Abstract
This article draws on data from a single element of a larger project, which focused on the issue of “how children develop a reputation as ‘naughty’ in the early years classroom.”1 The author draws attention to the (in)corporeal (re)formation of the line in school, undertaking a decomposition of the topological spaces of research/art/education. She attempts to decompose schoolchild iconography into the line as a product and subject of art practices, where it denotes space, gestures of containment, impulses to represent and make visible what might otherwise remain invisible. This experience of a methodological decomposition, (un)folding of the line in education into the line curated in the world of art, led the author to realize how the child could become not one idea and one image but many ideas folded into many images where the rituals and routines associated with the making of lines in school can be reconceptualized.

Untitled (1996), Louise Bourgeois.
This article aims to scrutinize educational ideas/images of the line as artifacts and performances of school culture, by decomposing them into the line as a product and subject of art practices, where it denotes space, gestures of containment, impulses to represent and make visible what might otherwise remain invisible. In a recent keynote presentation, Deborah Britzman remarked how in order to write, we have to destroy ideas and be able to repair them again. 2 This article hopes to do something of that methodological destructive and reparative work. Writing into the Deleuzian folds of possibility that provoke the continual deformation of ideas, I seek, to some extent, to quench my desire for a fantastic decomposition of the topological spaces of research/art/education. When discussing the idea of decomposition, Deleuze intimates that when a body encounters another body, or an idea another idea, it happens that sometimes one decomposes the other, destroying the cohesion of its parts. In this article, the decomposing encounters between research/art/education will attend to ways each discrete “body” of knowledge interacts and decomposes something of the other. Simultaneously, this process of decomposition bears a relationship with another Deleuzian idea, the fold, whereby, I would argue that for an idea to decompose or disintegrate, it is animated by a continual movement of folding and unfolding, “. . . to increase, to grow; whereas to fold is to . . . withdraw into the recesses of a world . . .” (Deleuze, 1993, p. 19).
Manifestations of the line take many forms in education, framing all manner of a child’s school experiences, including for example when children are asked to line up in the classroom, embodying a sense of linearity that seeks to curtail their every movement,
[Class is queuing up in the classroom, waiting to go out. T and two assistants are walking up and down the line]
T: OK. Let me see, is it the front the middle or the back of the line that’s the best part of the line. Ooh! It’s hard to choose today!
(Transcript of video footage
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This research article will use images of the line from the worlds of education and art to fold and unfold something of the straightened composition of the schoolchild, where the child becomes not one idea and one image but many ideas folded into many images. This will become an article of multiplicity where everything is always read and reread but we never see what it is we are reading in its entirety (Krissel, 2004). I turn to St Pierre (1997) to wonder what knowledge might be produced if an educational researcher (un)folds art into qualitative methodology that no longer seems adequate when “looking awry” (Žižek, 1991) at the child.
Qualitative Research in Education: Writing Into the Fold
. . . The outside is not a fixed limit but a moving matter animated by peristaltic movements, folds and foldings that together make up an inside: they are not something other than the outside, but precisely the inside of the outside . . . (Deleuze, 1988, pp. 96-97).
Matthew Krissel describes Deleuze’s fold as “. . . an ontology of becoming, of multiplicity, of a differentiation while maintaining a continuity . . .” (2004, p. 2). I want to use this concept of the fold in trying firstly, to understand something of the becoming of qualitative research in education, where differentiated moves to change, develop and shift the methodological field are always underpinned by a sense of, and commitment to ethical and political continuity. According to O’Sullivan (2011, p. 1) Deleuze’s idea of the fold is particularly mobilized in his books on Foucault and Leibniz, where the concept itself is put to work by one set of thoughts being folded into the thoughts of another. An example of how this idea might be evoked in qualitative research comes from MacLure (2011) who demonstrates ways that thinking becomes folded into the thinking of others. She mobilizes questions about the “crumbling edifice of Enlightenment” by folding them into the work of Patti Lather (1997), Bettie St Pierre and Wanda Pillow (2000). Her questions muse amongst ideas about “working the ruins,” already set in motion by these writers, presupposing that there are Enlightenment ruins to be worked. MacLure folds in her contemplations—“where are the ruins? Are things as ruined as we have hoped?” (2011, p. 998), thereby unsettling any assumption that we have managed to be ruinous, and yet knowing that without such an assumption having already been made, her own questions would have no legitimized (con)text. MacLure rearticulates an argument within qualitative inquiry that keeps nonlinear ideas (un)folding back into themselves to simultaneously keep opening up and folding in spaces for thought. Ideas are kept in folding motion as Flaxman (2009) suggests, one delicate strand of thought is woven into another, subtending a third, folded back over a fourth, unspooling in ever more idiosyncratic and wandering lines (cited in Jones & Roffe, 2009, p. 15).
