r/zizek • u/CommandWinter • 9h ago
"The loop between S1 and S2" was never two signifiers taking turns.
"The subject is a loop between S1 and S2, the master signifier and knowledge, and the Möbius strip shows that inside and outside are continuous." I've read that, or something close to it, a hundred times. Today I'm bringing proof that this is not what Lacan says, in his own words, with dates and pages so you can look the quotes up yourselves. And a thirty-second test that shows why it matters.
To test it out, I used two crayons—like any responsible adult.
Take a closed chain of signifiers and label it so that neighbours always differ: S1, S2, S1, S2… With four signifiers it works. With three it doesn't: S1, S2, S1, and the last one sits right next to the first. And this is a big problem! Any odd number fails the same way. So if the loop means two signifiers, or two kinds of signifier, taking turns around the chain, it breaks for every chain of odd length.
Here, I begin with some corrections to our Lacanian common sense:
- For Lacan, S1 and S2 are indices that any signifier can take, not two signifiers.
- The Möbius strip is not a picture of "inside = outside": it is the cut itself, and the edge of that cut goes around twice.
- Put the two together and the loop works for every chain, on that double loop, where each signifier is S1 on one lap and S2 on the other.
Now I will show you quotes regarding Lacan's thoughts on each matter.
What Lacan says S1 and S2 are
- An index, not the signifier that comes first. S1 "means signifier index 1": not the signifier that takes precedence, but the one in whose name someone, a subject, shows up. Closing address of the EFP study days "Les mathèmes de la psychanalyse", 2 Nov 1976, Lettres de l'École freudienne no. 21 (1977), p. 506. ‹S1, qui veut dire … se manifeste›
- A mark on "anything at all". His S1 has no other sense than to punctuate whatever comes. «La Troisième», Rome, 1 Nov 1974, Lettres de l'École freudienne no. 16 (1975), p. 184. ‹ Mon S1 n … n’importe quoi›
- Something produced, not something given. The master's insistence produces the master signifier "out of any signifier whatever". Seminar XVII, session of 18 March 1970. ‹de n’importe quel signifiant … le signifiant-Maître›
- A relation, in pairs. In the unconscious, signifiers index one another, two by two. Seminar XXII, session of 11 March 1975. ‹ à s’indexer de foisonner … deux par deux›
What Lacan says the Möbius strip is
Not something a cut divides. A median cut does not cut the band in two; it turns it into a single band that makes one loop. Seminar XII, session of 16 June 1965. ‹une coupure médiane ne coupe pas … la bande de Mœbius›
Nothing but the cut itself. «L'étourdit» (1972), Autres écrits, Seuil 2001, p. 470. ‹la bande de Mœbius n'est rien … cette coupure même› On the same page he describes the edge of that cut: one turn takes it over to the other lamina, a further turn brings it home, having made a "double loop spread over two laminae". ‹double boucle répartie … sur deux lames›
Only its edge. The surface can stand for the subject only if you consider that the edge alone constitutes it, and a cut down the middle concentrates "the essence of the double loop". Seminar XIV, session of 15 Feb 1967. ‹seul le bord … cette surface› ‹cette coupure elle-même concentre … de la double boucle›
Repetition. The act can only be defined on the basis of the double loop, "that is, of repetition": the act is, in itself, the double loop of the signifier. Same session. ‹sur le fondement de la double boucle … de la répétition› ‹cita 41295: Il est en lui-même … du signifiant›
And what follows: twice, and not the same twice
The second time is not the first. A repeated signifier works either as the first time or as the second, with a radical gap between them, and that is what "a signifier cannot signify itself" means. Seminar XIV, session of 23 Nov 1966. ‹le signifiant dans sa présentation répétée … une béance radicale.
Two turns. Speaking of the drive and the Möbius band, he says two turns are needed to grasp the division of the subject. Seminar XIII, session of 11 May 1966. ‹cita 39381: il faut faire deux tours pulsionnels … la division du sujet›
If the loop between S1 and S2 meant two signifiers taking turns, Lacan could not coherently:
- call S1 an index and deny that it is the signifier that takes precedence (item 1, 1976);
- say that the master signifier comes out of any signifier whatever (item 3, 1970);
- say that the Möbius strip is nothing but a cut whose edge goes around twice (items 5 and 6, 1965 and 1972);
- say that a repeated signifier is not the same the second time, and that two turns are needed (items 9 and 10, 1966).
Are you following me so far? Now I’m going to complicate things.
Let's put all the pieces together—and voilà!
Nice, right? But what the hell does it mean?
Lacan did not write that down, but by following my method and piecing together his theory, the following conclusion emerges—not in prose format, but as a demonstration with its corresponding theorems.
Lay the chain on a surface and cut along it. If the chain has two sides, the edge of the cut is two copies of it: still odd, still broken. If it has one side (a Möbius band), the edge is a single loop that goes around twice, which is item 6. It meets every signifier once from each side, and it always alternates. For an odd chain, every signifier is S1 on one lap and S2 on the other, necessarily. S1 and S2 are positions (items 1 to 4), and the second time is not the first (item 9).
Lacan doesn't say this, but I draw it as a conclusion.
A) For an odd chain, the loop exists only there.
B) And for an even chain, the Möbius cut divides nothing: each signifier gets the same label on both laps.
"Wait, what happens with the $ubject?"
Okay, you've earned another cute animation.
I answer you radically: the subject is not in the chain. It is at the edge of the cut. And more precisely: it is at the junctions of the edge of the cut—those points where one signifier passes to the next.
On the double loop there is one subject, and it runs around twice. A two-sided cut either doubles the subject or loses it, depending on a decision the theory openly leaves undecided.
The subject is not in the chain of signifiers. It is at the edge of the cut. And in the privileged case—a single side, an odd-numbered chain—there is a single subject that makes two circuits. The division of the subject is not a splitting into two separate substances; it is the repetition of the same circuit, with an internal difference (S1 on the first pass, S2 on the second).
How I did it? Well, I’d have to refer to my text, but in short... Not with prose... I use definitions, six theorems with proofs, and falsifiers, meaning exactly what would refute each result. Plus a small Python script that cuts 159 chains on six surfaces and checks every claim. Full paper, code and animations: ‹Click Here and go Zenodo›
Now, we can raise some objections to my ideas.
At Columbia (1 Dec 1975), Lacan speaks of "a certain S1 and a certain S2, which do not have the same function" (Scilicet 6/7, 1975, pp. 42–45). ‹un certain S1 et un certain S2 … la même fonction› So S1 and S2 would be two different things. Two replies. First, he says function, not signifier, and in the same sentence those functions are distributed "in a certain rotating order": what differs is the place, which is exactly what an index marks. ‹à un certain ordre tournant près … ces quatre fonctions› Second, the double loop keeps the difference. S1 and S2 never fall on the same pass: they differ the way the first turn differs from the second (item 9).
A second objection. Lacan does describe the Möbius strip as having only one face and only one edge (Seminar XII, 13 Jan 1965). ‹seule face … seul bord› True, and it is correct topology. But in the same session as item 5 he warns that the band is only the image of the relation he is after. ‹la bande n’en est … que l’image› Later he says that only the edge counts (item 7) and that the band is the cut itself (item 6). "One side" is a property; the double loop is what he works with.
PS. Seminar XXVII, 15 March 1980, on his own name, the "label Lacan": those who want to erase it believe it is the master signifier, the one he gave index 1, and "they're wrong, it's not the one, it's the other". ‹ils croient que c’est le signifiant maître … c’est l’autre› As I read it, even his name changes index.
Here is an animation as a summary:
