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Dance and Subtraction: Notes on Alain Badiou's Inaesthetics

Published online by Cambridge University Press:  09 February 2012

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In an essay entirely devoted to the subject of dance in Alain Badiou's Handbook of Inaesthetics [Petit manuel d'inesthétique (Badiou 2005b)], we find the following contentious statement: “Dance is not an art, because it is the sign of the possibility of art as inscribed in the body” (69). At first glance, this statement seems strangely familiar to the reader versed in writing about dance, particularly philosophical writing. “Dance is not an art”: Badiou critiques Mallarmé as not realizing this as the true import of his ideas. It is familiar because it attests to a certain problem in aesthetic thinking, one that relates to the placement and position of dance and the works that comprise its history into what can be seen as certain evaluative hierarchies, particularly vis à vis the relation of dance to other art forms, and in particular, those involving speech and writing. Dance seems to suffer from a certain marginalization, subtraction, or exclusion, and its practice seems to occupy a place of the perennial exception, problem, or special case. The strangeness of the statement, on the other hand, relates to the widespread view outside of academic writing that the status of dance “as art” is actually completely unproblematic. What follows therefore is a critical commentary on this assertion of Badiou, placed both in the context of Badiou's writing, and in the wider one pertaining to the problem of exclusion just outlined.

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Copyright © Congress on Research in Dance 2011

In an essay entirely devoted to the subject of dance in Alain Badiou's Handbook of Inaesthetics [Petit manuel d'inesthétique (Badiou Reference Badiou and Toscano2005b)], we find the following contentious statement: “Dance is not an art, because it is the sign of the possibility of art as inscribed in the body” (69). At first glance, this statement seems strangely familiar to the reader versed in writing about dance, particularly philosophical writing. “Dance is not an art”: Badiou critiques Mallarmé as not realizing this as the true import of his ideas.Footnote 1 It is familiar because it attests to a certain problem in aesthetic thinking, one that relates to the placement and position of dance and the works that comprise its history into what can be seen as certain evaluative hierarchies, particularly vis à vis the relation of dance to other art forms, and in particular, those involving speech and writing. Dance seems to suffer from a certain marginalization, subtraction, or exclusion, and its practice seems to occupy a place of the perennial exception, problem, or special case. The strangeness of the statement, on the other hand, relates to the widespread view outside of academic writing that the status of dance “as art” is actually completely unproblematic. What follows therefore is a critical commentary on this assertion of Badiou, placed both in the context of Badiou's writing, and in the wider one pertaining to the problem of exclusion just outlined.

“Dance is not an art:” Badiou is able to conclude the essay with this statement via an elaboration of six “principles” of dance, which see it defined subtractively from related principles for theater.Footnote 2 This method of subtractive “purification” will be familiar to anyone versed in Badiou's philosophy, but as will be seen in what follows, the problematic of the nature of dance and its placement leads to some important critical questions about Badiou's aesthetic theory (which he prefers to term “inaesthetics”), and indeed his philosophy in general, that this essay aims to elaborate.

What are these six principles of dance, as Badiou sees them? They arise from an initial assertion that dance, as a pure activity of the body, remains at the level of the presubjective, or preconceptual. Dancing gestures appear only to disappear, and therefore demonstrate “thought as event, but before this thought has received a name—at the extreme edge of its veritable disappearance; in its vanishing, without the shelter of the name” (61). This concept of “event,” which is central to Badiou's entire philosophical project, will require a detailed explication later. But first, Badiou's conception of dance can be summarized via the following six “axioms.” First, dance requires a “pure site” (63), or a space situated on the edge of the void of space. It takes place, or should take place according to Badiou, in a completely neutral and “virginal” spatial situation, devoid of theatrical décor and demands “space and spacing, and nothing else” (64). Second, the anonymity of space/setting extends to one of character. Badiou claims that dance, in stark contrast to the needs of theater, has no need of narrative structure (it deploys no roles), and, in terms of its characterization, “depicts nothing” (Badiou Reference Badiou and Toscano2005b, 64). Third, it asserts the “erased omnipresence of the sexes” (Badiou Reference Badiou and Toscano2005b, 64): It reveals only a pure form of sexual difference, in such a way that the couple male dancer/female dancer cannot be reduced or superimposed onto the couple man/woman.Footnote 3 Fourth, dance should effect a “subtraction from self” (65); following the seemingly paradoxical statement of Mallarmé—”the dancer does not dance” (Mallarmé Reference Mallarmé and Caws2001, 109). The (true) dancer never knows the dance she dances, the dance itself appearing as immanently spontaneous, improvisatory—a pure emergence of gesture without any appeal to pre-existing knowledge, belief, orthodoxy, etc. Fifth, dance should have no need for adornment, and essentially reveals “nudity” (Badiou Reference Badiou and Toscano2005b, 66), an absence of the décor of costume. The sixth and last principle relates to the spectator rather than the dance itself, and requires of him or her a kind of rigorous impersonality, free of the vicissitudes of sexualized or desiring gaze.

The six axioms should, as mentioned previously, be read subtractively, and attempt a determination of the nature of dance via a process of negation. For the most part, they describe a notion of what dance is not—and in particular, perhaps also what dance is not yet. Is Badiou describing a dance “to come”? And what it is not, according to Badiou, ultimately, is theater, which is in contrast: it names its place (situates and clarifies its setting), its constructs roles/narratives, it amplifies the sexuated positions often via exaggeration, it exceeds rather than subtracts itself, it requires costumed appearances; and it expects/creates a desiring spectator.

We will return to these six theses later, but in the meantime, let us consider the idea that motivates them, that dance is “thought as event, but before it has a name” (Badiou Reference Badiou and Toscano2005b, 61). Although this statement seems innocuous enough, the terms “event” and “naming” actually play a very precise role in Badiou's thinking, and one that will require a digression into his “subtractive ontology.” This will lead us to argue that Badiou's thinking on dance can be turned in on itself, so that, even within the context of his theory of event, there is an analogous (if disjointed) series of works in dance history broadly contemporaneous with Badiou's most often cited example of an event in art. The latter is the “Schoenberg event” in musical composition, whereas the trajectory of dance works is inaugurated, I will argue, by the name “Cunningham.” What connects the two artists is the familiar modernist motif of autonomy, coupled with formalized procedures for the generation of new material (in music, or in movement).