Deleuze (1993) refers to what could be described as labyrinthine topological and texturological experience of different kinds of folds, the continual deformation of objects, where no boundary exists between the organic and the inorganic, but each is folded into the other, becoming ‘both and neither/nor’ (Lomax, cited in Doy, 2002, p. 156). I am mindful of this notion drawn on in the work of Helen Mills, who turns her attention to the stone draperies of early modern Neapolitan convent architecture, where she notes,
. . . an ambiguity . . . remains as to whether we are looking at stone that is oozing into folds, or at cloth that has petrified. Wall and space are crumpled . . . Materiality itself is thrown into question . . . Hangings of stone indicate spaces that are not, suggest possibilities that are impossibilities . . . (Mills, 2004, p. 271)
Across the field of postmodern qualitative research, there seem to be similarities in the methodological struggles intimated within Mills’ interpretations of the fold that allude to suggestion, representation, illusion, both and neither/nor and possibilities that are impossibilities—the emergence of new kinds of struggle inevitably involving the production of new kinds of fold (Deleuze, 1993),
. . . A folding across lines to create uncertainty between boundaries, instead of defined boundaries of separation. These uncertainties create the potential of a multiplicity of folding and unfolding; a re-reading of an architecture of becoming . . . (Krissel, 2004, p. 3)
Such methodological (un)folding into uncertainty and the potential for multiplicity in qualitative research, conjures intriguing ways to disrupt familiar and iconographic images of the child sitting and working in school, so often peppered with the implicit straightening mechanisms of the adult world (Bohlmann, 2010). Although in his work, Bohlmann is referring to these mechanisms as ways to maximize the possibility of the child’s ‘heterosexual outcome’ (2010, p. 1), I would argue here that the idea of the straightening mechanisms of the adult world could evoke more intricately pervasive thoughts, particularly around the adult’s ubiquitous tendencies to curtail, rather than embrace children’s wonderfully relentless propensity for disruption, disorder, confusion and obstruction. I would argue that disruptive processes to the many different forms of adult straightening mechanisms in school, juxtaposed with art images might incite new kinds of struggle involving the production of different kinds of methodological folds, imagined as a series of effusive e(ir)ruptions in educational contexts, “. . . a space of groundless depth from which irrupts something that creates its own space and time . . . .” (Rajchman 1998, p. 16).
In similar ways to the surge of changes, movements and ruinous approaches to qualitative research, I hope to evoke a sense of being straightened as continually compromised and menaced by Deleuze’s idea of the fold, who’s function is to “avoid distinction, opposition, fatal binarity” (Badiou, 1994, p. 54). I suggest here that details taken from images and representations of the school child in fragmented association with images from the world of art will enable each to be decomposed, existing in the fold, “. . . what always matters is folding, unfolding, refolding . . ” (Deleuze, 1993, p. 137), being constantly in the process of redefinition and discovery (Tierney, 1993, in McDonough and McLaren, 1996). Decomposing the idea, image, and other manifestations of the straightened schoolchild into particular art images allows each to be dragged and dispersed among its own and each other’s mundane detail (MacLure, 2011, p. 1000). This process might enable us to accept something of the images’ loss of a previously stable and affirming identity and as Atkinson (2001) suggests, the opening up of new worlds which this affords. By folding images associated with school into pieces of art and research data, the following section of the article will attempt to play with the ideas of the fold and decomposition to unsettle usual patterns of association, assumed bodies of discrete knowledge that foreclose possibilities. I want to unfold the straight line from school into art,
. . . to bring other theories and identities to the fold with it—the straight and the perverse (Butler, 1993), the rationalist and the rhizomatic (Deleuze & Guattari, 1987), the emancipatory and the troubled (Lather, 1997; St. Pierre, 1997) so that we are . . . engaged in working at redefining, relocating or deconstructing the boundaries by which we create our patterns of thought and inquiry in the postmodern world . . . (Atkinson, 2001).

(left) Gormley (2000) and unidentified image (2005)
Deleuze notes that it is not the line that is between two points, but the point that is at the intersection of several lines (1993, p. 219). I am mindful that it is the child who captures my imagination as the point/curve/fold that unravels, (un)folds, causes the leakage of something at the intersections of the lines summoned in school iconography. Interestingly, “line” is found in discipline, cleanliness, guideline, outline, masculine and many more terms that conjure a colonial civilizing process. In the United Kingdom over past decades, school photographs, as well as routine classroom and playground behaviors in school, exude a profound and rather obsessional relationship with lines. Reisman (1985) proposes that minutes and hours are interred in lines as children become inculcated into the rituals associated with being able to (re)form this self-replicating tapeworm-like organism again and again. Notoriously manifested in the choreographed arrangement of children sitting or standing in horizontal rows/lines for the class or school photograph, we observe lines in many forms occupying incorporeal places and spaces, as well as bodies in school.
