The relation between Kruskal and Schwarzschild coordinates is analogous to that between hyperboloid and de Sitter coordinates; the Kruskal diagram is analogous to the hyperboloid diagram; and the crossing over of horizons in Kruskal space is analogous to the well-known crossing over of the particle horizon and the event horizon in cosmology.

In this paper, we present a time-varying and non-stationary but non-hyperbolic discount function that explains dynamic preference reversal. The new discount function emerges from an analysis of intertemporal consumption and savings choices with mortality risk and an altruistic factor. Our analysis shows that the process of updating survival information may also account for dynamic preference reversal.

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a (...) particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the *very same* region of spacetime. We shall defend the idea that these representations provide *complementary descriptions* of the same state of the field against the claim that they embody completely *incommensurable theories* of the field. (shrink)

This paper investigates the topological construction of Wedge Sum, with the aim of showing that it can be done mathematically, via a quotient construction, or logically, via Merge. Consistent and Inconsistent versions are given, while noting that the natural outcome of Merging is an inconsistent theory. Finally it is observed that algebraic constructions can also be treated via Merge, where the extra functionality makes for various triviality and non-triviality results.

The wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results—hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value (...) problem of differential equations; solutions defined on mutiply connected spaces. Section 3: geometrical theory of diffraction; identificiation of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a μ-sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function. (shrink)

This article discusses the quest for the mechanical advantage of the wedge in the eighteenth century. As a case study, the wedge enlightens our understanding of eighteenth-century mechanics in general and the controversy over “force” or vis viva in particular. In this article, I show that the two different approaches to mechanics, the one that favoured force in terms of velocities and the one that primarily used displacements—known as the ‘Newtonian’ and ‘Leibnizian’ methods, respectively—were not at all on par in (...) their ability to solve the problem of the wedge. In general, only those who used the Leibnizian concept of force or some related notion were able to get to the conventional results. This article thus rebuts the received view that the vis viva controversy was merely a semantic one. Instead, it shows that different understandings of “force” led to real and pragmatic differences in eighteenth-century mechanics. (shrink)

This article discusses the quest for the mechanical advantage of the wedge in the eighteenth century. As a case study, the wedge enlightens our understanding of eighteenth-century mechanics in general and the controversy over “force” or vis viva in particular. In this article, I show that the two different approaches to mechanics, the one that favoured force in terms of velocities and the one that primarily used displacements—known as the ‘Newtonian’ and ‘Leibnizian’ methods, respectively—were not at all on par in (...) their ability to solve the problem of the wedge. In general, only those who used the Leibnizian concept of force or some related notion were able to get to the conventional results. This article thus rebuts the received view that the vis viva controversy was merely a semantic one. Instead, it shows that different understandings of “force” led to real and pragmatic differences in eighteenth-century mechanics. (shrink)

In 2012, choreographer and dancer Jill Sigman of jill sigman/thinkdance and visual artist Janine Antoni collaborated to produce Wedge, a live performance at the Albright-Knox Gallery. In this essay, I describe the collaboration and the resulting work and examine the benefits and challenges of the collaboration. The discussion touches on broader issues pertaining to collaboration, co-authorship, artists' intentions, and interpretation.

In “Judy Benjamin is a Sleeping Beauty” (2010) Bovens recognises a certain similarity between the Sleeping Beauty (SB) and the Judy Benjamin (JB). But he does not recognise the dissimilarity between underlying protocols (as spelled out in Shafer (1985). Protocols are expressed in conditional probability tables that spell out the probability of coming to learn various propositions conditional on the actual state of the world. The principle of total evidence requires that we not update on the content of the proposition (...) learned but rather on the fact that we learn the proposition in question. Now attention to protocols drives a wedge between the SB and the JB. We have shown that the solution to a close variant of the SB which involves a clear protocol is P*(Heads) = 1/3 and since Beauty’s has precisely the same information at her disposal in the original SB at the time that she is asked to state her credence for Heads, the same solution should hold. The solution to the JB, on the other hand, is dependent on Judy’s probability distribution over protocols. One reasonable protocol yields P(Red) = 1/2, but Judy could also defend alternative values or a range of values in the interval [1/3, 1/2] depending on her probability distribution over protocols. (shrink)

Ethical concerns about randomising persons to a no-treatment arm in the context of Ebola epidemic led to consideration of alternative designs. The stepped wedge design, in which participants or clusters are randomised to receive an intervention at different time points, gained popularity. Common arguments in favour of using this design are when an intervention is likely to do more good than harm, all participants should receive the experimental intervention at some time point during the study and the design might be (...) preferable for practical reasons. We examine these assumptions when considering Ebola vaccine research. First, based on the claim that a stepped wedge design is indicated when it is likely that the intervention will do more good than harm, we reviewed published and ongoing SW trials to explore previous use of this design to test experimental drugs or vaccines, and found that SW design has never been used for trials of experimental drugs or vaccines. Given that Ebola vaccines were all experimental with no prior efficacy data, the use of a stepped wedge design would have been unprecedented. Second, we show that it is rarely true that all participants receive the intervention in SW studies, but rather, depending on certain design features, all clusters receive the intervention. Third, we explore whether the SW design is appealing for feasibility reasons and point out that there is significant complexity. In the setting of the Ebola epidemic, spatiotemporal variation may have posed problematic challenges to a stepped wedge design for vaccine research. Finally, we propose a set of points to consider for scientific reviewers and ethics committees regarding proposals for SW designs. (shrink)

The behavior of Lyapunov exponents λ and dynamical entropies h, whose positivity characterizes chaotic motion, under Lorentz and Rindler transformations is studied. Under Lorentz transformations, λ and h are changed, but their positivity is preserved for chaotic systems. Under Rindler transformations, λ and h are changed in such a way..

