This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. 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 intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. 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 • statements that are true but cannot be proven 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.

In the ten years preceding publication, the known solar system more than doubled in size. For the first time in almost two centuries an entirely new population of planetary objects was found. This 'Kuiper Belt' of minor planets beyond Neptune revolutionised our understanding of the solar system's formation and finally explained the origin of the enigmatic outer planet Pluto. This is the fascinating story of how theoretical physicists decided that there must be a population of unknown bodies beyond Neptune and how a small band of astronomers set out to find them. What they discovered was a family of ancient planetesimals whose orbits and physical properties were far more complicated than anyone expected. We follow the story of this discovery, and see how astronomers, theoretical physicists and one incredibly dedicated amateur observer came together to explore the frozen boundary of the solar system.

In the follow-up to his acclaimed Science in the Looking Glass, Brian Davies discusses deep problems about our place in the world, using a minimum of technical jargon. The book argues that 'absolutist' ideas of the objectivity of science, dating back to Plato, continue to mislead generations of both theoretical physicists and theologians. It explains that the multi-layered nature of our present descriptions of the world is unavoidable, not because of anything about the world, but because of our own human natures. It tries to rescue mathematics from the singular and exceptional status that it has been assigned, as much by those who understand it as by those who do not. Working throughout from direct quotations from many of the important contributors to its subject, it concludes with a penetrating criticism of many of the recent contributions to the often acrimonious debates about science and religions.

A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability. Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him. Math has a bad reputation: dull, difficult, detached from daily life. As a talking Barbie doll opined, “Math class is tough.” But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function (“The year: 1972. The scene: Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey”), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.

An exciting series of six original digest-sized novels based on the hit-TV series "The Outer Limits". The rulers of the planet Zanti have found a solution to the problem of what to do with undesirable misfits and dangerous malcontents who threaten their society--exile them to Earth! The leaders of Earth are powerless to object. Teenagers Ben Garth and Lisa Lawrence are outcasts, too. Now they're on the run and headed towards a terrifying showdown with the Zanti misfits.

There is nothing wrong with your television set...Fifty years ago, a new TV program called The Outer Limits exploded across the consciousness of an entire generation. A half-century later, Creature Features celebrates the Golden Anniversary of this classic and provocative series. The awe and mystery of the universe awaits!

Throughout its long history, and not just as the key aesthetic category for the Romantic Movement, the sublime has created the necessary link between aesthetic and moral judgment, offering the prospect of transcending the limits of measurement, even imagination. The best of science makes genuine claims to the sublime. For in science, as in art, every day brings the entirely new, the extreme, and the unrepresentable. How does one depict negative mass, for example, or the folding of a protein that is contagious? Can one capture emergent phenomena as they emerge? Science is continually faced with describing that which is beyond. This book, through contributions from nine prominent scholars, tackles that challenge. The explorations within Beyond the Finite range from the images taken by the Hubble Telescope to David Bohm's quantum romanticism, from Kant and Burke to a "downward spiraling infinity" of the 21st century sublime, all lucid yet transcendent. Squarely positioned at the interface between science and art, this volume's chapters capture a remarkable variety of perspectives, with neuroscience, chemistry, astronomy, physics, film, painting and music discussed in relation to the sublime experience, topics surely to peak the interest of academics and students studying the sublime in various disciplines.

Fundamental science will one day come to an end, argues Russell Stannard. Ultimately there will be experiments too vast to finance, areas of knowledge the human brain cannot comprehend, evidence that forever eludes us. His book explores the likely boundaries of our quest to understand the nature of time, matter, consciousness, and the universe.

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.