Christianity and Gambling: An Introduction

Religions hold complex relations with games and, in particular, with gambling. The article focuses on Christianity. On the one hand, the history of this religion shows a tendency to condemn games as source of distraction from spiritual rectitude and to stigmatize gambling, above all, as opening to metaphysical randomness and, as a consequence, as challenge to the idea of divine omniscience. On the other hand, Christianity has also sought to reinterpret games, and even gambling, as possible occasion for moral improvement and as useful distraction from the hardship of monastic life. A theological perspective that reaches its peak in Thomas Aquinas, but has its roots in Aristotle’s evaluation of playfulness, tends to suggest the need for eutropelia, meant as the citizens’ virtue to appropriately have fun

Some hyperbolic 4-manifolds with low volume and number of cusps

We construct here two new examples of non-orientable, non-compact, hyperbolic 4-manifolds. The first has minimal volume $v_m = 4{\pi}^2/3$ and two cusps. This example has the lowest number of cusps among known minimal volume hyperbolic 4-manifolds. The second has volume $2\cdot v_m$ and one cusp. It has lowest volume among known one-cusped hyperbolic 4-manifolds.Comment: 12 pages, 11 figure

Measuring stellar magnetic fields with the low resolution spectropolarimeter of the William Herschel Telescope

Despite the influence of magnetic fields on the structure and evolution of stars is largely demonstrated from the theoretical point of view, their observational evidence in non-degenerated stars is still rather scanty and mainly circumscribed to bright objects (V<10). Stellar magnetic fields are commonly measured on the basis of circular spectropolarimetry at high/middle resolution across the profile of metal lines. The present sensitivity of telescopes and spectrographs makes this still an almost prohibitive method for faint stars. In principle, stellar magnetic fields can be also measured on the basis of low resolution spectropolarimetry, with very important results obtained at the 8 m ESO telescopes with FORS1. The trade off between S/N and spectral resolution in measuring stellar magnetic fields justify an attempt, here presented, to perform these measurements at the 4.5 m William Herschel Telescope. HD3360, one of the stars with the weakest known magnetic field, and the magnetic chemically peculiar stars HD10783, HD74521 and HD201601 have been observed with the spectropolarimeter ISIS in the 3785-4480 A range. Measured stellar magnetic fields, from Stokes I and V spectra with S/N > 600, show an internal error of <50 G selecting the whole interval and <200 G within a Balmer line. Ripples in the Stokes V spectra of HD3360 result in an instrumental positive magnetic field certainly not larger than 80 G.Comment: 7 pages, 4 figures, MNRAS in pres

"Utrum figura dictionis sit fallacia in dictione. et quod non videtur". A Taxonomic Puzzle or how Medieval Logicians Came to Account for an Odd Question by an Impossible Answer

One of the singularities of Latin exegesis of Aristotle’s Sophistici elenchi, is that it arbitrarily brought together two families of fallacies, the «figure of speech» and the «accident», despite the fact that they are on either side of the divide between sophisms related to expression and sophisms independent of expression, a divide that lays at the heart of Aristotle’s taxonomy of sophistic arguments. What is behind this surprising identification? The talk is meant to show that it actually originates from a curious mistake in Boethius’ translation of Aristotle’s Sophistici elenchi, 22, 178b 36-37 which radically transformed the nature of the argument at stake. While it was originally an example of the fallacies related to the «figure of speech», Boethius’ translation wrongly brings about two arguments instead of one, both related to the «accident». This explains why authors from the Latin tradition came to think that fallacies of «figure of speech» were linked to fallacies of «accident» closely enough to ask whether they actually fell outside expression, even though it does not at first glance appear that such a possibility was allowed or even suggested by Aristotle’s text. This odd question illustrates some of the remarkable features of the medieval archive and how some of its most peculiar problems came to be. It specifically allows us to reconstruct the mechanisms through which a minor disturbance in the letter of the text leads to a whole new way of organising its exegetical material

A geometrically bounding hyperbolic link complement

A finite-volume hyperbolic 3-manifold geometrically bounds if it is the geodesic boundary of a finite-volume hyperbolic 4-manifold. We construct here an example of non-compact, finite-volume hyperbolic 3-manifold that geometrically bounds. The 3-manifold is the complement of a link with eight components, and its volume is roughly equal to 29.311.Comment: 23 pages, 19 figure