Thing Theory

This article is an extended review of Graham Harman's Heidegger Explained: From Phenomenon to Thing. The paper explains Harman's argument that Heidegger's famous broken tool incident - the account that introduces a critique of presence based on the withdrawn dimensions of things - has a much greater relevance than is usually imagined. It explores Harman's extrapolations from Heidegger to rethink the very nature of objects - or things in themselves, their relations to each other, and their own unfathomable inner being. The paper goes on to note the implications of this argument for thinking more generally about relationality, space, and the more-than-human

Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy

The algebraic matrix hierarchy approach based on affine Lie $sl (n)$ algebras leads to a variety of 1+1 soliton equations. By varying the rank of the underlying $sl (n)$ algebra as well as its gradation in the affine setting, one encompasses the set of the soliton equations of the constrained KP hierarchy. The soliton solutions are then obtained as elements of the orbits of the dressing transformations constructed in terms of representations of the vertex operators of the affine $sl (n)$ algebras realized in the unconventional gradations. Such soliton solutions exhibit non-trivial dependence on the KdV (odd) time flows and KP (odd and even) time flows which distinguishes them from the conventional structure of the Darboux-B\"{a}cklund Wronskian solutions of the constrained KP hierarchy.Comment: LaTeX, 13pg

Nonstandard Drinfeld-Sokolov reduction

Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (\A,\Lambda, d_1, d_0), where the $d_i$ are $\Z$-gradations of a loop algebra \A and \Lambda\in \A is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the $d_1$-grade zero part of \A into a vector space direct sum of two subalgebras. This permits one to interpret certain Gelfand-Dickey type systems associated with a nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework.Comment: 19 pages, LaTeX fil

Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies

Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra \G\otimes{\bf C}[\lambda,\lambda^{-1}] are studied. The graded Heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the Weyl group {\bf W}(\G) of the simple Lie algebra \G. A representative w\in {\bf W}(\G) of a regular conjugacy class can be lifted to an inner automorphism of \G given by $\hat w=\exp\left(2i\pi {\rm ad I_0}/m\right)$, where $I_0$ is the defining vector of an $sl_2$ subalgebra of \G.The grading is then defined by the operator $d_{m,I_0}=m\lambda {d\over d\lambda} + {\rm ad} I_0$ and any grade one regular element $\Lambda$ from the Heisenberg subalgebra associated to $[w]$ takes the form $\Lambda = (C_+ +\lambda C_-)$, where $[I_0, C_-]=-(m-1) C_-$ and $C_+$ is included in an $sl_2$ subalgebra containing $I_0$. The largest eigenvalue of ${\rm ad}I_0$ is $(m-1)$ except for some cases in $F_4$, $E_{6,7,8}$. We explain how these Lie algebraic results follow from known results and apply them to construct integrable systems.If the largest ${\rm ad} I_0$ eigenvalue is $(m-1)$, then using any grade one regular element from the Heisenberg subalgebra associated to $[w]$ we can construct a KdV system possessing the standard \W-algebra defined by $I_0$ as its second Poisson bracket algebra. For \G a classical Lie algebra, we derive pseudo-differential Lax operators for those non-principal KdV systems that can be obtained as discrete reductions of KdV systems related to $gl_n$. Non-abelian Toda systems are also considered.Comment: 44 pages, ENSLAPP-L-493/94, substantial revision, SWAT-95-77. (use OLATEX (preferred) or LATEX

Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction

The $p\times p$ matrix version of the $r$-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra $\widehat{gl}_{pr}\otimes {\Complex}[\lambda, \lambda^{-1}]$. Here a series of extensions of this matrix Gelfand-Dickey system is derived by means of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra $\widehat{gl}_{pr+s}\otimes {\Complex}[\lambda,\lambda^{-1}]$ using the natural embedding $gl_{pr}\subset gl_{pr+s}$ for $s$ any positive integer. The hierarchies obtained admit a description in terms of a $p\times p$ matrix pseudo-differential operator comprising an $r$-KdV type positive part and a non-trivial negative part. This system has been investigated previously in the $p=1$ case as a constrained KP system. In this paper the previous results are considerably extended and a systematic study is presented on the basis of the Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson brackets and makes clear the conformal ($\cal W$-algebra) structures related to the KdV type hierarchies. Discrete reductions and modified versions of the extended $r$-KdV hierarchies are also discussed.Comment: 60 pages, plain TE

Heterogenized Pyridine-Substituted Cobalt(II) Phthalocyanine Yields Reduction of CO2 by Tuning the Electron Affinity of the Co Center

Conversion of CO2 to reduced products is a promising route to alleviate irreversible climate change. Here we report the synthesis of a Co-based phthalocyanine with pyridine moieties (CoPc-Pyr), which is supported on a carbon electrode and shows Faradaic efficiency ∼90% for CO at 490 mV of overpotential (-0.6 V vs reversible hydrogen electrode (RHE)). In addition, its catalytic activity at -0.7 V versus RHE surpasses other Co-based molecular and metal-organic framework catalysts for CO2 reduction at this bias. Density functional theory calculations show that pyridine moieties enhance CO2 adsorption and electron affinity of the Co center by an inductive effect, thus lowering the overpotential necessary for CO2 conversion. Our study shows that CoPc-Pyr reduces CO2 at lower overpotential and with higher activity than noble metal electrodes, such as silver

Between the Natural and the Artificial: The Sublime Sexual Sensation of Car Crashes in J.G. Ballard’s Crash

At a time when technology progressively pushes back nature, the sexual act runs the risk of being denaturalised. The notion of the sublime, which I argue is how humans react to the machine as a surrogate for nature and as a sexual stimulus in Crash (1973), is therefore of central interest in this article. Ballard himself has described Crash as ‘the first pornographic novel based on technology’ (1973, 6). This engagement with a technologised sexuality is explored as a subjective narrative stance, which grants authenticity to the fictive alter ego, who can probe alternatives to an extra-textual reality. This narrative mode is notably potent in relation to the narrator’s estimation of the merge between sexuality and technology in the form of car crashes uniting Eros and Thanatos. I therefore suggest that Crash can be read as an attempt to localise the natural and human in a world dictated by artificiality and technology

Взаємозв’язок великих кондратьєвських циклів розвитку економіки і системних світових конфліктів

Однією з найважливіших проблем, що постала перед сучасною наукою у зв’язку із стрімким розгортанням глобальної економічної кризи, загостренням світових конфліктів, є вироблення науково обґрунтованих «метричних» експрес прогнозів розвитку суспільства на ближчу і далеку перспективу