Studies in Philosophy and Education

, Volume 32, Issue 4, pp 379–395

Mapping Teacher-Faces


    • School of EducationMurdoch University
  • Ian Cook
    • School of Politics and International StudiesMurdoch University

DOI: 10.1007/s11217-012-9335-2

Cite this article as:
Thompson, G. & Cook, I. Stud Philos Educ (2013) 32: 379. doi:10.1007/s11217-012-9335-2


This paper uses Deleuze and Guattari's concept of faciality to analyse the teacher's face. According to Deleuze and Guattari, the teacher-face is a special type of face because it is an 'overcoded' face produced in specific landscapes. This paper suggests four limit-faces for teacher faciality that actualise different mixes of signifiance and subjectification in a classroom in which individualisation and massifications are affected. Understanding these limit-faces suggests new ways to conceive the affects actualised in the classroom that are subjected to increasing levels of surveillance from education policy makers. Through this ‘partial mapping’ new possibilities emerge to “escape the face”.


FacialityTeachers and teachingDeleuze and GuattariEducationSubjectificationSignifiance


Teaching and schooling are among the most conspicuous practices, institutions and achievements of late-capitalist liberal-democracies. This has resulted in education’s continuous subjection to oversight and regulation. This concern with the teacher has long been present, but new ideas and techniques for overseeing teachers have resulted in teachers, in countries like the UK, USA and Australia, becoming enmeshed in intensified regulatory spaces (Ball 2003; Greene 2000; Troman 2008). The teacher has always been scrutinised by education policy-makers and parents, but the emergence of the performance culture has given rise to a new emphasis on teachers’ performances (Thompson and Cook 2012). This, when coupled with the increased prevalence and effects of high stakes testing (OFSTED, Race to the Top, NAPLAN), has opened the classroom to even greater scrutiny and, as Deleuze suggested, has opened out an otherwise enclosed space. The corporeal manifestation of the teacher can be understood to characterise the formerly fully enclosed space of the classroom, so with these changes has come even greater concern for the teacher in the classroom; which, for us, requires mapping of teacher-faces in the classroom. What does the face of the teacher have to do with education? Everything, because education policy is grounded in certain theories of the subject, “and if the subject changes, everything else must as well” (St.Pierre 2004, p. 293).

Deleuze and Guattari wrote that the art of philosophy is in “forming, inventing and fabricating concepts” (Deleuze and Guattari 1996, p. 2). In this paper we are using the concept of faciality to suggest a new concept of the teacher; we are not critiquing Deleuze and Guattari’s ideas, we seek to apply them, to map and suggest how we could move beyond the teacher-face landscape. In this spirit, we apply the work of Deleuze and Guattari to teacher-faces and understand them, not as parts of an individualisation process, but as a pre-existing set of virtualities that actualise in the classroom as interactions between many four-eye machines of faciality. Teacher-faces do not belong to bodies but to abstract machines at work in the classroom. Indeed, teacher-faces do not belong to teachers, and do not embody teachers. Teacher-faces may appear visible as concrete faces, but as virtualities they are four-eye machines ordering affects within the classroom.1 That these four-eye machines are at work in the classroom suggests one of the most important of the attributes of the teacher-face: that the teacher-face has a landscape, for “as well as producing a subject, faciality also produces the world he or she moves in and through” (O’Sullivan 2006, p. 311). In the theorisation that follows, faciality is both of the landscape and constructs the landscape.

The classroom is a landscape that evokes faces limited by the striations that order both that space and the bodies that periodically move within that space. This paper focuses on four face-landscapes at work within the same site (acknowledging that there are more possibilities and face-landscape permutations than we can illustrate). We employ Deleuze and Guattari’s “limit-face” to refer to the four faces we elaborate. The concept of ‘limits’ here is intended to imply parameters and not perimeters. Limit-faces are best understood as zones of probable intensities, or regions on maps where “gestures and movements” are resituated “thereby opening them up to possible lines of flight” (Deleuze and Guattari 2005, p. 14). The landscape of the classroom, and the extent to which the school functions as a disciplinary space of enclosure, ensure the normalisation of teacher and student selves, and requires that the school be “embedded in the past” (Symes and Preston 1997, p. xiii). Profound consequences flow from this embeddedness.

Whilst many of Deleuze and Guattari’s ideas have attracted widespread interest, the concept of faciality is yet to be fully examined. Most preceding accounts focus on faciality as a two-eyed machine. In these accounts, faciality is thought of as projected on a flat surface (Hansen 2003), a function of biology (Black 2011), part of an individuating process (Kauffman 2011) or a European machine of colonial judgement/racism that emerges from “the continent’s feudal, imperialist and capitalist regimes” (Watson 2008, p. 209). These studies usefully build the case that faciality is an ordering/othering machine that both normalises and hierarchises (Watson 2008) and in other cases is performed (Thompson and Bell 2011; Rutter 2007). While these accounts have merit, our interest lies in the complexity of facialities in striated space like classrooms. Faces are rarely performed alone, and in the case of the school, each face is always a machine connecting and co-generating meaning with other machines. There are no static faces. Our extension of the current work on faciality, supported by a close reading of Deleuze and Guattari’s work, is to argue that each faciality machine is manifested in meaning-exchanges between pairs of concrete faces within given landscapes that is, as a four-eye machine. For us, the complex relationships affected as four-eye machines is important if we are to realise Deleuze and Guattari’s maxim that we must “escape the face… dismantle the face and facialisations” (Deleuze and Guattari 2005, p. 171).


