In elementary derivations of the quantization of azimuthal angular momentum the eigenfunction is determined to be exp(im φ), which is “oversensitive” to the rotation φ → φ+2π, unlessm is an integer. In a recent paper Kerner examined the classical system of charge and magnetic pole, and expressed Π, a vector constant of motion for the system, in terms of a physical angle ψ, to deduce a remarkable paradox. Kerner pointed out that Π(ψ) is “oversensitive” to ψ → ψ+2π unless a (...) certain charge quantization condition is met. Our explicandum of this paradox highlights the distinction between coordinates in classical and quantum physics. It is shown why the single-valuedness requirement on Π(ψ) is devoid of physical significance. We are finally led to examine the classical analog of the quantum mechanical argument that demonstrates the quantization of magnetic charge, to show that there is “no hope” of a classical quantization condition. (shrink)

"The studies collected in this book are all concerned with aspects of the Platonic tradition, either in its own internal development in the Hellenistic age and the period of the Roman Empire, or with the influence of Platonism, in one or other of its forms, on other spiritual traditions, especially that of Christianity." [Book jacket].

Edited with New Translation by Richard McKirahan With a New Preface by Malcolm Schofield This book is a revised and expanded version of A.H. Coxon's full critical edition of the extant remains of Parmenides of Elea—the fifth-century B.C. philosopher by many considered "one of the greatest and most astonishing thinkers of all times." Coxon's presentation of the complete ancient evidence for Parmenides and his comprehensive examination of the fragments, unsurpassed to this day, have proven invaluable to our understanding of the (...) Eleatic since the book's first publication in 1986. This edition, edited by Richard McKirahan and with a new preface by Malcolm Schofield, is released on the 100th anniversary of Coxon's birth. This new edition for the first time includes English translations of the testimonia and of any Ancient Greek throughout the book, as well as an English/Greek glossary by Richard McKirahan, and revisions by the late author himself. The text consists of Coxon's collations of the relevant folios of manuscripts of Sextus Empiricus, Proclus and Simplicius and includes all extant fragments, a commentary, the testimonia, a complete list of sources, linguistic parallels from both earlier and later authors, and the fullest critical apparatus that has appeared since Diels’ _Poetarum Philosophorum Fragmenta _. The collection of testimonia includes the philosophical discussions of Parmenides by Plato, Aristotle and the Neoplatonists, most of which had been omitted by Diels. The introduction discusses the history of the text, the language and form of the poem, Parmenides’ use and understanding of the verb ‘to be’, his place in the history of earlier and later philosophy and the biographical tradition. In the commentary Coxon deals in detail with both the language and the subject matter of the poem and pays full attention to Parmenides’ account of the physical world. The appendix relates later Eleatic arguments to those of Parmenides. (shrink)

Traditional modes of system representation as dynamical systems, involving fixed sets of states together with imposed dynamical laws, pertain only to a meagre subclass of natural systems. This reductionistic paradigm leaves no room for final causes; constrained thus are the simple systems. Members of their complementary collection, natural systems having mathematical models that are not dynamical systems, are the complex systems. Complex systems, containing hierarchical cycles in their entailment networks, can only be approximated and simulated, locally and temporarily, by simple (...) ones. Anticipatory systems are, in this specific sense, complex, hence this introductory chapter on Complex Systems in the Handbook of Anticipation. (shrink)

Non-pharmaceutical interventions, including social distancing, quarantine, and isolation, are a potentially attractive means to limit the transmission of a pandemic virus. Many of these interventions are directed at children given children’s disproportionate role in amplifying epidemics. The ethics of non-pharmaceutical interventions can be analyzed using Nancy Kass’ ethics framework for public health. Such an analysis highlights the limited data supporting these interventions’ effectiveness. It also suggests the framework itself needs to be expanded to consider harms other than constraints on liberty (...) and to consider affirmative programs to mitigate these broader harms. (shrink)

This is the first-ever critical history of sociology in Britain, written by one of the world's leading scholars in the field. A. H. Halsey presents a vivid and authoritative picture of the neglect, expansion, fragmentation, and explosion of the discipline during the past century. The book examines the literary and scientific contributions to the origin of the discipline, and the challenges faced by the discipline at the dawn of a new century.