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This element describes an emerging and intriguing topic: computational indeterminacy. Indeterminacy occurs when a fixed physical system potentially computes several different functions, and there is no fact of the matter which of these is actually being computed by the system. The phenomenon of computational indeterminacy has potential significance for a number of fields, including neuroscience and cognitive science, artificial intelligence (AI), the theory of algorithms, and circuit design. Here we address foundational and philosophical issues. We also explain how the indeterminacy phenomenon impacts on current thinking about the nature of physical computation. Computational indeterminacy is the subject of a growing number of articles in specialist journals, and The Indeterminacy of Computation introduces the topic to a wider audience. The style is clear and informal, with many helpful diagrams. This title is also available as Open Access on Cambridge Core.
This Element revisits the conceptual history of freedom and democracy in Cold War South Korea. Cold War liberalism is usually told as a North Atlantic story of defensive anti-communism, the 'liberalism of fear', and pluralist scepticism towards mass politics. Yet behind that veneer lay another face - the technocratic administrative state - that became dominant once Cold War liberalism reached the decolonising periphery under the rubric of 'modernisation'. Through a conceptual historical analysis, this Element traces how freedom and democracy were continually recombined with nationalism, developmentalism and diverse moral-economic registers, generating conceptual problematics the metropolitan tradition had rarely been compelled to confront. From the Founding Constitution through 'Korean-style democracy' to the minjung turn and democratic transition, Cold War Korea emerges not as belated reception but as a vantage from which liberalism's constitutive tensions become visible.
This Element explores the politics of invasive alien species (IAS) through the lens of critical heritage studies, highlighting how species management intersects with cultural values, identity, and notions of belonging. Focusing on two Swedish case studies-the Garden Lupin and the Signal Crayfish-it examines how environmental and heritage discourses are entangled in practices of conservation and tradition. IAS management is framed as 'heritage work,' shaped by emotional attachments, historical narratives, and affective alliances. By treating IAS not only as ecological threats but as cultural phenomena, the Element challenges dominant ecological paradigms, emphasizing the socio-political dimensions of nature conservation. It argues that understandings of 'native' and 'non-native' are shaped by memory, tradition, and temporality, often leading to conflicting interpretations of landscape and heritage. This interdisciplinary approach offers new insights into the cultural dynamics underpinning environmental governance in the Anthropocene. This title is also available as Open Access on Cambridge Core.
This Element explores the colonial foundations and imperial design of offshore finance, arguing that tax havens are not anomalies but central to global capitalism. Centering the Caribbean and Puerto Rico, it shows how colonial legality and geopolitical subordination produced zones marked by a logic of inclusive exclusion, where secrecy, corporate power, and tax injustice are normalized. Drawing on TWAIL and law and political economy, the Element introduces the concepts of colonial state of exception and the corporate citizen as key legal formations of the colonial offshore economy. It examines how secrecy, financial services, and fintech enable corporations to externalize harm and evade accountability, and how tax reforms, like the OECD's Pillar Two and the UN Tax Convention, often reproduce colonial and racialized hierarchies. The Element concludes with a call to abolish the colonial offshore economy and to uplift grassroots movements across the Caribbean that demand transparency, sovereignty, and justice.
Focusing on democracy studies, this Element considers the different ways in which scholars have responded to fundamental conceptual and theoretical choices in the field and, drawing mainly on various metatheoretical ideas, suggests that some positions are better justified than others. It emphasizes the perils of maximalist definitions of democracy and argues against an aggregative, additive conception of democracy that does not recognize qualitative distinctions. It questions the assignment of causal primacy to economic, cultural, or political factors in explanations of democracy, and stresses the importance of causal interactions and reciprocal causation. It makes a case for modeling the temporal heterogeneity of causal relations. It favors explanations that incorporate causal mechanisms through multi-level models. It also sees the integration of specific models of democracy as a promising path to theoretical unification. In short, it scrutinizes several foundational ideas in democracy studies and proposes a reconstruction of the field's theoretical foundations.
This Element gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as functors, adjunctions, and strictication, and leading up to Cartesian Closed Categories, the core mathematical model of the lambda calculus and of functional programming languages. This methodology inverts the usual approach of proceeding from syntax to a categorical interpretation, by rationally reconstructing a syntax from the categorical model. The result is a graph syntax-more precisely, a hierarchical hypergraph syntax-which in many ways is shown to be an improvement over the conventional linear term syntax. The rest of the Element focuses on applications of interest to programming languages: operational semantics, general frameworks for type inference, and complex whole-program transformations such as closure conversion and automatic differentiation. This title is also available as open access on Cambridge Core.
