Introduction

We¹⁰ are now researching in education. With arts, geographies, philosophies and other affections, but in education. This is our specific domain (^{Deleuze, 2016}). This is where we seek to create. Far from a merely voluntarist, creative or ideal reason, which understands creation as a solution to given problems, we try to approach perspectives that enable a process of problem creation, as an invention of the self and the world (^{Kastrup, 2007}), where we understand ourselves more as an effect of the same than its univocal agents. And in this process, we work with lines. Lines of life, lines of formation, lines of inventive processes, lines of writing, of music, of escape, of subjectivation... These are the lines that populate our research. And that's how we create.

The discussions we present here are part of the operations that make up the method and initial discussions of the dissertation in progress, provisionally entitled 'Choreographies in lineament: litanies of a dance-research' - developed by the first author and supervised by the second author of this text, within the Art, Language and Curriculum research line of the Postgraduate Program in Education at the Federal University of Rio Grande do Sul. These articulations also go beyond and undo the limits of this specific work, as they end up overflowing in the midst of the relationships established within the guidance group coordinated by the second author. Throughout our experiments, we have sought to ally ourselves with certain references and horizons that encourage us to produce research methods and ethics in the face of this multiplicity, which produce not only aesthetic forms (ways of seeing/saying in education), but also political statements (what have we done with ourselves when researching, creating in education, with art and philosophy?) In this production of difference, questions emerge that instigate us and work to establish research practices that are therefore oriented towards inventiveness. Like ^{Kastrup (2001}; ²⁰⁰⁷), we rehearse possible, contingent, experimental answers to these questions, aiming to produce more problems that move us to continue investigating, rather than a definitive resolution of these problems, a stance that would be closer to the idea of creativity, which, according to the author, would be just one part of the creative process.

One of these questions, which guides this text, asks: 'what can dancing with lines of formation do in a research in education? In other words, how do these operations produce/constitute/compose movements in a research in education, especially in the context of the investigative operations invented in our steering group?' In order to rehearse answers to this and other questions, we need to make some conceptual revisits, promoting encounters that have been reverberating in our research. In this way, in the sequence, at first - and also as the center of our propositions - we articulate notions of settlement and lines present in the contributions of Tim ^{Ingold (2015}), Gilles ^{Deleuze (2016}) and in the joint production of Deleuze and Guattari (2010; 2012a). We then go through - and dance with - some propositions that concern our research operations in the field of education, in order to seek questions about how these aforementioned articulations work in the invention of research practices. This is how the text - the research- is populated with lines, creates interweavings and fabrics, makes a body, dances.

As teacher-researchers (^{Corazza, 2002}), we are constantly doing, undoing and redoing ourselves. Our research is therefore part of our training, and to shake up its lines is to set in motion points previously understood as fixed. To join speeds and intensities. When the research makes body, we make body with it. When we dance, the research dances. This way of placing ourselves in the life of research makes it something at once enchanting, threatening and surprising. Because to put thought into motion is therefore to transform ourselves.

From chaos to lines

We can begin our attempts to answer some of our research questions by assuming that, in the context of our research in education, we seek to compose with the notion of creation, in the terms proposed by Gilles ^{Deleuze (2016}, p. 332, free translation). In rehearsing about what happens when we have an idea, when something is created, the author argues that we are always having an idea 'in' a certain territory. "It is just as much an idea in painting, just as much an idea in a novel, just as much an idea in philosophy, just as much an idea in science". We therefore understand, in this philosopher's terms, that creations take place in a specific domain, and are therefore not universal ideas, ideas in general.

Allied to Paul Klee, for whom "[...] there is no work of art that does not appeal to a people that does not yet exist [...]" (^{Deleuze, 2016}, p. 343, free translation), Deleuze states that creating is like establishing and populating a desert. In this process, the desert is not an empty plane. Rather, the desert is "[...] a solitude that is already linked to a people to come, that invokes and awaits that people, that exists only thanks to it, even if it is still missing" (Deleuze & Guattari, 2012c, p. 49, free translation). The production of this plane involves cutting out the different existing sensibilities, running at infinite speeds. This notion also appears in 'What is philosophy?', the last work of the meeting between Deleuze and Guattari (2010, p. 257, free translation, emphasis in original). In their conclusion, they also return to Paul Klee when they suggest that creation is mobilized by plunging the brain into chaos, within the logic of the alliance between art, science and philosophy: "[...] that the shadow of the 'people to come' is extracted from chaos, as art invokes it, but also philosophy, science: people-mass, people-world, people-brain, people-chaos". A cut in the chaos for the invention of populating plans is not, therefore, a separation of specific lines out of the dive, but rather a way of facing intensities head-on, soaking in them, and making the machine work with them. Expressions created throughout these movements of cuts and dives are formed, in our research in education, at the intersection of lines - of writing, research, life... - as in Figure 1 below.

Figure 1 Cartographic experiment inviting people to read the text. Source: Prepared by the authors (2022). 