The face is an ordering function of both code and physical and temporal location. The face is “a link between a destination and an origin; the face arrives from somewhere and is on its way to somewhere else” (Rushton 2002, p. 225). The face also represents “Year Zero” or the beginning of the move from the tribal/primitive to the modern (Deleuze and Guattari 2005). It is an interplay of two axes. The first is significance, or “the structuralist logic of sign: interpreting language, actions, and life as an interplay of a signified and a signifier” (Markula 2006, p. 30). The second axis is subjectification or the “logic according to which an individual is turned into a singular subject or is assigned a molar identity” (Markula 2006, p. 30). What is significant is that the face is an organising, and a limiting, machine of capture. Paradoxically the face is also the site of possibility: “The face is, therefore, potential—it is of the order of the possible and the virtual… It is the face that opens up the world as an experience of possibility; it is the very conception out of which worlds are born” (Rushton 2002, p. 224). For Deleuze and Guattari, the face “is no longer to be perceived as an entity that expresses another feeling or idea” (Rushton 2002, p. 224).

In this context, faciality is an abstract machine that captures the multidimensional and polyvocal flows of possibility and forces them into one dimensionality and univocity. This is why the face is an ordering machine. The face is “not content to cover the head, but touches all other parts of the body, and even, if necessary, other objects without resemblance” (Deleuze and Guattari 2005, p. 175). In the shift from the primitive to the modern, faciality ensnares and entraps, through the “imposed norms which uphold whiteness, reason and secularised Christianity as the markers of human superiority” (Watson 2008, p. 208). The colonisation of the tribe brought “a generalized collapse of all of the heterogeneous, polyvocal, primitive semiotics in favour of a semiotic of signifiance and subjectification” (Deleuze and Guattari 2005, p. 180). Once your face has been recognised “the abstract machine has you inscribed in its overall grid” (Deleuze and Guattari 2005, p. 177). For teachers, as we shall argue below, this gridding is specific to a landscape that is both virtual (the past, ways of knowing) and actual (ways of moving, comportments of concrete faces) within the context of specific striated spaces like classrooms.

Within the abstract machine, signifiance manifests a semiotic world of white walls on which codes and signs are inscribed or imprinted. Subjectification is of the black holes that appear on the white wall. The face is a mix of the subjective and signifiatory:

Signifiance is never without a white wall upon which it inscribes its signs and redundancies. Subjectification is never without a black hole in which it lodges its consciousness, passion and redundancies (Deleuze and Guattari 2005, p. 167).

What is important is that the face does not come ready-made. Rather it is “engendered by an abstract machine of faciality (visagette)” (Deleuze and Guattari 2005, p. 167). This abstract machine produces the concrete face at the same time as black hole and white wall axes are produced. For the teacher, a concrete face is the face performed, physical, corporeal within the classroom. It is important to stress that faces are not chosen. This concrete face is an actualisation of the virtual terrain—the gridding of subjectivity and subjectification. These axes of subjectification and signifiance are both spontaneous events and copies or returns of previous faces. The face is both a unique event and a copy—a returning visage that resonates with the past but is not of the past (Deleuze and Guattari 2005, pp. 172–173).

Our challenge in this paper is to theorise the teacher-face, not as a static, corporeal representation of ‘teacher’, but as a fluid, and always multiply available, possibility that has been continually recreated from remnants that were once of the past. As Deleuze and Guattari assert, “you have to keep small supplies of signifiance and subjectification… and you have to keep small rations of subjectivity too in sufficient quantity to enable you to respond to the dominant reality” (Deleuze and Guattari 2005, p. 160). Each face manifests both subjectification and signifiance but there are always differing mixes, or ratios, of white walls to black holes. Black holes can expand so as to make the white wall appear to shrink. Black holes may seem to dwarf the signifiatory white wall with which they are mixed. On the other hand, white walls can overpower black holes, take up their space, striate their depths and cause them to shrink. As we shall develop later, this series of exchanges can be theorised as maximal exchanges of white-wall imprinting or black-hole flow. These are Deleuze and Guattari’s “limit-faces” (Deleuze and Guattari 2005).

Both work in the same way, however, as much as they work differently. For they work together to prevent the emergence of other possible concrete faces.

Whatever the differences between signifiance and subjectification, whichever prevails over the other in this case or that, whatever the varying figures assumed by their de facto mixtures- they have it in common to crush all polyvocality, set up language as a form of exclusive expression and operate by signifying biunivocalization and subjective binarization (Deleuze and Guattari 2005, p. 180).

The fact that they cannot succeed in crushing all polyvocality means that the exclusions that particular signifiance-subjectification mixes effect are not final (and, as we discuss later, escaping or dismantling specific facializations remains possible).

The question of the teacher-face is significant because it encapsulates what movement is possible within schools. For Deleuze and Guattari, the teacher-face is a special face; firstly because it is so overcoded by “social formations”, and secondly because it is a powerful manifestation of “face-landscape correlations” (Deleuze and Guattari 2005, p. 172). These processes are of the past and the future as much as they are of the present and these two processes (overcoding and face-landscape correlations) are significant if we are to dismantle the face. It is our contention, following Deleuze and Guattari, that to map these four-eye machines of faciality is to represent their possible overcoming. “The map is open and connectable in all of its dimensions; it is detachable, reversible, susceptible to constant modification” (Deleuze and Guattari 2005, p. 12).

