This chapter is about the prospect of proving that certain problems do not have polynomial-time algorithms (are not in P). Tractable problems (having low time complexity) are compared with seemingly intractable problems (having high time complexity). The class NP and NP-completeness are defined and elaborated. Several classic problems, including the seminal satisfiability problem, are proven NP-complete.

The prologue gives an overview and teaser for the whole book.

This chapter introduces the fundamental concepts of computational problems, algorithms, and time and space efficiency. These concepts are formally defined and illustrated with examples. The major time and space complexity classes P, EXP, L, and PSPACE are introduced. The chapter concludes by defining reductions, which are tools for relating complexities of different problems.

This chapter examines Aquinas’s account of God as omnipotent and eternal. Aquinas distinguishes active from passive power, attributing only active power to God, who as pure actuality is wholly the source of effects. Divine omnipotence, he argues, does not mean God can do just anything, but that God can bring about all that is absolutely possible – that is, all that does not involve contradiction. Hence God cannot undo the past or contradict his own immutability, though he can work miracles, which Aquinas understands not as interventions but as events beyond the natural capacities of creatures. The chapter considers modern critiques, such as Geach’s challenges to defining omnipotence and Plantinga’s free-will defence, and contrasts them with Aquinas’s view that divine causality grounds rather than negates human freedom. Turning to eternity, the chapter explains Aquinas’s claim that God is utterly unchangeable and ‘altogether at once’ (tota simul) thereby transcending time without negating his causal presence in history.

This chapter concludes the book by synthesizing its main themes and revisiting its central questions: What kind of ethics do we need to grapple with the planetary boundaries framework and the issues it raises? Is it sufficient to accept scientific frameworks as the baseline for ethics or are there other ways of knowing that matter both within and beyond western scientific frameworks? Key themes such as complexity, time, epistemic justice, and scale emerge as central to thinking across, and with, the interdisciplinary chapters that comprise this book, and these themes also suggest important considerations for future ethical engagements with the planetary boundaries framework.

Because sainthood requires a renunciation of worldly attachment, it eliminates the need to stabilize relational identity. The saint identifies him or herself in relationship to God, who has no physical form, requires no social context or explanation, and does not change over time. Instability is an essential requirement of relational reiteration; without shifting landmarks and potential mistakes, there is no need to deploy the form. Mary of Egypt is an exception who proves the rule in this respect. When mistaken by Zosimus for a devil, she reiterates the landmarks of her identity to prove her sainthood: not because she needs them but because he does. Similarly, The Seafarer positions the chronological past as integral to the speaker’s rejection of worldly pleasures, and that rejection as equally integral to his ability to arrive at the “hotter” joys of his destination; thus loss itself becomes a crucial social landmark of the speaker’s identity. Rather than trapping the speaker in a state of stasis, it is through the loss of worldly landmarks that the speaker may find his way to a heavenly realm.

The exiles, landowners, bookworms, and kings of early medieval English texts all faced a common problem: how do you know yourself, or anything else, in a relational and therefore constantly changing world? They answered that problem with relational reiteration: sometimes literally walking the edges of property bounds, and sometimes figuratively inviting a reader to walk the edges of a riddle’s solution, or an exile’s lost home. The reiteration of relational landmarks is a temporary solution; each time a relationship is altered or challenged, the bounds of relational identity must be traced anew. And in fact this problem of mutable identity changes only when literary characters or hagiographical narratives achieve Christian salvation, positioning God in these texts as an eternal relationship that cannot be lost, changed, or forgotten. But in the age of their making, most Old English and Anglo-Latin texts and characters relied upon reiteration to stabilize (or sometimes reimagine) their unsaved, ephemeral, relationally-constructed worlds.

This chapter explores time, death, and memory, analyzing material cultures of death in relation to deceased bodies, their material and visual representation, in historical contexts. It discusses anthropological perspectives on memory and time as articulated through material object domains, examining related issues of: temporal stasis (e.g., memorial effigies); process (e.g., transi tombs); temporal dimensions of memento mori; the interplay of preservation and decomposition in memory objects; aspects of fragmentation and display; and the imagery of darkness, light, and instruments used in the measurement of time. Each of these – significant in Western material cultures of death and memory – is examined in terms of how it materializes or visualizes bodies in transformation. Even when deceased bodies are represented as static, they tend to be animated through their relation to death, figured or evoked as moving presence. Bodies after death exist in time, perhaps most forcefully represented as decaying, disintegrating, or disappearing. Tracing aspects of death’s temporalities, as conveyed in memory objects and images, this chapter shows how varied and changing effects of time are registered by bodies rendered in paper, ivory, wood, wax, and other materials for memorial purposes and as means to reflect on acts of remembering.