This Element evaluates the current theory for categorizing syntactic objects, including some of its main findings. It starts with categorization within the lexicon, where the categories of lexical items form the basis for categorization of phrases that contain them. In current theorizing the identification of a category label for a given syntactic object is distinct from the operation that generates compositional structure, the binary, set-forming operation Merge – thus allowing each to be maximally simple. This Element established how the efficient search for and identification of a label is required for the interpretation of a syntactic object at the cognitive interfaces that process both phonetic form and meaning. It shows how the approach works for simple cases and how it extends to more complex ones in a step-by-step fashion, drawing on phenomena from several languages, providing insightful and surprising analyses.
Does the macro-level relationship between temperature and output comprehensively reflect the patterns observed sub-nationally? This Element quantifies heterogeneous productivity-growth responses to plausibly exogenous temperature and precipitation fluctuations using unbalanced panels over 1970-2018 (166 countries from Penn World Tables 10.01; >1,500 sub-national regions from MCC-PIK). It projects climate change-driven permanent damages to the level of GDP per capita by compounding physical risk-induced productivity-growth deviations over time. These transitory shocks are calculated by combining econometrically estimated response functions with an ensemble of NEX-GDDP CMIP6 simulations from 29 global climate models, which are extrapolated to 3,672 provinces covering 95% of global economic production. First, this study provides a basis for producing spatially disaggregated projections of climate-induced economic damages that consistently encompass most productive regions. Second, it shows that accounting for spatially granular climatic exposure and intra-country economic heterogeneity yields aggregated losses that alter the conclusions of previous global GDP models.
My aim in this short book is to defend Hegel from some famous objections from Marx (writing on his own or with Engels). Across both chapters, I will focus on a Marxist objection to the effect that Hegel misunderstands the ultimate bases of social structure and historical change. Indeed Hegel's account is not just flawed or incomplete but completely backwards (standing on its head). In the first chapter, I consider Marx's (and Engels') historical-materialist critique of Hegel, which charges him with neglecting the foundational role of the economic base in history and erroneously prioritizing the ideological and legal or political superstructure. In the second chapter I turn to politics, considering the young Marx's case in favor of radical democracy and against the Hegelian rational state.
A Critical Archaeology of Politics takes the reader on a journey across various ancient worlds to examine how to reconstruct their politics in a more coherent, imaginative, and accurate way. Drawing on non-Western epistemologies, relational ontologies, and ancient texts, this book attempts to eliminate our present concerns to recognize the often surprising power dynamics that shaped ancient politics. From Neolithic Türkiye, the Archaic Mississippi, to Medieval Western Europe and the Maya world, the reader engages with the gods of Land, magical politics, and travelling princes to explore how ancient politicians may have conceived of their world in ways which dramatically differ from our own. By surveying both the promises and pitfalls of anthropological archaeology, students, scholars, and the general public alike learn how to deconstruct their present to better reconstruct political pasts.
This Element highlights the coastal and island communities of the central Mediterranean as key actors in long-distance exchange networks with the Aegean and eastern Mediterranean during the Bronze Age. It presents a dynamic, interconnected landscape of people, goods, and ideas, emphasising multidirectional and multiscalar interactions and their impact on exchange and social identities. Organised thematically, geographically, and chronologically, it offers accessible insights for both specialists and non-specialists, combining detailed archaeological evidence with critical interpretation. The Element underscores the role of local conditions in shaping long-distance Bronze Age exchange networks and fostering social and cultural connections across the Mediterranean, opening fresh perspectives on exchange and identity.
Artificial systems now perform a striking range of cognitive tasks. This Element defends three claims. First, the status quo for cognitive work cannot survive. Whatever AI's trajectory, the package of features defining cognitive work – high skill requirements, credentials, wage premiums, resistance to automation, and low productivity growth – will be radically transformed. Second, the widespread displacement of humans from cognitive work, though it sounds alarming, may pose no special threat to human flourishing. Whatever makes work good for people is equally available outside cognitive work, and displacement enables leveraged gains in research and access to justice. Third, a world of ubiquitous cognitive assistance, though it sounds benign, carries distinctive moral risks, especially for children. Cognitive assistance works by reducing cognitive difficulty. But cognitive difficulty is necessary for the normal development of executive function – the capacities constitutive of autonomous agency. This title is also available as Open Access on Cambridge Core.
This Element provides an account of the ownership from 1833 to the present of the copy of Shakespeare's Second Folio (1632) held at the State Library of New South Wales in Sydney, Australia (SAFE 1/63). Tasmanian artist and author Louisa Anne Meredith was given the Folio in 1833 in Birmingham and brought it to Tasmania when she emigrated in 1839. Her letters reveal she treasured and studied the Folio until she sold it to four men (c. 1885–86) who gave it to colonial actress Essie Jenyns in 1887. Jenyns hand delivered the Folio to the Mitchell Library (part of the State Library) in 1920 shortly before she died. In this narrative diverse archival sources are used to reconstruct the nineteenth- and early-twentieth-century provenance of the Folio and explore its place in the British Empire's colonisation enterprise.
