there is always something statistical in our loves,
and something belonging to the laws of large numbers.
— (Gilles Deleuze|Félix Guattari, Anti-Oedipus, 294).

topology | temporality

pure sex1

the truth is that sexuality is everywhere
— (Gilles Deleuze| Félix Guattari, Anti-Oedipus, 293).

[1] The first associations concerning 'the spaces and the times of sexuality' are probably socio-cultural variations of where people have sex (planes, trains, automobiles) or statistics of when, and maybe of how often people have sex (for instance Mr. and Mrs. Smith). In general, the relation of sexuality to anything like a general topologics and a general chronologics is certainly not one of the most immediately obvious ones. Although mathematics, the science that provides the background to both of these logics, has developed immensely complex theories of space and of time, from the static grid of Cartesian space to the dynamic patchworks of Riemannian topology and from Newton's irreversible time to the multiple 'bundles of times' in complexity theory, mathematical concepts are not usually part of the repertoire of the cultural discourse on|of sexuality. We do not normally think of the specific variation of mathematical space in which sexuality takes place. If at all, space becomes important when it is a question of 'my place or your place.' Similarly, references to time in the everyday (or everynight!) discourse on|of sexuality generally does not refer back immediately to the mathematical theories about, say, concepts of the infinitely slow|fast, the infinitely short|long or of time-travel. If at all, such concepts come up in merely metaphorical statements such as 'I will love you forever' or 'I wish I could turn back time.' It is precisely the level of the directly mathematical, however, that my essay will address. Such a project can rely on a vast number of conceptual backdrops, because in contrast to the cultural discourse on|of sexuality, the psychoanalytically informed, theoretical discourse on sexuality is literally drenched in topological and chronological references. The reason for this is mainly the insistence of topology|chronology in the work of Jacques Lacan. In 'sexuality studies,' most of the references to projective planes, moebius-strips, Klein bottles and Borromean knots (as in the work of Diana Fuss, Marjorie Garber, Elisabeth Grosz or Lee Edelman), as well as references to calculus and geometry (as in the work of Cindy Patton, Eve Sedgwick or Lee Edelman) are offshoots of this insistence, as are references to the chronologics of retrovision [Nachträglichkeit]. Although it is difficult to measure the exact degree to which Gilles Deleuze|Félix Guattari's topological|chronological references develop from the same source, it is obvious that they do rely to some degree on the Lacanian topologics|chronologics even if their objective is a critique of the Lacanian system. In fact, because they develop their own, still largely uncharted topologics|chronologics, this critique often proceeds in strictly topological|chronological terms. What I will do in this essay is to delineate in some detail the topologics and the chronologics from within which Gilles Deleuze|Félix Guattari develop their theory of sexuality. When I say that I will talk about the spaces and the times of sexuality, therefore, I mean this quite literally and mathematically.

molecular sex

real sex

Letizia Alvarez de Toledo has observed that the vast library is useless. Strictly speaking, one single volume should suffice: a single volume of ordinary format, printed in nine or ten type body, and consisting of an infinite number of infinitely thin pages. (At the beginning of the seventeenth century, Cavalieri said that any solid body is the superimposition of an infinite number of planes.) This silky vade mecum would scarcely be handy: each apparent leaf of the book would divide into other analogous leaves. The inconceivable central leaf would have no reverse- Jorge Luis Borges, footnote to "The Library of Babel" (Ficciones 88).

[2] "We are statistically molarly heterosexual, but personally homosexual, without knowing it or being fully aware of it, and finally we are transsexual in an elemental, molecular sense" (70), Deleuze|Guattari note in Anti-Oedipus. The operational levels of these sexualities that traverse the "consolidate [consolidé]" (Cinema 1, 66) of the human subject in different directions and at different speeds are a super-individual level ('statistically molar') that concerns large aggregates, such as populations or collectivities. In terms of material aggregates, for instance, it operates on masses, mobs and multitudes, while in terms of cultural aggregates, it operates on the large discursive formations and regimes that implement specific orders of sexuality and that Foucault subsumes under the concept of 'bio-power,' an intra-individual level ('personal') that denotes the levels of conscious and semi-conscious psycho-material feedback-loops within the subject, and a sub-individual one ('molecular') that operates on levels of imperceptible multiplicities and thus from a Deleuzian perspective on levels of 'unconscious machines' within the subject that open the subject up to a general, non-individual, machinic ecologics. Psychoanalysis negotiates the first two of these levels, the heterosexual one as the symbolics of the law|name of the father (signifier|phallus) and the homosexual one as the imaginaries of the two narcissisms (primary|secondary), while the third level, which is the most important one for Deleuze|Guattari, lies out of psychoanalytic range, or, at least, is included in it only 'negatively' [→ for a critique of 'negativity' as a philosophical concept see in particular Deleuze's Bergsonism]. As Deleuze|Guattari state, not without irony, "we do not deny that there is an Oedipal sexuality, an Oedipal heterosexuality and homosexuality, an Oedipal castration, as well as complete objects, global images, and specific egos. We deny that these are the production of the unconscious" (Anti-Oedipus 74).
The closest psychoanalysis comes to address this third level, and thus to think a material desire and a physical reality, is when it talks about drives| instincts [in brief, the 'whole point' is that for Deleuze|Guattari "desire is never an undifferentiated instinctual energy, but itself results from a highly developed, engineered setup rich in interactions" (Plateaus 215)], and, related to that, about jouissance as the embodiment of an impossible, 'real' sexuality. This 'real sexuality' is excluded from the subject's psychic reality and thus from the space and interest of psychoanalysis except in its very negativity as excluded. Like the real in general, which, even while it causes the twisted topologics of Lacanian psychoanalysis - its 'projective plane' positions the symbolic and the imaginary on its 'two' sides, 'excluding the real' as the topology's fundamental twist - is itself famously excluded from the psychoanalytical field, psychoanalysis thinks jouissance as something that can be reached only on the 'inverted ladder of desire' ["jouissance must be refused, so that it can be reached on the inverted ladder … of desire" (Ecrits, 324)].

[3] The 'projective plane,' I should explain, is a mathematical concept that denotes an infinitely large space that is folded back onto itself at what are called 'points at infinity.' What is important about this concept is that this space is unilateral, which means that it has only one side.

Felix Klein describes the projective plane as a hemisphere with a line at infinity added to the rim ["We should attempt to imagine the projective situation long enough for it to be no longer too difficult to, for instance, pull some figure through the infinitely far away" (17)] on which opposite points are identified: "To every infinitely far away point of the plane there correspond … two points at the rim of the half-sphere; therefore, we have to regard … two of such diametrically opposed points as identical" (14). As Klein notes, "the simplest plane … that shows the same behaviour as the projective plane" (15) is a moebius-strip. Its infinite torsion|fold, which is defined by the topologics of the points at infinity, fundamentally undecides the notions of inside and outside [→ on the notion of the 'infinite fold' see especially Deleuze's The Fold: Leibniz and the Baroque]. As Deleuze notes in an indirect reference to the projective plane, it is inherently superficial because "the continuity between reverse and right side replaces all the levels of depths" (Logic 11).

[4] When Deleuze|Guattari state, therefore, that according to Lacan, "jouissance is impossible, but impossible jouissance in inscribed in desire. For that, in its very impossibility, it is the Ideal, the 'manque-à-jouir that is life" (Plateaus 154), they in fact provide a concise commentary on the topological distribution of the symbolic, the imaginary and the real field on the projective plane à la Lacan. According to the distribution of realms within these topologics, jouissance can be 'in psychoanalysis' only in relation to its fundamental unrepresentability and its inherently uneconomical violence, while for Deleuze|Guattari "all sexuality is a matter of economy" (Anti-Oedipus 11). As Julia Kristeva notes in relation to jouissance, "it [the body] joys, violently and painfully" (Horror 9). In opposition to this uneconomical violence, which can, ironically, only be 'reached' either in exremis [orgasm, violence, madness] or from within the economy of desire, Deleuze favors a 'Taoist' thought in which "desire ... loses any link with lack, with pleasure or orgasm, or with jouissance. It is conceived as the production of a flow, it defines a field of immanence, and a field of immanence—that means a multiplicity in which, effectively, any splitting of the subject into a subject of enunciation and a subject of the statement becomes strictly impossible, since in our revolving machine it was very simple: the subject of enunciation was the subject of impossible jouissance, the subject of the statement was the subject of pleasure and of the search for pleasure, and desire-lack was the splitting of the two. That should tell you to what degree, from Descartes to Lacan, this repugnant thought of the cogito is not only a metaphysical thought" (Dualism 98). Two ideas, then, separate Lacan and Deleuze both in general and in relation to sexuality. 1. Lacan's idea of the fundamental negativity of desire, which implies that one can only think of 'pure enjoyment' as violent and 'painful.' 2. the idea that, even were psychoanalysis to think of desire 'positively,' it would still consider this desire as a psychic, immaterial and individual one (it would remain attached to an individual human being and its 'speaking body,' its only materiality being, famously, that of the signifier). In contrast to such a desire, a Deleuzian desire is physical, material and singularized. Generally, the contrast is between a psychological and a physiological desire, which means between a physics (Deleuze) and a metaphysics (Lacan) of desire. If Lacan's unconscious is individual and 'immaterial,' the Deleuzian one is non-individual and material. If in psychoanalysis it is the individual who desires, in Deleuze|Guattari it is invariably a body that desires - but I am getting ahead of my argument.

