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‌‌‌‌  英:topology; 法:topologie

‌‌‌‌  拓扑学 (原先被莱布尼兹称作“定位分析”[analysis situs])是数学的一个分支,它处理的是空间中的各种图形在所有连续变形的过程中所保留下来的种种特性。这些特性是连续性 (continuity)、临近性 (contiguity)与限定性 (delimitation)。拓扑学中的空间概念是一种“拓扑空间”(topological space), 它并不受限于欧氏几何(二维与三维空间),甚至也完全不受限于那些可以说是只有一个维度的空间。因而,拓扑空间便免除了所有那些对于距离、大小、面积与角度的参照,而且其基础也仅仅在于一种封闭性或邻接性的概念。

‌‌‌‌  弗洛伊德曾经在《释梦》中运用了一些空间隐喻来描述精神,他在那里引用了费希纳的思想,即梦境中的活动场景不同于清醒的观念生活,而且他还提出了“精神位点”(psychical locality)的概念。弗洛伊德审慎地解释说,这个概念是一个纯粹地形学的概念,而不应当以任何解剖学的方式与身体位点相混淆(Freud, 1900a: SEV, 536)。他的“第一地形学”(通常在英文中被称作“地形学系统”[topographic system])就曾把精神划分为三个系统:意识 (Cs)、前意识 (Pcs)与无意识 (Ucs)。“第二地形学”(通常在英文中被称作“结构系统”[structural system])则将精神划分为三个机构:自我、超我与它我。

‌‌‌‌  拉康批评这些模型是不够拓扑学的。他指出,弗洛伊德在《自我与它我》(1923b)中借以阐明其第二地形学的那张图,导致弗洛伊德的大多数读者皆因为形象的直觉性力量而遗忘了该模型以之为基础的分析 (见:E, 214)。于是,拉康便对拓扑学产生了兴趣,因为他将其看作提供了一种非直觉性的、纯粹智识性的手段来表达就他关注的象征秩序而言是如此重要的结构 (STRUCTURE)概念。因而,拉康的拓扑学模型的任务便在于“防止想象的捕获”(E, 333)。与那些直觉性的形象不同,在这些形象中“知觉遮蔽了结构”,在拉康的拓扑学中“没有任何对于象征界的掩蔽”(E, 333).

‌‌‌‌  拉康认为,拓扑学并不只是表达结构概念的一种隐喻性方式;它是结构本身 (Lacan, 1973b)。他强调拓扑学给切口 (英:cut; 法:coupure)的功能赋予了特权,因为恰恰是切口把一种断续转化区别于一种连续转化。此两种转化在精神分析治疗中皆扮演着某种角色。拉康称莫比乌斯带 (MOEBIUS STRIP)是一个连续转化的例子,正如我们沿着这条带子连续地转圈,我们便会从一面转到另一面,所以主体也可以穿越幻想,而无须制造一种从内部到外部的神话性飞跃。拉康同样称莫比乌斯带是一个断续转化的例子,当截断中间的时候,它就转化成了具有不同拓扑性质的一个单一环路,它现在具有两个面而非一个面。正如切口在莫比乌斯带中操作了一种断续转化,所以由分析家提出的一则有效的解释也会以一种根本性的方式而修改分析者的话语结构。

‌‌‌‌  虽然在1950年代产生的L图式 (SCHEMA L)与其他图式可以被看作拉康对于拓扑学的首度入侵,但是那些拓扑学形式则只是在1960年代才开始凸显出来,当时拉康把他的关注转向了圆环面 (TORUS)、莫比乌斯带、克莱因瓶 (Klein's bottle)以及交叉帽 (cross-cap)(见:Lacan, 1961-2)。其后,在1970年代,拉康又把他的关注转向了更加复杂的扭结理论的领域,尤其是博洛米结(BORROMEAN KNOT)。至于拉康使用各种拓扑学图形的介绍,见:Granon-Lafont,1985。

‌‌‌‌  (topologie) Topology (originally called analysis situs by Leibniz) is a branch ofmathematics which deals with the properties of figures in space which are preservedunder all continuous deformations. These properties are those of continuity, contiguityand delimitation. The notion of space in topology is one of topological space, which isnot limited to Euclidean (two-and three-dimensional space), nor even to spaces which canbe said to have a dimension at all. Topological space thus dispenses with all references todistance, size, area and angle, and is based only on a concept of closeness orneighbourhood.

‌‌‌‌  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 thatof waking ideational life and proposes the concept of 'psychical locality'. Freud is carefulto explain that this concept is a purely topographical one, and must not be confused withphysical locality in any anatomical fashion (Freud, 1900a: SE V, 536). His firsttopography' (usually referred to in English as 'the topographic system') divided thepsyche into three systems: the conscious (Cs), the preconscious (Pcs) and theunconscious (Ucs). The 'second topography' (usually referred to in English as 'thestructural system') divided the psyche into the three agencies of the ego, the superego andthe id.

‌‌‌‌  Lacan criticises these models for not being topological enough. He argues that thediagram with which Freud had illustrated his second topology in The Ego and the ld (1923b) led the majority of Freud's readers to forget the analysis on which it was basedbecause of the intuitive power of the image (see E, 214). Lacan's interest in topologyarises, then, because he sees it as providing a non-intuitive, purely intellectual means ofexpressing the concept of STRUCTURE that is so important to his focus on the symbolicorder. It is thus the task of Lacan's topological models 'to forbid imaginary capture' (E, 333). Unlike intuitive images, in which 'perception eclipses structure', in Lacan'stopology 'there is no occultation of the symbolic' (E, 333).

‌‌‌‌  Lacan argues that topology is not simply a metaphorical way of expressing the conceptof structure; it is structure itself (Lacan, 1973b). He emphasises that topology privilegesthe function of the cut (coupure), since the cut is what distinguishes a discontinuoustransformation from a continuous one. Both kinds of transformation play a role inpsychoanalytic treatment. As an example of a continuous transformation, Lacan refers tothe MOEBIUS STRIP; just as one passes from one side to the other by following the stripround continuously, so the subject can traverse the fantasy without making a mythicalleap from inside to outside. As an example of a discontinous transformation, Lacan alsorefers to the moebius strip, which when cut down the middle is transformed into a singleloop with very different topological properties; it now has two sides instead of one. Justas the cut operates a discontinuous transformation in the moebius strip, so an effectiveinterpretation preferred by the analyst modifies the structure of the analysand's discoursein a radical way.

‌‌‌‌  While SCHEMA L and the other schemata which are produced in the 1950s can beseenas Lacan's first incursion into topology, topological forms only come intoprominence when, in the 1960s, he turns his attention to the figures of the TORUS, the moebius strip,Klein's bottle,and the cross-cap (see Lacan,1961-2).Later on,in the1970s,Lacan turns his attention to the more complex area of knot theory,especially theBORROMEAN KNOT.For an introduction to Lacan's use of topological figures,see Granon-Lafont(1985).