Mapping cosmopolis: moral topographies of the medieval city

Cosmopolis is a concept that has a long history in many cultures around the globe. It is a mirroring of the 'social' and 'natural' worlds, such that in one is seen the order and the structures of the other -- a mutual 'mapping'. In this paper I examine how the presence of cosmopolis -- a Christianised cosmopolis of the European Middle Ages -- was made evident in the representation and formation of cities at that time. I reveal a dualism between the social and spatial ordering of both city and cosmos which defined and reinforced social and spatial boundaries in urban landscapes, evident for example in the 11th and 12th centuries. Recently, Toulmin (1992) has taken the idea of cosmopolis to argue that it has been a persistent presence in Western - Enlightenment science, philosophy, and religion -- a 'hidden agenda of modernity'. I contend that, as an idea, cosmopolis has a much earlier circulation in European thinking, not least in the Middle Ages. Locating cosmopolis in the medieval and the modern periods then begs a question of what is it that really makes the two distinct and separate? All too often human geographers have emphasised discontinuities between the 'medieval' and 'modern' age, locating the 'rise of modernity' some time in the Enlightenment period. However, what 'mapping' cosmopolis reveals are continuities, binding time and space together, which when looked at begin to help query the modernity concept itself.

Rethinking the early medieval settlement of woodlands: evidence from the western Sussex Weald

The assumptions underlying the interpretation of the early medieval settlement of woodland are challenged through a detailed study of the Weald in western Sussex. The patterns of usage of woodland in England were very varied, and each area needs to be looked at individually. Systems of woodland exploitation did not simply develop from extensive to intensive, but may have taken a number of different forms during the early medieval period. In one area of the Weald, near to Horsham, the woodland appears to have been systematically divided up between different estates. This implies that woodland settlement may not always have developed organically, but this type of landscape could have been planned. It is argued that the historical complexity of woodland landscapes has not been recognised because the evidence has been aggregated. Instead, each strand of evidence needs to be evaluated separately.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.