Relations and locations: New topological spatio-temporalities in education

Abstract

This paper provides an account of the topological and its description of contemporary culture and use as a research methodology, a topological lens, generally, and in education research specifically. Some commentary is proffered on the relationships between the topological and the topographical, between relations and locations. A critical account is then provided on each of the papers in the special issue on the topological in education research and the specific contributions of each. The editors of the special issue make the important point that the topological is a spatio-temporal phenomenon, not just a spatial one. The topological does not exist in time and space, but rather constructs both and they change in a conjoint manner. As such, a topological lens rejects a construction of space as static and of time (and the temporal) as simply linear and chronological. The topological has been facilitated and articulated by and through practices of commensuration, datafication and digitalisation, flows and scapes, global connectivities and new relations, mobilities of various kinds and multiple networks. The paper argues that much greater emphasis has been given to the spatial in topological research; that is, there has been some neglect of the temporal in the spatio-temporal character of topologies.

Introduction

Lury et al. (2012) have written about the becoming topological of culture manifested in changing, emergent contemporary structures and spaces of power, particularly in new modes of governance enabled by advanced computational and analytical capacities, as well as the datafication and digitalisation of the social. These enable new relations, networks and connectivities. Lury et al. note the proliferation of relations and also argue that the topological is now emergent and evidenced in metrics, orderings, fractals, modelling, networking and mapping. We need also to see this becoming topological of culture as linked to the new spatialities that have accompanied globalisation (Amin, 2002). On this very point, Lury et al. observe, ‘Just as the rationality of culture is becoming co-extensive with the globe, the globe itself is simultaneously being brought into existence as a topological space’ (p. 28). They also argue that topology is now a way of analysing and understanding culture.

Education is a central element of culture, articulating and rearticulating it, reproducing it, challenging it, resisting and responding to it. Thompson and Cook (2015), utilising Lury et al.’s work and that of Deleuze and Guattari, speak of the becoming topologies of education. They align the concept of topology with Deleuze and Guattari’s concept of assemblage; noting, ‘For Deleuze and Guattari, topology (as assemblage) is a theorisation of selection and ordering, of elements and the connections and the relationships made possible as a result of this ordering function’ (p. 733). They also talk of the topological construction of subjectivities (cf topological reflexivity in Saari’s paper in this special issue) and pay particular attention to the ‘data effect’ in education, that is, the ways in which student testing and related data, both nationally and globally, function in topological ways and constitute new (spatial) relations of governance in education. The commensuration across difference necessary to such international and national data also works in a topological fashion.

With the topological, relations are more important than locations, the distant and the near distinction is partially elided (see Lewis et al., 2016), leading to what Amin (2002) describes as an overcoming (to some extent at least) of the ontological distinction between the abstract concept of space and the grounded concept of place (p. 395). Hartong (2021: 37) notes how topological research on data usage in education systems, for example, moves beyond considerations of the representational work of data and datafication to understand how these very things are brought relationally into being and in the process create new spaces and times of educational governance. We see here how data infrastructures and the flows (nationally and globally) of data express and enable the topological, as does the commensuration of phenomena reconstituted as digitalised data (datafication of the social) within and across national borders in processes of debordering and rebordering, which Karmijn van de Oudeweetering and Mathias Decuypere deal with so well in their paper in this special issue. They demonstrate how a topological lens enables our understanding of how mobilities constitute bordering, debordering and rebordering in relation to the European space. The emphasis in this research is thus on the constitutive work of the topological in relation to networked space and time. It is Lury et al.’s account of the becoming topological of culture and topology as a methodology for analysing culture, along with Thompson and Cook’s the becoming topologies of education, which constitute the backdrop to and the focus of the papers in this special issue.

