A divorce, particularly when there are children involved, is a disaster. The pain of loss, and the pain of worrying about A. and H., were with me every day.

The String Quartet written that year for a local ensemble, Music from Salem, looked both forward and backward. As in the Bartok Sixth Quartet, all three movements start with the same sorrowful theme. The first movement is slow, hesitant, and lyrical. The second is full of intense energy and quotes from the waltz section of And In The Air These Sounds. As in the Bartok, the third movement is a lament based solely on the melody that had served as a recurring introduction.

I also had another piece in which to channel intense feelings. Steve Klimowski of the Vermont Contemporary Music Ensemble asked me to write a short piece for bass clarinet and piano in response to the massacre of September 11th. I felt unqualified to make a musical statement about something so tragic, and on such a scale, and I was also wary of being associated with the brand of Islamophobic patriotism that accompanied the invasion of Iraq.

In composing the piece, I focused my mind not on politics, but on the pain of one imagined individual who had lost someone. I called the piece Dark Song.

Much of what I wrote up until this point had been to a greater or lesser extent rooted in tonality. But with my greater immersion in the world of late twentieth-century music, I now relied increasingly on invented scales or collections of tones, and this gave my music a different orientation. I was making much clearer determinations about what compositional pallet I was using at a given time.

The magazine here returned to printing letters from Berlioz which were thought to be of general interest. Ferdinand Friedland (1810–72) was a German industrialist and patron whom Berlioz had probably met in Breslau. The full heading of the article is ‘Musical Journey in Bohemia. To M. Friedland in Prague’; the translated part mostly concerns music in London. A personal note reflects Berlioz's attitude to the February 1848 revolution: ‘You’ll be reading this letter seven months after it was sent to you, but will you actually be reading it, my poor Friedland? Our beautiful Prague has been under attack! You will assure me that you’re still alive? They’re killing each other with as much enthusiasm as in Paris’.

London, 4 January 1848

You reproach me, my dear Friedland, for the long interruption in the account of my journey in Austria, and you seem to attribute the delay in my article about Prague to some sort of coolness I was feeling towards you. Your reproaches and suppositions are both unfair. I haven't written during the last four months because I’ve spent all that time in London, where I’m living such a terribly busy life that, far from having a moment for dreams and memories, I’ve barely got time for my job. To launch a serious opera house in England, with no repertoire chosen in advance, with a troupe of young singers most of whom had never appeared on a stage before, was a dangerous enterprise of considerable difficulty, as the outcome has already proved.

The ‘one priest, one benefice’ model was unrealistically simple. There was a mismatch between the social reality of benefices as economic units and the function they were theoretically meant to perform. Many yielded incomes far in excess of what was required; others did not produce enough to sustain their holders. In the latter case, one solution was to permit pluralism, enabling a poorly endowed priest to secure an adequate income. Pluralism might also be allowed at the other end of the scale, to support the men who governed Church and even State, provided deputies were appointed to perform the duties in the respective churches (no deputy being required for canonries). A wealthy parish could thus support both a deputy and an important absentee. Many canonries were virtually sinecures. The incongruity between resource and function could be managed, but not without a manager, and the papacy assumed that role.

Viking seems to be a word … that has expanded and developed to fill a gap, to give a name to a phenomenon which previously had no name but needed one.

Viking medievalism has been a topic of popular interest ever since Sir Walter Scott's The Pirate, a novel published in 1822 and set on Shetland. Scott's novel does not mention the word ‘viking’, but it does distinguish between the savage ‘Bersarkars’, ‘who used to run like madmen on swords’, and the noble war-leaders, ancestors of the Shetlanders, ‘the old Norsemen, who swept sea and haven with their victorious galleys, established colonies, conquered countries, and took the name of Sea-Kings’; this distinction between the good and bad Viking is intrinsic to later medievalist imaginings. In the nineteenth century, the most popular and best-known Icelandic saga was the late romantic Viking tale of Fridtjofr: Fridtjofs saga. Adapted in poetic form as Fritjofs saga by the Swedish bishop Esias Tegner in 1825, the saga relates the history of the noble Viking and his beloved Ingibjorg, his daring sea-voyages and his implacable enemies and quickly became very popular in both Germany and England. George Stephens translated it into English in 1839; this was, in fact, the first complete translation of an Old Norse saga into English. Fritjofs saga was an early example of transmedia medievalism and medievalism–tourism; set in the scenic Sognefjord, the story was instrumental in the establishment of the Norwegian tourist industry.