John Wyclif has too frequently been described as "Morning Star of the Reformation" and only recently begun to be studied as a fourteenth-century English philosopher and theologian. This work draws on recent scholarship situating Wyclif in his fourteenth-century milieu to present a survey of his thought and writings as a coherent theological position arising from Oxford's "Golden Age" of theology. Lahey argues that many of Wyclif's best known critiques of the fourteenth-century Church arise from his philosophical commitment to an Augustinian (...) realism evocative of the thought of Robert Grosseteste and Anselm of Canterbury. This realism is comprehensible in terms of Wyclif's sustained focus on semantics and the properties of terms and propositions, a "linguistic turn" characterizing post-Ockham philosophical theology. Arising from this propositional realism is a strong emphasis on the place of Scripture in both formal and applied theology, which was the starting point for many of Wyclif's quarrels with the ecclesiastical status quo in late fourteenth-century England. This survey takes into account both Wyclif's earlier, philosophical works and his later works, including sermons and Scripture commentary. Wyclif's belief that Scripture is the eternal and perfect divine word, the paradigm of human discourse and the definitive embodiment of truth in creation is central to an understanding of the ties he believes relate theoretical and practical philosophy to theology. This connection links Wyclif's interest in the propositional structure of reality to his realism, his hermeneutic program, and to his agenda for reform of the Church. Lahey's survey also highlights Wyclif's rejection of Bradwardine's determinism in favor of a model of human freedom in light of God's perfect foreknowledge, and also explores the relation of Wyclif's spatiotemporal atomism to his rejection of transubstantiation. This is the first book-length, comprehensive survey of Wyclif's thought, and will be of interest to students of later medieval theology, philosophy, history, and literature. (shrink)

Forrest and Gross expose the scientific failure, the religious essence, and the political ambitions of "intelligent design" creationism. They examine the movement's "Wedge Strategy," which has advanced and is succeeding through public relations rather than through scientific research. Analyzing the content and character of "intelligent design theory," they highlight its threat to public education and to the separation of church and state.

The behavior of Lyapunov exponents λ and dynamical entropies h, whose positivity characterizes chaotic motion, under Lorentz and Rindler transformations is studied. Under Lorentz transformations, λ and h are changed, but their positivity is preserved..

This essay explores Johnstone's idea that "rhetoric is a wedge." In particular, it explores the place of this idea in Johnstone's philosophy of argument, the need to confront this idea with argument, and ways of confronting it with ad rem and ad hominem arguments.

Forrest and Gross expose the scientific failure, the religious essence, and the political ambitions of "intelligent design" creationism. They examine the movement's "Wedge Strategy," which has advanced and is succeeding through public relations rather than through scientific research. Analyzing the content and character of "intelligent design theory," they highlight its threat to public education and to the separation of church and state.

We provide a finite axiomatization of the consequence $\vdash ^{\wedge}\cap \vdash ^{\vee}$ , i.e. of the set of common sequential rules for $\wedge $ and $\vee $ . Moreover, we show that $\vdash ^{\wedge}\cap \vdash ^{\vee}$ has no proper non-trivial strengthenings other than $\vdash ^{\wedge}$ and $\vdash ^{\vee}$ . A similar result is true for $\vdash ^{\leftrightarrow}\cap \vdash ^{\rightarrow}$ , but not, e.g., for $\vdash ^{\leftrightarrow}\cap \vdash ^{+}$.

Ethics has been identified as a central reason for choosing the stepped wedge trial over other kinds of trial designs. The potential advantage of the stepped wedge design is that it provides all arms of the trial with the active intervention over the course of the study. Some groups receive it later than others, but the study intervention is not withheld from any group. This feature of the stepped wedge design seems particularly ethically advantageous in two instances: when the study (...) intervention appears especially likely to be effective and when the consequences of not receiving the intervention may be dire. But despite an increase in the use of the stepped wedge design and appeals to its ethical superiority as the motivation for its selection, there has been limited attention to the stepped wedge trial in the ethics literature. In the following, I examine whether there are persuasive ethical reasons to prefer or to require a stepped wedge trial. I argue that while the stepped wedge design is ethically permissible, it is not morally superior to other kinds of trials. To this end, I examine the ethical justification for providing, withholding, and delaying interventions in research. (shrink)

I discuss two versions of the doomsday argument. According to ``Gott's Line'',the fact that the human race has existed for 200,000 years licences the predictionthat it will last between 5100 and 7.8 million more years. According to ``Leslie'sWedge'', the fact that I currently exist is evidence that increases the plausibilityof the hypothesis that the human race will come to an end sooner rather than later.Both arguments rest on substantive assumptions about the sampling process thatunderlies our observations. These sampling assumptions have (...) testable consequences,and so the sampling assumptions themselves must be regarded as empirical claims.The result of testing some of these consequences is that both doomsday argumentsare empirically disconfirmed. (shrink)