Art, science and philosophy play the role of three great planes of thought, or three 'chaoids', as the authors propose. Art creates, on a plane of composition, 'percepts' and 'affects'; science, on a plane of reference, 'functions'; and philosophy, on a plane of immanence, 'concepts'. These creations have the role not of 'representing' a given reality, but of 'confronting chaos'. Not to organize it, to transform it into order, into organization, into an organism, but to make it work 'machinically', in other words, to produce 'thought' which, from the perspective of these authors, needs to be triggered, deflated, generated by a force external to the individual who thinks, by violence. You always think 'with', therefore, never because you feel like thinking.

[...] the problem is not to direct or methodically apply a thought that is pre-existent by nature and by right, but to give birth to that which does not yet exist [...]. To think is to create, there is no other creation, but to create is, above all, to engender 'thinking' in thought (^{Deleuze, 2006}, p. 213, free translation, emphasis in original).

In this sense, we can say that the movement enunciated here - from chaos to lines -, in what we can feed from it to think about a certain production of research in education in alliance with art, philosophy and other affections, includes, to some extent, following up on the question suggested by ^{Corazza (2013}, p. 204, free translation), when the author asks: "How does didactic creation [and/or research creation] attribute value and meaning to elements of the percepts and affects fabricated by art; of functions, produced by science; and concepts, created by philosophy [...]?".

What lines populate the in-between, the connections, the between-materials coming from these fields in proposing experiments in educational research? What research methods, procedural and theoretical inventions, among others, can arise when we associate ourselves with these lines, seeking not to settle in each of these fields punctually, but to move between, or 'along' (^{Ingold, 2015})?

Tim Ingold also offers us some other indications of these problems when he states that

At first, people live in a world made up of lines, not things. After all, what is a thing, or even a person, if not a knot of all the lines, all the paths of growth and movement, that gather around it? In its origins, 'thing' referred to a gathering of people and the place where they met to go about their business. As the derivation of the word suggests, 'every thing is a parliament of lines' (^{Ingold, 2015}, p. 21, free translation).

In this way, we can suggest that the settlement, previously referred to as an act of creation, is given 'from' and 'with' the lines. Perhaps also associated with the meaning that ^{Deleuze (2016}) proposes for the concept of creation, not as the establishment of a separate object and/or resulting from a pre-existing mind or subject, but as the taking up of ideas in a specific domain - here, in this case, dealing with the specific domains established by the teaching-research that is outlined throughout research practices in education. Lines that come from diving into chaos and populating the plan drawn up about it. To ally oneself, therefore, with the people who do not yet exist, knotting their lines.

In a way that seems curiously aligned with Deleuze-Guattarian perspectives (although not directly), ^{Ingold (2015}) also allies himself with Paul Klee, insofar as he begins to present perspectives on walking, wandering, roaming: in other words, the free, inventive, spontaneous path, and not the simple connection between different points of departure and arrival, as in a journey made over the shortest distance and using the shortest time possible.

As Klee memorably points out, the line that develops freely, and at its own pace, 'goes for a walk' (1961:105). [...] While the active line of a walk is dynamic, the line that connects adjacent points in series is, according to Klee, 'the quintessence of the static' (ibid.:109). The former takes us on a journey in which there is no clear beginning or end, the latter shows us a collection of interconnected destinations that can be seen, as on a route map, all at once (^{Ingold, 2015}, p. 108, free translation, emphasis in original).

It is from this perspective of the walk proposed by ^{Ingold (2015}) that we give movement and articulation to the thought about some possibilities of settlement. It seems coherent to us, within our discursive community, to produce researches in education that invent - procedures, experimentations - in alliance with lines that go out for a walk, to wander. Researches in educarion that don't connect destinations, fixed points, or propose a path through a predetermined route, but that freely populates a plane along its powers, intensities, speeds and sensitivities. As Ingold (2015, p. 111, free translation) suggests, "[...] 'populating' and not just occupying the environments in which one inhabits". Or again, in the author's words:

I think that wandering is the fundamental way in which living beings, both animals and humans, populate the earth. And by populating I don't mean taking a place in the world already prepared in advance by those who arrived to live there. The settler is rather the one who participates from the inside in the ongoing process of coming into the world and who, leaving behind a vital itinerary, contributes to its fabric and texture (^{Ingold, 2015}, p. 119, free translation).

We work in our specific field, education, to produce arrangements that populate our researches with lines: matters in motion, which are how we put our work into the world, and thus constitute ourselves in act. For it is in this production that we become teacher-researchers in education - and here, along with Sandra ^{Corazza (2002}), we assume that teaching and research are inseparable, both between these spheres and between them and life. In this self-formation, we have drawn on some of the lines with which we have worked and we perceive sensitive new lines that emerge from the encounters promoted between arts, geographies, philosophies and other affections. Settlement, therefore, is not a goal to be achieved or a pre-established methodology to be replicated. Settlement is part of a research program. It is a movement that is established in act, throughout the inventive processes. We understand a settlement movement

[...] as the occupation of a certain space-time with compositions of written/read words and images that invite thought as creation, settlement as the invention of routes that open up possibilities for futures and learning. Settlement as creation, therefore (^{Mossi, 2020}, p. 11, free translation).

In order to structure this program, we have allied ourselves with the idea of experimentation put forward by David ^{Lapoujade (2017}, p. 78, free translation) when the author states that "[...] only by answering will we know what the question was". It is only by experimenting, testing, operating, setting our thoughts in motion, and therefore populating, that we construct our research and invent ourselves in the face of it. In our specific case, it has been by dancing that we have promoted our encounters, that we have made previously unseen lines visible. That we give these lines a provisional consistency and compose traces of our choreographies in lineament in a reserach in education. That we see the research create for itself a body that dances.

