The Fold

The Fold A Physical Model of Abstract Reversibility and Envelopment Elisabet Yanagisawa Academy of Design and Crafts, University of Gothenburg, Sweden For artistic research, the model of “the fold” is exceptionally interesting because it deals with how form and content intertwine in a physical model, and how concrete and abstract interrelate on the plane of consistency. This chapter focuses on chapter two—“The Folds in the Soul”—of Gilles Deleuze’s short but important book The Fold (1993). According to Deleuze, “We are moving from inflection to inclusion in a subject, as if from virtual to the real, inflection defining the fold, but inclusion defining the soul or the subject, that is, what envelops the fold, its final cause and its complete act” (ibid., 23). In other words, the theory of the fold is best understood as a progression, from inflection to envelopment. Each different fold captures a certain metaphysical condition. The concept of the fold also finds expression in Deleuze’s book Foucault (1988a), in the chapter “Foldings, or the Inside of Thought (Subjectivation)” (ibid., 94–123), which concerns reality and virtuality and how they indiscernibly turn into each other as in a grading scale. Framing the question of the meaning of the fold, Deleuze (1993, 26) writes: “Finally, in order that the virtual can be incarnated or effectuated, is something needed other than this actualization in the soul? Is a realization in matter also required, because the folds of this matter might happen to reduplicate the folds in the soul?” The fold is an abstract thought, but the study can likewise start from the reverse, from fold making. My own encounter with the metaphysics of the fold began with exploring physical fold making (figure 2.16.1). By letting folds coagulate, I “freeze” the process to a fixed form to let “‘a nondimensional point’ ‘between dimensions’” be visible (Paul Klee quoted in Deleuze 1993, 15). This first series is made as spontaneous events with melted beeswax and fabric, wherein natural laws of gravity and matter in conjunction with each other form the folds by themselves; it is an “autopoietic”1 method. Along with this theoretical presentation, I will demonstrate the outcome of my explorations in matter. 1 This term is used by Brian Massumi (2002, 280n13, in part quoting Guattari 1995, 7): “self-giving, or ‘autopoietic,’ . . . ‘with processes of the realization of autonomy.’” The term “autopoietic” is also employed by Félix Guattari (1995). 139 Elisabet Yanagisawa Figure 2.16.1. Spinoza’s two attributes One needs to recognise Deleuze’s metaphysical ground, which derives from Spinoza’s two attributes (figure 2.16.2). According to Spinoza, two attributes exist, namely, extension or matter, and thought in the immanent strata. Corresponding to the attributes in strata, the attributes exist in a parallel realm that Spinoza names “the power of the attributes.” Figure 2.16.1. In the immanent cosmology Spinoza presents in his Ethics, the attributes of thought and matter belong to the same dimension, namely, strata, or reality. Spinoza correlates strata with the power of the attributes, which is an abstract dimension parallel to the concrete attributes of thought and matter. This is why Spinoza’s philosophy is often term “parallelism.” The consequence of parallel140 Figure 2.16.1. Elisabet Yanagisawa, Folded Object, cotton fabric, pigment, beeswax. Photo by Elisabet Yanagisawa (EY). Courtesy of the artist. Figure 2.16.2. Spinoza’s two attributes and the power of the attributes. The “vertical line” is perforated. There are passages between the attributes and the power of the attributes. Illustration by Elisabet Yanagisawa. © Elisabet Yanagisawa. The Fold ism is a horizontal reality with passages between the attributes. A model of this metaphysics is the fold. The theory of the fold concerns power that is present in two dimensions: the power in the actual (that is, the visible reality) and power in the virtual (that is, the invisible power of the attributes). Effects are the attributes and the causes are the power of the attributes (Deleuze 1988b, 18–19). The four folds Deleuze (1993, 18) writes, “The fold is Power. . . . Force itself is an act, an act of the fold.” Power is the base of everything existing in reality. Power can be transformed into both thought and matter. Power can also emerge into all different folds; the perspective depends on what fold one is situated in. Deleuze presents four different types of folds, and each type manifests a certain subjective perspective. The first fold Deleuze describes is the inflection (figure 2.16.3). Through a simple S-formed sketch, Deleuze demonstrates how the point of inflection is the point where the concave turns to be convex. He refers to Paul Klee’s study on folds: “It is the point of inflection itself, where the tangent crosses the curve. That is the point-fold” (Deleuze 1993, 14). The inflection has two potential curves—the concave or the convex—two different powers that go in diametrically opposite directions. This point is what Leibniz calls “an ambiguous sign” (Leibniz quoted in ibid., 15). Why is it ambiguous? Because it is not possible to know the outcome of the direction from the start, line, or point. For Klee, this point is the beginning, “‘a site of cosmogenesis,’ ‘a nondimensional point’ ‘between dimensions’” (Klee quoted in ibid., 15). It captures the fundamental conditions of existence, the double forces of development: plus and minus, concave and convex. The first fold, the inflection, is thus vectorial and operates with symmetry. Inflection provides the elementary level of power constructed by a tension between opposite powers. Figure 2.16.3. The second fold is similar to the inflection, but there is a slight change— between the curves is a distance (figure 2.16.4). Deleuze (1993, 22) calls this kind of fold “projective” or “flat projection.” It is depicted as two mirroring curves that have a distance in between them. The space in between the curves 141 Figure 2.16.3. Inflection. Illustration by Elisabet Yanagisawa, referring to the illustrations in Deleuze’s The Fold (1993). Elisabet Yanagisawa is optional. Without this space, there is no extension. This is the condition of the fold in living matter wherein morphology is seen in “the fold; the crease; the dovetail; the butterfly; the hyperbolic, elliptical, and parabolic” (ibid., 16). It captures the general mode of existence, so to speak—the condition of the spatial mode of existence in strata. Figure 2.16.4. Figure 2.16.5. The third fold is a variation of an infinitely variable curve known as Koch’s curve, which is a series of “rounding angles” (Deleuze 1993, 16) (figure 2.16.5). This type of curve “never admits a tangent,” in other words, it remains concave and convexity never gets in: “It envelops an infinitely cavernous or porous world.” Deleuze calls these folds “Gothic arch and return” (ibid.). “Everything changes,” he writes, “when fluctuation is made to intervene in the place of internal homothesis” (ibid., 17). This fold captures an infinite, closed space; it is not totally closed, but the curvature is only of one kind, concave, a “homothesis.” How can everything change in this condition? The curve is made from inside the curve; in other words, it concerns a change of mind, a change of consciousness. I understand Koch’s Curve as a conical object (figure 2.16.6). 142 Figure 2.16.4. Projection. The illustration refers to Deleuze (1993, 16). Figure 2.16.5. Concavity—Koch’s Curve. The illustration refers to Deleuze (1993, 16). The Fold Figure 2.16.6. The fourth fold shifts in another way, a rarer type of folding. Deleuze (1993, 17) writes, “Transformation of inflection can no longer allow for either symmetry or the favored plane of projection. It becomes vortical” (figure 2.16.7). This fold seems to avoid the inflection and instead forms a spiral. Deleuze does not present a figure of the vortex, but according to his description one arrives at a DNA helix: “The line effectively folds into a spiral in order to defer inflection in a movement suspended between sky and earth, which either moves away from or indefinitely approaches the center of a curve and at each instant ‘rises skyward or risks falling upon us’” (ibid.). The fourth fold is about power relations between “sky and earth,” which is another way of saying two powers in a suspension. The line turns to a plane and bends into a spiral—two parallel lines that are connected. They never meet but interrelate through passages. This is now the model of parallelism, a plane of consistency that is twisting to a vortex. No inflection, no concavity, no convexity, no curvature mirroring: the reversibility is only rendered as parallel lines that are infinitely twisting (figure 2.16.8). Figure 2.16.7. 