Exchange and Four-Eye Machines

In theorising faciality for an analysis of teacher-faces, we encounter one of the many four-eye machines of faciality that populate the modern world, as pairs of black holes and white walls work together to produce strata of signifiance and subjectification. “The movement of the black hole across the screen… constitutes so many dichotomies of arborescences, like four-eye machines made of elementary faces linked two by two” (Deleuze and Guattari 2005, p. 177). Pairs of “concrete individualized faces”, such as teacher and student or worker and boss, “are produced and transformed on the basis of these units, these combinations of units” (Deleuze and Guattari 2005, p. 177). These movements manifest, among other things, ‘teaching’ and ‘being taught’. Each of the four-eye machines for faciality associated with these effects instantiates a relationship between sets of black holes and white walls. The question concerns the intra-actions or exchanges between faces manifesting within abstract machines of faciality.2 The four-eye machine “effectively functions as a collective micro-agency charged with scanning the subjectivity of a child beginning with consciential redundancies of the dominant faciality” (Guattari 2011, p. 89).

Describing the relationship between faces necessitates developing a schema for describing the effects that black holes and white walls have on each other.

The face constructs the wall that the signifier needs in order to bounce off of it; it constitutes the wall of the signifier, the frame or the screen. The face digs the hole the subjectification needs in order to break through; it constitutes the black hole of subjectivity as consciousness or passion, the camera, the third eye (Deleuze and Guattari 2005, p. 168).

In the classroom four-eye machines pair concrete faces within an abstract machine of faciality that manifest two exchanges between two sets of black holes and two white walls.

Important exchanges between, or the secondary effects of, black holes and white walls, are those of gazing and mirroring. The gaze manifests the depth of black holes (which are dug, are of the soul, and are found in the mind, the third eye and the camera’s lens). Flows pass between black holes as gaze. White walls produce surface effects of repetition or re-presenting (which are an effect of mirrors and movie screens) and, we suggest, impressing and imprinting. “The gaze is but secondary in relation to the gazeless eyes, to the black hole of faciality. The mirror is but secondary in relation to the white wall of faciality” (Deleuze and Guattari 2005, p. 171).

The exchanges between two set of black holes or two white walls are never, symmetrical, even if it is always reciprocal. This asymmetry relates to both the quantum and quality of transfers. Four-eye faciality machines ensure this asymmetry in that they do not allow equal exchanges between concrete faces. Greater and lesser flows are made to appear as if they emanate from black holes of differing dimensions and depths. Ostensibly, more highly encoded white walls seem to leave greater impressions on less encoded walls than appears to be left on them by an intra-action. The persistence of the transfer effects are another matter. Apparently deeper and older black holes seem to be less likely to be permanently affected by what appear to be less striated (shallower and newer) black holes. Seemingly more encoded-striated white walls are less likely to retain the imprints left by apparently less encoded-striated white walls and less encoded-striated white walls more likely to retain the imprint of their co-constitution through the abstract machine of faciality.

Both black holes and white walls are always at work in the classroom, then, and are always mixed by four-eye faciality machines. Their importance in the classroom lies in the crushing of polyvocality, which establishes only certain mixes as available. For “it is at the level of this mixture that they assert their imperialism, in other words, their common endeavour to crush all other semiotics” (Deleuze and Guattari 2005, pp. 181–182).

This mixing is important to specific flows of subjectification and significance operating within different landscapes to constitute different teacher-faces. Classrooms are (landscapic) correlates of teacher-faces. The teacher-face reterritorialises the head, but does so in a way that brings it into a corresponding, or complementary, landscape. Analysing teacher-faces, then, means enquiring into the way that the “absolute deterritorialisation” effected by the face “removes the head from the stratum of the organism, human or animal, and connects it to other strata, such as signifiance and subjectification” while paying attention to the teacher-face’s landscape; since “the face has a correlate of great importance: the landscape, which is not just a milieu but a deterritorialised world” (191). In addition, to analyse the teacher-face requires assessing “the states of mixture and the varying proportions of the elements”, which is essential because “one element may dominate another, one may be more or less powerful than the other” (Deleuze and Guattari 2005, p. 182). In developing an analsis of teacher-faces, following Deleuze and Guattari, “we are thus led to define limit-faces, which are different from both the facial units and the degrees of facial divergence previously defined” (Deleuze and Guattari 2005, p. 182).

As noted above, limit-faces are not borders or boundaries; they are zones of increased intensity and/or propensity. In a four-eye machine, the limit-face represents maximal exchanges between black-holes or between white-walls beyond which faces may begin to lose meaning (a point we return to when discussing dismantling or escaping the face). While we have settled on four limit-faces, this is not meant to imply a Cartesian ordering. As we will argue, it is not a case of moving from one limit-face to another, all limit-faces are at work in all classrooms and any affect within the classroom manifests or actualises all of these limit faces. So every classroom must be understood as virtualising every possible black hole-white wall mix so that every possible mix can be actualised and is equally available at every moment that a teacher is in the classroom.


Teacher-faces are affects produced by four-eye machines of faciality in the classroom that constitute and regulate flows between concrete faces in the classroom. Teacher-faces are contextual; they change in different spaces and at different times. Teacher-faces are one of many faces—parent-face, friend-face, citizen-face. But teacher-faces represent a special type of face because they are an overcoded face. An overcoded face, despite any attempt to wear it individually, always refers to “a line of rigid segmentarity along which everyone will be judged and rectified according to his or her contours, individual or collective” (Deleuze and Guattari 2005, pp. 200–201). At first appearance, teacher-faces are masks preceding a set of performances, or actualisations, that render concrete teacher and student. These faces do

not speak a general language but one whose signifiying traits are indexed to specific faciality traits. Faces are not basically individual; they define zones of frequency or probability, delimit a field that neutralises in advance any expressions or connections unamenable to the appropriate significations (Deleuze and Guattari 2005, p. 168).

