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Thus, the [[Moebius strip]] subverts our normal (Euclidean) way of representing [[space]], for it seems to have two sides but in fact has only one. The two sides are distinguished by the [[dimension]] of [[time]], the time it takes to [[traverse]] the [[whole]] strip. The figure illustrates how psychoanalysis problematizes binary oppositions ([[love]]/hate, [[inside]]/out, signifier/signified, [[truth]]/appearance): the opposed [[terms]] rather than be radically distinct, are viewed as continuous with each [[other]]. For [[instance]], the [[Moebius Strip|Moebius strip]] helps to [[understand]] the [[traversing]] of fantasy (<i>la traversée du [[fantasme]]</i>): only because the two sides are continuous it is possible to cross over from inside to outside. Yet, when passing a finger round the surface of the strip, it is [[impossible]] to determine the precise point where one has crossed over from inside to outside. With Slavoj [[Zizek]], the traversing of the <i>fantasme</i> implies to accomplish an act that disturbes [[The Subject|the subject]]'s [[fundamental fantasy]], unhinging the level that is even more fundamental than basic symbolic identifications. For Lacan, "fantasy is not simply a [[work]] of [[imagination]] as opposed to hard [[reality]], [[meaning]] a product of the [[mind]] that obfuscates the approach to reality, the ability to perceive things as they really are." Against the basic opposition between reality and imagination, fantasy is not merely on the side of the latter, it is rather that little piece of imagination by which [[The Subject|the subject]] gains access to reality - the [[frame]] that guarantees the [[sense]] of reality. Thus when the fundamental fantasy is shattered, [[The Subject|the subject]] sustains a [[loss]] of reality. Then, traversing the <i>fantasme</i> has [[nothing]] to do with a sobering act of dispelling the [[fantasies]] that obscure the clear [[perception]] of [[The Real|the real]] [[state]] of things or with a reflective act of achieving a critical distance from daily ruminations (superstitions). Fantasy intervenes as support when a line is drawn between what is simply our imagination and "what really [[exists]] out there." On the contrary, "traversing the <i>fantasme</i> involves [[The Subject|the subject]]'s over-identification with the field of imagination: in it, and through it, [[The Subject|the subject]] breaks the constrains of fantasy and enters the terrifying, violent territory of pre-synthetic imagination, where <i>disjecta membra</i> float around, not yet [[unified]] and domesticated by the [[intervention]] of a homogenizing [[fantasmatic]] frame."<br>
As for Lacan's assertion of [[The Subject|the subject]]'s constitutive <i>decentrement</i>, [[subjective]] experience is not regulated by [[objective]] unconscious mechanisms [[decentred]] with [[regard]] to [[The Subject|the subject]]'s [[self]]-experience and as such beyond [[control]], but by something more unsettling. For a standard view the dimension that is constitutive of [[subjectivity]] is that of phenomenal self-experience. In Lacan's perspective the [[analyst]] is the one who can deprive [[The Subject|the subject]] of the very fundamental fantasy that regulates the [[universe]] of self-experience. The [[subject of the unconscious]] emerges only when [[The Subject|the subject]]'s fundamental fantasy becomes inaccessible, is primordially [[repressed]], argues Zizek. Thus, the unconscious is the inaccesible phenomenon, not the objective [[mechanism]] that regulates phenomenal experience. When the subject displays [[signs]] of a fantasmatic self-experience that cannot be reduced to [[external]] [[behaviour]], what characterizes [[human]] subjectivity proper is the gap, <i>la béance</i>, that separates the two: fantasy becomes unattainable; it is this inaccessibility that makes the subject empty, <font face="LACAN" size="3">S</font>. The rapport totally subverts the standard notion of a directly self-experiencing subject. Instead, there is an impossible rapport between the empty, non-phenomenal subject and the phenomena that remain inaccessible. This actual rapport is registered by Lacan's articulation of [[fantasy]], <font face="LACAN" size="3">S</font> <> <i>a</i>, developed in [[Seminar]] XIV, <i>[[La logique du fantasme]]</i>.<br>
Lacan's interest in topology arises since he sees it as providing a non-intuitive, purely [[intellectual]] means of expressing the concept of structure. His [[topological]] models "forbid imaginary [[capture]]": unlike intuitive [[images]] in which perception eclipses structure, here "there is no hidden of [[the symbolic]]." Hence, topology replaces language as the main paradigm of structure: it is not a mere [[metaphor]] for structure, it's structure itself.