[5] Especially in the context of queer studies, it has been inviting to inscribe sexuality into the Lacanian topologics, for instance by staking the imaginary mirrorworlds of gaylesbianism against the 'molar' – to hijack a Deleuzian term – straight-jacket of the symbolic, heteronormative machine into which the subject is strapped. In such a scenario, queer theatricalities would, as in the work of Judith Butler, subvert heterosexual normativity. Butler, however, is hardly a Deleuzian. As she notes in Undoing Gender, "I confess, however, that I am not a very good materialist. Every time I try to write about the body, the writing ends up being about language" (198). In this context, Butler sides with Foucault, for whom sexuality is a historically dynamic function created by discursive formations as well as by formations of 'material culture' (dispositifs), whereas for Deleuze, sexuality goes beyond the (both discursive and material) materialities of human culture. The other point she makes pertains directly to the Lacanian topologics, to its 'constitutive lack' and the resulting negativity that has been highlighted in particular by Žižek and Badiou with whom Butler sides when she notes, in a curiously fuzzy grammar that makes it impossible to logically align 'lack' and 'negativity,' that "psychoanalysis seems centered on the problem of the lack for Deleuze, but I tend to center on the problem of negativity. One reason I have opposed Deleuze is that I find no registration of the negative in his work" (198, emphasis added). [Apart from the fact that there is, of course, a lot of registration of 'negativity' in Deleuze, the question is whether the 'but' in this sentence refers to a semantics in which lack and negativity are identical concepts or whether it denotes a shift from one term to a different one? In both cases, it seems to me, what is not addressed is precisely the 'relation' between the two terms]. The Deleuzian twist, however, does not lie in historical or psychic rearrangements of the symbolic and the imaginary sexualities, but in the alignment of the symbolic and the imaginary sexualities with a level of 'molecular transsexuality' that questions both of them to a similar degree and that changes the overall topologics and chronologics of the sexual field. In fact, queering, from a Deleuzian perspective, means to 'molecularize' sexuality and to 'make it real.'

[6] As in Lacan, this alignment proceeds 'on' a projective plane. The difference is that on the Deleuzian projective plane, the representational registers (in Lacanian terms, the symbolic|imaginary conglomerate) are positioned on the one side while the productive registers (in Lacanian terms, the real) are positioned on the other. On this plane (which provides the topologics for the 'plane of immanence' and for the 'surface of sense') there is, quite ironically, even less – if that is possible! - of a space|time for an imaginary 'queer utopia' than on the Lacanian one (which is, from a Deleuzian perspective, a 'plane of castration'). What the Deleuzian plane provides, however, is the possibility of true 'lines of flight.' From its topologics, as long as one stays within the psychoanalytic topologics as well as within its retroactive chronologics, every form|event of subversion, such as Butler's versions of 'lines of flight,' will remain under the shadow, and thus within the reach, of an overall molar machine that does not stop running on the 'negative force' of castration. As Deleuze|Guattari note, for instance, as long as one does not change the overall sexual topologics, "bisexuality … in no way precludes the prevalence of the masculine or the majority of the 'phallus'" (Plateaus 293) which means that in this case, "bisexuality is no better a concept than the separateness of the sexes" (276). It is only by completely changing the overall registers – which means precisely to think of and in the topologics and chronologics brought about by the inclusion of the realm of molecular sex – that the molar machine can be reprogrammed and that desire (a material desire fundamentally different from the psychic desire à la Lacan) has a chance to be de-coded and to flow; to leave the sphere of the Lacanian signifier and to enter "'natural' codings operating without signs" (117), or, as Deleuze calls it elsewhere, to enter the orbit of "the sign-particle as opposed to the sign-signifier" (Jouissance, 106).

[7] Lacanian psychoanalysis, which operates both within and as a molar machine, provides invariably what Deleuze|Guattari call 'n+1 sexes;' a sexuality based on a phallic, castrative survey machine that creates "sexual segments" (Plateaus 209) and segmentations and that is positioned on a supplementary dimension to that of sexuality [+1, the 'general']. In 'overcoded,' mastered systems of n+1 sexes, material desire is decelerated, dried-out, frozen and fetishized, which means that they tend to favor stasis, sterility and repetition and that they are afraid of (or at least that they are not conductive to) the production of the new, which relies, as I will show, not only on the metaphorics, combinatorics and architectonics of letters as the material of language but also on the material exchange and combinatorics of directly material particles [As Deleuze notes, "the important thing is to understand life, each living individuality, not as form or a development of form but as a complex relation between differential velocities, between deceleration and acceleration of particles" (Ethology, 626)].

[8] Invariably, n+1 sexes are based on traumatic repetition compulsions and circular obsessions. The castrative mathematics that drive the plot of John Rechy's novel Numbers, for instance, are 'based' on the protagonist's endless reservoir of lack that he finds impossible to fill, and that leads him to a self-imposed, more and more desperately accelerating series of sexual encounters. His only superficially 'self-imposed,' in actual fact symbolically organized, mathematical calculus demands of him a ludicrous amount of acts-to-be-performed in a constant acceleration towards an impossible, 'transcendental' jouissance. In the case of Rechy, one might, in an analogy to self-constrained writing, talk of self-constrained sex. Rechy's sexual architectures and mathematics are invariably based on the concept of a fundamental lack and they show how much of homosexuality remains under the shadow of heterosexual normalizations. A work such as City of Night, for instance, in which most of the homosexual relationships rely on 'intensified' and displaced [verschoben] heterosexual norms, which means that they are ultimately nothing but heterosexual relationships in drag, shows the dilemma of a subversion that is simultaneously a mimicry in all its tragedy and splendor.

[9] In another register, J.G. Ballard's novel Crash shows to what extent n+1 sexes produce sexualities that can think of themselves only as prosthetic devices. In the novel, obsessions are not played out in the interpersonal arena, as in Rechy, but in an arena that has added the auto-machine, as a vehicle of intensified speed and destruction, to the sexual mix. Ballard describes this scenario in terms of fetishes and protheses, evoking the destructive marriage of man and machine, automotive fetishism, orgasmic auto-disasters and wounded desires. Before one attaches such a machinic universe to the Deleuzian logic, one should note the different functions and definitions of machines. Ultimately, Ballard's automotive machines create traumatic scenarios whose products are death and destruction. They might subvert the molar machine of the contemporary order of sexuality, but, as in Rechy, subversion and mimicry often create terrifying and monstrous organizations. If Ballard's 'Bodies without Organs' are literally auto-destructive, Rechy's are metaphorically so.

[10] For any sexual arrangement to truly escape the realm of n+1 sexes, it needs to literally change the 'coordinates' of sexual space:

For example, no "gay liberation movement" is possible as long as homosexuality is caught up in a relation of exclusive disjunction with heterosexuality, a relation that ascribes them both to a common Oedipal and castrating stock, charged with ensuring only their differentiation in two noncommunicating series, instead of bringing to light their reciprocal inclusion and their transverse communication in the decoded flows of desire […]. In short, sexual repression, more insistent than ever, will survive all the publications, demonstrations, emancipations, and protests concerning the liberty of sexual objects, sources, and aims, as long as sexuality is kept – consciously or not – within narcissistic, Oedipal, and castrating co-ordinates that are enough to ensure the triumph of the most rigorous censors (Anti-Oedipus 350-51).

