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

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st

First measurement of the BSB_S meson mass

If simplified, every information retrieval problem can be solved when the information need implied by its expression has been identified. We are interested in the criteria used in realising a good information retrieval problem expression. We have listed these criteria through some principles and maxims which first characterized the communication between two persons are applied. We choose to use the gricean maxims because they are the most favoured for this type of situation. Secondly, we have tried to identify some others principles that can be used to realise a good information retrieval problem expression. The principles by Grice can not resolve all forms of error associated with this particular form of communication. In our work, we defined three other principles namely: adhesion principle, reformulation principle, memorization principle. We give some examples of situations where the principles we have formulated are not applicable and the consequences. We present the possible applications of our new model: MIRABEL, which can help in the description of information retrieval problem from. It also compels its user to use essential good expression principle implicitly

Measurement of the tau lepton lifetime with the three-dimensional impact parameter method.

A new method is presented for the measurement of the mean $\tau$ lepton lifetime using events in which $\tau$'s are pair-produced and both $\tau$'s decay to hadrons and $\nu_\tau$. Based on the correlation between the two $\tau$'s produced at a symmetric $e^+ e^-$ collider, the 3DIP method relies on the three-dimensional information from a double-sided vertex detector and on kinematic constraints for the precise measurement of the $\tau$ decay angles. Using the data collected from 1992 to 1994 with the ALEPH detector at LEP, a $\tau$ lifetime of $288.0 \pm 3.1 \pm 1.3$\fs is obtained from the sample in which both $\tau$'s decay to one charged track, and $292.8 \pm 5.6 \pm 3.0$\fs from the sample in which one $\tau$ decays to one prong and the other to three prongs. The results show small statistical correlations with those derived from other methods. When combined with the previously published ALEPH measurements, the resulting $\tau$ lifetime is $291.2 \pm 2.0 \pm 1.2$\fs