Zeno's Paradox

Unraveling the Ancient Mystery Behind the Science of Space and Time

Author: Joseph Mazur

Publisher: Penguin

ISBN: 1440639639

Category: Science

Page: 272

View: 9741

The fascinating story of an ancient riddle?and what it reveals about the nature of time and space Three millennia ago, the Greek philosopher Zeno constructed a series of logical paradoxes to prove that motion is impossible. Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno?s Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs?but through it all, the paradox of motion remains.
Posted in Science

Zeno's Paradoxes

Author: Wesley C. Salmon

Publisher: Hackett Publishing

ISBN: 9780872205604

Category: Science

Page: 317

View: 8436

A reprint of the Bobbs-Merrill edition of 1970. These essays lead the reader through the land of the wonderful shrinking genie to the warehouse where the infinity machines are kept. By careful examination of a lamp that is switched on and off infinitely many times, or the workings of a machine that prints out an infinite decimal expansion of pi, we begin to understand how it is possible for Achilles to overtake the tortoise. The concepts that form the basis of modern science—-space, time, motion, change, infinity-—are examined and explored in this edition. Includes an updated bibliography.
Posted in Science

Plato’s Parmenides

Author: Plato

Publisher: Univ of California Press

ISBN: 0520224035

Category: History

Page: 193

View: 5117

"Scolnicov’s aim is to provide a new translation of Plato’s Parmenides, with a commentary designed to show that the arguments of the second half of the dialogue, the purpose of which has long been a matter of scholarly dispute, make sense as an attempt to establish the necessary logical and epistemological conditions for Plato’s own theory of forms and participation. In particular, Scolnicov attempts to show that the otherwise bewildering concatenation of arguments and hypotheses answers to a style of argument paralleled in other dialogues. Scolnicov also argues that the dialogue is intended as a serious rebuttal of Parmenides’ monist philosophy. Scolnicov’s thesis is thus diametrically opposed to those who think that the dialogue is intended as a successful critique of Plato’s own theory in the light of arguments adapted from Parmenides."—Denis O’Brien, author of Etudes sur Parménide; Empedocles' Cosmic Cycle: A Reconstruction from the Fragments and Secondary Sources "Scolnicov’s introduction presents a very clear account of Parmenides’ method and the contrast that Plato’s use of hypothesis presents to it as early as the Meno. Scolnicov then offers a clear account of Plato’s method and the way it establishes an idea of philosophical method in general: not a reasoning from first principles but a disclosing of the principles at the foundation of one’s prior convictions in order to test those principles. He subsequently takes up the principle of noncontradiction in particular before tackling the questions Parmenidean philosophy might raise about the doctrine of participation. An immensely clear and interesting introduction and way into the Parmenides."—Georgia Warnke, author of Justice and Interpretation: Studies in Contemporary German Social Thought
Posted in History

The Three Paradoxes

Author: Paul Hornschemeier

Publisher: Fantagraphics Books

ISBN: 1560976535

Category: Comics & Graphic Novels

Page: 80

View: 7345

The Three Paradoxes is an intricate and complex autobiographical comic by one of the most talented and innovative young cartoonists today. The story begins with a story inside the story: the cartoon character Paul Hornschemeier is trying to finish a story called "Paul and the Magic Pencil." Paul has been granted a magical implement, a pencil, and is trying to figure out what exactly it can do. He isn't coming up with much, but then we zoom out of this story to the creator, Paul, whose father is about to go on a walk to turn off the lights in his law office in the center of the small town. Abandoning the comic strip temporarily, Paul leaves with his camera, in order to fulfill a promise to his girlfriend that he would take pictures of the places that affected him as a child. Each "chapter" of the story is drawn in a completely different style, with strikingly unique production and color themes, and yet, somehow, despite (or perhaps because of) this non-linear progression, it all comes together as one story: a story questioning change, progress, and worth within the author's life.
Posted in Comics & Graphic Novels

The Hare and the Tortoise

Author: Aesop

Publisher: The Rosen Publishing Group, Inc

ISBN: 1499483635

Category: Juvenile Fiction

Page: 24

View: 4252

When an arrogant hare thinks he�s the best around, who could possibly bring him down? One determined tortoise is about to try! Readers will delight in this beautiful retelling of one of Aesop�s most beloved fables. Clean, simple language makes the story accessible, while adorable illustrations draw in even reluctant readers. As they follow the epic race between hare and tortoise, readers will see how boastfulness can catch up to even the fastest runner, and how a good work ethic can carry anyone to victory. This classic tale introduces readers to important values such as commitment, humility, and sportsmanship in a fun way, making it a valuable addition to any library.
Posted in Juvenile Fiction

Paradoxes from A to Z

Author: Michael Clark

Publisher: Routledge

ISBN: 1136218041

Category: Philosophy

Page: 296

View: 8820

Paradoxes from A to Z, Third edition is the essential guide to paradoxes, and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo, and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus’ Ship, and the Prisoner’s Dilemma, taking in subjects as diverse as knowledge, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely solutions. This third edition is revised throughout, and adds nine new paradoxes that have important bearings in areas such as law, logic, ethics and probability. Paradoxes from A to Z, Third edition is an ideal starting point for those interested not just in philosophical puzzles and conundrums, but anyone seeking to hone their thinking skills.
Posted in Philosophy