From the edges of the carpet clearly demarcating where the children are to sit, lines frame all manner of a child’s school experiences. For example, lines drawn on the playground to enable ball games; children forming ‘beautiful and orderly’ lines in the classroom, in the hall, in the playground; errors being underlined; singing a line of a song; working with number lines; sitting with straight backs to form bodily lines with fingers forming a vertical line across the lips to listen to a story or hands up to make another straight line to answer questions. There have been punishments that involve writing lines; handwriting practice that uses differentiated lines to guide lower and upper case letter formation; the construction of story lines, indicators of children’s achievement within Literacy; the learning of lines to excel in the Christmas production or Eid assembly; sitting in lines as the children file into the hall and sit down in class rows for the assembly.

Unidentified images (2004, 1961)
In the U.K. Early Years Foundation Stage (Department for Children Schools and Families [DCSF], 2008) there are numerous references to the idea of the line. The Early Learning Goals state that young children are expected to be able to push a toy in a straight line; draw lines using gross motor movements; understand that they can use lines to enclose a space; understand a story line or narrative; and adults should chalk a line for children to follow. Although there are no suggestions that young children should learn how to make bodily lines, at 40 to 60 months old, s/he is expected to value and contribute to her own well-being and self-control by working as part of a group or class, taking turns, understanding that there needs to be agreed values and codes of behavior for groups of people including adults and children, to work together harmoniously (DCSF, 2008, p. 34). These ideas of self-control and agreed codes of conduct, echo Reisman’s study of the microlegal system of queues (1985), where the ability to line up contributes to the maintenance of public order and a civilized society. Adults/Teachers “. . . police the norm in order to increase the likelihood of aggregate conformity to the norm in the future . . .” (Reisman, 1985, p. 444).

Research video footage (2007) and Germinal (1967), Louise Bourgeois.
Given such a landscape of education riddled with the making of lines, I am intrigued by Mitchell’s work on the relationship between textile and architecture. This work prompts me to consider how thread begins as a line drawn out as matter through the action of spinning (2006). Thread(s) reaching, as they spin through space serve to demarcate, but for Deleuze (1986), the point is to make those threads unfold, irrupt, twirl, vibrate, tangle or break. My unfolding work here leans to this idea of twisting threads as I fold images of the child in school iconography into artistic images, twisting epistemological threads to the point of discomfort, destabilizing the viewers’ ontological security, by defamiliarizing the everyday versions of children and engaging with the unhomely in the domesticating projects of school (MacLure et al. 2010). As a menacing contributor to the straightening mechanisms of the adult world (Bohlmann, 2010), I am preoccupied by two questions arising from the apparent making of lines in school iconography: what is communicated visually and affectively by the making and remaking of lines? And second, how can we go about interrupting what feels like the violence of the line? Throughout the following section, these questions will be opened up, by folding thoughts of the line in school into images of the line in art.
The Line: Claiming Space for Sight
Mitchell (2006) writes that a line of thread cuts through space like an incision, marking a passage for sight. In the process of defining what does not seem to be there, Fred Sandback’s sculpture (below) defines what is there. Before Sandback’s threads of fine steel give physical form, together with impressions of incorporeal palpability to the space his work delimits, the expanse of (gallery) space is impenetrable, unperceivable, which could suggest our understandings of that space is limited, as it has no definition.

Untitled (sculpture Nr. II) (1968/1983), Fred Sandback.
Deleuze and Guattari note, “. . . there is no line separating earth and sky; there is no intermediate distance, no perspective or contour; visibility is limited . . .” (1987, p. 421). Children running around and playing in the school playground evokes similar feelings of potential open and undesignated space(s) that become carved up by the use of lines painted on the ground for ball games and children’s bodies being lined up at the end of playtime. The introduction of, and insistence on lines in this context constructs something of our particular need to understand space, architecture and the child. The playground offers children the space to unravel, scatter, chase, hide, crouch, stretch, and turn, but as they become organized by the lines painted on the playground, children make a different kind of sense of an expanse of nonparticular grey tarmac. The painted lines evoke the tennis baseline, or football centre line, they prompt games played on a court or pitch, carving meaningful spaces out of/on the ground. Similarly to the organization of the painted lines, the teacher’s whistle blows and their bodies freeze, becoming fine steel rods. They become static sculptures that seem to exude a strong sense of resilience in relation to taking control of movement. Mitchell (2006) writes of how the thread, once pliable, wound, twisting, supple and soft, changes to extend uniformly in a single, linear direction. Marking the end of playtime, lines emerge, creating a fine scaffolding of apparent and material structure (Mitchell, 2006), children become straight and taut, conferring order within a complexity of sense impressions, constituting an organized or organizing perception of space (Mitchell, 2006, p. 345). Deleuze and Guattari write of “. . . an extraordinarily fine topology that relies not on points or objects, but rather on haecceities, on sets of relations . . .” (1987, p. 421). In contrast to the more fluid state of the children at play in the playground, suddenly their bodily lines give a sense of the “thisness” of the space becoming striated with what Marcussen (2008) might suggest are enclosures almost like roads that exhibit constancy of orientation and metric regularity. The lines cut through the space of the playground, making it almost tactile, making hidden sight/site lines of the schoolchild visible once again as a mapping of outdoor space and the children become tamed through the structure of the line. The children become more recognizable as ordered, calm, composed before entering the school building. Children making lines in the playground, similar to the lines created in Sandback’s work, bring order to what it is that adults are looking at that might otherwise remain invisibly disordered, fluid and chaotic. This leads me to consider Étienne-Jules Marey’s work experimenting with lines and ways to tame/capture movement.

