This chapter examines the foundations and limits of computation and their implications for artificial intelligence. It begins with the Entscheidungsproblem and Alan Turing’s formulation of the universal Turing machine, introducing the idea that computation itself can be studied independently of any physical machine. The chapter explains the halting problem and related undecidability results, showing that some well-defined questions cannot be answered by any algorithm, even in principle. It then turns to computational complexity, distinguishing between problems that are solvable in theory and those that are solvable efficiently, and introduces the P versus NP problem as a central open question. The chapter explores how computational hardness can function not only as a limitation but also as a resource, underpinning modern cryptography through one-way functions and key-exchange protocols. Finally, the discussion turns to artificial intelligence, contrasting early rule-based approaches with modern machine learning and neural networks. Recent advances in deep learning and large language models are presented as the culmination of decades of theoretical insight, highlighting both their remarkable capabilities and the enduring structural limits imposed by computation itself.

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.

Classical methods such as ordinary least squares (OLS) were designed for datasets with just a handful of predictors. However, the trend over the last 30 years or so has been towards larger datasets, in particular where the number of predictors may be large even compared with the number of observations --- so-called high-dimensional data. In such settings, it may be advantageous to consider penalised estimators that reduce variance, at the expense of introducing some bias. We study both ridge regression and Lasso estimators, with the latter having the attractive property that it performs simultaneous variable selection and parameter estimation. The Lasso can be computed efficiently using coordinate descent, and we present finite-sample guarantees on its prediction, estimation and variable selection performance. We also consider extensions such as the square-root Lasso, the debiased Lasso and complementary pairs stability selection.

The Coda shows how the post-Enlightenment desire for a science of verse has been fundamental to contemporary machine learning technologies. It also reflects on the historical development, ideological commitments and epistemological foundations of the normal scientific study of poetry, both at its inception and in its enduring legacies, inquiring into what is at stake when techno-scientific reason attempts to exert its full domination over the poetic imagination, into how the nineteenth-century dream of a science of verse has shaped contemporary scientific exploration. It does so via the often-overlooked mid-century poet and scientific critic Josephine Miles.

The twenty-first century is a digital century, and the use of digital media and data-analyzing technology has become widespread and even trendy in the humanities. What does this mean for the legacy of the Holocaust? What are the advantages and challenges of digitalization in the context of Holocaust archives, for example with online access to videos of survivor testimony? Are there new strategies for representing or analyzing the Holocaust that draw on the techniques of digital humanities? This chapter explores the uses (and abuses) of digital technologies for both analyzing the history of the Holocaust and presenting that history to a public audience. It also considers the question of the post-survivor future, for example holograms of survivors, and what this says about “authenticity” and authority.

This paper presents the main topics, arguments, and positions in the philosophy of AI at present (excluding ethics). Apart from the basic concepts of intelligence and computation, the main topics of artificial cognition are perception, action, meaning, rational choice, free will, consciousness, and normativity. Through a better understanding of these topics, the philosophy of AI contributes to our understanding of the nature, prospects, and value of AI. Furthermore, these topics can be understood more deeply through the discussion of AI; so we suggest that “AI philosophy” provides a new method for philosophy.

Methods for analyzing and visualizing literary data receive substantially more attention in digital literary studies than the digital archives with which literary data are predominantly constructed. When discussed, digital archives are often perceived as entirely different from nondigital ones, and as passive – that is, as novel and enabling (or disabling) settings or backgrounds for research rather than active shapers of literary knowledge. This understanding produces abstract critiques of digital archives, and risks conflating events and trends in the histories of literary data with events and trends in literary history. By contrast, an emerging group of media-specific approaches adapt traditional philological and media archaeological methods to explore the complex and interdependent relationship between literary knowledges, technologies, and infrastructures.

Starting off substantive engagement with Sun Tzu with a focus on calculation serves a positive purpose. It is a way of emphasizing to contemporary audiences that there is more to Sun Tzu than being tricky or unorthodox – the strands of his way of war that readers, at least Western ones, widely note and often lionize. In present usage, the umbrella term “calculation” is intended to serve as a flexible rubric capable of covering intendedly rational judgments of more than one kind, many intuitive, others more formally structured.