Rather than remaining queer only within and against a set of heterosexual norms and heteronormative practices, the Deleuzian project calls, in its propagation of a molecular transsexuality, for a generalized transversalization of sexuality.

the mathematics of sex

infinite sex

[11] What is molecular transsexuality, however, other than a sexy term that evokes vistas of decoded flows of material desire and a general undoing of sexual segmentations? Unfortunately, this question can only be answered via a longer detour through the overall Deleuzian ecologics of thought, especially through its topological and chronological underpinnings. Let's call it foreplay.

[12] It is symptomatic that both Lacan and Deleuze are eminently mathematical thinkers and that for both, the best psychoanalysis|philosophy is often a mathematical one. They differ, however, in that Lacan invariably stresses pure mathematics [set-theory, the theory of knots] while Deleuze stresses 'applied mathematics' [infinitesimal calculus, fractal mathematics and the mathematics of complexity theory] and in that a Lacanian mathematics|ontology starts with zero while a Deleuzian mathematics/ ontology starts with infinity.

[13] Somewhat ironically, the mathematical procedure I want to use to introduce a Deleuzian 'transsexual mathematics' would at first sight seem to lend itself equally well to a Lacanian logic, because it is based on such 'heteronormative' concepts as a 'straight' line and a logic of 'cuts.' For this procedure one can imagine two beginnings. 1: an infinitely long, straight line is cut in half (mathematically, one can of course always cut infinity in half!) by marking a point on it. A second point is added, which makes of the infinite line a finite one - at least this is how it would seem at first sight. A third point is then inserted that is equidistant from the two initial points. The routine of adding more equidistant points is then repeated ad infinitum. 2: a line is drawn between two points (between two points there is, by definition, always the possibility of a finitely long line). After this opening, one proceeds exactly as in the first routine. I have stressed the two possible 'openings,' because only the first procedure is truly Deleuzian, as it starts with the line ["a point is always a point of origin, but a line of becoming has neither beginning nor end" (Plateaus 293)]. Still, in both cases, the endlessly repeated cutting of the line implies a fractal descent into smaller and smaller plateaus of discrete points and continuous lines [→ for more about the logic of fractal space, see especially the chapter on smooth and striated space in A Thousand Plateaus].

[14] The logics that both routines follow are those of continuity and of infinity (the continuity of the line and the infinite repetition of the routine), two terms that are among the most seminal in Deleuzian philosophy [both, of course, are also seminal in Leibniz's invention of infinitesimal calculus, which Deleuze addresses in detail in The Fold: Leibniz and the Baroque]. Although mathematically and 'objectively,' the lines get shorter the more one 'descends,' if the ratio of the fractal zoom into the procedure exactly counterbalances the reductions in length created by the procedure, one encounters perceptually and thus 'subjectively,' always 'exactly' the same operation, the same line and the same points. Even while in the field of pure mathematics, the line|point ratio can be made to be always identical, in the actualized world, every plateau of the fractal descent is defined by its specific, local continuity|discontinuity. This infinitesimal, recursive procedure, which describes abstractly what mathematicians call, in a more specifically numerical context, 'Dedekind cuts,' not only models the topologics of Deleuzian space, it also presides over his idea of the material|mental and thus the sexual world.

[15] Dedekind cuts describe a mathematical procedure that negotiates the problem of continuity by way of the concept of infinity. They are named after the German mathematician Richard Dedekind, for whom the realization that a line is separated into two parts by a cut helped solve the problem of how "to pass with facility and rigor from the discrete to the continuous and back;" in purely mathematical terms: of how to make the continuum of real numbers countable, and thus representable, in terms of classes of discrete, discontinuous rational numbers and thus to "secure a real definition of the essence of continuity" (Essays 2).

[16] Symptomatically, the routine involves both temporal and spatial aspects, as it regards "the domain of real numbers as a continuum, identifying it as it were with such aggregates as the totality of instants in duration, or the totality of points on a line" (Dantzig 102). Dedekind proceeds from the image of a straight, continuous line on which the system of rational numbers is noted as, L: (1.2.3...). The mathematical problem is that "in the straight line L there are infinitely many points which correspond to no rational number" (Essays 8). As Dedekind notes quite laconically, "the above comparison of the domain R of rational numbers with a straight line has led to the recognition of the existence of gaps" (10). If each rational number is separated from the next one by a gap, Dedekind's objective is to create so many numbers that "the domain of numbers shall gain again the same completeness, or as we may say at once, the same continuity, as the straight line" (9), his deceptively simple realization being that "if all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions" (11). "For brevity," Dedekind argues "we … call such a separation a cut [Schnitt] ... We can then say that every rational number ... produces one cut" (12-13). The "incompleteness or discontinuity of the domain ... of all rational numbers" (15) consists precisely in that "not all cuts are produced by rational numbers" (15). To re-constitute this continuity, Dedekind defines irrational numbers as cuts lying between the cuts produced by rational numbers. In Dedekind's procedure, therefore, every rational and every irrational number is literally identical to a cut. From this follows that if one considers the line as an infinity of numbers, it once more "possesses ... continuity" (20).

[17] The continuous line is thus identical to an infinity of cuts; an infinity of recursive, fractally decreasing numerical intervals. As Prigogine|Stengers note, stressing once more the temporal aspects of the procedure, "an infinitesimal quantity is the result of a limiting process; it is typically the variation in a quantity occurring between two successive instants when the time elapsing between these instants tends toward zero. In this way the change is broken up into an infinite series of infinitely small changes" [Order, 58)]. Or, as Herman Weyl notes, "in order to subject a continuum to mathematical treatment it is necessary to assume that it is divided up into 'elementary pieces' and that this division is constantly defined by repeated subdivision according to a fixed scheme ... The effect is that the continuum is spun over with a subdivision net of increasing density" (90). Ultimately, via the procedure, "the irrational is reduced to the rational, the continuous to the discrete, the curvilinear and the skew to the straight and the flat" (Dantzig 28). Quite paradoxically, then, Dedekind defines mathematical continuity as an infinite number of cuts into an 'ideal continuity.' In fact, the cuts break up the continuum while, at the same time, they make it countable as a continuum. Continuity, then is both unaccountable and countable, depending on the point-of-view from which it is approached.

[18] The procedure provides such an important shorthand of the Deleuzian system because it diagrams the operational logics for a machinic universe that consists of an infinity of - both material and immaterial - machinic cuts. In fact, for Deleuze every perception|percept [→ Deleuze differentiates between individual perceptions and nonindividual percepts], including micro-perceptions|percepts, is a cut into an 'originary,' continuous multiplicity that is, like the continuity of the straight line, at the same time both infinitely cut and thus countable (it is produced, at every moment, by infinitely many machinic cuts, in analogy to the reconstruction of the continuity of the line by an infinity of numerical cuts) and continuous and thus uncountable (in analogy to the initially continuous line, it is a 'continuous hyle'). Both of these aspects make it, in different ways, fundamentally unthinkable. [It is "that which must be thought and that which cannot be thought. It is the nonthought within thought. It is the base of all planes, immanent to every thinkable plane that does not succeed in thinking it. It is the most intimate within thought and yet the absolute outside. An outside more distant than any external world: it is immanence" (Philosophy 59)]. As Deleuze notes in Bergsonism, "Bergson thus brought to light 'two very different kinds of multiplicity,' one qualitative and fusional, continuous ["a virtual and continuous multiplicity that cannot be reduced to numbers" (Bergsonism 38)], the other numerical ["a numerical multiplicity, discontinuous and actual" (38)] and homogeneous, discrete. It will be noted that matter goes back and forth between the two" (Plateaus 484).

[19] The procedure thus embodies precisely the 'state' in which it is possible for matter to shift between static positionings (points) and becomings (lines) which is why Deleuze invariably relates lines ('of flight') to becomings, while he relates points to segmentations and to 'arrests' of movement, between representations (significant, discrete cuts) and productions (intensive, continuous lines), between digitalics and analogics, between striation and smoothing and between reterritorialization and deterritorialization. In all of these cases, matter is not relegated to one side only, but, as Deleuze notes, it shifts imperceptibly between them, in a projective topologics that does not decide between them. Like 'sense,' its immaterial 'equivalent' [→ see The Logic of Sense for the projective topologics of 'sense'], matter moves between registers that are positioned on a unilateral, projective plane. In fact, the projective plane of 'matter' and 'sense' is, ultimately, the same 'plane of immanence.'

the topologics of sex

imperceptible sex

[20] Interesting, but hardly sexy, one might note at this point. There is, however, a clear and present relation between the mathematical procedure I have just described and a Deleuzian theory of sexuality, because the dis|continuity of the mathematical line –the continuity of any line between two points – is analogous to the dis|continuity of the space in which Deleuze's thought, and thus a Deleuzian sexuality, develops: the space of the 'plane of immanence,' whose fractal topology is quite literally embodied by the infinite descent 'into' the line.

