This is a revision of John Trimmer’s English translation of Schrödinger’s famous ‘cat paper’, originally published in three parts in Naturwissenschaften in 1935.

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.

Over the years, the Serengeti has been a model ecosystem for answering basic ecological questions about the distribution and abundance of organisms, populations, and species, and about how different species interact with each other and with their environment. Tony Sinclair and many other researchers have addressed some of these questions, and continue to work on understanding important biotic and abiotic linkages that influence ecosystem functioning. In common with all types of scientific inquiry, ecologists use predictions to test hypotheses about ecological processes; this approach is highlighted by Sinclair’s research that explored why buffalo and wildebeest populations were rapidly expanding. Like other scientists, ecologists use observation, modeling, and experimentation to generate and test hypotheses. However, in contrast with much biological inquiry, ecologists ask questions that link numerous levels of the biological hierarchy, from molecular to global ecology.

Forecasting elections is a high-risk, high-reward endeavor. Today’s polling rock star is tomorrow’s has-been. It is a high-pressure gig. Public opinion polls have been a staple of election forecasting for almost ninety years. But single source predictions are an imperfect means of forecasting, as we detailed in the preceding chapter. One of the most telling examples of this in recent years is the 2016 US presidential election. In this chapter, we will examine public opinion as an election forecast input. We organize election prediction into three broad buckets: (1) heuristics models, (2) poll-based models, and (3) fundamentals models.

How do children process language as they get older? Is there continuity in the functions assigned to specific structures? And what changes in their processing and their representations as they acquire more language? They appear to use bracketing (finding boundaries), reference (linking to meanings), and clustering (grouping units that belong together) as they analyze the speech stream and extract recurring units, word classes, and larger constructions. Comprehension precedes production. This allows children to monitor and repair production that doesn’t match the adult forms they have represented in memory. Children also track the frequency of types and tokens; they use types in setting up paradigms and identifying regular versus irregular forms. Amount of experience with language, (the diversity of settings) plus feedback and practice, also accounts for individual differences in the paths followed during acquisition. Ultimately, models of the process of acquisition need to incorporate all this to account for how acquisition takes place.

This chapter introduces you to foundational knowledge regarding frameworks and models which is applied in later chapters. Theoretical models and frameworks serve as the ‘connective tissue that meshes theory and practice’. The chapter presents an overview of some of the most pertinent models and frameworks that can support you in designing lessons or learning experiences that incorporate digital technologies. It also highlights how you can reflect on the integration of technology into your teaching.

This chapter begins with models of educator knowledge, TPACK and the UNESCO ICT model, followed by the WHO workflow that helps you plan for using digital technologies in learning. The chapter also examines models and frameworks for considering the degree of integration of technology into teaching (SAMR and RAT/PICRAT) and concludes with educator acceptance models (TAM and CBAM).

Inferences are never assumption free. Data summaries that do not account for all relevant effects readily mislead. Distributions for the Pearson correlation and for counts, and extensions accounting for handling extra-binomial and extra-Poisson variation are noted. Notions of statistical power are introduced. Resampling methods, the bootstrap, and permutation tests, extend available inferential approaches. Regression with a single explanatory variable is used as a context in which to introduce residual plots, outliers, influence, robust regression, and standard errors of predicted values. There are two regression lines – that of y on x and that of x on y. Power transformations, with the logarithmic transformation as a special case, are often effective in giving a linear relationship. The training/test approach, and the closely allied of cross-validation approach, can be important for avoiding over-fitting. Other topics include one- and two-way comparisons, adjustments when there are multiple comparisons, and the estimation of false discovery rates when there is severe multiplicity. Discussions of theories of inference, including likelihood, and Bayes Factor and other Bayesian perspectives, ends the chapter.

Multilevel multicomponent complex adaptive systems are not reducible to the sum of the causal effects of independent variables. Causal inference, which has a privileged place in contemporary IR (and many other social sciences) cannot address systems effects, which arise from interdependent elements and operations (not the impact of independent variables on dependent variables). Systems effects explanations explain why by showing how. They identify mechanisms and processes of causation. They thus are able to establish causal efficacy; that is, show how processes produce – actually cause – outcomes (rather than merely identify some elements that are part of an unspecified causal process). Such an understanding leads us away from a “laws and theories” conception of science, which remains popular in Physics and Chemistry, towards a “models and mechanisms” understanding, which predominates in the life sciences (which, on their face, seem a much better model for the social sciences).

Mainstream social science, when it looks for parallels with the natural sciences, tends to look to classical Physics, which stresses laws, causes, and theories. I argue that we should look instead to Biology, which explains principally with processes, mechanisms, and models. Here I look briefly at Evolutionary Biology and Developmental Biology, where reductionist gene-centric explanatory programs have failed – decisively and spectacularly (and relatively recently). Evolution involves not just genes (let alone selfish genes) but multilevel processes of modular tinkering, very much like what I have called continuous (trans)formation, including processes of co-evolution that are strikingly analogous to what we see in the social world. Similarly, gene expression, rather than a largely mechanical DNA-directed bottom-up process, is as much a matter of manipulating and transforming genetic material as it is processing the information that it contains. Gene expression can only be properly performed within multiple, complexly intertwined, self-organizing regulatory networks. More broadly, I argue that Systems Biology, which is on the cutting edge of twenty-first-century Biology, provides an attractive model for relational/systemic social sciences.

Information about the natural world comes from many sources. In controlled experiments, the responses of similar groups to a treatment are compared, and differences in the responses suggest that the treatment may have had an effect. Where controlled experiments would be impossible or unethical studies that compare conditions in two or more similar situations that differ in place or time may be appropriate. Statistical analysis allows investigators to evaluate the probability that observed results are due to chance. Historical records, natural records such as fossils, oral traditions, traditional ecological knowledge, and observations from citizen scientists and parataxonomists are also important. Researchers often develop models to predict how a system behaves under specified conditions. This is useful when a system, such as the Earth’s climate, cannot be observed directly. Science provides a framework within which results can be compared to predictions and conclusions can be modified as new evidence becomes available. Arguments and information about the natural world should be evaluated critically for misleading statements and potential bias.

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.