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Statistical mechanics employs the power of probability theory to shine a light upon the invisible world of matter's fundamental constituents, allowing us to accurately model the macroscopic physical properties of large ensembles of microscopic particles. This book delves into the conceptual and mathematical foundations of statistical mechanics to enhance understanding of complex physical systems and thermodynamic phenomena, whilst also providing a solid mathematical basis for further study and research in this important field. Readers will embark on a journey through important historical experiments in statistical physics and thermodynamics, exploring their intersection with modern applications, such as the thermodynamics of stars and the entropy associated with the mixing of two substances. An invaluable resource for students and researchers in physics and mathematics, this text provides numerous worked examples and exercises with full solutions, reinforcing key theoretical concepts and offering readers deeper insight into how these powerful tools are applied.
This chapter traces the development of an economic sublime associated with modern neoclassical economics. A precursor to Fredric Jameson’s postmodern “hysterical sublime,” the sublimity of neoclassical economics derived from the thrilling sense that, through math, economics could access vast and terrifying universal forces, and connect individuals directly to them. However, the most popular expression of the economic sublime was not mathematical but literary, and consisted primarily of naturalist novels that chronicled human encounters with economic laws allegedly so regular, universal, and inexorable that they amounted to a new branch of physics. Through readings of novels by Theodore Dreiser, Jack London, and Frank Norris, this chapter shows how literature helped train readers to understand neoclassical economics not just as natural, but also as an indispensable source of romantic pleasure.
This chapter aims to layout, more in detail, how Giambattista Vico weaved the different conceptual threads he gathered from such tradition to further his ambitious humanistic agenda. Vico’s philosophy of knowledge is an eclectic chimaera with many shortcomings and productive confusions. The chapter also focuses on Vico’s immediate context and intellectual references and explores four fundamental issues that surrounded and inspired the formulation of this seminal praxis epistemology: the relation between ancient and modern conceptions of knowledge; the idea that we know as makers of concepts and things; the relationship between ‘scientific’ discoveries and their conceptual criticism and the Vichian connection between the philosophy of knowledge and history as framed in his New Science.
The discovery of anaesthesia transformed the human condition, and unplanned awareness returns a patient to the nightmare that was surgery before anaesthesia and effective analgesia. Significant advances in the pharmacology and technology of anaesthesia have still not brought reliable means of monitoring its depth much closer, although because awareness is such a serious complication, considerable research effort has been dedicated to the search for methods of detection. Some of these remain research tools or are not yet in widespread use, but you should have some idea about which of them may in due course find their way into clinical practice. Most current interest centres around bispectral index (BIS) monitoring, with recommendations both from the Association of Anaesthetists and from NICE, which are summarised in this section, and it is likely that the oral will focus more on BIS than on the other technologies.
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.
Vitruvius’ De architectura (c. 35–23 BCE) offers an ideal lens through which to view the emergence of the Imperial artes. In the introduction to his work, Vitruvius develops an elaborate theory of architectural knowledge that connects the discipline with other branches of specialized knowledge and gives pride of place to causal explanations of architectural method via natural first principles. Vitruvius’ theory is tailored to architecture but is of wider importance in that it establishes a general notion of ars predicated on the scientific premises sketched in Chapter 2. True to his expansive conception of the discipline, throughout his treatise Vitruvius carefully explains his methods in terms of natural first principles, demonstrating their fundamental soundness. His advice for orienting city streets and walls (Book I) and for choosing building materials (Book II) exemplifies his characteristic interest in connecting architecture with a broader understanding of nature.
Causation in Physics demonstrates the importance of causation in the physical world. It details why causal mastery of natural phenomena is an important part of the effective strategies of experimental physicists. It develops three novel arguments for the viewpoint that causation is indispensable to the ontology of some of our best physical theories. All three arguments make much of the successes of experimental physics. This title is also available as Open Access on Cambridge Core.