[21] Deleuze thinks of the plane of immanence as an inherently dynamic field over which fluxes, forces and intensities ["continuums of intensity, blocs of becoming, emissions of particles, combinations of fluxes" (Dialogues 105)] travel at various speeds and in various alignments. It is 'virtuality in real-time,' a field "peopled by anonymous matter, by infinite bits of impalpable matter entering into varying connections" (Plateaus 255). It "has haecceities for content" (263, my italics). Ultimately, it is the true "Body without Organs" (154) [In this context, one should note the recursive structure of the Body without Organs. The "BwO is that glacial reality where the alluvions, sedimentations, coagulations, foldings, and recoilings that compose an organism – and also a signification and a subject – occur […] If the BwO is a limit, if one is forever attaining it, it is because behind each stratum, encasted in it, there is always another stratum" (Plateaus 159)], a space of "positive absolute deterritorialization" (134) and of "uninterrupted continuum" (154). Its most important characteristics are 1. its unilaterality, 2. its "variable curvature" (Philosophy 39), 3. its "fractal nature" (39) and 4. the "infinite speed" (42) with which particles move on|in it. This plane is directly related to a Deleuzian theory of sexuality, because it is the plane on which a molecular transsexuality plays itself out. Which means, unfortunately, that I will have to take another detour. More foreplay.

[22] The first characteristic [unilaterality] defines the plane of immanence as a 'projective plane.' The second characteristic [variable curvature] defines it as a plane whose every site is spatially irregular and thus specific and which is thus always and everywhere singular (a sphere, for instance, has a non-variable, regular curvature). [→ see in this context in particular Deleuze's references to the work of Bernard Cache]. The third characteristic [fractality] defines it as a space made up of infinitely many plateaus situated on a fractal number of dimensions. [One model|schema of the plane of immanence is that of a 'fractal sponge,' whose structure is defined by an infinite regress|recursivity. As Deleuze notes, "an infinitely cavernous or porous world […] Mandelbrot's fractal dimension is a fractional or irrational number, a nondimension, an interdimension" (Fold 16). Deleuze links mathematical fractality specifically to the philosophical problem of infinity: "it is this fractal nature that makes the planomenon an infinite that is always different from any surface or volume determinable as a concept. Every movement passes through the whole of the plane by immediately turning back on and folding itself and also folding other movements or allowing itself to be folded by them, giving rise to retroactions, connections, and proliferations in the fractalization of this infinitely folded up infinity" (Philosophy 38-39)]. The fourth aspect of the plane of immanence [the ideally infinite speed with which particles move over it and compose it] defines it as not only spatially but also temporally infinite. Movement on some of its levels happens 'too fast for thought.' In fact, Deleuze considers the mind|brain not only as a machine of spatial reduction (framing) but also as one of temporal deceleration; as the gap that introduces the realm of 'effects and quasi-causes' into that of the 'state-of-affairs.' As Deleuze states in Bergsonism, "perception is not the object plus something, but the object minus something" (24-5). In fact, the brain is quite literally a 'Dedekind machine.' It "divides up excitation infinitely" (52) and "in relation to the motor cells of the core it leaves us to choose betweeen several possible reactions" (53). [→ for more on the Deleuzian concept of brain|mind see especially The Logic of Sense, and Cinema 1]. Deleuze|Guattari develop the notion of infinite speed from the fact that the 'virtual' movements that ideally define the plane of immanence follow the dynamics of a deterministic chaos. The various movements of formation|production that take place on the plane are dynamic, 'sensitive to initial conditions' - Deleuze|Guattari also talk of the plane as being in a state of 'unstable equilibrium' - and, at each moment, open to unexpected catastrophes. ["The universe is made up of modifications, disturbances, changes of tension and of energy, and nothing else" (Bergsonism 76)]. As Deleuze notes, "chaos is characterized less by the absence of determinations than by the infinite speed with which they take shape and vanish" (Philosophy 42). In fact, "chaos is defined not so much by its disorder as by the infinite speed with which every form taking shape in it vanishes … chaos is an infinite speed of birth and disappearance" (118). Infinitely small, unconscious excitations|percepts move over the plane of immanence with infinite speed ('at the speed of chaos'), while conscious perceptions are no longer infinitely small and no longer infinitely fast. ["From a psychic point of view, chaos would be a universal giddiness, the sum of all possible perceptions being infinitesimal or infinitely minute; but the screen would extract differentials that could be integrated in ordered perceptions" (Fold 77). Or, as Guattari states, the "plane of machinic interfaces" (Chaosmosis 58) is defined by "a deterministic chaos animated by infinite velocities. It is out of this chaos that complex compositions, which are capable of being slowed down in energetico-spatio-temporal coordinates or category systems, constitute themselves" (59)].

[23] It is on this fundamentally multiplicitous plane that material reality 'takes place,' assembling and disassembling itself and it is on this plane that material systems develop their specific 'planes of consistency' through routines of organizing and slowing down 'infinitely fast molecular movements.' Simultaneously, it is also the plane on which psychic reality 'takes place,' assembling immaterial 'planes of transcendence' [→ for the organization of the plane as a space of n-1 dimensions see A Thousand Plateaus]. Although the sexual "event is properly inscribed in the flesh and in the body" (Logic 221-222), the topologics of the plane of immancence bring about the possibility of 'continuous' foldings of hardware onto software; the "folding ... and projecting [of] the entire corporeal surface of sexuality over the metaphysical surface of thought" (218).

[24] To return to Lacanian psychoanalysis for a moment, in the Deleuzian topologics, the material|productive realm is neither defined by a logical negativity (it is not in the position of the Lacanian real), nor by the 'false' stability of an essential form|order. The plane of immanence is a positive, intensive field that cannot be separated from the countless processes of dynamic production that pass over it on all of its fractal levels, including both material and immaterial productions (the production of production and the production of representations).

[25] We are now in a position to measure out in which ways the plane of immanence relates, as Deleuze noted in the introductory quote, sub-individual, intra-individual and super-individual levels. On the most molecular level, the plane of immanence|consistency is organized according to "haecceities, events, incorporeal transformations that are apprehended in themselves; nomadic essences, vague yet riotous; continuums of intensities or continuous variations … becomings, which have neither culmination nor subject, but draw one another into zones of undecidability; smooth spaces; composed from within striated space" (Plateaus 507). On an intra-individual level, it is organized according to the material|mental modes by which the human organism 'sustains' itself, and on a super-individual level, by the natural|cultural machines [the natural|cultural distinction being, in fact, no longer operative] that organize 'masses' of individuals and singularities. Any sexual arrangement, then, consists of a coupling of various machines (or of the coupling of a machine to 'itself' via a set of feedback-loops between micro-machines within the larger machine) and of "a set of practices" (150).

immanence	corpuscular sex
Joven virgen autosodomizada por su propia castidad (1954)	La noia dels rulls (1926)

"everywhere a microscopic transsexuality"

[26] Which brings me, finally, to sexuality, because the Deleuzian topologics allow for the organization of a sexuality that includes the sub-individual, moelcular level. If one considers the plane of immanence as the field of multiplicity, virtuality and potentiality in which consolidates are actualised, this implies that sexuality is invariably an ecological, machinic arrangement. Some of the machines in this ecology are cultural and 'human,' others are biological, physical, chemical, meteorological, geographical and ultimately 'nonhuman.' It also implies that sexuality can be broken down to an infinitely small, molecular level. About the first implication Deleuze notes, "the interactions which organisms have with the organic and inorganic components of an ecosystem are typically of the intensive kind (in the enlarged sense), an ecosystem itself being a complex assemblage of a large number of heterogeneous components: diverse reproductive communities of animals, plants and micro-organisms, a geographical site characterized by diverse topographical and geological features, and the ever diverse and changing weather patterns." It is here that one might evoke Deleuze's infamous 'wasp-orchid' (Plateaus 293) aggregate as a heterogeneous, asymmetrical conjunction of two 'evolutionary series' into a sexual machine. [On the plane of immanence various machines unfold, through a number of routines, branching out dynamically into complex morphogenetic architectures and orders. Seen from this perspective, the human body - which literally is nothing but its development, because it is defined as a constant becoming rather than as a static being - consists of a series of un|folding routines, some of which can catastrophically develop into 'other bodies,' which means that through small variations|bifurcations, the folding sequence can shift into different parameters|attractors according to a non-linear logic of positive feedback-loops]. In fact, in such an ecology, "there is no such thing as either man or nature now, only a process that produces the one within the other and couples the machines together … the self and the non-self, outside and inside, no longer have any meaning whatsoever" (Anti-Oedipus 2). Obviously, in such a machinic field, denominations such as nature|culture or natural|artificial lose their validity as defining thresholds.

