A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Primary care nurses' experiences of how the mass media influence frontline healthcare in the UK

Background: Mass media plays an important role in communicating about health research and services to patients, and in shaping public perceptions and decisions about health. Healthcare professionals also play an important role in providing patients with credible, evidence-based and up-to-date information on a wide range of health issues. This study aims to explore primary care nurses' experiences of how mass media influences frontline healthcare.<p></p> Methods: In-depth telephone interviews were carried out with 18 primary care nurses (nine health visitors and nine practice nurses) working in the United Kingdom (UK). Interviews were recorded and transcribed. The data was analysed using thematic analysis, with a focus on constant comparative analysis.<p></p> Results: Three themes emerged from the data. First, participants reported that their patients were frequently influenced by controversial health stories reported in the media, which affected their perceptions of, and decisions about, care. This, in turn, impinged upon participants' workloads as they had to spend additional time discussing information and reassuring patients. Second, participants also recalled times in their own careers when media reports had contributed to a decline in their confidence in current healthcare practices and treatments. Third, the participants in this study suggested a real need for additional resources to support and expand their own media literacy skills, which could be shared with patients.<p></p> Conclusion: In an ever expanding media landscape with greater reporting on health, nurses working in the primary care setting face increasing pressure to effectively manage media stories that dispute current health policies and practices. These primary care nurses were keen to expand their media literacy skills to develop critical autonomy in relation to all media, and to facilitate more meaningful conversations with their patients about their health concerns and choices.<p></p&gt

Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics

We examine some of Connes' criticisms of Robinson's infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes' own earlier work in functional analysis. Connes described the hyperreals as both a "virtual theory" and a "chimera", yet acknowledged that his argument relies on the transfer principle. We analyze Connes' "dart-throwing" thought experiment, but reach an opposite conclusion. In S, all definable sets of reals are Lebesgue measurable, suggesting that Connes views a theory as being "virtual" if it is not definable in a suitable model of ZFC. If so, Connes' claim that a theory of the hyperreals is "virtual" is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren't definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in his Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes' criticism of virtuality. We analyze the philosophical underpinnings of Connes' argument based on Goedel's incompleteness theorem, and detect an apparent circularity in Connes' logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace (featured on the front cover of Connes' magnum opus) and the Hahn-Banach theorem, in Connes' own framework. We also note an inaccuracy in Machover's critique of infinitesimal-based pedagogy.Comment: 52 pages, 1 figur

The advantages of being unpredictable: How emotional inconsistency extracts concessions in negotiation

Integrating recent work on emotional communication with social science theories on unpredictability, we investigated whether communicating emotional inconsistency and unpredictability would affect recipients' concession-making in negotiation. We hypothesized that emotional inconsistency and unpredictability would increase recipients' concessions by making recipients feel less control over the outcome. In Experiment 1, dyads negotiated face-to-face after one negotiator within each dyad expressed either anger or emotional inconsistency by alternating between anger and happiness. In Experiment 2, participants received angry and/or happy messages from a simulated negotiation opponent. In Experiment 3, participants read a scenario about a negotiator who expressed either anger or emotional inconsistency by alternating between anger and disappointment. In all three experiments, emotional inconsistency induced recipients to make greater concessions compared to expressing a consistent emotion. Further, in all three experiments, the effect of emotional inconsistency was mediated by recipients' feeling less control. These findings qualify previous research on anger in negotiation and demonstrate the importance of feelings of control for negotiation outcomes