This chapter deals with one aspect of the relations between the United States and Franco's Spain – and vice versa – during the years in which the policy implemented by President Harry S. Truman and Secretary of State Dean Acheson required the Franco regime to make liberalizing reforms. The policy was opposed by some sectors of Congress, the armed forces, various economic interests, personalities from the world of culture and the press, and a part of public opinion, who pressed for a change that would take Spain out of diplomatic “quarantine” and no longer exclude it from the strategic and economic alliances struck by the United States in Western Europe. Paradoxically, the president and Acheson implemented the policy at the same time as their administration was doing its utmost to contain communism. Of course, Franco was at the head of one of the most doctrinally anti-communist regimes in Europe, so they clearly gave more weight to the fascist nature of the regime and Spain's friendship with the powers defeated in 1945 than to its undeniable anti-communism. This raises various issues such as the singularity of Spain's position in the immediate post-war period; the struggle between the executive and legislative powers in the United States to direct foreign policy; the increasing influence of the armed forces on the design of this foreign policy; the relations between the Allies in the years of transition from anti-fascism to anti-communism as the fundamental paradigm of international relations, with Spain being a surviving case that aroused anti-fascist feeling; and the influence of personal factors – beliefs, feelings, emotions, prejudices – on politics, in particular those of Truman and his anti-Franco sentiments.

Even though it is unlikely any of those living in late medieval Kent would have seen a copy of what has come to be known as the Gough Map, they would have recognised their ‘country’ due to its position between the great walled city of London (to the northwest) at the head of the Thames Estuary and English Calais across the Narrow Seas (to the east). For any potential Kent audience, the key features would have been the named coastal and riverine towns across the county and the dominance of the river systems that fed into the Thames Estuary and by extension the North Sea. While it is likely the map's early London provenance may explain this apparent topographical emphasis on the relationship between Kent and the capital (and its river), politically, economically and even socially this would have been viewed as appropriate by many in Kent, especially among the leading citizens of the various towns and cities and their rural peers. For even though there are no roads shown as passing through Kent, the marking of the recently rebuilt Rochester Bridge across the Medway would have been sufficient for those familiar with the county to denote the importance of the ancient route from London to Dover via the two episcopal cities of Rochester and Canterbury.

Therefore, the Gough Map is a helpful entry into this contextual exploration of Kent's history during a period that saw a complex mix of continuity and change in all aspects of society. Although much of the emphasis here will be on the maritime communities, as Gough highlights, inland urban communities were similarly part of this network of waterborne commerce. As a case in point, the stone from the quarries near Maidstone was carried from there via the River Medway and the Thames Estuary to Whitstable, and thence from that port by cart to Canterbury for the rebuilding of the city's Newingate in the late fifteenth century.

In the year 1373, a young woman in the burgeoning city of Norwich fell dangerously ill, during which illness she experienced visions of the crucified Christ. Some twenty years later, this woman, Julian of Norwich, withdrew into a local anchorhold, a sealed cell attached to a church, in order to live a solitary life devoted to God. There she wrote and rewrote her meditations on her earlier visionary encounters. In the second of her two texts especially, Julian forged a witnessed theology in which God's divine love manifested as a devoted mother nurturing the whole of humanity. For Julian, this feminised apparition of divine love was ultimately ‘oure lords mening’ and, moreover, ‘made alle things profitable to us’.

