Smooth and Striated Spacetime, Part 2

A continuation of the project begun in the previous post; thanks especially to Benoît Le Bouteiller and Antonella Marreiros for their help in the preparation of this essay.

~

In part 1, I introduced the framework of the smooth and the striated as it was originally developed by Pierre Boulez [1] (and later expanded and amplified by Deleuze and Guattari [2][3]). In this essay, I would like to discuss possible clinical applications of these concepts. In doing so, I will put Boulez’s framework into dialogue with the late teaching of Lacan.

For those who are perhaps less familiar with the trajectory of Lacan’s work, it should be noted that in the last 10 years of his life and teaching, Lacan dove wholeheartedly into the study of mathematics in order to elucidate the nature of the real of the human being, turning his attention especially toward the field of topology. At least by 1970, Lacan appears to be shaping a new hypothesis—that the real is a topological object. In L’Etourdit, written in 1972, the matter is made clear for those who can parse Lacan’s difficult prose: in this text, psychic structure = the real = a topological space, and language is the locus where the structure is “brought to light.”[4] Quietly, Lacan had instigated a revolution in his own conceptual system. Whereas in his early and middle periods, the subject was essentially conceived of as an effect of the signifying chain (and the real defined as negativity, the “impossible” limit point of all symbolization and imagining), in Lacan’s late work there emerges a constitutive dimension more fundamental than the signifier; the real is no longer only pure negativity, but something substantive about which we can make inferences using our clinical observations and topology’s formal rigor with respect to the configurations of space. Finally, in the fading twilight of Lacan’s teaching career (and his life), he begins to emphasize the importance of temporalizing our topological renderings of psychic structure, of not losing sight of the inherent plasticity of subjectivity.[5] In short, the trajectory of Lacan’s work could be said to pass from an ontology of lack to a metaphysics of movements in the spatiotemporal field of the real.

The topological turn in Lacan’s teaching brought about a number of significant reconfigurations of his theoretical framework. In several cases, concepts that had been essential for many years were retained but transformed, undergoing a process of resignification that accorded to them a new function within the emerging paradigm founded on the idea of the real as a topological space.

One such concept is jouissance (which, in the interest of simplicity, we could loosely define as drive satisfaction—without excluding its dimension of going beyond the pleasure principle). While jouissance had hitherto been conceptualized as a unitary phenomenon and referred to in the singular, in the late Lacan, it became multiple. In a first decisive step, Lacan posited a jouissance that is “beyond the phallus.”[6] He initially identified this jouissance as feminine, envisioning it to be operating outside the purview of the signifier, in contrast to what he began to call phallic jouissance. Later on, feminine jouissance would be denoted as the Other jouissance, losing its gendered connotations.[7] Finally, Lacan added a third form of jouissance, one that corresponds to sense or meaning.[8][9]

Though Lacan studied many different topological objects (including the torus, the Moebius strip, and the Klein bottle), his use of knot theory (and more specifically the Borromean link) is probably the most widely known aspect of his work on topology. Lacan’s engagement with knot theory proved fortuitous in many respects; one of the advantages of this study was that it provided him with a more subtle way of explicating the three modes of jouissance (as well as a number of other aspects of the psychic apparatus). In this rendering of the Borromean knot (based on Lacan’s work in Seminar 22[10]), we see the three forms of jouissance depicted as distinct territories (see below).

Courtesy of Antonella Marreiros

In the above diagram, you will see the three registers (Real, Symbolic, and Imaginary) arranged in a Borromean configuration (meaning that while no two rings are interlocking with one another, the three as a totality are interlocking; if one of the rings is cut and “set free,” so are all of the rings unchained). Additionally, you will notice the delineation of specific territories where the different registers overlap and intermingle with one another. Moving from left to right, we can locate the following territories of jouissance:

JA — Jouissance Autre (Other Jouissance)

Location: juncture of the Real and the Imaginary

JΦ — Jouissance Phallique (Phallic Jouissance)

Location: juncture of the Symbolic and the Real

Sens — Jouissance du sens (Joui-sense or Jouissance of Meaning)

Location: juncture of the Imaginary and the Symbolic

Essentially, I want to suggest that these distinct fields of jouissance are different spacetimes inhabited by the subject (it is equally true to say that the subject is inhabited by them!) and that these modes of jouissance qua spatiotemporalities can be correlated with the smooth and striated framework developed by Boulez. The rest of this current essay will be dedicated to demonstrating these correlations.

Sense and Inhibition

We can begin with the field of meaning (the jouissance of sense, at the intersection of Symbolic and Imaginary), which I postulate to be a territory characterized by a maximal degree of striation. Here the signifier and signified meet and intermingle under the aegis of the big Other (whose lack is occluded), with the consistency of the Imaginary working to further reinforce the effect of coherence. The movements possible within such a spacetime are always limited to a finite set of variants given in advance. To conceptualize this space musically, we can imagine a composition whose transmutations lawfully adhere to a predetermined system of harmonic and melodic development and whose time feel is governed by the functions of pulse and meter.