143 Figure 2.16.6. Elisabet Yanagisawa, Folded Object—Cone, cotton fabric, pigment, beeswax. Photo by EY. Courtesy of the artist. Figure 2.16.7. Vortex. Illustration by Elisabet Yanagisawa, © Elisabet Yanagisawa. Elisabet Yanagisawa Figure 2.16.8. Objectile After giving a basic description of the theory of reversibility and the images of four different folds, Deleuze considers the conditions of the folds and the relationships between the two dimensions. First, he presents the idea of the objectile: “The new status of the object no longer refers its condition to a spatial mold—in other words, to a relation of form-matter—but to a temporal modulation that implies as much the beginning of a continuous variation of matter as a continuous development of form” (Deleuze 1993, 19). This indicates a continuous development of instinctual properties of the mind. This development changes the form of the fold continuously, because the fold is elastic and in constant motion—it is a power that is alive. Deleuze implies that changing things in one dimension reciprocally affects the other dimension. Thus, modulating things in spatiality affects the temporal; or, rather, in other words, the virtual. This “is not only a temporal but also a qualitative conception of the object, to the extent that sounds and colors are flexible and taken in modulation.” Sounds and colour indicate strata. “The object here is manneristic, not essentializing,” Deleuze continues, “it becomes an event” (Deleuze 1993, 19). It is no longer an essential object: it is an abstraction. It has transformed into an event during the process of folding. But what is an event? In a parallel reading of Whitehead, “event” means “soul.” In chapter 6 of The Fold, “What Is an Event?,” Deleuze (ibid., 76) draws the reader’s attention to “the transformation of the concept into a subject” by referring to “the [Platonic] school” as being “somewhat like a secret society,” in which Plato is the school’s leader and Whitehead his successor. One now arrives at what Deleuze (ibid., 12) calls a “Baroque perspective.” Depending on what fold one is encapsulated in as a subject or soul, one therefore has that perspective of reality. Thus, there exist different perspectives, which relate to one’s temporal or virtual condition. 144 Figure 2.16.8. Elisabet Yanagisawa, Folded object—Vortex, cotton fabric, pigment, beeswax. Photo by EY. Courtesy of the artist. The Fold Point of view Deleuze introduces the concept of the point of view, which is related to concavity and Koch’s curve. The point of view is the subject’s potential in a certain condition; in other words, the potential of the subject that begins first at the third fold, which is the concave curve, with no convexity. “That is why the transformation of the object refers to a correlative transformation of the subject” (Deleuze 1993, 19–20). Stated otherwise, changes in the form of the object make changes in the subject. Nevertheless, how can a form be modulated so that the corresponding power of the form is changed? Only through a radical intervention. In the “first instance” of folds, the subject does not discern the point of view. It seems that this point of view is a condition that occurs first in the development of the subject, on its way to emerging as a soul. Perspectivism does not imply a subjective relativism. “It is not a variation of truth according to the subject, but the condition in which the truth of a variation appears to the subject” (ibid., 20). The point of view is about a condition that is described in other terms as a “proximity of concavity” (ibid.). From this it can be concluded that this condition starts from the third fold. Why does Deleuze make these four categories, and why is the soul presented as gradually maturing? Everything seems to concern the final cause, the envelopment. The vortex is also named the “envelopment.” Spatial distance and virtual proximity According to Deleuze (1993, 22), “Leibniz can define extension (extensio) as ‘continuous repetition’ of the situs or position—that is, of point of view: not that extension is therefore the attribute of point of view, but that the attribute of space (spatium), an order of distances between points of view, is what makes this repetition possible.” This means that the attribute of matter needs distance between the points of views. The distance makes the spatium. Distance at the third fold is concavity. Deleuze states that the fourth fold is without distance; it is a situs without space, a non-distant space. It is a site of proximity. Such a site is temporal or virtual, and its condition is different from a three-dimensional perspective. Let us examine more closely the make-up of the fold. First, Deleuze presents the conical section (figure 2.16.9). The top of the cone is a point of view. There is no curve that changes into convexity. Deleuze divides the fold groups into folds of first and second degree. The second-degree folds are inflection whereas the first-degree folds are point of view and envelopment. 