But first, let us ask an important question: For the aesthetician, and the dance theorist in particular, why is Badiou an important figure? To answer this, it may be helpful to briefly situate Badiou's thinking within the tradition of European philosophy of the last hundred years or so. To cut a very long story somewhat short, one of the main concerns of this tradition has been an attempt to reconcile two different accounts of the human subject, characterized by Jacques Lacan's distinction between the “subject of the enunciated” and the “subject of the enunciation”: “The case of linguistics is subtler as it must take into account the difference between the enunciated and enunciation, that is, the impact of the subject who speaks as such (and not of the subject of science)” (Lacan Reference Lacan1967). An analogy from dance may make this distinction clear. Francis Sparshott (Reference Sparshott and Kivy2004) refers to what might be called the central dichotomy or “parallax” of the experience of watching dance: On one hand there is the experience of viewing “mere flesh” or “actual material stuff in motion” (280), (or, in other words, the body reduced to a mere mechanical system); on the other there is the (contrary) impression of the “gesturing human, its movement not merely vital but essentially meaningful as expressions of a conscious, perceptive, motivated being” (280). The first view of the dancer represents the anonymized “subject of the enunciated,”—the third-person entity subjected to the manipulation of anti-humanistic and autonomous socio-symbolic structures and ideologies beyond its control and/or the human reduced to the dispassionate object of rational scientific study (as in Althusser, Foucault, Lacan, etc.). The second view represents the subject's own individual capacity for “enunciation,” characterized by the first-person vicissitudes of lived experience/human freedom prioritized by the phenomenological tradition (as in Sartre, Fanon, Merleau-Ponty, etc.), which resist delineation by these same formal structures. What is characteristic of Badiou is his attempt to align both the “subject” and the “subject of science” via an overarching appeal to a renewed concept of “truth” that emphasizes both Sartrean ideas of subjective fidelity and commitment, as well as formalizing the trajectories of such commitments by an appeal to anti-humanistic mathematization. Badiou's aesthetics proceeds along similar lines: The artist is one who is able to act “in fidelity” to a “truth-procedure” that can be defined without any recourse to subjective particularity. It is in this sense that Badiou deserves to be taken seriously. Against the tendency in much “postmodernist” art towards a ubiquity of personal expression (for its own sake) conjoined with the ideologies of an undiscriminating cultural relativism, Badiou wants to return to a quasi-Platonic ideal of art as something partly universal and ahistorical, despite its localization in historical “worlds.” This puts his views on music, for example, at odds with someone such as Theodor Adorno, who sees these same timeless or “autonomous” qualities of art in terms of what opposes them dialectically (namely the idea that the “commodity status” of artworks is an effect of their status as autonomous—a view that therefore stresses their historically contingent formation). And in terms of the phenomenological tradition, we will see later how Badiou proposes a radical view of phenomenology as essentially “objective” rather than “subjective” via an appeal to a theory of “appearing” or “being-there” that rests only on “transcendental” conditions that are mathematical, not subjective in nature. It is for this reason that Badiou's importance to the phenomenologist is essentially a negative one, as his “objective-phenomenology” or “anti-phenomenology” can be shown to create problems for the thinking of Heidegger, Husserl, and Merleau-Ponty, etc., which require careful consideration, and suggest aspects of the human condition that phenomenology may well have obscured.Footnote 4 And for the dance theorist, Badiou is important insofar as there is a strong argument for showing how a consideration of specific danced choreographies can pose significant problems for a philosophical position like the one defended by Badiou. Rather than being the “poor relation” in the field of aesthetics, dance can show, and show uniquely in this case, how the work of a respected philosopher can run into difficulties, especially in relation to an aesthetics that aims to extract the corporeal body from its claims to truth.

Badiou's Subtractive Ontology

Badiou's theory of event, and the “truth-procedure” that accompanies it, are expounded in the two volumes of L'être et l'événement (Badiou Reference Badiou and Feltham2005a, Reference Badiou2006a), which are, in part, also a theory of the metaphysics of the human subject. In the first volume, Being and Event, the old philosophical problem of ontology is given a striking new formulation. Being “as such,” the science of being qua being (being that is subtracted from all particularity) is, in a radical move, equated with the infinite as pure multiplicity, that is, a multiplicity subtracted from any unity or unifying process, any “counting-for-one.” Being, argues Badiou, cannot be thought in terms of, or in opposition to, any transcendent One, God, or Deity (a “being-beyond-being,” as in Hegel) or as some kind of intensive process or quasi-biological vitalism (as in Deleuze). As such, Badiou argues, the only rational (and non-”theological”) thinking of being can be via mathematics. Thus the problem of ontology as such is subtracted from philosophy and can only be thought via mathematization, and since we are speaking of infinite quantities, and since it is the only rational thinking of infinity available, through the transfinite set theory of Georg Cantor.Footnote 5

