This chapter begins the study of random vectors in high dimensions, starting by showing their norm concentrates. We give a probabilistic proof of the Grothendieck inequality and apply it to semidefinite optimization. We explore a semidefinite relaxation for the maximum cut, presenting the Goemans–Williamson randomized approximation algorithm. We also give an alternative proof of the Grothendieck inequality with nearly the best known constant using the kernel trick, a method widely used in machine learning. The exercises explore invariant ensembles of random matrix theory, various versions of the Grothendieck inequality, semidefinite relaxations, and the notion of entropy.

In a time of great contest and confusion over the future of democracy as a governing principle, the example of Abraham Lincoln continues to provide encouragement and direction about democracy’s viability in the face of immense challenges. In The Political Writings of Abraham Lincoln, Allen Guelzo brings into one volume Lincoln’s most famous political documents and speeches from his earliest days as a political candidate under the banner of the Whig Party, to his election and service as the first anti-slavery Republican president, from 1861 to 1865, and the nation’s leader in the fiery trial of civil war. While many anthologies of Lincoln’s political documents routinely concentrate on his presidential years or only on his anti-slavery writings, Guelzo concentrates on documents from Lincoln’s earliest political activity as an Illinois state legislator in the 1830s up through his presidency. The result is an accessible resource for students, researchers, and general readers.

In this chapter, I explore three female folk song collectors: Lucy Broadwood, Annes Geddes Gilchrist and Dorothy Marshall, and three women from whom they collected songs – to provide wider commentary on the contributions of women to the first English folk song revival and their marginalization. In doing so, I examine the role of women in the first folk song revival, feminist practices in the archive, and a growing resurgence of interest in women and folk music. By exploring three examples of collecting in the first folk song revival, I illuminate the women who operated in the margins of the folk music movement and have since been marginalized by its history. I contend that by paying closer attention to what is found in the margins of manuscripts and other archival material, it is possible to glean information on the singing tradition, and collection practices, of women in the first folk song revival.

Hans Kelsen was one of the first major legal and political thinkers to argue that political parties are indispensable to democracy. This chapter deals with an important but largely overlooked aspect of Kelsen’s thinking about parties, which will be called party constitutionalism. In short, party constitutionalism refers to the idea that party organisations should be regulated by constitutional norms in order to ensure that parties are democratically organised. Kelsen developed this idea at a time when constitutions had little to say about the status of parties, and even the normative desirability of the party form was contested. After reconstructing Kelsen’s case for party constitutionalism, the chapter turns to the question of how the constitutional regulation of parties has evolved in the second half of the twentieth century. It is argued that even in countries where constitutions prescribe that parties must be democratically organised, intra-party democracy has rarely flourished. However, the sobering reality of party constitutionalism should not blind us to the lasting importance of Kelsen’s observation that democracy is ill served by elite-dominated, oligarchic parties. In fact, Kelsen’s work can help inspire a broader conversation about how parties should be organised and how their internal life can be regulated.

The manageability of the technical obstacles set out in Chapter 4 established, this chapter turns to the adaptive challenges amalgamation faces – most notably its inconceivability to the judiciary. The chapter details the maladaptive constraints that underlie the constitutional drafters’ and legal establishment’s resistance to embracing vernacular law as part of South Africa’s ‘law of general application’ or ‘common law’, as well as the urgency of overcoming such resistance. Depicting the severe decline in institutional trust and rising support for undemocratic governance amidst the public’s waning hopes of material security, the chapter argues that, to strengthen South Africa’s rule of law, constitutionalism must be founded on the vernacular legal traditions that resonate with everyday South Africans, who often feel alienated by a legal system rooted in ‘uncommon’ law. Alter-Native Constitutionalism offers a sustainable path to transformation that would counteract public disillusionment with a constitutionalism that embraces rigid colonial precedents and simultaneously restore trust in the judiciary as the last line of defence. The chapter therefore argues for judicial praxis that re-envisions courts as mediators supporting collective agency, rather than mere adjudicators, thus fostering a relational approach aligning with Ubu-Ntu and honoring the country’s diverse normative traditions and social justice aspirations.

In a time of great contest and confusion over the future of democracy as a governing principle, the example of Abraham Lincoln continues to provide encouragement and direction about democracy’s viability in the face of immense challenges. In The Political Writings of Abraham Lincoln, Allen Guelzo brings into one volume Lincoln’s most famous political documents and speeches from his earliest days as a political candidate under the banner of the Whig Party, to his election and service as the first anti-slavery Republican president, from 1861 to 1865, and the nation’s leader in the fiery trial of civil war. While many anthologies of Lincoln’s political documents routinely concentrate on his presidential years or only on his anti-slavery writings, Guelzo concentrates on documents from Lincoln’s earliest political activity as an Illinois state legislator in the 1830s up through his presidency. The result is an accessible resource for students, researchers, and general readers.

There are significant ambiguities in how “atheism” is to be understood or interpreted. Having considered these, we turn to Hume’s arguments and assess to what extent his views in the Dialogues should be interpreted in these terms. While it is evident that Hume opposed “superstition” and that he was, in this sense, plainly an irreligious thinker, this does not settle the question of his “atheism”. Although Hume has been read by some as an theist of a minimal kind, and by others as a sceptic or agnostic, both these accounts are rejected. Hume was, it is argued, a “hard sceptical atheist”, by which we understand him to take the view that we have probable (non-dogmatic) grounds for denying the theist hypothesis in all its forms. His “speculative atheism” is accompanied by a “practical atheism” which, while firmly opposed “superstition”, is willing to ally itself with both sceptics and those theists (or deists) who share Hume’s opposition to “superstition”.

