Toward the Spatiotemporal Real
These elaborations emerged in an ongoing correspondence with my colleague Carla Ferro, a psychoanalyst and philosopher based in Brazil. The formulations presented here might be thought of as a provisional step towards a rethinking of subjectivity and the psychoanalytic process from the vantage point of Lacan’s late hypothesis of the topological real, with a little help from Deleuze and Guattari (and, I’d like to think, under the benevolent gaze of Spinoza and Leibniz…)
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The spacetime of the psyche is not static, nor is it homogeneous. Rather, it is a dynamical system subject to continuous variation and characterized by teeming multiplicity and unfathomable complexity: that is, the system is always a collection of subsystems (which are themselves constantly becoming, transforming, and comprised of their own subsystems, ad infinitum).
As a provisional framework, psychical spacetimes (and their subsystems) can be classified along a continuum characterized by varying degrees of differentiation, the poles of which we can name using the conceptions of smooth and striated (as originally elaborated by Pierre Boulez[1][2] and then further developed by Deleuze and Guattari[3][4]).
Smooth spacetime is relatively open and connected, allowing for a more extensive scope of movement within the space. Striated spacetime, by contrast, has been subjected to a higher degree of folding, delineation, and partitioning. At its extreme, striation can produce grid-like configurations and metricization. With a preponderance of striation comes greater restriction of the possibilities for movement and interrelation amongst the elements contained in the space.
The aforementioned elements which traverse the space can include the whole range of processes discernible to the psyche, and these events interact within a constantly evolving network of relations. These relations are akin to functions within topology[5] and morphisms within category theory.[6] Acknowledging the musical origins of the smooth-striated framework, we might also conceive of the relations as “intervals.”
A constellation of events could include (as an arbitrary example) fragments of self-representation, components of representations of others, a percept of a bodily process, an affective tone, a linguistic sign or set of signs, a set of velocities of objectal movement and exchange, and quotients of relative intensity (this list could be extended indefinitely).
The constellation occurs within a space which has a certain character along the smooth/striated continuum, and the character of the space determines the kinds of relations that are possible between the events within the constellation. In fact the constellation and the space that it inhabits are ultimately congruent, qualitatively speaking.
A constellation is a moment in the becoming of the spacetime of the subject. Its spatiality is given by its topological characteristics (which I am classifying along the smooth/striated continuum). The constellation’s temporality is given by the character of the movements of the elements vis-a-vis one another, the transformations of their intervals. The phenomena are not static but in motion (albeit at varying speeds).
In fact, the events are best understood as lacking an essence of their own and instead as being defined by the web of relations that they participate in.[7] This web itself is always subject to movement and reconfiguration. The events which populate a given constellation are ultimately nothing but forces or intensities possessing certain potentialities of motion. The motion is defined by its relative change of position vis-a-vis the other objects (which are themselves also moving), by its inherent level of intensity or vibrancy, and by its velocity (the speed at which it currently has a capacity to change its interval).
Ultimately, all constellations are momentary, ephemeral, and singular, each moment irreducible to any other. And yet, in relatively striated spaces the range of possible motion and intervallic reconfiguration undergoes restriction by virtue of the folding and delineating of subspaces, and its barriers, disconnections, holes, and breaks. The sometimes highly ornate stratification of these spaces results in constellating movements that bear a special temporality: that of repetition.
Leitmotifs, refrains, strange attractors…these repeating phenomena can be experienced as a solace, a creation, an expression, an albatross. It is by virtue of his or her strange attractors that the subject articulates a style, a way that is his or her own in the world. At the same time the strange attractor, the loop, the constellation-turned-refrain is emblematic of all that the subject will regard as symptomatic. Style and symptom, mutually inextricable.
Psychoanalysis in the key of the spatiotemporal endeavors to map the territories and the movements without applying meanings. The ethics of the method is made good in its radical commitment to horizontality. That is, there is no constellation purported to be deeper or more primary than another, no ensemble of elements that explains another, and therefore no verticality. Links and correspondences certainly occur, and structural invariants can be identified without taking the additional falsifying step of treating one constellation as a metaphor for another.
In mapping the terrorities and temporalities of the subject, there is a treatment of the leitmotifs, one in which the potentiality for the new is revealed, hitherto having been occluded by the self-reinforcing circuitry of repetition. The moment of unveiled potentiality, for which we might playfully propose the name “bright circumstance,”[8] is always an irruption of the smooth within striation, like the sudden emergence of a pitch that had previously gone unheard (more precisely, inaudible) because its frequency is between the delineated pitch series which constituted the elements of the leitmotif. As Deleuze and Guattari say, “all progress is made in and by striated space, but all becoming occurs in smooth space.”[9]
1. Boulez, P. (1986). Orientations: Collected Writings. (M. Cooper, Ed. & Trans.). Faber and Faber.
2. Boulez, P. (1979). Boulez on music today. (S. Bradshaw & R. R. Bennett, Trans.). Faber & Faber.
3. Deleuze, G., & Guattari, F. (1987). A Thousand Plateaus: Capitalism and Schizophrenia. (B. Massumi, Trans.). University of Minnesota Press.
4. Deleuze, G. (2006). Two Regimes of Madness: Texts and Interviews 1975-1995. (D. Lapoujade, Ed., A. Hodges & M. Taormina, Trans.). Semiotext(e).
5. Adams, C., & Franzosa, R. (2007). An Introduction to Topology: Applied. Pearson.
6. Cheng, E. (2024). The Joy of Abstraction. Cambridge University Press.
7. Bradley, T.-D., Bryson, T., & Terilla, J. (2020). Topology: A Categorical Approach. MIT Press.
8. A friendly homage to the wonderful band Glass Ghost: https://westernvinyl.com/artists/glass-ghost.php
9. Deleuze, G., & Guattari, F. (1987). A Thousand Plateaus: Capitalism and Schizophrenia. (B. Massumi, Trans.). University of Minnesota Press.