Populating by the encounter: a [research] dance[s]

"Why walk there when I could shuffle-ball-change the whole way?" asked O'Neal LaRon Clark in a letter to his teacher, bell hooks, reproduced in the book 'Teaching to Transgress' (^{Hooks, 2013}, p. 261, free translation). We think of this shuffle-ball-change, this waddle in our teaching-research movements. Betting on this ethical-aesthetic-political stance, we joined the aforementioned walk through by Klee-Ingold double and twisted it, composed it into a dance. To do so, we operate a dance in the manner of Paul ^{Valéry (2012}), for whom this is an art with movements, an insurgency that is not measured by the economy of forces nor does it conclude in the resolution of specific objectives. Rather, it is an artistic manifestation that seeks, in the midst of the body's movements, the production and modification of senses, the creation of sensations. It is the blocks of sensations, the percepts and affects (^{Deleuze & Guattari, 2010}) that are preserved and proliferate beyond the art itself. We experimented with this type of conservation, proliferation and resistance from the research movements that we enunciate in dancing, because, rather than proving hypotheses, we see the need to produce with lines that emerge from the research and dance beyond its limits, beyond the research itself. A brief experiment with the establishment of these sensations was carried out in the epigraph of the dissertation mentioned here, shown in Figure 2.

We don't use dance as a metaphor here, but rather as a research practice, as an inventive power that concomitantly brings out the materials and effects of the research. By materials we mean what the research, mobilized by a guiding question, manipulates, twists, reassembles, expresses or manifests in a common field of problems with art and philosophy in education, and by effects what emerges from these experiments - in general, writing and reading, actions which are often accompanied by images, not as representation, illustration, reaffirmation of ideas, but as tension, friction, conversation, invitation to thought as creation. The aim here is not to produce a prescriptive methodology that aims to be applied as a research formula. Rather, it's about what effectively, in our encounters and in our inventions of methods, can give rise to new lines of research. Because in our encounters, in our methods, dance occupies this frontier place between concept and field of research, in openness to practices - which are not disassociated from theories at any time. To this end, we don't necessarily dance extensively, covering a specific space, a support, a stage - although the choice not to perform extensive dance doesn't place it in a hierarchically inferior position to our practices, because we have enormous admiration for dance. What we produce are intensive movements, considering body and thought in unity.

Figure 2 Appropriation of a piece of music to the research interests. Source: Prepared by the authors (2022). 

When we turn our attention to the movements, we think along with the african-gaucha dance master Iara Deodoro, who draws attention to the dance that takes place 'between' the movements, a sensation that "[...] is found in the interval, in that little core" (^{Costa, 2020}, s/p, free translation). An intensive dance that seeks, in alliance with art, to create percepts and affects that flood the specific domain of education, overflowing the functions of logical science and the concepts of philosophy.

Art is the language of sensations, which makes you enter into words, colors, sounds or stones. Art has no opinion. Art undoes the triple organization of perceptions, affections and opinions, which it replaces with a monument made up of percepts, affections and blocks of sensations that act as language (^{Deleuze & Guattari, 2010}, p. 208, free translation).

Making the forces that are engendered in the research falter, getting rid of the desire to fulfill a certain established objective and to take advantage of precisely the powers of this faltering in a free development that pulls us out of comfort without losing sight of learning. We didn't pre-establish as a parameter that we would dance as ^{Valéry (2012}, p. 29, free translation, emphasis in original) proposes, but in our practices, in act, we realized that, as the author proposes, a "[...] state of dance is created".

Researches, then, that invent with these alliances - with art, philosophy and other affections. Researches that, before proving or revealing something, provoke through the creation of states (of body, of thought). Researches that invite the lines - of force, of learning, of formation - to dance. In this sense, below we present three variations that arise from our research. We don't present them as representations of universal methodologies, nor do we seek to exhaust their possibilities here. In these writings, we make compositions with these learning-inventions (^{Kastrup, 2001}), so that we launch them into a world about to unravel and remake itself. Here are some of the threads we have worked with, with the intention that they will be pulled, thrown into new dances, and that new wefts will be produced with them.

Doing [research in] education: operating in the encounter with arts and geographies

Along the operations we have been doing, and the reverberations they produce in these lines of writing, we have identified some vectors of forces in the midst of the dives we make when researching education with arts, philosophies and geographies. In this sense, here-now we can dimension research in alliance with the notion of encounter. Encounter because we write, research and do education based on the encounter between different bodies, with different backgrounds and different possibilities for doing research. Because it is in the encounter where material exchanges and sharing take place, where affections flood bodies and produce variation. When multiple trajectories meet, when different lines intertwine to produce a knot, Tim ^{Ingold (2015}) suggests that a unique place is produced. And it is precisely from these places that we are able to propose perspectives for a world about to be made, that we launch our proposals and ways of doing research. We understand the field of [research in] education as 'space' in the way proposed by British geographer Doreen ^{Massey (2008}): always unfinished, open to multiple possibilities. And it is from smaller places that proposals and negotiations are launched which, in a change of scale, produce the great space. We therefore start from what we produce in our research sites so that we can form part of the stories that produce the Research space, which is also unfinished and open. We don't aim to capture its totality, but to create cracks through which we can dance. Still with Ingold (2020), we think of composing with a 'minor tone' in education, producing different sensations through the medium and through the gaps in what is seen as 'major', large or even absolute. Breaking down what is rigid in Research - in the great Research in Education. Making the teacher-researcher's body deviate a little from its hard lines (^{Deleuze & Guattari, 2012}a), allying itself with smaller becomings, with sensations that set it in motion.

