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Above the Horizon there is no Sky

The Letter, Issue 43, Spring 2010, Pages 53 - 77

Above the Horizon there is no Sky[1]

Jean-Pierre Georgin and Erik Porge

This paper takes one of Lacan’s “o objects” – the look – as its starting point. Lacan developed his thinking on the implications of perspective geometry for painting in 1966 in his seminar on The Object of Psychoanalysis where he showed its importance in Velasquez’s Las Meninas. Georgin and Porge develop the linkages between projective geometry and topology in order to show the gap which exists between the look and the gaze – the look being on the side of the subject and the gaze being on the side of the object, hence opening up a gap which is one of the avatars of the cross-cap.

Keywords: Lacan; o object; the look; topology; painting; projective plane As Lacan recalls on the occasion of the anniversary of the twenty-third centenary of the death of Aristotle, the o is “complex in the extreme”. If there is one aspect of this “object” which is imagined by the breast, the faeces, the look, the voice, there is another one which draws its real from a (logical or mathematical) writing and designates topological presentations.

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