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The Infinite Tortoise

Author : Joel Levy
ISBN : 9781782436386
Genre : Philosophy
File Size : 65.99 MB
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A clear, concise and fascinating guide to philosophical thought experiments and how they've shaped our understanding of the world. From Plato's Cave to Descartes' Demon, and from Zeno's paradoxes to Hilbert's Hotel, great thinkers have used thought experiments and paradoxes to try and work out complex ideas in the simplest way possible. Perhaps the most famous thought experiment is that of Zeno's Achilles and the tortoise. If both Achilles and the tortoise move at constant speed, why will Achilles never catch up with the tortoise when the tortoise starts ahead of him? Zeno argues that when Achilles reaches the point where the tortoise started the race, the tortoise will have already moved on. And as Achilles runs on to where the tortoise was last, when he reaches that point the tortoise has moved again. Therefore Achilles will never catch up with the tortoise as the distance he must run gets smaller and smaller and each time he has less and less time to run. Starting in Ancient Greece, Joel Levy guides us through the mind-bending world of thought experiments and their role in revealing the complexity of morality, exploring the limitations and the infinite possibilities of the human mind.
Category: Philosophy

The Infinite Book

Author : John D. Barrow
ISBN : 9781407072746
Genre : Science
File Size : 45.32 MB
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‘A delight. Popular science doesn’t come much better than this’ Independent Everything you might want to know about infinity - in history and all the way to today's cutting-edge science. Infinity is surely the strangest idea that humans have ever had. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Can you do an infinite number of things in a finite amount of time? Is the Universe infinite? Infinity is also the place where things happen that don't. What is it like to live in a Universe where nothing is original, where you can live forever, where anything that can be done, is done, over and over again? These are some of the deep questions that the idea of the infinite pushes us to ask. Throughout history, the infinite has been a dangerous concept. Many have lost their lives, their careers, or their freedom for talking about it. The Infinite Book will take you on a tour of these dangerous questions and the strange answers that scientists, mathematicians, philosophers and theologians have come up with to deal with its threats to our sanity.
Category: Science

The Infinite

Author : A.W. Moore
ISBN : 9781351381253
Genre : Philosophy
File Size : 57.58 MB
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We are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantor’s remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and Gödel, and deriving inspiration from Wittgenstein. He concludes this part with a discussion of death and human finitude. For this third edition Moore has added a new part, ‘Infinity superseded’, which contains two new chapters refining his own ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. This new part is heavily influenced by the work of Deleuze. Also new for the third edition are: a technical appendix on still unresolved questions about different infinite sizes; an expanded glossary; and updated references and further reading. The Infinite, Third Edition is ideal reading for anyone interested in an engaging and historically informed account of this fascinating topic, whether from a philosophical point of view, a mathematical point of view, or a religious point of view.
Category: Philosophy

The Tortoise And Achilles

Author : Larry Ottman
ISBN : 1882564243
Genre : Mathematics
File Size : 40.31 MB
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Calculus is the study of the infinite and since much of secondary mathematics is designed to prepare one for the study of calculus, wrestling with the ideas of the infinite, even if informally, is extremely important for a student's mathematical development. That is the purpose of this book. Among the first to discuss these ideas was the Greek philosopher / mathematician Zeno, and not long after him, Archimedes came the closest to "discovering" Calculus without the tools of modern mathematics. Though none of Zeno's actual writings survive, Aristotle recorded accounts of Zeno's thoughts on the infinite, time and space in what have come to be known as Zeno's Paradoxes. One of those specifically involves the idea of a race in which a slower runner is given a head start and investigates the possibilities of the faster runner "catching up." This has come to be known as "Achilles and the Tortoise." These characters are our hosts as we use Geometry Expressions to investigate Archimedes methods, ideas of the infinite, and Zeno's Paradoxes in an introduction to Calculus, without using Calculus.
Category: Mathematics

Mathematics A Concise History And Philosophy

Author : W.S. Anglin
ISBN : 0387942807
Genre : Mathematics
File Size : 89.98 MB
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This concise introduction explores the key mathematical and philosophical aspects of the history of mathematics. Detailed explanations of mathematical procedures used by famous mathematicians give readers a greater opportunity to learn the history and philosophy through problem solving. 23 illustrations.
Category: Mathematics

The Infinite Voyage

Author : Martin Ernst-Wolfgang Luther
ISBN : PSU:000032416954
Genre : Metaphysics
File Size : 74.37 MB
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THE INFINITE VOYAGE: A METAPHYSICAL ODYSSEY, ISBN 0-9615847-3-4, 6X9 pap., 256 pp., notes, illus., appendixes, indexes, bibliog. June 1996, $19.95 CWO, $21.95 net 30 days. A 1997 AWARD WINNER from MIDWEST INDEPENDENT PUBLISHERS ASSOCIATION. THE INFINITE VOYAGE probes the cutting edge of science, philosophy, & religion in addressing the ancient questions of human destiny. Part I sets the parameters of the inquiry in the framework of modern physics. Part II explores the paradoxes encountered & their metaphysical implications. In a clear & incisive manner the reader is led step- by-step, through the conundrums of science to a consideration of the role of mind & self in the determination of what is real & relevant in consciousness. CHOICE MAGAZINE review: "CLEAR & TECHNICALLY SOUND... INTERESTING & RELIABLE... INTELLIGENT REFLECTIONS... THE NON-MATHEMATICAL DISCUSSION {OF BELL'S THEOREM} IS ONE OF THE CLEAREST OF ITS KIND."--{6/97}. Other reviewers: "VERY THOUGHT-PROVOKING," "BRILLIANT INSIGHTS," "SCHOLARLY & WELL-WRITTEN." To order call TOLL-FREE 1-800-484-2273, ext. 1466, or (612) 869-4579. MARWOLF PUBLISHING, 6941 MORGAN SOUTH, MINNEAPOLIS, MN 55423. Volume Discounts.
Category: Metaphysics

Black Tortoise Red Raven

Author : Simone Marnier
ISBN : 9780595390595
Genre : Fiction
File Size : 28.20 MB
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Black Tortoise, Red Raven, the compelling sequel to the novel White Tiger, Green Dragon, continues to weave a captivating tale as it follows the courageous pilgrimage of a young woman scholar as she travels the length of the Yangtze River.Scholar Li, the daughter of Tu Ming and Shen Tao, flees a revolution in eastern China and travels west with a caravan of rug merchants. A Taoist intellectual and master of the tantric arts, the teenager encounters spiritual masters from unfamiliar traditions during her 1,500-mile expedition toward the foothills of the Himalayas. As she journeys to the Red Raven Temple, her spiritual understanding grows and she learns important life lessons from yogis, "crazy Zen" practitioners, Muslims, Buddhists, and Jews. Just as she is about to reach her final destination, Li's life is forever changed when she encounters an extraordinary stranger who bears an uncanny resemblance to a historical figure.Black Tortoise, Red Raven not only opens the doors to personal growth and spiritual understanding for Li; it will also lead anyone who has a receptive spirit, open mind, and loving heart on the same journey to finding their true purpose in life.
Category: Fiction

Infinitesimal Calculus

Author : James M. Henle
ISBN : 9780486151014
Genre : Mathematics
File Size : 60.64 MB
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Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.
Category: Mathematics


Author : Charles Seife
ISBN : 1101199601
Genre : Mathematics
File Size : 72.48 MB
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Popular math at its most entertaining and enlightening. "Zero is really something"-Washington Post A New York Times Notable Book. The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.
Category: Mathematics