This chapter outlines Hopkins’s knowledge of contemporary energy physics as it decisively shapes his distinctive poetry and the metaphysic that undergirds it. The discussion begins with Hopkins’s appreciation of meteorology in his ‘Heraclitean Fire’ sonnet, of the earth’s atmosphere as a vast thermodynamic system. The figure that this poem presents of man as a lonely ‘spark,’ and the pyrotechnics of ‘As kingfishers catch fire,’ ‘The Windhover’ and ‘God’s Grandeur,’ are then glossed through the optical application of the energy concept in spectroscopy. Finally the chapter considers field theory and Clerk Maxwell’s reassessment of the Newtonian principle of force through the energy concept as the distributive principle of stress, tracing Hopkins’s use of this physical concept in his writings on mechanics, nature and most momentously in the definitive formulation of his metaphysic of stress, instress ,and inscape in 1868 and the concurrent advent of his metrical principle of Sprung Rhythm.
Hegel's Philosophy of Nature constitutes the second part of his mature philosophical system presented in the Encyclopaedia of the Philosophical Sciences, and covers an exceptionally broad spectrum of themes and issues, as Hegel considers the content and structure of how humanity approaches nature and how nature is understood by humanity. The essays in this volume bring together various perspectives on Hegel's Philosophy of Nature, emphasizing its functional role within the Encyclopaedia and its importance for understanding the complexity of Hegel's philosophical project. Together they illuminate the core ideas which form Hegel's philosophical framework in the realm of nature.
Familiarity with chemistry from children’s toy kits leads Weinberg to investigate physics, the subject that underlies all of chemistry. He reads George Gamow’s Mr. Tompkins books, among others. He is admitted to the famous Bronx High School of Science, where he becomes friends with Shelly Glashow and Gary Feinberg, who would also become well-known physicists. He wins a New York state scholarship to Cornell.
This chapter argues that Hegel’s aim in his philosophy of nature is not to compete with natural science but to show that there is reason in nature – reason that science cannot see but that works through the causal processes discovered by science. It considers first the transition from Hegel’s logic to his philosophy of nature and argues that the latter continues the project of the former, starting with reason, or the “absolute idea”, as nature, as sheer externality. It then argues that Hegel derives nature’s categories logically – a priori – from the idea-as-externality, and subsequently matches them with empirical phenomena (rather than constructing categories to fit the latter). It provides an abridged account of Hegel’s physics in order to show how the categories of physical (as opposed to mechanical or organic) nature are derived from one another and how they are embodied in physical phenomena, such as sound, heat, and magnetism. It then concludes by arguing that, contrary to appearances, Hegel’s conception of light complements, and is not simply at odds with, that presented by quantum physics.
While dismissing what he regards as empty, extrinsic use of analogy in the spurious play of contemporaneous philosophies of nature, Hegel acknowledges the importance of analogy and appreciates its role in many empirical scientific discoveries. In the Logic, Hegel provides a speculative-rational criterion to distinguish between superficial and well-grounded analogies, for both inorganic and organic bodies, using an example of his “syllogism of analogy” drawn from celestial mechanics. Hegel’s point is that, from the standpoint of philosophical science, what empirical science may view only as “parts” of a complex form are essentially mutually related as interdependent moments of one whole. This chapter discusses the role of analogy in Hegel’s Absolute Mechanics, accounting for his view that the structural or constitutive form of the organism already begins to appear in the ‘ideal’ point of unity which governs the movement of free, independent bodies in the solar system, and for his reappraisal of the solar system as manifesting a thoroughgoing unity (Physics). Finally, this chapter argues for the thesis of a sufficient legacy of Kant’s analogical theory of the arrangement of the heavenly bodies in Hegel’s self-sublating finite mechanical account of the starry vault in his Philosophy of Nature.
Focusing on the physics of the catastrophe process and addressed directly to advanced students, this innovative textbook quantifies dozens of perils, both natural and man-made, and covers the latest developments in catastrophe modelling. Combining basic statistics, applied physics, natural and environmental sciences, civil engineering, and psychology, the text remains at an introductory level, focusing on fundamental concepts for a comprehensive understanding of catastrophe phenomenology and risk quantification. A broad spectrum of perils are covered, including geophysical, hydrological, meteorological, climatological, biological, extraterrestrial, technological and socio-economic, as well as events caused by domino effects and global warming. Following industry standards, the text provides the necessary tools to develop a CAT model from hazard to loss assessment. Online resources include a CAT risk model starter-kit and a CAT risk modelling 'sandbox' with Python Jupyter tutorial. Every process, described by equations, (pseudo)codes and illustrations, is fully reproducible, allowing students to solidify knowledge through practice.