In their introduction to this special issue, Mathias Decuypere, Sigrid Hartong and Karmijn van de Oudeweetering also importantly give emphasis to the temporal aspect of the topological, which is sometimes neglected. Here they note, ‘Originating from the mathematical analysis of forms, social topology explains times and spaces as relational, dynamic, and continuously unfolding, yet, at the same time, as manifesting in powerful agential forms’. They continue, observing that with a topological lens, ‘space and time are understood as heterogeneous and differentially enacted compositions – spaces and times – made, produced and (de-)stabilized in and through relationships, exchanges, and interactions’. The topological lens thus rejects conceptions of space and time as simply backdrops to other activities. Rather, it sees mobility and digitalisation as constituting and enabling different space-times. Important in the introductory essay, is the emphasis on the intimacy between space and time in the topological, encaptured in talk of ‘spatio-temporalities’ and the acknowledgement that space and time change conjointly. The authors of the introduction quote Connor (2004) approvingly here, ‘Topology’ can thus be thought of as ‘geometry plus time, geometry given body by motion’ (emphasis added).

My real sense is that the temporal aspect of the spatio-temporal has largely been neglected in much of the research in education informed by a topological lens. Here I am using temporal in the sense suggested by McLeod (2017: 13), ‘not as a fancier word for time, but as signifying the messy, moving relations between past, present and future’. While the papers in this special issue provide ways forward for the use of the topological in educational research, it seems they too are stronger on the spatial aspect than on the temporal. More recently, there has been a renewed focus on the temporal in the sociology of education and policy sociology in education (See Gulson et al., 2022; Lingard, 2021c; Lingard and Thompson, 2017; Webb et al., 2020). This work has relevance for research conducted through a topological lens. Yet we know that everything takes time and eventually time takes everything. ¹

The concept of the spatio-temporal is a recognition that we live and work in the interrelatedness between time and space, both of which help constitute the local, national, supranational, regional and global. Sassen (2001), for example, has argued that one impact of globalisation has been new, emergent national and global spatio-temporalities. She suggests that our lives and work are affected by the imbrications between these spatio-temporalities. Here she observes that national and global spatio-temporalities ‘significantly overlap and interact in ways that distinguish our contemporary moment’ (p. 260). Both national and global spatio-temporalities are in continuous states of becoming. Relevant to research on education is her further observation that: ‘A possible outcome of these dynamics of interaction between the global and the national . . . is an incipient and partial denationalization of domains once understood and/or constructed as national’ (p. 261). Additionally, Sassen’s argument is that these interactions work in multiple directions across national and global spaces and temporalities in ways uncovered by a topological lens. We thus must think well beyond simply seeing the global as affecting the national and local in a top-down, unidirectional manner (Larsen and Beech, 2014). Rather, as the papers in this special issue very well illustrate, the topological enables a sighting and documentation of multiple relations and networks across multiple spaces and in multiple directions.

The papers in the special number contribute to extending the research and scholarship in education utilising topological theorising and also to topology as mode of analysis, as research methodology. As such, they build on recent scholarship in education that uses a topological lens (e.g. Decuypere and Simons, 2016; Gulson and Sellar, 2019; Gulson et al., 2017; Hartong and Piattoeva, 2021; Lewis, 2020; Lewis et al., 2016). They seek, though, to move beyond the conceptual and theoretical advances of a topological lens and want as well to develop topological methodologies and ways of doing research, interacting with the empirical through such a lens. Importantly, they also regard the topological lens as a complement to other modes of theorising and conducting research for other purposes. The next section that deals with the topological and the topographical is a case in point.

The topological and the topographical

The Lury et al.’s observation, referenced above, that the global is being brought into existence as a topological space is an important and insightful one. New computational capacities, global data infrastructures, practices of commensuration, datafication and digitalisation, along with flows, mobilities, ideascapes, policyscapes help to create this global topological space. We see a very real proliferation of networked relations (Lury et al., 2012: 8), cutting across static spaces and creating new kinds of spatial relations. Their observation applies as well to the emergence of a global education policy field and the enhanced significance of global education policy discourses, along with international large-scale assessments, following the end of the Cold War, and the almost global hegemonic dominance of a neoliberal imaginary of globalisation. The work of international organisations in education such as the OECD can in this way be seen as ‘constitutive of the global and not an after-effect’ (Sobe, 2015). To that point, that is the beginning of this century, education and education policy in developed nations had been set solely within the jurisdiction and remit of the nation and sub-national units within it.

