**On intervals.**

Comments on a definition by Badiou

Mario Montalbetti

Février 2020
**Éditeurs :**

Cécile Chanvillard & Jean Stillemans

**Comité de rédaction :**

Cécile Chanvillard
Pierre Cloquette
Renaud Pleitinx
Jean Stillemans

**Diffusion :**

laboratoire analyse architecture
Faculté d'architecture, d'ingénierie architecturale, d'urbanisme
Place du Levant 1 boîte L5.05.02
1348 Louvain-la-Neuve
Belgique

<figure><img src="image_1.png" /></figure>

https://uclouvain.be/fr/instituts-recherche/lab/laa

© Les Pages du laa, 2020

ISSN : 2593-2411
**On intervals.**

Comments on a definition by Badiou

Mario Montalbetti
Barely 10 months ago, on the 26th of April of 2019, during a conference at this very University, Alain Badiou gave a definition of Architecture. [I would like to thank Marc Belderbos for providing me a copy of Badiou's conference and for much context.] The definition is as follows:

> Architecture [is] ... the violent interval between the Real and the Symbolic.
> [“L'Architecture [est] ... l'intervalle violent entre le Réel et le Symbolique.”]

In fact, Badiou didn't say exactly that. What Badiou actually said was the following :

> Architecture *should be* ... *like a type of* violent interval between the Real and the Symbolic.
> 
> [“L'Architecture devrait être ... comme une espèce d'intervalle violent entre le Réel et le Symbolique.”]

This is a weaker version of the definition I presented first as it makes use of a modality, a simile and a generic form. However, for the sake of this presentation I will work with the stronger version quoted above and it will be the point of departure for what I wish to say here tonight.

So,

> Architecture [is] ... the violent interval between the Real and the Symbolic.

I have three spontaneous reactions to this definition.

First, the definition makes use of well-known Lacanian terms (like the Real and the Symbolic) but crucially leaves aside the Imaginary, the third term involved in Lacanian constructions involving language and the unconscious (cf. Seminar XX, *Encore*, 10.22.1973—even though the use of the three terms pre-date the Borromean Knot). But it must be noted that the exclusion of the Imaginary has one immediate consequence: meaning is excluded from the definition. And this is so because Lacan specifically excluded meaning from language (that is, from the Symbolic) as early as his Seminar III of 1955-56 (“... meaning is by nature imaginary”, December 7, 1955). Thus, Architecture is not a question of meaning<fnref n="1" />.

My second spontaneous reaction is that the definition is not only an attempt at defining Architecture but also an attempt at trying to situate it. Thus, it tacitly assumes the question “Where is Architecture?” both with respect to itself and with respect to the other Arts. Indeed, according to Badiou, the position of Architecture among the other Arts is unusual. He proposes a three-way partition of the Arts,

> a) *Arts of Contemplation*, where the materiality of the work of art is offered to the eye, as in painting or sculpture;

<footnote n="1">1 cf. M. Montalbetti, “Architecture is meaningless” in C. Chanvillard, P. Cloquette, R. Pleitinx et J. Stillemans (eds.), *Pourquoi est-il si difficile de parler d’Architecture?*, UCL Presses, Louvain-la-Neuve, 2014—pp.31-41.</footnote>
b) *Arts of Duration*, where the work exists in its deployment in time, as in music or film; and

c) *Arts of the Body*, where the work exists in the organic expressions of the human body (the human voice included), as in the theatre.

But Badiou notes that Architecture doesn't fit squarely in any one of these categories because Architecture partakes of all three of them. It is an Art of Contemplation (in that it is, quite obviously, a visual art); it is an Art of Duration (not only because it exists in time and is materially conditioned by time, but also because it is a witness to the passage of time—forcing categories such as *ancienneté*, for example); and it is an Art of the Body (because it is directly concerned with living bodies, with their lives, movements, needs,...). Inasmuch as Architecture transverses this three-way partition, Badiou concludes that Architecture is unclassifiable (*inclassable*) and Architects are the agents of an ungraspable, elusive diagonal that runs through all these forms of art but doesn't fit squarely in any one of them.

Let me note at this point that Badiou, who has written extensively about poetry, leaves the poem aside in this classification. I will come back to this omission later.

