# Schema L

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## Formalization

The various "schemata" that begin to appear in Lacan's work in the 1950s are all attempts to formalize by means of diagrams certain aspects of psychoanalytic theory.

The schemata all consist of a number of points connected by a number of vectors.

## Algebra

Each point in a schema is designated by one of the symbols of Lacanian algebra, while the vectors how the structural relations between these symbols.

## Topology

The schemata can be seen as Lacan's first incursion into the field of topology.

## Schema L

The first schema to appear in Lacan's work is also the schema which he makes the most use of.

This schema is designated "L" because it resembles the upper-case Greek lambda.[1]

Lacan first introduces the schema in 1955, and it occupies a central place in his work for the next few years.[2]

Two years later, Lacan replaces this version of the schema with a newer, "simplified form."[3]

## Readings

Although schema L allows many possible readings, the main point of the schema is to demonstrate that the symbolic relation (between the Other and the subject) is always blocked to a certain extent by the imaginary axis (between the ego and the specular image).

Because it has to pass through the imaginary "wall of language," the discourse of the Other reaches the subject in an interrupted and inverted form. (see communication)

The schema thus illustrates the opposition between the imaginary and the symbolic which is fundamental to Lacan's conception of psychoanalysis.

## Treatment

This is of practical importance in the treatment, since the analyst must usually intervene in the symbolic order rather than in the imaginary.

Thus the schema also shows the position of the analyst in the treatment:

"If one wants to position the analyst within this schema of the subject's speech, one can say that he is somewhere in A. At least he should be. If he enters into the coupling of the resistance, which is just what he is taught not to do, then he speaks from a' and he will see himself in the subject."[4]

## Intersubjective Relations

By positioning different elements in the four empty loci of the schema, schema L can be used to analyze various sets of relations encountered in psychoanalytic treatment.

For example Lacan uses it to analyse the relations between Dora and the other people in her story, [5] and also to analyse the relations between the various people in the case of the young homosexual Woman.[6].

## Intrasubjective Structure

In addition to providing a map of intersubjective relations, schema L also represents intrasubjective structure.

Thus it illustrates the decentering of the subject, since the subject is not to be located only at the point marked S, but over the whole schema.

"He is stretched over the four corners of the schema."[7]

## Other Schemata

In addition to schema L there are several other schemata that appear in Lacan's work (schema R; schema I;[8] the two schemata of Sade[9])

All of these schemata are transformations of the basic quaternary of schema L, on which they are based.

However, unlike schema L, which serves as a constant point of reference for Lacan in the period 1954-7, each of these schemata only appears once in Lacan's work.

By the time the last of these schemata (the schemata of Sade) appear, in 1962, the schemata have already ceased to play an important part in Lacan's discourse, although it can be argued that they lay the groundwork for Lacan's more rigorous topological work in the 1970s.

## References

1. Lacan, Jacques. Écrits. Paris: Seuil, 1966. p. 53
2. Lacan, Jacques. The Seminar. Book II. The Ego in Freud's Theory and in the Technique of Psychoanalysis, 1954-55. Trans. Sylvana Tomaselli. New York: Nortion; Cambridge: Cambridge Unviersity Press, 1988. p. 243
3. Lacan, Jacques. Écrits. Paris: Seuil, 1966. p. 548; Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p. 193
4. Lacan, Jacques. The Seminar. Book III. The Psychoses, 1955-56. Trans. Russell Grigg. London: Routledge, 1993. p. 161-2
5. Lacan, Jacques. Le Séminaire. Livre IV. La relation d'objet, 19566-57. Ed. Jacques-Alain Miller. Paris: Seuil, 1991. p. 142-3
6. Lacan, Jacques. Le Séminaire. Livre IV. La relation d'objet, 19566-57. Ed. Jacques-Alain Miller. Paris: Seuil, 1991. p. 124-33
7. Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p. 194
8. Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p. 197, 212
9. Lacan, Jacques. Écrits. Paris: Seuil, 1966. p.774, 778