People often say that “Freudian is all nonsense,” or “What is even psychoanalysis?” or “Psychoanalysis is all fake.” While psychoanalysis may seem like a pseudoscience, there are many interesting ideas that connect the discipline with math and science. One such idea comes from Jacques Lacan, a renowned psychoanalyst and philosopher, who used mathematical symbols to illustrate his theories of psychoanalysis.
One of the topological shapes Lacan used was the Mobius strip. The Mobius strip is a circular strip with only one continuous surface and one edge. On any other normal surface, we cannot cross from one face to another without crossing an edge, but on the Mobius strip, the surface is not divided into two regions by any border between the inner and outer sides. We can see its paradoxical nature when an object “travels” on one of its surfaces; the object only has to travel across the circle twice before it comes back to the original starting point.
Lacan used the strip to illustrate co-existing relationships between binary oppositions. Psychoanalysis was historically interested in proving the paradoxical, cohesive, and hybrid nature of binary oppositions. These oppositions can be any pair of words that have opposite meanings, such as inside/outside, love/hate, good/bad, and etc. Unlike how people conventionally view oppositions as separate and distinct “opposites,” Lacan preferred to visualize them as features on a Mobius strip. Lacan, agreeing with the famous linguist Ferdinand de Saussure, maintained that because of how we construct our language, either side of the opposition cannot exist without its counterpart. He presented two opposites as the inside and the outside of the Mobius strip respectively, an analogy which indicates that the two sides are connected and transcended. Locally, at any single point, we can see a distinct inner and outer side, suggesting a clear conflicting relationship. But globally, if we look at the entire model, we cannot see where one side turns to the other side; here the opposition only proves the inseparability between the two opposites.
The model of the Mobius strip also enhances the idea of the unity and inseparability of binary oppositions. There is are interesting similarities between the Mobius strip and the yin-yang shape. The yin-yang model, however, suggests that there is still a boundary between the two opposite sides, represented as the curve between the sharply contrasted colors. The Mobius strip shows not only that there is never an edge between the two seemingly opposite sides (inner/outer), but also that there is always a gradual transition between them.
Additionally, Lacan used the Mobius strip to illustrate his theories about subject and desire. He said that a person’s inside and outside are connected, just like the inside and the outside of the Mobius strip. Because of the special nature of the strip, it means that our subjectivity no longer has an interior or an exterior; we are always on neither inside nor outside of our identity. So the question remains: where are we then, really? The explanation from the Mobius strip model is that we are never on a certain fixed point on the strip. Rather, we are always moving along on the strip, without knowing where we are on it. Not knowing where we are on the strip does not really matter, as there is really no difference no matter where we stand; we never know where exactly the Mobius strip switches from one side to the other. It echoes the idea of the mobility of identity—we never have a stable identity. Instead, we have a constant process of self-identification.
The Mobius strip model offers a 3D model of the gradated spectrum of conventional oppositions, proposing the possibility of eliminating dichotomy in our society. For example, through this model, gender traits are no longer categorized as male or female. Instead, gender identification is a wide spectrum with masculine and feminine ends. In addition, the model also shows that we are always redefining our identity through our interactions with our surroundings. We are always being constituted, and reconstituted. We always have the opportunity to change our path that forms our identity. There is no such thing as predetermination or fate, but rather we are constantly moving along our path of self-identification.