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Topology is rapidly transforming itself into a new paradigm stretching across sciences and arts, theory and practice, and industry and the academy.

The TRU has been set up to explore the two inter-related ways in which topology provides a conceptual language for understanding relationships, intensities and transformations - outside its original field of mathematics. One is as a methodological tool in social sciences and architecture. The other is as a tool for performance across a range of arts and creative practices. Both are interested in topology’s understanding of transformation and non-metric relationships.

TRU Rationale, aims, and objectives

Topology is rapidly transforming itself into a new paradigm stretching across sciences and arts, theory and practice, and industry and the academy. The TRU has been set up to explore the two inter-related ways in which topology provides a conceptual language for understanding relationships, intensities, and transformations - outside its original field of mathematics. One is as a methodological tool in social sciences and architecture. The other is a tool for performance across a range of arts and creative practices. Both are interested in topology’s understanding of transformation and non-metric relationships. 

1 Topological methodologies: One application of topology is a methodological tool for helping to understand social, cultural and psychological issues. Here the emphasis is on a product - how topological concepts can be applied to understand various phenomena, data and issues, and thereby to produce new knowledge. Examples of this approach would include geographer’s use of topology to help understand processes of globalisation (Amin, Otlacan); and the topology of social networking. In philosophy topology figures in work of Etienne Balibar, Giorgio Agamben, Bruno Latour, Manual Delanda, Peter Sloterdyk, Rosi Braidotti, Michel Serres and Alain Badiou. In psychoanalysis, Lacan used the topological Borromean knot of to describe the relationship between the Real, Symbolic, Imaginary.

2 Topological performances: The second way the TRU makes use of topology is in relation to performance practices. Here the emphasis is often on a process and aesthetic values - how topological concepts are used to explore new forms of creative expression and how these can provide embodied ways of understanding topological concepts. Numerous artists, sculptors, and designers have used topology to inform and inspire their work, as with, for example, Anthony Gormley, Ernesto Neto, Cecil Balmont and Olafur Eliasson, Kathy Prendergast and others. Topology has also been used in locative media mapping and the sonic arts by Bruce Nauman and Schafer-Krebs. This draws on a tradition of work initiated with Murray Shafer and Barry Truax’s soundscapes and Janet Cardiff’s sound walks.

Originated by Leibniz as analysis situs, topology is a branch of mathematics known as “rubber sheet geometry.” It provides methodologies for understanding the dynamic change that can be applied to any relationships, intensities or multiples (material, social, cultural or aesthetic) that are invariable through transformation. Unlike the traditional Euclidean geometry, topological geometry is not concerned with measurement. Instead, it provides mathematical formulations of continuous surfaces without tearing, cutting or pasting. Topology provides the basis for many nonlinear dynamics, as well as chaos and catastrophe theories. Topological relationships are possibly more familiar than might be thought, as with the topological (rather than topographic) London tube map, or the knots that have been a key feature in Celtic, Coptic and Islamic design, or the puzzling beauty of the Möbius strip.

As a Media and Communications Department initiative the TRU objectives are to:

  • make a distinctive contribution to the Department’s research profile and REF narrative
  • create impact for the department and the College in public fora, debate and exhibition spaces
  • stimulate research and teaching in a currently exciting and innovative area that is very much in keeping with the Department’s interests and ethos
  • attract research funding and sponsorship
  • amplify links within the department, with other departments, universities organisations

Projects and interests

To stimulate interest in topology, the TRU is very much open to developing, helping to support and promoting any topologically related projects from within the department and elsewhere. Sonic topology is one area of particular interest, exploring corporeal movement and embodied ways of knowing.

Creative Sound Design Ltd

The TRU builds on the department’s research interests and record of related events:

The Future of Light and Sound (March 2009)

http://vimeo.com/4154890

Synaesthesia Symposium (March 2009)

Large Scale Immersive Audio Experiment (October 2009)

Performing Topology Symposium (March 2010)

Media and the Senses conference (May 2011)

This parallels the interests of other departments, particularly Sociology, with Celia Lury’s ATCD (A Topological Approach to Cultural Dynamics) three-year EEC funded program (2007- 2010) 

Topology reading list

Abbas, Niran (ed) (2005) Mapping Michel Serres, Ann Arbor: The University of Michigan Press  

Ragland, Ellie and Milavanovic, Dragan (eds) (2004) Lacan: Topologically Speaking, New York: Other Press

Eldelsztein, Alfredo (2009) The Graph of Desire: Using the Work of Jacques Lacan, London: Karnac Books

General
Massumi, Brian (2002) Strange Horizon: Buildings, Biograms and Body Topologic, in Parables of the Virtual: Movement, Affect, Sensation, Durham: Duke University Press

Connor, Steven (2004) Topologies: Michel Serres and the Shapes of Thought, Anglistik, 15 (2004): 105-117

Social Sciences
A Topological Approach to Cultural Dynamics (ATACD)

Amin, Ash, 2002, "Spatialities of globalisation" Environment and Planning A 34 (3) 385 – 399

Otlacan, Eufrosina and Otlacan, Romulus-Petru, (2006) "Informational topology and globalisation process", Kybernetes, Vol. 35 Iss: 7/8, pp.1203 – 1209

Smith, B (1994) Topological Foundations of Cognitive Science in C. Eschenbach, C. Habel and B. Smith (eds.), Topological Foundations of Cognitive Science, Hamburg: Graduiertenkolleg Kognitionswissenschaft, 1994

Arts and Architecture
Ernesto Neto, Olafur Eliasson

<Sabine Schafer//Joachim Krebs> (2007) TopoSonic Arts: Kehrer Verlag

http://www.rubedo.co.uk/

Phenomenology
Rosen, Stephen M (2004) Topology, in Dimensions of Apeiron: A Topological Phenomenology of Space, Time, and Individuation, Amsterdam-New York: Editions Rodopi B.V. pp 168 -210

Rosen, Stephen M (2006) Topologies of the Flesh: A Multidimensional Exploration of the Lifeworld, Athens: Ohio University Press

Mathematics
Richeson, David S (2008) Euler's Gem: The Polyhedron Formula and the Birth of Topology, Princeton: Princeton University Press

Sossinsky, Alexiei (2004) Knots: Mathematics with a Twist, Boston: Harvard University Press

Psychology
Piaget, Jean, and Inhelder, Bärbel (1956) The child’s conception of space trans. from the French by F.J.Langdon and J.L.Lunzer, London: Routledge and Kegan Paul

Kapadia, Ramesh (1974) A Critical Examination of Piaget-Inhelder’s View on Topology, Educational Studies in Mathematics 5 (1974) 419 - 424

Sheets-Johnstone (1990) The Hermeneutics of Tool-Making: Corporeal and Topological Concepts, in The Roots of Thinking, Philadelphia: Temple University Press, pp 25 - 70

Kurt Lewin
Back, Kurt W. (1992) "This business of topology." Journal of Social Issues 48(2): 51-66.

Lacan and Psychoanalysis

http://www.lituraterre.org/Illiteracy-The_lost_topology_of_psychoanalysis.htm