In the middle of a heterogeneous group, a geography graduate meets a teacher mentor from the arts. We operate in this encounter in search of inventions in education - with geographies, and arts, and... It is produced in alliance with a chaotic attractor - a notion that arises in modern mathematical physics, but here is highlighted by Gilles Deleuze's borrowing of it, when proposing a zigzag atthe letter Z from his abecedary (^{Boutang, 2001}) and also what Deleuze and Guattari (2010) establish when they rehearse creation allied to dives into chaos. Together with these philosophers, we have appropriated the chaotic attractor - also called the strange attractor and the dark precursor - as a phenomenon that allows singular powers to emerge amidst the forces and intensities of chaos. That which makes us zigzag through multiplicity, producing flashes and glimmers. Virgínia ^{Kastrup (2001}), who works with reverberations of the Deleuze-Guattarian contribution by proposing the notion of learning in alliance with invention, suggests that teaching takes place precisely as a chaotic attractor. It rejects transmission in order to ally itself with what is created in the encounter. And it is on the basis of these precursors that we see flashes of light emerge in our encounters, from which we move the forces that drive our research.

In the beginning, cartography

[...] neither inscription nor description has anything to do with the creation of lines (^{Ingold, 2015}, p. 179, free translation).

One of these flashes that emerged amidst the zigzags of the lines of formation and teaching with which we work is the practice of producing what we call Domain Specific Maps of our researches. This practice is carried out within the scope of our advisory group and originates in the aforementioned research coordinated by the second author of this article. The map development exercise was one of the first activities carried out by the first author during his master's research in education. The research Specific Domain Map (Figure 3) brings together ideas, concepts, notions, phrases, memories, words, desires and, above all, connections. In fact, more than connections, they are real paths, journeys not merely between fixed points, but 'along' (^{Ingold, 2015}) lines of thought, producing variation in all the parties involved in the process. Because in these traces, consistency is made up of the process of going out to scratch, of walking across the paper. Lines of research ambitions.

The map does not represent the research, but is a constituent part of it. For this reason, it is not intended to present everything that is done throughout its pages, nor does it imply that the final text will be a written version of what has been crossed out on the map. It is not a pre-established route. It doesn't appear so that we can just visualize ideas, but so that we can create new ones by experimenting. Its lines set thinking in motion, they operate by cracking stable consistencies. Experimenting with the map can help to test how things that are important to the research are related when they are brought together, but above all when we give expression to the lines that run through the materials, concepts, alliances and operative propositions of an investigation. What effects can emerge from this composition? What new arrangements can be sought, tested and proposed? How can they work, and even how can they not work? The map, then, "[...] has, rather, a pilot role. [...] it doesn't work to represent something real, but constructs a real to come, a new kind of reality" (^{Deleuze & Guattari, 2011}, p. 106, free translation). In the counterpoint of control over research, it is at the service of producing consistency for some intensities that traverse chaos at infinite speed without predetermined form or function.

Figure 3 Specific Domain Map of the first author's dissertation research. Source: Prepared by the authors (2022). 

Without explaining what is crossed out or falling prey to the temptations of an interpretation, for now we'll just pay attention to the string that runs across the map, connecting corpo [body] and mundo [world]. Understanding its limited size, the string cannot complete the desired route if the idea is to pass through all the things that populate the map. It is necessary to choose where the string goes, through which regions its dance produces the most appropriate sensations for the moment of the work. You may also decide to disconnect corpo from mundo, or you may decide to look for another piece of string, or other threads, somewhere else. There are no rules preventing any of this, as the idea is to carry out the operations that seem most appropriate and coherent. Unusual variations. Let's just keep one question in mind: does it work?

The research Specific Domain Map visually presents a series of lines. In the perspectives with which we work - especially ^{Ingold (2015}) and ^{Deleuze and Guattari (2012}a) - the lines are ontologically prior to their inscription or description. They don't start to function in the world from the moment we identify and inscribe them, as in the paper map presented here. Rather, maps are a constituent part of these lines, or give expression to them, like a caesura in the chaos that suggests a possible visibility, suggests form to the forces that, until the production of the map, ran at infinite speed in the amorphous chaos that precedes thought. They are not the mere representation of an external reality, but the invention and very establishment of realities of investigation.