[27] If nature is no longer 'natural' but machinic, then sexuality is no longer the most 'natural' thing in the world. In fact, Deleuzian sexuality is infinitely machined, a term that again evokes Leibniz, who negotiates such a generalized machinics in the context of the difference between 'natural' and 'artificial' machines; the difference being precisely that natural machines are infinitely machined, while artificial ones are only finitely machined. While the human body is an infinitely machined natural automaton, the bodies of an artificial chessplayer or a mechanical duck can only be finitely machined, artificial automata.

[28] Symptomatically, it is Leibniz, with his fascination for the 'fractal worlds' made visible by the microscope, who presides over the Deleuzian idea of a fractal, chaotic body, suspended into the endlessly differentiated milieu of a larger, machinic, ecological body. In fact, Deleuze looks into the human body with the same fascination that Leibniz looked into the drop of water under the microscope, both finding that "each individual, body and soul, possesses an infinity of parts which belong to him in a more or less complex relationship. Each individual is also himself composed of individuals of a lower order and enters into the composition of individuals of a higher order" (Dialogues 59). The difference between the human body and the 'body' of the plane of immanence is that the former is already a specific, topologically and temporally framed and thus to varying degrees bounded organization, (in other words, that it is to some degree singularized|individualized), [an animal, a thing, is never separable from its relations with the world. The interior is only a selected exterior and the exterior, a projected interior" (Ethology, 628)] whereas the latter consists of the infinite set of the relations of all bodies, things and materials, making up the set of infinitely fast movements and affects from which bio-sexual architectures are created. In Cinema 1 Deleuze provides an image of the relation between the bounded set and its 'relation' to the immanent plane. The open, continuous set of the plane of immanence consists of the infinity of singular sets that are in themselves infinite: "the set of all these sets forms a homogeneous continuity, a universe or a plane ... of genuinely unlimited content" (16). The beginning of singularization (respectively: individuation) and thus closure is, cinematically speaking, a framing: "the determination of a closed set [is] ... framing" (12). There is, however, always a relation between the framed, closed set and the out-of-field, which means that perfect closure is impossible because ultimately, everything is connected to everything else: "A closed system is never absolutely closed; but on the one hand it is connected in space to other systems by a more or less 'fine' thread, and on the other hand it is integrated or reintegrated into a whole which transmits a duration to it along this thread ... a duration which is immanent to the whole universe" (17).

Cabeça ao estilo de Rafael Explodindo (1951)

Maxima Velocidad de la Madona de Rafael (1954)

[29] A series of paintings by Salvador Dali might be said to 'illustrate' the retroactive speeding up of the human figure, the 'becoming-speed' of the human figure that results from its opening up to the level of the molecular. Its dissolution into the infinitely fast dance of particles making up the plane of immanence is most directly illustrated by a painting called, symptomatically, "Maximum Speed of Raphael's Madonna."[In Dali's dictionary, the aphrodisiacal Rhinozeros horn invariably relates to matters-of-sexuality]

[30] In order to reach the molecular level, anybody has to be broken down into 'its' infinitely fine, imperceptible continuities. It has to become a multiplicity of intensive lines rather than of segmenting points [in terms of Anti Oedipus, it has to become 'production' rather than 'representation']. What this means is that one has to become simultaneously more and more abstract and more and more material. ["The situation is the same in biology: the great cellular divisions and dichotomies, with their contours, are accompanied by migrations, invaginations, displacements, and morphogenetic impulses whose segments are marked not by localizable points but by thresholds of intensity passing underneath, mitoses that scramble everything, and molecular lines that intersect each other within the large-scale cells and between their breaks" (Plateaus 201)].

[31] In fact, making use of another Deleuzian term, molecular sex plays itself out in the arena of subindividual percepts and "nonsubjective affects" (341) rather than in that of individual perceptions and affectations, because "on the plane of consistency, a body is defined only by a longitude and a latitude: ["We call longitude of a body the set of relations of speed and slowness, of motion and rest, between particles that compose it [...] We call latitude the set of affects that occupy a body at each moment, that is, the intensive states of an anonymous force (force for existing, capacity for being affected" (Ethology, 629)] in other words the sum total of the material elements belonging to it under given relations of movement and rest, speed and slowness (longitude); the sum total of the intensive affects it is capable of at a given power or degree of potential (latitude). Nothing but affects and local movements, differential speeds" (Plateaus 260). ["The affect is impersonal and is distinct from every individuated state of things: it is none the less singular, and can enter into singular combinations or conjunctions with other affects" (Cinema1 98)].

the plane of consistency knows nothing about substance and form: haecceities, which are inscribed on this plane, are precisely modes of individuation proceeding neither by form nor by the subject. The plane consists abstractly, but really, in relations of speed and slowness between unformed elements, and in compositions of corresponding intensive affects (the 'longitude' and 'latitude' of the plane). In another sense, consistency concretely ties together heterogeneous, disparate elements as such: it assures the consolidation of fuzzy aggregates, in other words, multiplicities of the rhizome type (Plateaus 507).

Deleuze always stresses that the human subject is made up of a heterogeneity of 'series' without a common perspective-point: "Individual or group, we are traversed by lines, meridians, geodesics, tropics, and zones marching to different beats and differing in nature" (Plateaus 202). There is nothing metaphorical and nothing individual about molecular sexuality. On a molecular level, everything is decidedly material, physical and 'particular.' A molecular sexuality consists of real distributions of particles [productions], not of mirrorings or copies of images [as representations]. In fact, the material distribution is what differentiates becomings and 'impersonations|performances:' "Sexuality is the production of a thousand sexes, which are so many uncontrollable becomings. Sexuality proceeds by way of the becoming-woman of the man and the becoming-animal of the human: an emission of particles" (Plateaus 278-9). ["becoming is to extract particles between which one establishes the relations of movement and rest, speed and slowness that are closest to what one is becoming, and through which one becomes. This is the sense in which becoming is the process of desire. This principle of proximity or approximation is entirely particular and reintroduces no analogy whatsoever. It indicates as rigorously as possible a zone of proximity or copresence of a particle, the movement into which any particle that enters the zone is drawn [...] A haecceity is inseparable from the fog and mist that depend on a molecular zone" (Plateaus 273-4)].

[32] Maybe at this point, the Deleuzian side of the quarrel some feminists have with his idea of sexuality – becoming woman and becoming girl – might become clearer. For Deleuze, 'woman' and 'girl' do not so much designate subjects, "their individuation […] proceeds not by subjectivity but by haecceity, pure haecceity. […] They are pure relations of speeds and slownesses, and nothing else" (Plateaus 271) as they designate movements towards non-subjectivity. The girl is, in fact, the plane of immanence:

The girl is certainly not defined by virginity; she is defined by a relation of movement and rest, speed and slowness, by a combination of atoms, an emission of particles: haecceity. She never ceases to roam upon a body without organs. She is an abstract line, or a line of flight. Thus girls do not belong to an age group, sex, order, or kingdom: they slip in everywhere, between orders, acts, ages, sexes; they produce n molecular sexes on the line of flight in relation to the dualism machines they cross right through [...] the girl is the becoming-woman of each sex, just as the child is the becoming-young of every age (Plateaus 277).

pack | family

particular sex

[33] It is on the unthinkable, a-personal, sub-individual but decidedly not un-livable plane of immanence [→ life, according to Deleuze, does not lie in the organism, but always in the spaces between organisms] on which a molecular transsexuality - a "nonhuman sex" (Anti-Oedipus, 294) that is part of a "microscopic transsexuality" (295) – 'takes place' and plays itself out and on which the "difference between the human and the 'nonhuman' sex" (294) is constituted. Or, from a complementary angle, it is the microscopic transsexuality which, together with other molecular series, engineers the plane (infinitely fast at every moment). Its invariably communal, massive logic is the reason why "making love is not just becoming as one, or even two, but becoming as a hundred thousand" (296), why there are "not one or even two sexes, but n sexes" (296) and why a "molecular sexuality … is no longer that of a man or of a woman" (Dialogues 131). In fact, every sexual distribution of particles creates a specific sexual ecology, "for the two sexes imply a multiplicity of molecular combinations bringing into play not only the man in the woman and the woman in the man, but the relation of each to the animal, the plant, etc. a thousand tiny sexes" (Plateaus 213).

