A barrier or bridge? Serious problems revealed in the UK citizenship test

Thom Brooks has examined the UK citizenship test and finds that it is highly irrelevant to living in this society, has many inconsistencies, and suffers from serious gender imbalance. To make matters worse, changes to the test this year have transformed it from being a practical trivia quiz to being purely trivial. Greater care needs to be taken to ensure balance and consistency, and it is worth reconsidering the purpose of the test

A note on normal generation and generation of groups

In this note we study sets of normal generators of finitely presented residually $p$-finite groups. We show that if an infinite, finitely presented, residually $p$-finite group $G$ is normally generated by $g_1,\dots,g_k$ with order $n_1,\dots,n_k \in \{1,2,\dots \} \cup \{\infty \}$, then $$\beta_1^{(2)}(G) \leq k-1-\sum_{i=1}^{k} \frac1{n_i},$$ where $\beta_1^{(2)}(G)$ denotes the first $\ell^2$-Betti number of $G$. We also show that any $k$-generated group with $\beta_1^{(2)}(G) \geq k-1-\varepsilon$ must have girth greater than or equal $1/\varepsilon$.Comment: 10 pages, no figure

Inherence and Denomination in the Trinity

The present paper describes an ”ontological square’ mapping possible ways of combining the domains and converse domains of the relations of inherence and denomination. In the context of expounding and extending medieval appropriations of elements drawn from Aristotle’s Categories for theological purposes, the paper uses this square to examine different ways of defining Substance-terms and Accident-terms by reference to inherence and denomination within the constraints imposed by the doctrine of the Trinity. These different approaches are related to particular texts of thinkers including Bonaventure and Gilbert of Poitiers

Be Careful What You Wish For: Popular Music in an Age in Which “Information Wants to be Free”

This article posits that the widespread adoption of music recording files as the “preferred” form for the storage, retrieval, and dissemination of music is not, and never has been driven by users/listeners; that this is an oversimplified understanding of what has happened since roughly the turn of the century. Instead, the article makes the historically-based argument that what has happened has been driven by the industry side of the equation – even in the face of what is, again, an oversimplified understanding: that the record industry has undeniably suffered and contracted in size and revenue as a result of the digital turn. The overarching significance of this argument is an attempt to bring some much needed perspective to the many analyses of what has been going on in the realm of popular music and the music industry, and to suggest what the consequence of this state of affairs might mean for the future of both the music and its industry