|French: bande de moebius|
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 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." It is only because the two sides are continuous that it is possible to cross over from inside to 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 "inside" to "outside" (or vice versa).
- Lacan, Jacques. The Seminar. Book XI. The Four Fundamental Concepts of Psychoanalysis, 1964. Trans. Alan Sheridan. London: Hogarth Press and Institute of Psycho-Analysis, 1977. p. 273