The face of the teacher is not constant; rather it is a variation of frequency and intensity, “a set of speeds and slownesses between unformed particles, a set of nonsubjectified affects. It is the entire assemblage in its individuated aggregate that is a haeccity” (Deleuze and Guattari 2005, p. 262). As a haeccity, the teacher-face “has neither beginning or end, origin or destination; it is always in the middle. It is not made of points, only of lines”. (Deleuze and Guattari 2005, p. 263). Teacher-faces, as we have noted, call up and are called up by a landscape that is both of the institution and the past. So the teacher-face is both affected as a concrete face, a face within the particular school, and represents a face that echoes or resonates with faces that have come before. Within the school, concrete teacher-face are connected to, and measured against, teacher-face abstractions such as “good/bad, professional/unprofessional, caring/indifferent, knowledgeable/unknowledgable, competent/incompetent and so on” (Popkewitz 1998). The abstract machine of faciality at work in the classroom manages these historical and social possibilities to actualise concrete teacher’s faces (as various expressions of the abstract) because “certain social formations need face, and also landscape. There is a whole history behind it” (Deleuze and Guattari 2005, p. 180).

When we think of teacher-faces, either to enact them or to remember how they were enacted, we see a teacher-face populated by past contests between significance and subjectivity—a reterritorialised offering. Faciality “organises a field of possibilities, determines, at least to a certain extent, what we are capable of seeing, doing, being” (O’Sullivan 2006, p. 311). The importance of these contexts, technologies, apparatuses is that they construct a terrain within which facialities move, negotiate and circulate. The abstract machine of faciality is a machine of enclosure. It corporealises virtualities within the school in which ‘individuals’ are made to circulate, rather than a terrain they traverse. In short, faciality ensnares and entraps the ‘self’ within gridded and striated possibilities such that those caught in them are “stuck circulating within the terrain of the school, rather than striking out on journeys through the terrain” (Thompson and Bell 2011, p. 411).


In being landscapified and overcoded, teacher-limit-faces are accretions of past actualisations and have ‘histories’. Characterising teacher-faces as ‘limits’, then, requires evaluating ideas about teaching from the past that continue to manifest in contemporary institutions. This also requires illustrating limit-faces in the operation and regulation of ordering flows and other interactions that occur between the white walls and black holes of four-eye machines in classrooms. We utilise four teacher-limit-faces that are affected as concrete teacher-faces as idealised intensities of maximal flow or imprinting. We associate each teacher-limit-face with a particular thinker (Plato, Rousseau, Bentham and Neill) because their works illustrate specific zones of intensities or flow within the four-eye machines of teacher-student. We do not contend that these theorists taught in this way; though some of the inferences we have drawn about the teacher-faces associated with the positions we attribute to these philosophers will be noted in accounts of the four teacher-faces. We found these illustrations useful because the concepts (perhaps planes of immanence) that have come to be associated with their names indicate common flows within the classroom. In mapping these limit-faces, we intend a provocation, that the “phenomena of massification, bureaucracy, leadership, fascization” conceal “which lines nevertheless survive” (Deleuze and Guattari 2005, p. 14).

Limit-faces suggest zones of increased or heightened intensity. In a sense, they are common possibilities of facialisation within landscapes. They represent extreme flows and imprintings. While we have selected four faces to illustrate and map four-eye machines, there are no doubt many more: a Confucian limit-face, a Montessori limit-face, many more need to be mapped, but four are of particular interest for this analysis because these limit-faces are always virtually present and influence all actualisations in the classroom. Transition within and between concrete teacher-faces associated with different limit-faces is instantaneous, and concrete teacher-faces cannot be ‘worn’ continuously and forever, as if carved from stone. A ‘Teacher’ may constantly move from mix to mix, oscillating violently or gradually flowing. In enacting multiple four-eye machines in a class of many students, teachers may actualise more than one concrete face in the same moment.

The production of colours on television screens may serve to illustrate this complex exchange. Colour televisions produce an apparently infinite range of colours through the interaction of red, green and blue electron streams and red, blue and green phosphorous dots. In order to introduce red into a colour a specific number of red electron streams are shot at a particular number of red dots. The greater the stream of red electrons and the greater the number of red dots being exited the more intense the red that is produced. Rarely, though, will this red stream not be accompanied by streams of blue and green striking corresponding blue and green dots [if no electron streams hit no dots (black is produced) and if all streams strike all dots (white results)]. The point of this analogy is that faces (like colours) are actual manifestations of a combination of flows and mixes. While faces do not pre-exist their production and actualise the possibilities made available by the machines that produce them, however, but because of the history of affects, certain faces are much more likely to actualise than others, especially as some are encoded as desirable. The diagrammatic of faciality3 (see Fig. 1) maps these four limit-faces in a classroom-landscape. As we have argued, the limit-faces are not boundaries, they are regions or zones of intensities.
Fig. 1

A partial mapping of the teacher-face

As a map, Fig. 1 shows the teacher-faces as zones or regions of intensity. The space in between the limit faces represents the mixes of faciality flows that are always available. The hexagon represents the landscape of the classroom that contains the teacher-limit-face. The dotted boundary represents passage through the map, escaping the face or the potential for new lines of flight made available by this exercise. The meandering lines represent the potential to ‘escape the face’.