A Paradox Logic

Author: Nathaniel S. Hellerstein

Publisher: World Scientific

ISBN: 9789812796110

Category: Mathematics

Page: 257

View: 7126

This book is about OC diamondOCO, a logic of paradox. In diamond, a statement can be true yet false; an OC imaginaryOCO state, midway between being and non-being. Diamond''s imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, GAdelian meta-mathematics and dilemma games."
Posted in Mathematics

Labyrinths of Reason

Paradox, Puzzles, and the Frailty of Knowledge

Author: William Poundstone

Publisher: Anchor

ISBN: 9780307763792

Category: Philosophy

Page: 288

View: 5330

This sharply intelligent, consistently provocative book takes the reader on an astonishing, thought-provoking voyage into the realm of delightful uncertainty--a world of paradox in which logical argument leads to contradiction and common sense is seemingly rendered irrelevant. From the Trade Paperback edition.
Posted in Philosophy


The Nine Greatest Enigmas in Physics

Author: Jim Al-Khalili

Publisher: Broadway Books

ISBN: 0307986802

Category: Science

Page: 256

View: 5960

A fun and fascinating look at great scientific paradoxes. Throughout history, scientists have come up with theories and ideas that just don't seem to make sense. These we call paradoxes. The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds. For example, how can a cat be both dead and alive at the same time? Why will Achilles never beat a tortoise in a race, no matter how fast he runs? And how can a person be ten years older than his twin? With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle. Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic. In doing so, he brings to life a select group of the most exciting concepts in human knowledge. Paradox is mind-expanding fun.
Posted in Science

Enlightening Symbols

A Short History of Mathematical Notation and Its Hidden Powers

Author: Joseph Mazur

Publisher: Princeton University Press

ISBN: 1400850118

Category: Mathematics

Page: 312

View: 5406

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.
Posted in Mathematics

The Lamentations of Zeno

A Novel

Author: Ilija Trojanow

Publisher: Verso Books

ISBN: 178478222X

Category: Fiction

Page: 176

View: 934

A literary fiction about climate disaster and a scientist imploding on a journey to the Antarctic Zeno Hintermeier is a scientist working as a travel guide on an Antarctic cruise ship, encouraging the wealthy to marvel at the least explored continent and to open their eyes to its rapid degradation. It is a troubling turn in the life of an idealistic glaciologist. Now in his early sixties, Zeno bewails the loss of his beloved glaciers, the disintegration of his marriage, and the foundering of his increasingly irrelevant career. Troubled in conscience and goaded by the smug complacency of the passengers in his charge, he starts to plan a desperate gesture that will send a wake-up call to an overheating world. The Lamentations of Zeno is an extraordinary evocation of the fragile and majestic wonders to be found at a far corner of the globe, written by a novelist who is a renowned travel writer. Poignant and playful, the novel recalls the experimentation of high-modernist fiction without compromising a limpid sense of place or the pace of its narrative. It is a portrait of a man in extremis, a haunting and at times irreverent tale that approaches the greatest challenge of our age—perhaps of our entire history as a species—from an impassioned human angle.
Posted in Fiction

Wittgenstein on Rules and Private Language

An Elementary Exposition

Author: Saul A. Kripke

Publisher: Harvard University Press

ISBN: 9780674954014

Category: Philosophy

Page: 150

View: 637

In this book Saul Kripke brings his powerful philosophical intelligence to bear on Wittgenstein's analysis of the notion of following a rule.
Posted in Philosophy


A Paradox Logic

Author: Nathaniel Hellerstein

Publisher: World Scientific

ISBN: 9810232438

Category: Mathematics

Page: 276

View: 2750

This book is about "delta", a paradox logic. In delta, a statement can be true yet false; it is an "imaginary" state, midway between being and non-being. Delta's imaginary value solves many logical dilemmas unsolvable in two-valued Boolean logic. Delta resolves these paradoxes -- Russell's, Cantor's, Betty's and Zeno's. Delta has two parts: inner delta logic, or "Kleenean logic", which resolves the classic paradoxes of mathematical logic; and outer delta logic, which relates delta to Z mod 3, conjugate logics, cyclic distribution, and the voter' paradox.
Posted in Mathematics

My Dog: The Paradox

A Lovable Discourse about Man's Best Friend

Author: The Oatmeal,Matthew Inman

Publisher: Andrews McMeel Publishing

ISBN: 1449437710

Category: Humor

Page: 32

View: 7431

This eponymous comic became an instant hit when it went live on The Oatmeal.com and was liked on Facebook by 700,000 fans. Now fans will have a keepsake book of this comic to give and to keep. In My Dog: The Paradox, Inman discusses the canine penchant for rolling in horse droppings, chasing large animals four times their size, and acting recklessly enthusiastic through the entirety of their impulsive, lovable lives. Hilarious and heartfelt, My Dog: The Paradox eloquently illustrates the complicated relationship between man and dog. We will never know why dogs fear hair dryers, or being baited into staring contests with cats, but as Inman explains, perhaps we love dogs so much “because their lives aren’t lengthy, logical, or deliberate, but an explosive paradox composed of fur, teeth, and enthusiasm.”
Posted in Humor