Non-normative sexual and gender identities are not new to Africa, but their representation in literary texts has grown significantly over the past two decades, establishing queer literature as a burgeoning genre. This chapter focuses on what defines “queer” in African literature and examines its key features. It compares literary production from different regions of the continent, highlighting both continuities and diversity in the representation of queerness. Particular attention is given to Anglophone and Francophone literary traditions to consider the similarities and divergences in representations of queerness across these linguistic and cultural contexts. These literary analyses are interwoven with scholarly debates, showing how literature and academic discourse on African queerness inform and influence one another. Drawing on Keguro Macharia’s concept of “frottage,” the chapter examines how interactions between African and queer identities can evoke both generative and conflictual affects. The chapter ultimately interrogates the politics of queer representation in literature, particularly in queerphobic contexts in Africa. In so doing, the chapter explores how literature not only makes queerness visible but also negotiates difference and nonconformity.

I take this chapter as an opportunity to ask what Hume might think of rational religious belief given developments in philosophy of religion, epistemology and contemporary cognitive science of religion (which explores the natural roots of religion). To that end, I will consider some basic findings in the cognitive science of religion concerning the origins of religion in human nature. I will also reflect on some significant developments in twentieth-Century philosophy, including recent developments in religious epistemology, that I think Hume might have found insightful. I will argue that twenty-first-century Hume, perhaps ironically in line with the thought of Alvin Plantinga and Nicholas Wolterstorff (who in turn align themselves with Thomas Reid), would defend rational belief in God.

Richard Wagner’s pervasive influence on the French mélodie appears most openly in César Franck and his devoted students. Their chromatic language draws inspiration from the German composer, yet differs in significant ways, including a strong orientation toward subdominant harmony, as in Henri Duparc’s “L’invitation au voyage.” A survey of Franck’s songs leads to an exploration of the song cycles of Ernest Chausson and Guy Ropartz, which extend their teacher’s celebrated method of “cyclic composition.” Wagnerism intertwines with the hothouse aesthetic of Decadence in these fascinating mélodies, in which chromatic extravangance matches the precious refinement of poets like Maurice Maeterlinck and Jean Lahor.

This chapter explores the potential of realist evaluation methodology to uncover the complexity of implementing an English for Specific Purposes programme at a Saudi university. Realist evaluation draws on the principle of retroduction, which necessitates the redescription of causal components of an event into theoretically significant terms for a closer approximation to reality. The chapter investigates the interaction between underlying causal mechanisms and teachers’ reasonings that operate in a particular context, an interaction which leads to particular outcomes. To this end, we outline how the English for Specific Purposes programme was conceptualised, designed, and implemented, before we explain how relevant theories were defined by analysing the responses of the teachers who implemented the programme. The findings highlight the importance of viewing the role of ESP teachers and acknowledging the need for collaboration across disciplinary boundaries. The study provides further insight into the process of theorising from participants’ responses in the study of both embedded practices and underlying causal mechanisms operating within a specific professional community.

In a time of great contest and confusion over the future of democracy as a governing principle, the example of Abraham Lincoln continues to provide encouragement and direction about democracy’s viability in the face of immense challenges. In The Political Writings of Abraham Lincoln, Allen Guelzo brings into one volume Lincoln’s most famous political documents and speeches from his earliest days as a political candidate under the banner of the Whig Party, to his election and service as the first anti-slavery Republican president, from 1861 to 1865, and the nation’s leader in the fiery trial of civil war. While many anthologies of Lincoln’s political documents routinely concentrate on his presidential years or only on his anti-slavery writings, Guelzo concentrates on documents from Lincoln’s earliest political activity as an Illinois state legislator in the 1830s up through his presidency. The result is an accessible resource for students, researchers, and general readers.

In a time of great contest and confusion over the future of democracy as a governing principle, the example of Abraham Lincoln continues to provide encouragement and direction about democracy’s viability in the face of immense challenges. In The Political Writings of Abraham Lincoln, Allen Guelzo brings into one volume Lincoln’s most famous political documents and speeches from his earliest days as a political candidate under the banner of the Whig Party, to his election and service as the first anti-slavery Republican president, from 1861 to 1865, and the nation’s leader in the fiery trial of civil war. While many anthologies of Lincoln’s political documents routinely concentrate on his presidential years or only on his anti-slavery writings, Guelzo concentrates on documents from Lincoln’s earliest political activity as an Illinois state legislator in the 1830s up through his presidency. The result is an accessible resource for students, researchers, and general readers.

This chapter is about how William James’s ideas about consciousness can elucidate our understanding of what literature is and does. The thrust of the argument is that James’s psychology, in its insistence on and poetic invocation of consciousness as being nothing outside of the processing of the world as experienced, and the radically experiential and pluralistic philosophy built on this claim, offers a powerful alternative to the psychoanalytical models of consciousness as a mechanism of suppression and censorship that dominate the field of literary studies to this day, with vast implications for our conception of literature’s social function and use. The aim is to show how James’s ideas about consciousness are endowed with a radical openness to sense perception that comes with both an aesthetics of cognition and an ethics of democratic receptivity in tow; and to demonstrate that James fathoms these two strands as mutually engaged in a world-making operation that necessitates a literary imagination.