This chapter is on communication complexity, which measures the minimum number of bits that two parties must exchange to collaboratively compute a function when the input is split between the parties. Techniques for upper and lower bounds for deterministic and randomized communication complexities are covered. The chapter also presents applications of communication complexity to topics that don’t involve explicit communication, such as streaming algorithms, data structures, and integrated circuit layout.

This chapter maps IB activities from the vantage point of the firm. Shifting the analytical focus from territories to organizations, it examines how MNEs configure and fragment their value chains across borders. The chapter distinguishes between international fragmentation and ownership fragmentation. Drawing on value-chain analysis and global production network research, the chapter shows how firms distribute R&D, manufacturing, marketing, and support functions across locations to exploit cost differentials, knowledge pools, and market proximity. It also highlights divergent organizational forms, including vertically integrated structures, outsourcing arrangements, and factoryless production models. The chapter introduces three core dilemmas that arise from these configurations: the international fragmentation dilemma, the ownership fragmentation dilemma, and the international complexity dilemma. These tensions reflect trade-offs between efficiency, control, coordination, and flexibility. By mapping how firms organize their cross-border activities, the chapter provides a foundation for understanding the strategic rationales behind internationalization, which are examined in Chapter 10.

This introductory chapter sets the stage for the book by examining how modern science advances not through the steady accumulation of facts but through profound conceptual shifts that reshape our understanding of reality. It contrasts long-established scientific ideas – such as heliocentrism, evolution, and Newtonian mechanics – with the less widely understood revolutions of the twentieth century, including relativity, quantum mechanics, chaos theory, and computational limits. The chapter emphasizes that many modern scientific theories challenge intuition while remaining accessible at the level of ideas, even when their mathematical formulations are complex. A unifying theme is the emergence of uncertainty, unpredictability, and fundamental limits – not as shortcomings of human knowledge but as intrinsic features of nature itself. The chapter also introduces a computational perspective that recurs throughout the book, highlighting how simple rules can generate extraordinary complexity across physical, biological, and informational systems. Finally, the introduction outlines the book’s scope, audience, and structure, explaining how each chapter focuses on a central scientific insight that reveals a deeper unity underlying diverse phenomena.

The epilogue reflects on the unifying themes that emerge across the scientific ideas explored in this book and considers their implications for the future of knowledge. A central lesson is that modern science has revealed fundamental limits – to prediction, to certainty, and even to what can be known in principle. From Gödel’s incompleteness theorems and Turing’s limits of computation to quantum uncertainty and chaotic dynamics, uncertainty appears not as a failure of understanding but as a structural feature of reality. A second recurring theme is that extraordinary complexity can arise from simple underlying rules, whether in computation, physics, biology, or planetary processes. Looking forward, the epilogue considers the growing role of artificial intelligence in scientific discovery, suggesting that future insights may increasingly be generated by systems whose internal reasoning is difficult for humans to interpret, even when their results can be verified. The book concludes by arguing that making sense of modern science requires embracing both humility and curiosity, as humanity navigates a future shaped by powerful ideas, computational tools, and enduring uncertainty.

This chapter introduces the fundamental concepts of computational problems, algorithms, and time and space efficiency. These concepts are formally defined and illustrated with examples. The major time and space complexity classes P, EXP, L, and PSPACE are introduced. The chapter concludes by defining reductions, which are tools for relating complexities of different problems.

Change isn’t always orderly. Sometimes, it’s messy, emergent, and unpredictable. Chapter 3 introduces an organic perspective – one that sees change as a constant process unfolding through interaction, context, and chance. Instead of controlling change, this approach focuses on sensing, responding, and evolving. Drawing on ideas like complexity theory and informal networks, it reveals a more fluid way of understanding transformation. While it resists neat solutions, this perspective expands how we think about change - and challenges us to embrace uncertainty as part of the process.

This chapter examines Aquinas’s doctrine of divine simplicity, situating it within the broader landscape of classical theism in contrast to theistic personalism. After outlining Aquinas’s conviction that while God’s existence can be demonstrated, God’s essence remains incomprehensible, the discussion turns to Summa Theologiae, 1a, 3, where Aquinas denies that God is composite in any respect. He argues that God is not a body, nor composed of form and matter, essence and existence, substance and accidents, or genus and difference. Instead, God is pure actuality, identical with his essence and existence, and thus utterly simple. The chapter compares these claims with parallel treatments in the Sentences, Summa Contra Gentiles, and Compendium Theologiae. Finally, it surveys modern objections – particularly from Alvin Plantinga, Richard Swinburne, and others – that divine simplicity undermines God’s personhood, freedom, or responsiveness. The chapter concludes that many such criticisms misrepresent Aquinas, who presents simplicity chiefly as a way of ruling out what God cannot be.

Abstract: What is the basis for the emergence of ‘complex societies’ in the Mediterranean and on its islands? Why did it happen in different places and at different times? In this chapter, we consider the unusual trajectory of Mediterranean social evolution in later prehistory. We show that many Mediterranean societies exhibiting evidence for vertical differentiation developed – counter-intuitively – on islands and coasts, and did so over the broad span from 3000 to 1000 BC. We consider the reasons behind this, illustrating how island environments, demography, structures of wealth distribution, and climatic change may intersect to drive otherwise inexplicable patterning. In doing so, we sketch what a more fully developed theory of Mediterranean social complexity might look like.

Romanos’ funeral freights the reign of Michael IV with the burden of Michael’s past, his betrayal of Romanos, false oath, deception of Zoe, and rumours of collusion in Romanos’ death. Psellos knits these elements together with Michael’s fine performance as emperor to produce a conscience-driven, tormented figure trying to save his soul and serve his people. It is a new departure, unrepeated, into a psychological analysis of guilt, shame, and the hidden aspects of the human psyche, with Michael’s illness a metaphor for what can and cannot be known or said. Book Five draws the reader out of the dark psychic region of Book Four, through a brief, paranoid, and jerky reign characterized by poor theatricals, to an energizing, open, and collective action with a telos. Having exiled his benefactor John, Michael V tonsures and exiles Zoe, and the City rises as one to tear the imperial buildings from the earth and reset the social contract. Psellos portrays the rising as divinely inspired and articulated, with the demos assuming the empire. Imbued with ironies, their movement is neos, gives rise to lacrimae rerum, and restores the Macedonian line.

We introduce the simplest photonic spin glass by leveraging the so-called random energy model (REM), which allows one to derive a phase diagram with reasonable mathematical complexity. We introduce some concepts of nonequilibrium thermodynamic phases in a multimode photonic system.

Now that the notion of the Anthropocene is more than a quarter century old, it is possible to review its career. With a special focus on the notion’s trajectory in literary studies, this chapter assesses that career in three ways. First, it makes the language-theoretical point that the Anthropocene is less a rigid denominator than a necessary misnomer: a term that cannot possibly capture the vast realities it is assumed to name, and is better thought of as a catalyst for debate. This helps explain why the recent dismissal of the Anthropocene as a chronostratigraphic unit hardly affects the term’s popularity. Second, it tracks the development of the term in literary studies to show how a term that initially signaled ecological urgency began to signify theoretical complexity in the 2010s and, somewhat later, also an increasing awareness of diversity. Third, it underlines that the particular way in which literary studies conceives of the Anthropocene is affected by the specific affordances of literature, which is reflected in the association of the Anthropocene with interdisciplinarity, multiscalarity, embodied experience, the ontology of writing, and a mood of impending disaster.