Paradox On The Brink Of Eternity

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 +++

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.

Austin Farrer in his later years was striving for new depths of simplicity and insight. This collection of Farrer sermons, preached mainly to undergraduate audiences, is the third to be published since his death. Even readers who never heard him speak can form from the printed text a true impression of his qualities of imagination, humor, and spirituality.For preachers he not only advocates but illustrates preaching as a creative art; to the 'ordinary' Christian he shows how worthwhile it is to take trouble with the questions of faith: to face them as issues of truth, to probe them this way and that, and to feel that language and imagery are friendly tools for undertaking the work. For theologians, too, he has a message: not to conceive their task too narrowly and to let a wide range of human resources, mind and heart, contribute to the task of clothing in words our experience of God.

This book is composed of a series of studies in the history of political thought from late antiquity to the early-eighteenth century. They range broadly across theories of kingship, political theology, constitutional ideas, natural-law thinking, and consent theory.