Experimenting with lines in motion (1894), Étienne-Jules Marey.
Marey was interested in analyzing the walk of man and of horse, the flight of birds and insects and in 1873 published La Machine Animale. He went on to study lines in motion, using the idea of movement to interrupt the line as well as the line being put to work to capture (apprehend, take possession of) movement. In 1899, he was pursuing a line of thought constantly present in his work: How could one observe the invisible? Perhaps one way is to interrupt what is visible, what we can see—in this case, the line.

Smoke machine study of the movement of air (1901), Etienne-Jules Marey.
Marey’s photographs of the smoke machine (above) show how the shapes of wisps of smoke differed according to the obstacles encountered in their trajectory. To interrupt the lines of air/smoke, an obstacle could be placed in the middle of the trails, allowing the viewer to observe how different shapes affected the airflow. This work provokes thoughts around the child who refuses to line up satisfactorily, “. . . Satisfactory behaviour at school is no longer good enough… the government’s behaviour expert said today . . .” (Times, Nicola Woolcock, April 15, 2009).
. . . the teacher asks children to line up ready for playtime. Once she’s left the room (leading the line out to play), Jake pretends to stab himself in the stomach, says “Aargh!” and falls to the floor. A couple of the children who were behind him in the line, step over him before he jumps up and re-enters the line . . . (Limefield
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Research video footage (2007). Smoke machine study of the movement of air (1901), Etienne-Jules Marey.
In the video still above, children are lining up with their coats on, waiting to go out to play. There is one child refusing to line up “satisfactorily.” As Reisman (1985) notes, like a benign nucleus of fury at the mere fact of having to wait, he turns around to face the opposite direction and taunts the boy behind him. He attempts to initiate contact with another member of the line, who responds cautiously because lining up norms are being violated. This child becomes the obstacle encountered by Marey’s wisps of smoke, altering the airstream, a point of resistance. He articulates both the orderliness of other children in the line as well as an interruption to that order. My eye is drawn towards him, he is perceived as problematic, but simultaneously gives shape to what otherwise cannot be seen.
Marey’s early experimenting with obstacles and airflows have been used more recently in lethal ecology work (Tavares, 2008), where airflows appear as a central element of intervention in the preservation of the life of populations. These ideas lead me to question how the child refusing to line up satisfactorily, becomes a case where the necessary folding of a “hazardous” into the atmosphere (Tavares, 2008) against the uniformity of the line, serves to reinscribe the parameters of schoolchild (dis)orderly conduct. Any “disorderly” child is seen to pollute and contaminate the form of the line (itself representing/signifying order), interrupting the airstream, unfolding awkwardly into the urban fabric of the classroom.
Within the works of Sandback and Marey there is a sense of the line as ordered chaos, making still and then mimicking a sense of movement and/or deliberate obstruction. In school, perhaps we call upon the line to make order from maelstrom, as children are required to calm their energies, yield to this straightening mechanism, yet some cannot do this, or maybe do not realize they are expected to do this, or even decide they do not want to conform in this way to the line. Reisman (1985) suggests people who are able to stand in line, “. . . must think in terms of linear time and space in order to participate in this type of organization . . .” (1985, p. 423), which raises interesting thoughts around the psychological, physical and bodily order necessary for the child to at least mimic ordered chaos, of the mind, of a disciplined body, of the teacher’s skills to render the child “proper” or appropriate (Jones et al., 2010). Sandback hints at ordered space, something that tames the disorderly chaos of unfocussed sight, “. . . grasping control through which the space of the body can reach out into the world as ‘straightness’ of a line and as an ‘ordering’ of spatial relationships . . .” (Mitchell, 2006, p. 345). Perhaps his work helps us to frame space so that we can understand that space in more recognizable ways—we know what it is we are supposed to be looking at and how we are supposed to be understanding what we are looking at. Similarly to Massumi’s notion of simulation,
. . . an effective illusion . . . reinjected into reality and sets to work . . . It abstracts from bodies . . . a transcendental plane of ideal identities . . . Then it folds that ideal dimension back down onto bodies . . . in order to force them to conform to the distribution of identities it lays out for them . . . (Massumi, 1987, p. 93)
The organization or lining up of children’s bodies in space begins their conformity to the distribution of more recognizable pupil identities that the straightening process of school(ing) lays out for them. Those that refuse to line up satisfactorily are deferring one particular “proper” identity for an alternative transgressive identity that nevertheless becomes as pervasively recognizable and (dis)reputed as the former.