In contrast, the process of human subjectification begins, and can only begin, with a “truth-event”—a radical intervention into a particular situation [the latter thought of as a structured and potentially infinite multiplicity of elements: “words, gestures, violences, silences, expressions, groupings, corpuscles, stars: it is of no ontological consequence” (Hallward Reference Hallward2003, 94)]. Every situation however contains a place impervious to such presentation. Starting with just this “void” of the situation,Footnote 6 which is always contained therein but not presented (not “counted-for-one,” and hence indiscernible), this subjective intervention “names” the event by providing a nomination of the void, a naming of its “place of no-place.” As an example, think of the French sans-papiers, a collection in the situation of contemporary French politics, but not presented in it, and as such, indiscernible within the situation. This distinction between merely “present” and “presented” is crucial: The migrant worker maintains a physical presence within the situation, but from the standpoint of the state, remains invisible (such a worker has none of the usual labor rights afforded to the “normal” citizen, and exists outside of its formal identification procedures). The subject then acts “in fidelity” to the event by faithfully connecting as many elements of the situation as possible with this name (or “trace”). For example, in the case of the sans-papiers, the trace could be the simple nomination “everyone who is here is from here [tous les gens qui sont ici sont d'ici].”Footnote 7 What is clear here is that the terms “name,” “trace,” and “nomination” refer to the nature/enunciation of something symbolic; in the above context, one may think of them as being similar to the announcement to some kind of “manifesto” (as in the various statements of the founders of surrealism, futurism, etc., in modernist art). In terms of dance for example, such a trace might involve the following nomination “There can be an organization of human movement entirely subtracted from the strictures of classical ballet.” After the nomination of a trace, so the theory goes, the faithful subject acts in fidelity to it in the future anterior, namely by proceeding as if the new truth were generally applicable, “forcing” it into the realm of presentation, and in so doing, radically altering the situation itself. In the above case, for example, fidelity to the event would involve a commitment to certain types of choreographic decision-making: “How is dance organized outside of narrative structure?” “What happens when body parts are given (full) asymmetric autonomy?” “Fidelity” then necessitates a rigorous investigation aimed at answering these types of questions in such a way that the event, and the imperative that its trace enunciates, are temporally extended without compromise. Badiou defines the full result of these subjective investigations as truths if they have the property of a rigorous universality (that they are “generic”) to all in the situation without concession to the norms, validations, opinions (doxa), etc. of the pre-existing “state of the situation”; one thinks here, literally, of the “State” in a dominant political hegemony, for example. Moreover, such truth-events can arise in one of only four “conditions,”—those of politics, science, art, and love—and it becomes the job of philosophy to identify and discern the trajectory of these.

In the sequel to his Handbook of Inaesthetics, Logiques des mondes, Badiou supplements but does not replace this conception of the dichotomy of being and event, and instead addresses the problem of how being, as pure multiplicity, appears in a particular situation, now called a “world.” The problem is now one of the thinking being in its organized localization “in-a-world,” and every world is equipped with a way of mathematically “measuring” infinite multiples according to their degrees of identity or difference or, in short, their intensity.Footnote 8 It is precisely here that Badiou breaks off from the phenomenological tradition. Phenomenology, he claims, and with an obvious sense of mischievous contradiction, is “objective” because the logic of appearance is essentially mathematical/topological, not perspectival, in nature. Localized being appears as an “intrinsic determination” of its being-as-such, in opposition to Kant or Husserl, who see appearance as being correlated with a transcendental relation between perceiving subject and perceived object. Badiou, for the same reason, is also opposed to the “experiential” linkage of a Heideggerian Dasein and its lived-in environs. For Badiou, “being” and “being-there” are always coextensive: Something always already simultaneously exists and exists-somewhere. But the subject and its transparent self-consciousness are constituted by the logic of appearance, not constitutive of it (as in Husserl): “For the phenomenologist, the real is in the final analysis consciousness. For me, consciousness is at best a distant effect of assemblages and their eventual caesura, and the subject is through and through not constituent, as it is for Husserl, but constituted. Constituted by a truth” (Badiou Reference Badiou2006a, 185–186). And should there be any confusion about what this means for the body, as it is defined in the phenomenology of Merleau-Ponty as the presence of consciousness to the world, Badiou is characteristically unwavering: “If it is necessary ceaselessly to recall that it is from structure alone that the body draws the symptomal appearance of its effects … it is to the extent that the phenomenological vulgate, by separating the body from the letters that target it, institutes the presence-to-the-world of the body as the ontology of originary experience” (Badiou Reference Badiou2006a, 500).

But to return to Logics of Worlds, the ontological treatment differs from the one in Being and Event in that the world of “pure” being presented there is seen as just one “world among many.” While its logic is classical, obeying the logical laws of noncontradiction and excluded middle, the worlds of the Logics are, by contrast, heterogeneous (classical but also modal or intuitionist, in which the law of excluded middle fails).Footnote 9 While this “many worlds interpretation” may strike some as fidelity to little more than cultural relativism, Badiou's point is exactly the opposite. As Slavoj Žižek (Reference Žižek2006) puts it:

Postmodern relativism is precisely the thought of the irreducible multitude of worlds, each of them sustained by a specific language-game, so that each world “is” the narrative its members are telling themselves about themselves, with no shared terrain, no common language between them; but the problem of truth is how to establish something that, in the language of modal logic, remains the same in all possible worlds…. The passage to truth is therefore the passage from language (“the limits of language are the limits of my world”) to letter, to “mathemes” which run diagonally across a multitude of worlds. (37)

The term “matheme” comes from Lacan, who like Badiou, sought to “mathematize” his own “world,”—that of psychoanalysis: “Mathematical formalization is our goal, our ideal” says Lacan in Seminar XX. It is precisely this symbolic formalization, which moves into the abstract of the (mathematical) letter, that links the notion of necessary truth outlined by Žižek to the “trace” of Badiou's “truth-event.”

In each of these heterogeneous worlds, there exists a kind of “zero-level” of appearing called its “inexistent,” an appearing within a world of minimal intensity, and as with the “void” of Being and Event, this is the key site of potential change, the “evental site,” which contains those elements that have a minimal or invisible existence according to the rules that regulate how things appear in a world, and thus entertain no observable relationship with the other elements of the world. The dominant logical structure of a world ensures that the appearing, or “being-there,” of such elements is indistinguishable from mere “non-being.” The event is now a radical change in the world from the evental site—a singularity with maximal consequences: “The maximally true consequence of an event's (maximal) intensity of existence is the existence of the inexistent” (Badiou Reference Badiou2006a, 377), a kind of uprising of the inexistent.

