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Seminar of March 18, 1975

I have already evoked the discovery made by Michel Thom of an error in Figure 6 of thelast published of my seminars. Felix Culpa, this was a fortunate error since it gave him occasion

to invent some Borromean knots of a special type, which are only unmade beginning from one

end. It is only in one direction (sens) and not in the other that all are unknotted. And in thedirection in which all are unknotted, they are freed one by one, and not immediately.This invention is indeed for me the proof that I do not speak without effect. What I know

thanks to these two friends, Soury and Thom, puts me on the path.

The knots are something quite original, with perhaps--I am not sure--the ambiguity of"the original." What would confirm this is that it is not so easy to get back there. And, then, the

original is not what one begins with. Historically, the Borromean knot is not found under the

hoof of a horse. One did not take an interest in it until very late. Me, when I caught wind of the

knot--I found it in the notes that someone had taken at Guilbaud's seminar--I immediately hadthe certitude that this was something of great value (prcieux) for what I had to explain. I

immediately found the rapport of the rounds of thread of this knot, of these three particular

consistencies, with what I had recognized from the beginning of my teaching; which I would nodoubt have not emitted, being little inclined to it by nature, without a call, tied in a more or less

contingent fashion to a crisis in analytic discourse. It is possible that with time I would have

aperceived that this crisis had to be unknotted, but there had to be certain circumstances for me

to pass to the act. The three rounds thus came to me like a ring to a finger, and I immediatelyknew that the knot incited me to articulate (noncer) something that would homogenize the

symbolic, the imaginary, and the real.

What does this mean, "homogenize"? It is obvious, as Pierre Soury remarked previouslyin a little note he communicated to me--I take great care to give each his due--they are somewhat

similar, but, he adds, "between the similar (pareil) and the same (mme), there is room for a

difference." Putting the accent on the similar is very precisely of what homogenization consists,

the pushing forward of the s, which is not the same, but the similar.What do they have of the similar? I believe I must designate this with the term

consistency, which is already to advance something rather incredible.

What indeed can the consistency of the imaginary, and of the symbolic and the real, have

in common? Do I, by this statement (nonc), render you enough sensible that the termconsistency arises with the imaginary?

Parenthesis. Figuring the knot is not easy. I do not say "figuring it for yourself" ("se" le

figurer), because I completely eliminate the subject. I take my departure, on the contrary, fromthe thesis that the subject is determined by the figure in question. Not that it would be its double.

But it is from the wedgings of the knot, from what in the knot determines the triple points--it is

by the tightening (serrage) of the knot that the subject is conditioned.

Figuring the knot is not easy (commode). I have already given you some proofs of this inmy muddlings over the question of the oriented knot.

To the real of the Borromean knot, you can add this: the differentation of each of these

rounds. The simplest way is to color them. Although Goethe notes it nowhere in his Theory ofColors, color is in itself pregnant with differentation. There is a limit, certainly, since the

number of colors is not infinite, but, finally, thanks to color, there is some difference. Thus, you

introduce differentiation into the round by coloring in a different way each of the rounds. Youcan go as far as to orient them. I have then asked the question of whether this differentiation

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leaves the knot not similar, but always the same.

It is effectively always the same, but there is only one way to demonstrate it: it is to

demonstrate that, in every case--what does "case" mean?--it is reducible to the similar.I was indeed convinced that there is only a colored knot, but I waffled a little concerning

the oriented knot. Orientation, in fact, concerns ayes or no for each of the knots, and I have

been led astray by the relation of each of theseyeses or nos with the other two. I have not goneso far as to think that there are eight or four knots, but I have battered my brains to know if therearen't two. Thus, it is no small result to have obtained from Pierre Soury, after having asked

explicitly for it, the demonstration?--no, the monstration [showing] that there is only one

oriented Borromean knot.Let us remark that he can only do this by way of what I have called the flattening out.

This flattening out is something that merits being individualized, because the knot, I have shown

you, is not at all flat by nature. That one must go by way of the flattening out to emphasize the

sameness of the oriented knot, is this not a sort offatum of thought, which in attaching it tooclosely to the true, lets the real slip through its fingers? This is indeed what I brought out last

time in distinguishing the concept and the truth. The concept limits itself to a taking (prise), as

the word capere indicates, and a taking does not suffice to insure that the real is what one has inhand.

