Category Archives: Topologies

What is Strategy? The Topological Exercise of Power

Topology of Power

What does it mean to say that power operates ‘topologically’ in politics, economics and everyday life?  Topology concerns non-Euclidean geometries – the kinds one might observe if one stretched a drawing of a triangle. Another example of a topological transformation is if one added dimensions to the drawing, extending the triangle into a 3 dimensional pyramid or developing and imagining it even further in more dimensions.

The topological character of power is that it exceeds ‘action on bodies’ or ‘action on others’ actions’ (cf. Foucault). Using techniques and administrative apparatuses, power can be projected as ‘action at a distance’. ‘Reach’ is a keyword that describes this extension of power to actualize it and put it into action despite intervening distances and mediations . For example, we talk of ‘the long arm of the law’.

The powers of a topological sensibility

Powers are multiple, subtle and include influence. ‘Reach’ describes the influence an actor may have on other actors.

Powers exists in and as ‘power relations’, whether the parties are aware that power is a factor. That is, power doesn’t have to be exercised as much as it simply has to have an effect. As such it is not a concrete thing but a virtual or intangible thing. It is real but not actual, ideal but not abstract. It has a multiple quality. There is no single ‘power.’

Sovereignty’ designates the aggregate powers exercised by the state. History is the time of this power-exercise. Territory is the space of the exercise of sovereignty.

However, States can no longer pretend to guarantee their citizens’ safety from other threats that are themselves powerful. These might include the threats of drone strikes and collateral damage and death (Pakistan, Somalia), of chemical poisoning by nerve agents (UK Skripal nerve agent poisoning), from drifting radiation particles (Scandinavia after the Chernobyl disaster), or from pandemics (SARS in Toronto Canada).

The polis, now often associated with cities, is the space of the demos, the people and democratic opinion.  It is a distinct space-time of assembly and belonging and as such a distinct topological entity.  It is not just a different scale.


Strategy’ is a political technology that aims to persuade by establishing the spatiotemporal and other background conditions of a debate. A common strategy is public ‘consultation’ which aims to establish a ‘pubic will’ extracted from a population that legitimates a political course of action and/or the exercise of power. Power is not always exercised strategically, but even whimsical applications of power, if consistent, can be described as part of a strategy.

Tactic’ is the deflection of strategies, in the absence of control over the spatiotemporal and other dimensions of the context of a situation or of the exercise of power (cf. DeCerteau).

Influence,’ the multiplicity of powers, means that strategy is not closed off from the public or subaltern groups, or even individuals that act through social media as ‘influencers’.

Social media technologies and platforms have created new manifolds or spaces of power that exceed the reach of sovereign territories. These technologies are political and their strategic use for disinformation, persuasion has reconfigured the terrain of politics and the reach of these social media actors in general. For example, influencing the US election, extended Russia’s reach into the processes of the US sovereign state as well as into American territory.

Why? The reach of a topological sensibility

All this is more quickly grasped if one has a topological sensibility, looking to dimensions and influences rather than fixed actors such as “the State”.  This approach allows us to move from understanding positions of strength in a debate, project or struggle toward how to actualize that position as effects, to understand its reach; or to put it simply, to understand the power of the position explicitly.

Bearing the topological qualities of power in mind allows us to compare in one plane, so to speak, between power-geometries that are fixed, and to see the operation of power-topologies that stretch or bring new dimensions to the exercise of power. It allows a point-to-point comparison that pinpoints the effectiveness of the transformation that has occured despite the differences in appearances or the complexity of any resulting folded, stretched, involuted or flattened topologies.

Rob Shields (University of Alberta)


Comparison with Michel DeCerteau’s notion of tactics and strategy from The Practice of Everyday Life (translated from French 1984)

Strategy: “the calculus of force-relationships which becomes possible when a subject of will and power (a proprietor, an enterprise, a city, a scientific institution) can be isolated from an ‘environment.’  A strategy assumes a place that can be circumscribed as proper (propre) and thus serve as the basis for generating relations with an exterior distinct from it (competitors, adversaries, ‘clienteles,’ ‘targets,’ or ‘objects’ of research). Political, economic, and scientific rationality has been constructed on this strategic model”(Certeau xix);
Tactic: “a calculus which cannot count on a ‘proper’ (spatial or institutional localization ),nor thus on a borderline distinguishing the other as a visible totality. The place of a tacticbelongs to the other.  A tactic insinuates itself into the other’s place, fragmentarily, without  taking  it over in its entirety, without being able to keep it at a distance…”(Certeau xix).
Operations: goes along with tactics as actions that form a “network of an antidiscipline”(Certeau xiv-xv).
Trajectory: “suggests a movement, but it also involves a plane  projection; a flattening out… a graph… a line that can be reversed” (Certeau xviii).