The Line: A Pathway Done by Sewing, but Hidden in Plain Sight
In 1913-1914 Duchamp made the 3 Standard Stoppages, three pieces of thread fixed in the random curves into which they had fallen. He referred to the results as “canned chance” and mounted them like specimens in a natural history museum. Duchamp later made, three wooden measuring sticks based upon the curves of the fallen threads (see image below), and then declaring them to be a new measuring system, put all the elements of his system in a croquet box. One of the concepts here was perhaps to become more aware of generalizations, Duchamp spoke of how the mind uses them in constructing reality (Gold, 1958).

3 Standard Stoppages (1913-1914), Duchamp.
Duchamp’s 3 Standard Stoppages is suggestive of ways I can begin to conceptualize the line as a more chaotic, nongeneral phenomena, perhaps questioning whether things that I presume to be absolute or contrived, may be so, or merely “canned chance” (Duchamp, 1914), or something of a complex version of both and neither/nor. This work provokes a series of thoughts for me in relation to the idea of the bodily line in school: the chaos of chance encounters being tamed in pursuit of being able to generalize and standardize notions of the proper child. The paradoxical notion that Duchamp’s work is built around an element of chance, yet when asked about the laws of chance in his work, Duchamp opens up a challenge to us, “. . . I have hidden this in plain sight. I have given you deliberate hints. Why don’t you be critical and look carefully . . .” (Shearer and Gould, www.toutfait.com, 1999). The idea of chance might intimate this piece of work almost produces itself, at a distance released from the control of the artist, creating a kind of unsigned piece, yet simultaneously it is also saturated with Duchamp’s signature playfulness. This returns me to the idea of the teacher’s gesture used to prompt “proper” classroom behavior. A knowing glare in assembly, a touch on the shoulder in the line, a holding of a hand in the playground, or an encouraging comment on the carpet can/should render the child’s behavior more appropriate. Although these practices seem like various degrees of a relatively light touch and in some instances a hands-off approach, moving towards a corporeal discipline, they do seem unsigned, practices almost removed from specificity as they are not associated with any one teacher. Simultaneously they are riddled with authority, contributing to a process of proselytizing by daily regimes of school(ed) order, conditioning expectations, layered with each child’s undertaking and responsibility to conform. These are standard practices relating to the nurturing of standardized behaviors.
Data from our ‘Becoming a Problem’ project suggests teachers continually reinforce the making of children’s bodily lines by “asking” them to sit beautifully/properly/nicely, put hands up and wait to be chosen to speak (MacLure et al., 2010, p. 12). These general persuasions for children to display bodily order (mimicking specimens in a natural history museum) are laden with unspoken expectations that render the child appropriated (or not) by the age of 4 or 5 years. In the classroom or in assembly, teachers might glare, touch, make comments or offer suggestions to children, “Now let me see who is sitting beautifully . . .” (Assembly, Martinsfield
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). In response to such comments, most children seem compelled to make particular associations with terms such as “sitting sensibly” or “beautifully” by performing a whole series of necessary adjustments to their bodies. This often involved them making sophisticated interpretations in order to render themselves appropriate and proper,
. . . Being “sensible”—a common term for appropriate behaviour—may be significantly open to interpretation . . . Ellie, . . . must inspect her own past behaviour and future intentions, and identify the nature of Mrs F’s dissatisfaction with her, in order to know what she will have done in order to “behave more sensibly . . .” (MacLure et al., 2010, p. 13)
Most children knew that sitting beautifully, properly or sensibly meant they were expected to cross their legs, sit up with backs straight, stop talking with fingers on their lips. So the children embodied standardized responses to ritualized classroom practices and expectations reinforced throughout the whole school on a daily basis. However, although most children can recognize and decipher the necessary inferences from a teacher’s signifying glare, touch or comment, there are some who cannot interpret the brief signals. There are also those who can, but nevertheless choose to respond in unexpected ways. An element of Duchamp’s work represents a complication to the idea of sameness and standardization. Duchamp (cited in Moure, 1984) emphasizes that it is the relation among the three thread events in approximate reconstitution of his measure system in 3 Standard Stoppages that diminishes the authority of the meter. He tells us that his new measurement scheme takes the relation among events as the measure. So, in looking at the standard practices in school to establish “proper” bodily lines, it is the relations that move intricately among child(ren) and move menacingly between the child(ren) and the adult(s) that become the interesting “measure” of how the “proper” child is constituted, reinforced and maintained. Here Shearer and Gould’s reflections on this aspect of Duchamp’s work becomes relevant,
. . . one can only appreciate the deep and delicious irony, the provocation of thought, and the tweaking of the most literal of all conventions—for the meter was defined . . . as a new and liberating device, based on the size of the earth itself . . . and therefore constant, unvarying, and capable of serving all people as an absolute standard . . . (www.toutfait.com, 1999)
Duchamp’s joke about the meter involves a claim that the three one meter-long threads were dropped from a height onto a plane, each twisting as it pleases, creating a new image of threadness and meterhood. Duchamp (1960) states that even though the meter does not completely lose its identity, our doubt must lead us to give up our belief in the absoluteness of the old perspective of the meter. This fortunate “loss of identity” returns me to the child who does not respond to the teacher’s prompt to become “proper” in the classroom. Those children who, via Duchamp’s falling, twisting thread, also seem reminiscent of Marey’s obstacles in the airstream, where some children “. . . always exceed the pathways of the stoppages in degrees of irregular wiggling . . .” (Shearer & Gould, www.toutfait.com, 1999). Each interrupts the rational basis of the classroom, as they collapse onto and get secured into the canvas of the classroom as “non-standards.” They become a new representation of the same unit of length (the child), but with a resistance to being logical and rational.

