What sort of evidence can we bring to bear on such a problem? It is precisely at this point that the study of learning asserts not only its theoretical importance, but even its necessity as it may be impossible to recognize the co-variation and symmetry that define the logic of commercial practice without assuming the perspective of a partial participant whose vector or trajectory of participation effectively leads from one limit of the field to the other. Indeed, it is essential that we “bring ‘degrees of development or perfection’ into the picture.”¹¹⁶ By following and recording the essential moments of K’s passage from the field’s minimum limit to its maximum limit, from a state that “scarcely rate[s] a score for being alive” to a state of relative “well-being,” we open ourselves to the possibility of recognizing a certain connection.¹¹⁷ The social field accounts for the two-fold truth of society’s working relations: such a truth cannot be stated in terms of “capital” precisely because it concerns the very conditions that capital itself presupposes. It is the social field that has the potential to account for the connection between those very relations and a complex process that deserves to be called “learning” that accounts for the experience of how “newcomers become part of a community of practice”.¹¹⁸
The anthropology of apprenticeship has established, under widely varying historical periods and cultural contexts, a kind of progression in which the learner moves “backward” relative to the corresponding “production process”. Our task is to specify the indexical ground or point of departure and the terminus or point of arrival of the learner conceived as a “legitimate peripheral participant”. Moreover, what appears as the points of departure and arrival for the newcomer-learner should appear as precisely the opposite for full participants in the productive process: “the ordering of learning and everyday practice do not coincide: production activity-segments must be learned in different sequences than those in which a production process commonly unfolds, if peripheral, less intense, less complex, less vital tasks are learned before central aspects of practice.” That is, the sequences in question are effectively reversed. For example, “tailors’ apprentices… progressively move backward through the production process to cutting jobs”.
When the production process in question is tied to the economy of money-wages, legitimate peripheral participation can be represented using the same vector scheme that we introduced in the previous section (see Figure 1.22).
The orientation and magnitude of the learning vector are determined by the specific community of practice in question; the sense, however, is no longer determined by the productive activity characterizing that community but by the process of legitimate peripheral participation.
Beyond this, we must account for the magnitude of the vector. The unit of measure for the magnitude of any particular labor-learning vector is intensity: “legitimate peripherality is a complex notion, implicated in social structures involving relations of power. As a place in which one moves toward more-intensive participation, peripherality is an empowering position.”¹¹⁹ In framing the problem in terms of intensity, we afford ourselves the means of empirically measuring the magnitude of a given labor-learning vector and, more profoundly, an objective means of comparing the vectors characterizing otherwise disparate communities. When we say “more-intensive,” we obviously don’t mean to suggest that intensity can be reduced to a question of abstract quantities. On the contrary, what we mean is that the production process invariably concerns a given “activity system” that can be broken down into a series of meaningful “activity-segments”.
Take, for example, the case of the tailor’s apprentice: “Learning processes do not merely reproduce the sequence of production processes. In fact, production steps are reversed, as apprentices begin by learning the finishing stages of producing a garment, go on to learn to sew it, and only later learn to cut it out.” In this description, one finds precisely three activity segments that can be glossed by the words “cutting” — “sewing” — “finishing”.
In the final analysis, only when the magnitude of a given vector–-labor, capital, learning or otherwise–-has been determined with respect to the generative structures of the field do we draw near an adequate account of a concrete “trajectory of participation”.¹²⁰ And if K’s experience working in the dealership constituted a bona fide apprenticeship, there should be clear evidence of a backward or retrograde relationship between two progressions, between the progress or development entailed in apprenticeship learning (from less to more intense) and that of the productive process itself (from more to less intense).