And finally, my third spontaneous reaction to Badious definition is that it is almost oracular. Indeed, after stating his definition, Badiou quickly ends up his lecture by saying “Voilá !”—leaving us with the task of unpacking it, and perhaps even interpreting it.

So let's proceed.

## II

At the beginning of Badiou's definition there is a name: *Architecture*. There is little to say here except that names are unstable (cf. Plato, Letter VII, 343a-b). Indeed, 'Architecture' may name a certain discipline, perhaps even a certain theory in the modern sense of the term, that is, a set of operations that work on, and generate, a certain *écriture*; but 'Architecture' may also name, metonymically, the material objects produced by Architects, the buildings themselves. It is in the unstable character of the name 'Architecture' that Badiou finds much food for thought. Indeed, if a building is destroyed, does its Architecture remain? If the Cathedral of Notre Dame burns, as it did last year—an example thoroughly examined by Badiou in his lecture—has its Architecture burned with it? Has Architecture itself burned with it? Is Architecture only an Idea, or is it inescapably connected to bodies that dwell/pray/take refuge in it?

Notice, that what Badiou has offered is a definition of the term 'Architecture' not of buildings. The term 'Architecture' names, but buildings themselves do not. A building is not a name of anything. This is important to bear in mind for something I will develop later.
And, following the name “Architecture” in Badiou’s definition, following, that is, the *definiendum*, there is an interval, a violent one at that, that starts the *definiens*. Architecture is an interval...

What is an interval? It is an opening, a distance between two points in space or time. An interval is what is at stake in Zeno's paradox of Achilles and the tortoise. According to the story, Achilles will never reduce to zero the interval between him and the tortoise provided that the tortoise has a head start and keeps moving. But, what Zeno did not see... Lacan did. Indeed, Achilles will not catch up with the tortoise, but... it can surpass it. Achilles *can*, and probably will, win the race but what Achilles cannot do is reduce to zero the interval between him and the tortoise. In this, Zeno's paradox is another case of “there is no *rapport sexuel*”. But Lacan noted another thing concerning this paradox and that is that “the tortoise does not escape the destiny that weighs upon Achilles”. Achilles will end up catching up with the tortoise... at infinity (Seminar XX, November 21, 1972). I will come back to this in a moment.

Now, this (violent) interval, which Architecture is, lies between the two terms that frame its limits, that is, the Real and the Symbolic. Architecture is thus the violent interval between the Real and the Symbolic. It is a space, a distance, an opening, between them.

Now, what can such an interval be? First of all, an interval is not an intersection. I mention this because Lacan himself has worked with the idea of intersections between the three domains that define his Borromean Knot when it is flattened. For example, he calls the intersection between the Real and the Symbolic the *Jouissance phalic* (*Jf*), that is the *jouissance* that fails.

<figure><img src="image_2.png" /></figure>

Has Badiou given us just another name for the *Jouissance phalic* as his definition of Architecture? Not really. Again, intersections are not intervals, but if so, we need to be more specific about intervals. We have said that an interval is an opening, a distance, between two points. As such it looks like the opposite of an intersection. But then, let's try to be much more precise by making use of a simple mathematical notion of interval: an interval is a set I of Real Numbers lying between any two numbers. So, for example, the set of numbers in between 0 and 1 constitute an interval.

< --- | --- | ----- | -------------| ----- | --------| --- >
    0  0.11 0.1459...  √.3  7/8    1
Now, a key question regarding intervals is whether its limits (0 and 1 in this case) belong to the interval or not. In fact, three different types of intervals are possible. Thus we have,

<table><tr><td>i)</td><td>open interval:</td><td>(0, 1)</td><td>0 and 1 are excluded from I.</td></tr><tr><td>ii)</td><td>closed interval:</td><td>[0, 1]</td><td>0 and 1 are included in I.</td></tr><tr><td>iii)</td><td>semi-opened:</td><td></td><td></td></tr><tr><td></td><td>a)</td><td>(0, 1]</td><td>0 excluded, 1 included.</td></tr><tr><td></td><td>b)</td><td>[0, 1)</td><td>0 included, 1 excluded.</td></tr></table>