Research video footage (2007)
In the still images taken from research video footage above, two boys articulate moments of both the implausible imagining of Lomax’s both and neither/nor (cited in Doy, 2002, p. 156)—both, and neither familiarity nor shock. When a disruptive child is part of the classroom/school, he is still a child, a pupil, but s/he is not the same, as s/he refuses to partake in Massumi’s effective illusion of the whole. Some children refuse to conform to the distribution of identities set out for them (Massumi, 1987). They do not (always) sit up straight with legs crossed and hands on their laps. Instead, one boy here shows his fists to the teacher as she takes the register, repeatedly refusing to cooperate with her despite her frequent requests to “sit nicely on the carpet.” The other boy is expected to sit quietly in the hall, but intermittently waves and flaps his arms and hands around in the air throughout the assembly. Shearer and Gould (1999) point out that there are many contradictions in Duchamp’s 3 Standard Stoppages. For example, contrary to Duchamp’s claim that he dropped three pieces of string, each exactly one meter long, each from a height of exactly one meter, and each only once, onto a canvas, gluing each string to the canvas in the exact position of its chance fall, they propose that the pieces of thread were carefully sewn into the fabric feigning chance encounters. Interestingly, there are instances where the “non-standard” (behavior of the) child resists the lure of (con)forming bodily lines and chooses not to fall into the fabric of the classroom/school so straightforwardly. Does this child need to be made secure by being sewn into place, requiring firmer intervention? Ellie (below) does not make the necessary associations expected of her. Despite previous prompts from the teacher, she refuses to sit up straight, cross her legs and keep her finger on her lips, so the teacher makes necessary (a)mends by leaving far less to chance and instead, sewing Ellie more tightly into position:
. . . Mrs F starts a whole-group activity on the carpet. Ellie, come and sit by me. Why? Because you’ll behave more sensibly, that’s why . . . (MacLure et al., 2010, p. 13).
Duchamp’s work encapsulates the Readymade idea of taking the concrete and applying nonconcrete ideas to it. Here, this aspect of his work has been folded into the idea of children’s resistances to forming bodily lines in school and represents a stoppage or “invisible mending,” a pathway done by sewing, but hidden in plain sight. Shearer (1998) notes how an invisible mending among events, despite their differences, represents what we must do to make any generalization. It is worth contemplating what “invisible mending” teachers (need to) do to the child who is not compliant but hazardous in all her glorious curves, contours and nonlinear differences.
The Line: Rereadings of an Architecture of Becoming
[Nathan, Joshua and Kyle are at the drawing table. N draws some lines across J’s paper]
I’ll do a gun. Do you want a gun?
No, rockets don’t have guns do they?
This isn’t a gun anyway, it’s a telescope . . . anyway I’m off.
Look at my mint rocket
I know . . . I’ve seen it
I’m drawing an astronaut now (Limefield 6 ).
Interestingly what began on Joshua’s paper as a series of lines, soon became the imag(in)ing of a gun, a rocket, a telescope, an astronaut. Out of the singularity of the line came an (un)folding of a multiplicity of possibilities, some of which constitute disruptive hopes (the gun) hidden among more acceptable imaginings. In this latter section, I want to move toward a sense of the line as more deliberately disruptive to how I might look at the idea of the child in school. In school iconography, the formation of the line seems to have evoked a distraction from other potential ways of looking at the child, the teacher and schooling practices. However, the artistic eruptions folded into this paper (and in the classroom dialogue above) have helped to draw attention towards the complexity of the child (un)folded in school as integral to the straightening mechanisms of the adult world (Bohlmann, 2010). However, with my desire to straightforwardly know, understand and in doing so, “tame” the child still hanging flimsily in the balance, together with urges to untangle the complexities and straighten out the dilemmas presented herein, as my quasirealist longings lurk menacingly in the anterior of my mind, I want to return to ways the line in art can be folded in to frustrate further those fragile yearnings.

Installation view of First Papers of Surrealism exhibition, New York, 1942.