One of the limit-faces available is typified by the concrete teacher-face manifesting as much white-wall (signifiance) as possible. We have called these faces ‘Formal’, because they grid the teacher-face as external authority, and attempts to occlude interiority and depth. The exchanges that pass this limit-face go to maximising signifiance between the two faces and minimising subjectification. In theorising these limit-faces, we take this to the extreme, suggesting that exchanges are simply those of white-wall imprinting, although for concrete faces some black hole flow must always be present, otherwise the face cannot be sustained. Maximal signifiance is derived from four-eye machines through which the teacher’s face becomes authoritarian and care is manifest for absolute and external truth-forms. This is best considered as an ordering or coding orchestrated through imprinting or mirroring.

For Plato, education drew learners out of states of ignorance (the cave) and into truth (the sunlight).4 This was a process of bringing the ideas in students’ minds into harmony with the essential nature of things so their ideas would be correct. The teacher’s role was to unveil these signified and purified ‘forms’. For a society to flourish, Plato reasoned, citizens, particularly in their youth, needed instruction that prepared them to be “a better person, in terms of virtuous behaviour and service to the state” (Lawton and Gordon 2002, p. 17). Education was the vehicle for preparing the young to be the active and just citizens required for a good society, or, at least, an education provided by a teacher who possesses the truth. For such a teacher, “education is the constraining and directing of youth towards that right reason, which the law affirms, and which the experience of the eldest and best has agreed to be truly right” (Plato 1969, p. 123).

Plato believed that the essence of education was the search for abstract truth rather than engagement with the physical world (Ozmon and Craver 2003). Impassive (unemotional) reflection on and of the good and true was the goal of education. Seeking to maximise white wall interactions allows for an impersonal face:

Let each one of us leave every other kind of knowledge and seek and follow one thing only, if peradventure he may be able to learn and discern between good and evil, and so to choose always and everywhere the better life as he has the opportunity… A man must take with him into the world below an adamantine faith in true and right (Plato 1969, p. 103).

The minimisation of subjectifying exchanges between black holes operates synchronously with formal-limit-faces of dispassionate, objective mentoring (a disinterested and disembodied being alongside inducing a care for truth). To achieve the ideal version of this face, students must learn to still their desires and drives and take the path of truth in order to know and serve the ‘good’. Formal limit-faces privilege dispassionate, objective knowledgeable miens—the concrete faces as marker-register of the moral code, to care for through students’ “souls, and not their bodies: and the triumph of my art is in thoroughly examining whether the thought which the mind of the young brings forth is a false idol or a noble and true birth” (Plato 1969, p. 231). Pedagogy is understood as a set of one-on-one interactions, as the four-eye machine function in parallel (they affect as a pair at a time and not as many faces together). Rote-learning, textbook exercises, silent reading, learning from the cannon, studying the Classics and Philosophy are examples of these pedagogies. Formal-limit-faces become concrete when they manifests flows actualised within the classroom that privilege reflection on those ‘legitimate’ truths that have been discovered by others. This exchange aimed to form student faces that would take on characteristics associated with being “a better person, in terms of virtuous behaviour and service to the state” (Lawton and Gordon 2002, p. 17).


Unlike Formal-limit-faces, these limit-faces are actualised as maximal black-hole exchanges through each teacher-student four-eye machine. Natural-limit-faces regulates toward maximal subjectification flows and minimal signifiance flows between the concrete faces of teacher and student. For these concrete faces: Black holes open (pupils dilate, lips part, smiles and winks may appear) such that subjectification flows are enabled, while white walls are mobile and produce shadows and other depth effects that minimise signifiance exchanges. Like Formal faces, these limit-faces manifest themselves best as sets of one-on-one exchanges. These limit-faces also compel, if they do not force, all the concrete teacher and students faces that form to take the position of ‘teacher’ face at some time.

For Rousseau, the principal function of education was to facilitate the inner, natural goodness of children by removing them from the corrupting influence of civilisation.5 External influences corrupt the child and the only way to overcome this is to bring the child up “in the country far from those miserable lacqueys… far from the vile morals of the towns, whose gilded surface makes them seductive and contagious to children” (Rousseau 1969, p. 60). The concrete teacher-face selected here expresses learning as a human and subjective process; for the child is to “see with his own eyes and feel with his own heart” (Rousseau 1969, p. 60).

Rousseau dismisses approaches to education in which young people are to be taught or imprinted with externalised, civilised ‘truths’. Instead, he advocated teacher-student (and student–teacher) flows that recognise the innate value within each learner. In natural-limit-faces the student and teacher share a physical co-presence. The face each wears is informed through the flow—the event horizon of black-hole to black-hole, that in a natural view prioritises relationships, trust, empathy and humanity that order and striate the ‘human’. The teacher-face is judged not by how well they impart abstract knowledge but in how well they relate.

It is very strange that ever since people began to think about education they should have hit upon no other way of guiding children than emulation, jealousy, envy, greediness, base cowardice…. With every piece of precocious instruction which you try to force into their minds you plant a vice in the depths of their hearts (Rousseau 1969, p. 91).

Rousseau theorised teaching as private tutoring. For Rousseau, the tutor’s face produced flows that enabled, encouraged and supported young people’s desires to learn in experiential ways. “Let his unreasonable wishes meet with physical obstacles only, or the punishment which results from his own actions, lessons which will be recalled when the same circumstances occur again” (Rousseau 1969, p. 42).

Not only does this limit-face actualise concrete teacher-faces of support and encouragement, it also selects teacher-faces that allow interactions and flows in the opposite direction. While much flows from the concrete teacher-face, an important function of the concrete teacher-face selected by this limit-face is to allow reverse flows.

