This chapter yokes sartorial fashion and the literary trends that cultural colossus Rabindranath Tagore shapes and critiques in the early twentieth century. Bringing the figure of the dandy to a global stage in his late novel Shesher Kobita or Farewell Song (also translated as The Last Poem, 1928), Tagore lightly cloaks a manifesto on self-fashioning, modernist literary form, and the power of style. Farewell Song not only draws upon the history of textiles in Bengal, but also occasions a contest of fashions between British and Bengali forms of dress. The ensuing debate between Fashion and Style speaks across aesthetic fields and serves to highlight India’s rightful place on the modernist literary stage.

After introducing basic notions on finite extensions of local fields, including tamely ramified extensions, inertia groups, and so on, we define the main subject, lower ramification subgroups. We also define log monogenic extensions and extend the classical equalities, including the conductor-discriminant formula, to this type of extension. Finally, we study the norm map of the multiplicative groups and its relation with ramification of the extension. As a preliminary to the definition of Henselian local rings, some general results on etale morphisms of rings are studied at the beginning of the chapter.

Although extremal set theory began with Sperner’s theorem from 1928, most of the subject has centered around so-called intersection theorems initiated by Erdős–Ko–Rado, and developed by Kleitman, Katona, Frankl, Füredi, and others. This chapter discusses some of these early developments.

A rich vein of physics and useful magnetic phenomena is associated with transverse magneto-transport of electron and spin currents. First is the spin Hall effect and the related anomalous Hall effect. Other variants arise as a result of spin-orbit coupling, chirality and the lack of a centre of symmetry in a crystal or thin film stack. Quantized electrical conductance is related to the Landau levels. Associated magnetic phenomena are Landau diamagnetism, quantized conductance and the quantum Hall effects in two-dimensional electronic systems. Dissipationless edge and surface currents arise that may be unpolarized as in the quantum Hall effect, or spin polarized, as in topological insulators. Possible ‘emergent’ magnetic fields are discussed and related to real space and reciprocal space lattice topology. Analogous effects associated with heat currents include the spin and anomalous Nernst effects.

Diagrams are essential for interpreting complex datasets and making discoveries. This chapter examines how diagrams in use make private thoughts, models, and phenomena accessible intersubjectively and complex datasets surveyable. When designed and used conventionally, diagrams are bearers of tradition and culture. This chapter shows that they can also be resources for scientific understanding, pruning and cultivating datasets, and achieving social accountability. Diagrams are the ground on which scientists can play and experiment with data: researchers suspend sequential courses of action for explorations in which they gain insights into possible interpretations and their work’s robustness as they decide which action among alternatives to make consequential. This chapter describes this play in the making of a discovery. As diagrams are standardized and used at many places, the resistance that their users experience can be ascribed to their efforts to be accountable to researchers elsewhere.

The micromagnetic structure of ferromagnets and ferrimagnets is a consequence of minimizing their free energy, which includes a self-energy term due to the dipole field Hd(r). Free energy in micromagnetic theory is expressed in the continuum approximation, where atomic structure is averaged away and M(r) is a smoothly varying function of constant magnitude. The result of the energy minimization is domain formation in most cases. The Stoner–Wohlfarth model is an exactly soluble model for coercivity based on the simplification of coherent reversal in single-domain particles. The concepts of domain-wall pinning and nucleation of reverse domains are central to the explanation of hysteresis and coercivity in real materials. The magnetization processes of a ferromagnet are related to the modification, and eventual elimination of the domain structure with increasing applied magnetic field.

This chapter analyses the concept of primary establishment as developed in the case law of the Court of Justice of the European Union (CJEU). It focuses on how the Court has interpreted the freedom of establishment under Articles 49 and 54 TFEU, particularly in relation to the right of companies to incorporate and operate across borders. Key judgments such as Daily Mail and Überseering are examined to illustrate the evolving legal principles governing primary establishment. The chapter also discusses the implications of this jurisprudence for regulatory arbitrage, national company laws and the broader integration of the internal market.

One aim of Chapter 6 is to tie together several strands of argument developed in the previous chapters. First, we shall return to the “urge” (to assimilate, to conflate the normative and the assertoric) signaled in the first two chapters. Here we will explore the hypothesis that the urge ultimately amounts to our overwhelming desire, and temptation, to experience what I call in Chapter 1 ‘metaphysical awe.’ Second, following some remarks from Lectures and Conversations on Aesthetics and Religious Belief, we will take one’s succumbing to such temptation as an indication of a seriously flawed ‘style of thinking.’ However, the main aim of the chapter is to connect the hypothesis above with a reading of Wittgenstein’s controversial views on Cantor’s proof. It is argued that what primarily concerns Wittgenstein are the assimilationist tendencies embodied in transfinite set theory, and its encouragement of a sensationalist style of thinking (i.e., its serving as a source of metaphysical awe). Toward the end of this chapter, I begin examining his often decried ‘revisionism’ – the idea that he proposes revisions to mainstream mathematical results, including Cantor’s.

This book argues that news, as a transatlantic commodity, was just as valuable as sugar, tobacco, or cotton. It does so by focusing on news reports and storylines from the Atlantic world in printed newspapers, and the ways in which metropolitan and colonial authorities subsequently managed public communications. The book investigates how newspapers – ‘new media’ at the time – covered distant but urgent transoceanic conflicts with a weekly periodicity, using primary sources from Atlantic societies like Spain, Portugal, France, the Low Countries, and the British Isles, from so-called second-row Atlantic states such as Italy and the Holy Roman Empire that do not currently feature in the field’s predominant discourse of empire, and from emerging colonial societies in North and South America. It reveals the idiosyncratic rhythm of communications in the Atlantic world, which challenged news writers to navigate judiciously between speculation and confirmation, and demonstrates that the circulation of information was underlying all other transatlantic exchanges – of people, commodities, values, and ideas – that have been the staple of Atlantic history.

The most famous geometric application of ramification groups is the Grothendieck–Ogg–Shafarevich (GOS) formula that computes the Euler–Poincaré characteristic of an étale sheaf on a curve over a field of characteristic p. The GOS formula is deduced from the Lefschetz trace formula, which is a consequence of the Poincaré duality. We recall briefly the basic constructions on étale cohomology such as the cycle class of divisors, trace mapping, and so on.

I present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Greece, beginning with its origins: the formative people, places, and various intellectual schools of thought. Writing about the current state of the topic, I reflect on influential factors that are either facilitating or inhibiting the study of PoR, including publication options, topical emphases, practitioners, orientations, methodologies, and professional organizations.

I offer opinions concerning future development topics that are emerging as important in the immediate future and/or are perennially important in order to stimulate creative and useful research including Western theoretical relevance, the extent to which Western PoR theories may or may not contain reasonable expectations and concepts for this region, contextual nuances, Indigenous theoretical concerns, collaborative research opportunities, and common faux pas – reflections on what people unfamiliar with this region commonly and incorrectly assume about conducting PoR work in this context.