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.

    Philosophers, artists and poets have long explored its meaning while scientists have found that its structure is different from the simple intuition we have of it. From Boltzmann to quantum theory, from Einstein to loop quantum gravity, our understanding of time has been undergoing radical transformations. Time flows at different speeds in different places, the past and the future differ far less than we might think and the very notion of the present evaporates in the vast universe. With his extraordinary charm and sense of wonder, bringing together science, philosophy and art, Carlo Rovelli unravels this mystery, inviting us to imagine a world where time is in us and we are not in time.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    Well, I was diagnosed 24 years ago, and I still learned something new on every page.”—Michael Kinsley, Vanity Fair columnist and author of Old Age: A Beginner’s Guide Here is the book that John Vine and his wife, Joanne, wish they could have consulted when John was first diagnosed with Parkinson’s disease—a nontechnical, personal guide written from the patient’s perspective. Relying on his experiences over the past 12 years, John writes knowledgeably about all aspects of the disease. John also interviewed other Parkinson’s patients and their partners, whose stories and advice he includes throughout the book. “I wish we’d had John Vine’s book when my brother-in-law was diagnosed. The book is highly informative, unflinchingly honest, and reassuringly optimistic. It’s just what the doctor should have ordered.”—Cokie Roberts, best-selling author and political commentator on ABC News and NPR “John Vine details, in a compelling and accessible way, his experience with Parkinson’s disease. His book is an extraordinary guide to living successfully with Parkinson’s, and a must read for all who want to better understand the condition. Although diagnosed with Parkinson’s, my father lived an active and productive life until his death at age 94. As the book makes clear, while each patient’s journey is unique, common approaches are indispensable in treating the symptoms of the disease.”—Eric H. Holder, Jr. served as the 82nd Attorney General of the United States from 2009 to 2015 “John Vine has written the best primer I’ve ever read for newly diagnosed Parkinson’s patients and their families. It helps them cope with the shock of diagnosis, gives them (jargon-free) the scientific basics they need to know, describes the symptoms they may experience (making clear that every case is different) and catalogs the resources available to navigate living with Parkinson’s. John humanizes the book by describing his own experience and that of 22 other patients and their partners. I’d urge every neurologist to have copies of Vine’s primer on hand to help new PD on their journey forward.”—Morton Kondracke, author of Saving Milly: Love, Politics and Parkinson’s Disease and a member of the Founders' Council of the Michael J. Fox Foundation “My husband has PD, and I devoured this book. It’s wise, wonderfully readable, and, above all, helpful. Since John Vine has PD, he speaks with great authority about the challenges, both physical and psychological. If you have Parkinson’s, live with someone who has it, or just know someone battling the disease, A Parkinson’s Primer is for you.”—Lesley Stahl, award-winning television journalist on the CBS News program 60 Minutes “This is a remarkable book describing the personal experiences of many individuals, including the author, living with Parkinson’s disease. It captures the fact that although there are many possible symptoms in this disease, each person experiences different symptoms and copes with them in various ways. The thoughtful and insightful comments and coping strategies should be helpful for persons with PD, and their partners, regardless of the stage of the disease.”—Stephen Grill, MD, PhD, Director of the Parkinson’s & Movement Disorders Center of Maryland John M. Vine is a lawyer at Covington & Burling LLP in Washington, DC, where he is the senior member and former head of the firm’s employee benefits group. He was diagnosed with Parkinson’s in 2004.

    

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    This seminal work is reproduced here for a whole new generation to enjoy. In Sagan's typically lucid and lyrical style, he discusses many topics from astrophysics and solar system science, to colonization, terraforming and the search for extraterrestrials. Sagan conveys his own excitement and wonder, and relates the revelations of astronomy to the most profound human problems and concerns: issues that are just as valid today as they were thirty years ago. New to this edition are Freeman Dyson's comments on Sagan's vision and the importance of the work, Ann Druyan's assessment of Sagan's cultural significance as a champion of science, and David Morrison's discussion of the advances made since 1973 and what became of Sagan's predictions. Who knows what wonders this third millennium will reveal, but one thing is certain: Carl Sagan played a unique role in preparing us for them.

    

    Cox and Forshaw's contention? There is no need for quantum mechanics to be viewed this way. There is a lot of mileage in the 'weirdness' of the quantum world, and it often leads to confusion and, frankly, bad science. The Quantum Universe cuts through the Wu Li and asks what observations of the natural world made it necessary, how it was constructed, and why we are confident that, for all its apparent strangeness, it is a good theory.The quantum mechanics of The Quantum Universe provide a concrete model of nature that is comparable in its essence to Newton’s laws of motion, Maxwell’s theory of electricity and magnetism, and Einstein’s theory of relativity.