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According to Jacques [[Lacan]], the [[unary ]] [[trait ]] is the elementary [[form ]] of the [[signifier ]] as pure [[difference ]] that supports [[symbolic ]] identification.

In the second of the [[three ]] forms of identification described by [[Freud]], the [[subject ]] [[identifies ]] regressively with a [[love ]] [[object ]] or rival by adopting a "single trait" of the [[other ]] person ([[einziger ]] Zug) (1921c, p. 107). [[Dora]]'s cough, for example, was an imitation of her [[father]]'s.

Lacan recognized this single trait as a signifier. Or more precisely, insofar as this signifier is isolated and is not part of a [[chain ]] of [[signifiers]], it is first a [[sign ]] or an "insignia of the Other" (cf. Lacan, 1957-58, p. 304; 2002, p. 253). This insignia of the Other constitutes the nucleus of the ego-[[ideal]].

In his [[seminar ]] on Identification (1961-62), Lacan used [[Saussure]]'s [[linguistics]], to compare the einziger Zug with the signifier as a distinct element. Thus he translated it as "unary trait" to emphasize its [[mathematical ]] [[sense]], comparing it with a binary [[number]].

[[Ferdinand de Saussure ]] defined the signifier negatively. It is not the same, but is different from the other signifiers in a given [[structure]]. This implies that a signifier is also different from itself. This pure difference characterizes the unary trait. As an example of the first [[primitive ]] indication of the [[existence ]] of the signifier, Lacan referred to a prehistoric hunter carving notches into a piece of bone. One notch signifies each kill, with no reference to the different types of prey or the [[particular ]] events of each hunt. Each [[animal ]] killed counts as one, and that is the only aspect of the hunt marked by the trait.

Of course, the traits in a series [[need ]] not resemble each other. They do not need to be identical in [[order ]] to be the same. In fact, the contrary is [[true]]. Because no simple trait is recognizable as a [[thing ]] itself, once it becomes part of a series you cannot tell which was the first mark.

When [[the thing ]] is erased, the unary trait remains as symbolic of its [[absence]]. Thus the trait transforms the [[absent ]] thing into an object of [[desire]]. A second mark, indistinguishable from the first, creates a [[hole ]] in which this object is lost. Thus the unary trait merges with the [[phallic ]] mark and the [[castration ]] [[threat]], insofar as it forever prohibits access to the incestuous Thing. The existence of the subject of the [[enunciation ]] is suspended by the trait that names it, but this subject immediately [[disappears ]] in the trait that fixes it, such that the subject only [[exists ]] between two traits.

To [[formalize ]] the unary trait, Lacan relied on the topology of the [[torus]], insofar as the unary trait is the mark of a [[double ]] [[loss]], the loss of an object, which corresponds to the central hole of the torus, and the absence of the subject of the [[unconscious]], which is the uncounted turn of the repeated [[demand]]. A single cut that makes a Möbius [[strip]], where the two surfaces are one, corresponds to the structure of the unary trait, identical neither to itself nor to the structure of the subject.

# [[Freud, Sigmund]]. (1921c). Group [[psychology ]] and the [[analysis ]] of the ego. SE, 18: 65-143.# [[Lacan, Jacques]]. (1958). The direction of the [[treatment ]] and the principles of its [[power]]. In [[Bruce Fink ]] (Trans.),[[Écrits]]: A selection. New York: W. W. Norton, 2002.# Lacan, Jacques. (1964). The four fundamental [[concepts ]] of [[psychoanalysis ]] (Alan [[Sheridan]], Trans.). New York: W. W. Norton, 1978.# Lacan, Jacques. (1957-58). Le Séminaire-Livre V, Les [[Formations ]] de l'[[Inconscient]]. [[Paris]]: Seuil, 1998.# Lacan, Jacques. (1961-62). Le Séminaire-Livre IX, [[L'identification ]] (unpublished seminar).