Given this simple notation we are faced with two interesting questions. The first one is that given that intervals are defined as sets of Real Numbers between any two numbers, what does it mean to say that there is an interval between two concepts (the Real and the Symbolic)? I will not be able to discuss this question in detail here but let me say the following. Yes, an interval can be taken as a mathematical notion (as I have been doing here) or as figurative one. In fact, sometimes we use 'interval' to denote a pause or a break between two events. But this reading makes no sense as a definition of Architecture. Thus, I would like to suggest the idea that an interval between two concepts is a metaphor. This is not to dismiss the notion of interval nor to degrade it. On the contrary, metaphors are one of the two key processes of language according to Lacan (the other one being metonymy). However, it will take a special type of metaphor to do the work needed here. Indeed, metaphors are usually taken as semantic devises of substitution: instead of "a" we mean "b". But, if we keep closer to Lacan's original idea, metaphor (and metonymy) are Symbolic processes, not Imaginary ones. This means, that metaphor is an a-semantic (or pre-semantic) process of substitution. Thus, if we can make sense of the idea of a purely symbolic notion of metaphor, then we may have a tool to explore the nature of Badiou's interval even further. But, enticing as it may sound, I will have to leave this idea for now because it would take us to complications for which we have no time tonight.

However, if we return to Badiou's actual definition of Architecture, not the one I have forced on him but the one that reads, "...une espèce d'intervalle violent...," that is, as a type, a form, a species, of interval, then the way is open to a non-mathematical character (perhaps even a metaphoric one in the sense just described) of Architecture's interval.

The second interesting question that emerges from the typology of intervals stated above (open, closed, semi-opened) is, of course, what kind of interval is Badiou's violent interval between the Real and the Symbolic. Here are the possibilities:

<table><tr><td>i)</td><td>(R, S)</td><td>: the interval excludes both R and S</td></tr><tr><td>ii)</td><td>[R, S]</td><td>: the interval includes both R and S</td></tr><tr><td>iii)</td><td>(R, S]</td><td>: the interval excludes R but includes S</td></tr><tr><td>iv)</td><td>[R, S)</td><td>: the interval includes R but excludes S</td></tr></table>

Of course, the answer depends on what Badiou takes R and S to be.
Here is when it gets interesting because in his conference, I believe Badiou makes use of two different notions of the Real. On the one hand, there is the classical Lacanian notion of Real, that is, the Real as impossibility. To state it more clearly: the Real can be seen as the inevitable residue of any process of symbolization. Whenever one makes use of the Symbolic, something ends up being excluded, something is set aside as un-symbolizable. That something could be transcendental (like sexuality in Freud) or contingent, depending on what has been actually symbolized (like in Derrida). So the classical Lacanian Real is a failure, structurally installed in the Symbolic itself. Let me call this version of the Real, Real 1 (R1).

Let me be a bit more precise as we will make use of all this in a moment. I quote Lacan from his Seminar II (June 29, 1955).

> "What's at issue [regarding language] is a succession of absences and presences, or rather of presence on a background of absence, of absence constituted by the fact that a presence can exist there. There is no absence in the Real. There is only absence if you suggest that there may be a presence there when there isn't one."
> 
> [My emphasis.]

If the Symbolic is an interplay of absences and presences, then the Real has no absence whatsoever. As O. Masotta once said "it is thick and dense like the liver of a goose". Given that there are no absences in the Real, the Symbolic, which is an interplay of absence/presence, cannot symbolize it. This is exactly what I call Real 1 (R1).

But there is another notion of the Real, which I believe Badiou also makes use of and which has been defined by Žižek as the inverse of R1. If R1 was the Real as impossibility, then this new notion (call it R2) is "the impossibility as Real". That is, a Real that, even if un-symbolized, is confronted as such by the Symbolic.

Badiou makes use of this R2 in his conference. For example, he urges the Symbolic process to "import... a fragment of the Real" and to "get closer to the Real". It is also in this sense, I believe, that he talks about "the Real of social inequality". That is, this is a Real that must be confronted by Architecture and not just left aside as a residue of Symbolization proper. It is a Real that directly confronts the fact that bodies dwell in, and are an inescapable part of, Architecture.