Overlapping communities. How does situated learning hold up when the workplace in question is an organization that combines a number of distinct revenue-producing activity systems such as K experienced in the dealership? The “concept of community underlying the notion of legitimate peripheral participation, and hence of ‘knowledge’ and its location in the lived-in world, is both crucial and subtle.” We define “community of practice [as] a set of relations among persons, activity and world, over time and in relation to other tangential and overlapping communities of practice.”¹²¹ This formulation raises two specific questions: that of legitimate peripheral participation with respect to “overlapping communities of practice” and that of “tangential” social structures and how they might account for “‘knowledge’ and its location in the lived in world”.
Recognizing that legitimate peripheral participation can be visualized by reversing the ordinary sense of a labor vector, what happens when the target situation involves not one community of practice but several “overlapping communities of practice”? More specifically, what are the consequences for legitimate peripheral participation? Given the terms of the question and assuming there are three overlapping communities of practice belonging to a single same world or organization, we can discern two answers or possible scenarios. In the first scenario, legitimate peripheral participation remains indifferent to the fact that the organization or firm consists of three departments (see Figure 1.23). That is, whether or not the situation entails overlapping communities of practice, legitimate peripheral participation is still determined to be a function of each individual community and its organizational unit or department.
By conceiving learning as legitimate peripheral participation we can say in precise terms what is problematic about such a scenario: in effect, it assumes that we are talking about the experience of three different subjects or legitimate peripheral participants. When we further specify that the situation concerns a single newcomer-apprentice like K, this scenario tends to break down.
To begin with, it breaks down in terms of direction and sense: all three vectors share a common direction and sense, which means it would be redundant to say that a single legitimate peripheral participant had to re-learn the same lesson three times over. Similarly, all three vectors share a common aggregate of departure, namely money-wages (w). This, we argue, is an instance of how the magnitude of a vector can be determined as a function of a “tangential” social structure. In effect, that very structure partially determines first activity-segment constituting the magnitude of each labor-learning vector. This being the case, the first activity-segments of each vector will be similarly determined. Again, as was the case with respect to direction and sense, it would be redundant to say that a single legitimate peripheral participant had to re-learn what essentially is the same lesson over and over again.
What happens, however, when the activity-segments under consideration are no longer determined by a common tangential social structure? That is, what happens when legitimate peripheral participation moves away from money-wages (w) toward “more-intensive” activity segments? Assuming that learning is indeed a partially “empowering” process, we can restate the question by asking, what happens when the margin of freedom of the labor-learning vector or well-being of the worker increases?¹²² In fact, when the vector under consideration involves an activity-segment that is no longer overdetermined as a function of a tangential social structure, other considerations must be taken into account. Assuming that each of the three learning-vectors under consideration has at least two activity-segments, then we expect the particular qualities characterizing each of those second-position segments will further determine the quality of the first-position segments. This begins to account for the variation between activity-segments that would otherwise be identical with respect to the tangential social structure (in the present case, money-wages).
However, as the second-position activity-segments introduce variation with respect to the first-position segments, a second kind of tangential structure determines the otherwise “free” or independent second-position activity-segments to conform to or resonate with one another. In effect, they form a set that is no longer determined as a function of a common limit (the economic instance in the form of money-wages) but now as a function of a common or shared position in a wave or larger field. Above, the scenario in question proved inadequate because it appeared to have the same learner re-learning the same thing over and over again. In this case, the scenario proves inadequate because it fails to capture what the model predicts as the consistent and systematic relations between heterogeneous activity-segments constituting otherwise distinct labor-learning vectors. When it fails to account for the fact that the learner is doing more than encountering activity-segments characterized by particular qualities, it essentially fails to account for the possibility that the trajectory of participation of the newcomer-apprentice is more than the simple reversal of the productive process.
How then do we account for the obvious fact that the three learning vectors in question do not have the same number of activity-segments? It does not suffice, however, to say that the legitimate peripheral participant can simply follow the labor-learning vector with the greatest magnitude. Doing so would suffice in terms of direction, sense and the two instances of tangential structure that we have already considered, but it does not account for the variety of particular qualities characterizing the activity-segments of the three labor-learning vectors. Such considerations bring us face-to-face with what is perhaps the single most important question we raise and answer in this volume of our larger publishing program: If we do not wish to “presume too literal a coupling of work processes and learning processes,” or what we have been treating here as the coupling of labor and learning, then what exactly is it that ultimately distinguishes the one from the other? In other words, what is the essence of legitimate peripheral participation? In fact, everything that we have assumed in the first scenario fails to uncouple labor and learning in any profound way. What we have said with respect to learning is no less true from the point of view of labor: what could be more literal a coupling than the simple reversal of sense? If learning does nothing more than retrace the path of labor, then how can we claim that “learning is an integral part of generative social practice in the lived in world”?¹²³ On the contrary, unless the necessity of learning is determined in some other way, it would appear to be no more than a trivial part of practice or, at most, a theory of reproduction — specifically the reproduction of the various forms of labor characterizing the world as it is.
The importance of our vector schemes or diagrams asserts itself at this very point. If our line of reasoning appears to have reached something of a dead end, then we must revisit some of our earlier assumptions. We have proceeded from the understanding that the complete specification of a vector entails three terms: magnitude, sense and direction. Concerning the first, we have found no reason — empirical or theoretical — to distinguish labor and learning in terms of magnitude. Concerning the second, we found both the observations made by the anthropology of apprenticeship and the concept of legitimate peripheral participation lead us to assume that the difference between labor and learning was a difference in sense (represented by the reversal of arrows); as we suggested above, this is an obvious difference, one that continues to presume a literal coupling of labor and learning.
What remains, then, is the question of direction or orientation. In fact, the solution to what would otherwise be an insurmountable obstacle in our effort to determine the essence of learning presents itself when we withdraw our initial assumption concerning precisely that dimension of the situation. Specifically, when we recognize the possibility that the direction of the learning-vector in question is determined independently of the direction of the related labor-vectors, a second scenario presents itself (see Figure 1.24).¹²⁴
What is immediately apparent when we compare Figure 1.24 with Figure 1.23 is the necessity of taking into consideration relations between overlapping communities of practice in the study of learning. Why? It now seems that the essence of learning remains hidden or obscured when we restrict our observations to a single community of practice. Indeed, only when learning sheds its feigned modesty or apparent deference to productive activity do we observe its complex relations between heterogeneous communities of practice and other social structures.
Labor and learning are approximately the same in terms of magnitude, obviously distinguished by sense, and essentially heterogeneous in terms of direction or orientation. Learning is uncoupled from the labor process when we are able to determine its direction as diagonal or transversal relative to both the horizontal lines of parallel forms of productive activity and the vertical line of the economic instance. Recognizing as much, one must assume that even in the case of isolated communities of practice (for example, a company consisting of a single department), learning always deviates from the direction of the labor-vector (see Figure 1.25).
The fact that the direction and sense of the learning-vector determines it to move away from rather than toward the limit case of wage-labor, that is the zero point of intensity (w), signifies that legitimate peripheral participation is always a function of increasing intensity and an empowering process.¹²⁵
Relations of power. Having addressed the question of legitimate peripheral participation with reference to “overlapping communities of practice,” we will now address the same question with reference to other tangential structures and their possible relations to “‘knowledge’ and its ‘location’ in the lived-in world”.¹²⁶ We proceed as if those structures are essentially concerned with “relations of power”: “Although apprenticeship has no determined balance of relations of power as an abstract concept, it does have such relations in every concrete case. Any given attempt to analyze a form of learning through legitimate peripheral participation must involve analysis of the political and social organization of that form, its historical development, and the effects of both of these on sustained possibilities of learning.”¹²⁷ Above, we made a strategic decision to restrict ourselves to considering just one-half of society’s working relations, namely labor or revenue-producing activity. At this point, our analysis must continue by considering the other half, namely, capital or property relations.
Previously, we presented labor and capital as having both the exact same direction or orientation and the exact same sense or forward thrust (see Figure 1.21). We distinguished them by placing labor or “profit-making” behind and capital or “profit-taking” out ahead of the economic instance (money). In this way, we determined labor’s aggregate of arrival (money-wages) and capital’s aggregate of departure (money-profit) as two sides of the same social structure or economic instance (wages-capital). What remained to be determined were their respective magnitudes and possible relations.
Using the concept of legitimate peripheral participation, we illustrated how a focus on learning has the potential to shed some light on the magnitudes of productive activity systems. The question now is whether or not those same formulations have the potential to shed some light on the magnitudes of property relations. In fact, as soon as the question is stated in this manner it becomes apparent that legitimate peripheral participation provides little if any way to talk about such matters. If, for example, learning is understood as having the opposite sense of the property-vector, then the learning-vector would always end precisely where it began, namely at the economic instance (p). The logic essentially breaks down at this point.
Recognizing as much, we must rework or extend our analysis in order to account for the form of learning as it relates to society’s working relations taken as a whole and not merely with respect to its productive activities? As we have already indicated, the answer concerns “the concept of community underlying the notion of legitimate peripheral participation, and hence of ‘knowledge’ and its ‘location’ in the lived-in world”. Specifically, “a community of practice is a set of relations among persons, activity, and world, over time and in relation with other tangential and overlapping communities of practice. A community of practice is an intrinsic condition for the existence of knowledge, not least because it provides the interpretive support necessary for making sense of its heritage. Thus, participation in the cultural practice in which any knowledge exists is an epistemological principle of learning. The social structure of this practice, its power relations, and its conditions for legitimacy defined possibilities for learning (i.e. for legitimate peripheral participation).”¹²⁸ While the concept of “community of practice” concerns “an intrinsic condition for the existence of knowledge,” that condition is anything but certain. “There are central issues that are only touched upon in this monograph, and that need to be given more attention. The concept of ‘community of practice’ is left largely as an intuitive notion, which serves a purpose here but which requires a more rigorous treatment. In particular, unequal relations of power must be included more systematically in our analysis. Hegemony over resources for learning and alienation from full participation are inherent in the shaping of the legitimacy and peripherality of participation in its historical realizations.”¹²⁹ Others have responded to this requirement by offering a more rigorous treatment of the term.¹³⁰ In what follows, we offer a treatment of our own.
While “the term community” does not “imply necessarily co-presence, a well-defined, identifiable group, or socially visible boundaries,” it “does imply participation in an activity system about which participants share understandings concerning what they are doing and what that means in their lives and for their communities.”¹³¹ It seems to us that it is precisely this understanding of “community” that has the potential to clearly distinguish two possible subjects, namely the subject of “knowledge” and the subject of “practice”: while the former assumes the products of historically situated activity systems subject to unequal distribution, the latter concerns the functioning of those very systems; the former concerns what “I believe” and the latter what “I do”; the former presupposes the maintenance of a memory (for example, the ledger and the report card) and the latter relations of contiguity in motion (for example, the contiguous segments of the activity system in question).
This line of reasoning eventually led us to ask whether or not there is a relation between the “ambiguity of labor” and that of “capital” and its agents. We have seen how a focus on learning has the potential to go a long way in accounting for the ambiguity of labor in terms that are considerably different or even directly at odds with those used by the sociologist. For him, it is precisely capital (incorporated and institutionalized history) that accounts for variations in “the real conditions of the performance of labor”. In other words, the sociologist uses the various “forms of capital” to explain “the experience of labor”. Assuming this represents a fair reading of his views, what we are proposing is something along the lines of a reversal: instead of explaining productive activity in terms of property relations, we find it necessary to explain property relations by appealing to the learning curriculum that is demonstrably present in society’s working relations.
This means we must include “unequal relations of power…more systematically in our analysis.” In fact, this is what we attempted to do by demonstrating the importance of taking into consideration legitimate peripheral participation as a function of overlapping communities of practice. In effect, the diagonal or transversal vector of learning not only indicates the growing power of the legitimate peripheral participant, but also measures the relative power of each of the overlapping communities of practice. In this way, we have quietly introduced a new unit of measure into society’s working relations, a unit moreover that does not presuppose the “distinction between productive and non-productive, or profitable and non-profitable work” precisely because it refers to the ground on which such a distinction appears to depend, namely intensive degrees of participation.¹³² So long as learning is not recognized as an integral part of commercial practice, money (wage-price-profit) presents itself as the only unit of measure that can account for the diverse forms of productive activity characterizing those very relations. Without learning, money remains not only “the overall constraint” but also the sole measure capable of giving society’s working relations “its whole value”.¹³³ As a result, anything more than “wage-labor” (w) –- that is, the “well-being” that the sociologist attributes to workers who win or are allowed “the freedom to organize their own work”–-is characterized in terms of “self-exploitation” and “misrecognition”. According to him, a worker who enjoys his job is also the worker who has been duped into displacing his or her “interest from the external profit of labor (the wage) to the intrinsic profit” of his or her particular occupation.¹³⁴ We are not saying the sociologist is wrong; rather, we are saying that the terms of his account strike us as prejudging the situation.
The objectivity of money derives precisely from the fact that it is somehow “external” to the productive process. In contrast, the study of learning brings to light a unit of measure that is no less objective for being “intrinsic” to that very process. We will say that the former enters the field by way of relations of extensity and the latter only reveals itself in relations of intensity. Relations of extensity inhere when diverse forms of activity are subject to comparison relative to an alien measure. This has a homogenizing effect on our perception of the situation. In the last instance, everything appears to be a function of money. Relations of intensity, however, inhere when diverse forms of activity and relations of power are taken on their own terms. More specifically, we will show that the consistent and systematic relations between heterogeneous activity-systems can only be ascertained in an objective manner by passing through or following those very relations as a function of what the ethnographer of copresence calls “lived space”.¹³⁵
The important thing to stress at this point is that the emerging field promises to do more than simply depose relations of extensity by putting relations of intensity in their place. Rather, that very field offers us an account of how the one is transformed into the other and vice versa. We mean to show that the objective field in question is characterized by both sets of relations: “[If] it is true that at the heart of power relations and as a permanent condition of their existence there is an insubordination and a certain essential obstinacy on the part of principles of freedom, then there is no relationship of power without the means of escape or possible flight.”¹³⁶
What happens when legitimate peripheral participation is no longer defined only in relation to overlapping communities of practice but in terms of a more general movement that takes into consideration the social field as a whole? We find that all of the characteristics of legitimate peripheral participation remain intact so long as one recognizes that the “backward” movement only relates to half of the field, namely the half defined by a community’s or communities’ productive “capacity”. However, given the preliminary results above, we “must increase the possibility for movement backward and forward.”¹³⁷ Moreover, given what we already understand about legitimate peripheral participation and taking into consideration such a possibility, what now appears is a decentering movement going from the extensive to the intensive. In this way the learning curriculum unfolds in its entirety (see Figure 1.26).
The center of the field is defined by the economic instance (money-capital), now determined as simultaneously a function of both wages (w) and profit (p). The field of participation itself is the ultimate ground, not this or that community of practice. It is only the field which constitutes a “whole…whose combinations create a landscape — shape, degrees, textures — of community membership”. We can say without contradiction that the center of that field is precisely the “periphery” with respect to situated learning. Indeed, there is no contradiction when legitimate peripheral participation is understood as simultaneously a decentering movement relative to the “specific gravity” shaping the field of commercial practice, namely the relations of extensity that determine the role of money as a general equivalent, and a center-seeking or “centripetal movement” with the goal of something like “full participation” defined in terms of relations of intensity: “There may seem to be a contradiction between efforts to ‘decenter’ the definition of person and efforts to arrive at a rich notion of agency in terms of ‘whole persons’. We think that the two tendencies are not only compatible but that they imply one another, if one adopts as we have a relational view of the person and of learning: it is by the theoretical process of decentering in relational terms that one can construct a robust notion of ‘whole person’ which does justice to the multiple relations through which persons define themselves in practice.”¹³⁸
 Gilles Deleuze and Felix Guattari, A Thousand Plateaus, p. 46.
