Vicious Circles and Infinity PDF Download

Author: Patrick Hughes
Publisher: Penguin Group
ISBN:
Category : Fiction
Languages : en
Pages : 126

View

Book Description

Author: Patrick Hughes
Publisher: Jonathan Cape
ISBN: 9780224011860
Category : Paradox
Languages : en
Pages : 104

View

Book Description

Author: Agustin Rayo
Publisher: MIT Press
ISBN: 0262039419
Category : Mathematics
Languages : en
Pages : 321

View

Book Description
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

Author: Theodore Spencer
Publisher:
ISBN:
Category : The poet of the month
Languages : en
Pages : 40

View

Book Description

Author: Brad Stulberg
Publisher: Rodale Books
ISBN: 1635653444
Category : Self-Help
Languages : en
Pages : 192

View

Book Description
The coauthors of the bestselling Peak Performance dive into the fascinating science behind passion, showing how it can lead to a rich and meaningful life while also illuminating the ways in which it is a double-edged sword. Here’s how to cultivate a passion that will take you to great heights—while minimizing the risk of an equally great fall. Common advice is to find and follow your passion. A life of passion is a good life, or so we are told. But it's not that simple. Rarely is passion something that you just stumble upon, and the same drive that fuels breakthroughs—whether they're athletic, scientific, entrepreneurial, or artistic—can be every bit as destructive as it is productive. Yes, passion can be a wonderful gift, but only if you know how to channel it. If you're not careful, passion can become an awful curse, leading to endless seeking, suffering, and burnout. Brad Stulberg and Steve Magness once again team up, this time to demystify passion, showing readers how they can find and cultivate their passion, sustainably harness its power, and avoid its dangers. They ultimately argue that passion and balance--that other virtue touted by our culture--are incompatible, and that to find your passion, you must lose balance. And that's not always a bad thing. They show readers how to develop the right kind of passion, the kind that lets you achieve great things without ruining your life. Swift, compact, and powerful, this thought-provoking book combines captivating stories of extraordinarily passionate individuals with the latest science on the biological and psychological factors that give rise to—and every bit as important, sustain—passion.

Author: Grzegorz Tomkowicz
Publisher: Cambridge University Press
ISBN: 1107042593
Category : Mathematics
Languages : en
Pages : 367

View

Book Description
The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.

Author: R. M. Sainsbury
Publisher: Cambridge University Press
ISBN: 9780521483476
Category : Philosophy
Languages : en
Pages : 180

View

Book Description
This revised and expanded edition provides a valuable and accessible introduction to paradoxes.

Author: Patricia Spadaro
Publisher: SCB Distributors
ISBN: 0981603319
Category : Self-Help
Languages : en
Pages : 176

View

Book Description
“Patricia Spadaro is a marvelous guide through the inner realms of the heart. I always feel uplifted by her words." —Marianne Williamson, #1 New York Times bestselling author of A Return to Love Honor Yourself: The Inner Art of Giving and Receiving (winner of two national book awards) skillfully guides us through one of the key stressors and paradoxes of our time—how to balance what others need with what we need, how to give and to receive. Should I sacrifice for others or take time to care for myself? Be generous or draw boundaries? Stay in a relationship or say goodbye? When I give to others, do I really need to give up myself? Tensions like these are not only a natural part of life, they are life. But rather than focusing on how to pamper ourselves, Honor Yourself goes to the heart of the problem so you can find real solutions. While modern society is ill-equipped to bring us back into balance, the sages of East and West are experts, and Honor Yourself explores their practical, and surprising, advice. Combining wisdom from around the world with real-life stories and a treasury of tools, it exposes the most potent myths about giving that can sabotage your relationships, career, finances, even your health, without you knowing it. With candor and compassion, it shows how to move beyond the myths to the magic of honoring yourself so you can live a life filled with possibility and passion and give your greatest gifts to your loved ones, your community, and the world. We are called to master the delicate dance of giving and receiving in virtually every area of our lives, and this beautiful work offers empowering and heartfelt ways to do it. It will free you to celebrate your own gifts and greatness as you explore the dynamics behind setting boundaries, being honest about unhealthy people in your life, honoring endings, using feelings to stay true to yourself, finding your own voice, giving with the heart rather than the head, and much more. Just as importantly, Honor Yourself will teach you the steps for staying in balance. For when you learn the steps, you can perform the dance—and that's when the magic begins.

Author: Stan Wagon
Publisher: Cambridge University Press
ISBN: 9780521457040
Category : Mathematics
Languages : en
Pages : 276

View

Book Description
Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.

Author: Godehard Link
Publisher: Walter de Gruyter
ISBN: 3110199688
Category : Mathematics
Languages : en
Pages : 673

View

Book Description
The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume. The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes therefore, to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.