The whole purpose of Duchamp’s Sixteen Miles of String exhibit (contributing to Andre Breton’s First Papers of Surrealism exhibition) was to veil or distort the gallery paintings from the viewers. According to Filipovic (2010), Duchamp even invited some children to play ball or jump rope as part of the exhibit and when some gallery spectators complained, the children replied as they had been instructed, “Marcel Duchamp has asked us to come and play here” (www.toutfait.com, 2008). Duchamp’s tangled mesh does not cut off vision completely, as it seemed to be the frustration, not the elimination of sight that is desired (Filipovic, 2010). Nevertheless, Duchamp’s entwinement between and in front of so many of the things “on display” constituted a decided barrier between the spectator and the works of art. According to Vick (2008), several of the artist-participants were disappointed that spectators could not properly see their artworks due to Duchamp’s mesh, which was precisely the point. He suggests the installation has generally been discussed in terms of separation and dislocation—the twine deemed a dividing barrier, or what Demos calls “. . . the maximal obstacle between paintings and viewing space . . .” (2001, p. 94). Although the extent to which Duchamp’s twine obstructed the art exhibition is contentious, the idea that his installation would be concerned with new, intriguing, and even playful methods of looking at art is not surprising (Kachur, 2003). Vick (2008) claims that experimenting with sight was for Duchamp a lifelong preoccupation—a work like To Be Looked at (from the Other Side of the Glass), with One Eye, Close to, for Almost an Hour (1918) predates the exhibition and demonstrates an early example of how Duchamp chose to engage the practice of looking.
These notions of using lines of thread to distract, frustrate, reference, distort and veil an otherwise unfettered line of sight are intriguing. They revert back to either/or scenarios, where we have either a clear or hampered vision and understand children as either limbs of Satan, or angels of innocence (Eckstein, 1967). I return momentarily to Marey’s smoke machine that caused the object/obstacle to become visible. If we were ever able to clear the classroom space of Duchamp’s sixteen miles of string, Marey’s obstacles and disruptions to the airstream (whether behavioral, conceptual, ideological, social, cultural, political), would we not begin drawing new lines, constructing new obstacles, so that we can reposition ourselves in different ways, in an attempt to tame the disarming uncluttered space(s) that Fred Sandback’s incorporeal palpability renders understandable? This leads me back towards what is becoming a circuitous argument, with the lure, familiarity and safety of quasirealist longings of classroom video footage that claims to unclutter, capture, decipher, notice and attend to the child’s figure as distinct from the fore/back/ground in evidence-based ways, “You may make a rupture, draw a line of flight, yet there still is a danger that you will stratify again everything . . .” (Deleuze & Guattari, 1987, p. 10). With a desire to resist be(com)ing uncluttered and to stratify once again, I want to return to the idea of decomposition.
Decomposing Folds
This is not a article that seeks to stop children being lined up in school, for the class photograph or in the playground, although if that is a potential outcome, so be it. It is not seeking to find a solution to the more pervasive straightening mechanisms that seem to infest the adult world, but if it causes pause for thought on this, so be it. However, it is a methodological unfolding, decomposing, destroying and repairing of ideas that find form in education/social science research/art, so as to rethink those ideas in new ways. Despite being started a couple of years ago, this article, these ideas remain always germinal, being in the earliest stages of their development. Here, I am mindful of the notion of germination, where something has to be ‘put back’ (a process of fertilizing) so that the exhausted, repetitive, and barren elements of education, such as the (re)making of lines in school and qualitative research methodologies, can in a sense be rejuvenated. As with the Deleuzian decomposing fold, the process of rotting, disintegration and breaking down, renders my writing interminably deferred into a continual movement of folding and unfolding into the destruction and reparation of the next idea, but in preparation for the “earth” to be invigorated. Enthusiastically I hold onto the possibilities that continue to menace my interminable relationship with the writing of these ideas, as my daughter once commented pointing to one of her found objects: “. . . and this one . . .” she sighed, “. . . I don’t think this will ever be finished . . .”
Louise Bourgeois’ sculpture “Germinal,” turns me to the flourishing of ideas that have surfaced momentarily in this article, as they fold and unfold, decompose, are destroyed and then repaired, lures me to images of fertility, quivering, swelling, cracking and overflowing life whispering itself ceaselessly into being. With these ideas in mind, I turn back into Deleuze’s notion that it is not the line that is between two points, but the point that is at the intersection of several lines (1993, p. 219), “. . . at the cross point of countless social threads . . .” (Frisby, 2002, p. 187), “. . . in an open-ended swirl of extensions and supplementations . . . as they pass through different assemblages . . .” (Lee, in Prout, 2005, pp. 115-116). My focus throughout this article has been on the idea of a methodological (un)folding of the line in education into the line curated in the world of art, evoking a process existing in the fold of mutual decomposition. It has been variously conceptualized as a thread, a fine steel rod, vapors of smoke and multiples of children stretching in a tapeworm-like structure between two points. But how can these ideas be reorganized to accommodate the significance of the Deleuzian point as the intersection of many lines? How can the world of art provoke such a conceptual move, where the child becomes not one idea and one image but many ideas folded into many images? How might this shift from the singularity of the line to the potential multiplicity of the point help reconceptualize the rituals and routines associated with the making of lines in school or at least how these rites are understood?