This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of 'physical representation' (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of 'the Relativity Principle,' or 'Galileo's Ship.' This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the past century, namely understanding the physical significance of the notion of 'local' gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary representational media such as the covariant phase space formalism.
John Buridan devotes an extensive discussion to final causality in two questions of his commentary on Book ii of the Physics: one asks whether the end is a cause (q. 7) and the other asks whether the necessity in natural operations derives from the end or from matter (q. 13). These two questions are the focus of this essay, which provides a detailed presentation of Buridan’s view, explaining its philosophical significance and setting it in the context of the medieval debate about final causality. It also points out the originality of Buridan’s view. Departing from the dominant medieval interpretation of Aristotle’s concept of the final cause, Buridan does not try to defend the idea that the end to which an action or change is directed is properly speaking a cause of that action, and in doing so he undermines the main assumptions at work in the Aristotelian account of finality in nature.
By first providing a summary of the main arguments in each chapter and then highlighting the ways, elaborated in this study, in which Empedocles’ physics is consistent with his religious interests in rebirth and purification, Chapter 8 sets out the main conclusion of this book, namely that rebirth and purification are an integral part of Empedocles’ physical system; indeed, that rebirth seems to be a premise of some of his physical principles and theories. In doing so, in addition to a new textual reconstruction of the proem of the physical poem, this book offers new insights into pivotal concepts and much debated issues of Empedocles’ thought, such as the conceptualization of rebirth and the notions of daimon, soul and personal survival, the purpose and role of physical doctrine for release from rebirth, the reconstruction of the cosmic cycle and the analysis of its moral significance. Finally, it is emphasized that this novel reconstruction of Empedocles’ thought, together with the book’s methodological standard, can provide a key to approaching and re-evaluating the character and aims of the thought of other early thinkers and of fifth-century natural philosophy in general.
This engaging undergraduate text uses the performance, recording, and enjoyment of music to present basic principles of physics. The narrative lays out specific results from physics, as well as some of the methodology, thought processes, and 'interconnectedness' of physics concepts, results, and ideas. Short chapters start with basic definitions and everyday observations and ultimately work through standard topics, including vibrations, waves, acoustics, and electronics applications. Each chapter includes problems, some of which are suited for longer-term projects, and suggestions for extra reading that guide students toward a deeper understanding of the physics behind music applications. To aid teaching, additional review questions, audio and video clips, and suggestions for class activities are provided online for instructors.
From beginning to end, the De rerum natura upsets expectations. This book's premise is that Lucretius intentionally provokes his imagined male audience, playfully and forcefully proving to them that they are not the men they suppose themselves to be. From astral bodies to the magnetic draw of human sexuality to the social bonds linking parents to children, Lucretius shows that everything is compounded material, both a source of atomic issue and receptacle of atomic ingress. The universe, as Lucretius presents it, is a never-ending cycle of material interpenetration, connectivity, and dissolution. Roman men, in the vastness of it all, are only exceptional in their self-defeating fantasies. Close analysis of Lucretius' poetics reveals an unremitting assault upon the fictions that comprise Roman masculinity, from seminal conception in utero to existential decomposition in the grave. Nevertheless, Lucretius offers an Epicurean vision of masculinity that just might save the Republic.
In this chapter, I present Aristotle’s arguments in his books on Physics defending the claim that there is purposiveness in nature independent of thinking, foresight and deliberation. Hegel’s arguments for objective purposiveness are correctly understood only in light of those of Aristotle. In fact, I argue that the sense in which teleology is for Hegel the truth of mechanism (and, ultimately, of causality) is the sense in which, for Aristotle, final causes are the cause of ‘that which comes to be by nature’ and the cause of other kinds of causes (matter, efficient causes and even form) being where they are and having the effects that they eventually have. The chapter revises Aristotle’s understanding of this connection.
The physics chapter by Klaus Wendt, Andreas Pysik and Johannes Lhotzky aims at promoting deeper understanding of the complex phenomenon of the rainbow and encourages learners to demonstrate and share their understanding through a Wikipedia article. In this deeper learning episode, learners carry out a number of experiments on spectral colours and colour sequences. They organise the information gathered and explain the physics concepts and processes underlying the phenomenon. The authors use innovative ways of scaffolding academic language development to increase the meaning-making potential of younger learners.