[34] In opposition to the psychoanalytic organization, the logic of this plane knows not so much families as it knows masses and packs. [In a pack, "there is a circulation of impersonal affects, an alternate current that disrupts signifying projects as well as subjective feelings, and constitutes a nonhuman sexuality" (233). It stakes an open, massive logic against the structural|individual and closed logic of psychoanalysis, because it is the latter that "join[s] sexuality to the familial complex" (Anti-Oedipus 58, my italics). From within psychoanalysis, in fact, there are only two choices: either a subjection to the family affair, or the loss of sexuality as such: "The Freudian blackmail is this: either you recognize the Oedipal character of infantile sexuality, or you abandon all positions of sexuality" (Anti-Oedipus 100). This is why Deleuze|Guattari "maintain […] that castration is the basis for the anthropomorphic and molar representation of sexuality" (Anti-Oedipus 295). The sexual overcoding, in fact, goes hand in hand with a semiotic overcoding in which the signifier (and psychoanalysis' annexing of its logic) overcodes any number of "nonsignifying signs" (Anti-Oedipus 73). [Representation overcodes production, a process that produces the Lacanian subject: "a subject split into a subject of enunciation and a subject of the statement, who has the impression of producing statements which, in fact, are produced by machinic assemblages or by the multiplicities acting in him" (Dualism, 105)]. In fact, psychoanalysis defines the two choices vis-à-vis language by a similar exclusion: either as that of the neurotic or as that of the psychotic. Packs do not operate by cultural rules and channelings as they do by contiguity [Darwin's stress on heredity is where Deleuze|Guattari part from him], by swarming rather than by individual movement and by material contagion rather than by immaterial projection. As they note, "for us, on the other hand, there are as many sexes as there are terms in symbiosis, as many differences as elements contributing to a process of contagion" (Plateaus 242). A difference similar to that between packs and families lies between the originary war machine ["a war machine: a physics of packs, turbulences, 'catastrophes,' and epidemics" (490)] and a war machine operationalized by the state: "sexuality brings into play too great a diversity of conjugated becomings; these are like n sexes, an entire war machine through which love passes [...] What counts is that love itself is a war machine endowed with strange and somewhat terrifying powers" (278); which is why Deleuze, in Anti-Oedipus also talks of "infernal" (83, 109) desire machines]. The challenge is to think of molecular sex as 'originating' from this plane rather than from the attraction between individuals, or, the latter only in case this attraction is referred back to the presence of the plane in the individual through its molecular elements. In terms of subjectification, this implies thinking of the subject as emerging from molecular dances and masses (Plateaus 34-5) ["We each go through so many bodies in each other" (Plateaus 36), "everyone is a little group" (Anti-Oedipus 362) and "there are no individual statements, only statement-producing machinic assemblages" (Plateaus 36)] and to think of it as being ultimately made up of nonhuman aggregates. Ultimately, a molecular sexuality has to do with "the faceless figure of the libido" (36), with "collective assemblages" (80) and a "nonsubjective living love" (189). In operational terms, molecular sexuality relates and distributes particles:

Sexuality is no longer regarded as a specific energy that unites persons derived from the large aggregates, but as the molecular energy that places molecules-partial objects (libido) in connection, that organizes inclusive disjunctions on the giant molecule of the body without organs … and that distributes states of being and becoming according to domains of presence or zones of intensity … For desiring-machines are precisely that: the microphysics of the unconscious (Anti-Oedipus 183).

What this means is to see molecular sexuality as the true sexual agent, with individual sexuality and procreation merely machines in the service of the general, autopoietic ecology of 'real sex.' Somewhat like in Burrough's idea that 'language is a virus' and that human beings are merely its carriers, "sexuality is not a means in the service of generation; rather, the generation of bodies is in the service of sexuality as an autoproduction of the unconscious" (108). From this point of view, individuals – in particular oedipalized individuals - are not so much molecular conduits as they are molar stoppages and breaks in the generalized flow and distribution of sexuality on the body without organs|plane of immanence: "subject is desire itself on the body without organs, inasmuch as it machines partial objects and flows, selecting and cutting the one with the other, passing from one body to another, following connections and appropriations that each time destroy the factitious unity of a possessive or proprietory ego (anoedipal sexuality)" (72).

[35] Subjectification under the law of castration implies a full territorialization, whereas molecular sexuality "an anoedipal sexuality, an anoedipal heterosexuality and homosexuality, an anoedipal castration" (74) denotes deterritorializations and points towards a 'breaking down' of subjectification and a 'becoming imperceptible' that Deleuze finds illustrated in Matheson's novel Shrinking Man. For Deleuze, the novel shows that "there is always a perception finer than yours, a perception of your imperceptibility, of what is in your box" (Plateaus 287). [→ for the concept of a recursive material unconsious, see also Michel Serres: "At this point the unconscious gives way from below [recedes into the depths]; there are as many unconsciousnesses in the system as there are integration levels. It is merely a question, in general, of that for which we initially possess no information. … Each level of information functions as an unconscious for the global level bordering it … What remains unknown and unconscious is, at the chain's furthermost limit, the din of energy transformations: this must be so, for the din is by definition stripped of all meaning, like a set of pure signals or aleatory movements. These packages of chance are filtered, level after level, by the subtle transformer constituted by the organism … In this sense the traditional view of the unconscious would seem to be the final black box, the clearest box for us since it has its own language in the full sense" (Hermes, 80, my brackets)]; that there are are more and more microscopic and fine levels of perceptions that lie beyond human thresholds of perception: "The imperceptible is the immanent end of becoming, its cosmic formula. For example, Matheson's Shrinking Man passes through the kingdoms of nature, slips between molecules, to become an unfindable particle in infinite meditations of the infinite" (Plateaus 279). ["In the final analysis, we would have to speak of a perception which was no longer liquid but gaseous. For, if we start from a solid state, where molecules are not free to move about […], we move next to a liquid state, where the molecules move about and merge into one another, but we finally reach a gaseous state, defined by the free movement of each molecule" (Cinema1 84)].

[36] In fact, the novel traces almost programmatically how the protagonist's attachment to his wife and to the familial logic complete with the gradual regression from an adult to an infantile sexuality gradually gives way to a logic of 'packs' (cats, spiders), only to enter, finally, a purely molecular level and a molecular perception: ["Even at the level of the most elementary living beings one would have to imagine micro-intervals. Smaller and smaller intervals between more and more rapid movements" (Cinema1 63); "an atom, for example, perceives infinitely more than we do and, at the limit, perceives the whole universe" (64)]. Gradually, the protagonist vanishes in a purely molecular tableau, becoming part of the level of haecceities, in a movement that also goes towards a molecular sexuality: "to become imperceptible oneself, to have dismantled love in order to become capable of loving" (197). There is, however, a difference to a Deleuzian becoming-imperceptible, because while the protagonist is 'within' the molecular tableau, his consciousness is still 'as big' as it is in the beginning, whereas "a natural play of hacceities, degrees, intensities, events, and accidents [...] compose individuations totally different from those of the well-formed subjects that receive them" (Plateaus 253).

[37] While the plot of the film that was made from the novel follows relentlessly the stages of the protagonist's 'becoming-imperceptible,' in the novel, retrospectives are inserted between detailed description of the final 6 days. Quite laconically, the titles of these retrospectives are mere measurements: 68 inches, 49, 42, 35, 21, 18, 7. Mathematically, this series of subtractions of rational numbers will end with 0, for instance 7 minus 5 minus 2.