In the comments I make to you and that you have, I don't know why, the patience to

accept, it is impossible for me to inform you at every instant what I do in speaking to you. Your

presence proves to me that I do something that concerns you. But in what mode does thathappen? To say that you understand something of it is not even certain at the level where what I

say is sustained. But there is nonetheless something that is worthy, and it is this something that I

situate in saying that we understand each other(on se comprend). We understand each otherhasno other substratum than we kiss each other(on s'embrasse). This, however, is not exactly what

we do. There is an equivoke here, which, like all equivokes, has a smutty side. For my part, I

force myself to put a little humor in my recognition of this smuttiness as presence.

It is indeed this that gives weight to the way I slice the knot, in stating that there is nosexual rapport.

This does not mean that the sexual rapport does not roam the streets. It remains to be put

in evidence that everything has to be recentered on thisfrotti-frotta, this fiddling around(fricotage), to make a call to what? To the real, to the real of the knot. Freud made a step by

simply aperceiving that one has never spoken of anything but that, and that everything

philosophy did pursued the sexual rapport to overflowing ( plein bord). By stating that there isno sexual rapport, I designate a very local point. Marking an R, to be put between x and y, to

designate the relation, is from the very start to enter into the game of the written. Now, for what

concerns the sexual rapport, it is strictly impossible to write xRy. There is no logicizable

elaboration, and at the same time no mathematical one, of the sexual rapport--this is the accent Iput on the statement "there is no sexual rapport."

This is to say that, without recourse to these different consistencies--homogeneous as

such, certainly, but nonetheless different from being named imaginary, symbolic, and real--there

is no possibility of afrotti-frotta. The difference between these consistencies cannot be reducedto a writing that would be supported, I mean, that would resist the test of mathematics, and that

would permit us to insure the sexual rapport.

These modes are those about which I have had my say (pris la parole), symbolic,imaginary, and real, and I will not say that they are obvious. I force myself simply to empty

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them out (les vider), which does not mean the same thing, because viderreposes on vide

[empty] and vidence on voir[to see]. Is this to say that I believe in it? I believe in it in the sense

that it affects me as a symptom. I have already said what the symptom owes to the believing in

it. I am trying to give to thisI believe in itanother form of credibility. It is certain that I will

founder there. This is no reason to not undertake it, if only to demonstrate the beginning

(l'amorce) of the impossible, already my impotence.The knot is supposed by me to be the real in the fact of what it determines as ex-sistence,I mean in how it forces a certain mode of turn-around. The mode in which one round of thread

ex-sists to another is that with which I displace the by itself unsolvable question of objectivity.

Objectivity thus displaced seems less silly (bbte) than the noumena. It is strictly impossible tonot make emerge, on the basis of the noumena conceived of in opposition to the phenomena, the

metaphor of the hole--but you are going to see that this is an after effect.

There is nothing to say about the noumena, except that perception has the value of

deception. But it is we who call it a deception, this perception. Perception itself says nothing. Itdoes not say; it is we who make it say. We speak all alone--I remark this apropos of no matter

what dire. We offer our voice, but this is a consequence, for the dire is not the voice; the dire is

an act. The noumena is nothing other than the hole, this hole that we find again in our symbolic,

named as such, and beginning with the topology of the torus.

The torus is distinguished from the sphere by a mode of writing by which are also

distinguished the homo, homeo, and automorphisms. Its foundation is always what one calls acontinuous transformation. A transformation that encounters the obstacle of another cord

supposed to consist is what makes the torus--which I would call on this occasion a gut-torus

(tore-boyau).Make a hole there in the torus, introduce your hand, and trap what is at its center (Figure

1). One sees clearly that there is discordance between this hand and what it grips. One can also

suppose another torus at the interior of the torus (Figure 2). How far can we take this? . . .