What follows in Badiou's account is a discussion of the “points” associated with a truth-event, and a revised definition, of some importance for us later, of “body.” The former has a clear association with the famous Lacanian “point de capiton,” that which, in one gesture, “quilts” the ideological field by stopping the “sliding” of the process of signification.Footnote 10 For Badiou, such a point is simply a choice, a binary “yes/no” decision (on which the future of the event depends) that the subject of an event is forced to make: “A faithful subject is the form of a body whose organs treat a worldly decision ‘point by point’” (Badiou Reference Badiou2006a, 421), and “the reduction to the two of infinite multiplicity” (423). Thus the “body” of an event is not the individual animal body of the faithful subject, but an incorporeal, immortal body comprising all the investigations, consequences, productive turns, and dead-ends that make up the configuration of the event's trajectory. The “body” of the Schoenbergian serialist event in music, for example, is more like the “body of works” that comprise it (also including Alban Berg and Anton Webern, etc.), and its “subject” the equally corporeally indistinct “subject of the trace” (anyone or anybody who is faithful to it). The emphasis that Badiou places here on the “incorporeal” nature of the event sets him on an obvious collision course with dance and other art forms like performance art. And his insistence that the “body” of the event is in opposition to the somatic, “real” body will exacerbate this collision: “The body is not the body,” Badiou claims, in a recent interview (Sedofsky Reference Sedofsky and Sedofsky2006). In fact, Badiou it seems is no fan of the corporeal body when it comes to the interrogation of truth: “Art is not the sublime descent of the infinite into the finite abjection of the body and sexuality. It is the production of an infinite subjective series through the finite means of a material subtraction” (Badiou Reference Badiou and Corcoran2006b, 143). At stake here is Badiou's resistance to a concept of art sutured to the expression of particularity; be that “ethnic, egoistic or personal” (143), and again, this statement has important consequences for the aesthetics and indeed politics of dance.

But for now, having given broad definitions of the terms involved and in an attempt to avoid undue abstraction, let us now turn our attention to a particular world and a particular event—the musical event that Badiou claims was inaugurated by Arnold Schoenberg. The digression into a musical example is necessary, as it outlines important differences with how Badiou views the two art forms (dance and music) that are instructive to understanding his views on dance alone. In addition, it is via a close comparison with the following example that we can introduce a hitherto unspecified trajectory of dance works into Badiou's account of aesthetics that is in some ways, I will argue, structurally homologous with the musical case.

Schoenberg's Event

The name of Schoenberg is a constant reference in Badiou's writing. For instance: “… there was a continuation through rupture of veritable musical creation, which, from Schoenberg to Brian Ferneyhough, liquidated tonality and constructed a universe of musical singularities, serial and post-serial” (Badiou Reference Badiou, Clemens and Feltham2003, 121). In the same passage, an explicit distinction is drawn between this event and any supposed alternatives to it within twentieth-century music, from the symphonic “artifices of the finishing tonality” (Mahler, Strauss, Rachmaninov) to the “great creation” of jazz and all “youth music,” from “rock to techno” (Badiou Reference Badiou, Clemens and Feltham2003, 121). But the evental (veritable) status of the serialist event is seen as both primary and singular—the “real of music as art, and not … the decomposed forms of symphonism or the demagogic forms of youth music” (122). In terms of a historical trajectory, Badiou nominates the period and body of works between Schoenberg's Variations for Orchestra (1926) and, bizarrely, only the first version of Répons by Boulez (1981), but it is perhaps important to emphasize that Badiou is not concerned with precise dates here, but more with the enunciation, subsequent consequences, and non-corporeal body (musical works, written and performed) associated with the trace of the serialist event, which he defines as “… an organization of sounds able to deliver a musical universe on a basis entirely subtracted from classical tonality” (Badiou Reference Badiou and Clemens2007a, 30).

Several other points need also to be made immediately. First is that the dodecaphonic technique itself (the specific combinatorial gesture relating to the new organization/succession of pitch) is not in itself representative of the event, but merely its starting point—an operation that, due to its obvious nonrelation with tonal practice, confirms a fidelity to the trace. Moreover, it is clear that the Schoenbergian solution, that of a “democracy of all tones” via a certain combinatorial ordering, is not the only possibility. The crucial point is that it constitutes a pure, formalized decision. The only norm is that it makes a presentation, a nomination as such of what was previously unpresented. Thus it takes the form of an axiomatic decision. Different categories of fidelities are possible in the form of consequences, and here there exist two distinct modalities. The first takes the form of adjustments continuous with the interior of the old world—a compositional strategy that Badiou associates with particular works of Alban Berg. But the second is the more radical—the complete forcing of the consequences of the trace, via a series of discontinuous “points” or “choices without appeal” (Badiou Reference Badiou and Clemens2007a, 32), onto all musical parameters, including duration and timbre. A “point” in this context takes the form of a series of questions such as, What happens to the issue of durations once one has a series of tones? Here the model is Anton Webern in, for example, the Variations for Orchestra (1940), but Badiou should also perhaps include the “total serialism” of Boulez and Stockhausen here, too. The difference between Berg and Webern, as Badiou sees it, is instructive nevertheless; the former constitutes a figure, while still faithful to the trace, that represents a “weak” subject, because the “sequential construction is easier in moments of opening” (Badiou Reference Badiou and Clemens2007a, 32). More praiseworthy is the “courage” of Webern, and his “point-by-point” construction; he is “the name of one who generalises and solidifies the constructive dimension of the new acoustic world” (Badiou Reference Badiou and Clemens2007a, 32). And it is perhaps only with Webern, Badiou suggests, that the event actually acquires its status as such, because without his intervention, “It couldn't be proven that the Schoenberg-event was really a caesura in the world of tonal music at the beginning of the 20th Century, because its consequences would have been too narrow or incapable of treating difficult strategic points with success” (Badiou Reference Badiou and Clemens2007a, 32).