Works cited:

de Certeau, M. (1984). The Practice of Everyday Life. Berkeley: University of California Press.

de Certeau, M. (1985). Practices of Space. In M.Blonsky (Ed.), On Signs (p. 134ff.). Oxford U.K.: Basil Blackwell.

Topology of Denial

Climate Change, Declining Sea Ice, Extinction of Polar Bears

Topology of a Changing Climate: Evidence and Denial
The “space” of 2 intersecting issues: declining Arctic sea ice and the future of polar bears in climate change denying blogs and scientific papers (from Harvey et al in Bioscience (Nov 29 2017)).


Analysis of statements about the future of polar bears and declining Arctic sea ice reveals a polar contrast between climate change deniers’ blogs and evidence-based scientific reports.  This produces the hints of a manifold or topological space where the debate is both polarized around a left-right axis and features another line of flight (“will adapt”) that nonetheless remains within the 2 limiting dimensions of the graph of affirmation vs. denial.

Charts from Jeffrey A. Harvey Daphne van den Berg Jacintha Ellers Remko Kampen Thomas W. Crowther Peter Roessingh Bart Verheggen Rascha J. M. Nuijten Eric Post Stephan Lewandowsky Ian Stirling Meena Balgopal Steven C. Amstrup Michael E. Mann (2017). Internet Blogs, Polar Bears, and Climate-Change Denial by Proxy. BioScience.

Rob Shields (University of Alberta)

Tax Havens-R-Us: Digital non-geographies and the financial gaming of distance and difference

In today’s world of off-shore tax havens,i quantitative easing,ii high frequency trading,iii and rampant global asset and real estate speculation it seems that a sort of gamified monetary space-race is going on and that it’s advancing with increasing speed. This monetary space-race game is one that is partially defined by both off-shoring and “on-shoring,” by both making assets disappear behind the legal shrouds provided by nation states that profit by providing secrecy to wealthy international clients and conglomerates, and by making virtual assets material in the form of, for example, international real-estate speculation.

But this immaterial/material financial binary is not adequate if we are to identify more comprehensively the space and spaces – the game dynamics – being put to work in service of global finance capital. For example, as but one expression of this monetary space-race, the recent tax haven scandals surrounding Panama’s Mossack Fonseca (which after two weeks of headlines is barely discussed anymore) is not so much about securing or profiting from locating capital in distant geographical spaces – tax-free islands, sandy beaches, and sun-drenched shell-company postal boxes, as it is about taking advantage of new and emerging forms of: 1) interstitial temporal spaces; 2) immaterial or undetectable digital spaces; and / or 3) invisible spaces that, as far as the public is aware, simply do not exist. That is, despite superficial appearances, the new monetary space-race is less about physically off-shoring capital and currency, than it is about staying ahead of the embittered and comparatively impoverished masses and the increasingly indebted governments ever more desperate for funds by hiding, or making invisible, digital money that’s been stored in “the cloud,” on the internet, or on an array of hard-drives. In other words, generating financial distance between wealth and the tax-hungry governments who would love access to it is not achieved through the separation offered by geographical space, but through the creation of new spaces, non-spaces, unknowable spaces that may or may not be physically located in a data-centre or business park next to you in Canada, London, New York,iv or Delaware.v

Continue reading Tax Havens-R-Us: Digital non-geographies and the financial gaming of distance and difference

Topologies and Landscape Architectures 1: Topology. Landscript 3

Vrin, Val Lumnezia, Switzerland

Topology, Landscript 3.  Christophe Girto, Anette Freytag, Albert Kirchengast, Dunja Richter (eds). Institute of Landscape Architecture ETH Zürich. Berlin: Jovis. 2013.

Landscript 3 Topology is the outcome of a workshop and the project ‘Topology – on designing landscape today’ that looked at the integrative role of landscape architecture and sought a theoretical foundation that would strengthen the aesthetic theory and pedagogy of landscape architecture in the context of new, interdisciplinary perspectives on buildings, the environment and cities. Shortcomings in the translation makes for some difficult reading. Topology here refers to changing the extent, scale and dimensions of the tasks that landscape architecture has set for itself. Stepping beyond the garden of traditional landscape architecture, or the vista of landscapes, the profession is now interested in spatial relations more generally. Topology builds on Aristotle’s definitions of topoi and topic as a rhetorical concern with sorting out what the parts of an argument will consists of and preparing them.

There are a few nuggets that leap out of the text:

Design is understood as the taming of complexity, (Kirchengast p.26).

Lucius Burckhardt, a Swiss sociologist and urban planner, and André Corboz, an architectural historian, are introduced for their theory of landscape as a social product (2006) and as a concept projected onto the environment. In Die Kunst, Stadt un Land zum Sprechen zu bringen (Basel 2001) Corboz emphasizes that and territory is an historical palimpsest. Links to the American landscape historian J.B. Jackson are noted. A later post will compare with the work of Augustin Berque.

