Explainer #1: A Brief History of Lacanian Schematics
Our book Event Horizon draws on Lacanian psychoanalysis as well as the work of critic and thinker Hiroki Azuma. In two explainer posts for this blog, we outline key ideas and concepts from both. We hope they help those of you who may not be familiar with them. These posts, together with our regular blog posts, can be read alongside the book.
We begin Chapter 1 with a discussion of conspiracy thinking in our present moment. We primarily develop Lacan’s notion of the Discourse to make sense of how phenomena like post-truth, QAnon or anti-vaxxers relate to capitalism and in particular what we call Networked AI. In this post, we introduce some background to this. To learn more, we encourage readers to read Lacan’s Seminar II on Schema L (Lacan 1991), Seminar III on Schema R (1993), Seminar VII on topologies of extimacy (1997) , and Seminar XIII on Graph of Desire (2016) for a more thorough understanding of his mathemes.
In the early years of his career circa 1895, Sigmund Freud set out to build a rigorous scientific basis for psychology and neurobiology, at the time still very much undifferentiated. What resulted is now known as Freud’s Project for a Scientific Psychology (Freud 1981), in which he outlines a schematic of neuronal systems. In it, he posits the existence of three functions: the φ-system that carries quantitative perception of the outside world Q, the ψ-complex that processes internal thoughts and memories, and the ω-system that acts as a mediator between the two through signifying chains, converting quantitative perception into qualitative attention and facilitation (Freud 1981).
When Lacan advocates for a return to Freud and places language at the center of psychoanalytic thinking, claiming that the unconscious is structured like a language, he was precisely referring to this discovery by Freud. Lacan would use other terms to denote similar concepts: the Real, in which raw perceptions of an outside world unmediated by language will result in incomprehensible experiences or trauma, the Imaginary, which is the domain of internal thoughts, memories, and fantasies, and the Symbolic, which is the domain of language, including science, law, religion, social contracts, and so on.
The above triangle is usually drawn with the Symbolic on the bottom left corner, the Real on the bottom right, and the Imaginary at the top. We have deliberately rotated the triangle by 120º counter-clockwise in order to highlight its parallel with the original Freudian triangle, and thus emphasize its Freudian roots.
For Lacan, φ denotes reality itself, which is different from the Real but is instead a projection of the real world in the Imaginary. For its part, the Imaginary projects onto the Symbolic a kind of effectively functioning totality, in the name of God, the Law, or other Names-of-the-Father, notated as S(A). This is barred (i.e. necessarily incomplete), but the bar constitutes it as true. Finally, the Symbolic gives meaning to the real world by positing a semblance. However, since Real effects can never fully be subsumed under language, this semblance is always lacking, thus giving rise to an object-cause of desire (a). We can also read that the interaction of two domains produces an effect situated in the third: reality is situated in the Symbolic, the object-cause of desire is Imaginary, and the Subject, in so far as it finds itself as a gap in the Other, is Real. The letter J at the centre of the triangle denotes jouissance, tied to but separate from the Real. This is a keystone in Lacanian thinking upon which he will build the rest of his teachings.
Lacan would later go on to topologise the original triad of Real-Imaginary-Symbolic as a Borromean knot, as we briefly explain in the Introduction chapter of the book. From the year 1975 onwards starting in Seminar XXIII, he would add a fourth ring, that of the sinthome holding the three together in an effect of jouissance. However, the triangle itself did not go away. Throughout the years 1954–1955 as outlined in his Seminar II, Lacan turned his attention to the Subject and the object-cause of its desire and began his foray into topology. Below, we can see how Lacan removes the position of jouissance from the original two-dimensional schema and brings it into a third dimension of a’, the dimension of the symptom.
This tetrahedron is the basis of his Schema L, in which he outlines the position of the Real Id (Es, notated by the letter S), the Imaginary ego (a), the symptomatic small other (a’), and the Symbolic big Other (A).
Lacan would go on to develop various schemas in the following years before coming to a theory of discourses in Seminar XVII, fifteen years after his original investigations. It is from this tetrahedron, its edges vectorised with specific directions (albeit different from the original triangle), that we get its projection as what we may now be familiar with as the formulas of discourse that Lacan outlined in his Seminar XVII. In this view, one can see that the basis for the discourse formulas is simply his Schema L rotated 90º clockwise.
