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.

Centuries of self-imposed isolation have transformed Nulapeiron into a world unlike any other - a world of vast subterranean cities maintained by extraordinary organic technologies. For the majority of its peoples, however such wonders have little meaning. Denied their democratic rights and restricted to the impoverished lower levels, they are subjected to the brutal law of the Logic Lords and the Oracles, supra-human beings whose ability to truecast the future maintains the status quo. But all this is about to change. In a crowded marketplace a mysterious, beautiful woman is brutally cut down by a militia squad's graser fire. Amongst the horrified onlookers is young Tom Corcorigan. He recognizes her. Only the previous day she had presented him with a small, seemingly insignificant info-crystal. And only now, as the fire in the dying stranger's obsidian eyes fades, does he comprehend who - or what - she really was: a figure from legend, one of the fabled Pilots. What Tom has still to discover is that his crystal holds the key to understanding mu-space, and so to freedom itself. He doesn't know it yet, but he has been given a destiny to fulfill - nothing less than the rewriting of his future, and that of his world... Spectacularly staged, thrillingly written and set in a visionary future, Paradox places John Meaney at the forefront of science fiction in this new century.

America needs better options for resolving potential crises In recent years, the Pentagon has elevated its concerns about Russia and China as potential military threats to the United States and its allies. But what issues could provoke actual conflict between the United States and either country? And how could such a conflict be contained before it took the world to the brink of thermonuclear catastrophe, as was feared during the cold war? Defense expert Michael O'Hanlon wrestles with these questions in this insightful book, setting them within the broader context of hegemonic change and today's version of great-power competition. The book examines how a local crisis could escalate into a broader and much more dangerous threat to peace. What if, for example, Russia's “little green men” seized control of a community, like Narva or an even smaller town in Estonia, now a NATO ally? Or, what if China seized one of the uninhabited Senkaku islands now claimed and administered by Japan, or imposed a partial blockade of Taiwan? Such threats are not necessarily imminent, but they are far from inconceivable. Washington could be forced to choose, in these and similar cases, between risking major war to reverse the aggression, and appeasing China or Russia in ways that could jeopardize the broader global order. O'Hanlon argues that the United States needs a better range of options for dealing with such risks to peace. He advocates “integrated deterrence,” which combines military elements with economic warfare. The military components would feature strengthened forward defenses as well as, possibly, limited military options against Russian or Chinese assets in other theaters. Economic warfare would include offensive elements, notably sanctions, as well as measures to ensure the resilience of the United States and allies against possible enemy reprisal. The goal is to deter war through a credible set of responses that are more commensurate than existing policy with the stakes involved in such scenarios.

Travel to the Stars . . . A Dream Fulfilled or Humankind's Worst Nightmare?Ed Walker's last mission almost ended in catastrophe. Although the NASA astronaut had been able to save the lives of his crewmates, he's still in danger of going down in history as the commander of the mission that wrecked the International Space Station. So he can hardly believe his luck when he's chosen to head the first manned exploration of the outer solar system.One of his new crew members is the young physicist David Holmes, who is studying the mysterious disappearance of three space probes.But as their spaceship approaches interstellar space, humanity's most pressing question is no longer: Are we alone in the universe? It is rather: Are we ready for the truth?For fans of Apollo 13, The Martian and Interstellar+++ Winner of the 2015 Storyteller Award at the Frankfurt International Bookfair +++

“This impassioned book invites readers to the deep end of life where authentic soul work and human transformation become pressing concerns.” —Publishers Weekly 2019 Independent Publisher Book Awards Gold Medalist in the Aging/Death & Dying Category From bestselling author Parker J. Palmer comes a brave and beautiful book for all who want to age reflectively, seeking new insights and life-giving ways to engage in the world. “Age itself,” he says, “is no excuse to wade in the shallows. It’s a reason to dive deep and take creative risks.” Looking back on eight decades of life—and on his work as a writer, teacher, and activist—Palmer explores what he’s learning about self and world, inviting readers to explore their own experience. In prose and poetry—and three downloadable songs written for the book by the gifted Carrie Newcomer—he meditates on the meanings of life, past, present, and future. With compassion and chutzpah, gravitas and levity, Palmer writes about cultivating a vital inner and outer life, finding meaning in suffering and joy, and forming friendships across the generations that bring new life to young and old alike. “This book is a companion for not merely surviving a fractured world, but embodying—like Parker—the fiercely honest and gracious wholeness that is ours to claim at every stage of life.” —Krista Tippett, New York Times-bestselling author of Becoming Wise “A wondrously rich mix of reality and possibility, comfort and story, helpful counsel and poetry, in the voice of a friend . . . This is a book of immense gratitude, consolation, and praise.” —Naomi Shihab Nye, National Book Award finalist

Our conception of logical space is the set of distinctions we use to navigate the world. Agustín Rayo argues that this is shaped by acceptance or rejection of 'just is'-statements: e.g. 'to be composed of water just is to be composed of H2O'. He offers a novel conception of metaphysical possibility, and a new trivialist philosophy of mathematics.

International capital flow and domestic financial market structures explain why some countries are more vulnerable to banking crises.