Rob Shields, Spatial Questions: Cultural Topologies and Social Spatialisation. Sage, Thousand Oaks, CA, 2013, 216 pages, $52.00 hardback. ISBN 9781848606654.

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A while ago, in one of his seminal lectures delivered to the Graduate School of Design at Harvard, Bruno Latour argued that “[t]here is probably no more decisive difference among thinkers than the position they are inclined to take on space” (2009: 5). Rob Shields’ Spatial Questions dwells on this matter extensively. Engaging with spatial theory in most of its incarnations, the book contributes to conceptualisations of topology in the socio-cultural arena. This thought-provoking book adopts a critical stance that aims to transcend the metaphorical treatment of topology and clarify the potential of a topologically informed toolset fitted for spatial analysis. According to Shields, “a ‘cultural topology’ as a critical theory and method” (page 1) could provide the answer to our spatial concerns. The argument builds upon a laborious survey of the various genealogies of space that have informed Western spatial thought—from antiquity to the present day.

The book is structured in six chapters and it includes a collection of illustrations providing chronological accounts of key thinkers on space. It also includes a glossary of key terms, which I found a very useful companion, especially in relation to some of the philosophical and mathematical ideas invoked in the discussion. In the preface, Rob Shields describes Spatial Questions as “a work of thresholds, edges and folds—a topology in many senses” (page xi); point taken, since after going back and forth for several times between its chapters I realised that more than being a book that explores topological thinking, this is also a book that could be read in a topological way. Approached in a linear fashion, Spatial Questions provides a dense overview of the contributions to Western spatial thought, from early East Asian and East Mediterranean works in philosophy and mathematics to the development of non-Euclidean geometry and present day conceptualisations of space and time. Sometimes the overview becomes too dense at the expense of clarity concerning the main argument. And yet, the genealogies presented in the book are open to a non-linear reading, in which connections between different strands of thought (and different sections of the book) can be assembled in a topological fashion.

From the many questions that Shields addresses in the book, the one I have found the most resourceful is how the interplay between centre and periphery is at stake in pressing the argument for a cultural topology agenda. This is a theme that Shields explored at length in Places on the Margin (1992) and in his treatment of social spatialisation, which provides a critical response to the elusive character of space as a master category and form of knowledge that is never fully accessible. However, rather than focusing on how the relation between centre and periphery feeds into the enactment of different spatialisations, I would like to discuss how it translates into Shields’ own mapping of a genealogy of space. A topological account of the alternative histories and cultural representations of space would require a different take on the notion of time (an idea anticipated by Shields in the book’s introductive notes, page xii), or what Michel Serres refers to as a philosophy of “co-presence of the archaic and the contemporary” (2012: 369). As in Raphael’s fresco The School of Athens, this would allow distant figures to enter into dialogue even for an instant, with the Pythagoreans and the Peripatetic School to sit next to the astronomers of the Islamic Golden Age and Copernicus (page 50) or for Euclid, Apollonius and Archimedes’ diagrammatic reasoning to permeate the pioneering works of Hilbert, Klein or Poincaré in the framework of modern mathematics (Netz, 2003).

According to Brian Rotman, once mathematical diagrams are understood in terms of their performative dimension, i.e. as “embodied acts that bridge the gulf between thought and the sign” (2012: 256), the focus shifts toward their topological properties in order to account on how the abstract and the material become knotted in different configurations (see also Netz, 2010). This treatment of the diagrammatic would bring us closer to Shields’ own approach in mapping the discursive realms that fold in alternative histories and cultural representations of space. Topology, or rather topological thinking, provides the means for Shields to coil up contrasting spatialisations and negotiate the tensions, and affinities, between classical and post-classical readings of space.

The reader will find many examples in the book. One is the clash between Lenin’s dialectical-materialist agenda and Ernst Mach’s ideas, which took off with the concourse of Henri Poincaré and Albert Einstein to the development of the Theory of General Relativity (pages 65-67). As Shields argues in the final part of the book, “[t]opological approaches can take apart the static poles of ontology” (page 156) and it is through the painstaking process of carving out these complex genealogies that topology can undermine the taken for granted categories used in the treatment of space and time. To use Serres’ words, these epistemological exercises would better fit a percolation model rather than a chronological reading, in which history would be conceived “as a complex surface, conveying wormholes of sheer acceleration, bottlenecks of stoppage or equilibrium, zones of stationary values, several fragmentations…” (2012: 377).

In the last two chapters of the book, Shields provides a survey across some of the most important works that informed the establishment of topology as a formal branch of mathematics and their different articulations within social and cultural theory.  The references to Euler’s contribution to graph theory, Gauss and Riemann’s development of non-Euclidean geometry or Rene Thom’s catastrophe theory (among many others) are complemented by more ample accounts on the works of Deleuze, Foucault, Michel Serres or the STS scholars, particularly those of John Law and Annemarie Mol. This serves as a stepping stone in setting up a cultural topology agenda that would transcend the metaphorical treatment of topology and provide a means to reconcile multiple spatialisations, by offering “cultural studies a  new ‘dimensionality’ and level of precision regarding spatial and temporal relations, flows and transformations” (page 158).

Although I share Shields’ enthusiasm for the potential of topological thinking to fine-tune spatial theory to the challenges of complexity, the part I have troubles with his argument is the matter of precision. If we are indeed on the ‘cusp’ as Shields argues in the concluding section, then topology could be rather seen as a ‘boundary object’ that social science scholars are joggling with until it cools down; and perhaps it is better this way.  I think this aspect is related to a point that keeps returning in Spatial Questions and that has to do with the issue of observation; of what one observes and how one observes, topologically. The Real might be “plush-like” on the surface (page 123), but on the flip side could also prove as abrasive as sandpaper. Shields quotes Gamow’s account on Einstein “who was probably the first to realize the important fact that the basic notions and laws of nature, however well established, were valid only within the limits of observation and did not necessarily hold beyond them”(page 147).

If we are to take Lucretius’ boundary challenge seriously, there will be many tossing spears at the elastic boundaries of topology, and the question here is: ‘how far do these boundaries stretch?’ I think there is still a long way to go to domesticate topology—if this goal could ever be achieved. Yet, topology’s conceptual dimension has already proved fertile enough to stimulate new imaginaries in which to address various spatial questions. Thus, instead of aiming for precision, I would rather plead for specificity and for making clear how different approaches to topology establish continuous functions across different realms of thought, spatial and not-so-spatial categories.

Shields takes up this challenge seriously and to my knowledge, Spatial Questions provides one of the most complete accounts in the recent literature engaging with topology. The reader might be deceived by the apparently slim format, which nevertheless packs material that could easily inform several volumes on the topic. Spatial Questions is a welcome contribution to spatial theory and, given the prominence of the topic nowadays, as well as the hype built around the topological over the past years, the book might equally appeal to geographers and to a broader audience within the social sciences. 

References

Latour B (2009) "Spheres and networks: two ways to reinterpret globalization" A Lecture at Harvard University Graduate School of Design (February 17).

Netz R (2003) The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge: Cambridge University Press.

Netz R (2010) What Did Greek Mathematicians Find Beautiful? Classical Philology 105: 426–44.

Rotman B (2012) Topology, Algebra, Diagrams. Theory, Culture & Society 29: 247–60.

Serres M and T Adkins (2012) Differences: Chaos in the History of the Sciences. Environment and Planning D: Society and Space 30: 369–80.

Shields R (1992) Places on the Margin: Alternative Geographies of Modernity. London: Routledge.