[38] Towards the end of both novel and film Cary has overcome his initial panic. He has cut all cords to his molar life and is in fact beginning to look forward to his vanishing. In the beginning, he was afraid because he believed in a human, finite, subtractive mathematics: "in six days he would be gone" (6), "for what reality could there be at zero inches" (11). Towards the end, however, he realises that nature operates according to a mathematics of the infinite, which means that his becoming imperceptible is "a thing of potential value, not just ... a curse" (143). The novel points specifically to Carey's shift from a logic of subtraction [finitude] to an infinitesimal logic [infinity], and thus from the idea of an individual life to that of 'a life' and with it, from a subtractive 'Lacanian' mathematics, which is, as I noted above, based on the concept of zero, to a Deleuzian one that is based on the concept of infinity. In particular the idea that nature does not contain a zero resonates with the Deleuzian mathematics and is probably the reason why the book was so 'attractive' for Deleuze. As Carey notes in his final monologue,

how could he be less than nothing? Last night he had looked up at the universe without. Then there must be a universe within, too. Maybe universes. He'd always thought in terms of man's own world and man's own limited dimensions. He had presumed upon nature. For the inch was man's concept, not nature's. To a man, zero inches mean nothing. Zero meant nothing. But to nature there was no zero ... He would never disappear because there was no point of non-existence in the universe. There was food to be found, water, clothing, shelter. And, most important, life. Who knew? ... Scott Carey ran into his new world, searching (188).

In opposition to the novel, the film negotiates the becoming-imperceptible in religious terms. Symptomatically, it is now God for whom zero does not exist:

I was continuing to shrink, to become... what? The infinitesimal? What was I? Still a human being? Or was I the man of the future? If there were other bursts of radiation, other clouds drifting across seas and continents, would other beings follow me into this vast new world? So close - the infinitesimal and the infinite. But suddenly, I knew they were really the two ends of the same concept. The unbelievably small and the unbelievably vast eventually meet - like the closing of a gigantic circle. I looked up, as if somehow I would grasp the heavens. The universe, worlds beyond number, God's silver tapestry spread across the night. And in that moment, I knew the answer to the riddle of the infinite. I had thought in terms of man's own limited dimension. I had presumed upon nature. That existence begins and ends in man's conception, not nature's. And I felt my body dwindling, melting, becoming nothing. My fears melted away. And in their place came acceptance. All this vast majesty of creation, it had to mean something. And then I meant something, too. Yes, smaller than the smallest, I meant something, too. To God, there is no zero. [shouts] I still exist!

the dance of life

pure sex2

[39] The perspective-point of a Deleuzian theory of sexuality is ultimately a nonorganic 'life' and, related to that, "a pure plane of immanence […] upon which unformed elements and materials dance that are distinguished from one another only by their speed […] A fixed plane of life upon which everything stirs, slows down or accelerates" (255).

[40] This life lies in the imperceptible passages between both organic and non-organic systems: "If everything is alive, it is not because everything is organic or organized but, on the contrary, because an organism is a diversion of life. In short, the life in question is inorganic, germinal, and intensive, a powerful life without organs […] everything that passes between organisms" (499). What this means is that both what we call 'living' and 'nonliving' systems are ultimately subtractions from 'a life:' [→ for more on a life see Pure Immanence: Essays on A Life] ["not all Life is confined to the organic strata: rather, the organism is that which life sets against itself in order to limit itself, and there is a life all the more intense, all the more powerful for being anorganic" (503), Deleuze notes, as well as "even when they are nonliving, or rather inorganic, things have a lived experience because they are percptions and affections" (Philosophy 154) and although "not every organism has a brain, and not all life is organic, but everywhere there are forces that constitute microbrains, or an inorganic life of things" (213)]. If "unformed matter, the phylum, is not dead, brute, homogeneous matter, but a matter-movement bearing singularities or haecceities, qualities and even operations" (Plateaus 512), then the origin of sexuality lies in 'living organisms' only from one point-of-view. From another point-of-view, it lies in 'a life' that these subjects 'decelerate' and thus actualize and make perceptible. [→ other, less complex decelerators are the 'tick' [→ for more on the tick and affects see "Ethology: Spinoza and Us"] and Flusser's 'vampyroteuthis infernalis']. As with Leibniz' monads, life is scaled from the infinitely small [molecules] to the infinitely large [the earth|chaosmos], individuals being complex consolidates embedded within this 'sexual continuity.'

[41] The projective plane of immanence, then, is ultimately the plane of 'a life' and the plane of 'a' sexuality. Although the plane denotes logically the level of perfect continuity (the unthinkable hyle perception and thought cut into), it is 'present' in any in-between space between discrete points. It embodies the 'reciprocal presupposition'of an 'analog life' and a life cut up by digital perceptions, of 'becomings' and states of 'being.' The 'immanence' of the plane is the reason why being, as a 'steady state,' does not exist. Being is nothing but the illusion of stasis because any 'static state' consists, if one descends deeply enough into its systems of formation, or if one speeds up the time-scale of one's observation enough, of infinitely many movements and becomings, some of them infinitely small and thus imperceptible: glass flows, mountains move.

[42] Becomings, according to this logic, lie at the beginning of 'a' life and 'a' sexuality and they subsist in every seemingly static state as invisible, imperceptible animations. Even the most molar sexuality, therefore, is open to molecular lines of flight. One imperceptibly small stumbling (as the material equivalent of stuttering) may cause a marching group to begin to dance, similar to the way in which the tucking at a sleeve may cause a revolution in Kleist. From a Deleuzian point-of-view, a 'queering' of sexuality implies finding imperceptible beginnings for sexualities that are grounded in the powerful nonhuman life to which we are immanent and to find machinic practices that are 'in the service' of this life's anonymous sexuality and 'its' desire for 'newness' and for 'continuous change.'What this means is that although it makes sense to relate it 'by default' to matters of sexuality, ultimately, queering, as a material, molecular operation, is not restricted to specific spaces and discursive formations and thus not to the field of sexuality. It can happen at any point and at any moment 'in a life.' As a specific form of 'traversalization,' it invariably aims at speeding things up and at making things flow.

the event of sex

haecceity

[43] For the sexual field, the challenge of queering lies in finding and inventing sexual practices that follow the logic of production|life, of the intensive movements of autopoiesis, of networkings and of mutations. Life, in its spatio-temporal movements between ecosystems that actualize it, operates within machinic processes of couplings, systemic dockings and integrations. There might be a lesson in the fact that the power of an ecosystem lies in its affectability and in its power to affect, in its elasticity|plasticity and in its openness to minor, molecular influences (its ability to read minor-scale formations) and in its 'gift' to be affected by the dance of haecceities. It breaks open crusted sexualities by realigning and recombining molar sexual machines and thus cuts through positionings|assemblages such as hetero- or homosexual. Ultimately, it feedbacks sexual politics (gender) with sexual physics (sexuality) and thus it opens up complex, intensive ecologies. ["there is no longer a form, but only relations of velocity between infinitesimal particles of an unformed material. There is no longer a subject, but only individuating affective states of an anonymous force" (Ethology, 630)]. It is always a material movement and a material practice: "the event is finally the very identity of the statement and of desire, whatever takes place implies the constitution of a body without organs. As long as you have not made your body without organs, alone, with someone else, with n people, nothing is possible" (Dualism, 105).

[44] Like Easy Rider, Zabriskie Point or Thelma and Louise, Sam Mendes'|Alan Ball's movie American Beauty is one of those movies that, from within a deep saturation with and investment in Hollywood conventions, traces the ultimately tragic attempt to construct such a body without organs. In fact, American Beauty (visually a movie that is part Spielberged and Lynched, resulting in a visual mode that might be called 'lynch light') is in many ways a 'stationary road movie.' Symptomatically, the automotive machine assembled in it is not destructive, as in Ballard, but a libidinous man|boy-car assemblage that is charged with an intensely erotic energy ["Mine. 1970 Pontiac Firebird. The car I've always wanted and now I have it. I rule!"].

[45] It is part of this 'conventionality' that the molar machines do not allow for such a construction and invariaby find ways of 'striking back.' (Another reason for the movie's 'tragic' outcome, of course, lies in the fact that Lester's journey ultimately points towards reproductions rather than towards new productions. As the soundtrack highlights, it is a journey into the past rather than into the future ["I know I didn't always feel this... sedated. But you know what? It's never too late to get it back," Lester comments at some point]. Ultimately, it is only Jane and Ricky who will embark on a line of light towards something 'new').