Badiou ends this extraordinary Variante Musicale with examples from twentieth-century music of the four “affects” that, for the first time in his writing, “signal the incorporation of the human animal into the subjective process of a truth” (Badiou Reference Badiou and Clemens2007a, 34). The first, the affect of terror, names the desire to install the event in one decisive blow via a grand discontinuity; not surprisingly, and not, I suspect, without some amusement among musicians, this affect of terror is associated with the name of Boulez. Later however, this same composer learns the affect of justice: “the power to relax the abruptness of the construction where necessary” (34). The affect of courage, the constant investigation of points and openings is, as we have seen, associated with Webern, while Dutilleux and Stravinsky, as names of the affect of anxiety, are “tardy enthusiasts” (34) who did not want the rupture of the event in the first place and adhere to it only slowly, as in Stravinsky's “conversion” to dodecaphonism, dating from his collaboration with Balanchine on the ballet Agon (1957).

Contemporary Dance and Choreographic Formalism

What is clear about Badiou's conception of the Schoenberg event is that it comprises a complex of not just musical works, but is coextensive with a certain formal procedure—that of the “democratization of tones,” or the combinatorial reordering of pitches that simultaneously determines both the dodecaphonic techniqueFootnote 11 and undermines any possibility of a tonal-musical organization. It is also worth expanding at this point on some of the key musical characteristics that are constitutive of “tonal organization.” With obvious simplification, these are manifested in rules of “voice leading”Footnote 12 within a given tonal area or key that constrain the harmonic possibilities of the various instrumental forces, and introduce a magnetic pull in the music to certain collective, or “cadential,” intersections. These important structural points or tensional “resolutions” have an associated emotive or affective character that has perhaps been best described by Leonard Meyer (Reference Meyer1961) as the enjoyment associated with the sense of an expectation being met (i.e., music generates structural tensions in order to create/anticipate the enjoyment associated in their collective resolution). And the formal procedure of serial thinking in music systematically dismantles these collective expectations through the dissolving of first, any stable sense of key, and second, through the abandonment of the technique of cadentially driven voice leading.

But is there not a similar formalism at work in some dance works of the twentieth-century? When one thinks of one of the characteristic aspects of the choreography of Merce Cunningham, for example, it is clear that an analogous “naming” of the inexistent (in dance up to that historical point) is present, and one that “democratizes” movement from the rigid strictures of classical ballet. It could also be seen as democratization with respect to the expressive procedures associated with Isadora Duncan, or in a very different sense, with Martha Graham. Some of these aspects are familiar: the disavowal of a particular type of “expressivity” in dance, the decoupling of the movements of different body parts, a de-emphasis with regard to situated “narratives,” etc. Hence it is not possible to nominate a sometimes disparate trajectory in twentieth century dance, which has, as its trace, the following nomination: There can be an organization of human movement entirely subtracted from the principles of classical ballet. How are such works achieved? One key aspect is that, following some (but not all) works of Cunningham and others in the tradition of “contemporary dance,” separate body parts receive full, non-organic, and asymmetric autonomy (in analogy with the Schoenbergian “democracy of tones”). There is also the deliberate destruction of entrained relationships with music—a movement from, to put it in Deleuzian terms, a “direct” to “free indirect” relation,Footnote 13 via the incorporation of chance events into the construction of both movement and sonic material. In some of the works of this trajectory, there is also the absence of programmatic narrative, neutrality of costume and spatial backdrop, absence of sexuated position, etc. (or, in short, a recombining of some of Badiou's “six theses” outlined in the introduction). Dance is transformed via an uprising of its inexistent: the asymmetric, the non-organic, the use of weight, the non-narrated, the absence of deliberately portrayed affect, etc. Cunningham's dances, like serialist music, resist the idea of a convergence to a common goal; they absent themselves from predetermined emotive response, and re-orientate the dancer's body through a rethinking of the role of weight and balance. But we need to be careful here. Not all of Cunningham's oeuvre can be characterized by a simple appeal to Badiou's subtractive theses, which is a point of some general importance for Badiou's concept of “event” in general. In fact, the early work of Cunningham does not always conform to principles of asymmetry, and, in addition, Cunningham's unique dancing persona introduces ineliminable subjective aspects of difference that could be referred to as a “character” (and hence are far from an “anonymized” ideal). Moreover, one could also argue that a deliberate absence of portrayed affect introduces its own kind of affect (an experience of what might be called “forced neutrality”). Indeed, as Mark Franko (Reference Franko1995) has pointed out, it is a mistake in any case to associate the name of Cunningham with a uniformly anti-expressive movement in dance—an argument that tends to collapse his mixed output into a kind of teleological master narrative that stresses the more radical aspects of his choreography at the expense of other more historically conservative residues. As such, though it might be tempting to inaugurate a Badiouian “Cunningham event” in analogy with the case of Schoenberg (such an inauguration would not be at odds with Badiou's account, which stresses that fidelity to a particular event can suffer periods of neglect, diversions, dead-ends, etc.), how coherent in this case would such an event be? And does the example of Cunningham not reveal problems with the concept of “event” as such? In the “real world,” it appears that events and their dutiful subjects may inhabit situations that are more heterogeneous and contingent than Badiou would have us believe. It is for this reason, and others, that the dance theorist might find more purchase in a Deleuzian phenomenology of dance, which has the merit of theorizing artworks in their capacity to affect (as “blocs of sensations”) and as such, still has real need for the human body, if only as a conduit to the “deterritorialized” realm of impersonal affect as such (freed from its subjective and individuated states of “affection”). Deleuze “splits the difference,” as it were, between Badiou's rigorously impersonal aesthetics and the more phenomenologically influenced accounts of art (such as that of Merleau-Ponty) that stress the activation by artworks of the perceptions and sensations of the lived body. Indeed, Deleuze and Guatarri (Reference Deleuze and Guatarri1994) state: “By means of the material, the aim of art is to wrest the percept from perceptions of objects and the states of the perceiving subject, to wrest the affect from affections as the transition from one state to another: to extract a bloc of sensations” (167) and “Flesh is only the developer which disappears in what it develops: the compound of sensation” (183).

