This chapter provides a short introduction to the ozone boundary in the planetary boundaries framework.

This chapter provides a short introduction to climate change in the planetary boundaries framework.

This chapter provides a short introduction to the freshwater boundary in the planetary boundaries framework.

This chapter provides a short introduction to the ocean acidification boundary in the planetary boundaries framework.

This chapter provides a short introduction to the aerosol boundary in the planetary boundaries framework.

This chapter provides a short introduction to the novel entities boundary in the planetary boundaries framework.

This chapter provides a short introduction to the biodiversity boundary in the planetary boundaries framework.

This chapter provides a short introduction to the land system boundary in the planetary boundaries framework.

“The Poet” is what Adorno calls a “carpet essay,” which weaves its announced topics of the poet and poetry into a host of other subjects: character and expression; reception and abandonment; beauty and love; the present, new, and near; the Neoplatonic One or “whole”; and a fundamental “flowing” or “metamorphosis.” Chapter 8 focuses on Emerson’s romantic and proto-existentialist pronouncement that “the man is only half himself, the other half is his expression”; his theory that language “is fossil poetry”; and the proto-pragmatic picture of language in his statement that “all language is vehicular and transitive, and is good, as ferries and horses are, for conveyance, not as farms and houses are, for homestead.” Other topics treated are the place of what Kant calls “unbounded” ideas in Emerson’s account of poetry, thinking as a mixture of reception and activity, and the connections and differences of “Experience” and “The Poet.”

This chapter argues that Western border thinking emerges concurrent with early formulations of conquest and labor management. Tracing an arc that begins with Spanish philosopher Juan Maldonado and concludes with African philosopher Achille Mbembe, the chapter discusses the utility of borders to the concepts of self, property, and freedom. It further argues that such conceptual work of borders has also been challenged and reconceptualized by contemporary poets and novelists including, most famously, Gloria Anzaldúa, as well as Sandra Cisneros, Alfredo Aguilar, and Eric Gansworth (Tuscarora). Each of these attend to the ways borders serve as generators of revenue for states and as abjection machines, but also as places of habitation, as processes, and as dense horizontalities, rather than as fixtures on a nested hierarchy of scales.

The chapter resituates the ideas of empire and nation in relation to the category of space. It delineates the centrality of the concept of space for understanding the imperial and contemporary world-system and the development of colonial capitalist modernity. Drawing on theorists that include but are not limited to Karl Marx, Frantz Fanon, Henri Lefebvre, Nikos Poulantzas, Raymond Williams, and Edward Said, the chapter seeks to understand how their works engage with space as a critical concept, and how their theorizations deploy the category of space to illuminate the production of new kinds – and conceptions – of space in colonial capitalist modernity: the metropole and the colony; notions of the core, periphery, and the semiperiphery; and the modern world-system as a concatenation of spaces – that is, a set of contiguous and nominally equal nation-states separated out from each other through the novel spatial form of the border. The chapter also examines theorizations of the nation to underline it as an ideology of space.

The Introduction situates the book within the context of urban sociology, highlights the importance of the study, and outlines the arguments and contributions. I discuss my approach to the study of public spaces as multilayered sociological entities, rather than mere physical containers of events, people, and the built environment of cities. Studying how public spaces function at the city level, I argue that the meanings and values assigned to places are closely tied to where they are located and how they are used. Approaching public spaces as places where economic, political, gender, and social hierarchies are both reinforced and undermined, I show the complexity of social relations and coexistence in a rapidly changing urban environment. Key themes from urban sociology, sociology of culture, and inequality will be used to lay out the book’s arguments and contributions. I will also discuss my methods and provide an overview of the rest of the chapters.

In the conclusion, I bring the components of the book together, arguing that the findings in each chapter relate to a broad framework that explains the social functions and meanings of public spaces. I discuss how perceptions of self and others, in both the economic and cultural senses, act as essential components of urban experience. Through these discussions, this concluding chapter lays out the opportunities and limits of studying public spaces as a means of understanding social relations in changing urban contexts, and it suggests potential paths for future research.

Theme #9 is about exploiting dynamics already present in a situation to advance one’s interests. Many Sun Tzu ideas find a place here, reflecting Sun Tzu’s keen appreciation of war’s larger context (Passage #1.1) conjoined with the inherently dynamic quality of Sun Tzu’s core concept of shi.

A ‘manifold with corners’ is a space locally modelled on [0,infinity)^k x R^{n-k}, just as manifolds are locally modelled on R^n. Triangles, squares and cubes are examples. A manifold with corners X has a boundary dX, a manifold with corners of dimension one less. The boundary of a triangle is the three edges. If f : X -> Y is a smooth map of manifolds with corners then f need not map dX -> dY, i.e. boundaries are not ‘functorial’. But we can extend the boundary to the ‘corners’ C(X), a manifold with corners of mixed dimension, which is functorial, i.e. f extends to C(f) : X -> Y.

There are several notions of smooth map of manifolds with corners. We choose the ‘b-maps’ of Richard Melrose. There are two notions of tangent bundle, the ordinary tangent bundle TX, functorial under smooth maps, and the ‘b-tangent bundle’ bTX.

‘Manifolds with g-corners’ are a generalization with exotic corner structure. They have some nicer properties, e.g. existence of b-transverse fibre products.

Manifolds with corners occur in many places. e.g. in TQFTs, and analysis of partial differential equations. Some moduli spaces in Morse theory, Floer theories, and Symplectic Geometry are manifolds with corners.