A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    Augustine equate nothingness with the Devil? What tortuous means did 17th-century scientists employ in their attempts to create a vacuum? And why do contemporary quantum physicists believe that the void is actually seething with subatomic activity? You’ll find the answers in this dizzyingly erudite and elegantly explained book by the English cosmologist John D. Barrow.Ranging through mathematics, theology, philosophy, literature, particle physics, and cosmology, The Book of Nothing explores the enduring hold that vacuity has exercised on the human imagination. Combining high-wire speculation with a wealth of reference that takes in Freddy Mercury and Shakespeare alongside Isaac Newton, Albert Einstein, and Stephen Hawking, the result is a fascinating excursion to the vanishing point of our knowledge.

    This 8-hour free course introduced the study of philosophy and the methods employed by The Open University in teaching philosophy.

    In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy.In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

    Half a century later, only robots have been to the Red Planet and our astronauts rarely venture beyond Earth orbit.Now Mars is back With everyone from Elon Musk to Ridley Scott and Donald Trump talking about it, interplanetary exploration is back on the agenda and Mars is once again the prime destination for future human expansion and colonisation. In Destination Mars, astrophysicist and science writer Andrew May traces the history of our fascination with the Red Planet and explores the science upon which a crewed mission would be based, from assembling a spacecraft in Earth orbit to surviving solar storms. With expert insight, he analyses the new space race and assesses what the future holds for human life on Mars.

    Ten dimensions? Most of us have barely gotten used to the idea that there are four.Using simple geometry and an easygoing writing style, author Rob Bryanton starts with the lower dimensions that we are all familiar with, then uses those concepts to build one layer upon another, ultimately arriving at a way of imagining the tenth dimension.Part scientific exploration, part philosophy, this unique book touches upon such diverse topics as dark matter, Feynman's "sum over paths", the quantum observer, and the soul. It is aimed at anyone interested in leading-edge theories about cosmology and the nature of reality, but it is not about mainstream physics. Rather, Imagining the Tenth Dimension is a mind-expanding exercise that could change the way you view this incredible universe in which we live.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    In this unconventional introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Unlike most popular physics books—which give readers a taste of what physicists know but shy away from equations or math—Susskind and Hrabovsky actually teach the skills you need to do physics, beginning with classical mechanics, yourself. Based on Susskind's enormously popular Stanford University-based (and YouTube-featured) continuing-education course, the authors cover the minimum—the theoretical minimum of the title—that readers need to master to study more advanced topics.An alternative to the conventional go-to-college method, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

    Cosmic Universe and Human History, microcosm and macrocosm, inorganic and living matter coexist and form a unique unity manifested in multiple forms. The Physical and the Mental constitute the form and the content of the World. The world does not consist of subjects and objects, the “subject” and the “object” are metaphysical abstractions of the single and indivisible Wholeness. Man’s finite knowledge separates the Whole into parts and studies fragmentarily the beings. The Wholeness is manifested in multiple forms and each form encapsulates the Wholeness. The rational explanation of the excerpts and the intuitive apprehension of the Wholeness are required to combine and create the open thought and the holistic knowledge. This means that the measurement should be defined by the ''measure'', but the responsibility for determining the ''measure'' depends on the man. This requires that man overcomes the anthropocentric arrogance and the narcissistic selfishness and he joins the Cosmic World in a friendly and creative manner.

    Simmons advocates a careful approach to the subject, covering such topics as the wave equation, Gauss's hypergeometric function, the gamma function and the basic problems of the calculus of variations in an explanatory fashions - ensuring that students fully understand and appreciate the topics.

    In the hands of one of today’s hottest young physicists, that simple fact of breakfast becomes a doorway to understanding the Big Bang, the universe, and other universes, too. In From Eternity to Here, Sean Carroll argues that the arrow of time, pointing resolutely from the past to the future, owes its existence to conditions before the Big Bang itself, a period modern cosmology of which Einstein never dreamed. Increasingly, though, physicists are going out into realms that make the theory of relativity seem like child’s play. Carroll’s scenario is not only elegant, it’s laid out in the same easy-to- understand language that has made his group blog, Cosmic Variance, the most popular physics blog on the Net. From Eternity to Here uses ideas at the cutting edge of theoretical physics to explore how properties of spacetime before the Big Bang can explain the flow of time we experience in our everyday lives. Carroll suggests that we live in a baby universe, part of a large family of universes in which many of our siblings experience an arrow of time running in the opposite direction. It’s an ambitious, fascinating picture of the universe on an ultra-large scale, one that will captivate fans of popular physics blockbusters like Elegant Universe and A Brief History of Time.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies beautiful forms, forms whose hallmarks are symmetry—harmony, balance, proportion—and economy. There are other meanings of “beauty,” but this is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that “all things are number,” to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentiethcentury physics. Though the ancients weren’t right about everything, their ardent belief in the music of the spheres has proved true down to the quantum level. Indeed, Wilczek explores just how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos.Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost literally the same equations that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. The universe itself, suggests Wilczek, seems to want to embody beautiful and elegant forms. Perhaps this force is the pure elegance of numbers, perhaps the work of a higher being, or somewhere between. Either way, we don’t depart from the infinite and infinitesimal after all; we’re profoundly connected to them, and we connect them. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves.Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.