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Author: Norman Manea
Publisher: Yale University Press
Published: 2012-05-29
Total Pages: 370
ISBN-13: 0300179952
DOWNLOAD EBOOKExploring the language and psyche of the exiled writer, offers a critique of American writers and the author's fellow Romanian writers, answering questions on censorship and linguistic roots.
Author: Jesper Lützen
Publisher: Oxford University Press
Published: 2023-01-26
Total Pages: 305
ISBN-13: 0192867393
DOWNLOAD EBOOKMany of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat's last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. Lützen argues that the role of impossibility results have changed over time. At first, they were considered rather unimportant meta-statements concerning mathematics but gradually they obtained the role of important proper mathematical results that can and should be proved. While mathematical impossibility proofs are more rigorous than impossibility arguments in other areas of life, mathematicians have employed great ingenuity to circumvent impossibilities by changing the rules of the game. For example, complex numbers were invented in order to make impossible equations solvable. In this way, impossibilities have been a strong creative force in the development of mathematics, mathematical physics, and social science.
Author: David S. Richeson
Publisher: Princeton University Press
Published: 2021-11-02
Total Pages: 450
ISBN-13: 0691218722
DOWNLOAD EBOOKA comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.
Author: Nicolai Hartmann
Publisher: Walter de Gruyter
Published: 2013-03-22
Total Pages: 524
ISBN-13: 3110246686
DOWNLOAD EBOOKNicolai Hartmann's Possibility and Actuality is the second volume of a four-part investigation of ontology. It deals with such questions as: How do we know that something is really possible? Is the possible only the actual? Is the actual only the possible? What is the difference between ideal and real possibility? This groundbreaking work of modal analysis describes the logical relations between possibility, actuality, and necessity, and it provides insight into the relations between modes of knowledge and modes of being. Hartmann reviews the history of philosophical concepts of possibility and necessity, from ancient Megarian philosophy to Aristotle, to Medieval Scholasticism, to Leibniz, Kant, and Hegel. He explains the importance of modal analysis as a basic investigative tool, and he proposes an approach to understanding the nature of human existence that unifies the fields of ontology, modal logic, metaphysics, and epistemology. This brilliant and fascinating work is relevant to many topics of debate in contemporary philosophy, including the ontology of possible worlds, the metaphysics of modality, the logic of counterfactual conditionals, and modal epistemology. It illuminates the nature of real, ideal, logical, and epistemic possibility.
Author: Fredric Jameson
Publisher: Verso Books
Published: 2016-07-12
Total Pages: 371
ISBN-13: 1784784516
DOWNLOAD EBOOKFredric Jameson's pathbreaking essay "An American Utopia" radically questions standard leftist notions of what constitutes an emancipated society. Advocated here are-among other things-universal conscription, the full acknowledgment of envy and resentment as a fundamental challenge to any communist society, and the acceptance that the division between work and leisure cannot be overcome. To create a new world, we must first change the way we envision the world. Jameson's text is ideally placed to trigger a debate on the alternatives to global capitalism. In addition to Jameson's essay, the volume includes responses from philosophers and political and cultural analysts, as well as an epilogue from Jameson himself. Many will be appalled at what they will encounter in these pages-there will be blood! But perhaps one has to spill such (ideological) blood to give the Left a chance.
Author: John D. Barrow
Publisher: Oxford University Press, USA
Published: 1999
Total Pages: 294
ISBN-13: 0195130820
DOWNLOAD EBOOKAstronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.
Author: David C. Brody
Publisher: Jones & Bartlett Publishers
Published: 2011-01-28
Total Pages: 432
ISBN-13: 1449662633
DOWNLOAD EBOOKThe highly anticipated Second Edition of Criminal Law introduces students to the underlying principles, legal doctrine, and rules regarding crimes, defenses, and punishment in substantive criminal law. Innovative in its case study approach, this thoroughly updated revision will help students develop analytical skills, while learning the content and context of substantive criminal law. Now with a more student-friendly format, this text guides students through theory and practice, using a blend of old and new materials to foster understanding of what the law is, how it evolved, the principles on which it is based, and how it applies to various circumstances.
Author: Augustus Layres
Publisher: BoD – Books on Demand
Published: 2022-02-15
Total Pages: 246
ISBN-13: 3752566752
DOWNLOAD EBOOKReprint of the original, first published in 1867.
Author: Sidney A. Morris
Publisher: Springer Nature
Published: 2022-11-26
Total Pages: 233
ISBN-13: 3031056981
DOWNLOAD EBOOKThis textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction. Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel’s original approach. Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.
Author: Dennis Wuerthner
Publisher: University of Hawaii Press
Published: 2020-04-30
Total Pages: 403
ISBN-13: 0824882598
DOWNLOAD EBOOKOne of the most important and celebrated works of premodern Korean prose fiction, Kŭmo sinhwa (New Tales of the Golden Turtle) is a collection of five tales of the strange artfully written in literary Chinese by Kim Sisŭp (1435–1493). Kim was a major intellectual and poet of the early Chosŏn dynasty (1392–1897), and this book is widely recognized as marking the beginning of classical fiction in Korea. The present volume features an extensive study of Kim and the Kŭmo sinhwa, followed by a copiously annotated, complete English translation of the tales from the oldest extant edition. The translation captures the vivaciousness of the original, while the annotations reveal the work’s complexity, unraveling the deep and diverse intertextual connections between the Kŭmo sinhwa and preceding works of Chinese and Korean literature and philosophy. The Kŭmo sinhwa can thus be read and appreciated as a hybrid work that is both distinctly Korean and Sino-centric East Asian. A translator’s introduction discusses this hybridity in detail, as well as the unusual life and tumultuous times of Kim Sisŭp; the Kŭmo sinhwa’s creation and its translation and transformation in early modern Japan and twentieth-century (especially North) Korea and beyond; and its characteristics as a work of dissent. Tales of the Strange by a Korean Confucian Monk will be welcomed by Korean and East Asian studies scholars and students, yet the body of the work—stories of strange affairs, fantastic realms, seductive ghosts, and majestic but eerie beings from the netherworld—will be enjoyed by academics and non-specialist readers alike.
