Abstract
Rob Shields’ Spatial Questions seeks to provide a conceptual framework – cultural topology – to draw together various postmodern, poststructuralist, and relational approaches to space. Unlike others who use topological figures as metaphors for folded, stretched, or deformed spaces, topology is not a metaphor or epithet for Shields. Rather, he appeals to the rigours of mathematical topology to systematize post-Euclidean theorizations of space in critical social theory. To get there, he reviews the role of space in western metaphysics from the ancient Greeks through Enlightenment to a few branches of mathematics and recent critical social theory. Here, the book contributes a detailed review to literature on the history of geographic thought that – though brief – offers a more critical consideration of theories of space in mathematics and physics. He asks for each thinker, is space ontological, metaphysical, substantive, or virtual? And what are the implications of thinking space one way or another? This section of the book leads to a recapitulation of his previous work, in which he argues that understanding space is virtual, real without being actual, and becomes actualized through social relations. Spatial formations are the products, he has argued elsewhere, of social spatialization.
At the heart of Spatial Questions is a critique of Lefebvre’s chronological analysis of socially produced spaces. For Shields, social spatialization produces overlapping and coexistent spatial forms, not sequential ones. Cultural topology provides, Shields argues, a conceptual vocabulary and ontology that privileges multiplicity, simultaneity, transformation, and relationality. Topology’s spaces are multidimensional, allowing analysis beyond four dimensions and spatial distribution. Topological spaces have their own metrics, produce their own terms of analysis, and transform through their own timings and spacings. Methodologically then, cultural topology requires attending to the specific rhythms, relations, and spacings emergent in a site. Much of this will sound familiar to readers of recent work on scale, flat ontology, affect, emergence, and relational space in geography, and readers of Deleuze and DeLanda more broadly. But in advocating fine-tuned, site-specific analysis, his argument echoes many calls for ethnographic, site-based, and situated research. The book offers an alternative to Cartesian metaphysics and Euclidean geometry to ground studies of space, but left me asking, need we appeal to mathematics to achieve this?
Shields’ goal is to show how topology ‘provides mental handholds’ for thinking about socio-spatial processes in multiple dimensions, to provide a language for the heady language of multiplicity, emergence, deformation, twists, torsions, and folds. His attempt to draw in such a wide range of social theoretical thought (from Jameson to Butler to Deleuze to Bachelard), however, stretches his argument to the point of breaking. The final chapters review recent engagements with topology thoroughly, and in this the book provides a wonderful starting point for anyone interested in the topic. But rather than providing the systematic topological approach promised at the outset, he takes on the terminology of each new thinker. By the end of the book, one is awash with overlapping terminologies. Anyone seeking a starting point is provided with many, but without a critical discussion of these different deployments of topology. Those interested in topology in particular, and histories of space more broadly, will enjoy the book, but those looking for a succinct framework for operationalizing cultural topology may be disappointed.