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The Torus – An Introduction

The Letter, Issue 43, Spring 2010, Pages 79 - 105

The Torus – An Introduction

Tony Hughes

Lacan used topology to theorise in a scientific way the structure of the subject. The topological field is a central part of his thinking and the first indications of this took place in the Rome Discourse in 1953 and continued up to the end of his life by which time topology had, perhaps, inspired his theory of the Borromean knot which led to his exposition of the sinthome. Lacan initially focused on four main areas of topology – the torus, the Moebius strip, the Klein Bottle and the cross-cap. This paper is an introduction to the torus with particular emphasis on three sessions of the seminar on Identification, namely 28 February, 7 March and 14 March 1962. Lacan’s use of a multitude of diagrams is seen to be helpful when following the development of this complex aspect of his theoretical analysis of the structure of the subject.

Keywords: torus; subject; unary trait; cut; interior eight; Russell’s paradox

At first sight, topology would seem to be entirely foreign to the clinic of psychoanalysis. We see “funny” topological shapes drawn on paper by Lacan as we wind our way through his seminars and they evoke a response of anxiety and bewilderment. We ask ourselves “what on earth have these shapes to do with the human subject?” Our initial reaction may lead to a foreclosure to engage with the diagrams and the logical development accompanying them which assists in the conclusion that Lacan draws that topology is not a metaphor for structure but is structure itself. Our view of topology would be even more perplexing if we were to engage with this topic from the perspective of L’Etourdit written in July 1972, which has no topological diagrams, the intent of which is to situate the logic of the process purely in the symbolic and remove any imaginary overtones which might distort our understanding of the way in which it should be applied.

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