Hidden dynamics in models of discontinuity and switching

AbstractSharp switches in behaviour, like impacts, stick–slip motion, or electrical relays, can be modelled by differential equations with discontinuities. A discontinuity approximates fine details of a switching process that lie beyond a bulk empirical model. The theory of piecewise-smooth dynamics describes what happens assuming we can solve the system of equations across its discontinuity. What this typically neglects is that effects which are vanishingly small outside the discontinuity can have an arbitrarily large effect at the discontinuity itself. Here we show that such behaviour can be incorporated within the standard theory through nonlinear terms, and these introduce multiple sliding modes. We show that the nonlinear terms persist in more precise models, for example when the discontinuity is smoothed out. The nonlinear sliding can be eliminated, however, if the model contains an irremovable level of unknown error, which provides a criterion for systems to obey the standard Filippov laws for sliding dynamics at a discontinuity

A Critical Analysis of Neural Buddhism\u27s Explanation of Moral Transformation

As non-theistic arguments for morality become increasingly sophisticated and complex, they are harder to criticize without first admiring their skillful design and near-artistry. One such argument involves a relatively new innovation that is the child of naturalism and eastern philosophy—Neural Buddhism. Like two world-renowned designers collaborating on a new garment, Naturalism and Buddhism have come together in this distinct program to offer something inventive, especially in its explanation of moral transformation. However, this critical analysis will ultimately reveal that Neural Buddhism’s explanation of moral transformation is incapable of providing good answers to several compelling criticisms

Book Review: East-West Dialogues: An Interreligious Encounter

A review of East-West Dialogues: An Interreligious Encounter by Satyaraja Dasa Adhikari (Steven Rosen) and Rev. Alvin V. P. Hart