[46] The movie, which follows Lester Burnham's assembly of a line of flight towards a 'becoming boy|girl,' and thus towards becoming truly queer, opens onto the panorama of a fully 'capitalized' family and the various entanglements of its members in their specific molar machines, such as the capitalist machine and the ideological state apparatus of high-school sexuality. (Symptomatically, both Lester's work and Angela's model-sexuality are commented on as modes of prostitution, which links sexuality tightly to the capitalist machine). Almost programmatically, the movie presents the most common sexual pathologies produced by systems of n+1 sexes. 1. Angela Hayes, a cross between the 'Blue Angel' and 'Dolores Haze,' is the lolita-like virgin teen-beauty wannabe model who desperately attempts to be 'special' and who will turn only at the end from being a perfect surface for phallocratic projections ["spec-tacu-lar"] and from being a perfect phallocratic flirt to being a vulnerable little girl. 2. Carolyn Burnham, the most pressured character of all, is driven into a masochistic, hysterical affair with the successful citizen and real-estate king Buddy Kane ["Fuck me, your majesty!"], somewhat like that other hystericized housewife, Deborah Clasky in Spanglish, who also has an affair with a real-estate agent. 3. Frank Fitts, the closet gay colonel projects his repressed homosexuality onto Lester and kills him in a bout of ultimately self-directed rage after he is 'dismissed' by him. 4. Jane Burnham, the 'freak' who does not correspond to the norms of teen sexuality. 5. Ricky Fitts, the similarly 'freakish,' son of a violent father and of a mother who has been thoroughly incapacitated by her control-obsessed and violent husband, who can see the world only mediated through the filter of a video camera ["I'm not obsessing. I'm just curious"] and who deals drugs to maintain his lifestyle.

[47] From that completely pressured and 'decelerated' state, the movie charts Lester's 'retroactive smoothing' – after he sees Ricky quit his job, he finds the power to quit his job as well ["I think you just became my personal hero!"] - and his disentanglement from the grasp of the molar machines (most importantly, the work-family nexus) that have gradually and 'imperceptibly' overcoded his life. ["I feel like I've been in a coma for the past twenty years. And I'm just now waking up"]. Amongst others, they have reduced his sexuality to a lonely, joyless, exhausted masturbation under the shower in the morning. ["Look at me, jerking off in the shower... This will be the high point of my day; it's all downhill from here"].

[48] From this lifeless zero degree of energy|intensity, the movie, like a true road movie, steadily 'accelerates.' From his closed-circuit sexuality, for instance, Lester shifts towards an increasingly intense experience of his formerly 'anaesthecized' body and of its capacity to affect and to be affected. This growing elasticity can be seen in how his initially measured, clumsy movments gradually give way to impulsive, graceful ones. He delights more and more in 'what his body can do.' ["I want to look good naked"]. More and more, molar stasis unfreezes into molecular process; a dynamization that goes hand in hand with an increasing anti-oedipalization and with a shift from capitalism to schizophrenia [as Lester notes, he has regained a state in which it is once more possible to surprize myself: "It's a great thing when you realize you still have the ability to surprize yourself."] In the last moments before his death, Lester realizes that he actually feels 'great' and in tune with the world, which, from a Deleuzian perspective means that he is thoroughly molecularized and thus 'queered.'

[49] Throughout, however, the movie highlights the power and the tenacity of the cultural, always specifically American formations of sexuality, beauty and desire. (Lester is first 'awakened' to beauty|sexuality through the cultural stereotype of the cheerleader-turning-stripper and only in the last moment shifts from predator to mentor; Ricky follows, for a long time, a voyeuristic regime; Carolyn is in a continual state of hysteria). It is only towards the end of the movie that these cultural formations dissolve, and that a level of a nonhuman sexuality is addressed.

[50] In this context, the central scene of the movie involves a video made by Ricky that records a moment from the world of nonhuman affects: fifteen minutes of a plastic bag moving in a pocket of atmospheric turbulence. From a Deleuzian perspective, this bag and the wind are, not only in a manner of speaking, 'making love.' It is when Ricky shows this video to Jane, his 'object of desire,' that the spectators realize that he uses the video-camera not so much to voyeuristically spy on people but to help him remember|record moments of intense beauty [Ricky Fitts: "I was filming this dead bird." Angela Hayes: "Why?" Ricky Fitts: "Because it's beautiful"].

[51] Programmatically, the mise-en-scene in which the screening of the video is embedded provides a running commentary in which its physics are translated into metaphysics. The simultaneity of these two sides of the 'surface of sense' is negotiated by the complex architecture of the image- and the soundtrack. The former shows the film on a 'screen within the screen,' with the heads of the two spectators visible from behind. While the 'interior images' show the world of nonsubjective, purely material affects (the bag dances with the wind), the frame of the two heads ties the image to Ricky's monologue on the soundtrack, by which the nonhuman affects are transposed onto a level of individual, immaterial affectations (the bag dances with Ricky). Taken together, the two tracks illustrate the feedback loops between material sensations and immaterial sense (the feedback loops between affects and meaning): "Do you wanna see the most beautiful thing I ever filmed?" Ricky asks Jane, layering his feelings and memories over the images:

It was one of those days when it's a minute away from snowing and there's this electricity in the air, you can almost hear it. And this bag was, like, dancing with me. Like a little kid begging me to play with it. For fifteen minutes. And that's the day I knew there was this entire life behind things, and... this incredibly benevolent force, that wanted me to know there was no reason to be afraid, ever. Video's a poor excuse, I know. But it helps me remember... and I need to remember... Sometimes there's so much beauty in the world I feel like I can't take it, like my heart's going to cave in.

What the scene communicates for both spectators is a 'pure life' and the presence of a 'benevolent' (life)-force ('conventionally,' this force might also be a religious force, which somewhat undercuts the physical reading and points to the fact that physics can easily turn not only into metaphysics but also, as in The Incredible Shrinking Man, into 'transcendence'). It is precisely the sensibility for this anonymous force that serves as a conductor for the erotic energy|electricity between the two, which unloads itself, immediately after the screening, in their first kiss. The fact that this process could also be described as a chemical reaction caused by the film as a catalyst only highlights its material, directly physical nature.

[52] The ending of the movie repeats the scene, although it does so with a difference. Not only does it show a different part of the dance, it is now also visually unmediated|unframed, taking up the whole screen. It is now Lester Burnham's voice-over from 'beyond' life (like Sunset Boulevard, the structure of the movie implies a 'life after death,' although this is more of a narratological strategy than a religious promise: ["My name is Lester Burnham. This is my neighborhood; this is my street; this is my life. I am 42 years old; in less than a year I will be dead. Of course I don't know that yet, and in a way, I am dead already"]) that perspectivizes it. Lester repeats some of Ricky's words, but again, it is a repetition 'with a difference':

I could be pretty pissed off about what happened to me... but it's hard to stay mad, when there's so much beauty in the world. Sometimes I feel like I'm seeing it all at once, and it's too much, my heart fills up like a balloon that's about to burst... And then I remember to relax, and stop trying to hold on to it, and then it flows through me like rain and I can't feel anything but gratitude for every single moment of my stupid little life... You have no idea what I'm talking about, I'm sure. But don't worry... you will someday.

In these two scenes, the movie reaches its perspective-point: the nonhuman, material level of the plane of immanence|consistency. As Deleuze describes it,

inscribed on the plane of consistency are haecceities, events, incorporeal transformations that are apprehended in themselves; nomadic essences, vague yet rigorous; continuums of intensities or continuous variations, which go beyond constants and variables; becomings, which have neither culmination nor subject, but draw one another into zones of proximity or undecidability […] A powerful nonorganic life that escapes the strata, cuts across assemblages, and draws an abstract line without contour (Plateaus 507).

Although both descriptions in American Beauty are charged with an anonymous erotics, Lester's even more than Ricky's advocates a giving-over of one's subjectivity to the weird and wonderful nonhuman ecologies that surround it and flow through it, making of every moment a becoming, an event, a haecceity. (Similarly, Deleuze is always at his most poetic when he describes hacceities and the physics of 'a life,' especially in Pure Immanence: Essays on A Life). As Lester notes in the first words of his final monologue, evoking Deleuzes infinite logics, the event of death|life is both infinitely short and infinitely long. It is at once moving at infinite speed and stationary: "I had always heard your entire life flashes in front of your eyes the second before you die. First of all, that one second isn't a second at all, it stretches on forever, like an ocean of time..."