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(national, regional, school, classroom) forces that operate through the 'system'. While these forces change, they work through a discursivity that produces disciplinary affects, but in a different way. This new-old disciplinarity, or 'database effect', is here represented through a topological approach because of its utility for conceiving education in an increasingly networked world.The increasing utility of topological approaches to understanding social phenomena was clearly demonstrated in a recent double-issue of Theory, Culture & Society. For its editors, attempts to understand the emerging social must engage with topology as "surfaces that are spaces in themselves are not only self-organizing and emergent, but their self-organization brings being and knowing, ontology and epistemology, into new kinds of relations" (Lury, Parisi, & Terranova, 2012, p. 20). Using a mathematical construct to conceptualize social spaces, which might otherwise be understood discursively, may appear unusual. The metaphysics of mathematics, however, has long engaged with the social, for example in Leibniz's concept of incompossibility (Deleuze, 2006), Hacking's (1990) theorisation of statistics, governance and normalcy and Badiou's (2005) argument that mathematics is ontological and has always been significant for understanding multiplicity, continuity and the changes of forms and figures.While this mathematical turn is important, particularly in the age of big data and the consequent impact of datafication on social ontologies and professional/personal subjectivities, the use of topology as a heuristic for articulating the becoming-self in education surfaces has only recently been used in wider education analysis (Lingard & Sellar, 2013;de Freitas, 2014). Using topology to understand cultures and societies is not new, since Euler's solution to the problem of the 7 Bridges of Konigsberg, theorists have been intrigued by the potential of topology to tell us something about the ways that environments, people and customs/cultures connect in productive ways. For example, Lacan was absorbed by the potential for topological figures to "theorise the relationship of scientific 1 We are very grateful to Sam Sellar and Andrew Murphie for their helpful feedback and suggestions on early drafts of this paper. We would also like to thank the reviewers for their helpful comments.
(national, regional, school, classroom) forces that operate through the 'system'. While these forces change, they work through a discursivity that produces disciplinary affects, but in a different way. This new-old disciplinarity, or 'database effect', is here represented through a topological approach because of its utility for conceiving education in an increasingly networked world.The increasing utility of topological approaches to understanding social phenomena was clearly demonstrated in a recent double-issue of Theory, Culture & Society. For its editors, attempts to understand the emerging social must engage with topology as "surfaces that are spaces in themselves are not only self-organizing and emergent, but their self-organization brings being and knowing, ontology and epistemology, into new kinds of relations" (Lury, Parisi, & Terranova, 2012, p. 20). Using a mathematical construct to conceptualize social spaces, which might otherwise be understood discursively, may appear unusual. The metaphysics of mathematics, however, has long engaged with the social, for example in Leibniz's concept of incompossibility (Deleuze, 2006), Hacking's (1990) theorisation of statistics, governance and normalcy and Badiou's (2005) argument that mathematics is ontological and has always been significant for understanding multiplicity, continuity and the changes of forms and figures.While this mathematical turn is important, particularly in the age of big data and the consequent impact of datafication on social ontologies and professional/personal subjectivities, the use of topology as a heuristic for articulating the becoming-self in education surfaces has only recently been used in wider education analysis (Lingard & Sellar, 2013;de Freitas, 2014). Using topology to understand cultures and societies is not new, since Euler's solution to the problem of the 7 Bridges of Konigsberg, theorists have been intrigued by the potential of topology to tell us something about the ways that environments, people and customs/cultures connect in productive ways. For example, Lacan was absorbed by the potential for topological figures to "theorise the relationship of scientific 1 We are very grateful to Sam Sellar and Andrew Murphie for their helpful feedback and suggestions on early drafts of this paper. We would also like to thank the reviewers for their helpful comments.
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