In Warum ist Landschaft schön? die Spaziergangswissenschaft (Berlin: Schmidt 2006) Burckhardt argues: “Since spatial landscape – as in the case of an English garden – his first produced through the eyes of a viewer, it is not only pictorial also significantly structured by time”. Burckhardt suggested taking “walks as an instrument in order to adequately involve this dimension of time. Strolling denotes a time-based organization of the space from a subjective perspective enables the formation of spatial relationships.”

“He did not consider planning and design to be active processes of creation an organization that resulted in “good form” and “clear systems”… ([But] the recognition and direction of the invisible impetus within systems… Determined scratch that no longer determined by the objects and their technical, practical functions.”

Landscape “flows” with the times and changes constantly. It is not an objective entity that can be defined as synthetic product of interaction relation that needs to be situated within the system of reference.  This provides links to my position that landscape as an intangible virtuality is both real and ideal and distinct from the actually existing fauna and flora.

This position is summarized in Gion Caminada’s development planning of the isolated Swiss village of Vrin, which exploits its remoteness in a manner that provides lessons for planners in other rural communities everywhere.

-Rob Shields, University of Alberta

Topological Atlas


In a world of rising inequalities and growing conflict borders are multiplying and becoming increasingly complex. Whilst the border as spatial metaphor is used extensively in architecture, borders as political and material realities are often overlooked. This conference explores architecture’s relationship with border geographies.

This conference was organized in November at Sheffield University’s School of Architecture by the Theory Forum  It had an architecture focus but the notion of the topological has broad relevance for understanding the “reach” of agency and of powers beyond physical boundaries.  This might be thought of as part of a wider movement in the social sciences that challenges Cartesian and Baconian notions of the empirical and of objects, dimensions and causality within the commonsensical everyday visual spatialisation that is the foundation of classical science.  The organizers ask:

How do we represent borders as topological spaces rather than the flat two-dimensional planes of standard maps? What happens when rigid political borders cross fluid ecologies? How are ecological borders acknowledged or not in planning and design?

Ecological borders not only operate at the level of the landscape or territory, but also at the level of the body. Posthumanist discourse blurs the borders of who or what we consider human. In a technologically mediated world, where does the border between the body and the environment lie?

This is reflected in the papers that headlined the conference.  To choose only two:

Celia Lury: Double Blind, Double Bind: The plane that disappeared – (a problem of first and second order observation)?

The empirical focus of this paper is ‘the disappeared plane’, Malaysia Airlines Flight 370 (MH370/MAS370), the scheduled passenger flight from Kuala Lumpur to Beijing that lost contact with air traffic control on 8 March 2014 at 01:20 MYT, less than an hour after takeoff. The paper explores how it is possible for a plane to ‘disappear’ in an era of total planetary observation by describing the composition of a surface of visualization in terms of the boundary-making capacities of hypotheses of sight. It will be argued that, as a function of algorithmic rules of digital computation, today’s surfaces produce a patterning of vision that is cross-cut by multiple orders of observation and a whole variety of depths, intensities, neuroses, psychoses, and densities. In dialogue with Galison’s work on secrecy, the paper aims to show how the apparently edgeless surface of the locally flat surface of global planetary vision is striated not only by multiple corridors and targets, but also by blind spots, fuzzy patches and edges, resulting in the production of the recursive fractal of public-private in terms of degrees of public-ness and complex patterns of political and economic inclusion, exclusion and belonging.

Omar Nagati: Blurring boundaries, reconstituting borders: Examples from Cairo public space since 2011

Over the past three years, Cairo has been experiencing major political transformations played out on its streets and in its public space. Throughout alternating conditions of flux and restoration, disruption and reestablishment of “order” CLUSTER has been involved in a number of research and documentation projects as well as design schemes and intervention strategies to account for these changes and critically engage its spatial implications.

Over the past three years, Cairo has been experiencing major political transformations played out on its streets and in its public space. Throughout alternating conditions of flux and restoration, disruption and reestablishment of “order,” CLUSTER has been involved in a number of research and documentation projects as well as design schemes and intervention strategies to account for these changes and critically engage its spatial implications.

These projects range from the microscale of sidewalks and in‐between spaces, to the city scale of infrastructure and public services. One common theme underlying these examples is the constant interplay of contestation and negotiation between not only competing interests and stakeholders, but also competing frames of reference and normative orders, whereby borders between public and private, formal and informal, and the spatial and political are being repeatedly blurred and reconstituted.

This presentation offers a background for the broader context of the rapidly shifting political and urban landscapes in Cairo during the past few years, and discuses a few examples ranging from street vendors, downtown passageways, to informal development along the Ringroad and Ard al Liwa community Park.

 Further papers here.

-Rob Shields, University of Alberta