This chapter explores Augustine’s monumental City of God, written in the wake of the 410 sack of Rome, as a response to critics who blamed Christianity for the empire’s decline. Augustine constructs a dual vision of history structured around two metaphorical cities: the City of Man, grounded in pride and temporal ambition, and the City of God, formed by love of God and oriented toward eternal peace. The chapter examines Augustine’s theological reframing of history as linear, purposeful, and governed by divine providence, in contrast to the cyclical models of ancient historians. It analyzes his critique of pagan religion, his nuanced appropriation of Platonism, and his demonology, all of which served to delegitimize traditional Roman cults while affirming Christianity’s supremacy. At the heart of the chapter is Augustine’s doctrine of predestination and his unsettling insistence on humanity’s dependence on divine grace. The City of God emerges as both a critique of Roman imperial pretensions and a charter for a Christian understanding of time, politics, and salvation, whose legacy would profoundly shape medieval and modern thought.

This chapter examines multipartite quantum systems using matrix product states and quantum circuits, including ZX calculus.

The Epilogue situates the close of late antiquity and the rise of Islam within a broader narrative of continuity, exchange, and transformation. It opens with Gregory the Great’s reflections on unity and diversity in the Christian Church, marking the culmination of the late antique synthesis of faith, philosophy, and governance. From there, it turns eastward to the origins of Islam, recounting Muhammad’s revelatory experience and the early spread of a faith that would, within a century, unite vast territories from Arabia to Spain and Central Asia. The emergence of Islamic centers of learning—Baghdad, Bukhara, Samarkand—revived Greek philosophy in Arabic translation and interpretation, producing thinkers such as Al-Kindi, Al-Farabi, Avicenna, and Averroes, whose reconciling of faith and reason later informed the scholastic debates of the Latin West. The chapter closes with a return to Europe and to figures like the twelfth-century scribe Guda, whose self-portrait in a manuscript reminds us that women, too, shaped medieval intellectual life. Across these worlds, the Epilogue underscores that “Western” thought has always been the product of conversation—between Greeks, Romans, Jews, Christians, and Muslims; between men and women; between faith and reason.

This chapter extends bipartite analysis to mixed states, covering quantum discord and entanglement measures.

This chapter discusses alternative entropy measures like Tsallis and Rényi, emphasizing their roles in prediction and compression tasks.

This final chapter on Israel’s writing prophets highlights those whose messages supported postexilic restoration during the Persian period. As in earlier chapters, we will need to consider the conditionality of prophecy as well as its “forthtelling” rather than “foretelling” nature.

In 539 bce, the Persian king Cyrus allowed the first group of Israelite exiles to return to Jerusalem, now part of the administrative province of Yehud. The prophets Haggai and Zechariah serve to inspire this rebuilding process, particularly of the temple. We will observe in Zechariah growing evidence of a messianic hope in a future Davidic king as well as a literary shift from eschatology to apocalyptic forms. Malachi, dated around 470 bce, builds on earlier Old Testament prophetic themes of purity and covenant faithfulness. Much harder to date is Joel, as it contains sections indicative of two entirely different periods of Judah’s history; however, we will note the “day of Yahweh” theme in Joel, portrayed this time as a terrible day of reckoning for the nations. Jonah is unique as a narrative, conveying through rather humorous form the serious concern of Yahweh for all peoples.

This chapter provides a comprehensive overview of the neurotechnologies used to record and stimulate brain activity, from invasive techniques like optogenetics and intracranial electrodes to noninvasive methods such as electroencephalography and functional magnetic resonance imaging. It explains how these technologies are evaluated based on criteria like spatial resolution, temporal resolution, safety, and portability. With this framework, each technology is evaluated in terms of its power and constraints. This chapter highlights the trade-off between technological power and practical constraints, emphasizing the need for safer, more adaptable devices for both clinical and research purposes.

Expanding citizenship characterised New Zealand in the late twentieth century, when ruptures in the very meaning of New Zealandness obliged people to adapt to new ideas about who belonged to the nation and what belonging entailed. The country reshaped political institutions to reflect that its people and culture had grown more diverse and connected to the world and to accommodate the concept of biculturalism.

So deep was Aotearoa in the watery world of the Pacific that it remained for a long time unknown to Europeans, other than as a part of the mythical great southern land, Terra Australis. Surely there had to be a continent in the South Pacific to balance the weight of land in the Northern Hemisphere? As it proved, there was not. New Zealand is immersed in the Pacific, surrounded by 2000 kilometres of ocean, a fact that is reflected in Māori waka (canoe) traditions. Only in the late eighteenth century did its full outline register in European consciousness through the process of physical discovery.