So we have two uses of the Real, R1 and R2: "the Real as impossible" and "the impossible as Real" respectively. Which one will define Badiou's interval? We will see in a moment. Before that, we should establish what version of the Symbolic is Badiou employing for his interval. And here again, we find in Badiou's conference two notions of the Symbolic, which I will call S1 and S2.

S1 is classical Lacan, the Symbolic as a structure of pure differences. As such, S1 is an interplay between a missing signifier (Ø), an absence, and a lexicon (a treasury, a *trésor*) of signifiers (L). Such interplay is traditionally called the "signifier pair". There are other versions of Ø such as "-1" or *extimité*, or absence, or zero-signifier,... but they all reduce to the same. The Symbolic works because there is a missing piece which allows all the other pieces to move and produce signifier effects, very much like in the moving squares puzzle in Fig. 1.
<figure><img src="image_3.png" /><figcaption>Fig. 1</figcaption></figure>

(Only that in the case of language there is no pre-ordained figure like “La Jaconde” that should be the end-result of our moves—although this is an open question depending on how strong one takes the Big Other to be).

Badiou makes use of another sense of Symbol/Symbolic, which I will call S2, one that essentially reduces to the idea of representation (i.e., the notion that “a is in place of x”). So, for example, in his lecture Badiou states that Architecture is a symbol of “the death of the powerful” (Egyptian pyramids), or of “the diversity of gods” (Greek temples), or of “the power of the State” (Versailles),..., or of “the wealth of the rich” (*les grandes villas*). How to integrate this use into our picture? Well, first of all, “symbols” are not part of the Symbolic. Symbols, as representations, belong inside the Imaginary... and as such ought to be excluded from Badiou’s definition. And second, this idea of symbol as representation seems to be part of the inevitable visual character of Architecture. Recall that Architecture draws a diagonal across all three types of Arts (Visual, Duration, Body). So we must assume (or incorporate) this visual property within Architecture. If S1 was defined as a system of pure differences, now S2 cannot. Here the differences are not ‘pure’ any longer. At the same time, S2 *is* the result of S1 at work. Only that, Badiou argues that Architecture must not “sacrifice the Real of social inequality in favor of the unity of the Symbolic”. I believe here lies the gist of the question.

What is the unity of the Symbolic? It is not just the idea of the pure interplay between the missing signifier (Ø) and the *trésor* of signifiers (L). Crucially, it is also the idea that what governs such interplay is the big Other: the Name of the Father, the State, the Law, God,... a figure of Authority. One of such figures is Grammar. Grammar is the unity of the Symbolic, for it determines that all of its products (words, phrases, texts, discourses,...) are non-singular, that is, are the result of pre-determined operations that will make them look very much alike. Any deviation from prescribed Grammar is rendered un-grammatical and rapidly dismissed... like mad individuals sent to an asylum. The Symbolic must generate un-unique products.

Now we can take Badiou’s S2 as an impure form of the Symbolic, that is, as a non-unified Symbolic in the following sense: that Architecture should aim at the unique, at the singular, so to speak at the un-grammatical and that is only possible if it defies (the Big Other as Big) Grammar, that is, if it defies the unifying order that rules the interplay between signifiers—at the same time that it makes full use of them.

Let us regroup.
We considered a typology of intervals that offered open, closed and semi-opened intervals
depending on whether the limits of the interval were included or not within the interval.
Next we considered Badiou's interval between R and S. And finally we asked what kind
of interval Badiou was referring to. These, again, are the possibilities:

i) (R, S) : the interval excludes both R and S

ii) [R, S] : the interval includes both R and S

iii) (R, S] : the interval excludes R but includes S

iv) [R, S) : the interval includes R but excludes S

Furthermore, we have discovered two different notions each of the Real and the Symbolic,
R1 and R2 on the one hand, and S1 and S2 on the other. Briefly recapitulating:

R1 = the Real as impossible (a residue of Symbolization)

R2 = the impossible as Real (the un-inscripted Body)

S1 = (Ø, L)

S2 = S1 minus Grammar (as Big Other)

So let's try to define Badiou's interval.

There is a key moment in his lecture in which Badiou states the following:

> "Architecture must import the division of the Real and the Symbolic within a
> space capable of withstanding (*supporter*) the universality of such gap without
> being hung up on the process of internal differences inside the Symbolic itself".

