An exploration of the scientific limits of knowledge that challenges our deep-seated beliefs about our universe, our rationality, and ourselves.
Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.
Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.
Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Название: Changing Images in Mathematics ISBN: 0415868270 ISBN-13(EAN): 9780415868273 Издательство: Taylor&Francis Рейтинг: Цена: 7654.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book focuses on the major developments in the history of contemporary (19th and 20th century) mathematics as seen in the broader context of the development of science and culture.
Автор: Van Brummelen Glen Название: Heavenly Mathematics ISBN: 0691148929 ISBN-13(EAN): 9780691148922 Издательство: Wiley Рейтинг: Цена: 4744.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. "Heavenly Mathematics" traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.
"Heavenly Mathematics" is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
Автор: Mirja Hartimo Название: Phenomenology and Mathematics ISBN: 9400731965 ISBN-13(EAN): 9789400731967 Издательство: Springer Рейтинг: Цена: 29209.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This collection of essays aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It combines both historical and systematic studies from various angles by primary scholars in this emerging field.
Автор: Hawkins Thomas Название: Mathematics of Frobenius in Context ISBN: 1461463327 ISBN-13(EAN): 9781461463320 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book on focuses on the work of Ferdinand Frobenius in linear algebra, its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. Also covers the Berlin school of mathematics and the guiding force of Weierstrass.
Автор: Bochner Salomon Название: Role of Mathematics in the Rise of Science ISBN: 0691614938 ISBN-13(EAN): 9780691614939 Издательство: Wiley Рейтинг: Цена: 11088.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The central theme of these essays is the nature and role of mathematics, its growth and spread, and its involvement with ever-wider areas of knowledge. The author attempts to determine the decisive and creative aspects of the abstractness" of mathematics which have made it the dominant intellectual force that it is. He frequently confronts the math
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