Our final part of the volume addresses what we have loosely framed as reflections on an anthropology of death “beyond death.” It opens with Aja M. Lans’s powerful critique of the ways in which the material afterlife of death in the form of human skeletal collections has historically worked to erased life – specifically Black lives and the biographies of living people whose remains have become objects of display or tools of bioarchaeological pedagogy. In exploring her own encounters with the violence inherent in producing and maintaining those collections, she invites us to consider the “corporeality of the body and its exploitation both during life and after death.” Her chapter sets the scene for the chapters to follow, each in its own way wrestling with questions that extend from the phenomenon and experiences of death. The framing of “beyond death” that binds these particular chapters urges reflection not only on death’s afterlife of mourning and memory but also some of the radical innovations and ruptures introduced by the pandemic that have both methodological and theoretical consequences for the field going forward.

This chapter advances the premise that one way in which racism impacts health and developmental outcomes is through the experiences of the finite resource of time. Although all humans experience the same twenty-four hours in a given day, how those hours are allocated, how much agency over how those hours are spent, and the lived experiences of that time are stratified by structural systems such as racism. Taking a lifecourse perspective, we describe how human development is shaped as much by social factors as biological influences, using time as an example. Ultimately, stratified experiences of time set the stage for racism to shape even the most fundamental of human experiences. We call upon the field to deepen our study of the connections between time, racism, and health inequities, and offer a few recommendations for future research.

In foundational African narratives, time, decolonization, and modernity are bound together. This chapter looks at how, at its moment of emergence in the second half of the twentieth century, modern African fiction, whose aim was to rationalize African notions of time and account for both colonial history and what appeared to be failing projects of decolonization, was motivated by the desire to account for a temporal impasse: the fact that the old colonial order had disappeared but the future promised by the political class was yet to come. This temporal impasse explains the confluence of realism and modernism in postcolonial African fiction. In their themes, forms, and tone, the novels published in the 1960s set out to negotiate the empty space of a stalled decoloniality. Using Chinua Achebe’s Arrow of God as a case study, the chapter reflects on the novel as a mode of mediating historical time conceived as both past and present, simultaneously preoccupied with the teleology of the temporality ushered in by colonialism even after decolonization.

The Introduction combines a contextual introduction to disability in Kinshasa with an outline of the research problem as the tension between exceptionality and normality in a city that has long defined itself as in ‘crisis’. The interlocutors, their city, the times in which they lived, and their livelihood activities were all subject to ambiguous judgements as to whether they stood out as a negative or positive example, or if they were better viewed as simply part of the general experience of life in the wider community. The Introduction thus outlines the focus on mobility-impaired people in the grey area between work and welfare, where ‘crisis’ (mpiaka) opens a discursive space for experimentation, critique, and evaluation. The unpredictability that marks life in Kinshasa, in this respect, leads people to constantly reckon their social and economic value projects in relation to time. The Introduction introduces how crisis confronts people with choices of realising the short-term values of ‘fending for yourself’ or the long-term values of cultivating dependent relationships.

This chapter deals with the narrative treatment of time in Alejo Carpentier’s “Historia de lunas,” “Oficio de tinieblas,” “Viaje a la semilla,” “Semejante a la noche” and El acoso. These fictions were marked by an epochal climate in which a sense of civilizational crisis prevailed, as can be seen in the proposals of Oswald Spengler, Arnold Toynbee or Mircea Eliade, thinkers who left their mark on Carpentier’s historical thinking. The analyses of these narratives focus on the way in which their author deploys competing temporalities, a feature that shows how the historical dimension of his narrative was not limited to the recreation of past scenarios. Furthermore, in these works it is possible to trace a theory of historical becoming, a reflection on the teleology of its processes and the meaning of its occurrence.