Clearly, the space Badiou is refering to is the interval; and such interval must be able to
withstand the universality of the gap between R and S without being hung up on the
unity of the Symbolic itself. The universality of the gap I read as the infinitude of the gap.
But recall that it is at infinity that Achilles catches up with the tortoise. No wonder that
Badiou states that such an interval must be *violent*.

Thus, I propose the following as Badiou's interval:

(R1 [R2, S2] S1)

That is, we exclude R1 and S1 as part of the interval but include R2 and S2. In other
words, we are left with:

[R2, S2]

Architecture is thus the interval (space) capable of withstanding the infinity of the violent inclusion of R (as R2) and S (as S2) within an interval that excludes both, the impossible as un-symbolizable and the unifying niceties of a pure Symbolic.

We can reword this last statement in terms of Badiou's actual definition: Architecture *should be* the space in which R and S meet violently (at infinity).
Now, is this itself an impossibility? Does Architecture exist as such or is it infinitely deferred in modality? Is Architecture something that *is not* but something that (constantly) *should be*? And furthermore, how is this violent interval to be actually construed? How do R and S catch up? I have no direct answers to all these questions. But, I will try to provide an indirect approach, even a negative one, by incorporating Badiou's silence about Poetry in his lecture.

### III

While thinking about Badiou's definition I encountered a very strange object, which, according to its author *is* a piece of Architecture. The strange object is a table that the Japanese Architect Junya Ishigami designed and constructed in 2006.

It is an unusual object. First, its measurements: the table is 9.5m long by 2.6m wide and 1.1m in height. It is a long table. The table top is a single sheet of aluminum barely 3mm thick...

...but it weighs 700k! It is not hard to appreciate that with such characteristics a 'normal' table will collapse on itself due to the force of gravity. Here is a sketch by Ishigami himself showing the top bending (Fig. 2).

<figure><img src="image_4.png" /><figcaption>Fig 2</figcaption></figure>
On intervals.

For the table top to stay flat some calculations must be made to counteract gravity, for example, bending it in the opposite direction (Fig. 3).

<figure><img src="image_5.png" /><figcaption>Fig. 3</figcaption></figure>

But Ishigami added further problems to the construction of his table. He added a series of objects (fruits, pots, baskets, bread, plates, flowers,...) which he distributed on the table and whose weigh should also be a factor in order to obtain the resulting flatness of the top (Fig. 4).

<figure><img src="image_6.png" /><figcaption>Fig. 4</figcaption></figure>

After calculations, Ishigami realized that the table top should be rotated one and half times to achieve its required flatness. Again this is his sketch (Fig. 5).

<figure><img src="image_7.png" /><figcaption>Fig. 5</figcaption></figure>
The end result, once constructed, is the following (Fig. 6):

<figure><img src="image_8.png" /><figcaption>Fig. 6</figcaption></figure>

One last comment: the table is so unstable that if you barely touch it with your fingertips, it starts making waves as if it were a mass of water.

Now we can ask ourselves, what did Ishigami accomplish? Is it Architecture, as he claims? Is it a table, as he also claims? If we follow Badiou's definition, it is neither, nor Architecture nor a table. It is not a table because it is a table only under extreme conditions (you can't use it, you can't touch it) and only visually (a victim of the Imaginary). It is a table in the same sense that Magritte's pipe is and is not a pipe. You cannot place things on it, nor extract things from it, you can't eat on it,..., you can't even touch it!

On the other hand, it is not Architecture because, as Badiou would say, it is still too “hung up on the unity of the Symbolic”. What unity is this? The unity of the structural calculus that will support the unstable integrity of the table, plus the Symbolic ‘game’ of exhibiting objects on the table as if they were words on a dictionary. That is, what is being exhibited is the raw power of objects to designate themselves outside of any other context that is not properly linguistic. “This is bread, and this is a fork, and this is a vase,..., (even “this is a table”) etc.” Indeed, what Ishigami’s table obscures is that it is its construction that is being exhibited and not the objects on top of it. Not even a table is being exhibited. What Ishigami exhibits is a purely differential symbolic calculus that holds everything together under extreme conditions of observation.