So, a dance: choreographies; twists

"[...] breaking the supposed integrity of spatial structures towards a generative space-time choreography that is always in movement" (^{Massey, 2008}, p. 88, free translation). Proposing a way of thinking about education in conjunction with the philosophies of Spinoza and Deleuze, Sandra ^{Corazza and Tomaz Tadeu (2003}) return to the famous question posed by the Dutch philosopher, a question that he himself never got to answer, and which has produced many echoes and reverberations in the thought of this French philosopher and the thought of difference with which he is allied and which he helps to outline. The question: what can a body do? 'What can', here, does not take on the dimension of what a body can or cannot do, something that we would answer through the illusion of lists or tables denoting innate faculties, but rather pays attention to the powers of this body, its limits and porosities in terms of its ability to affect and be affected throughout encounters (with people, things, sensations...) - which for Spinoza, and for those who ally themselves with his thought to produce new movements, is always understood to be inseparable from the mind; matter and thought in unity.

Operating from the encounters - in which bodies affect each other, in which bodies make and unmake their powers - the Corazza-Tadeu duo sees cartography as a way of making visible some of the lines that we wouldn't have been able to perceive without these operations. "That's what a cartography, a diagram, a plane of immanence is for. To find out what a body can do" (^{Corazza & Tadeu, 2003}, p. 69, free translation). Here, then, we turn to thinking about 'what can’ a dancing body do. As we have already mentioned, we are interested in the gaps, the intervals between movements populated by lines in dance. And here we begin to produce twists in our thinking, experimenting with what interpenetrates on the levels of art, geography, education and philosophy. We allied ourselves with a gap that ^{Corazza and Tadeu (2003}, p. 60, free translation) offer us when they say that "[...] only a plane of immanence can make the curriculum dance [...]" and we then thought about what kind of work, what kind of experimentation is insurgent in order to be able to produce these states of dance - in ^{Valéry's (2012}) terms - in a unique alliance between the planes of immanence of philosophy, the composition of art and the organization of sciences such as geography and education itself in some terms.

Well then, the idea of making twists in thought, working in alliance with the philosophies we have mentioned, and considering that our specific domain is education, leads us to bet on the dimension of learning 'from' and 'in' the body. We understand that a movement of thought is a movement of the body. Our dance, therefore, is a dance with ideas, a dance with learning. More precisely, a dance with lines of learning that we have identified aong life, teaching, research, academic grading and self. Assuming, therefore, an uncontrollable characteristic that learning denotes, since learning is precisely something that cannot be captured (^{Kastrup, 2001}; ^{Gallo, 2003}), we draw on some of the lines of strength, learning and formation that seem to emerge from the encounters and movements of invention with researches and then invite these lines to dance. Not in the sense of reproducing memorized steps, but of potentiating sensations, producing spins, jumps and somersaults throughout the research movements and allying ourselves with what is created with this state of the body in dance, with the sensations of this dance.

We work with sensations because, as ^{Deleuze and Guattari (2010}) mention, the perceptions and affections of what we experience are allied to opinion, to the umbrella that protects us - or seems to protect us - from chaos. But it is by tearing through this umbrella that we can face chaos head-on, so that we don't limit ourselves to what happens only in the instant, but can reverberate what remains, what vibrates, what overflows. In our terms, reverberate what is created when dancing; in the authors' terms, the sensations in their blocks: percepts and affects. Sometimes we find it strange how these sensations gain strength through the structures of academic research - an example is shown in Figure 4, through one of the pages of the first author's dissertation - but this strangeness doesn't paralyze us - actually, it moves us.

Figure 4 Example of a page from the dissertation produced by the first author. Source: Prepared by the authors (2022). 

With the intensities of a dance, we give provisional consistency to the lines, producing what we have been calling 'choreographies' in a 'dance-research'. Thus, we find ourselves with cracks in our understandings of cartography - with the license to mix, in an encounter, specificities of the cartographies produced by geography and those produced by philosophy. Part of these fissures and strangenesses - sensations that we don't want to get away from, but with which we produce a thinking-dancing-writing - leads us to work with dimensions that cross the different planes of thought, the 'chaoids' mentioned earlier in the philosophies of ^{Deleuze and Guattari (2010}). This is what we mean when we mention taking forward Sandra ^{Corazza and Tomaz Tadeu's (2003}) suggestion about the possibilities of putting a curriculum to dance with a plane of immanence. In our case, we are investigating what overflows 'between' the chaoids and produces particular lineaments with sensations and states of dance. We ally ourselves with what Silvio ^{Gallo (2003}, p. 68, free translation) proposes, for whom working with these philosophies in the field of education takes place in "[...] an intersection of planes: the plane of immanence of philosophy, the plane of composition of education as art, multiple planes of prospection and reference of education as science(s)". These methods and ways of doing research in education lead us to constantly question what we are creating. Because our research is populated with lines that emerge in the dance of encounter, but can we define what we are creating?

It is by working at the intersection of planes that we launch ourselves into inventive movements with our research. We shake up the lines of a formation, giving movement to points that were previously considered fixed. In the interval between movements, dance, as Iara Deodoro suggests (^{Costa, 2020}). This mobilization of body states is combined with the production of works 'in composition', in other words, works that move towards the sensations of art - because it is with art that plane of composition is made - overflowing the functions of logical science and the concepts of philosophy. Therein lies our dance, in the state of the body that moves at the same time with the lightness of one who touches the skies and maintains the balance of one who does not lose the security and firmness of the ground.