Author: R. M. Sainsbury

Publisher: Cambridge University Press

ISBN: 0521896320

Category: Philosophy

Page: 182

View: 2698

A paradox can be defined as an unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Many paradoxes raise serious philosophical problems, and they are associated with crises of thought and revolutionary advances. The expanded and revised third edition of this intriguing book considers a range of knotty paradoxes including Zeno's paradoxical claim that the runner can never overtake the tortoise, a new chapter on paradoxes about morals, paradoxes about belief, and hardest of all, paradoxes about truth. The discussion uses a minimum of technicality but also grapples with complicated and difficult considerations, and is accompanied by helpful questions designed to engage the reader with the arguments. The result is not only an explanation of paradoxes but also an excellent introduction to philosophical thinking.
Posted in Philosophy

Zeno of Elea

Author: H. D. P. Lee

Publisher: Cambridge University Press

ISBN: 1107480272

Category: Philosophy

Page: 132

View: 9801

Originally published in 1936, this book presents the ancient Greek text of the paraphrases and quotations of Zeno's philosophical arguments, together with a facing-page English translation and editorial commentary. Detailed notes are incorporated throughout and a bibliography is also included. This book will be of value to anyone with an interest in Zeno and ancient philosophy.
Posted in Philosophy

On Location

Aristotle's Concept of Place

Author: Benjamin Morison

Publisher: Oxford University Press on Demand

ISBN: 0199247919

Category: History

Page: 194

View: 2978

On Location is the first book in English exclusively devoted to a highly significant doctrine in the history of philosophy and science--Aristotle's account of place in the Physics. The central question which Aristotle aims to answer is: What is it for something to be somewhere? Ben Morison examines how Aristotle works from simple observations about replacement to a definition of the notion of the place of a body--the inner limit of that body's surroundings. Thisdefinition lies at the heart of what we say about places, for instance when we say that we cannot be in two places at once, or that two bodies cannot be in the same place at the same time. Morison also assesses Aristotle's brilliant, though often obscure, criticisms of rival theories.This authoritative exposition and defence of Aristotle's account of place not only allows it to be properly understood in the wider context of the Physics, but also demonstrates that it is of enduring philosophical interest and value.
Posted in History

The Universal Book of Mathematics

From Abracadabra to Zeno's Paradoxes

Author: David Darling

Publisher: John Wiley & Sons

ISBN: 0471270474

Category: Mathematics

Page: 383

View: 4195

Reference book on mathematics.
Posted in Mathematics

Essential Relativity

Special, General, and Cosmological

Author: W. Rindler

Publisher: Springer

ISBN: 1475711352

Category: Science

Page: 319

View: 4293

This book is an attempt to bring the full range of relativity theory within reach of advanced undergraduates, while containing enough new material and simplifications of old arguments so as not to bore the expert teacher. Roughly equal coverage is given tospecial relativity, general relativity, and cosmology. With many judicious omissions it can be taught in one semester, but it would better serve as the basis of a year's work. It is my hope, anyway, that its level and style of presentation may appeal also to wider c1asses of readers unrestricted by credit considerations. General relativity, the modern theory of gravitation in which free particles move along "straightest possible" lines in curved spacetime, and cosmology, with its dynamics for the whole possibly curved uni verse, not only seem necessary for a scientist's balanced view of the world, but offer some of the greatest intellectual thrills of modern physics. Nevertheless, considered luxuries, they are usu ally squeezed out of the graduate curriculum by the pressure of specialization. Special relativity escapes this tag with a ven geance, and tends to be taught as a pure service discipline, with too little emphasis on its startling ideas. What better time, there fore, to enjoy these subjects for their own sake than as an und- v vi PREFACE graduate? In spite of its forbidding mathematical reputation, even general relativity is accessible at that stage.
Posted in Science

Divergent Series

Author: Godfrey Harold Hardy

Publisher: American Mathematical Soc.

ISBN: 0821826492

Category: Mathematics

Page: 396

View: 1896

Review of the original edition: This is an inspiring textbook for students who know the theory of functions of real and complex variables and wish further knowledge of mathematical analysis. There are no problems displayed and labelled ``problems,'' but one who follows all of the arguments and calculations of the text will find use for his ingenuity and pencil. The book deals with interesting and important problems and topics in many fields of mathematical analysis, to an extent very much greater than that indicated by the titles of the chapters. It is, of course, an indispensable handbook for those interested in divergent series. It assembles a considerable part of the theory of divergent series, which has previously existed only in periodical literature. Hardy has greatly simplified and improved many theories, theorems and proofs. In addition, numerous acknowledgements show that the book incorporates many previously unpublished results and improvements of old results, communicated to Hardy by his colleagues and by others interested in the book. --Mathematical Reviews
Posted in Mathematics