay is adapted from one with the same title read to the British Society for the History of Science on 20 October 1958—the anniversary, by a striking coincidence, of the birth of W. H. Young . To his memory I dedicated the talk, and now rededicate its publication, not only because I am his daughter and of all that means, but because he invented a method, the method of monotone sequences, which shows the powerfulness of inequalities as a (...) mathematical tool supremely. (shrink)

The manuscripts of Harriot discussed in this paper are essentially rough notes marginal to his systematic treatment of algebra, of which a small part was published posthumously. The central theme is the sign-rule for multiplication; but the incidentals open up an aspect of symbolism in mathematics entirely new for the time. A more restricted aspect of the same theme was touched on by Commandino in his Euclid, quoted by Harriot as rightly blaming ‘those that thinke that minus per minus shal (...) produce plus’; Commandino's authority was Cardano, in a similarly marginal departure from his great Ars magna, the de Aliza, which Harriot also cites in the same reference. The ostensible motivation, to preserve intact the Euclidean tradition in geometry, plays a very minor role in Harriot's notes. The basic aim, to elude the fatal link with imaginaries, they do touch on. More dimly underlying the arguments are the crucial logical facets of the problem, which Harriot faced with a greater conceptual clarity, formulating in words, however, only his own conclusion: the choice of sign-rule is the user's—a fact not fully recognised by mathematicians generally until the 19th century. (shrink)

This is a companion paper to my preceding one on Harriot's experimentations in the field of the sign-rule of multiplication in algebra. Cardano had earlier attacked the conventional rule in a chapter of his De Aliza regula liber, published in 1570 as an appendix to the second edition of his Ars magna. He returned to the subject in a brief tract, published nearly a century later in his collected works as Sermo de plus et minus. Only Cardano's valid contention that (...) the standard ‘proof’ of the accustomed sign-rule was faulty made impact, in the Euclidean background to which the ‘proof’ belonged. His cause was to preserve the purity of the Euclidean tradition. It overshadows the true aim in the De Aliza chapter, but the Sermo reveals it plainly as far from retrograde: he wished to retain all the new techniques of algebra that brought in not only ‘minus’ quantities but also their square roots, and to escape the ‘impossible’ status of these last. This the rebel sign-rule did for him by making every root of a ‘minus’ just another ‘minus’. (shrink)

Torporley's ‘Congestor analyticus’, completed in 1627 in the library of the Earl of Northumberland at Petworth, was seen by Rigaud in the 1830s among the mathematical manuscript collection of the Earl of Macclesfield. Torporley's additional copy of the introductory part, preserved at Sion College, has been used for the present report. Torporley's prime objective was the presentation of some of Harriot's work. His first example concerns a classical problem in number theory. The complete solution, by an inductive process based on (...) tables of differences, is given in a few folios of the British Library collection of Harriot manuscripts. Torporley's transcription and commentary contrast forcibly today with the immediate illuminating impact of Harriot's original. (shrink)

Do the rich descriptions and narrative shapings of literature provide a valuable resource for readers, writers, philosophers, and everyday people to imagine and confront the ultimate questions of life? Do the human activities of storytelling and complex moral decision-making have a deep connection? What are the moral responsibilities of the artist, critic, and reader? What can religious perspectives—from Catholic to Protestant to Mormon—contribute to literary criticism? Thirty well known contributors reflect on these questions, including iterary theorists Marshall Gregory, James Phelan, (...) and Wayne Booth; philosophers Martha Nussbaum, Richard Hart, and Nina Rosenstand; and authors John Updike, Charles Johnson, Flannery O'Connor, and Bernard Malamud. Divided into four sections, with introductory matter and questions for discussion, this accessible anthology represents the most crucial work today exploring the interdisciplinary connections between literature, religion and philosophy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Invention of Art History in Ancient Greece: Religion, Society, and Artistic RationalisationJohn C. McEnroeJeremy Tanner. The Invention of Art History in Ancient Greece: Religion, Society, and Artistic Rationalisation. Cambridge Classical Studies. Cambridge: Cambridge University Press, 2006. xvi + 331 pp. 62 black-and-white ills. Cloth, $99.In his introductory chapter, Jeremy Tanner quotes J. J. Winckelmann's eighteenth-century description of the Apollo Belvedere: "Among all the works of (...) antiquity which have escaped destruction, the statue of Apollo is the highest ideal of art... In the presence of this miracle of art, I forget all else, and I myself take a lofty position for the purpose of looking on it in a worthy manner" (6). Tanner makes it clear that Winckelmann, widely regarded as the founder of modern art history, was not simply recording a personal reaction. Instead, Winckelmann's notion of artworks as autonomous objects of aesthetic experience was deeply rooted in the transformation of the basic institutions of art during [End Page 423] the Enlightenment. These included changes in patronage and production, and the introduction of the new philosophy of aesthetics. The new conception of art as a form of individual expression was tied not only to the notion of personal liberty but also to the growing obsession with national identities. Winckelmann's rapturous response to the Apollo Belvedere is understandable only as a part of this broader set of social and intellectual currents.The kinds of art history that Tanner is concerned with in this book are quite distinct from Winckelmann's and belonged to profoundly different cultural networks. Tanner lays out three goals for the book: first, to analyze art as a form of material culture that was both shaped by society and, in turn, helped to shape society; second, to develop an analytic framework for comparing classical and modern art history without conflating the two; third, to move art history to the explanatory level, exploring not only how classical art developed over the long term, but why. Tanner's approach is sociological, drawing especially on the work of the once influential American sociologist, Talcott Parsons (1902–1979) and the semiotics of Charles Sanders Peirce (1839–1914). As a result, Tanner shifts from the traditional focus on artists to the interaction of artists, patrons, and viewers.In chapter 2 ("Rethinking the Greek Revolution," 31–96) Tanner addresses one of the central problems in art history, the apparently sudden transformation from abstraction to naturalism in Greek art in the beginning of the fifth century B.C.E., famously described by E. H. Gombrich as "the Greek Revolution." Why, after generations of continuity within the Archaic style, did Greek artists, alone among the artists working in the broader Middle Eastern tradition, develop the naturalistic style of art represented in, for example, Polykeitos's Doryphoros? For Gombrich, the "Greek Revolution" was fundamentally a matter of artists breaking from ingrained patterns and attempting, as individuals, to match the appearance of their statues with the natural world. Other writers, including several contributors to Diana Buitron-Oliver, ed., The Greek Miracle: Classical Sculpture from the Dawn of Democracy (Washington, D.C., 1992), have described the change in terms even more deeply grounded in Winckelmann: the revolution in style was a product of the birth of individuality and personal freedom that accompanied the birth of democracy in classical Greece.Tanner is specifically concerned with what the "Greek Revolution" meant for cult statues. While he rejects the simplistic equation democracy = naturalism as an explanatory device, Tanner nevertheless holds that political changes, marked by the Kleisthenic reforms, had profound effects on both the makers and the viewers of art. Through most of the sixth century B.C.E., the aristocracy was in firm control of religious art. Through the forms of the kouros and kore, aristocrats merged their identities with those of the gods. Through their sponsorship and control of the sanctuaries, they controlled the access ordinary viewers had to images of the sacred. While the immediate effects of the Kleisthenic reforms may have been more complex than Tanner implies, over the course of a generation the authority of the traditional aristocracy declined, and the sponsorship of cult images was... (shrink)

This volume contains comprehensive and scholarly editions of three Anglo-Saxon saints' lives: Birinus of Dorchester-on-Thames, Kenelm of Winchcombe, and Rumwold of Buckingham. Rosalind Love provides the Latin texts, based on all known manuscript versions, with a facing-page English translation, together with full annotation and a historical introduction which sets these works in the context of the development of hagiographical literature. Dr Love traces the growth and changes in hagiographical writing, one of the most important genres of medieval literature and (...) essential to the understanding of the religious mentality of the Middle Ages, and shows how the eleventh century saw significant new directions emerge in the cult of the saints and the writing of saints' lives. (shrink)

“Respirators, not furnished” is a phrase that appears in Muriel Rukeyser’s poetic sequence The Book of the Dead, addressed to the catastrophic silicosis epidemic that afflicted miners of the Hawk’s Nest Tunnel. Using the example of Rukeyser’s text, which I taught as part of a course on extractionism during the early months of the pandemic and again in its aftermath, the essay asks what it means to read on the precipice of disaster and what disasters of reading are threatened by (...) our current moment. (shrink)

It is traditionally believed that cerebral activation (the presence of low voltage fast electrical activity in the neocortex and rhythmical slow activity in the hippocampus) is correlated with arousal, while deactivation (the presence of large amplitude irregular slow waves or spindles in both the neocortex and the hippocampus) is correlated with sleep or coma. However, since there are many exceptions, these generalizations have only limited validity. Activated patterns occur in normal sleep (active or paradoxical sleep) and during states of anesthesia (...) and coma. Deactivated patterns occur, at times, during normal waking, or during behavior in awake animals treated with atropinic drugs. Also, the fact that patterns characteristic of sleep, arousal, and waking behavior continue in decorticate animals indicates that reticulo-cortical mechanisms are not essential for these aspects of behavior. (shrink)

It is often assumed that engaging in a one‐on‐one dialogue with a tutor is more effective than listening to a lecture or reading a text. Although earlier experiments have not always supported this hypothesis, this may be due in part to allowing the tutors to cover different content than the noninteractive instruction. In 7 experiments, we tested the interaction hypothesis under the constraint that (a) all students covered the same content during instruction, (b) the task domain was qualitative physics, (c) (...) the instruction was in natural language as opposed to mathematical or other formal languages, and (d) the instruction conformed with a widely observed pattern in human tutoring: Graesser, Person, and Magliano's 5‐step frame. In the experiments, we compared 2 kinds of human tutoring (spoken and computer mediated) with 2 kinds of natural‐language‐based computer tutoring (Why2‐Atlas and Why2‐AutoTutor) and 3 control conditions that involved studying texts. The results depended on whether the students' preparation matched the content of the instruction. When novices (students who had not taken college physics) studied content that was written for intermediates (students who had taken college physics), then tutorial dialogue was reliably more beneficial than less interactive instruction, with large effect sizes. When novices studied material written for novices or intermediates studied material written for intermediates, then tutorial dialogue was not reliably more effective than the text‐based control conditions. (shrink)

The ratification of the United Nations Convention on the Rights of the Child (UNCRC) demands that those participating nations, adopt the aims of the convention as state responsibilities toward their child citizens. The central premise of the convention is clear: that it is the right of all children to develop to their full potential. The authors propose six basic interdependent developmental requirements if the child is to reach ‘full potential’. Without prioritising any one need, but instead concentrating on the facilitation (...) of complete care of the child, the paper aims to examine how the UNCRC may finally be realised. This is achieved by highlighting several key situations and associated factors, which contribute to deficient care. Whilst the factors leading to the creation of such situations are often culturally specific, the consequences for the child, and the implications for care providers (parents, aid agencies, and policy makers), are often very similar within and between continents. (shrink)