This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    It is the best and most successful guide to reading comprehension for the general reader. And now it has been completely rewritten and updated. You are told about the various levels of reading and how to achieve them – from elementary reading, through systematic skimming and inspectional reading, to speed reading, you learn how to pigeonhole a book, X-ray it, extract the author's message, criticize. You are taught the different reading techniques for reading practical books, imaginative literature, plays, poetry, history, science and mathematics, philosophy and social science. Finally, the authors offer a recommended reading list and supply reading tests whereby you can measure your own progress in reading skills, comprehension and speed.This a previously-published edition of ISBN 9780671212094

    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.

    DLC: Quantum theory.

    Today, scientists are attempting to measure the entire universe and to determine its origin. Although the methods have changed, the quest to chart the horizons of space and time continues to be one of the great adventures of science.Measuring the Universe is an eloquent chronicle of the men and women– from Aristarchus to Cassini, Sir Isaac Newton to Henrietta Leavitt and Stephen Hawking–who have gradually unlocked the mysteries of "how far" and in so doing have changed our ideas about the size and nature of the universe and our place in it. Kitty Ferguson reveals their methods to have been as inventive as their results were–and are–eye-opening. Advances such as Copernicus's revolutionary insights about the arrangement of the solar system, William Herschel's meticulous creation of the first three-dimensional map of the universe, and Edwin Hubble's astonishing discovery that the universe is expanding have by turns revolutionized our concept of the universe. Connecting centuries of breakthroughs with the political and cultural events surrounding them, Ferguson makes astronomy part of the sweep of history.To measure the seemingly immeasurable, scientists have always pushed the boundaries of the imagination–today, for example, facing the paradox of an ever-expanding universe that doesn't appear to expand into anything. In Kitty Fergeson's skillfill hands, the unimaginable becomes accessible and the splendid quest something we all can share.

    Snyder exposes the political passions, religious impulses, friendships, rivalries, and love of knowledge—and power—that drove these extraordinary men.  Whewell (who not only invented the word “scientist,” but also founded the fields of crystallography, mathematical economics, and the science of tides), Babbage (a mathematical genius who invented the modern computer), Herschel (who mapped the skies of the Southern Hemisphere and contributed to the invention of photography), and Jones (a curate who shaped the science of economics) were at the vanguard of the modernization of science.  This absorbing narrative of people, science and ideas  chronicles the intellectual revolution inaugurated by these men, one that continues to mold our understanding of the world around us and of our place within it.  Drawing upon the voluminous correspondence between the four men over the fifty years of their work, Laura J. Snyder shows how friendship worked to spur the men on to greater accomplishments, and how it enabled them to transform science and help create the modern world.

    In this amazingly comprehensible history of the universe, Simon Singh decodes the mystery behind the Big Bang theory, lading us through the development of one of the most extraordinary, important, and awe-inspiring theories in science.

    It is often rational to act against our own best interests, he argues, and most of us have moralviews that are self-defeating. We often act wrongly, although we know there will be no one with serious grounds for complaint, and when we consider future generations it is very hard to avoid conclusions that most of us will find very disturbing.