Following the end of the Cold War signified at large by the fall of the Berlin Wall, social theory, including social science approaches and methodologies in education, were challenged to move beyond ‘methodological nationalism’ (Beck, 2000). This moment saw, for example, in relation to policy sociology in education, a renewed emphasis on how global discourses and policies affected national education systems and policies. The focus was on the work of say the OECD for the rich nations of the globe and how their international large-scale assessments helped reframe the work of national and sub-national schooling systems of member and other participating nations and constituted an emergent global education policy field. Here we saw talk of rescaling of policy for example as globalisation, or more specifically a neoliberal imaginary of globalisation (Rizvi and Lingard, 2010) circulated globally by international organisations, had real impact, reframing schooling policy as human capital production and the most significant economic policy of any given nation in the context of the globalisation of the economy and some related loss of national economic sovereignty. Such a rescaling account, though, still took the nation as an a priori container. In a critical account of much of the research on this rescaling and global impact, Larsen and Beech (2014) argued that in such analyses ‘[p]lace as local and space as global constitute “master categories” that have dominated much of the research on the impact of globalization on local communities and places’ (p. 197). The effects were assumed to go in a one-way, top-down direction from the global to the national and then to the local.

The challenge to methodological nationalism in the social sciences (Beck, 2000) was predicated on a rejection of the assumption that the social, the society and the nation were straight-forwardly homologous. Hitherto, as noted, education policy had been under the jurisdiction of the nation-state; a national matter framed by a Westphalian binary divide between national and international politics, with these latter politics seen as the playing out of bilateral and multilateral relations between nations. However, what was happening from the turn of the century was the emergence of a global field constituted by the topological work of international organisations. For example, the OECD with main PISA and subsequently PISA for Development and PISA for Schools was creating the globe and all of its schooling systems as a commensurate space of measurement in a topological way. These moves were instigated as much by nations and schooling systems within nations as by the OECD itself; they were co-constructed. Think, for example, of how the USA pressured the OECD to create PISA; think of how a philanthropic trust in the USA pressured the OECD to establish PISA for Schools (Lewis et al., 2016); think of the work of some developing nations in respect of the making of PISA for Development. In all of this, we can see the new spatialities associated with globalisation (Amin, 2002) and the ways a topological lens enables effective analyses. In the context of globalisation, Clarke (2019) has argued persuasively that methodological nationalism has been replaced in policy and political science research, and I would argue in sociology of education and policy sociology in education, by what he calls ‘methodological globalism’.

Across the last several years we have witnessed something of the rise again of nationalism articulated by right-wing populism, specifically a form of ethnonationalism, which has spawned new racisms and opposition to refugees, ethnic others and the mobile cosmopolitan global elites (Rizvi, 2022; Rizvi et al., 2022). Now given this empirical reality of opposition to neoliberal globalisation from the right and the rise of ethnonationalism, think of Brexit, Trump’s America First, I would argue strongly that we now need to move beyond the binary of an either/or, methodological nationalism/methodological globalism because of the new spatialities associated with globalisation understood through a topological lens. Topological research on education policy has also demonstrated the necessity of rejecting a straight-forward, top-down impact of global policy discourses, international large-scale assessments and policies. Rather, as suggested by Larsen and Beech (2014) and Sobe (2015) (also see Lingard, 2021b), we must move beyond this binary and this purblind, blinkered, anaemic account of global/national/local relations. Here Larsen and Beech argue that we must go beyond multiple binaries and uni-directionality: space/place, global/national, international/national, and national/local to understand what they describe as the multiple geographies and cartographies of power and policy, which work in multiple directions and in multiple ways. For example, the national has been central to the constitution of the global and vice-versa. Australia’s declining PISA performance was backdrop to the creation of national testing in a nation where schooling is the Constitutional responsibility of the states and territories. All schools and school systems were thus pulled into a national plane of measurement, of commensuration, in a topological way creating an emergent de facto national schooling system (Lingard et al., 2015). There was also clearly a global backdrop to this development, which was also supported by the states and territories. The OECD in relation to PISA for Schools now reaches inside nations in a topological and relational way to sub-national schooling systems and schools, which had called on the OECD to do this. The workings of the topographical space of the nation thus continues to change, demanding a move beyond methodological nationalism and methodological globalism. New topological spatialities also demand this move. As the papers in this special issue well illustrate, a topological lens will assist in that theoretical and methodological move.

