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Topology
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{{Top}}[[topologie]]{{Bottom}}
=====Toplogical Space=====The [[Freudnotion]]'s topographies of the psyche owe much [[topology|space]] in [[topology]] is one of [[topology|topological space]], which is not limited to nineteenthEuclidean (two-century theories of cerebral localizationand [[three]]-dimensional [[space]]), nor even to spaces which ascribe different mental functions can be said to different areas of the brainhave a [[dimension]] at all.IT was the study of dreams that led Freud [[topology|Topological space]] thus dispenses with all references to the conclusion that unconscious activities such as dreaming are quite divorced from the conscious mind distance, size, area and literally take place angle, and is based only on ''ein anderer Schauplatz'' (another stage a [[concept]] of closeness or theatre)neighbourhood.
=====Sigmund Freud=====/* In what have been called his two "[[Freudtopology|topographies]] evolved two distinct topographies.The " (the first, elaborated between dating from 1900 and 1915the second from 1923), describes an apparatus comrpising [[unconsciousFreud]], [[preconscious]] and [[conscious]] systems, with mechanism of resorted to [[censorshipschema]] s to prevent ideas from moving between them.Considerations of representability and other mechanisms of the [[dream-workrepresent]] filter or censor the content various parts of dreams and fantasies before allowing them to enter the [[consciouspsychic apparatus]] mind, usually because and their sexual content is unacceptable to conscious thought-processesinterrelations.The second or 'structural' topography, elaborated from 1920 onwards, describes a structure of trhree agencies known respectively as the [[id]], the These schemas implicitly posited an equivalence between [[egopsychic]] space and the [[super-ego]]Euclidean space.*/
[[Freud]] used spatial metaphors to describe the psyche in ''[[The Interpretation of Dreams]]'', where he cites G. T. Fechner's [[idea]] that the [[scene]] of [[action]] of [[dreams]] is different from that of waking ideational [[life]] and proposes the concept of '[[psychical]] locality'. [[Freud]] is careful to explain that this concept is a purely topographical one, and must not be confused with [[physical]] locality in any [[anatomical]] fashion.<ref>Freud, 1900a: SE V, 536</ref> His "[[topology|first topography]]" [[divided]] the [[psyche]] into three systems: the [[conscious]] (Cs), the [[preconscious]] ([[Pcs]]) and the [[unconscious]] ([[Ucs]]). The "[[topology|second topography]]" divided the [[psyche]] into the three [[agencies]] of the [[ego]], the [[superego]] and the [[id]].
[[Lacan]] criticizes 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>{{E}} p. 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}} p. 333</ref>
Unlike intuitive [[images]], in which "[[perception]] eclipses structure", in [[Lacan]]'s [[topology]] "there is no occultation of the [[symbolic]]."<ref>{{E}} p. 333</ref>
=====Structure=====
[[Lacan]] argues that [[topology]] is not simply a [[metaphor]]ical way of expressing the concept of [[structure]]; it is [[structure]] itself.<ref>{{L}} "[[Works of Jacques Lacan|L'Étourdit]]," ''[[Scilicet]]'', no. 4, 1973: pp. 5-52</ref> He emphasizes 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.
=====Figures=====
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>{{L}} ''[[Works of Jacques Lacan|Le Séminaire. Livre IX. L'identification, 1961-62]]'', unpublished.</ref> Later on, in the 1970s, [[Lacan]] turns his attention to the more [[complex]] area of [[knot]] [[theory]], especially the [[Borromean knot]].
==References==
<references/>
[[Category:Jacques Lacan]]
[[Category:MathematicsDictionary]][[Category:Concepts]]
[[Category:Terms]]