So here I would like to open a different flank to examine Badiou's definition. I would like to suggest that Ishigami's table is a poem (or something very close to it). And, I will do so by stating that the poem is the result of a different interval than the one I suggested as Badiou's defining interval for Architecture.

Recall that in his survey of the three-way partition of the Arts (Arts of Contemplation, of Duration, and of the Body), Badiou stated in his conference that Architecture didn't fit squarely in any one of them because Architecture participated in all three types of Art. Badiou thus concluded that Architecture was unclassifiable (*inclassable*) because Architecture draws an ungraspable, elusive diagonal that runs through all these forms of Art. But, we also noted that in his survey of works of Art, Badiou was mute about poetry—strangely so,
because he has written extensively about poetry throughout his books<fnref n="2" />.

Now, if you consider poetry in view of this three-way partition of the Arts it comes out as the direct opposite of Architecture. If Architecture partook of all three types of Art, Poetry partakes of none. Poetry is not visual (on the contrary, poetry is blind), nor is it an art of duration (if there is time in poetry it is geological time in the sense that it is all there at the same time), nor, finally, is it an art of the body (not even voice is indispensable). Thus, Poetry occupies, within the spectrum of the Arts, the position opposite to the one occupied by Architecture (something, I believe, Hegel foresaw some time ago in his *Lectures on Aesthetics*).

My immediate reaction to this is that in Poetry the relevant interval must be different from the one in Architecture. Thus, if Architecture's interval (I) is (i) below, then Poetry's is (ii):

(i) Architecture's I: [R2, S2]

(ii) Poetry's I: [R1, S2]

That is, Poetry is confronted with a different Real than Architecture, not with R2, the Real of the (un-inscripted) body, but with R1, what appears to be a failure of the Symbolic order. What is that? In short, it is Syntax. And it appears as a failure to the Symbolic only because Syntax cannot be symbolized. Badiou puts it different in a different context: there is no metaphor for syntax. It, Syntax, can only be formalized. In this sense, there is no Signifier for Syntax. In this sense, also, Syntax coincides, in my view, with its most biological sense. The basic structures of language uncovered by Chomsky some 20 years ago are biologically determined by a process of concatenation called merge, of which, a formal expression is the following:

<figure><img src="image_9.png" /></figure>

...that is, a hierarchical (non-linear) structure—but whose really interesting expression is the following:

<footnote n="2">² As early as L'Être et l'Événement of 1988 but consistently throughout—for example, *Conditions* (1992), *L'antiphilosophie de Wittgenstein* (2009), *Que pense le poème?* (2016).</footnote>
<figure><img src="image_10.png" /></figure>

a case of what is usually called *internal* merge, which allows for displacement: the movement of an already merged element to a different position inside the structure. This process allows for such defining properties of natural language as making questions, self-reflexive statements, quantification, and the like.

Such is Syntax as Real; formalizable but not symbolizable.

Now, Poetry's (violent) interval is between S2 (the lexicon of signifiers) minus the unifying grip of the Big Other or, if you prefer, of Big Grammar, and this version of Syntax as Real. Such a violent interval is rarely seen in actual poems. But, I will show you one which exhibits all the properties I have been talking about. It is a poem by the Peruvian poet César Vallejo and was written in 1937, barely six months before his death. It has no title, but is commonly referred to by its first verse ("La paz, la abispa,...").

La paz, la abispa, el taco, las vertientes,
el muerto, los decílitros, el búho
los lugares, la tiña, los sarcófagos, el vaso, las morenas,
el desconocimiento, la olla, el monaguillo,
las gotas, el olvido,
la potestad, los primos, los arcángeles, la aguja,
los párrocos, el ébano, el desaire,
la parte, el tipo, el estupor, el alma...

Dúctil, azafranado, externo, nítido,
portátil, viejo, trece, ensangrentado,
fotografiadas, listas, tumefactas,
conexas, largas, encintadas, pérfidas...

Ardiendo, comparando,
viviendo, enfureciéndose,
golpeando, analizando, oyendo, estremeciéndose,
muriendo, sosteniéndose, situándose, llorando...