The argument here is that a topological lens is very well placed for researching and understanding changing empirical realities of the multiple criss-crossing spatialities and mutable relations associated with globalisation and the morphing and changing ways that nation-states work in relation to both global and internal pressures. The topological provides a productive lens for researching and understanding the changing imbrications of global/regional/national/local relations (Lingard, 2021b). Relations between people, places and processes have become as significant as location. Yet, and here I agree with the editors of this special issue, Mathias Decuypere, Sigrid Hartong and Karmijn van de Oudeweetering, that the nation as a topological and topographical space remains important in education and education policy. One needs to think here of some of the stringent criticisms of the OECD’s education work, including of PISA and the OECD’s expanding testing regime, proffered by a very senior federal official in the USA during the Trump Presidency (Lingard, 2021a).

The contributions of the papers in this special number to topological analyses in education research

Utilising Lury et al.’s work (2012), Antti Saari focuses on what she refers to as ‘topological reflexivity’ in educational policy discourses. This kind of reflexivity functions through the new technologies that help to seemingly eradicate distance by bringing the distant close in a relational way, and by increasing mobility and commensurability that allow multiple phenomena to be placed on a ‘plane of comparison’. This is Lury et al. (2012) definition of the becoming topological of culture. Topological reflexivity, both cognitive and affective, alludes to the ways policy makers now think about policy in relation to various topological configurations. We might see this as the disposition or habitus of policy makers (cf Lingard et al., 2015). The contribution of Saari’s paper is to provide an analysis of this topological reflexivity in educational policy discourses in Finland from a Lacanian psychoanalytical perspective, basically in respect of the governing of desire as necessary to anticipatory governance, a temporal focus in her analysis (cf Gulson et al., 2022; Webb et al., 2020). Saari provides Lacanian psycho-analytical intellectual resources to analyse and understand representations of desired future schooling structures and practices in some Finnish education policy plans. An important contribution to education policy studies is the dispositional concept of ‘topological reflexivity’ of policy makers and those creating plans, models for future schooling constituted as future learning environments. Important too here is the notion that the new ideal for policy forever lingers elusively in the distance, which creates its appeal for overcoming senses of loss in the current manifestations. The imagined future of policy: the temporal aspect. Saari’s is a most useful and original contribution to the topological literature in education.

In their contribution, Karmijn van de Oudeweetering and Mathias Decuypere report on two on-line European Commission education initiatives, Online Linguistic Support (OLS) and Blend-in, which they regard as non-human policy actors. The first focuses on the language learning of mobile European Erasmus students and was also about helping construct a border-less European Education Area (EEA), but in addition it did have some focus on language support for refugees but only for a limited time, what the authors call remediating the refugee crisis in Europe. The second online initiative Blend-in was constructed specifically for migrants and refugees to Europe and focussed on new bordering practices enabled by digitalisation, as opposed to the largely de-bordering practices of OLS and support for mobility of European students across EU member state borders. In their documentation and analysis, van de Oudeweetering and Decuypere are concerned with the socio-technical architectures and user-interfaces of the two programmes. The topological and topographical thus come together in the work of the two programmes, which frame different constructions/materialisations/entanglements of time and space, different spatio-temporalities. They also argue that while both have a role in constructing a borderless, yet synchronically bordered EEA, both programmes also acknowledge the principle of subsidiarity of the national members’ roles in education. Van de Oudeweetering and Decuypere’s analysis demonstrates how the use of social topology as both theoretical and methodological lenses demonstrate bordering practices in respect of EEA and refugees as ongoing spatial and temporal enactments. As they note, ‘With the focus on the entanglement of spaces and times, social topology showed interchanges between fixed forms of nations, institutions, and website architectures, and constantly moving transnational, personalized, and ecological forms as well as app- and platform architectures’. This is an important insight, that is, the mix of fixity and mobility (cf Peck and Theodore, 2015) and the insight that the topological affects time as well as space, as is their focus on non-human policy actors. We see in their insightful analysis, a debordering inside Europe across the EU’s member nations and yet a kind of bordering around Europe in respect of refugees. What is important in this analysis as well is the clear acknowledgement of the spatio-temporal aspects of the topological, not just the spatial.