These operations of safety and risk at the same time lead us to think of composition - the work with sensations in art - in the same way as the refrains that ^{Deleuze and Guattari (2012}b) invent in the production of their philosophies: jumping, turning, singing a little song, whistling, a tra-la-la, producing a place that gives us the safety of a house, but a house whose lines are always changing, a house to which we will never return, because it no longer exists. These compositional propositions go hand in hand with some of the notes presented in Silvio ^{Ferraz's 'Livro das sonoridades' (2005}, p. 78, free translation), especially when the author suggests that we think of "[...] music as being that place where, at the same time as we are thrown into it, we are thrown out". Ferraz (2005) explicitly uses this concept to think of music within its specific domain. Here-now, we dare to summon to a dance some lines that cross sonorities, populating a plane of composition - intersecting planes of immanence and organization - and making other lines sensitive. In this operation, some lines of dance stand out, after all this field doesn't happen far from the field of music, but the two are always in alliance. For Iara Deodoro - with whom we have teamed up to think about dance in between movements - "[...] music and dance are two elements that complement each other. There is no batucada, whatever it may be, with the body standing still" (^{Truvão, 2017}, s/p, free translation). And with these compositions that sing, play and dance, we give provisional consistency to the lines that emerge from the research. Therefore, in our case, there is no dance-research that doesn't summon up a multiplicity of lines for its composition. Lines of writing, lines of life, lines of sound, lines of learning, lines of strength and invention. Lines of a formation set in motion, undoing and remaking itself in dance in between research-teaching movements. This is how we keep our teaching formation and selfmaking open, choreographing.

A good job, an effect of its own, an overtaking of language...

Let's now take a brief look at the movements that are taking place in the master's research in education we are discussing here. When we propose a dance-research project, we often come up against the need to define some of its singularities, to affirm some of its differences, what in fact produces cracks in the great research. The emergence of a way of doing research in education. To this end, we can think along the lines of Roland ^{Barthes (2005}a; ²⁰⁰⁵b), who in the last years of his life dedicated himself to a kind of pursuit of the novel, in other words, to outlining the conditions for writing that unfolds in a novelistic mode, something that can only be said - or only cause the singular sensations it intends to cause - through a novel as a relationship between form and content. We think of this in conversation with the notion of the specific domain of creation enunciated by ^{Deleuze (2016}). We have shifted these Barthesian and Deleuzean thoughts in order to put into writing lines, then, that which, it seems, can only be said, or can only provoke the intended sensations, through a dance-research and its choreographies. Since we are allied with the 'effects of dance' (^{Valéry, 2012}), we are looking for an own effect' (^{Barthes, 2005}a) for a dance-research.

Throughout our experiments, it seems to us that this is a question of overtaking a certain language: that of the larger surveys. Not a rejection, a destruction, but a composition alongside, underneath and in between, which is made at the same time, which produces fissures - Figure 5, for example, emerges creating gaps in the structure of the research and also of this text itself. As a result, we find research companies that add intensity to our movements and give strength to our searches. Kuniichi ^{Uno (2018}, p. 74, free translate, emphasis added), when producing philosophy allied to the work of Hijikata Tatsumi, the Japanese choreographer who invented the dance that in the Western world we call 'butô', instigates us when he says that "Hijikata was looking for something that overflowed dance through dance. This something overtakes dance, but also mocks this overtaking. Dance is experimented with in order to question this 'something', this gesture of overtaking". Because it is something like this, close to this 'something', that we seek to produce with dance-research. We have therefore shifted the meanings of these authors' writings to our inventions in education. This is something that gains strength throughout the proposition of overtaking a language when we take up ^{Barthes' proposition (2005}b, p. 138, free translate) that "[...] language = generalized morality". Because we are, and we have stated this along these lines of writing, much more interested in producing small ethics that falter from this morality and in its stratifications produce cracks. A 'something' that questions the hard lines of morality. Still with ^{Uno (2018}, p. 49, free translate), and without ever forgetting that thought and body occur in unity, we put on our dance floor, in our intersecting research plans, the author's proposition that "[...] since there is always language that dominates the center of the institutions that control the body, it will be necessary to modify language itself". It will therefore be necessary to modify the very structures of major research in education, and for this we dance with smaller movements, we invent with a dance-research.

Figure 5 What is created? Source: Prepared by the authors (2022). 

And along these movements we meet other bodies that dance. They do it in more or less explicit ways. Sometimes we have to invite them to the dance, sometimes they appear to us already dancing, and it's they who get us to dance. In the dance-research mentioned here, we work with different materials that have aroused our interest and set our thoughts in motion. These materials can come from the sciences, philosophies, the arts... and we give them all the same value, without differentiating them hierarchically. The question is much more about how they make the research machine work than what they are or where they come from. One of those materials that arrive at the ball without even needing an invitation, but acting like bodies that drag us by the waist, is the film 'Good Work', by French filmmaker Claire ^{Denis (Denis & Grandperret, 1999}). In the film, as in a significant part of Claire Denis' work, bodies speak far beyond (or below) words. Where dialogues would normally take place, dances appear. There is a whole game, a montage that presents us with movements of bodies deviating from the harsh and generalized morals typical of a military environment. Dance as an ethic of life, as an escape - in the manner of the learnings with which we dance through these choreographies. There is a tension between hard, malleable and escape lines (^{Deleuze & Guattari, 2012}a).

