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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.

The result is a figure 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 clearly distinguished, but when the [[whole ]] strip is traversed it becomes clear that they are in fact continuous.

The two sides are only distinguished by the [[dimension ]] of [[time]], the [[time]] it takes to [[traverse ]] the whole strip.

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]].

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).