145 Elisabet Yanagisawa Figure 2.16.9. The point of view is a certain important fold, according to Deleuze. Why? “In each area point of view is a variation or a power of arranging cases, a condition for the manifestation of reality” (Deleuze 1993, 21). The point of view is a point that opens up a new relation to the soul. It is a passage to the power of the attributes, or, in other words, to the virtual or temporal. Deleuze continues: “We would need a more natural intuition to allow for this passage to the limit. . . . It is an envelope of inherence or of unilateral ‘inhesion’: inclusion or inherence is the final cause of the fold, such that we move indiscernibly from the latter to the former. Between the two, a gap is opened which makes the envelope the reason for the fold: what is folded is the included, the inherent” (ibid., 22). The final aim is the envelopment. To understand this metaphysics, it seems that one needs to be in the third fold—that is, the point of view—because it is at this site that things change perspective and are not the same as in the former folds, namely, the inflections. There is “a gap” between the conditions of the third and the fourth folds in terms of individual conditions. Simple intuition is something one might train and develop, if the potential is there. In other words, Deleuze is stating that intuitive knowledge depends on individual conditions. In reality, what does it mean that the envelope is closed? “It can be stated that what is folded is only virtual and currently exists only in an envelope, in something that envelopes it” (Deleuze 1993, 22). This seems to denote that an individual or a subject exists in reality as one of many (ordinary) individuals, looking like everyone else, but that “what is folded is only virtual”; that is to say, a person has the capacity for another perspective for seeing than those in the first, second, and third folds. The monad Deleuze (1993, 22) writes, “Inclusion or inherence has a condition of closure or envelopment, which Leibniz puts forward in his famous formula, ‘no windows,’ and which point of view does not suffice to explain. . . . It is necessarily a soul, a subject.” “No windows” means a closed condition (figure 2.16.10). Deleuze’s aim in this theory is to convey a message about the development of the subject/ soul as a process of individuation. The transversal from fold to envelopment embraces a development from actual to virtual, but folded within, the subject is a folded force. Moreover, the first two folds are spatial and the third fold seems to have a capacity to move between the spatial and the virtual, while the fourth fold is a non-spatial place, a fully temporal condition, but invisibly enfolded in a closure. 146 Figure 2.16.9. Cone. Illustration by Elisabet Yanagisawa, © Elisabet Yanagisawa. The Fold Figure 2.16.10. In order not to understand the envelopment as simply a state wherein all individuals meld into a universal spirit, Leibniz introduced the monad. The monad is an individual entity and simultaneously a term meaning the universal spirit. “He borrows this name [“monad”] from the Neoplatonists who used it to designate a state of One, a unity that envelops a multiplicity, this multiplicity developing the One in the manner of a ‘series’” (Deleuze 1993, 23). Giordano Bruno brought “the system of monads to the level of this universal complication: the Soul of the world that complicates everything” (ibid.). Deleuze’s theory of the fold is a development in this succession of concepts. Multiplicity means force. In Deleuze’s interpretation, the One envelops force, and reciprocally the force develops the One in different series and in different conditions of the fold. The monad is thus a gate, a passage for the universal spirit to transverse the two dimensions: the realm of the attributes and the power of the attributes. Deleuze contends that the immanent plane of consistency is the only way for these transformations and developments to take place. In the power of the attributes there exists only power, which is pure virtuality. It is in the immanent condition that the subject/soul undergoes this process. Deleuze (1993, 24) writes about the world soul or the Spirit: “It is therefore enveloped by an infinity of individuated souls of which each retains its irreducible point of view. It is the accord of singular points of view, or harmony, that will replace universal complication and ward off the dangers of pantheism . . . whence Leibniz’s insistence upon denouncing the hypothesis . . . of a Universal Spirit that would turn