In this field, the subject produces sense, which confers stability upon his or her lifeworld. In certain instances, this sense will be marshaled to defend the subject against the lack in the Other (represented in the diagram by the hole containing the symbol S(A)) and/or the -φ of castration (found in the hole of the Imaginary). That is to say, meaning is often produced in an attempt to restore cohesion and solidity when the subject is forced to contend with the incoherence of the social order (i.e. the lack in the Symbolic) or the lack in the subject him or herself. Notably, the field of sense is proximate to the region denoted as inhibition, where the Imaginary encroaches upon the register of the Symbolic. What to make of this juxtaposition? Could we say that the production of sense—by way of the interlinking of Symbolic and Imaginary processes—carries the risk of a disequilibrium, wherein the pressure for imaginary coherence and meaning becomes so great that the movement of the signifiers is impeded?

Other Jouissance and Anguish

Turning to the other end of the spectrum, we can correlate the field of the Other jouissance (at the crossing of Real and Imaginary) with the Boulezian notion of smoothness. Crucially, this mode of jouissance operates outside the purview of the Symbolic. I don’t take this to mean that language as such has no bearing on this territory of the subject; rather, it seems to me that signifiers indeed have a function in this domain, but that their articulation need not accord with the conventions that govern the Symbolic order. At an extreme, this is the domain in which the linking of S1 to S2 (master signifier and elaborated knowledge) might be superseded by a series of S1s that do not form a chain. Alternatively, there might occur segments of chained signifiers that produce heterodox patterns impervious to the normative dictates that accrue to the processes of signification within the domain of the Symbolic. Here in the field of the Other jouissance, poetic effects abound. Equally though, it’s the realm of that which eludes language, of dynamics of body and being that do not find their way into the signifier at all. From time to time in this territory, we can only echo Arthur Eddington and say “something unknown is doing we don’t know what.”

Imagined musically, the Other jouissance would constitute a sonic landscape recalcitrant to preordained structure both in terms of pitch (where unanticipated frequencies and intervals would readily emerge) and rhythm (where time would be “amorphous” and without pulse, musical events occurring in a temporality that defies metricity or predictability). What is produced in the field of the Other jouissance? The surprising, the unprecedented, the singular. As Deleuze and Guattari aptly observe, “all becoming occurs in smooth space.”[11]

As in the case of sense (which is juxtaposed to inhibition), the Other jouissance is also proximate to a dynamic interplay wherein one register encroaches upon another. In this instance, we are dealing with anguish, which represents the incursion of the Real into the Imaginary. I take this to indicate that while the Other jouissance is characterized by a high degree of entropy, it is not without its own internal dialectic of orderliness, receiving at least a modicum of coherence from the influence of the Imaginary. Anguish, on the other hand, would constitute a moment of maximally entropic potential within the dynamical system of the subject, where not only does the subject not have recourse to signifiers, but where even the fundamental substrate of bodily consistency is threatened by the intruding force of the Real.

Phallic Jouissance and the Symptom

As we move our attention to the field of phallic jouissance (where the Symbolic and the Real interpenetrate), the dialectic of smooth and striated takes on a different form of intricacy. In this territory the subject produces endless iterations of signifiers, desires, and strivings which paradoxically return him or her to the same place: the scene of the fundamental fantasy. Phenomena that initially appear to manifest entropic novelty reveal themselves to be variations on a relatively static motif that underpins and orders the movements that occur in this region of subjectivity. Appropriately, this is the domain of the classical formations of the unconscious (the dream, the slip, the parapraxis) and of repetition in its fullest Freudian sense. A musical analog for this form of jouissance might be a structure of apparent randomness in pitch or rhythm that periodically exposes its highly striated organizing principles. Alternatively, we can imagine a melodic-harmonic development generally characterized by a high degree of unpredictability but punctuated by repetitive leitmotifs or refrains.

Phallic jouissance neighbors the symptom, a dynamic incursion of the Symbolic into the Real. I am tempted to think of the symptom as a kind of overflow of phallic jouissance resulting from the stifling of the truth that is articulated in the motif of the fantasy. When repression operates to a degree of intensity that it impedes the movement of desire in accordance with the logic of the fantasy, the symptom is the recourse for the repressed truth. The symptom is always a conversion (not just in the sense given this term by Freud in his work on hysteria)—a conversion of the fantasmatic truth of phallic jouissance to another form. The refrain is transposed to a new key, we could say. Or a better representation might be to imagine a melody which, after finding no receptive ear, resorts to a synesthetic leap to a different sensory pathway—becoming a color, for instance.

