Metaphor and criticism

The prevalence of colourful metaphors and figurative language in critics' descriptions of artworks has long attracted attention. Talk of ‘liquid melodies,’ ‘purple prose,’ ‘soaring arches,’ and the use of still more elaborate figurative descriptions, is not uncommon. My aim in this paper is to explain why metaphor is so prevalent in critical description. Many have taken the prevalence of art-critical metaphors to reveal something important about aesthetic experience and aesthetic properties. My focus is different. I attempt to determine what metaphor enables critics to achieve and why it is so well-suited to helping them achieve it. I begin by outlining my account of what metaphors communicate and defend it against objections to the effect that it does not apply to art-critical metaphors. I then distinguish between two kinds of art-critical metaphor. This distinction is not normally drawn, but drawing it is essential to understanding why critics use metaphor. I then explain why each kind of metaphor is so common in criticism

The dispensability of metaphor

Many philosophers claim that metaphor is indispensable for various purposes. What I shall call the ‘Indispensability Thesis’ is the view that we use at least some metaphors to think, to express, to communicate, or to discover what cannot be thought, expressed, communicated, or discovered without metaphor. I argue in this paper that support for the Indispensability Thesis is based on several confusions. I criticize arguments presented by Stephen Yablo, Berys Gaut, Richard Boyd, and Elisabeth Camp for the Indispensability Thesis, and distinguish it from several plausible claims with which it is easily confused. Although I do not show that the thesis is false, I provide seven grounds for suspicion of our sense (if we have it) that some metaphors are indispensable for the purposes claimed by advocates of the Indispensability Thesis

Lsdiff M and the Einstein Equations

We give a formulation of the vacuum Einstein equations in terms of a set of volume-preserving vector fields on a four-manifold ${\cal M}$. These vectors satisfy a set of equations which are a generalisation of the Yang-Mills equations for a constant connection on flat spacetime.Comment: 5 pages, no figures, Latex, uses amsfonts, amssym.def and amssym.tex. Note added on more direct connection with Yang-Mills equation

The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at each point. We explicitly find the subgroup of the symmetry group that preserves the one-instanton moduli space. This action simply corresponds to a scaling of the moduli space.Comment: AMSLatex, 19 pages, no figures. Some discussions clarified, and citations made more accurate. I am grateful to the referee for detailed comments. Version to appear in Communications in Mathematical Physic

A Spinorial Hamiltonian Approach to Gravity

We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class constraints from the Hamiltonian theory. In four dimensions, when restricted to the positive spin-bundle, these variables reduce to the standard Ashtekar variables. In higher dimensions, the theory can either be reduced to a spinorial version of the ADM formalism, or can be left in a more general form which seems useful for the investigation of some spinorial problems such as Riemannian manifolds with reduced holonomy group. In dimensions $0 \pmod 4$, the theory may be recast solely in terms of structures on the positive spin-bundle $\mathbb{V}^+$, but such a reduction does not seem possible in dimensions $2 \pmod 4$, due to algebraic properties of spinors in these dimensions.Comment: 20 pages, Latex 2e. Published versio

Cosmic Strings and Chronology Protection

A space consisting of two rapidly moving cosmic strings has recently been constructed by Gott that contains closed timelike curves. The global structure of this space is analysed and is found that, away from the strings, the space is identical to a generalised Misner space. The vacuum expectation value of the energy momentum tensor for a conformally coupled scalar field is calculated on this generalised Misner space. It is found to diverge very weakly on the Chronology horizon, but more strongly on the polarised hypersurfaces. The divergence on the polarised hypersurfaces is strong enough that when the proper geodesic interval around any polarised hypersurface is of order the Planck length squared, the perturbation to the metric caused by the backreaction will be of order one. Thus we expect the structure of the space will be radically altered by the backreaction before quantum gravitational effects become important. This suggests that Hawking's `Chronology Protection Conjecture' holds for spaces with non-compactly generated Chronology horizon.Comment: 15 pages, plain TeX, 2 figures (not included), DAMTP-R92/3

Valiente Kroon's obstructions to smoothness at infinity

We conjecture an interpretation in terms of multipole moments of the obstructions to smoothness at infinity found for time-symmetric, conformally-flat initial data by Valiente Kroon (Comm. Math. Phys. 244 (2004), 133-156).Comment: To appear in GR

A positive mass theorem for low-regularity Riemannian metrics

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give a (negative) lower bound on the ADM mass of metrics for which the scalar curvature fails to be non-negative, where the negative part has compact support and sufficiently small $L^{n/2}$ norm. We show that a Riemannian metric in $W^{2, p}_{loc}$ for some $p > \frac{n}{2}$ with non-negative scalar curvature in the distributional sense can be approximated locally uniformly by smooth metrics with non-negative scalar curvature. For continuous metrics in $W^{2, n/2}_{loc}$, there exist smooth approximating metrics with non-negative scalar curvature that converge in $L^p_{loc}$ for all $p < \infty$.Comment: 21 pages. The results on the positive mass theorem were announced in arxiv:1205.1302, with a sketch of the proo