complication into an abstract operation in which individuals would be swallowed up.” The Universal Spirit or the collective mind is 147 Figure 2.16.10. The four folds and their conditions. Illustration by Elisabet Yanagisawa, © Elisabet Yanagisawa. Elisabet Yanagisawa the sum of all souls; it has transformed them through the point of view to allow another perspective. The human soul is divided into two parts, of which one is virtual and in the power of the attributes, and the other has a body in the plane of consistency. The perspective of the point of view compels the subject to get its passage opened for a kind of deep-seated intuition. The point of view is a gate to the virtual. When the soul is a monad, it distributes a closed and safe space for the collective mind. Series “The world is an infinite series of curvatures or inflections,” writes Deleuze (1993, 24), “and the entire world is enclosed in the soul from one point of view.” What is the meaning of the “series”? Each individual is a series of configurations, expressed through a singularity. Individuals are variations that undergo many “rhythmic and melodic” movements (ibid., 25). It appears that this refers to a continuous affirmable development, but they can “also follow the contrary, or retrograde, movement” (ibid.). As can the form of concavity and convexity, the development too can form in two directions, either forward or backward. The individual is a configuration in a series of configurations throughout the plane of consistency that express one’s soul. In the virtual realm, the non-space, however, the soul is a unique entity, encompassed by the world soul. Can this understanding become general knowledge? As demonstrated earlier, Deleuze (1993, 24) indicates that the comprehension of this metaphysical reality is vouchsafed as a condition in the point of view: “The point of view, the summit of the cone, is the condition under which we apprehend the group of varied forms or the series of curves to the second degree.” It appears that the position of the point of view is capable of apprehending both spatial and temporal perspectives, and it also “brings forth the connection of all the related profiles, the series of all curvatures or inflections” (ibid., 24). Deleuze poses a seemingly elementary question, why is it necessary to depart from the world or the serial order? Alternatively put, why is all this concealed in oblivion? Deleuze’s (1993, 25) response is simple: “If not, the theme of the mirror and of point of view would lose all meaning.” I only can add that this is something to contemplate. Perhaps, when it is kairos, we will awake and want to seek the answer and then we will understand individually as a realisation. What is the soul? Deleuze (1993, 26) states that the soul is an effect of this process: “The soul results from the world that God has chosen.” In what way has the world chosen the monad? The world or God has chosen each monad because it is the right time (kairos) for God’s life to exist through it. The monad is a gate between the spatium and the power of the spatium, that is, the virtual. Thus, the monad is a sensuous entity that perceives and expresses the development of the world. “The world must be placed in the subject in order that the subject can be for the world” (ibid., 26). 148 The Fold Conclusion To develop the world soul, the individual needs to develop from inflections to envelopment. Envelopment is proximity and a non-distant place, a virtual entity that is enfolded into the individual carnal body that still lives in strata. The soul is eternal and never dies, but it can become retrograde, degenerate, and turn in an opposite mode. If this is so, the development of the soul decelerates, and not without conflict and hostility toward other souls. By creating folds in strata, new folds in the virtual mode of existence are made. These constitute new codes, which become inscribed into the virtual grid. By creating sensible folds in strata, the properties double their existence into the virtuality. Potentials expand, life expands. The metaphysics of the fold is in fact the pure metaphysics of proximity and sensibility. References Baroque. Translated by Tom Conley. Deleuze, Gilles. 1988a. Foucault. Translated London: Athlone Press. First published and edited by Seán Hand. Minneapolis: 1988 as Le Pli: Leibniz et le Baroque (Paris: University of Minnesota Press. First Minuit). published 1986 as Foucault (Paris: Minuit). Guattari, Félix. 1995. Chaosmosis: An Ethico———. 1988b. Spinoza: Practical Philosophy. 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