But, to return to Badiou, what we can say is that, in the works of Cunningham (and others following him), there is no question that there remain aspects of a choreographically formalized procedure (or “grammar”) that determines in part the movement choices of performers, and for which the ideals of non-narrative, absence of sexuated position, asymmetry, etc. are at least intentionally approached, if not ever completely realized. This brings us to our first major criticism of Badiou's theory of dance. Dance, as Badiou sees it, is an art form in which gestures “appear only to disappear,” and the problem here seems to be that dance is unable to formulate a symbolic means of presenting its own activity; it seems to lack a formal way of referring to itself, or, in the terms defined earlier, it is imprisoned in its own “evental site,” unable to raise itself from the status of an aggregate to a lasting presentation. But Badiou's assertion that dance “appears only to disappear” or is “a pure instance, forever effaced” (Badiou Reference Badiou and Alberto2007b, 160) could surely also be applied to music. A single sound in itself, and hence at a larger structural level, music itself could be said to have a homologous temporal envelope to that of a danced gesture: A sound appears only to attenuate, to fade away into silence. So what is the difference exactly? For Badiou it seems, what is “left behind” by the musical gestures of Schoenberg is precisely the “diagonal truth” of the formalized methodology that marked their gestation. What is left is the “trace,” the formal/symbolic nomination of the musical procedure. Dance, according to Badiou, lacks formal mechanisms that can produce this permanence. And the Schoenbergian “trace” is the formal procedure that acts on music's symbolic matrix, its notation, and technical parameters, and the problem for Badiou seems to be that dance lacks such symbolic co-ordinates with which it can refer to itself:

Let us illustrate this problem by means of an analogy: can a choreography be rigorously annotated? In the wake of Russian ballets and Isadora Duncan, dance is a crucial art precisely because it is only act. The paradigm of a vanishing art, dance does not produce works in the ordinary sense of the term. What is its trace, where does it circumscribe the thinking of its own singularity? (Badiou Reference Badiou and Alberto2007b, 159; my emphasis)

Badiou seems to follow in a long line of aestheticians who, as we saw in the introduction, see dance as a certain problem, exception, or special case. And its exceptional status is in virtue of the “non-traceability” of its immanent act, or to put it another way, dance is unlike other art forms due to a lack of an adequate mechanism for the formalization of its materials. For, as Badiou points out in the same volume:

Formalisation is basically the great unifying power behind all the century's undertakings—from mathematics (formal logics) to politics (the Party a a priori form of any collective action), by way of art, be it prose (Joyce and the odyssey of forms), painting (Picasso, the inventor of a suitable formalisation in the face of every occurrence of the visible) or music (the polyvalent formal construction of Alban Berg's Wozzeck). But in “formalization” the word “form” is not opposed to “matter” or “content,” but is instead coupled to the real of the act. (2007b, 160)

But in some works comprising what could be called “abstract contemporary dance,” which we can now define as the works of those choreographers “faithful” to the singularity approached by Cunningham (the non-narrative, non-affective, asymmetric, etc.), do we not see precisely this same kind of formalization? And not just via the somewhat imperfect historical attempts in the twentieth century to produce an adequate dance notation (Laban notation, and so forth). William Forsythe's use of isometries (space-preserving maps on Euclidean three-space), for example, formalizes the way in which dancers “internalize” a geometric structure and then map this onto representations comprising their own “body-image” [to use a term of Shaun Gallagher (Reference Gallagher2005)]. This represents, in the terms used earlier, a matheme for the choreographic process, and one that has a universal applicability. Such compound representations act as signifiers for the genesis of the movement material: A dancer enters into a mimetic relationship with ideas such as “line” and “surface,” and these relationships can then enter into additional synchronous and diachronous transformation via their own intrasystemic logics. These logics can, for example, involve metonymic and metaphoric substitution. An idiomatic Forsythe technique, for example, is for a dancer to metaphorically relocate the movement of one body part onto another, so that arm and leg movements engage interchangeably in the same mimetic relationship to geometric lines and planes. And, of course, this same geometric interchangeability is also present in Cunningham's “divergent series” of movements that allow for both the autonomy and asymmetry of bodily subdivision.

Hence what Badiou misses is simply the precise difference between dancing as such and the choreographic and pedagogic predetermination, not merely of movement itself, but aspects of the ideational representations of its practitioners (the way dancers change their body mappings or body images due to the external intervention, particularly through pedagogy, of pictures, linguistic and non-linguistic signifiers, diagrams, and notation, etc.). Badiou elides the distinction between dancer and choreographer; he seems to restrict his focus to movement itself, not the collaborative process between the two that produced it. Indeed, Badiou seems to have little time in the essay for the role of the choreographer in general. In fact, choreography is only mentioned twice in Dance as a Metaphor for Thought: “After all, one could imagine that dance exposes an obedient and muscled body to our gaze, a body simultaneously capable and submitted. In other words, a regime of the body in which the body is exerted for the sake of its subjectification to choreography” (Badiou Reference Badiou and Toscano2005b, 59). Badiou opposes such a subjectification, and, in the same passage, speaks of his own “certain vision” of dance in which “we put aside every representation of dance that depicts it as an external constraint imposed on a supple body or as the gymnastics of a dancing body controlled from outside” (Badiou Reference Badiou and Toscano2005b, 60). What these remarks seem to suggest is that Badiou's “certain vision” of dance is actually much closer to a kind of spontaneous free improvisation, and an improvisation that is subject only to what he calls the “restraint” of the dancer him/herself (a restraint that he claims is necessary to avoid the “spontaneous vulgarities [of a] primitive ecstasy or forgetful pulsation of the body” [60; my addition]).

