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Synopsis of Jacques-Alain Miller, ‘Supplément: Les graphes de Jacques Lacan’

[‘Supplement: Jacques Lacan’s Graphs’]

CpA 2.7:167–175

In this highly compressed appendix to volume two of the Cahiers, Jacques-Alain Miller provides readings of five sets of graphs or schemas that appear in Lacan’s Ecrits: the L Schema, the ‘inverted bouquet illusion’, the R Schema, the Networks of Overdetermination, and the Graphs of Desire. These various constructions, Miller notes, serve as ‘analogies’ for configurations of unconscious structure.

Miller prefaces his interpretations of the graphs with a warning: since perception (the Imaginary) tends to eclipse a grasp of structure (the Symbolic), any schema or graphic representation of a structure ‘will infallibly lead the subject “to forget in an intuitive image the analysis on which it is based” (E, 574/478). It is the task of symbolism to forbid imaginary capture’, which accounts for its ‘difficulty’ (CpA 2.7:169/858).

I. The Schema of the Intersubjective Dialectic

This ‘L schema’ (E, 458/548) is the simplest of the graphs reproduced here. It shows, Miller explains, ‘that the dyadic relation between the ego and its projection a a′ (indifferently its image and that of the other) constitutes an obstacle to the advent of the subject, S, in the locus of its signifying determination, A’ (CpA 2.7:170/859).

II. The Optical Model of the Ideals of the Person

Lacan adopts the figure of the ‘inverted bouquet illusion’ (E, 673-681/563-570) from Henri Bouasse’s Optique et Photométrie dites géométriques (1934) in order to symbolise the logic of a phase of Imaginary development that ‘precedes (according to an order of logical dependence) the mirror stage’. This phase involves various configurations of the relation between the subject, his ‘real image’ and his ‘specular image’: the corresponding schemas thereby formalise the ‘imaginary and real functions of object a’. The third and most significant of the three variations of this figure proposed by Lacan is intended to show how ‘psychoanalysis, which operates in the symbolic [...] is able to reshape an ego that is [...] constituted in its imaginary status’ (E, 677/567). According to Miller, it represents ‘the moment of the treatment in which the analyst [...], neutralising himself as imaginary other, cancels out the mirage effects produced by the subject, and in which the latter overcomes the dyadic relation and empty speech to perceive his real image: he accedes to the language of his desire’ (172/860).

III. The Structure of the Subject

Lacan’s R Schema (E, 553/462, with variations developed in relation to Schreber and Sade) offers a ‘composition of the Symbolic, the Imaginary, and the Real’. Miller suggests that it can be read in two ways, as a representation of (i) ‘the statics [la statique] of the subject’ (articulating together the subject’s identification with the Imaginary object or phallus, his ‘situation of himself in the register of the symbolic’, and the ‘Real’ field ‘framed and maintained by the imaginary relation and the symbolic relation’) and of (ii) ‘the subject’s history’ (following the movement from ‘the imaginary identifications that form the child’s ego until he receives his status in the real from symbolic identification’) (173/861).

IV. The Networks of Overdetermination

These several figures represent configurations of memory and anticipation (175/863).

V. The Graphs of Desire

Lacan develops this elaborate figure in four successive stages in his 1960 essay ‘The Subversion of the Subject.’1 On Graph 1, Miller explains, ‘one may read the inversion that constitutes the subject in his traversing of the signifying chain. This inversion takes place by anticipation, whose law imposes at the first intersection (on the vector → S-S′) the last word (also to be understood as the solution [fin mot], that is, punctuation) and retroaction, enunciated in the formulation of intersubjective communication, which necessitates a second intersection, in which the receiver and his battery [sa batterie] are to be situated. Graph 2 combines, starting from the elementary cell, imaginary identification and symbolic identification in subjective synchrony; the signifying chain here receives its specification as speech. It becomes the vector of the drive, between desire and phantasy, in the complete graph – the intermediary graph simply punctuating the subject’s question to the Other: “What does he want from me?” which is to be inverted in its return, “What do you want of me?”’ (175/863).

References to this text in other articles in the Cahiers pour l’Analyse:


English translation:

Miller’s text was included as an appendix to Lacan’s Ecrits, and Bruce Fink’s translation appears in his complete edition of Lacan’s Ecrits (NY: Norton, 2006), in E, 903-908/858-863. A partial version was included in Alan Sheridan’s translation of Lacan’s Ecrits: A Selection (London: Tavistock, 1977).

Selected bibliography:

  • Lacan, Jacques. Ecrits. Paris: Seuil, 1966. Ecrits, trans. Bruce Fink, in collaboration with Héloïse Fink and Russell Grigg. New York: W.W. Norton, 2006.


1. For an exceptionally lucid reading of this essay, and of the various configurations of its graph, see Philippe van Haute, Against Adaptation: Lacan’s ‘Subversion of the Subject’ (New York: Other Press, 2002).