This way of making cinema that Claire Denis offers us in 'Good Work' enters the dance-research beyond an object or an audiovisual reference, not least because, as we mentioned, our operations take place in a prior sphere¹¹ to the Western-modern separation between subject and object. The body "[...] is a thickness that exists before subject and object are divided" (^{Uno, 2018}, p. 75, free translate). Along our choreographies, 'Good Work' is part of the construction of a research method. In what way? Through fragments and smaller writings brought together in the settlement of a research. Producing dances in singular places, in between movements, creating bodies in the emergence of lines that unfold along the encounters between bodies, texts and images. We have teamed up with the film to produce a research that, populated with lines, dances in education. We don't pursue the sensations created by Good Work', because we understand that these are produced by the ideas created in cinema, in its specific domain (^{Deleuze, 2016}). But we overflow part of these sensations by producing a dance in a research in education. Very briefly, and without intending to limit or close off the inventive possibilities in the encounter between educational research and a film - after all, we will never be able to deal with the whole, and nor do we want to - we can use the following phrase - shown in Figure 6 - by director Claire Denis (^{Karam, 2019}, p. 105, free translation, quoted and appropriated for this research by the authors) in an interview with the British newspaper 'The Guardian', on the occasion of the release of her film:

Source: Quote by Claire Denis from ^{Karam (2019}, p. 105) appropriated by the authors (2022) and superimposed on a frame from the movie 'Good Work' (^{Denis & Grandperret, 1999}).¹²

Figure 6 Appropriation of a phrase from director Claire Denis. Less explanation, more encounter 

Along course of smaller movements, we are giving shape to a research. A research that seeks to exceed language as a norm and moral, that seeks to exceed hard methodologies, that seeks ways of saying and doing research in education from the emergence of its differences, from the effects of its own way of launching itself into a world that is being made and remade all the time. We twist the cartographic methods and propose a research in choreography. In this dance, we compose our writings - we do [research in] education - on refrains, in litanies. Smaller leaps and turns. Launches combined with the intensities of chaos. Changes in sensations. Without previously stipulated objectives, which would have to be achieved along a specific route, but provoking variation 'along' (^{Ingold, 2015}) all the movements. We are much closer to a child's somersault, which ^{Valéry (2012}) presents as a movement that doesn't want to reach another place, but to create for itself the sensations of a new one, of a future. A rhythm that swings and goes crazy, detaches itself from the hard lines that try to stiffen the body, allies itself with what falters, stutters, before returning to a point that becomes a line and moves through the territory (^{Deleuze & Guattari, 2012}b). By allying ourselves with a becoming (Deleuze & Guattari, 2012c) line of a point, we mention the ruptures that the line produces in the systematic attempts to leave it fixed at a point. Because it seems to us that dance does not take place in an intentionality, but in another condition, as the concept of becoming connotes (Deleuze & Guattari, 2012c). We create our lines of escape without destroying the hard lines (Deleuze & Guattari, 2012a), but by affirming our alliances with that which overflows by deviating through the folds of larger structures. Dancing, we launch our research into the world, proposing ways of doing [research in] education. We chanted our tra-la-la, now we're doing research!¹³

Final considerations: openings [to dance even more with researches in education]

In our research work, we pointed that we are doing education. And that this work takes place in an encounter between teacher-researcher bodies with academic backgrounds in the arts and geography. We therefore assume that we are working at the intersection of planes of thought, taking advantage of sensations from the arts and concepts from philosophies to create cracks between the functions of logical science - understanding both education and geography as sciences. We don't intend to limit our work by closing off potential possibilities. Our intention is to provide a real possibility for working and experimenting with lines, avoiding falling into the infinite intensities and speeds of the chaos in which we plunge. We believe that ideas arise from experimentation in a specific domain of creation (^{Deleuze, 2016}). And when we situate this domain on a particular dance floor, when we invite its lines to dance with our encounters, we see new lines emerging, we see new bodies making themselves - and learning to dance - between educations with arts, geographies, philosophies and other affections that accept the invitation to a dance. We see a way of being emerge in the face of a state of dance (^{Valéry, 2012}). Bodies that dance and write to move thought, to make thought think, and not think in order to dance or write. Like Iara Deodoro's dance (^{Costa, 2020}), which emerges 'between' the movements, dance-research also emerges 'between', resonating Valéry's (2012) state of dance in lines of writing.

This work of putting a research to dance in education - of dancing along the lines of teacher formation, as the guiding question of this article suggests - gains strength and consistency - albeit a provisional consistency - along with the movements of operating an experimentation at the intersection of the planes of immanence, organization and composition. In this way, we don't lose or erase important characteristics of these planes, but take advantage of possible overflows between them. If a desert to be populated is established over a domain, the work of populating it does not happen in a chaotic way, but from the lines that are drawn from the chaos. It's a job that requires rigour, even if it's far from the constraints of a larger methodology, organizations or hard morals (the good teacher, the good way of researching). Between the hard lines, which can be reminiscent of military training, and the escape produced by a dancer - both images in ‘Good Work' -, the research makes its body in the manner shown below, in Figure 7.

