Geography,space and the re-emergence of topological thinking

Geography and power

Allen’s ‘topological twists’ is a topical contribution to ongoing debates on the changing spatialities and forms of power in the globalizing world of interactions. It is also an effort to scrutinize the nuances of such keywords as topology, network, scale and territory. Allen invites us to rethink some categories related to clear-cut topographies (location, distance, near/far, here/there, inside/outside, borders/border-crossings) in the context of power. This issue has been touched upon in philosophy, postcolonial studies, International Relations studies and political geography for decades, but it is increasingly significant, since spaces are increasingly understood as heterogeneous and being in the process of becoming.

Following the train of relational thinking he suggests that power is a relational effect of social interaction that may bridge the gap between ‘here’ and ‘there’ (and absence and presence) through a ‘succession of mediated relations or through the establishment of simultaneous presence’ (Allen, 2003: 2). He argues that power is never power in general, but always power of a particular kind: modalities of power such as authority, domination, seduction, manipulation or coercion have their own relational spatialities. He also illustrates how topological thinking helps to understand how spatialities of power are constituted and modified through social relations across spaces and distances, rather than merely radiating from certain locations.

We can contrast this ‘multiple’ view with other recent geographic theories of power. John Agnew (2005) has scrutinized the geographies of global power and hegemony. For him political power is exercised from sites that vary in their geographical reach that can be hierarchical, network-based, territorial or contiguous. It is the balance between levels of hierarchies of power that determines the spatiality or geographical configuration of political power at a given time (p. 39).

Richard Peet (2007) puts even more stress on structural mechanisms and unevenly distributed sources and objects of power. For him power means control, by a person or an institution, over the minds, livelihoods and beliefs of others. Power takes three forms: ideological (control over rationalities), economic (control over capital) and political (control over practice) (p. 22). The geography of power refers to the concentration of power in a few spaces that control a world of distant others. This geography of economic, ideological and political power is largely concentrated into the key cities of western capitalist states. The task of his theory is the transformation of power through policy-making. This should happen by exposing the structures, centers and mechanisms of power, by analyzing critically its intellectual foundations and undemocratic justification and by being committed to support the opponents of such power structures.

If Allen ‘locates’ power in complex relational ‘topologies’ related to actors’ social relations, Agnew and Peet strive to ‘locate’ it also in space that is structured along certain sociospatial principles, thus paying more attention to the concentration of power and related economic and political processes that create uneven development.

Topological thinking

Topology is a major field of mathematics that studies the spatial properties of an object or network that ‘remain true when that object is stretched’ (Harris, 2009: 762). Topology has long, but often unrecognized, roots in social science. Think, for example, of the following citation:

We use the term ‘social space’ in the Riemannian sense, i.e., as a mathematical (geometric) construct defined as a manifold in which positional relationships of any kind may be expressed. From this point of view we may employ spatial constructs to depict relationships quite independent of direction and distance. These may be relationships of connection, position, or any other properties of a qualitative, nonmetrical nature. According to Riemann, spaces may be constructed of any dimensions and properties provided they are logically consistent. He also showed that the properties of a space may be dependent upon the dynamics of processes within that space. Topology, as the geometry of such spaces, may therefore be of great importance to sociology as a solution of the controversy over quantitative vs. qualitative methods … The use of spatial constructs and terms with reference to social relationships is, of course, very ancient and merely reflects the fact that relational thinking tends to structure itself in spatial terms. (Lundberg, 1939: 131)

This text is not from current network theorists, but from Lundberg’s (1939) The Foundations of Sociology where this neopositivist strived to make sociology a science in the spirit of law-seeking physical sciences. This tendency to formalize social topologies and their inherent powers/autonomy has endured in Anglophonic sociology (Burr, 1980). Similarly topological approaches are important in computer science and operational research.

As is well known, geographers became familiar with geometric thinking along with location theory. During the heydays of positivist thinking, scholars like Bunge (1962) saw geometry as the language of geography and used topology to illustrate transport networks. Also Harvey (1969) discussed extensively the roles of topology as part of his excursion into ideas of spaces. The efforts to make sense of what ‘space’ is led Anglophonic geographers to look at the texts written by philosophers, physicists and cosmologists. Ideas were often borrowed roundly and some authors soon recognized a need to move from ‘absolute’ to relative and relational space or from Euclidean metric spaces to some other spaces. Such debates were at the background when geographers looked at social space. More recently, geographers have found topology important in the context of GIS and graph theory.

Current interest in topology marks a revival of this old idea but from a different direction. As Murdoch (2006: 12) has observed, new ideas are promoted by poststructuralist authors (actually he does not mention previous social scientific discussions on this idea). Besides sociologists, authors such as Badiou, Deleuze, or Lacan have referred to ‘topology’, whatever it means to each of them and how they relate it to geometry (Gómez, 2009).

Allen’s topological thinking comes from this new direction where space is seen as a (performed) product of networked entities (or objects). For Allen, power relations are not positioned in space or extended across it, but rather they compose the spaces of which they are part – i.e. it reminds us of Leibniz’s relational philosophy of space (‘space is a coexistence of objects’). This concept was recognized by Anglophonic geographers in the 1960s when new ideas of space were actively searched. In German geography, the Leibnizian idea of space was noted before the Second World War (Paasi, 2011).