Lewis and Hartong focus on data infrastructuring with the empirical case being EDFacts, the federal data infrastructure in the USA created in 2007, which collects data and monitors performance of schools, school districts and states across the nation. The use of infrastructuring also signifies processes and practices rather than simply a state entity. The goal of EDFacts is to place data at the centre of policy, management and budget decisions in all K-12 schools across the USA. This is a substantial federal intervention in what has been historically the local management of American schools linked to US history and construction of democracy. The very specific foci of Lewis and Hartong’s paper are emergent practices and ‘new shadow’ professionals surrounding data infrastructuring and the datafication of schooling. These new shadow professionals include data stewards in the federal department, and EDFacts coordinators and EDFacts submitters at state level. Additionally, they seek to develop the topological as a theoretical framework, but importantly, also as a methodology, as a contribution to policy sociology in education. They regard data infrastructures as socio-technical assemblages and thus their analysis is about showing and understanding how the human and technical work together to ensure the flows of standardised, quality data. Here the technical can be seen as non-human policy actors; a stance also taken up by van de Oudeweetering and Decuypere in their paper in this special issue. The idea of data flows – ‘flowability’ – is important here as a central logic of data infrastructures; multidirectional flows from place to place, from producers to consumers and so on. Their analysis also demonstrates what they refer to as ‘data submission’, that is, the continuous submission of data to EDFacts, but also, and importantly, professional submission to the data. We see here the datafication of schooling systems, of teachers and of students.

Much research in this domain has argued that it is teachers who are de-professionalised by the gaze and constitutive work of data flows enabled by data infrastructures such as EDFacts. In contrast, Lewis and Hartong argue persuasively that the new shadow professionals are equally subject to surveillance by the data they help to constitute, clean up and standardise. This is similar to Zuboff’s (2019) argument about the data we render to social media being used to surveil us and massage our desires and life practices in what she calls ‘surveillance capitalism’ and what Couldry and Mejias (2019) refer to as ‘data colonisation’. They also see the relations between the federal department and states and schools affected by the work of EDFacts as functioning as new topological spaces of the governance of education through de-and re-bordering, but at the same time acknowledge that the old borders of federalism (topographical) still function in parallel. EdFacts in a largely unacknowledged way is helping constitute a quasi-federal, perhaps national, system of schooling in the US (As an aside, there is a global context to this rescaling, but that is another argument for another time.). It is interesting in respect of this quasi-federal-national system to reflect on the creation of the beginning of the collection of statistics about US schooling in 1857, now the National Center for Education Statistics, after the end of the Civil War, as one way of attempting at that time to unify the divided nation after the Civil War. There are multiple contributions of this paper by Hartong and Lewis, but important to note here is that the topological relations created by EDFacts, while they de-border across state and local boundaries, also, re-border in helping constitute a quasi-national system of schooling in the federalist USA.