Polyphony and Polyrhythm

The utility of this model hinges upon the clinician’s capacity to mantain a dynamic perspective—that is, to conceptualize the different modes of jouissance (as well as the correlated phenomena of inhibition, symptom, and anguish) as perpetually in motion and in interaction with one another. The clinician must aspire to hold a dialectical tension comprised of local and global effects, attending not only to the dynamics within each territory but also to the evolving gestalt of the system as a totality. There is always an interplay of resonance and response, of event and counterevent, of compensations, attenuations, amplifications, feedback loops…

For instance, on certain occasions we witness what appears to be a reciprocal exchange between the smooth and the striated: when an intensification of Other jouissance provokes a compensatory response in the domain of sense. Plunged headlong into the entropic and ineffable, the subjective economy converts the surfeit of Other jouissance into anguish, causing the subject to attempt a restabilization by way of meaning. He or she fortifies a conceptual system that becomes ever more rigid but is nevertheless haunted by the enigmatic echoes reverberating from the field of the Other jouissance. Deleuze and Guattari had already gotten a hold of this insight when they cautioned that if one is too reckless in the leap into the domain of the body without organs (which I correlate with the Other jouissance) that a countervailing consolidation and solidification might occur, with fascistic implications.[12] In essence, what Deleuze and Guattari think of as the line of flight of the “schizo”[13] can—if the conditions of the flight are less than optimal—result in a psychic backlash of paranoia. Here it should be noted that paranoia can be linked to instances where the striations of sense are intensified to the point of fearful hostility toward any phenomenon that does not accord to the grid of a totalizing meaning.

The clinician’s conception of the interplay of the modes of jouissance (the possible iterations of which are vast) should not however confine itself to the expectation that all three forms of jouissance will be operative in every subject at all times. In fact, one of the further advantages of this model is that it might help the clinician to attend to instances wherein a particular field of jouissance becomes unavailable within the subjective economy at a particular moment. In certain cases we can theorize an occlusion of one or more of the avenues of jouissance (either from topological events occurring within a Borromean configuration, or from the loss of the Borromean configuration as demonstrated by Lacan in Seminar 23 [14]). These occlusion can be brief, long-term, or can even exhibit a rhythm of periodicity.

Whomever we are working with, we can presume that we are encountering an array of spacetimes which comprise a dynamical system. Striated rhythms are punctuated by smooth syncopations. Amorphous landscapes are coexisting and interacting with highly intrincate, labyrinthine grid-like configurations. There are leitmotifs and refrains scattered about in the evolving music of the psyche, intensifications of force and density, openings into hollow canyons where the reverberations accumulate. The analytic process contributes to the mapping of these evolving territories while being inextricably entwined in those territories itself.

Notes:

1. Boulez, P. (1971). Boulez on music today (S. Bradshaw & R. R. Bennett, Trans.). Harvard University Press.

2. Deleuze, G., & Guattari, F. (1987). A thousand plateaus (B. Massumi, Trans.). University of Minnesota Press. (Original work published 1980)

3. Deleuze, G. (2007). Two regimes of madness: Texts and interviews 1975-1995 (A. Hodges & M. Taormina, Trans.; D. Lapoujade, Ed.). Semiotext(e).

4. Lacan, J. (1972). L'Etourdit (J. Stone, Trans.). Retrieved from http://www.freud2lacan.com

5. Lacan, J. (1978-1979). Seminar 26: Topology and Time (D. Collins, Trans.). Retrieved from http://www.apwonline.org

6. Lacan, J. (1972-1973). Seminar XX: Encore (On Feminine Sexuality, The Limits of Love and Knowledge) (B. Fink, Trans., 1998). W.W. Norton & Company.

7. Lacan, J. (1974-1975). Seminar XXII: RSI (Gallagher, Trans.). Retrieved from http://www.lacaninireland.com

8. Lacan, J. (1974-1975). Seminar XXII: RSI (Gallagher, Trans.). Retrieved from http://www.lacaninireland.com

9. Lacan, J. (1974). The Third (La Troisième) (P. Dravers, Trans.). In Get Real (The Lacanian Review, Issue 7).

10. Lacan, J. (1974-1975). Seminar XXII: RSI (Gallagher, Trans.). Retrieved from http://www.lacaninireland.com

11. Deleuze, G., & Guattari, F. (1987). A thousand plateaus (B. Massumi, Trans.). University of Minnesota Press. (Original work published 1980)

12. Deleuze, G., & Guattari, F. (1972/2009). Anti-Oedipus: Capitalism and schizophrenia (R. Hurley, M. Seem, & H. R. Lane, Trans.). Penguin Books.

13. A term they never employ in the pejorative sense.

14. Lacan, J. (1975-1976). The seminar of Jacques Lacan. Book XXIII: The sinthome (A. R. Price, Trans., 2016). Polity Press.