    Price begins with the mystery of the arrow of time. Why, for example, does disorder always increase, as required by the second law of thermodynamics? Price shows that, for over a century, most physicists have thought about these problems the wrong way. Misled by the human perspective from withintime, which distorts and exaggerates the differences between past and future, they have fallen victim to what Price calls the double standard fallacy: proposed explanations of the difference between the past and the future turn out to rely on a difference which has been slipped in at thebeginning, when the physicists themselves treat the past and future in different ways. To avoid this fallacy, Price argues, we need to overcome our natural tendency to think about the past and the future differently. We need to imagine a point outside time -- an Archimedean view from nowhen --from which to observe time in an unbiased way. Offering a lively criticism of many major modern physicists, including Richard Feynman and Stephen Hawking, Price shows that this fallacy remains common in physics today -- for example, when contemporary cosmologists theorize about the eventual fate of the universe. The big bang theory normallyassumes that the beginning and end of the universe will be very different. But if we are to avoid the double standard fallacy, we need to consider time symmetrically, and take seriously the possibility that the arrow of time may reverse when the universe recollapses into a big crunch. Price then turns to the greatest mystery of modern physics, the meaning of quantum theory. He argues that in missing the Archimedean viewpoint, modern physics has missed a radical and attractive solution to many of the apparent paradoxes of quantum physics. Many consequences of quantum theoryappear counterintuitive, such as Schrodinger's Cat, whose condition seems undetermined until observed, and Bell's Theorem, which suggests a spooky nonlocality, where events happening simultaneously in different places seem to affect each other directly. Price shows that these paradoxes can beavoided by allowing that at the quantum level the future does, indeed, affect the past. This demystifies nonlocality, and supports Einstein's unpopular intuition that quantum theory describes an objective world, existing independently of human observers: the Cat is alive or dead, even when nobodylooks. So interpreted, Price argues, quantum mechanics is simply the kind of theory we ought to have expected in microphysics -- from the symmetric standpoint.Time's Arrow and Archimedes' Point presents an innovative and controversial view of time and contemporary physics. In this exciting book, Price urges physicists, philosophers, and anyone who has ever pondered the mysteries of time to look at the world from the fresh perspective of Archimedes' Pointand gain a deeper understanding of ourselves, the universe around us, and our own place in time.

    Einstein famously quipped that God does not play dice with the universe, and Schrödinger is equally well known for his thought experiment about the cat in the box who ends up “spread out” in a probabilistic state, neither wholly alive nor wholly dead. Both of these famous images arose from these two men’s dissatisfaction with quantum weirdness and with their assertion that underneath it all, there must be some essentially deterministic world. Even though it was Einstein’s own theories that made quantum mechanics possible, both he and Schrödinger could not bear the idea that the universe was, at its most fundamental level, random.As the Second World War raged, both men struggled to produce a theory that would describe in full the universe’s ultimate design, first as collaborators, then as competitors. They both ultimately failed in their search for a Grand Unified Theory—not only because quantum mechanics is true, but because Einstein and Schrödinger were also missing a key component: of the four forces we recognize today (gravity, electromagnetism, the weak force, and the strong force), only gravity and electromagnetism were known at the time.Despite their failures, though, much of modern physics remains focused on the search for a Grand Unified Theory. As Halpern explains, the recent discovery of the Higgs Boson makes the Standard Model—the closest thing we have to a unified theory—nearly complete. And while Einstein and Schrödinger tried and failed to explain everything in the cosmos through pure geometry, the development of string theory has, in its own quantum way, brought this idea back into vogue. As in so many things, even when he was wrong, Einstein couldn’t help but be right.

    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.

    Using illustrations and examples from science fiction pulp magazines and comic books, The Amazing Story of Quantum Mechanics explains the fundamental principles of quantum mechanics that underlie the world we live in.Watch a Video

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Strevens calls this scientific code the iron rule of explanation, and reveals the way in which the rule, precisely because it is unreasonably close-minded, overcomes individual prejudices to lead humanity inexorably toward the secrets of nature.“With a mixture of philosophical and historical argument, and written in an engrossing style” (Alan Ryan), The Knowledge Machine provides captivating portraits of some of the greatest luminaries in science’s history, including Isaac Newton, the chief architect of modern science and its foundational theories of motion and gravitation; William Whewell, perhaps the greatest philosopher-scientist of the early nineteenth century; and Murray Gell-Mann, discoverer of the quark. Today, Strevens argues, in the face of threats from a changing climate and global pandemics, the idiosyncratic but highly effective scientific knowledge machine must be protected from politicians, commercial interests, and even scientists themselves who seek to open it up, to make it less narrow and more rational—and thus to undermine its devotedly empirical search for truth.Rich with illuminating and often delightfully quirky illustrations, The Knowledge Machine, written in a winningly accessible style that belies the import of its revisionist and groundbreaking concepts, radically reframes much of what we thought we knew about the origins of the modern world.

    A preeminent scholar, writer, and teacher, he has had a profound influence on millions of people. To him, mythology was the "song of the universe, the music of the spheres." With Bill Moyers, one of America's most prominent journalists, as his thoughtful and engaging interviewer, The Power Of Myth touches on subjects from modern marriage to virgin births, from Jesus to John Lennon, offering a brilliant combination of intelligence and wit.