Such a vision of God, while hardly mainstream during the fourteenth and fifteenth centuries, nevertheless chimed readily with what has been termed by scholars the ‘affective turn’ within late medieval spiritual practices in England and beyond. Indeed, in Bishop's Lynn near Julian's hometown of Norwich, another local woman, Margery Kempe, who would later spend six weeks in Bristol mixing with the town's wealthy and literate merchant community, was also experiencing visionary encounters with God, which she too would eventually translate into written text. Driven in part by these experiences, in the year 1413 (some four years before her Bristol sojourn), this mercantile wife and mother to fourteen children visited Julian in her Norwich cell, keen to receive guidance and draw on the older visionary's experience in order to make sense of her own visions and the intensely somatic and uncontrollable bodily and spiritual ecstasies they incited.

In 1486, when nine-month-old Miles Frebrygge was playing with a Thomas Becket pilgrim badge given to him by an older boy, he ‘eventually put it in his mouth, as is the custom of such [children]’. The badge, too large to fit down young Miles's throat began to choke the child. His panic-stricken father desperately tried to help his son but could not remove the badge; unable to breathe, the signs of life left poor Miles. The father turned to prayer and repeatedly called upon ‘the most distinguished King Henry’ and ‘the most compassionate Mary’ to help his child, whereupon Miles, through the miraculous power of the dead king, suddenly spat out the badge and was able to breathe again.

Throughout this book, we have journeyed into the world of Alfonso X's imperial ambitions and their profound imprint on the Estoria de Espanna. Alfonso's reign, marked by cultural efflorescence, also bore the weight of his relentless pursuit of the crown of the Holy Roman Empire. This dream, born from his familial ties to the Staufen emperors, and the legacy of the Imperium Hispanicum that his father Fernando III had tried to revive, faced formidable challenges. From papal opposition to the reticence of Castilian-Leonese nobles, Alfonso's quest was fraught with obstacles from the very beginning.

Yet, Alfonso X's determination never wavered: why would a king so stubbornly pursue an aspiration that the papacy had denied from its very inception? In the context of the fight for both imperial and Peninsular hegemony, Alfonso X leveraged his privileged position to reinforce his dominant role in the Iberian Peninsula, a legacy inherited from the unification of Castile and Leon by his father, Fernando. This, combined with the rapid advance of the Christian kingdoms against Islam in the thirteenth century, and the enduring imperial idea linked to the kingdom of Leon – embodied by monarchs such as Alfonso VII, the emperor – made Alfonso X's connection to the Staufen family the final element necessary to consolidate his imperial ambitions.

Given these circumstances, the arrival of the Pisan emissaries could not have been timelier. The proposal to crown Alfonso X as Holy Roman Emperor provided the perfect opportunity to assert his Iberian superiority. At this point, Alfonso inherited two imperial strands: the legacy of the Imperium Hispanicum from Fernando III and his predecessors, and his Staufen lineage through his mother, Beatriz of Swabia. This convergence fuelled his concentrated effort to claim the German imperial crown, traditionally known as the Fecho del Imperio, one of Alfonso's most significant and costly endeavours.

The random geometric graphs considered in this chapter are derived from a configuration of points that are independently placed in an underlying Euclidean space, according to some distribution. Each pair of points that are separated by a distance less than some given threshold is joined by an edge, and the graph then consists only of vertices, corresponding to the points, and of the edges between them, with the positional information discarded. In this model, the edges are no longer independent, and the neighbourhood structure is quite different from the tree-like neighbourhoods in Chapters 11–14; for instance, the average local clustering coefficient is not typically close to zero, even in sparse graphs. A giant component is shown to be unlikely to exist if the density of points is low enough, and to be almost certain to exist if the density of points is high enough, with the ratio of the critical densities fixed as the number of points grows. A subgraph threshold theorem is established, complemented by a number of distributional approximations to the counts of subgraphs; the independence of the positions of the underlying points simplifies this discussion. Under suitable asymptotics, typical shortest path lengths are shown to grow like a power of the number of points, rather than logarithmically, as was the case for the models in Chapters 11–14.