I will only remark that, contrary to opinion, a child’s tutor should be young, as young as a man may well be who is also wise. Were it possible, he should become a child himself, that he may become the companion of his pupil and win his confidence by sharing his games (Rousseau 1969, p. 241).

Natural-limit-faces order concrete student faces that initiate interactions and flows and the four-eye machines work in parallel, as student faces are not required to turn to each other (ideally there are no other students).

As for my pupil, or rather nature’s pupil, he has been trained from the outset to be as self-reliant as possible, he has not formed the habit of constantly seeking help from others, still less of displaying his stores of learning. On the other hand he exercises discrimination and forethought, he reasons about everything that concerns himself. He does not chatter, he acts (Rousseau 1969, p. 60).

An important effect of the maximisation of black holes is that it manifests engagement. Learning is through doing and for doing. It is not for quiet contemplation, but for active reshaping of the world according to the natural principles that are embedded within each individual. The light is not to be found outside, but is within and has to be actively cultivated. While the Natural may alter the ways that faciality is communicated in comparison to the Formal, it is no recipe for escaping the face because it constitutes its own striated subjectivity. Compassion, itself, becomes a capturing motif—how well does the teacher care for the student? Thus, like Formal faces, we must remember that natural-limit-faces are machines of capture; they are also ordering machines.


Professional-limit-faces regulate according to the principle outlined for the Formal teacher-face: limiting black hole flows and maximising white wall exchanges. The difference is a massification, the teacher faces a class, not an individual. Within this landscape, the four-eye machines of faciality are in series. In being coupled to the factory, in the machine of capitalism, this classroom is regulative toward increasing productivity. It is not a matter of minimising subjectification and maximising signifiance to instantiate some ideal. It is a matter of minimising subjectification flows and maximising signifiance flows toward greater capacity to act productively with others. While both select for maximal signifiance interactions and minimal subjectification flows, the difference between Formal-and Professional-limit-faces is that the former selects faces that work to individuate and the latter selects those that tend to massify.

This recalls the centrality of inspection to the concrete teacher-face recommended in Bentham’s works.6 Bentham is well-known, thanks to Foucault, for his ‘Panopticon’ or that system of punishment that “reverses the principle of the dungeon” through making the inmate permanently visible (Foucault 1991, p. 200). Inspection has two effects: first it means that the concrete student face is examined according to some model. Professional-limit-faces, which order concrete faces of and for examination, must enable maximal white wall to white wall interactions. The second effect of inspection is to initiate a series that constitutes the knowing face as the expert face. At least, it does so for schools designed for the working class. While other principles might apply to schools for the elite, according to Bentham, educating the working class was required “as a matter of police, to prevent a multitude of immoral and vicious beings, the offspring of ignorance, from growing up around us, to be a pest and a nuisance to society” (Hunter 1994, p. xi).

A defining feature of Professional-limit-faces is that the concrete teacher-face stands as a marker of, or substitute for, the face of an expert. In one sense, the series constituted by the four-eye machines associated with Professional-limit-faces passes outside the classroom, and even outside the school, to include absent concrete faces that ‘authorise’ the concrete teacher-face in the classroom. Maximal signifiance interactions and minimal subjectification flows are like those of Formal-limit-faces, but whereas Formal-limit-faces select for faces that turn to the sun, Professional-limit-faces select for those who turn to those in authority.

In the final letter of his Panopticon, Bentham argued that the most effective school for the working-class is one in which the student is continually visible to the eye of the master. In doing this, the school becomes a place where the student is made more productive:

All play, all chattering - in short, all distraction of every kind, is effectually banished by the central and covered situation of the master, seconded by partitions or screens between the scholars, as slight as you please (Bentham 1995).

In his, largely forgotten, Chrestomathia, Bentham is clear that the concrete teacher-face does not pass as an authority, but as a placeholder for an authority. So exchanges are ‘as if’ they were between concrete student faces in the classroom and the face of an abstracted (white-walled) expert that is not actualised (but exists virtually) in the room. In the Chrestomathic school, older students taught younger students because the ‘grown-up’ teacher “is liable to have an opinion of his own, and with it a will of his own, contrary to that of his superior and employer” (Bentham 1816, p. 9). The problem with ‘grown-up’ faces is that they will not function as conduits and may produce unauthorised white-wall affects, or even black-hole flows, and not facilitate the desired imprinting by external expertise.

The architecture of Bentham’s ideal school is a clear expression of the operation of this four-eye machine, as it should ensure that “every human object in the whole building can be kept within the reach of the Head-Master’s eye” (Bentham 1816, p. 11). The Head-Master provided the connection to external expertise required for these limit-faces, as “general inspection and direction is the business which must be done by him, and cannot be done by any one else” (Bentham 1816, p. 11). This only produces the proper affects if Head-Masters were inspected by expert “Visitors”. For “the good effects producible by the judgement they pronounce … are completely dependent upon the knowledge which they possess” (Bentham 1816, p. 11). The “National Society”, which inspected Visitors and the education system in general, was made up of eminent professionals to ensure that white wall exchanges ensured conformity to an external standard. We see this manifesting through centralised curriculum, with strict requirements as to what would be studied and how learning would be measured. Students sit in rows and undertake individual tasks that culminate in external examinations that measure ‘expertise’.

