Chapter 6 is concerned with theories and models in economics. Economists typically prefer to speak of “models” rather than “theories” and of “generalizations” or “assumptions” rather than “laws.” Economists still speak of theories, but only when referring to subdivisions of the discipline. Why? What are models and how are they related to theories? Why are economists so enamored of models? Do they supersede or incorporate laws? Without settled definitions of theories or models, it is unclear whether the focus on models is just a change in terminology, or whether there is something interestingly different in the practice of contemporary economics. This chapter surveys philosophical conceptions of theories and defends a view of theories as sets of lawlike statements that are systematically interconnected. It argues that models should be understood as conceptual explorations without empirical commitments. They are definitions of predicates or kinds of systems. Models can be used to theorize, explain, or predict, when one offers theoretical hypotheses asserting that parts of the real world belong to the extension of the predicate a model defines.

Analogy is a core cognitive capacity encompassing basic similarity (“this is like that”), relational similarity (proportional analogies of the form A:B::C:x), and complex system mappings, in which the elements of one situation are structurally aligned with the elements of another. The latter permits complex inferences from a known source situation to a less familiar target situation. Because of its centrality in human thinking, analogy has been the subject of numerous computational modeling efforts. Models of similarity come from multiple traditions in cognitive science, including associationist approaches (such as connectionist models), “traditional” symbolic approaches (such as graph matching and production systems), and hybrid symbolic/connectionist approaches. This chapter reviews and evaluates several models from these various approaches in terms of their ability to simulate basic similarity, relational similarity, and system mapping.

Estimates of the economic costs of climate change rely on guesswork in the face of huge uncertainties, and arbitrary judgements about what is important. The models can produce any number their creators want them to; and typically, they trivialise the risks. Despite being described as ‘worse than useless’ by leading academics, economic analysis of this kind has been credited with a Nobel Prize, and it continues to inform government policy.

This chapter introduces the concepts and methods used by the other chapters in the volume, using the long-standing problem of estimating the land carrying capacity of classical Attica to illustrate the benefits of probabilistic modelling. We begin by surveying the development of techniques for managing uncertainty in ancient history (1.1) and past work on the specific problem of Attica’s land carrying capacity (1.2). The chapter then turns to theoretical questions about the nature of uncertainty and probability (1.3), introducing the ‘subjectivist’ conception of probability as degree of belief, a theoretical framework that makes probability a powerful tool for historians. We go on to discuss the procedure of using probability distributions to represent uncertainty about the actual value of a quantity such as average barley yield in ancient Attica (among other variables relevant to the problem of land carrying capacity) (1.4), the need to be aware of cognitive biases that distort our probability judgements (1.5), the use of Monte Carlo simulation to combine uncertainties (1.6), the potential problem of epistemic interdependence (1.7), the interpretation of the outputs of a Monte Carlo simulation (1.8), and the use of sensitivity analysis to identify the most important sources of uncertainty in a simulation. The appendix illustrates model code in R.

This introduction begins by surveying earlier scholarship on the Roman imperial court, arguing that the landmark works have been unduly confined to the court in the city of Rome, to particular time periods, and to certain narrowly defined themes. It then discusses the definition of ‘court’, presenting the social definition used in the book, namely a circle of people in reasonably regular personal contact with the emperor. The introduction also considers what kinds of historical knowledge in relation to the Roman court are possible. The sources lack the focus and detail needed for a narrative history of the court; nor can we convincingly posit a model that encapsulates the impact and operation of the court over c. 300 years. Instead, one should identify features of court life and culture that recur, even if they did not exist (or are not evidenced) under every emperor.

This chapter examines the role of three kinds of narratives in producing knowledge about the rupture process of the Tohoku earthquake of 2011. I show that each of the three kinds of narratives appears in one of three stages on the way from data recorded of the earthquake to a reconstruction of the rupture process. In the first stage, rupture narratives are produced by computational tools called source models. In the second stage, a set of details that is taken accurately to represent features of the actual rupture process is distilled out of these conflicting rupture narratives through the use of a ‘research narrative’. In the third stage, these distilled details are strung together into an integrating narrative. This integrating narrative is used as a research tool for formulating questions, the pursuit of which has led to the production of further evidence about the rupture process.

Humans and other animals face decisions on which food items to harvest, when to quit searching and when to move on to the next patch. This chapter starts by describing optimal foraging theory (OFT), which has been used to understand and to predict foraging behaviour in animals as well as humans. We follow this by describing how cultural issues, such as taboos and religious beliefs, can affect optimal foraging in humans. We describe how OFT has been applied to human foraging and why it has been criticized by some researchers. We show that a number of alternatives to OFT models applied to humans have been suggested. Because there are different prey species and food is not distributed uniformly, prey and foraging space must be selected by human foragers. We continue by defining group hunting and sexual division in hunting roles as crucial elements in human foraging strategies. We end the chapter by discussing conservation and sustainability and linking this to the ecologically noble savage concept introduced in the previous chapter.

This chapter highlights the various types of cyberattacks and how data analytics methods can potentially be used to analyze these attacks.

The project of Greenlees et al. on understanding rational G-spectra in terms of algebraic categories has had many successes, classifying rational G-spectra for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as rational toral G-spectra for arbitrary compact Lie groups. This chapter provides an introduction to the subject in two parts. The first discusses rational G-Mackey functors, the action of the Burnside ring and change of group functors. It gives a complete proof of the well-known classification of rational Mackey functors for finite G. The second part discusses the methods and tools from equivariant stable homotopy theory needed to obtain algebraic models for rational G-spectra. It gives a summary of the key steps in the classification of rational G-spectra in terms of a symmetric monoidal algebraic category. Having these two parts in the same place allows one to see clearly the analogy between the algebraic and topological classifications.

Testing is an important element in the software development cycle. This chapter examines where software testing fits into a number of software process models: the waterfall model, the V-model, incremental and Agile development, eXtreme Programming, and SCRUM.

This chapter examines questions of governance in colonial contexts, noting important similarities between colonial governance and governance approaches in corporations.

Mathematical models of biological populations and communities are the most common type of representation in ecology, with a wide array of functional forms and many different types of variables and parameters. This complexity and the uneasy relationship between theoretical and empirical work in ecology makes for fertile philosophical fodder. For example, most ecological models are highly idealized, incorporating unrealistic assumptions to make mathematical model analysis tractable. This is troubling in ecology as mathematical ecologists often uncritically emulate mathematically sophisticated models of physics to ensure their modeling is mathematically rigorous. Showing the characterization of ecological stability as Lyapunov stability as indefensible is one goal of this chapter. Another goal is assessing the ecological promise of individual-based models (IBMs) and the philosophical issues they pose. IBMs do not aggregate over, or abstract from, the details of interactions between individual organisms. This modeling strategy is part of a more general, well-vetted “methodologically-individualistic” approach to representing the world often employed in social sciences. Debates about methodological individualism in the social sciences reveal insights about how individual-based ecological modeling should be understood and indicate their reductive potential in ecology.

This chapter examines the development of digital business. It commences with a reflection on the huge benefits arising from digitalisation, including greater productivity, more competition, greater choice and convenience, innovation and profitability. It also notes that it is extremely difficult to separate the digital economy from the rest of the economy. The key features of digital businesses include direct and indirect network effects, economies of scale, anti-competitive lock-in effects, the importance of data and complementarity. The four most significant new types of business models are explained: multi-sided platforms, resellers, vertically integrated firms and input suppliers. Lastly, there are observations made about the key characteristics of highly digitalised business models which have significance and importance in the context of looking at the challenges to the international tax system.