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===Topology===[[Image:Lacan-mobeiusstripmoebiusstrip.jpg|thumb|right|250px|Moebius strip]]The [[moebius strip]] is one of the [[figures ]] studied by [[Lacan]] in his use of [[topology]]. It is a [[three]]-dimensional [[figure]] that can be formed by taking a long rectangle of paper and twisting it once before joining its ends together.

It ===Space===The result is a three-dimensional figure that which subverts our normal (Euclidean) way of representing [[space]], for it seems to have two sides but in fact has only one. Locally, at any one point, two sides can be formed by taking a long rectangle of paper and twisting clearly distinguished, but when the [[whole]] strip is traversed it once before joining its ends togetherbecomes clear that they are in fact continuous.

==Space=Time===The result is a figure which subverts our normal (Euclidean) way two sides are only distinguished by the [[dimension]] of representing space[[time]], for the [[time]] it seems takes to have two sides but in fact has only one[[traverse]] the whole strip.

Locally===Binary Oppositions===The figure illustrates the way that [[psychoanalysis]] problematizes various binary oppositions, such as [[inside]]/[[outside]], [[love]]/[[hate]], at any one point[[signifier]]/[[signified]], [[truth]]/[[appearance]]. While the two sides can [[terms]] in such oppositions are often presented as radically distinct, [[Lacan]] prefers to [[understand]] these oppositions in terms of the [[topology]] of the [[moebius strip]]. The opposed terms are thus seen to be clearly distinguishednot discrete but continuous with each [[other]]. Likewise, but when the whole strip [[discourse]] of the [[master]] is traversed it becomes clear that they are in fact continuouswith the [[discourse]] of the [[analyst]].

==Time==The two sides are only distinguished by the dimension of [[time]], the [[time]] it takes to traverse the whole strip. ==Binary Oppositions==The figure illustrates the way that [[psychoanalysis]] problematizes various binary oppositions, such as [[inside]]/[[outside]], [[love]]/[[hate]], [[signifier]]/[[signified]], [[truth]]/[[appearance]]. While the two terms in such oppositions are often presented as radically distinct, [[Lacan]] prefers to understand these oppositions in terms of the [[topology]] of the [[moebius strip]]. The opposed terms are thus seen to be not discrete but continuous with each other. Likewise, the [[discourse]] of the [[master]] is continuous with the [[discourse]] of the [[analyst]]. =="Traverse the Fantasy"===The [[moebius strip]] also helps one to understand how it is possible to "traverse the fantasy."<ref>{{S11}} p.273</ref>  It is only because the two sides are continuous that it is possible to cross over from [[extimacy|inside]] to [[extimacy|outside]].  Yet, when one passes a finger round the surface of the [[moebius strip]], it is [[impossible ]] to say at which precise point one has crossed over from "[[extimacy|inside]]" to "[[extimacy|outside]]" (or vice versa).