Democratic Limit-Faces

Like natural-limit-faces, democratic-limit-faces actualise as concrete teacher-faces of unregulated learning. These limit-faces, however, privilege the social interaction between teachers and students and, in this sense, are machines of massification. Unlike professional faces, which establishes teacher-faces in hierarchies (above students, below external ‘experts’), Democratic-limit-faces impede the passage of hierarchies in favour of democracies and the privileging of equality and co-humanity. As machines of faciality, they maximise black hole flows that increase the capacity for creativity with and toward others.

The concrete faces that actualise this limit-face may be found in the writing of A.S. Neill.7 Teachers bring their depths to and in the service of students (and acquire greater depth through doing so). These four-eye faciality machines are arranged in series. Rather than imprinting an ordering face of black-hole flows governs through social interactions and not laws, rules or expertise. The teacher-face and the student face gaze at each other, and are ordered or captured by their co-humanity. They ‘see’ each other not as adversaries or dangers needing to be controlled, but as individuals. Co-presence is actualised in this teaching space. Black hole flows pass back and forth between the concrete faces of teacher and student. “Good teachers… used their free time mixing with the kids” (Neill 1972, p. 149). Equally important, though, are black-hole flows between students, as the concrete teacher-face becomes one of many similar faces.

Neill’s Summerhill School, like those ‘progressive’ schools that developed in the UK, Australia and the US between the 1950s and 1980s, was to be ‘democratic’ (Brighouse 2006). In this school students and teachers were to be treated as political and social equals. The school operated as a “self-governing school, democratic in form” where all governance is decided at weekly General School Meetings (Neill 1962, p. 33). All students and staff had one vote at these meetings and decided on any matter that could be raised by any member of the school community. According to Neill, self-government “is not to only make laws but to discuss the social features of the community as well” (Neill 1962, p. 36). When making final decisions about the school “the vote of a child of six counts as much as my vote does” (Neill 1962, p. 10).

Summerhill was organised to “make the school fit the child” (rather than the Professional ideal where the child was moulded to fit the school) (Neill 1962, p. 2). To do this, schools should not be “based on an adult conception of what a child should be” (Neill 1962, p. 2). Maximal black-hole flows required a community that renounced the signifiatory codes that, for Neill, were transmitted to the student as Professional-limit-faces. Inspection was objectionable for “Summerhill is primarily for living and it refuses to be judged by a body of people who think of learning and teaching methods and discipline” (Neill 1972, p. 155). Being able “to put her or his lessons across” was not central: “I want teachers with some humour, with no dignity; they must not inspire fear and they must not be moralists… I do not want he-men with strong personalities” (Neill 1972, p. 150). Teachers had to “renounce all discipline, direction, all suggestion, all moral training, all religious instruction” (Neill 1962, p. 2). This renunciation constructed a specific teacher-face in the landscape of Summerhill; for the ‘human’ itself is a concept of striation, for ordering flows and exchanges.

Democratic limit-faces select concrete faces that produce and control significant black hole flows. These flows affect connection and collective (democratic) action by selecting against “duty, obedience, profit, power” and for “fun, games, love, interesting work, hobbies, laughter” (Neill 1962, p. 138). For Neill’s “criterion of success is the ability to work joyfully and live positively” (Neill 1962, p. 24). By selecting for faces that regulate black hole flows, students will be able to engage and manage deep ‘inner’ feelings in such a way as to conduce to the common good. Democratic-limit-faces internalise and massify the good, Formal-limit-faces externalise and individualise the good.

Neil commented that many of the teachers that he saw graduating when he lectured at teacher colleges were captured by an externalised and incorporealised signifiance.

When I lecture to students at teacher training colleges and universities, I am often shocked at the un-grownupness of these lads and lasses stuffed with useless knowledge. They know a lot; they shine in dialectics; they can quote the classics – but in their outlook on life many of them are infants. For they have been taught to know, but they have not been allowed to feel. These students are friendly, pleasant, eager, but something is lacking in the emotional factor, the power to subordinate thinking to feeling. I talk to these of a world they have missed and go on missing. Their textbooks do not deal with human character, or with love, or with freedom, or with self-determination. And so the system goes on, aiming only at standards of book learning – goes on separating the head from the heart (Neill 1962, p. 16).

For Neill, maximising black-hole flows represented an opportunity to repair many of the negative traits of the human condition (signifiatory excesses). The teacher whose face expressed love, freedom, and the power of emotions within a democratic landscape would produce students able to resist the excesses of rationality, profit and violence. To minimise signifiatory exchanges, lessons, curricula and timetables were abandoned. Individual choice mediated by intra-group flows, meant that students manifested inner self-direction (learning at their own pace and according to their own interests). For Neill was not concerned about the work his former students did, but for “their character, their sincerity, their tolerance; I like to think that they have a better chance of being pro-life than disciplined, moulded children have” (Neill, 1972, p. 159). Maximal black hole flows, however, were always accompanied by white wall exchanges. For his goal was to produce students who were “hard-working, tolerant, (and) pro-life” (Neill, 1972, p. 160). Black-hole flows are ordering machines as much as white-wall imprintings.

Escaping the Face

As Deleuze and Guattari stated, the point of any mapping, whether it be of faciality machines or any other machines, is to uncover and potentially release lines of flight. The teacher-limit-faces outlined above in no way exhaust the field of limit-faces as they pertain to the teacher, they are intended as an illustration, and deliberately provocative ones at that. Deleuze and Guattari remind us, though, the destiny of human beings is to escape the face, or to “become imperceptible, to become clandestine…but by strange true becomings that get past the wall and get out of the black holes” (Deleuze and Guattari 2005, p. 171). This challenge, as we have suggested above, is a particular problem in the landscape of the overcoded classroom. The four limit-faces outlined here are persuasive and compelling accounts of what teachers should do and be: they should care for knowledge, care for the innate value of each individual student, discipline them, teach students to respect authority and expertise, promote democratic values. The list goes on. In a heavily striated or encoded space like the classroom, the face of the teacher is overcoded to such an extent that it may appear difficult to change.