But from where, or whom, does the necessary “restraint” originate? Badiou has little to say about this, but on considering the work of Cunningham in particular, we may argue that this individuated sense of “restraint” is precisely the subjective interpretation of, reaction to, or collision with the externally imposed “grammars” of the choreographic process. Dance, post-Cunningham, is an artform in which movement is produced from a collision between the immanent (the various conditions in the “here-and-now” of the dancer's position, his/her relationship to other dancers, current somatic markers, etc.) and the more-than-immanent (the properties of grammar, geometric paradigm, signifier, or in short “representation”). Dance therefore never lacks representation as such but remains, immanently, in tension with representation. And this tension acts analogously to what Fredric Jameson (Reference Jameson1973) has described in another context as “vanishing mediator”: The collision of representation with the immediacy of the somatic “actualizes” the danced gesture, but as soon as it has done so it disappears, only to reappear again, in a reformulated guise, in the genesis of new movement material. Dance, therefore, vanishes twice: once as a structuring thought, and once as the gesture that is produced by the collision of this thought with the body. Carrie Noland (Reference Noland2010), in a discussion of Cunningham's innovations in dance, makes a related point:

… dynamics are thus not preconceived by the choreographer but instead emerge from the dancer's creation of unscripted, “discovered” transitions leading from one movement, or one movement sequence (phrase) to the next. These transitions providing continuity are forged by the dancer's own coping mechanism, her way of assimilating each movement into a new sequence, a new logic, that only the body can discover in the process of repeated execution. (54)

Dance then, in Cunningham's conception, relates to the idea of psyche/soma constituting a “thought in movement.” In these terms, dance is not merely a “metaphor for thought” (as Badiou sees it), but is, at least partially, thinking itself. And one is tempted here to make a speculative hypothesis that relates dance to current neuroscientific and cognitive psychological research that interfaces with phenomenology. The correspondence between conscious and representing “body image” and the unconscious and nonconceptual “body schema” [to use the other term coined by Shaun Gallagher (Reference Gallagher2005), defined roughly as the system of motor capacities that enable movement/posture to be monitored] acts, as it were, “all the way down,” the former modifying the latter via a process that could best be described in terms of the term “plasticity.”Footnote 14

We can also extend these ideas, as mentioned before, to form an entire historical trajectory of dance works, from Cunningham through to William Forsythe, Rosemary Butcher and Jonathan Burrows (to mention just a few names), whose choreographic methods remain in fidelity to a style of dance that has, to use Badiou's metaphor, “liquidated” the regime of classicism and moreover has done so, at least in part, by formal choreographic means. Indeed these means, at least in the case of a choreographer like Forsythe, are strikingly similar to a geometric paradigm that Badiou celebrates elsewhere apropos new art forms: “… it is less a substitution of forms for their schema than it is a logic of the hidden invariants of every deformation. We should affirm, in art, the idea of intelligent deformations” (Badiou Reference Badiou and Corcoran2006b, 147). But when Forsythe, as we have seen, formalizes his choreographic process through the use of isometries,Footnote 15 is he not exactly mirroring this geometric method that Badiou endorses? Forsythe affirms “intelligent deformations” of three-dimensional space that are executable/actualized via a certain mimetic procedure; the dancers internalize this geometry (which we can think of as approaching the status of matheme), as mental representations, and then “actualize” it in their own unique manner, and via/through their own uniquely personal sense of embodiment. And it is for a similar reason that Mark Franko and Sabine Huschka emphasize the “intermedial” nature of Forsythe's technique, “not as an exclusively body-technology interface but rather as a metaphoric process in which choreography and movement transliterate propriocepted perception, memory, dance-technical knowledge, narrative fragments, and theatrical modes of address” (Franko Reference Franko2010, vi).

Other formal procedures are indeed common in the trajectory of what we can call “abstract contemporary dance,” from the minimal geometries that are traced in Rosemary Butcher's early movement material to Jonathan Burrow's use of spatial and temporal ratios (for example in the Stop Quartet of 1986).Footnote 16 But here as elsewhere, the formal procedures, for they are formal in Badiou's sense, are not a subtractive element characterizing the trajectory of these works, but act only as choreographic stimuli for their gestation. In dance, and in relation to Cunningham and his followers in particular, the formal procedure never exists in isolation from the individual embodied dancer who actualizes its (universal) import. And this is exactly where Badiou has a specific problem with dance, because the way dance is thought and produced post-Cunningham necessitates at least a partial return to the corporeal, somatic body; the “point-by-point” investigations of the event happen, and are partly constituted, in the here-and-now of the phenomenology of individual danced experience, something that forces a return to the particularity of personal expression. Faced with the dilemma posed by dance, Badiou must make his own binary decision: either modify the subtractive singularity of the status of “event” or exclude dance from participation. He chooses the latter.

Dance, Desire, and Heterogeneity

But returning once more to Badiou's “six theses,” we can see other grounds for critique. When Badiou for example calls for the evacuation of desire in the dance spectator or the effacement of sexuated positions, we are left wondering whether such a situation is actually compatible with the whole complicated phenomenology of witnessing human movement, particularly in relation to psychoanalytic theories (like that of Jacques Lacan) that stress the “always already” omnipresence of desiring states in the human subject. Desire cannot, as it were, simply be turned on/off as if it were simply a light switch. The advantage of Lacan's approach is that contra Badiou, it emphasizes the split cogito-like nature of human subjectivity, a split arising from the enunciated/enunciation distinction outlined earlier, and never more apparent than in the experience of dance, and resulting in a performer or spectator who is never entirely free of the demands of his or her libidinal economy. In fact, we could go as far as to claim that this split is partially constitutive of the experience of watching dance; one can never simply remove a desiring gaze from the picture, however noble Badiou's intentions are to the contrary. To summarize: Can Badiou's “rigorously impersonal” dance spectator ever actually exist?

