Comment on "Some novel delta-function identities"

We show that a form for the second partial derivative of $1/r$ proposed by Frahm and subsequently used by other workers applies only when averaged over smooth functions. We use dyadic notation to derive a more general form without that restriction.Comment: 4 page Comment on an AJP paper. The second version modifies the discussion and corrects some misprints. This version will appear in AJP

Comment on Octet Baryon Magnetic Moments in the Chiral Quark Model with Configuration Mixing

The importance of exchange currents, and of conserving isotopic spin at both the quark and baryon levels in application of the chiral quark model to any calculation of baryon magnetic moments is emphasized.Comment: 5 pages, Latex fil

Pascal’s wager and the origins of decision theory: decision-making by real decision-makers

Pascal’s Wager does not exist in a Platonic world of possible gods, abstract probabilities and arbitrary payoffs. Real decision-makers, such as Pascal’s “man of the world” of 1660, face a range of religious options they take to be serious, with fixed probabilities grounded in their evidence, and with utilities that are fixed quantities in actual minds. The many ingenious objections to the Wager dreamed up by philosophers do not apply in such a real decision matrix. In the situation Pascal addresses, the Wager is a good bet. In the situation of a modern Western intellectual, the reasoning of the Wager is still powerful, though the range of options and the actions indicated are not the same as in Pascal’s day

Feature selection methods for solving the reference class problem

Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary Big Data science: the correct reference class is that determined by the features relevant to the target, and relevance is measured by correlation (that is, a feature is relevant if it makes a difference to the frequency of the target)

Science by Conceptual Analysis: The Genius of the Late Scholastics

The late scholastics, from the fourteenth to the seventeenth centuries, contributed to many fields of knowledge other than philosophy. They developed a method of conceptual analysis that was very productive in those disciplines in which theory is relatively more important than empirical results. That includes mathematics, where the scholastics developed the analysis of continuous motion, which fed into the calculus, and the theory of risk and probability. The method came to the fore especially in the social sciences. In legal theory they developed, for example, the ethical analyses of the conditions of validity of contracts, and natural rights theory. In political theory, they introduced constitutionalism and the thought experiment of a “state of nature”. Their contributions to economics included concepts still regarded as basic, such as demand, capital, labour, and scarcity. Faculty psychology and semiotics are other areas of significance. In such disciplines, later developments rely crucially on scholastic concepts and vocabulary

Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid