The notion of discontinuity for a reading of the spatial configurations of social division

12North America, as does France, has a long history of research on segregation and the social division of space resulting in a large body of literature. However, the issue of discontinuities has never been directly addressed (François, 2002). Indeed, while these terms encompass a set of metaphors describing the existence of breaks separating homogeneous spatial units, methodological investigations have mostly focused on measuring the concentration of populations or identifying large urban areas of social homogeneity (Brun, Rhein, 1994). In a move initiated by the Chicago School, many indices or multivariate statistics were produced, thus meeting the needs of a highly ethnic US context [7] (Grafmeyer, Joseph, 1984). These methods are interesting but present serious shortcomings in the analysis of the social division of space (White, 1983; Wright et al., 2005; Clark, 2006; Duncan et al., 2012). The most numerous are, first, the lack of information on spatial patterns and neighborhoods, and second, the focus on specific populations and the inability to include a range of more or less inter-related indicators (Apparicio, 2000).

13It seems necessary to understand the spatial patterns of social division due to effects related to the association of social difference with spatial proximity. By spatial configuration, we are referring to the positions of spatial groups relative to each other. At least two theoretical configurations can be identified: polarization and fragmentation. Polarization refers to the simple partition of the city wherein large, homogeneous areas are separated by gradients. Taken to the extreme, this leads to a dual structure as described in many major cities and transposed – unmodified – to other cities. Fragmentation corresponds to a more complex spatial structure where groupings are fragmented and dispersed throughout urban spaces. Classic measures of segregation however cannot capture these spatial configurations; despite the fact that they are decisive due to the contextual effects they elicit.

14The issue of neighborhood effects was first developed in the United States, and continued in France with a different approach [8]. However, both approaches postulate the existence of social effects linked to the spatial concentration of homogeneous populations, particularly in terms of social relationships, opportunities, and access to urban resources (Authier, 2006). Coupled with the fact that “the space counts” and that we can “assume that the distance determines the form of the social relationship” (François et al., 2002; Hipp, Perrin, 2006), one can thus assume that the neighborhood affects the shapes and trajectories of social relationships (François, 2002). This postulate is not the focus of our research but it does help justify the interest for fragmented situations in general and discontinuities in particular, where social distance is associated with spatial proximity.

15Two approaches shaped the study of the links between the proximity and similarity of places. The first and most developed dates back to the 1971 article by economist Thomas C. Schelling, which proposed a dynamic model of segregation to explain the formation of racially homogeneous spaces in the United States. There is an abundant literature on positive spatial auto-correlation, a principle stating that two nearby locations are more similar than two distant ones. For Jean-Christophe François (2002), this approach leads to the consideration of spatial gradients and does not capture the social disruptions in the spatial distribution of populations. Furthermore, the second approach considers discontinuities, in a broad sense, to be “what separates two neighboring and different spatial sets.” Therefore, the question is no longer about the intensity of segregation but the forms of spatial separation based on inequalities and social disparities at the neighborhood level. This perspective offers the advantage of encompassing the range of situations between segregated contexts and diversity, to render different types of cities comparable, and even more, to understand the different social aspects of spatial separation (Le Goix, Vesselinov, 2012).

Social, spatial, and temporal trajectories in the discontinuities of intermediate cities

16As markers of social separation, discontinuities more widely reflect the fragmentation of urban spaces. As such, they must be interpreted according to three criteria: social, spatial, and temporal. The first criterion is «social» because the division of space is not limited to a single criterion, particularly in the United States where age, socio-professional categories, race, income, and other fields do not necessarily overlap despite correspondences and logics of self-segregation within homogeneous groups. This holds particularly true for Albany, where discontinuities associated with wealth and ethno-racial groups are mainly located in central areas whereas heterogeneity related to life cycles appears in suburban areas (Figure 3). Each field can create its own discontinuities, which are then qualified as elementary; we are dealing with the “slope between two spatial units on a measuring scale with a single indicator” (Le Goix, 2003). In cases where these discontinuities overlap, they form a structural discontinuity that becomes a major fact of the social division of space through the definition of recurring spatial forms. It is hypothesized that the more a discontinuity is structural, the more radical is the separation between neighboring spatial units.

Fig. 3

Multivariate dimensions of the divisions of social space in Albany

Multivariate dimensions of the divisions of social space in Albany

Analyse en composantes principales sur les 665 block groups à partir de 10 variables (80 % de variance expliquée dans les quatre premiers critères) renseignant l’appartenance ethno-raciale (populations blanches, noires, asiatiques, hispaniques), l’âge (moins de 18 ans, 18 à 25 ans, 25 à 45 ans, 45 à 65 ans, plus de 65 ans), la population sous le seuil de pauvreté, le revenu médian des ménages.

17The second criterion of analysis is the spatial dimension of discontinuities. We have postulated that the shape and position within cities reflect different processes and variations in the intensity of spatial separation. Thus, Jean-Francois Christophe (2002), in the case of educational areas in Paris and its suburbs, demonstrated that annular discontinuities reveal control strategies used by the actors present. Other forms are recurrent: rectilinear discontinuity suggests a clear break, while intermittence on the contrary indicates a porous structure.

18The third criterion consists of temporal discontinuities. Indeed, discontinuities are linked to urban dynamics and are de facto evolving objects in terms of intensity and form. Several types of evolution are possible and can be combined, such as stability, disappearance, or changes of intensity. As stated by François Durand-Dastès “any location with a certain permanence corresponds to the workings of a system with a certain stability” (1984). We thus assume that the temporal stability of a discontinuity is associated with a stronger social separation. The analysis of trajectories of discontinuities should allow the identification within segregation mechanisms of those things that are tied to a permanent structure and those related to social change.

19This intra-urban analysis will focus on a database, under construction, of U.S. intermediate cities. It combines four census surveys carried out between 1980 and 2010 [9] and the American Community Survey (ACS) [10]. This range depends on both the quality of the data, since definitions change, and the availability of data standardised on a fine scale. Indeed, the diachronic analysis is confronted with the changes in the meshwork grid over time, which implies a reconstructive phase for the mesh starting with the most recent and using the interpolation technique [11]. Thus, the scale of block groups, the most detailed subdivision of the census (between 600 and 3 000 inhabitants) for which data are available, seems more relevant because it accurately captures the discontinuities. In addition, the use of this level reduces the risk that discontinuity phenomena operate within the spatial units under study and yet remain hidden during analysis. Finally, discontinuities can be apprehended using measures of dissimilarity and their spatial forms, their trajectories, and their identified overlays (Figure 3).

20The identification and the social, spatial and temporal characterizations of discontinuities in intermediate cities in the United States is a key to understanding the spatial patterns of social separation. Understanding the dynamics of fracture lines in these cities tests the unity or diversity of this group of cities, and thus helps to discover any similarities with the metropolises, which have been extensively studied elsewhere. Finally, this analysis is the first step in a more comprehensive understanding of discontinuities and fragmentation in urban spaces.

Do discontinuities challenge the city?

22Segregation and discontinuities are repeatedly seen as a dysfunction of cities, especially in the intermediate segment of the hierarchy, where the social-spatial problems are theoretically resolved or diluted. These very meaningful discourses are part of a double reference: the debate on urban fragmentation and an organicist definition of the city.

23The issue of urban fragmentation developed in the 1990s in France, amid a profusion of discourses on “the urban issue” or “the breaking up of cities” and the risk of ambiguity with other terms such as segregation, polarization, and separation. Françoise Navez-Bouchanine (2002) distinguishes two approaches to fragmentation. The first is social and based on a process that consolidates populations with a common identity through affinity or attribution. Another is spatial and observes fragmentation through privatization, political fragmentation, isolation, and physical barriers. The approach, in terms of fragmentation, therefore cuts across different urban dimensions to account for social and physical separation, often attributing causality to metropolization or globalization. It therefore relies implicitly on the notion of discontinuity, in a multidimensional manner, to feed alarmist discourse on the social fragmentation of urban societies that could undermine the cohesion of cities.

24The debate on fragmentation is in a second repository that defines the city organismically. This is a common stance in the United States with the sociological tradition of the Chicago School and the inertia of ethnic and racial issues. The goal is to define the city as a coherent and cohesive whole, whose function lies in its ability to integrate and assimilate people into a larger whole. The city then forms a spatial system, that is to say, a set of social and spatial elements connected by interactions that would be challenged by fragmentation and discontinuities (François, 2002). In other words, this approach considers discontinuities as a break in cities’ integrative capacity, resulting in the destabilization of the system that could lead to a breakdown in independent systems. Though there does not seems to be any real or permanent breaks within U.S. cities, urban sociology and radical geography – as seen in English language research – discuss such separations, notably with the distinction between the core and the periphery (Clark, 1988) or through the incorporation process.