Contrary to currently typical claims in geography to abandon ‘this’ or ‘that’ category, Allen’s proposal is more placatory. He states that while topology poses a challenge to the more clear-cut topographies common to the spatial arrangements of territorial and networked power, it does not displace or replace them: each spatial frame has its place in understanding power’s geographies and much depends upon the questions asked about power and its institutional relationships. Respectively, he suggests, topological understanding merely bring us into line with many of the shifting geographies of power practiced by various agencies.

The problem is that we do not have any context-free means to decide what is in general the best way to understand the relations between space and power, i.e. whether topographical, network, or topological understanding (or perhaps still some other emergent idea) will work best in making sense of the contextual, heterogeneous features of the relational social world. Respectively, Allen’s suggestion that much depends upon the questions asked about power is most laudable.

We should not take any concept of space for granted. Since social science is studying open but yet contextual worlds, a perpetual strive towards conceptualization is needed. As Harvey (1973: 13) notes, space is ‘neither absolute, relative or relational in itself, but it can become one or all simultaneously depending on circumstances’ and, further, ‘the problem of the proper conceptualization of space is resolved through human practice with respect to it’. Human practice – an issue accentuated also by Allen – forces us to reflect on the meanings of context: social life and culture that have their impact on how increasingly relational, stretching spaces are shaped and how the narratives on geographies and identities are situated.

Another question is to what extent we do need to lean on geometric vocabularies? Is there a risk of ‘geometric fetishism’ when we use them as analogies, metaphors or even metonyms? A fitting example is Massey’s (1993) ‘power geometry’ which has been ‘twisted’ in literature in innumerable ways that often are far away from the original idea. A hint of such a risk is present in Allen’s article where not only is the idea of geometry referred to innumerable times in mathematical or metaphorical sense, but also recent ideas of territory, state, scale, or network are ‘geometricized’ perhaps more than is necessary. I found this somewhat confusing, since the efforts of the early ‘social topologists’ (or positivist geographers) to formalize social space in the name of Science are far away from Allen’s theoretical intentions.

The changing territories

Allen’s recognition of the (historically contingent) modalities in the relations ‘between’ space, objects, and power is pertinent in the current complex world. Yet we still have certain sociospatial elements that we cannot write off. While the functions and whole understanding of territories, for example, have changed and borders are increasingly crossed, they have not vanished. They are mobilized and modified in new ways for different purposes by the state/statecraft and innumerable other ‘small’ and ‘big’ actors operating inside and outside of such units. This is part of the multiple character of territory, its perpetual becoming and related relations of power and, if you like, de- and reterritorialization.

Allen (1999) has earlier noted how we still live in a world of fenced-off territories and exclusion, again reminding us of the need to problematize power, identity, and simple binary thinking. Human territories – processes that become institutionalized but can also come to an end as part of the production and reproduction of space – display how absolute, relative, and relational aspects of space became fused in material practices (boundary-making), representations (mapping), and lived meanings (affective loyalties to territorial units) (Harvey, 2009: 174). Hassner (1997) has suggested that territory is a piece of land (that can be marketed, sold, exploited as a sacred heritage), and it may be a seat of power and a functional space. Respectively, territory compasses dimensions of identity, of authority and of administrative bureaucratic or economic efficiency in the management of social mechanisms. And, I would add, territory is even more. Besides more conventional spatial elements like ‘border’ or ‘sovereignty’, territory is thus related to phenomena such as a passport, citizenship, taxation, legislation, governance, democracy, voting, police, army, war, socialization, hegemonic/counter-hegemonic ideologies, nationalism/regionalism, resources, uneven development, identity narratives, passionate emotions, fear, love, hate, othering, exploitation based on class, gender, and ethnicity. Territories are also related to international agreements, alliances, interactions, and transactions. Territories are also increasingly related to border-crossing capabilities that may challenge one-sided views on bounded spaces and also force us to rethink the location of borders.

Context makes a difference also in the case of territories. I will take one example related to NGOs, the state, and sovereignty (all discussed by Allen) to show the need for a contextual sensitivity. Keck and Sikkink (1998: 215–216) conclude their study that, for the most part, activists in the North see the erosion of sovereignty as a positive thing: ‘for human rights activists it gives individuals suffering abuse recourse against the actions of their own state; for environmental activists it allows ecological values to be placed above narrow definitions of national interest’ (p. 215). They state how northerners often consider that a weaker sovereignty might improve the political clout of the most marginalized people in developing countries. Many activists in the south may have a different view: rather than seeing sovereignty as a ‘stone wall blocking the spread of desired principles and norms, they recognize its fragility and worry about weakening it further’. And even where third world activists may oppose the policies of their own governments, ‘they have no reasons to believe that international actors would do better, and considerable reason to suspect the contrary. In developing countries it is as much the idea of state, as it is the state itself, that warrants loyalty’ (p. 215).

Coda

John Allen’s account provides conceptual tools to scrutinize the current complex spatialities of power. It also supports the idea that the globalizing ‘world is not getting so small that there is room for only one story’ (Massey, 2010), a story that leans one-sidedly on topography, networks, topology, scale, region, or place. Whatever perspectives we find useful in interpreting the relations of the spatial worlds (and words), the aim should be to hold the multiple and singular together (Murdoch, 2006). This means that rather than some given conceptual perspectives, the marriage between ‘conceptualization’ and ‘contextual’ has be a crucial part of our research.