Después, éstos, aquí, después, encima,
quizá, mientras, detrás, tanto, tan nunca,
debajo, acaso, lejos,
siempre, aquello, mañana, cuánto
¡cuánto!...
Lo horrible, lo suntuario, lo lentísimo,
lo augusto, lo infructuoso,
lo aciago, lo crispante, lo mojado, lo fatal,
lo todo, lo purísimo, lo lóbrego,
lo acerbo, lo satánico, lo táctil, lo profundo...

La paix, la guêpe, le talon, les pentes,
le mort, les décilitres, le hibou,
les lieux, la teigne, les sarcophages, le verre, les brunes,
l'ignorance, la marmite, l'enfant de chœur,
les gouttes, l'oubli,
la puissance, les cousins, les archanges, l'aiguille,
les curés, l'ébène, le mépris,
la partie, le type, la stupeur, l'âme...

Ductile, safrané, externe, net,
portatif, vieux, treize, sanglant,
photographiées, prêtes, tuméfiées,
connexes, longues, enrubannées, perfides...

Brûlant, comparant,
vivant, enrageant,
frappant, analysant, écoutant, frissonant,
mourant, se soutenant, se situant, pleurant...

Après, ceux-là, ici, après, dessus,
peut-être, pendant, derrière, tant, tellement jamais,
en bas, ou alors, loin,
toujours, cela, demain, combien,
combien !...

L'horrible, le somptueux, le très lent,
l'auguste, l'infructueux,
le néfaste, le crispant, l'humide, le fatal,
le tout, le très pure, l'obscure,
l'âpre, le satanique, le tactile, le profond...

(Translation by F. Maspero (intervened))

Critics have, almost unanimously, called this poem 'experimental'. But, remember that critics use the word 'experimental' whenever they don't know what to say about an object they don't understand, especially one written by a notorious poet. In any case, they never really say what the experiment is.

So let's try and say something more. It seems at first that there is no Syntax in the poem, just a bunch of signifiers. In fact, there is some but very little. For example, when Vallejo writes "la paz" (*la paix*) there is syntax between the determiner ("la") and the noun ("paz"). But it is clear that Vallejo has largely produced an object in which syntax is nowhere to be found, or hard to find—an absence. In this, it already looks very much
like Ishigami’s table. In both cases we have the following: a certain construction that
exhibits a series of objects. In Isgihami’s case, a table that exhibits useless objects; in
Vallejo’s case, a poem that exhibits words (Signifiers) which are equally useless (in that
they don’t do what they are supposed to do: combine with other words). In both cases
only ‘naming’ is possible, but no signifier effects are produced. Note furthermore that
what is really being exhibited in both cases are not objects/words but a hidden absence:
structural calculus in Ishigami, outright syntax in Vallejo.

This, I believe, is evidence that what is being confronted in Vallejo’s poem is Syntax as
real. What is being confronted is the impossibility to confront Syntax in Symbolic terms.
This is why the other end of the interval is S2, a Symbolic without the unifying grip of
Grammar (as the Big Other). Indeed, every single verse is, in this sense, un-grammatical.

Vallejo’s poem suggests much more. The ‘table’ on which it is set reveals an absence of syntax but at the same time a source of structure. I explain. Notice that Vallejo’s poem is not just a bunch of words but a bunch of words ordered in verses. So, in traditional terms, the first stanza of the poem is an 8-verse stanza. More interestingly, each verse is constructed making use of the two most basic metric structures of the Spanish verse: the hendecasyllable (an 11-syllable line) and the heptasyllable (a 7-syllable line). And this goes on all throughout the poem: it is a conversation between 11 and 7 syllable structures, which arrange themselves ignoring (or sometimes trying to destroy) what is left of verse patterns.

You must have to take my word for it<fnref n="3" />, but the only signifier in the first stanza that cannot
be integrated into the 11 and 7 syllabic structure is the noun “aguja” (needle, aiguille). It
is not an accident, I guess, that precisely that noun that names the instrument that allows
one to connect pieces together is singled out in the poem as impossible to integrate. It is
not an accident because what is manifestly set aside by the poem, Syntax, is precisely the
instrument that connects the pieces together, the needle.

