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.

For the scholastic philosopher William Ockham (c. 1285-1347), there are three kinds of heresy. The first, and most unmistakable, is an outright denial of the truths of faith. Another is so obvious that a very simple person, even if illiterate, can see how it contradicts Divine Scripture. The third kind of heresy is less clear cut. It is perceptible only after long deliberation and only to individuals who are learned, and well versed in Scripture. It is this third variety of (...) heresy that J.M.M.H. Thijssen addresses in Censure and Heresy at the University of Paris, 1200-1400. The book documents 30 cases in which university trained scholars were condemned for disseminating allegedly erroneous opinions in their teaching or writing, and focuses particularly on four academic censures that have occupied prominent positions in the historiography of medieval philosophy. Thijssen grants central importance to a number of questions so far neglected by historians regarding judicial procedures, the authorities supervising the orthodoxy of teaching, and the effects of condemnations on the careers of the accused. He also places still current questions regarding academic freedom and the nature of doctrinal authority into their medieval contexts. (shrink)

The aim of this paper is to contribute to the clarification of concepts usually found in books on quantum mechanics, aided by knowledge from the field of the theory of operators in Hilbert space. Frequently the basic distinction between bounded and unbounded operators is not established in books on quantum mechanics. It is repeatedly overlooked that the condition for an unbounded operator to be symmetric (Hermitian) is not sufficient to make it self-adjoint. To make things worse, nearly all operators in (...) quantum mechanics are unbounded. Often one finds statements such as: For any linear operator A we can write a Hermitian operator HA=(A+A+)/2, where Hermitian is thought to mean self-adjoint. Along these lines, self-adjointness of the momentum operator in generalized coordinates, taken from that expression, is questioned. In particular, the redescription in terms of spherical polar coordinates and its implications for the eventual loss of self-adjointness of the momenta conjugate to them are studied. (shrink)

The construction of the quantum-mechanical Hamiltonian by canonical quantization is examined. The results are used to enlighten examples taken from slow nuclear collective motion. Hamiltonians, obtained by a thoroughly quantal method (generator-coordinate method) and by the canonical quantization of the semiclassical Hamiltonian, are compared. The resulting simplicity in the physics of a system constrained to lie in a curved space by the introduction of local Riemannian coordinates is emphasized. In conclusion, a parallel is established between the result for various coordinates (...) and a proposed procedure for quantizing the semiclassical Hamiltonian for a single coordinate. (shrink)

This book is a collection of papers on the metaphysics and natural philosophy of John Buridan (ca. 1295-1361), one of the most innovative and influential ...

OBJECTIVE: To report and analyse the pattern of end-of-life decision making for terminal Chinese cancer patients. DESIGN: Retrospective descriptive study. SETTING: A cancer clinical trials unit in a large teaching hospital. PATIENTS: From April 1992 to August 1997, 177 consecutive deaths of cancer clinical trial patients were studied. MAIN MEASUREMENT: Basic demographic data, patient status at the time of signing a DNR consent, or at the moment of returning home to die are documented, and circumstances surrounding these events evaluated. RESULTS: (...) DNR orders were written for 64.4% of patients. Patients in pain (odds ratio 0.45, 95% CI 0.22-0.89), especially if requiring opioid analgesia (odds ratio 0.40, 95% CI 0.21-0.77), were factors associated with a higher probability of such an order. Thirty-five patients were taken home to die, a more likely occurrence if the patient was over 75 years (odds ratio 0.12, 95% CI 0.04-0.34), had children (odds ratio 0.14, 95% CI 0.02-0.79), had Taiwanese as a first language (odds ratio 6.74, 95% CI 3.04-14.93), or was unable to intake orally (odds ratio 2.73, 95% CI 1.26-5.92). CPR was performed in 30 patients, none survived to discharge. CONCLUSIONS: DNR orders are instituted in a large proportion of dying Chinese cancer patients in a cancer centre, however, the order is seldom signed by the patient personally. This study also illustrates that as many as 20% of dying patients are taken home to die, in accordance with local custom. (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)

J. M. M. H. Thijssen - Nicolas d'Autrécourt et la Faculté des Arts de Paris - Journal of the History of Philosophy 46:1 Journal of the History of Philosophy 46.1 172-173 Muse Search Journals This Journal Contents Reviewed by Johannes M. M. H. Thijssen Radboud University Nijmegen Stefano Caroti and Christophe Grellard, editors. Nicolas d'Autrécourt et la Faculté des Arts de Paris . Quaderni di Paideia, 4. Cesena: Stilgraf Editrice, 2006. Pp. 329. e32.00. This book is a coherent set of (...) papers resulting from a conference organized by its editors, Stefano Caroti and Christophe Grellard. In the opening paper, William Courtenay rightly observes that the 1330s are an understudied period in the intellectual history of the University of Paris, especially with respect to its.. (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)

By way of conclusion we may add the following three items to A. Maier's and G. Federici-Vescovini's investigations: 1. The Questiones super libris Physicorum in the ms. Cesena, B. Malatestiana S.VIII.5 have been incorrectly attributed to John Buridan. Their real author is Albert of Saxony. 2. The ms. Cesena, B. Malatestiana S.VIII.5 ff. 4ra-4vb contains the Prologue and the tabula questionum of the Questions on De gen. et corr., whereas the ms. Vat. lat. 3097 ff. 103ra-146rb has the complete text. (...) This Prologue and the questions 1 and 3 can also be found in Vat. lat. 2185 ff. 50ra-50vb. This text certainly cannot be considered as another copy of Buridan's well known Questions on De gen. et corr. Neither is it certain that Nicole Oresme is their author, as A. Maier seems to believe. There are indications pointing in the direction of a redaction other than the one known, of Buridan's Questions. In any case this possibility cannot be ruled out by the material that has been presented here. 3. The ms. Cesena, B. Malatestiana S.VIII.5 has at one time had the same owner as the codices Vat. lat. 2159, 2160, 2185 and 3066, and the codices Cesena, B. Malatestiana S.VII.5 and S.VIII.2. This owner was in all probability Bernardus a Campanea of Verona, a physician. (shrink)

In this survey, I should like to present an overview of the scholarly literature that appeared during the last decade or so in the field of fourteenth-century natural philosophy. This survey is partial in both senses of the term: it is fragmentary, and occasionally, it records my disagreements with some of the scholarly literature. Before narrowing down its scope it might be well to raise two methodological problems which one encounters when attempting to deal with the history of late-medieval natural (...) philosophy of the sort with which this survey is concerned. First, the terminology of «natural philosophy», and second, the relation between natural philosophy and theology in the late Middle Ages. (shrink)