But the most serious objection to Badiou's subtractive account of dance arises in relation to recent work by Jacques Rancière (Reference Rancière2009) on the intersection between politics and aesthetics. One could argue that dance, especially in its multiple and hybrid configurations in the twenty-first century, is resistant to such subtractive or “purifying” strategies, due to its radically heterogeneous material. Rancière makes this point succinctly:

Badiou's “Affirmationist Manifesto,”Footnote 17 which comprises a synthesis of his vision of art, reveals a Badiou more concerned to reaffirm a “specificity of art” subject to the educative vision he confers upon it. Taking this path, inaesthetics can only run into modernism's main antinomy. This antinomy is simple to formulate: the more one emphasizes art in its specificity, the more one is led to identify that “specificity,” with the experience of radical heterogeneity … (87)

In other words, the more one tries to essentialize or purify dance via a process of subtractive or negative determination, the more one realizes that this “essence” is no more than dance's own resistance to the concept of “essence” itself. The “necessary” aspect of dance lies precisely in its contingency: Dance today is, at one and the same time, an abstracted sculptural kinetics of bodies, as in the work of Rosemary Butcher and other choreographers faithful to choreographic modernism, but it is also a compound of movement and speech, as in the Tanztheater of Pina Bausch, or the celebration of the “abject body” by Raimund Hoghe. But it is also a whole host of other alternatives, including a participation in technological practice, from the relatively new phenomenon of filmed or “screened” dance, as in Tacita Dean's film about the Cunningham Company, Craneway Event (2010); movement-based and technologically mediated installation, such as Gary Hill's Tall Ships (1992); or even some works of the visual artist Bill Viola. And this threatens to render obsolete Badiou's resurrection of the Hegelian idea of a “hierarchy” of arts. For like Hegel, Badiou distributes the arts according to their ascending power of speech: Dance, due to its alleged “illiteracy” thereby remains at the bottom of this hierarchy, while the poem has pride of place at the top, with Mallarmé as its particular champion. Indeed, it is the expressly literal arts, those arts of the letter, and hence those closest to the concept of matheme—poetry, theater, and the novel that Badiou seems to hold most dear, and in these cases, there is more a celebration of the text itself than any of its various appearances, manifestations, or interpretations involving real performers.

But dance today exemplifies Rancière's “radical heterogeneity,” and there is no longer a full separation of it from these same literal arts, acts of speech, or other intervening materials and media. Seen in this way, Badiou's view of dance, though in some ways inspiring, seems to be split in two different directions. On the one hand, a modified version of event, and one that returns it partially to the body, would seem to suggest the inclusion in his schema of a singularity that has, post-Cunningham, already happened, and continues to unfold. On the other, Badiou seems to evoke a vision of dance that might take forever to arrive. Hence it seems sensible to conclude with a question: Where might future developments in (and between) dance, dance studies, and philosophy (particularly phenomenology) lead? The “return” to ideas implicating the body/embodiment, which have been partly inspired by Merleau-Ponty, in the work of current philosophers, and cognitive scientists such as Shaun Gallagher and Alva Noë, may be one answer. The latter refers to dance explicitly, for example, as paradigmatic of the new theories of “embodied” or “enacted” cognition (Noë Reference Noë2002).

Footnotes

1. Badiou is referring here to the discussion of dance in Mallarmé (Reference Mallarmé and Caws2001).

2. See, for example, the essay “Theses on Theater” in the same volume (Badiou Reference Badiou and Toscano2005b, 72–78).

3. Here, as elsewhere in his writing, Badiou endorses the “logic of sexuation” of Jacques Lacan: The positions “man” and “woman” are neither performative (in the sense of Judith Butler) nor genetic, but are the result of two incommensurable positions taken apropos the impasses of the process of signification.

4. Such a consideration is beyond the scope of this article, but see Badiou (Reference Badiou2006a, 46–48) for an introduction to this line of thinking.

5. German mathematician (1845–1918) most celebrated for his proof that the set of “real” numbers is, in opposition to the set of “natural” numbers, nondenumerable.

6. In Badiou's set-theoretic ontology, the “empty set,” whose existence is nondemonstrable and can only be decided upon by an axiomatic decision.

7. See Hallward (Reference Hallward2003, 233). The “trace” here is the favorite slogan of La Distance Politique, a political bulletin to which Badiou, as political activist, frequently contributes. Of course, this “event” exists in the contemporary situation only as a certain “potentiality.”

8. Badiou compares the various degrees of “appearing” of the depicted elements (a temple, its columns, trees, figures, etc.) in a painting (or, in his terms, “world”) that appears on the cover of the French edition (the painting in question is La Baignade, by Hubert Robert).

9. The law of excluded middle can be formulated as “either p or not-p.” Modal logics, by contrast, allow possibilities.

10. Think of how various terms used today “float freely” in terms of their meaning, such as the term “to be ecological.” If we filter this plurality of meaning through a point de caption like “Communism,” its meaning becomes more fixed; one can be more sure of what an “ecological communist” is. The term point de capiton refers in French to the button that holds together a mattress, hence the term “quilting.”

11. A method of musical composition that stipulates that all the twelve chromatic pitches in the scale be utilized once, and only once, in thematically important material.

12. This term refers to the harmonic rules that govern how musical dissonances should be resolved.

13. See for example the extraordinary discussion of the relation between image and sound in Deleuze (Reference Deleuze, Tomlinson and Galeta1989, 216–225).

14. Following the term of Catherine Malabou (Reference Malabou2008). See also Clark (forthcoming).

15. See, for example, the instruction videos available online at: http://www.youtube.com/watch?v=9-32m8LE5Xg (accessed December 2010). Allow me one small point of correction to Forsythe here. Although many of the mappings he describes here are isometries, some are not (in the strict mathematical sense). For example the gestural mapping from a line extending between the palms to a “shortened” version of the same line extending between the points of two outstretched fingers is clearly not distance-preserving, and is better described mathematically as a projection.

16. Can we also not categorize the “affective modes” of the subject of contemporary dance? William Forsythe, in his insistence on using trained classical dancers, seems to play a homologous role to that of Alban Berg's position in the Schoenberg event (forcing the consequences of the “new world” onto the “old”), whereas Rosemary Butcher seems more like Anton Webern, abandoning virtuosity in favor of a minute “point-by-point” interrogation of what, in an analogy with music, might be called the “timbral” or qualitative possibilities of movement itself (abstracted outside of what might be considered “dance” at all).

17. Rancière is referring here to Badiou's “Third Sketch of a Manifesto for Affirmationist Art” (Badiou Reference Badiou and Corcoran2006b, 133–149).

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