25Furthermore, rather than seeing the discontinuity as a symptom of a breakdown, we would like to suggest it be defined as a spatial link, that is to say, the means by which neighboring and different spaces enter into contact. The discontinuity is then both a product of social and spatial logics and a geographic feature helping to define social relations forming on both sides – in other words, a spatial component of the social dimension. As a spatial relationship, discontinuities therefore vary between functioning as interfaces or separators; our goal is thus to unravel their logic. This approach recontextualizes the dynamics of discontinuities within a systemic perspective where each break is at the root of converging or diverging processes within the neighborhoods. As for the role of discontinuities, it is based on the social, spatial, and temporal dynamics of the separation seen previously. From the stance of urban fragmentation, it is also based on the links between different dimensions of the discontinuities.

A multidimensional definition of discontinuities: connections to urban fragmentation

26Within multidimensionality lies one of the key scientific interests of the notion of discontinuity. Indeed, there are several types of spatial breaks, which exist in different spaces and different metrics: social, territorial, topological, subjective, reticular (Berry, Kasarda, 1977). Following Kevin Lynch’s (1969) pioneering research on the fractures in several U.S. cities, these particular discontinuities can be viewed as dimensions completely integrated in the overall concept of discontinuity. Five dimensions are identifiable, illustrated by the example of Albany (Photo 1):

• the social dimension corresponds to residential segregation and refers directly to the logic of differentiating spaces along the axes and the criteria defined above;
• the morphological dimension refers to all spatial asperities (relief, railways, highways, rivers, parks, cemeteries, etc.) that can be used as a base for residential strategies or mechanisms of separation (Lynch, 1969);
• the political dimension is tied to the multiple limits and territorial grids that stretch across cities and define sets wherein specific territorial ownership policies and practices are deployed (Le Goix, 2003; Kato, 2006);
• the functional dimension refers to mobility and gaps in accessibility between neighborhoods, differentiating isolated areas along which discontinuities can be found. In the U.S., the shape and density of the road network is a key element. (Grannis, 1998; Duncan et al., 2012.)
• the symbolic or subjective dimension refers to the perceptions and representations that stem from the practices of a city’s residents and stakeholders. The perceived space is crisscrossed by barriers, borders between here and elsewhere, circumscribing areas that are attributed positive or negative values (Lynch, 1969).

Photo 1

Morphological discontinuity and symbol of dominance in Albany (New York)

Morphological discontinuity and symbol of dominance in Albany (New York)

Lower Albany, with its mainly black population, is separated from the upper part of the city by a slope. This physical break must either be climbed over or gone around.

27The joint spatial analysis of these five dimensions, contributing to the social division of space in intermediate cities, gives meaning to the notion of discontinuity as a spatial relation. First, overlaps between the dimensions of discontinuities help better differentiate – within segregation logics – between what is linked to cities’ permanent structures and what is due to social change. Furthermore, through existing connections, does the social dimension synthesize and take into account all other dimensions? Does it thus justify the approach in terms of a fragmentation that confers on social separation the more general meaning of the breaking up of cities? Finally, more than simply a binary reading that sets a discrete (fragmented) space against a continuous (graduated) one, the diversity and quantity of connections between dimensions characterize the intensity of spatial relationships that take place at the local level, which allows us to situate discontinuities on a scale of territoriality that ranges from the most radical fragmentation to the linear absence of social and spatial rupture. With this approach using a multi-dimensional definition of discontinuities, we are looking at precisely defining spatial patterns of social division and the conditions under which these separations can lead to the fragmentation of intermediate cities.

28Two intermediate cities will be examined in depth for the study of the articulations of dimensions of discontinuity. This is due on the one hand to the complexity of the process, which requires detailed investigation, and on the other hand, to the goal of generalizing these links to the entire category of cities. Both cities will be selected within the intermediate segment so as to grasp any possible variations according to regional contexts within the United States. The articulation of dimensions of discontinuities will be based on the construction of a geographic information system from which the social discontinuities can be analyzed through their intersections with other types of line plots. The census provides a number of geographical grids (municipalities, counties, states, school and church districts, etc.), morphological elements (relief, rivers), and transport infrastructure (road and rail networks). Geographical correspondences can be entered, which leads to a typology of arrangements of dimensions and the analysis of discontinuities on a territorial scale referring back to the degree of fragmentation.