Chapter 22 examines music in more detail, considered as a theoretical science dealing with the relations (or proportions) between numbers. The ontological status of the objects studied in theoretical music (‘harmonics’) is described and the primary proportions (or intervals), identified as concords, are presented. The importance of music as providing models for subordinate sciences, in particular ethics and physics, is sketched.

In his Life of Isidore, Damascius, as I argue in Chapter 9, described the lives of a wide range of figures of his period as exemplifying to varying degrees success or failure in progress through the scale of virtues, thus providing an edificatory panorama of patterns of philosophical perfection, a panorama which could serve to inspire people beginning the study of philosophy. Many of these figures in Damascius’ account were able to achieve lives lived on the level of the political virtues, but few were able to attain higher levels of virtue and very few the highest levels. Yet these exceptional examples could also serve to inspire.

Porphyry and Iamblichus added further levels of virtue to Plotinus’ scale of virtues. In Chapter 8 I discuss Iamblichus’ On the Pythagorean Life, which presents Pythagoras as a model of the political virtues. I show how, on this level, Iamblichus takes over Epicurean ideas about serenity, freedom from disturbance, a balanced control of desires and bodily needs and how, more generally, the Epicurean biographical practice of praising philosophical heroes as models to be imitated anticipates Iamblichus’ presentation of the figure of Pythagoras. I note also a wider use of Epicurean ethical ideas in Late Antique Platonism, in particular on the level of political virtues, the virtues of the discipline of bodily desires.

This chapter introduces the reader to the big picture of what analytics science is. What is analytics science? What types does it have, and what is its scope? How can analytics science be used to improve various tasks that society needs to carry out? Is analytics science all about using data? Or can it work without data? What is the role of data versus models? How can one develop and rely on a model to answer essential questions when the model can be wrong due to its assumptions? What is ambiguity in analytics science? Is that different from risk? And how do analytics scientists address ambiguity? What is the role of simulation in analytics science? These are some of the questions that the chapter addresses. Finally, the chapter discusses the notion of "centaurs" and how a successful use of analytics science often requires combining human intuition with the power of strong analytical models.

This chapter explores how metaphysical models, particularly the compositional and transformational approaches, can help elucidate the doctrine of the Incarnation. While these models face challenges, such as the Nestorian and Attributes Problems, various solutions have been proposed to address these issues and align the models with orthodox Christology. Ultimately, metaphysical models aim to provide coherence and plausibility to the mystery of the Incarnation, contributing to the ongoing work of analytic theology in understanding this central Christian doctrine.

The chapter will help you to be able to explain what Social Anxiety Disorder is and how it typically presents, including distorted mental representations and selective focus of attention, describe and use evidence-based CBT protocols for Social Anxiety Disorder, choose and use appropriate formulation models for CBT for Social Anxiety Disorder, describe the importance of using exposure to social situations in any treatment plan, develop a treatment plan for CBT for Social Anxiety Disorder, using appropriate measures, and take account of comorbidity in managing CBT for Social Anxiety Disorder

The chapter will help you to be able to explain what panic disorder is and how it typically presents, including unexpected panic attacks, and subsequent fear and attempted avoidance of further attacks, describe and use evidence-based CBT protocols for panic disorder, choose and use appropriate formulation models for CBT for panic disorder, describe the importance of using exposure to panic symptoms in any treatment plan, develop a treatment plan for CBT for panic disorder, using appropriate measures, and take account of comorbidity in managing CBT for panic disorder

Chapter 2 explores an important premise which underlies this critique of the law: it examines the idea that disfigurement inequality is a problem which merits a legal response – namely the granting of protective rights under the Act. It concludes that, despite some uncomfortable distinctions, there is a compelling case for a legal response in this area. The nature of law’s current response is then laid out. Relevant parts of the international legal framework – including EU law, the UN Convention on the Rights of Persons with Disabilities (‘CRPD’) and decisions of the European Court of Human Rights (‘ECtHR’) applying the European Convention on Human Rights – are explained by reference to the models of disability which implicitly inform them.

What is the nature of discovery? As a human being and a physicist, I can only observe one mind at work first-hand. This mind accepts every new scrap as a discovery, whether it originates in the external world of knowledge or springs from an internal process. To explore the nature of discovery from the point of view of the inner observer, I chose to turn over past experiences, fitting together days on which years of determined and dogged plodding resulted in a finished equation, or finally, a coherent assembly of disparate ideas gave the clue to why storm damage in breakwaters is like a phase change in liquid crystals. Old, unfashionable methods are suddenly useful with new computer architectures. Theory, experiment, observation, and simulation fit together as aids to thinking. The properties of complex systems can provide intuitive insight into the social science of science. We will need every ability to assemble the puzzle pieces in the coming years to discover how to extricate the planet from the difficulties in which we have placed it: as an observer and actor, I suggest that the evolution of human thinking, and of aids to thinking, are critical.

Psychiatric disorders are complex and multifaceted conditions that profoundly impact various aspects of an individual’s life. Although the neurobiology of these disorders is not fully understood, extensive research suggests intricate interactions between genetic factors, changes in brain structure, disruptions in neurotransmitter pathways, as well as environmental influence.

In the case of psychotic disorders, such as schizophrenia, strong genetic components have been identified as a key feature in the development of psychosis. Moreover, alterations in dopamine function and structural brain changes that result in volume loss seem to be pervasive in people affected by these disorders. Meanwhile, mood disorders, including major depressive disorder and bipolar disorder, are characterized by disruptions in neurotransmitter systems responsible for mood regulation, such as serotonin, norepinephrine, and dopamine. Anxiety and personality disorders also exhibit neurotransmitter dysfunction and neuroanatomical changes, in addition to showing a genetic overlap with mood and psychotic disorders.

Understanding the underlying mechanisms in the pathophysiology of these conditions is of paramount importance and involves integrating findings from various research areas, including at the molecular and cellular levels. This brief overview aims to highlight some of the important developments in our current understanding of psychiatric disorders. Future research should aim to incorporate a comprehensive approach to further unravel the complexity of these disorders and pave the way for targeted therapeutic strategies and effective treatments to improve the lives of individuals afflicted by them.

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.