Life, Logic, and the Pursuit of Purity

In the *Science of Logic*, Hegel states unequivocally that the category of “life” is a strictly logical, or pure, form of thinking. His treatment of actual life – i.e., that which empirically constitutes nature – arises first in his *Philosophy of Nature* when the logic is applied under the conditions of space and time. Nevertheless, many commentators find Hegel’s development of this category as a purely logical one especially difficult to accept. Indeed, they find this development only comprehensible as long as one simultaneously assumes that Hegel breaks his promise to let the logic do the leading. However, if Hegel were to in fact allow the logical development to be led by biological analogies at this point, problems would ensue. Not only would it contradict his own speculative method, which should secure the necessity of the categories, but it would also endanger the ontological generality of the category of life itself. Beyond undermining his method and the logical integrity of the category, however, I will argue that such a reading makes the transition to the next category of “cognition” unintelligible and problematic. My aim in the first part of this paper is to argue how logical life can be read as a pure category. I then argue in the second part how my reconstruction makes the transition to cognition intelligible without resorting to profane or supernatural interpretations

G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions

We present a tentative formulation of theories of gravity with suitable matter content, including in particular pure gravity in D dimensions, the bosonic effective actions of M-theory and of the bosonic string, in terms of actions invariant under very-extended Kac-Moody algebras G+++. We conjecture that they host additional degrees of freedom not contained in the conventional theories. The actions are constructed in a recursive way from a level expansion for all very-extended algebras G+++. They constitute non-linear realisations on cosets, a priori unrelated to space-time, obtained from a modified Chevalley involution. Exact solutions are found for all G+++. They describe the algebraic properties of BPS extremal branes, Kaluza-Klein waves and Kaluza-Klein monopoles. They illustrate the generalisation to all G+++ invariant theories of the well-known duality properties of string theories by expressing duality as Weyl invariance in G+++. Space-time is expected to be generated dynamically. In the level decomposition of E8+++ = E11, one may indeed select an A10 representation of generators Pa which appears to engender space-time translations by inducing infinite towers of fields interpretable as field derivatives in space and time.Comment: Latex 45 pages, 1 figure. Discussion on pages 19 and 20 altered. Appendix B amplified. 4 footnotes added. 2 references added. Acknowledgments updated. Additional minor correction

Representations of G+++ and the role of space-time

We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++. In particular, for E8+++, this applies to all its fundamental representations. However, there are some important examples, such as An+++, where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++. Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions.Comment: 45 pages, 9 figures, 9 tables, te

E10 and SO(9,9) invariant supergravity

We show that (massive) D=10 type IIA supergravity possesses a hidden rigid SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional reduction to one (time-like) dimension. We explicitly construct the associated locally supersymmetric Lagrangian in one dimension, and show that its bosonic sector, including the mass term, can be equivalently described by a truncation of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a decomposition of E10 under its so(9,9) subalgebra. This decomposition is presented up to level 10, and the even and odd level sectors are identified tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further truncation to the level \ell=0 sector yields a model related to the reduction of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated to the latter, is shown to be a proper subalgebra of E10, in accord with the embedding of type I into type IIA supergravity. The corresponding decomposition of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable by downloading sourc

Challenging workplace inequality : precarious workers’ institutional and associational power in Gauteng, South Africa

Abstract: The world of work has been reorganised, the numbers of workers employed through the standard employment relationship has declined and there has been an increase in non-standard employment: labour broking, outsourcing and other forms of precarious and temporary work. This has created highly unequal workplaces where atypical workers perform the same work as permanent workers for often half the wages of what a permanent worker receives. This article considers how precarious workers are organising, outside of trade unions, to fight against workplace inequality to gain rights to permanent work. This article develops the power resource approach (PRA) as a lens through which to explore how labour broker workers are organising in Gauteng. Through the analysis of two workplace case studies, the article examines how amendments to the Labour Relations Act (LRA) in 2015 provided new rights and a new avenue through which precarious workers could organise. The case studies illustrate the dynamic interactions between institutional and associational power, an often overlooked relationship , and demonstrate the multiple avenues through which precarious workers mobilise their power to fight against inequality

Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories

A description of the bosonic sector of ten-dimensional N=1 supergravity as a non-linear realisation is given. We show that if a suitable extension of this theory were invariant under a Kac-Moody algebra, then this algebra would have to contain a rank eleven Kac-Moody algebra, that can be identified to be a particular real form of very-extended D_8. We also describe the extension of N=1 supergravity coupled to an abelian vector gauge field as a non-linear realisation, and find the Kac-Moody algebra governing the symmetries of this theory to be very-extended B_8. Finally, we discuss the related points for the N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields

An E9 multiplet of BPS states

We construct an infinite E9 multiplet of BPS states for 11D supergravity. For each positive real root of E9 we obtain a BPS solution of 11D supergravity, or of its exotic counterparts, depending on two non-compact transverse space variables. All these solutions are related by U-dualities realised via E9 Weyl transformations in the regular embedding of E9 in E10, E10 in E11. In this way we recover the basic BPS solutions, namely the KK-wave, the M2 brane, the M5 brane and the KK6-monopole, as well as other solutions admitting eight longitudinal space dimensions. A novel technique of combining Weyl reflexions with compensating transformations allows the construction of many new BPS solutions, each of which can be mapped to a solution of a dual effective action of gravity coupled to a certain higher rank tensor field. For real roots of E10 which are not roots of E9, we obtain additional BPS solutions transcending 11D supergravity (as exemplified by the lowest level solution corresponding to the M9 brane). The relation between the dual formulation and the one in terms of the original 11D supergravity fields has significance beyond the realm of BPS solutions. We establish the link with the Geroch group of general relativity, and explain how the E9 duality transformations generalize the standard Hodge dualities to an infinite set of `non-closing dualities'.Comment: 76 pages, 6 figure

Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine and naphthalene

Anisotropic displacement parameters (ADPs) are commonly used in crystallography, chemistry and related fields to describe and quantify thermal motion of atoms. Within the very recent years, these ADPs have become predictable by lattice dynamics in combination with first-principles theory. Here, we study four very different molecular crystals, namely urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene, by first-principles theory to assess the quality of ADPs calculated in the quasi-harmonic approximation. In addition, we predict both thermal expansion and thermal motion within the quasi-harmonic approximation and compare the predictions with experimental data. Very reliable ADPs are calculated within the quasi-harmonic approximation for all four cases up to at least 200 K, and they turn out to be in better agreement with experiment than the harmonic ones. In one particular case, ADPs can even reliably be predicted up to room temperature. Our results also hint at the importance of normal-mode anharmonicity in the calculation of ADPs

QCD Corrections to Vector-Boson Fusion Processes in Warped Higgsless Models

We discuss the signatures of a representative Higgsless model with ideal fermion delocalization in vector-boson fusion processes, focusing on the gold- and silver-plated decay modes of the gauge bosons at the CERN-Large Hadron Collider. For this purpose, we have developed a fully-flexible parton-level Monte-Carlo program, which allows for the calculation of cross sections and kinematic distributions within experimentally feasible selection cuts at NLO-QCD accuracy. We find that Kaluza-Klein resonances give rise to very distinctive distributions of the decay leptons. Similar to the Standard Model case, within the Higgsless scenario the perturbative treatment of the vector-boson scattering processes is under excellent control.Comment: 22 pages, 20 figure

The density matrix in the de Broglie-Bohm approach

If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie-Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell appears to suggest that such an interpretation is not possible. Bell's argument is shown to be based upon a different understanding of the density matrix to that proposed here.Comment: 15 pages, 4 figure