Medieval conceptions of reason and the modes of thought in Piers Plowman

This thesis is an attempt to shed light on the related questions of how we should read Piers Plowman and of what kind of book its author was trying to write. In the first chapter it is argued that feminine line-endings are an important feature of Langland's metre, and consideration is given to how they affect our reading of the verse. It is suggested that the verse demands a slow and meditative reading, and that Langland's text emerges as a list of items not easily related to each other; the reader is challenged to work out connexions and thus in a sense to compose his own poem. The second chapter is an examination of the medieval conceptions and modes of thought that are associated with the word "reson". The term "reasonable" is later used to refer to these. In the last part of the chapter it is argued that Langland's aim is to make his readers seek salvation, and that he is aware of certain difficulties with the traditional, "reasonable" approaches of other moralists. His own book is "unreasonable"; its mixture of modes of thought, and hence of the thought-worlds they project, makes narrative consistency and definiteness of argument impossible. In the rest of the thesis some of the juxtapositions between modes of thought are examined. The. third chapter deals with "positive” juxtapositions, which create in the reader's mind a sense of satisfying, but nevertheless "unreasonable", illumination; the speech of Wit and the vision of the Passion and Crucifixion are discussed in detail. The fourth chapter deals with "negative" juxtapositions, which provoke a sense of bewilderment and dissatisfaction; discussion centres on Ymaginatiyf's speech in the C text, Need's speech, and the confessions of the Seven Deadly Sins

A numerical damped oscillator approach to constrained Schrödinger equations

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schrödinger equations with additional constraints. In fact, the method is general and can solve constrained minimization problems in many fields. We present the method for introductory applications in quantum mechanics including three qualitative different numerical examples: the radial Schrödinger equation for the hydrogen atom; the 2D harmonic oscillator with degenerate excited states; and a nonlinear Schrödinger equation for rotating states. The presented method is intuitive, with analogies in classical mechanics for damped oscillators, and easy to implement, either with coding or with software for dynamical systems. Hence, we find it suitable to introduce it in a continuation course in quantum mechanics or generally in applied mathematics courses which contain computational parts. The undergraduate student can, for example, use our derived results and the code (supplemental material (https://stacks.iop.org/EJP/41/065406/mmedia)) to study the Schrödinger equation in 1D for any potential. The graduate student and the general physicist can work from our three examples to derive their own results for other models including other global constraints.publishedVersio

The Dynamical Functional Particle Method for Multi-Term Linear Matrix Equations

Recent years have seen a renewal of interest in multi-term linear matrix equations, as these have come to play a role in a number of important applications. Here, we consider the solution of such equations by means of the dynamical functional particle method, an iterative technique that relies on the numerical integration of a damped second order dynamical system. We develop a new algorithm for the solution of a large class of these equations, a class that includes, among others, all linear matrix equations with Hermitian positive definite or negative definite coefficients. In numerical experiments, our MATLAB implementation outperforms existing methods for the solution of multi-term Sylvester equations. For the Sylvester equation AX + XB = C, in particular, it can be faster and more accurate than the built-in implementation of the Bartels–Stewart algorithm, when A and B are well conditioned and have very different size