Ontological Gaps

This essay pursues the development of Charles Taylor’s ontological thought by comparing his—insightful yet neglected—early paper “Ontology” (1959) with his little-known essay “Ethics and Ontology” (2003) and his most matured ontological position in Retrieving Realism (2015). It also puts a spotlight on Taylor’s unusual “interwoven” mode of argumentation in between ethics, phenomenology, and ontology. In so doing, I aim, first, to show Taylor’s remarkable consistency; second, to unravel his hybrid position in between ethics, phenomenology, and ontology; third, to argue for a tension between Taylor’s phenomenological approach to ethics and his claims about ontology; and, fourth, to highlight his ongoing hesitation with regard to ontological inquiry in general and issues of moral realism in particular.

MACINTYRE, RAWLS AND CAVELL ON GAMES, RULES AND PRACTICES

John Rawls and Alasdair Macintyre are usually portrayed as opponents in the liberal-communitarian debate. However, Stanley Cavell’s critique of Rawls’ early paper “Two Concepts of Rules”, helps us recognize a similarity between their accounts of rules, games and practices and the role that these play in moral life. This paper shows that both authors pay insufficient attention to personal relationships, the flexibility of our moral life, and the need to take responsibility for our moral positions. A scene from Thomas Hardy’s “Jude the Obscure” is used to show how this presents a serious problem for Macintyre’s model of tradition-based moral reasoning.

On Pure Quasi-Quantum Quadratic Operators of 𝕄2(ℂ) II

In this paper we study quasi quantum quadratic operators (QQO) acting on the algebra of [Formula: see text] matrices [Formula: see text]. We consider two kinds of quasi QQO the corresponding quadratic operator maps from the unit circle into the sphere and from the sphere into the unit circle, respectively. In our early paper we have defined a q-purity of quasi QQO. This notion is equivalent to the invariance of the unit sphere in [Formula: see text]. But to check this condition, in general, is tricky. Therefore, it would be better to find weaker conditions to check the q-purity. One of the main results of this paper is to provide a criterion of q-purity of quasi QQO in terms of the unit circles. Moreover, we are able to classify all possible kinds of quadratic operators which can produce q-pure quasi QQO. We think that such result will allow one to check whether a given mapping is a pure channel or not. This finding suggests us to study such a class of nonpositive mappings. Correspondingly, the complement of this class will be of potential interest for physicist since this set contains all completely positive mappings.

The giant impact hypothesis: past, present (and future?)

At the request of editors, this paper offers a historical review of early work on the giant impact hypothesis, as well as comments on new data. The author hereby claims (whether believable or not) that his interest is to move towards a correct model of lunar origin, not to defend a possibly incorrect idea, just because of being a co-author of a relevant early paper. Nonetheless, the 1974 giant impact hypothesis appears still to be viable.

Reconstructing David Huffman's Origami Tessellations1

David A. Huffman (1925–1999) is best known in computer science for his work in information theory, particularly Huffman codes, and best known in origami as a pioneer of curved-crease folding. But during his early paper folding in the 1970s, he also designed and folded over a 100 different straight-crease origami tessellations. Unlike most origami tessellations designed in the past 20 years, Huffman's straight-crease tessellations are mostly three-dimensional, rigidly foldable, and have no locking mechanism. In collaboration with Huffman's family, our goal is to document all of his designs by reverse-engineering his models into the corresponding crease patterns, or in some cases, matching his models with his sketches of crease patterns. Here, we describe several of Huffman's origami tessellations that are most interesting historically, mathematically, and artistically.

Reconstructing David Huffman’s Origami Tessellations

David A. Huffman (1925–1999) is best known in computer science for his work in information theory, particularly Huffman codes, and best known in origami as a pioneer of curved-crease folding. But during his early paper folding in the 1970s, he designed and folded over a hundred different straight-crease origami tessellations. Unlike most origami tessellations designed in the past twenty years, Huffman’s straight-crease tessellations are mostly three-dimensional, rigidly foldable, and have no locking mechanism. In collaboration with Huffman’s family, our goal is to document all of his designs by reverse-engineering his models into the corresponding crease patterns, or in some cases, matching his models with his sketches of crease patterns. Here we describe several of Huffman’s origami tessellations that are most interesting historically, mathematically, and artistically.

Microstructure simulation of early paper forming using immersed boundary methods

Paper forming is the first step in the paper machine where a fiber suspension leaves the headbox and flows through a forming fabric. Complex physical phenomena occur as the paper forms, during which fibers, fillers, fines, and chemicals added to the suspension interact. Understanding this process is important for the development of improved paper products because the configuration of the fibers during this step greatly influences the final paper quality. Because the effective paper properties depend on the microstructure of the fiber web, a continuum model is inadequate to explain the process and the properties of each fiber need to be accounted for in simulations. This study describes a new framework for microstructure simulation of early paper forming. The simulation framework includes a Navier-Stokes solver and immersed boundary methods to resolve the flow around the fibers. The fibers were modeled with a finite element discretization of the Euler-Bernoulli beam equation in a co-rotational formulation. The contact model is based on a penalty method and includes friction and elastic and inelastic collisions. We validated the fiber model and the contact model against demanding test cases from the literature, with excellent results. The fluid-structure interaction in the model was examined by simulating an elastic beam oscillating in a cross flow. We also simulated early paper formation to demonstrate the potential of the proposed framework.