Much problem solving and learning research in math and science has focused on formal representations. Recently researchers have documented the use of unschooled strategies for solving daily problems -- informal strategies which can be as effective, and sometimes as sophisticated, as school-taught formalisms. Our research focuses on how formal and informal strategies interact in the process of doing and learning mathematics. We found that combining informal and formal strategies is more effective than single strategies. We provide a theoretical account of (...) this multiple strategy effect and have begun to formulate this theory in an ACT-R computer model. We show why students may reach common impasses in the use of written algebra, and how subsequent or concurrent use of informal strategies leads to better problem-solving performance. Formal strategies facilitate computation because of their abstract and syntactic nature; however, abstraction can lead to nonsensical interpretations and conceptual errors. Reapplying the formal strategy will not repair such errors; switching to an informal one may. We explain the multiple strategy effect as a complementary relationship between the computational efficiency of formal strategies and the sense-making function of informal strategies. (shrink)

In this autoethnographic essay, I reflect on my brief personal experiences of conducting field research on ways in which way a small group of Tibetan Buddhist monks enact a monastic total institution in Ladakh, India. More specifically, I analyze my experiences in view of the relationship between dual and nondual mind, as discussed by Henry Vyner (2002) in Anthropology of Consciousness, and use this analysis to develop preliminary insights into the ways in which a Tibetan Buddhist monastery is constituted.

In this book, a dozen distinguished scholars in the field of the history of philosophy and science investigate aspects of the commentary tradition on Aristotle's De generatione et corruptione, one of the least studied among Aristotle's treatises in natural philosophy. Many famous thinkers such as Johannes Philoponus, Albert the Great, Thomas Aquinas, John Buridan, Nicole Oresme, Francesco Piccolomini, Jacopo Zabarella, and Galileo Galilei wrote commentaries on it. The distinctive feature of the present book is that it approaches this commentary tradition (...) as a coherent whole, thereby ignoring the usual historiographical distinctions between the Middle Ages, the Renaissance, and the seventeenth century. Frans de Haas and Henk Kubbinga address the Greek commentary tradition on De generatione et corruptione. Simone van Riet's essay is devoted to the Latin version of Avicenna's third treatise of his Kitab al Shifa, which discusses Aristotle's De generatione et corruptione. James Otte traces the intricate history of the identification of the Latin translator of Aristotle's treatise as Burgundio of Pisa. The essay by John Murdoch explores the fortuna of atomistic arguments in the Latin commentary tradition. Jurgen Sarnowsky, Henk Braakhuis, and Stefano Caroti examine various themes in the commentaries that were produced by the so-called Buridan School, that is, John Buridan, Albert of Saxony, Nicholas Oresme, and Marsilius of Inghen. The article by Silvia Donati focuses on the influential commentary by the Expositor, Giles of Rome. The final essay, written by Anita Guerrini, tackles Robert Boyle's attitude in the Origin of Forms and Qualities toward such Aristotelian key concepts as forms, matter, qualities, and mixture. These essays are prefaced by a preliminary survey by Hans Thijssen of Aristotle's text, its Latin translations and its Greek, Arabic and Latin commentaries. (shrink)

The number of discriminable colours is often assumed to be of the order of several million but the extent of detectable chromatic diversity present in individual natural scenes is an open question. Here, the aim was to estimate the number of discriminable colours seen in natural scenes. Hyperspectral data were obtained from a set of natural scenes over the range 400 - 720 nm at 10 nm intervals (Nascimento et al, 2002 Journal of the Optical Society of America A 19 (...) 1484 - 1490) and the representation of each scene in CIELAB space computed for all pixels of the image. The number of discriminable colours was estimated by counting the number of unit volumes in the three-dimensional volume defined by the scene when represented in CIELAB space. We found that the number of discriminable colours estimated in a scene could vary by an order of magnitude from scene to scene, but rarely exceeded 105, indicating a limited chromatic diversity. (shrink)

The purpose of the work was to produce a framework to guide the development of meritorious clinical trial proposals. The framework consists of essential features of rigourous methodology, ethical acceptability, and a component referred to as "community context". These three domains were woven together in a checklist format under the headings of general, scientific and ethical considerations. Since texts concerning clinical trial methodology do not integrate ethics criteria and ethics guidelines do not provide detailed scientific criteria in obvious and practical (...) ways, we outline a more contemporary and comprehensive set of guidelines. (shrink)