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The Klein bottle

The Letter, Issue 53, Summer 2013, Pages 57 - 85


THE KLEIN BOTTLE[1]

Tony Hughes


Some arguments about Lacan’s use of topology are explored in the light of the debate as to whether or not it adds anything beneficial to the clinic of psychoanalysis. This paper discusses the essential difference between sense and meaning and addresses Le Gaufey’s critique of the use of the Borromean knot to support Lacan’s formulae of sexuation. The issues raised by Lacan at the time of his first introduction of the Klein bottle are dealt with in some depth, in order to show the rigour of his endeavour. The addendum clarifies the use of the cut and the dimensions in Lacanian theory.


Keywords: Lacan, topology, Nobus, Le Gaufey, the Klein bottle, the cut, the suture, the dimensions


Lacan’s use of topology continued from the 1950s to the end of his life, and this project was facilitated by his friendship with the mathematician Georges-Th. Guilbaud. He put an enormous effort into developing this aspect of his work in order to make psychoanalysis an even more rigorous discourse.


In 1951, Lacan, Levi-Strauss, Guilbaud, and Benveniste met to work on structures and establish bridges between the human sciences and mathematics. Each made use of the teaching of the other as one might a topological figure. On the basis of that collective effort, Lacan was not satisfied with empty talk or mere reflections on the history of mathematics. For thirty years, with or without Guilbaud, he engaged in daily mathematical exercises…Privately they [he and Guilbaud] shared a common taste for mathematical games: strings, inflatable buoys, miniature designs, children’s cubes, the art of braiding and cutting, Queneau-like exercises in style. The field of topology retained the whole of Lacan’s attention; he never hesitated to blacken reams of paper to teach his audience the elements of his doctrine as transcribed in topological figures.[2]


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