 Paul Willis, Learning to Labor: How Working Class Kids Get Working Class Jobs, p.2.
 Jean Lave and Etienne Wenger, Situated Learning: Legitimate Peripheral Participaton, p.29. “Learners inevitably participate in communities of practitioners and that the mastery of knowledge and skill requires newcomers to move toward full participation in the sociocultural practices of a community.”
 Ibid, Situated Learning, p.36.
 “We have thus situated learning in the trajectories of participation in which it takes on meaning,”Ibid, p.121.
 Ibid, p.98.
 “As a place in which one moves toward more-intensive participation, peripherality is an empowering position,” Ibid, p.36. In “many work situations, the margin of freedom left to the work (the degree of vagueness in the job description which gives some scope for maneuver) is a central stake,” Pierre Bourdieu, Pascalian Meditations, p.204 (our emphasis). In relating “more-intensive participation” to “margin of freedom,” it should be apparent that we are approaching from a different angle “the real tendency towards increasing intensification of labor processes” that Paul Willis, following Harry Braverman, sees in the case of “monopoly capitalism” (Paul Willis, Learning to Labor, p.180). For example, the terms we have adopted here would determine that tendency to be one towards less-intensive forms or fewer degrees of participation and a shrinking margin of freedom. It would seem to follow, then, that legitimate peripheral participation draws attention to social formations that might depend on or exhibit an inverse or counter tendency to “the degradation of work” (Harry Braverman, Labor and Monopoly Capital: the Degradation of Work in the Twentieth Century, Monthly Review Press, 1975).
 Jean Lave and Etienne Wenger, Situated Learning, p.35.
 Pierre Bourdieu writes, “The objectification that was necessary to constitute wage labor in its objective truth has masked the fact which, as Marx himself indicates, only becomes the objective truth in certain exceptional labor situations: the investment in labor, and therefore miscognition of the objective truth of labor as exploitation, which leads people to find an intrinsic profit in labor, irreducible to simple monetary income, is part of the real conditions of the performance of labor, and of exploitation,” Pascalian Mediations, p.202. See also Bourdieu’s note concerning the essential “indifference” that Marx has to assume in order to arrive at an objective understanding of “wage labor”. When learning is conceived as a diagonal or transversal vector relative to the labor process itself, Marx’s wage-labor (the significance of which, as Bourdieu is careful to point out, is more theoretical than descriptive of actual work situations) effectively appears precisely at the ideal point where the learning-vector touches the economic instance (w).
 Such an analysis is indicative of the way we mean to follow Lave and Wenger when they “place more emphasis on connecting issues of sociocultural transformation with the changing relations between newcomers and old-timers in the context of a changing shared practice,” Jean Lave and Etienne Wenger, Situated Learning, p.49.
 Ibid, p.98.
 Ibid, p.42.
Etienne Wenger, Communities of Practice: Learning, Meaning and Identity (Cambridge University Press, 1998).
 Jean Lave and Etienne Wenger, Situated Practice, p.8.
 Pierre Bourdieu, The Logic of Practice, p.117.
 Pierre Bourdieu, Pascalian Meditations, p.204.
 Ibid, pp.204–5
 William F. Hanks, Referential Practice: Language and Lived Space among the Maya (1990).
 Michel Foucault, “The Subject and Power,” in Hubert L. Dreyfus and Paul Rabinow, Michel Foucault: Beyond Structuralism and Hermeneutics, 2nd Edition (University of Chicago Press, 1983), p.225.
 Michael Foucault, “The Masked Philosopher,” in Ethics: Subjectivity and Truth (Paul Rabinow, ed. The New Press, 1998), p.326.
 Jean Lave and Etienne Wenger, Situated Learning, pp.53–4.