Interesting “points” have emerged over the documenting of the line in this article, which include for example the potential interruption of hazardous obstacles; the line as carving space for site/sight; the relations between child(ren) and adult(s) as “measures” of what constitutes “proper”; and the line as a mechanism to disrupt and frustrate habitual ways of looking. These ideas seem to coalesce around the practices of making of lines, whether those lines are (in)corporeal, metaphorical, physical, ideological or political. The “points” unsettle the dichotomies of being in or out of line or being on one side or the other as they persist in being both and neither/nor. For example, a child who refuses to stand in line “properly,” sit up straight, put her finger on her lips and play by the (linear) rules, transgresses the system that enforces the norm, confusing the disciplining mechanisms that contribute to classroom order. She becomes a visible obstacle that diffuses Marey’s smoke, interrupting the sedation of the linear community, potentially becoming of point of interest, where multiple lines/curves/folds intersect. However, the recourse to familiarity, our habitual consciousness of such classroom events singles out the child as solely responsible for her own disruption to the multiplicity of straightening mechanisms operating in school that lie potently amongst liberal humanist discourses that resist denying the child’s agency to disrupt. With thoughts of the multiple uses of the line in art and returning to a Deleuzian thought, this recourse seems hopelessly inadequate, “. . . the conditions under which we know things . . . condemn us to have only inadequate ideas,[emphasis in original] ideas that are confused and mutilated . . .” (1988, p. 19). Being mindful of Deleuze’s notion of inadequate here as infused with knowing these ideas will always only ever be incomplete and partial, I do want to take up a more mundane notion of inadequacy to explore other possibilities here. Perhaps the child who will not line up or sit up still and straight confuses and mutilates a satisfactory decomposition that would usually render the teacher/child encounter harmonious. The child threatens the coherence of the encounter by jeopardizing the effects anticipated by the teacher/adult. The line is a standardizing mechanism by which the child and adult/teacher are, in this instance, suspended in a public stand-off, both unable to be rendered ‘proper’ as neither is able to accept their retrospective positions that assume authority or compliance adequately. The decomposition between the adult/child encounter remains awkwardly st(r)ained. The child should be in the line, but is not. The adult/teacher is imbued with privileges that mean she does not ever have to be in that line, but presides over it as a trophy and accomplishment. Here, the in/out, authority/compliance dichotomies flare up like a red rag to a bull. However, if we return to the Deleuzian idea of the point as the intersections of many lines, the inadequacy of the singular line in decomposition becomes apparent. Rather than acknowledging the accomplishment of the line and admonishing the refusing child as an obstacle, how can we see the decomposing encounters between child and adult/teacher as germinal, moments of fertility, quivering, swelling, cracking and overflowing with life whispering itself ceaselessly into being?
A child and a teacher/adult are both corporeal points where multiple gendered, racial, cultural, class lines intersect. Perhaps it is the unfolding decomposition of these unknowable, unfathomable, inadequate knowings of such intersections into each other that creates a cacophony of white noise, a fascinating theoretical construction. With a saturating combination of all lines that dissect, skirmish, underline and enclose the be(com)ings of the child and adult/teacher, the simultaneous point of both and neither noncompliance nor lack of authority, the experience of both and neither familiarity nor shock at the refusal to line up unfolds into the classroom encounter. The sharpness of the line fades into a discordant white noise where everything is experienced and nothing is decipherable.
Any intimation that lucidity and coherence render our ability (as researchers, as artists, as teachers) to see in uncluttered ways, becomes unsettled and unlike the quasirealist video footage, the child’s (and adult/teacher’s) figure becomes far from distinct from the fore/back/ground. Perhaps Duchamp’s work allows us to return to Deleuze’s idea of the fold, “. . . The fold can begin to reconsider questions of figure/ground contextualism. No longer creating a separation of figure/ground . . . but one where a continuous and reversible dialogue can occur . . .” (Krissel, 2004, p. 2). Here, lines of distraction, reference, distortion become both, and neither integral nor menacing to our vision of the child. The line can be understood to forge some order from chaos; bring stillness from movement; make visible what might otherwise remain inconspicuous; instigate unsigned chances where haphazardness and serendipity foil plans to anticipate or predict; distort and reference vision without foreclosing possibilities. Each one of my many encounters herein seems to demarcate the idea of the line as crucial to its own inevitable disruption. The line brings uneasiness to the ideas of chaos, vision, space, stillness, movement, sight. These frustrations by, desires for, dreams of, or disruptions to the line return me to Deleuze,
. . . A fold is always folded within a fold, like a cavern in a cavern. The unit of matter, the smallest element of the labyrinth, is the fold, not the point which is never a part, but a simple extremity of the line . . . (Deleuze, 1993, p. 18)
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Economic and Social Research Council [RES-062-23-0105 and RES-189-25-0122].
