The Gibbs Paradox Revisited

The Gibbs paradox has frequently been interpreted as a sign that particles of the same kind are fundamentally indistinguishable; and that quantum mechanics, with its identical fermions and bosons, is indispensable for making sense of this. In this article we shall argue, on the contrary, that analysis of the paradox supports the idea that classical particles are always distinguishable. Perhaps surprisingly, this analysis extends to quantum mechanics: even according to quantum mechanics there can be distinguishable particles of the same kind. Our most important general conclusion will accordingly be that the universally accepted notion that quantum particles of the same kind are necessarily indistinguishable rests on a confusion about how particles are represented in quantum theory.Comment: to appear in Proceedings of "The Philosophy of Science in a European Perspective 2009

Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE

Of all real Lagrangian--Grassmannians $LG(n,2n)$, only $LG(2,4)$ admits a distinguished (Lorentzian) conformal structure and hence is identified with the indefinite M\"obius space $S^{1,2}$. Using Cartan's method of moving frames, we study hyperbolic (timelike) surfaces in $LG(2,4)$ modulo the conformal symplectic group $CSp(4,R)$. This $CSp(4,R)$-invariant classification is also a contact-invariant classification of (in general, highly non-linear) second order scalar hyperbolic PDE in the plane. Via $LG(2,4)$, we give a simple geometric argument for the invariance of the general hyperbolic Monge--Amp\`ere equation and the relative invariants which characterize it. For hyperbolic PDE of non-Monge--Amp\`ere type, we demonstrate the existence of a geometrically associated ``conjugate'' PDE. Finally, we give the first known example of a Dupin cyclide in a Lorentzian space

Perturbed and Permuted: Signal Integration in Network-Structured Dynamic Systems

Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding of the system response requires assessment of the degree to which the effects of one signal modulate the effects of another. This paper develops a pair of structural metrics for sparse differential equation models of complex dynamic systems and demonstrates that said metrics correlate with proxies of the susceptibility of one signal-response to be altered in the context of a second signal. One of these metrics may be interpreted as a normalized arc density in the neighborhood of certain influential nodes; this metric appears to correlate with increased independence of signal response

Subverting the spaces of invitation? Local politics and participatory budgeting in post-crisis Buenos Aires

This paper examines the political situation in Argentina in the wake of the mass protests of December 2001, which became known as the Argentinazo. Following the unprecedented turmoil in the country, which led to the resignation of President De la Rua and to the largest sovereign default in history, business ground to a halt and unemployment soared, leaving over half the population living below the poverty line by June 2002. The paper considers what new forms of political participation have emerged since the Argentinazo and analyses their relationship to the state. In particular, it examines what Andrea Cornwall has termed "invited" spaces - whereby political spaces are opened up to non-state actors - and analyses what consequences they might have for democratic practices

Invariant Yang-Mills connections over Non-Reductive Pseudo-Riemannian Homogeneous Spaces

We study invariant gauge fields over the 4-dimensional non-reductive pseudo-Riemannian homogeneous spaces G/K recently classified by Fels & Renner (2006). Given H compact semi-simple, classification results are obtained for principal H-bundles over G/K admitting: (1) a G-action (by bundle automorphisms) projecting to left multiplication on the base, and (2) at least one G-invariant connection. There are two cases which admit nontrivial examples of such bundles and all G-invariant connections on these bundles are Yang-Mills. The validity of the principle of symmetric criticality (PSC) is investigated in the context of the bundle of connections and is shown to fail for all but one of the Fels-Renner cases. This failure arises from degeneracy of the scalar product on pseudo-tensorial forms restricted to the space of symmetric variations of an invariant connection. In the exceptional case where PSC is valid, there is a unique G-invariant connection which is moreover universal, i.e. it is the solution of the Euler-Lagrange equations associated to any G-invariant Lagrangian on the bundle of connections. This solution is a canonical connection associated with a weaker notion of reductivity which we introduce.Comment: 34 pages; minor typos corrected; to appear in Transactions of the AM