However, within every territorialising machine, lines of flight are possible. Arguably, it is already happening and has probably happened since ‘teaching’ was institutionalised. In Francis Bacon, Deleuze presented the artist as someone whose portraits dismantled the face through “being subjected to the techniques of rubbing and brushing” in order to construct figures as “zones of indiscernability or undecidability” (Deleuze 2004, pp. 19–20). If limit-faces do anything universally, they are machines of probable and/or discernable actions. For teachers to escape the face requires both becoming improbable and deterritorialising the space of the classroom. The concrete-teacher-faces actualised in the mixes between subjectivity and significance are in equal parts contradictory and compelling. Within policy reform agendas that amplify the intensity, or what is at stake with teacher-faces, perhaps we are seeing the teacher-face becoming more frightening/frightened or, as Ball suggests, a mapping of the “schizophrenia” of the landscapified teacher-face (Ball 2000). Escaping the face is becoming-urgent. One possibility for this escape for Deleuze and Guattari was the “probe-heads (guidance device)” (Deleuze and Guattari 2005, p. 190). Probe-heads “dismantle the strata in their wake, break through the holes of signifiance, pour out of the holes of subjectivity” (Deleuze and Guattari 2005, p. 190).

The probe-head dismantles the face through opening “a rhizomatic realm of possibility effecting the potentialization of the possible” (Deleuze and Guattari 2005, p. 190). For O’Sullivan, a probe-head is a “name for these alternative modes of organisation” (O’Sullivan 2006, p. 313). Thus, mapping teacher-faces is an exercise in mapping limit-faces as ordering machines. Mapping teacher-faces is important because limit-faces are “centralised and hierarchised on particular arborescent points” (Guattari 2011, p. 106). Escaping the face through “machinic rhizomatic systems” requires actualising neither “circularly aggregated eyes nor signifying layers accumulating in concentric zones” (Guattari 2011, pp. 101–102). A rhizomatic (re-)ordering of the probe-head means new, and sometimes troubling, possibilities for and of the teacher. Certainly we should look to those ordering machines of both teaching and schooling and ask what is beyond; what happens to teaching when curriculum, pedagogy, discipline, professionalism, knowledge, care become rhizomatic?8


The concrete face of the teacher that we see in a classroom expresses a faciality machine that is actualised in subjective and signifiatory exchanges between concrete faces. For teachers, it is a machine of capture and ordering that occurs within the specific landscape of the classroom. In this paper we have attempted a partial mapping of the four limit-faces that manifest teaching’s history in the classroom: Formal, Natural, Professional and Democratic. These limit-faces do not exhaust those available, even in Western classrooms; rather, they illuminate ways that teacher’s actualisations are captured within certain zones of intensities or probabilities. Through this partial mapping, we can begin to discern lines of flight that become available within new territories made available by technological, political and policy change at the level of the classroom. For the teacher, escaping the face requires a concerted effort to evade actualisation through four-eye machines that repeat past faces and to embrace the non-certain possibilities of the rhizomes. No easy task.


In this paper we are using ‘affect’ as designating multiple forms. Firstly, it builds on Deleuze’s reading of Spinoza to mean “the ability to affect and be affected” as “two facets of the same event” (Massumi and McKim 2009, p. 1). Secondly, affect encompasses the idea that when bodies are affected, or move to a “diminished or augmented state of capacitation”, this transition is felt (Massumi and McKim 2009, p. 2). Thirdly, each body has a “lived past” that means that when bodies affect/are affected “there’s a reactivation of the past in passage toward a changed future” (Massumi and McKim 2009, p. 2). At one level, teacher-faces operate at the level of affect.


In this paper we are theorising teacher limit-faces and illustrating some of the ways that exchange occurs within those limits. To do this, we assume that in maximal white-wall or black-hole exchanges, student-faces reciprocate those flows. However, we acknowledge that there are multiple possibilities for how student faces affect black-hole flows and white-wall imprinting. For example, some student-faces may block black-hole flow by intensifying white-walls, asking for homework, to be told what to do, to refuse discovery learning. Within the limits of this paper the theorising of concrete student-faces is not possible, but does require further attention.


We use the term diagrammatic specifically to designate Guattari’s theorisation that there exists a machinic form of faciality that escapes the human, is rhizomatic in its application and represents “lines of flight carrying quanta of diagrammatic possibilities” (Guattari 2011 p. 102).


Much has been written about Plato’s contribution to education that it is not possible to do justice to in this paper. For more information, see for example Barrow (1976) or Jacobsen (2003).


For more about Rousseau and education, see Hodgson (1969) or Gray (2012).


For more about Bentham and education, see Jones (1990).


For more about Neill and education, see Hemmings (1972) or Vaughan (2006).


This is a key question. There is an emerging body of work on Deleuze and Guattari’s ideas of nomadism and rhizomes that relate to curriculum and pedagogy (Cole 2008; Gough 2006; Roy 2003). The ontology of the teacher and/or teacher-faces has much to contribute to this theorisation of nomadism in our opinion.



Greg Thompson is funded by the Australia Research Council.

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© Springer Science+Business Media Dordrecht 2012