Using the theoretical frameworks of sociomateriality and social topology, along with the concepts of assemblage and relationality, James Lamb and Jen Ross analyse how technologies, specifically lecture capture, shape the topologies of higher education in the UK. The paper provides, inter alia, useful succinct accounts of these theoretical frameworks and concepts, while also providing an informative summative account of extant educational research that utilises social topology in the context of the becoming topological of culture (Lury et al., 2012) and of education (Thompson and Cook, 2015). Lecture capture is defined as the digital recording of teaching that actually occurs in physical classrooms, a practice common in most universities, but one that has become almost universal in the context of institutional lockdowns and move to online teaching in the Covid pandemic. This, for Lamb and Ross, is a move from lecture capture as a supplement to it supplanting the physical classroom lecture. Methodologically, Lamb and Ross’s approach is ‘speculative method,’ which aligns (onto-epistemological alignment) with the theories of sociomateriality and social topology and an ontological account of the world as always changing and in flux. Their empirical focus is on Twitter discussions around lecture capture, a domain with ever-changing implications for ethics in research. Analysis of 3 months of Twitter discussion around lecture capture (from February, 2020) revealed some major themes concerning: access, commerce, politics and policy, space, teaching and learning and technology. Academics expressed concern about the impact of the technologies associated with lecture capture upon their intellectual property and upon job security, with concern also expressed about the role of commercial interest (Edtech companies) in the work of the university and its potential neoliberalization. Certainly, the pandemic has opened an opportunity to the big EdTech companies to make a concerted move into the provision of higher education. The analysis in this paper focuses on the impact of learning capture on the spatiality and temporality of university life. Teaching was seen to move from the lectern and lecture theatre to the lap-top and living room, from physical presence to the virtual, from fixed to flexible time, with the lecture being seen to be a malleable paedagogical form, which deforms through lecture capture, but does not rupture. Thus the relevance of the topological. We see in this analysis the interweaving of political matters with the socio-technical topological relations within a specific set of organisations, namely UK universities.

Cole and Moustakim using the theoretical frames of Deleuze and Guattari seek to provide a social cartography of a very poor, distanced, outer, south-western suburb of Sydney and the role of a mobile educational van which visits once a week and provides the young people of Claymore (the pseudonym for the suburb) topological access to technologies of various kinds, computers, the internet, apps., online programmes etc. While the van appeared to be successful in engaging usually bored and disengaged young people, funding ended, demonstrating the seeming schizophrenic nature of much public policy. Cole and Moustakim suggest, after Auge (1995), that Claymore is a non-place, but I would suggest it is only a non-pace for those passing through it, be they researchers, those supporting the mobile educational van, travellers, but surely works in different ways for the inhabitants. The van provides topological connections to elsewhere and the description of the (apparently) desolate and dissolute nature of Claymore is also connected in topological ways to various centres of global capitalism and to the broader processes of uneven geographical development linked to neoliberal capitalism on a global scale.

Conclusion

In the introduction to this special issue of the European Educational Research Journal, Mathias Decuypere, Sigrid Hartong and Karmijn van de Oudeweetering make the point that the current world in which we live, one of global connectivities, multiple neworks and relations, datafication and digitalisation of the social and of new kinds of mobilities and flows, has challenged the most often taken-for-granteds of space as static and as a bordered container for activities (e.g. the nation) and time as straight forwardly chronological and linear. Globalisation has spawned new kinds of spatialities, temporalities, relationships, networks and mobilities. The topological provides a complementary account to the topographical: think of the bordering of Europe, both around Europe and between member nations, Europe and member nations as a prioiri containers, yet think of how mobility and the digital now enable the construction of the new space of the European, enable the debordering processes of Eurpeanization and the creation of a European Education Space (cf Lawn and Grek, 2012). These matters are dealt with in a most insightful way in Karmijn van de Oudeweetering and Mathias Decuypere’s contribution to this special issue. We can think of globalisation and associated spatialities in similar ways.

As the editors note in their introduction, the topological lens deals with both the spatial and the temporal in an a posteriori rather a priori manner. Lash (2012: 262) has made the point that topologies do not ‘exist in time and space’, but rather through ‘their own energetics, they drive their own time and space’. The topological speaks of spatio-temporalities.

