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 Lacan criticises these models for not being topological enough. He argues that the diagram with which Freud had illustrated his second topology in ''[[The Ego and the Id]]'' (1923b) led the majority of Freud's readers to forget the analysis on which it was based because of the intuitive power of the image.<ref>see E, 214</ref> Lacan's interest in topology arises, then, because he sees it as providing a non-intuitive, purely intellectual means of expressing the concept of [[structure]] that is so important to his focus on the symbolic order. It is thus the task of Lacan's topological models "to forbid imaginary capture."<ref>E, 333</ref> Unlike intuitive images, in which "perception eclipses structure", in Lacan's topology "there is no occultation of the symbolic."<ref>E, 333</ref> Lacan argues that topology is not simply a metaphorical way of expressing the concept of structure; it is structure itself.<ref>Lacan, 1973b</ref>He emphasises that topology privileges the function of the cut (''coupure''), since the cut is what distinguishes a discontinuous transformation from a continuous one.  Both kinds of transformation play a role in psychoanalytic [[treatment]]. As an example of a continuous transformation, Lacan refers to the [[moebius strip]]; just as one passes from one side to the other by following the strip round continuously, so the [[subject]] can [[traverse]] the [[fantasy]] without making a mythical leap from inside to outside. As an example of a discontinous transformation, Lacan also refers to the moebius strip, which when cut down the middle is transformed into a single loop with very different topological properties; it now has two sides instead of one. Just as the cut operates a discontinuous transformation in the moebius strip, so an effective interpretation proferred by the analyst modifies the structure of the analysand's discourse in a radical way. While [[schema L] and the other schemata which are produced in the 1950s can be seen as Lacan's first incursion into topology, topological forms only come into prominence when, in the 1960s, he turns his attention to the figures of the [[torus]], the moebius strip, Klein's bottle, and the cross-cap.<ref>see Lacan, 1961-2</ref> Later on, in the 1970s, Lacan turns his attention to the more complex area of knot theory, especially the [[borromean knot]].<ref>topology, 22, 34, 74, 89-90, 131, 144, 147, 155-6, 161, 164, 181-2, 184, 203, 206, 209, * 235, 244-5, 257, 270-1 [[Seminar XI]]</ref>

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