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Topology

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{{Top}}[[Topology]] (''topologie'') is a branch of [[mathematics]] which deals with the properties of figures in space which are preserved under all continuous deformations.These properties are those of continuity, contiguity and delimitation. The notion of space in topology is one of topological space, which is not limited to Euclidean (two- and three-dimensional space), nor even to spaces which can be said to have a dimension at all. Topological space thus dispenses with all references to distance, size, area and angle, and is based only on a concept of closeness or neighbourhood.{{Bottom}}
Freud used spatial metaphors to describe the psyche in ''=====Definition====="[[The Interpretation of DreamsTopology]]'', where he cites G. T. Fechner's idea that the scene of action of dreams " is different from that a branch of waking ideational life and proposes [[mathematics]] which deals with the concept properties 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 'first topography' divided the psyche into three systems: the conscious (Cs), the [[preconsciousfigures]] (Pcs) and the in [[unconscioustopology|space]] (Ucs)where are preserved under all continuous deformations. The 'second topography' divided the psyche into the three agencies These properties are those of the egocontinuity, the superego contiguity and the iddelimitation.
Lacan criticises these models for not being topological enough. =====Toplogical Space=====He argues that the diagram with which Freud had illustrated his second The [[notion]] of [[topology |space]] in ''[[The Ego topology]] is one of [[topology|topological space]], which is not limited to Euclidean (two- and the Id[[three]]-dimensional [[space]]'' (1923b) led the majority of Freud's readers , nor even to forget the analysis on spaces 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 can be said to have a non-intuitive, purely intellectual means of expressing the concept of [[structuredimension]] that is so important to his focus on the symbolic orderat all. It is [[topology|Topological space]] thus the task of Lacan's topological models "dispenses with all references to forbid imaginary capture."<ref>Edistance, 333</ref> Unlike intuitive imagessize, in which "perception eclipses structure"area and angle, in Lacan's topology "there and is no occultation based only on a [[concept]] of the symboliccloseness or neighbourhood."<ref>E, 333</ref>
=====Sigmund Freud=====
/* In what have been called his two "[[topology|topographies]]" (the first dating from 1900 and the second from 1923), [[Freud]] resorted to [[schema]]s to [[represent]] the various parts of the [[psychic apparatus]] and their interrelations. These schemas implicitly posited an equivalence between [[psychic]] space and Euclidean space. */
Lacan argues [[Freud]] used spatial metaphors to describe the psyche in ''[[The Interpretation of Dreams]]'', where he cites G. T. Fechner's [[idea]] that topology the [[scene]] of [[action]] of [[dreams]] is not simply a metaphorical way different from that of expressing waking ideational [[life]] and proposes the concept of structure; it '[[psychical]] locality'. [[Freud]] is structure itselfcareful to explain that this concept is a purely topographical one, and must not be confused with [[physical]] locality in any [[anatomical]] fashion.<ref>LacanFreud, 1900a: SE V, 1973b536</ref>He emphasises that His "[[topology privileges |first topography]]" [[divided]] the [[psyche]] into three systems: the [[conscious]] (Cs), the function of [[preconscious]] ([[Pcs]]) and the cut [[unconscious]] (''coupure''[[Ucs]]). The "[[topology|second topography]]" divided the [[psyche]] into the three [[agencies]] of the [[ego]], since the cut is what distinguishes a discontinuous transformation from a continuous one[[superego]] and the [[id]].
Both kinds of transformation play a role in psychoanalytic [[treatmentLacan]] criticizes these models for not [[being]] [[topological]]enough. As an example of a continuous transformation, Lacan refers to He argues that the diagram with which [[moebius stripFreud]]; just as one passes from one side to had illustrated his second topology in ''[[The Ego and the other by following Id]]'' (1923b) led the strip round continuously, so majority of [[Freud]]'s readers to forget the [[subjectanalysis]] can on which it was based because of the intuitive [[traversepower]] of the [[fantasyimage]] without making a mythical leap from inside to outside. As an example of a discontinous transformation<ref>{{E}} p. 214</ref> [[Lacan]]'s interest in [[topology]] arises, Lacan also refers to the moebius stripthen, which when cut down the middle is transformed into a single loop with very different topological properties; because he sees it now has two sides instead of one. Just as the cut operates providing a discontinuous transformation in non-intuitive, purely [[intellectual]] means of expressing the moebius strip, concept of [[structure]] that is so an effective interpretation proferred by important to his focus on the analyst modifies [[symbolic order]]. It is thus the structure task of the analysand[[Lacan]]'s discourse topological models "to forbid [[imaginary]] [[capture]]."<ref>{{E}} p. 333</ref> Unlike intuitive [[images]], in a radical waywhich "[[perception]] eclipses structure", in [[Lacan]]'s [[topology]] "there is no occultation of the [[symbolic]]."<ref>{{E}} p.333</ref>
While =====Structure=====[[schema LLacan]] and the other schemata which are produced in the 1950s can be seen as Lacan's first incursion into argues that [[topology, topological forms only come into prominence when, in ]] is not simply a [[metaphor]]ical way of expressing the 1960s, he turns his attention to the figures concept of the [[torusstructure]]; it is [[structure]], the moebius strip, Klein's bottle, and the cross-capitself.<ref>see {{L}} "[[Works of Jacques Lacan|L'Étourdit]]," ''[[Scilicet]]'', no. 4, 19611973: pp. 5-252</ref> Later onHe 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 the 1970s[[psychoanalytic treatment]]. As an example of a continuous transformation, [[Lacan turns his attention ]] refers to the [[moebius strip]]; just as one passes from one side to the more complex area [[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 knot theorya discontinous transformation, especially [[Lacan]] also refers to the [[borromean knotmoebius 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.<ref>TOPOLOGY (384) Just as the cut operates a discontinuous transformation in the [[CDmoebius strip]]</ref><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 so an effective [[interpretation]] proferred by the [[analyst]] modifies the [[structure]] of the [[analysand]]'s [[Seminar XIdiscourse]]</ref>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]].
 
=====See Also=====
{{See}}
* [[Borromean knot]]
* [[Moebius strip]]
{{Also}}
 
==References==
<references/>
[[Category:Psychoanalysis]]
[[Category:Jacques Lacan]]
[[Category:Dictionary]]
[[Category:Concepts]]
[[Category:Terms]]
[[Category:Concepts]][[Category:Psychoanalysis]]__NOTOC__
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