Source: Prepared by the authors (2022) in composition with frames from the movie 'Good Work' (^{Denis & Grandperret, 1999})

Figure 7 Example of a page from the dissertation produced by the first author: a dance text combined with bodies on stage 

Thus, it seems to us that we carry out movements that overflow along 'smaller' and 'intense' paths. Smaller because they don't ally themselves with the engenderings of larger practices, but take advantage of the stratified structures to build gaps, leaks, cracks, wiggles and twists with them. Like the suggestion of an 'education in a minor tone' that ^{Ingold (2020}, p. 78, free translation, emphasis added) makes from his readings of the philosophies of Deleuze and Guattari:

[...] the smaller no longer flows beneath the larger like a river beneath its banks. It is not below, but in the middle; its domain opens up from the intermediate place (mi-lieu) to encompass the world. The middle is not a hidden deposit; it is an opening to feel.

For fluidity along the movements of a dance-research, we need to work on the body that has been hardened by the hard lines that surround the affirmation of becoming a teacher-researcher. It needs a rehearsal, a preparation to find the lightness of a jump, the ease of a waist, the firmness of a raised neck, the suspension of gravity in a true flight. We therefore ally ourselves with the becoming (^{Deleuze & Guattari, 2012}c) that allows a body to let go of the harshness of a greater education, a greater teacher formation, a greater research. In turn, intense because, as already mentioned, in our research we don't dance for an extension, but for intensities. We are therefore allied to provoking a state of dance in the manner of Paul ^{Valéry (2012}), both in our reading and writing movements. This state, which, as the author suggests, is given, reverberates in the body. And it is with this state of the body, with the intensities that affections go through the body of the researcher-teacher who dances, that we carry out our researches - an experiment in this sense takes place with Figure 8, which closes this work. Affected by this dance, we unfold the lines of writing.

Through these writing movements made up of bodies flooded with the affections of a state of dance, we constitute ourselves as teachers - of geography, of the arts - researchers in education. Much more than delimiting an immutable object of research, it is a question of invoking an ethical-aesthetic-political posture of research in dance, allied to life in terms of the invention of the self and the world (^{Kastrup, 2007}). For it is these movements that constitute us, that allow for the emergence of singularities and differences that do not end with doing teaching-research, but overflow into the spheres of life, of acting as a guide to action. We assumed that there wasn't much sharpness about what we were creating with our research - that's why we joined ^{Lapoujade (2017}), for whom possible answers that occur in the midst of experimentation happen even before the questions have been asked - and this gains strength as we perceive these carto-body-choreographies produced along with twists of thought functioning as machines that are engendered in the education assemblage to ventilate it. And, in the process of creation, they resignify us as bodies-teachers-researchers who are opened up by the research movements carried out. Bodies that dance. We mobilize a thought - which is therefore a mobilization of the body - with the hyphen mentioned by ^{Corazza (2002}) when thinking about the spheres of 'research-teaching'. This mobilization does not refer to a posture of 'teachers who research', as an activity of searching for affirmations in hypotheses, but above all reinforces a proposition of life posture, an ethic in love with not-knowing, to mention another idea of this author. We place ourselves as teachers who research precisely because we don't know our hypotheses in advance, and in research we start to constantly return to our teaching training, undoing ourselves, remaking ourselves, inventing and creating a body that is not intended to remain still, closed or finished.

Figure 8 Experimenting with appropriate citations for research. Source: Prepared by the authors (2022). 

In our case, the reverberations of a dance and the states of dance that flood the body begin to compose new arrangements through the lines and hyphens that make us act and think in the face of a world. Intensive lines and flashes of a chaotic attractor dance zigzagging along the movements of teacher formation. Thus, when we read and write about our researches, we see new lines emerging. Lines that also zigzag, setting in motion the fixed points of a formation. A state of dance, in this research process, remakes the teacher-researcher. It puts them in a state of body that dances. Teacher-researchers-bodies-that-dance. Teaching-research-dance. Because in our movements, dance has never been a mere prop. Dance assumes a certain centrality in the constitution of these bodies that are made in their intensities. And who, through lines of writing in dance, set out to find new dances. When we invite words to dance, we recognize their movements, explore their intervals and respect their rests. This is the posture of experimentation that builds this research. At times, it makes the bodies-materials dissolve in movements of intensity, searching for the dance to come in their intervals. When we dance with words, we value what is unique about each one of them. We want each line of writing to dance, affirming its difference, its open body. In addition to ^{Ingold's (2020}) proposition of a minor tone in education, the author brings us the image of the poet as a craftsman of words, who in his ways of saying seeks what can be said precisely through poetry and its specific sensations. Instead of explanations, which, in the author's words, "[...] block the doors to feeling [...]" (^{Ingold, 2020}, p. 78, free translation), the idea that we come to meetings, such as classes, to "[...] make poetry together" (Ingold, 2020, p. 79, free translation). In other words, that we can take advantage of the affections produced by the bodies in encounter in order to, with them, find that which emerges specifically from encounters, which can only be said - and thus take on specific forms of the use of words - from singular encounters in the midst of multiplicity. It is with this power that we dance. It is with this poetic artisanship that we invite the lines to dance. It is with this 'minor tone' that we produce gaps and cracks in the great research and make an education flooded by a state of dance. Let's dance.