It is these changes that have demanded new ways of thinking about the spatial and the temporal in education research, particularly policy sociology in education, and the topological lens has been one significant descriptive and theoretical development in respect of these changes. The editors of the special issue have sought to extend the use of a topological lens in education research and as such have desired to make conceptual, theoretical, methodological and empirical contributions to the literature on topology and education. They have succeeded admirably in my view.

The becoming topological of culture creates new spaces and new times in relation to education, education policy, and the datafication and digitalisation of education; that is, new spatialities, new relations and new temporalities emerge, including new and multiple global and national spatio-temporalities (Lingard, 2021c; Lingard and Thompson, 2017; Sassen, 2001). It seems to me, though, that more emphasis in the emerging topologically framed research in education is given to the new multidirectional relations (e.g. local to national, local to global, global to local, etc.) now working in respect of education systems and education policy, than to the new temporalities. This also seems true of this excellent set of papers in this Special Issue of the European Educational Research Journal.

The proposal for this special issue noted that in relation to the simultaneous mobility and fixity of policy discourses today (Peck and Theodore, 2015) a topological lens for researching space- and time-making has been underutilised. I would suggest that with a topological lens as demonstrated in all of the papers in this special issue, new spatialities (topological relations as opposed to geographical positioning) have been considerably more closely studied and researched than have processes of time-making. This observation is true of this excellent collection of papers and suggests an area for future research utilising a topological lens; the topological as an analytical device for understanding contemporary changes, but also a descriptor of those very changes in relation to changing spatio-temporalities and education. That awareness is also a significant contribution of this special issue.

The editors in their excellent introductory essay note that from a topological perspective, time and space change conjointly. There is a need for more research in education that focuses on that. For example, there are demands for national testing in Australian schooling to move to real-time on-line continuous assessments, rather than simply being a one-off test at a particular point in time. National testing in Australia, through its reporting of the comparative test performance of 60 like schools for each school in the nation, works in a topological way, creating what have been called non-local locals for each school and a de facto national system (Lingard et al., 2013); this change, along with datafication and digitalisation, also potentially opens up the move to the collection of continuous real-time data; a new spatio-temporality for Australian schooling.

There is some interesting theoretical work to be done as well in thinking of the relationships between the topological lens and other theoretical frames, which seek to deal with the phenomena of mobilities, new spatialities, multiple networks, digitalisation and datafication. These include, as the editors point out: assemblage studies (see Thompson and Cook, 2015, here), research utilising Foucault’s concept of dispositif, sociomaterial approaches and work within a Science and Technology Studies (STS) framework, and I would add that utilising Actor Network Theory. There are perhaps some interesting possibilities as well through the use of a topological lens with network ethnography, which might be used to document and analyse the new cartographies and geographies of power and thus address the issue of the flat ontology implicit in much network ethnographic research.

The final point to make here is one that the editors make well; that is, that the topography of the nation and supranational political entities remain important and are involved in the construction of the topological and vice-versa. This is an important point; the topological works in, through and across the topography of nations and of the globe, while topological relations help construct both. The nation-state does not liquidate, but rather works in different ways and is affected by different networks and relations. As was argued earlier, there has been a recent resurgence of nationalisms around the globe in many nations expressed as right-wing populist critiques of the neo-liberal imaginary of globalisation. Those geopolitical changes remind us that the topographical remains important. Sometimes even, as noted earlier, the topological is useful in constructing the national read in a topographical way. Think of Lewis and Hartong’s contribution in this special issue, showing how EdFacts is helping constitute a de facto, as yet still emergent, national system of schooling in the USA. Think of the example reported above of how in Australian federalism, where schooling is the Constitutional responsibility of the states and territories, national testing and the documenting of ‘like school performance comparisons’, where each school is compared with socioeconomically like schools across the nation, functioning in a topological fashion, also helps create a national system of schooling. Yet, as the editors in their opening essay note, ‘topology does not take topography “for granted” as the sole representation of space, but dissects and analyses how topographies (e.g. territorially bound nation states) are made, and how they are established through topological relations’. The topological lens also allows us to see how the global is constituted through topological relations and networks.