In several previous chapters, we have been primarily concerned with providing upper bounds on the worst-case risk of specific procedures. Here, we seek instead lower bounds on the worst-case risk of any procedure. Such minimax lower bounds provide a benchmark against which we can measure the performance of proposed methods. The three main types of minimax lower bound we consider arise from Le Cam's two-point lemma, Assouad's lemma and Fano's lemma, and we will see several examples of how these results can be applied. Finally, we establish tools for controlling minimax quantiles, in an attempt to avoid the loss of information in reducing the (random) loss to its expectation (risk). In many cases, it is possible to characterise the dependence of minimax quantiles on the quantile level, thereby providing a finer-grained understanding of the difficulty of a statistical problem.

When we expand exploration of death-related behaviors to include other-than-human animals, what might be learned about ways of expressing emotion around death? In this chapter I probe the contours of animal grief. Who in the animal kingdom grieves, and in what ways? Describing grief expressed by animals ranging from rattlesnakes to chimpanzees, orcas to elephants, and cats to dairy cows, I show that claims of human exceptionalism around grief and mourning can and should be challenged. Human uniqueness is not threatened by this stance, as our species’ mortuary rituals do indeed differ from others’. Understanding animal grief may not only enlighten us about the nature of human grief but also offer ways to think about ecological grief, the crushing sense of loss some people experience as the climate crisis forces changes upon the land, animals’ lives, and our lives. Throwing open questions that link animal grief, human grief, and ecological grief may sharpen awareness of our responsibilities to other creatures, a transformation that itself invites new paths of resilience and multispecies relating.

The limited-liability corporation is a ubiquitous feature of modern life that many regard as morally neutral. Yet when we consult traditional ethical theories – such as deontology and virtue ethics – it seems that we cannot account for such leniency. The traditional theories namely imply that corporate bankruptcies are moral catastrophes in the sense that the owners and/or managers are allowed to escape responsibility and liability for their wrongdoings. In the present chapter, we seek to develop a theoretical explanation of people’s more lenient attitude. Our alternative view is that the ethical norms that are appropriate for attributing responsibility or liability in a market context are somewhat different from those that apply in other social contexts, such as the ordinary morality of civil life. This view is supported by our theory that the market is an ethically distinct part within an organic social whole, and conditional upon a social safety net that softens the excesses of market outcomes.

Massed graves usually mean social disorder caused by war, political violence, or natural disaster. But New York City has operated a massed grave on Hart Island for its unidentified, unclaimed, or very poor dead since the Civil War. For a municipality to have a working massed grave as part of civil society is highly unusual. About a million New Yorkers are buried without memorial on this uninhabited island, and until 2022 all the burial work was conducted by inmates from nearby Rikers Island. It remains difficult to visit. But the city has no plans to stop burying on Hart Island. It remains distressing but tolerated. Hart Island’s burials meet a civic responsibility to provide funeral welfare to the city’s most vulnerable. But New York City’s manner of doing so – reiterating old forms of indigent burial; restricting ritual, visits, and memorialization; accommodating their forgetting through mundane bureaucratic barriers – recalls forms of posthumous symbolic violence that equate to social death for those in its society least equipped to resist. Can something as extraordinary as a massed grave ever be made ordinary?

This chapter traces the peculiar genealogy of the modern mantelpiece urn, a now familiar cultural curiosity throughout the English-speaking world that has received surprisingly little attention in thanatology. The questions begging for attention include: When and how did funerary urns become acceptable to keep at home? What do they do? What do they mean? Why do we so often seem to have a joking relationship with them? An archival search through newspapers and funeral trade publications revealed that the practice goes back to the start of the industrial cremation movement in the 1880s. Further, they are strongly associated with spiritualism, Freemasonry, and other esoteric religious practices that flourished from the 1880s and 1920s. Although often pilloried by critics of cremation as distasteful and uncanny, from another point of view the mantelpiece urn blended seamlessly into the gothic clutter of the Victorian parlor. I argue that these early contexts and connections make the mantelpiece urn both legible and packed with meaning.

This chapter unpacks how narratives about Rwanda’s Twa are created. It seeks to understand how knowledge about Twa is produced, and how the Twa are created, re-created, and re-positioned as indigenous and development subjects in the jurisdictional encounters of the global discourses of development and indigeneity with national policies on unity and reconciliation. The chapter identities three main stories told of the Twa. The first story is that of indigeneity, of a forest people distinct, dispossessed, and suffering. The second tale is of a community historically marginalised but not ethnically different. The third account views Twa simply as poor and vulnerable, positioning them as national development subjects.

As a Black woman and anthropologist, I am positioned as an outsider within the field of American anthropology. Traditionally, Black people and our bodies have been reduced to objects of study within the discipline. Because I am a bioarchaeologist who works directly with the skeletal remains of Black Ancestors, my positionality compels me to think seriously about how anthropologists might address the field’s violent past while moving forward in more ethical ways. But are we effecting change with our work, or reproducing the same inequalities and harmful narratives? I advocate for engagement with Black feminisms to inform the practice of bioarchaeology and shift away from narratives that normalize the objectification and degradation of Black people.

In this chapter, we discuss proofs of geometric Manin’s conjecture II (Conjecture 7.4.10) for certain classes of algebraic varieties. The main idea is to use Mori’s famous Bend and Break techniques to prove the irreducibility of the moduli space of rational curves of a given class based on induction on the degree of that class.

This chapter historicizes the canonization of mid twentieth-century African American literature by breaking it down into three distinct phases over thirty-five years (1935 to 1970) and exploring it through the lens of five prominent writers: Richard Wright, Margaret Walker, Gwendolyn Brooks, James Baldwin, and Ralph Ellison. While these writers brought unprecedented acclaim to the field, opening doors for future Black writers, analyzing their artistic and political choices reveals that Black literary success has more to do with how well their literary politics align with the white literary mainstream – not with literary talent and skill. Unfortunately, the current African American literary canon of the mid-twentieth century still aligns with conservative Cold War literary politics, excluding a score of talented Black writers with more progressive politics. By attending to the literary shifts of the 1940s, it becomes clear how that canonization took place and why it must be undone and reconfigured.