Thus, Vallejo had to leave glimpses of the missing apparatus just to make the absence all
the more conspicuous. And again, what is absent, that without which there is no language,
is syntax in its crudest and barest form. Syntax as the poem’s Real. In more familiar
terms, Vallejo’s poem shows what cannot be said, that is, what cannot be symbolized.

IV

Let us regroup one final time in order to try and get to the end of this.

Architecture is the violent interval between the Real and the Symbolic. So is Poetry. But
both face, so to say, different Reals. In the case of Architecture it is a Real that confronts
the (human) Body and that confronts the fact that (human) bodies dwell in architectural
objects. Poetry, on the other hand, has Syntax as its Real, the biologically determined
way in which we chain our signifiers in order to produce language. But, both Reals
are such that they cannot be symbolized. Only formalized. And this is why meaning is

<footnote n="3">3 Or you may refer to my paper "La mesa de Ishigami y la idea del poema", a conference at the Universidad Diego Portales, Santiago de Chile, Chile, 17.10.2019.</footnote>
excluded from this symposium of the Arts. And this is why it is only violence that can
emerge from such interval. To borrow a phrase from Piera Castoriadis-Aulagnier, it is
"the violence of not understanding".

Thus, Badiou's definition of Architecture has set the way to re-think not only Lacan's Borromean Knot but also Architecture and the Arts in general, especially when Lacanian concepts are used outside the clinical practice. If something, what he has shown is that the notion of interval plays a key role in this analysis; interval as an alternative to mere intersection. To find the nature and workings of such an interval is a task that lies open in front of us. But the task is not to find an equivalent to Vallejo's poem in the realm of Architecture. Again, I claim their respective Reals are different. But it would be nice to have similar views of such violent (but at the same time, pleasing) intervals.
## Texte

Le 15 avril 2019, la cathédrale Notre Dame de Paris prend feu! L'incendie provoque, on le sait, un énorme émoi proportionnel à la charge des mémoires qui habitent l'édifice: le christianisme, les maîtres bâtisseurs du gothique, la Nation hypostasiée, la littérature et d'autres. Le président Macron et les très grandes fortunes de France tentent de transformer la catastrophe en effet d'aubaine et d'y capter quelques fragments de la hauteur morale qui leur manque.

Le 26 avril, 11 jours plus tard, Alain Badiou donne une conférence à l'Université de Louvain. Il revient sur l'incendie et analyse patiemment les multiples échos et effets de ce qu'il nomme un «accident architectural». Il conclut sa conférence en énonçant abruptement, au titre de définition: «L'Architecture devrait être... comme une espèce d'intervalle violent entre le Réel et le Symbolique.»

Le 20 février 2020, 10 mois plus tard, Mario Montalbetti donne une conférence à l'Université de Louvain qui s'arrime à la déclaration d'Alain Badiou qu'il commente à partir de ses propres positions, celle de poète et celle de linguiste.

## Auteur

Mario Montalbetti est linguiste, poète et essayiste. Docteur en linguistique (MIT, avec Noam Chomsky), il est professeur principal au Departamento de Humanidades de la Pontificia Universidad Catolica del Peru (PUCP). Il est membre fondateur de la revue *Hueso Humero*. Ses œuvres poétiques ont été réunies dans *Lejos de mi decírles* (Aldus, 2013). Il a publié également *lacan arquitectura*, avec Jean Stillemans (PUCP, 2009), *Cualquier hombre es una isla* (Fondo de Cultura Economica, 2014), *El mas crudo invierno* (Fondo de Cultura Economica, 2016), *Cajas* (Colecion Decir Arquitectura, PUCP, 2017), *Epícilos*, avec Marc Belderbos (Colecion Decir Arquitectura, PUCP, 2018), *Notas para un seminario sobre Foucault* (Fondo de Cultura Economica, 2018), *El pensiamento del poema* (Marginalia Editores, 2019). *Les pages du laa* ont publié en 2009 «Ce que Lacan n'a pas dit» (sur l'architecture) est aussi organisé comme ce qu'il a dit (sur le langage)».

<figure><img src="image_11.png" /></figure>

https://uclouvain.be/fr/instituts-recherche/lab/laa
© Les Pages du laa, 2020
ISSN: 2593-2411