The L and R schemas are two of Lacan's didactic diagrams; they articulate the dual relation, between the imaginary (which is dualistic) and the symbolic, (which adds a third element).
Human beings are at first captured in the symbolic order before they are aware of it. They enter into it, through the parades of speech, as in the fort/da game that Freud described in Beyond the Pleasure Principle (1920g). Schema L developed out of Lacan's study of Poe's story "The Purloined Letter" in his seminar of 1954-55. It depicts the "relation" of the subject with the absolute Other. As the arrows in the schema indicate, it is from the Other (i.e., the unconscious, the "treasure trove of signifiers") that a message reaches the subject in an inverted form. This message makes the subject "fade" when it is received (Figure 1).
In other words, the "relation" of the unconscious subject to the Other—that is, the relation the subject has with his or her own unconscious—is precarious and uncertain. In fact, it is always mediated by the subject's ego, which, according to Lacan's theory of the mirror stage, is based on the image of another. Thus, if we ignore the direction of the arrows, communication between S and A can only follow a trajectory that moves from other people—that is, the "small other"—to the subject's ego, that is, from the specular image to one's body image. These two are trapped in a Hegelian dialectic.
In "On a Question Prior to Any Possible Treatment of Psychosis" (1959), Lacan produced schema R, which extended and completed schema L. A distortion of schema R then produced schema I, which represents psychosis. And it is schema R in the form of a diamond that gives us the formula of fantasy: S̷ ◇ a (Figure 2).
This quadrangular schema represents the Oedipus complex in two different aspects, imaginary and symbolic. The square includes on the one hand the imaginary triangle mother-child-phallus, and on the other hand the symbolic triangle that structures the oedipal trio of father-mother-child.
The real is located between these two triangles. It is represented as a Moebius strip that simultaneously separates and unites the imaginary and the symbolic.
The relations of the terms on the outside of the square (M, mother; P, père, father; I, ego-ideal; φ , phallus) along with those from schema L placed on the inside of the schema (S, a, a′, A) are in the register of identification. This is how "The third term of the imaginary ternary [mother-child-phallus]—the one where the subject is identified, on the contrary, with his living being—is nothing but the phallic image, whose unveiling in this function is not the least scandalous facet of the Freudian discovery" (Lacan, 2002, pp. 186-87).
The real in the center of the schema is in fact a Moebius strip, the edges of which are rejoined when the strip is cut out and twisted so that points Mm and Ii meet. This strip only sustains itself by extracting of object a: "It is thus as representation's representative in fantasy—that is, as the originally repressed subject—that S̷, the barred S of desire, props up the field of reality here; and this field is sustained only by the extraction of object a, which nevertheless gives it its frame" (Lacan, p. 213, n. 14).
In Schema I, the schema of psychosis, the phallic and paternal symbolic poles are completely distorted in favor of the imaginary relation M-m (Figure 3).
"[This] symbolizes . . . that the [psychotic's] relation to the other qua relation to one's semblable . . . [is] perfectly compatible with the skewing of the relation to the Other with a capital O" (Lacan, p. 204).
See also: Four discourses; Graph of Desire; Matheme; Optical schema; Subject of the unconscious; Subject's castration; Topology. Bibliography
* Freud, Sigmund. (1920g) Beyond the Pleasure Principle. SE, 18: 1-64. * Lacan, Jacques. (2002). On a question prior to any possible treatment of psychosis. InÉcrits: A selection (Bruce Fink, Trans.). New York: W. W. Norton. (Original work published 1959) * ——. (1988). The Seminar of Jacques Lacan, Book II, The ego in Freud's theory and in the technique of psychoanalysis (1954-1955) (Sylvana Tomaselli, Trans.). New York: W. W. Norton.