The ego is the agent of speech: From what position is the discourse being spoken? The Id is now conveyed as the speech, text, or labour — which is, of course, not a one-to-one correspondence, but it can be said that the Id always occupies the domain of that which is spoken. It is the other being addressed: What or whom is the discourse for and about? The product is that which remains, the symptom of the discourse, its persistent object-cause of desire: What remainder does the discourse always fail to address? And finally, the big Other functions as the unconscious truth that animates the agent’s speech: What or who is actually speaking through the agent? This is the Freudian ‘other scene’ (Freud 1981), and key to Žižekian critique of ideology — in its very functioning, the Symbolic order always functions as the unconscious truth of our speech and our actions.
The arrows of the vectors are pertinent. The top arrow is the arrow of enunciation: in most cases, the agent is responsible for producing and reproducing the dominant text through which the world becomes meaningful. The discourse always produces a surplus. The surplus disrupts the agent and produces a sense of impotence in the unconscious. The unconscious speaks through the agent and colours the other in contradictions. The top arrow also marks a relationship of impossibility: ‘[…] There is no way, to say it all (sic). Saying it all is literally impossible: words fail,’ (Lacan 1974, 3). While at the bottom, the relationship between the symptom and the truth is that of impotence: What remains of the discourse will forever fail to address the unconscious in a proper manner, at least not until a proper analytical process.
All of these are generally written in a simplified form in the discourse formulas, with a line in the middle separating the conscious processes (ego formation, speaking, seeing the world) at the top and the unconscious processes (symptoms, fantasies, ideology) at the bottom.
These nodes within the discourse are then occupied by the four algebraic notations:
- $, or the barred Subject;
- S1, or the Master signifier;
- S2, or knowledge; and
- a, or the object-cause of desire.
These four elements and their interplay will become clearer upon further examination of the mechanisms of Lacan’s discourses.
What must be kept in mind is that placing these notations inside the standard formula of the discourse is not arbitrary, since it has a long history of investigation dating back to Freud’s early writings as we have briefly explained above. The formula itself should be understood as the two-dimensional projection of a three-dimensional tetrahedral vector arrangement. The turning of this tetrahedron is what gives rise to the various configurations, with its four elements in the projection occupying the following positions. Thus, its formation requires the algebras to be arranged in only four possible discourses.
As it turns out, the investigations carried by Freud’s Project for a Scientific Psychology (1981) bring us to the conclusion that psychoanalysis itself is, in fact, not a scientific discourse. The subject of analysis, the unconscious subject proper, is that which will always resist its subsumption into the scientific domain — the truth of the subject will always remain a hole in science.
Here, we can begin to shed new light on the crisis in the system of signifiers. To interrogate conspiracy thinking and knowledge production, it is important to first understand how knowledge (S2) is present in all kinds of discourses and remains adjacent to objet a, the object-cause of desire. In the four discourses above, we have two discourses in which knowledge is explicit, i.e. present as either the locus of speech or the content of speech itself:
- Discourse of the Master, where a new figure of power that is enacted speaks of a totalising knowledge through their words; and
- Discourse of the University, where knowledge speaks directly of objet a (in this case, scientific curiosity, dreams of innovation and progress, etc);
as well as two discourses in which knowledge is implicit, i.e. present as an unconscious source of speech or as its symptom:
- Discourse of the Hysteric, where a certain disturbing knowledge is a symptom produced by questioning the legitimacy of the Master; and
- Discourse of the Analyst, where unconscious knowledge is brought to speak forth (through objet a) in regards to the Subject.
For a full development of the theories presented in this blog post, please consider pre-ordering our book! Click on the link below to learn more, or go to Books Depository to place your order. Additionally, it would mean so much to us if you shared this post and gave this publication a follow!
References
Freud, S. (1981). Project for a Scientific Psychology. The Standard Edition of the Complete Psychological Works of Sigmund Freud. Volume I. Pre-Psycho Analytic Publications and Unpublished Drafts. London: The Hogarth Press and the institute of Psycho-Analysis.
Lacan, J. (1974). Le Seminaire. 1974–1975. RSI. Seminaire XXII. http://www.lacanianworks.net/?p=45.
Lacan, J. (1991). The Seminar of Jacques Lacan. Book II. The Ego in Freud’s Theory and in the Technique of Psychoanalysis. 1954–1955. New York: W. W. Norton & Company.
Lacan, J. (1993). The Seminar of Jacques Lacan. Book III. The Psychoses. 1955–56. New York: W. W. Norton & Company.
Lacan, J. (1997). The Seminar of Jacques Lacan. Book VII. The Ethics of Psychoanalysis. 1959–1960. New York: W. W. Norton & Company.