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These cords supposed to consist give some support to the metaphor of the hole, and allowus to elaborate mathematically a topology distinguished from that of the sphere. Every

imaginary supposition participates implicitly in the sphere insofar as it shines (rayonne)--Let

there be light! Only, concerning what there is of the consistency of the body, analysis revealsthat we have to come to the intestines (boyaux). Far from the polyhedrons that have occupied the

imagination, Timaein for centuries, it is the gut-torus that prevails. Besides, this is also a

sphincter.This renders sensible for you the relation of the body to the imaginary. I now ask you the

following question: can we think the imaginary, inasmuch as we are held to it by our body, in a

way that reduces its imaginarity?--or its imagery, if you like?One is in the imaginary. However elaborated one makes it--and this is what analysisleads us back to--one is in the imaginary. There is no means to reduce its imaginarity. It is here

that topology makes a step. It permits you to think--but it is a thought after the fact--that the

aesthetic, in other words, what you feel, is not in itself transcendental. The aesthetic is tied to

what is only a contingency, that it is this topology that is the right one for a body.Yet this is not a body all alone. If not for the symbolic, and the ex-sistence of the real,

the body would have no aesthetic at all, because there would be no gut-torus. The gut-torus is a

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mathematical construction, which is to say it is made from this nonexistent relation between the

symbolic and the real.

The notion of the knot that I promote is imagined, is figured, between imaginary,symbolic, and real, without for all that losing its weight of the real. But why exactly? Because

there is an effective knot, which is to say that the cords are wedged together. There are cases

where this turn-around no longer works because of the triple points that suppress ex-sistence.This what I have indicated to you in saying that the real is demonstrated to have no sense. Thereis no sense because only sense as vanishing, reduced to this triple point, gives sense to the term

real (Figure 3).

Likewise, in this other triple point is situated jouissance insofar as it is phallic--whichimplies its liaison with the imaginary as ex-sistence. The imaginary is the step of (pas de)

jouissance. Likewise, what gives consistency to the symbolic, is precisely that there is no Other

of the Other.

Is this to say that these figures are models? I have said that models recur to the pureimaginary. Knots recur to the real. They take their value from this: that they have no less

bearing in the mental than the real, even if the mental is imaginary. Every couple, all that there

is of the couple, is reduced to the imaginary. Negation is also a way of admitting--Freud insistson it from the start--a way of admitting there alone where the admission is possible, because the

imaginary is the place where all truth is stated, for a denied truth has as much imaginary weight

as an admitted truth: Verneinung-Bejahung.

How is it that the real only begins at number three? Every imaginary has some two in themix, as a remainder of this two effaced from the real. And this is how the two ex-sists to the

real.

Ex-sistence is the play of the cord until something wedges it; this is what plays on eachcord, as ex-sistence, to the consistency of the others. Freud renewed the accent on the

consistency of the real with an ancient term, the phallus--but how are we to know what the

mysteries placed under the term phallus? In accentuating it, Freud exhausted himself, but this is

done in no other way than its flattening out. It is a matter of giving weight to this consistency,and not only the ex-sistence, of the real.

Naming (Nommer)--which we could write n'hommer1-- naming is an act, from adding a

dit-mension, a dimension of flattening out. No doubt, Pierre Soury, in his monstration that thereis only one knot, distinguishes the turning around of the plane, the turning around of the round,

the turning around of the band, indeed, internal and external exchanges. These are only effects

of a flattening out. An exemplary recourse to the distance between the real of the knot and thisconjunction of domains that I wrote on the board, giving weight to sense.

Whether this clarifies the practice of analytic discourse, I leave to you to decide. I

propose, in closing today's meeting, this formulation of the triple identification that Freud

advances. If there is a real Other, it is not elsewhere than in the knot itself, and it is in this thatthere is no Other of the Other. If you identify with the imaginary of this real Other, it is the

identification of the hysteric with the desire of the Other--which passes to the central point.

Identify with the symbolic of the real Other, and you have the identification with the trait unaire.

Identify with the real of the real Other, and you obtain what I have indicated by the Name-of-the-Father, where Freud designates what identification has to do with love.

I will speak to you next time of these three forms of the Name-of-the-Father, those that

name the imaginary, the symbolic, and the real, for it is in these names that the knot holds.

1 A portmanteau ofnommer(to name) and homme (man).