This Element explores how waste and food leftovers were transformed into evidence of the natural and human past, valuable collector's items, and museum specimens. In the nineteenth century, rubbish pits became repositories of new sources for studying the non-written past. The following pages connect the history of nineteenth-century waste with prehistoric archaeology, the reutilization of refuse and the excavation of ancient rubbish dumps. Waste and trash are not trans-historic categories. Here, 'waste' refers to a broad range of results of human activity: from deliberately constructed rubbish tips for unwanted items, to less organized discards in lake dwellings and peat bogs, and large-scale management of urban waste that reshaped landscapes. Recycling did not begin in the nineteenth century, but new considerations about reuse and the growing scale of waste disposal provided palaeontologists and archaeologists with fresh lines of enquiry and a framework for addressing the problem of modern extinctions.
This Element advances the Scalar Deictic Space approach as a cognitive–discursive framework for analysing how political discourse constructs, differentiates, and dynamically reorganises identity, agency, urgency, and legitimacy. Building on the primacy of spatial cognition, SDS conceptualises political meaning-making as a scalar configuration anchored in a deictic centre, organised across proximal, medial, and distal zones of positioning. These zones reflect graded relations of intentionality, dependency, and symbolic alignment rather than fixed group memberships. By moving beyond binary Us–Other models, SDS reveals how political discourse internally stratifies the in-group, redistributing power and responsibility through shifting spatial, temporal, and modal configurations. Drawing on variety of examples including US, Iranian, and Ukrainian political discourse, the Element demonstrates how scalar positioning enables actors to legitimise action and project future while maintaining ideological coherence. As a dynamic analytical tool for tracing diachronic change in political worldviews, SDS critically examines cognitive foundations of political persuasion.
To deal with an increasingly large and sophisticated class of real life problems, image processing methods range from the traditional filtering and thresholding techniques to advanced variational models and deep learning algorithms. Regularization is a key concept in developing a variational model to ensure that a model has at least one solution and hence efforts in devising efficient algorithms worthwhile. High order and nonlocal regularization is particularly important, especially when the underlying problem (i.e. input image) requires one to minimize intensity differences within a large neighbourhood (e.g. beyond immediate voxels) for smoothness consideration. This Element aims to survey, review and discuss the state of the art techniques towards the latter kind of methods, emphasizing foundations, algorithms (and codes) and open challenges of high order and nonlocal regularizers for imaging tasks in commonly practised application scenarios.
Political consumerism is an important form of political participation in which citizens use market choices – boycotting and buycotting – to express political concerns and influence global economic and political institutions. Adopting a comparative perspective, the Element integrates evidence from a meta-analysis (109 studies and 1,300 tests), global survey data (66 countries and 97,000 respondents), and original cross-national research (5 countries and 7,500 respondents). Using each data source, the authors examine the roles of resources (education, income, and information/news), engagement (political interest, ideology, and environmental concern), and mobilization (online group ties and offline organization membership) in political consumerism and how these factors vary across countries in explaining political consumerism. The authors find that organizational membership, group ties on social media, political interest, and political ideology are consistent covariates of boycotting and buycotting, whereas education, information/news, and environmental concern depend on the country, political context, campaign, and activity (boycotting or buycotting).
Most studies of ancient Israelite families have taken children for granted. Scholarship assumed children were present but, thinking that children were invisible in the archaeological record, it did not pay much attention to them. In recent years, a new emerging field of inquiry promises to enrich and expand our understanding of children and the family in ancient Israel. Utilizing text and archaeology, this Element explores how children had an impact on the family and its household. It first considers why children were desired and explores the ways in which children entered the ancient Israelite household. The subsequent sections examine different aspects of a child's life within the family, including issues of gender and culture, household religion, death, and items used by children in their daily lives. What becomes apparent is that children were not overlooked by their families but were treated as a valuable component of the ancient Israelite household.
Since the release of ChatGPT in late 2022, computers have demonstrated fluent interaction with humans through language. For linguists and lawyers, whose work is primarily language-based, the impact is poised to be significant. This Element explores the science and technology underlying LLMs, showing how their successes validate linguistic theories and can help linguistics evolve, with a focus on forensic and legal applications. By walking through the concepts behind current LLMs and connecting them to linguistic principles, it demonstrates how LLMs can assist the forensic and legal linguist through two toy experiments - one in rule construction and one in authorship attribution - with interesting results. It concludes that, while LLMs warrant caution regarding their pitfalls, they can help forensic and legal linguistics achieve greater rigor and success, provided the community develops appropriate constraints and protocols for their use.