Date published: 2005/05/05

Alan Sokal is giving a lecture "Fermionic field theory for trees and forests" at the Centre for Mathematical Sciences on 12 May at 4 PM. He is known less for his physics than for his pretend article "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity" which was published in the journal "Social Text" and allows us all to mercilessly take the piss out of the crackpot social "scientists" who use pseudo-scientific mumbo-jumbo to try and hide their complete lack of anything useful to say. This kind of posturing seems to have largely started in France but apparently many American humanities departments have been hijacked by these people (and Cambridge is not immune).

It is therefore interesting to read the lecture abstract:

"We prove a generalization of Kirchhoff's matrix-tree theorem in which a large class of combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special case, we show that unrooted spanning forests, which arise as a q --> 0 limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. We show that this latter model can be mapped, to all orders in perturbation theory, onto the N-vector model at N=-1 or, equivalently, onto the sigma-model taking values in the unit supersphere in R^{1|2}. It follows that, in two dimensions, this fermionic model is perturbatively asymptotically free."

Compare that with a typical paragraph from his joke article:

"In string theory, the quantum-mechanical amplitude for the interaction of n closed or open strings is represented by a functional integral (basically, a sum) over fields living on a two-dimensional manifold with boundary. In quantum gravity, we may expect that a similar representation will hold, except that the two-dimensional manifold with boundary will be replaced by a multidimensional one. Unfortunately, multidimensionality goes against the grain of conventional linear mathematical thought, and despite a recent broadening of attitudes (notably associated with the study of multidimensional nonlinear phenomena in chaos theory), the theory of multidimensional manifolds with boundary remains somewhat underdeveloped. Nevertheless, physicists' work on the functional-integral approach to quantum gravity continues apace, and this work is likely to stimulate the attention of mathematicians."

A naive observer might be forgiven for thinking that the first paragraph is more of a joke than the second one. But a theoretical physicist will tell you that the first paragraph makes perfect sense, it just so happens that modern theoretical physics is far removed from the ordinary concepts of life.

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