We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    Coated in red dust, the terrain is bewilderingly empty. And yet multiple spacecraft are circling Mars, sweeping over Terra Sabaea, Syrtis Major, the dunes of Elysium, and Mare Sirenum—on the brink, perhaps, of a staggering find, one that would inspire humankind as much as any discovery in the history of modern science.In this beautifully observed, deeply personal book, Georgetown scientist Sarah Stewart Johnson tells the story of how she and other researchers have scoured Mars for signs of life, transforming the planet from a distant point of light into a world of its own.Johnson’s fascination with Mars began as a child in Kentucky, turning over rocks with her father and looking at planets in the night sky. She now conducts fieldwork in some of Earth’s most hostile environments, such as the Dry Valleys of Antarctica and the salt flats of Western Australia, developing methods for detecting life on other worlds. Here, with poetic precision, she interlaces her own personal journey—as a female scientist and a mother—with tales of other seekers, from Percival Lowell, who was convinced that a utopian society existed on Mars, to Audouin Dollfus, who tried to carry out astronomical observations from a stratospheric balloon. In the process, she shows how the story of Mars is also a story about Earth: This other world has been our mirror, our foil, a telltale reflection of our own anxieties and yearnings.Empathetic and evocative, The Sirens of Mars offers an unlikely natural history of a place where no human has ever set foot, while providing a vivid portrait of our quest to defy our isolation in the cosmos.

    And yet for many years it was equally baffling for scientists themselves. Manjit Kumar gives a dramatic and superbly-written history of this fundamental scientific revolution, and the divisive debate at its heart.For 60 years most physicists believed that quantum theory denied the very existence of reality itself. Yet Kumar shows how the golden age of physics ignited the greatest intellectual debate of the twentieth century.Quantum sets the science in the context of the great upheavals of the modern age. In 1925 the quantum pioneers nearly all hailed from upper-middle-class academic families; most were German; and their average age was 24. But it was their irrational, romantic spirit, formed in reaction to the mechanised slaughter of the First World War that inspired their will to test science to its limits.The essential read for anyone fascinated by this complex and thrilling story and by the band of young men at its heart.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    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.

    In Physics of the Impossible, the renowned physicist Michio Kaku explores to what extent the technologies and devices of science fiction that are deemed equally impossible today might well become commonplace in the future.From teleportation to telekinesis, Kaku uses the world of science fiction to explore the fundamentals—and the limits—of the laws of physics as we know them today. He ranks the impossible technologies by categories—Class I, II, and III, depending on when they might be achieved, within the next century, millennia, or perhaps never. In a compelling and thought-provoking narrative, he explains:· How the science of optics and electromagnetism may one day enable us to bend light around an object, like a stream flowing around a boulder, making the object invisible to observers “downstream”· How ramjet rockets, laser sails, antimatter engines, and nanorockets may one day take us to the nearby stars· How telepathy and psychokinesis, once considered pseudoscience, may one day be possible using advances in MRI, computers, superconductivity, and nanotechnology· Why a time machine is apparently consistent with the known laws of quantum physics, although it would take an unbelievably advanced civilization to actually build oneKaku uses his discussion of each technology as a jumping-off point to explain the science behind it. An extraordinary scientific adventure, Physics of the Impossible takes readers on an unforgettable, mesmerizing journey into the world of science that both enlightens and entertains.

    Why do we recognize patterns? Is there such a thing as positive stress? Are we genetically programmed to be in conflict with each other? Those are just some of the 150 questions that the world's best scientific minds answer with elegant simplicity.With contributions from Jared Diamond, Richard Dawkins, Nassim Taleb, Brian Eno, Steven Pinker, and more, everything is explained in fun, uncomplicated terms that make the most complex concepts easy to comprehend.

    The truth is that the solutions have been available for a long time -- in the writings of our Founding Fathers -- carefully set forth in this timely book.In The 5000 Year Leap: A Miracle That Changed the World, Discover the 28 Principles of Freedom our Founding Fathers said must be understood and perpetuated by every people who desire peace, prosperity, and freedom. Learn how adherence to these beliefs during the past 200 years has brought about more progress than was made in the previous 5000 years. These 28 Principles include The Genius of Natural Law, Virtuous and Moral Leaders, Equal Rights--Not Equal Things, and Avoiding the Burden of Debt. Published by the National Center for Constitut

    Have you ever wondered why ice floats and water is such a freaky liquid? Or why chillies and mustard are both hot but in different ways? Or why microwaves don't cook from the inside out? In this fascinating scientific tour of household objects, The One Show presenter and all-round Science Bloke Marty Jopson has the answer to all of these, and many more, baffling questions about the chemistry and physics of the everyday stuff we use every day.

     Is slipping on a banana peel really as hazardous to your health as the cartoons imply? Answer: Yes. Banana peels ooze a gel that turns out to be extremely slippery. Your foot and body weight provide the pressure. The gel provides the humor (and resulting head trauma). Can you die by shaking someone s hand? Answer: Yes. That's because, due to atomic repulsion, you've never actually touched another person s hand. If you could, the results would be as disastrous as a medium-sized hydrogen bomb. If you were Cookie Monster, just how many cookies could you actually eat in one sitting? Answer: Most stomachs can hold up to sixty cookies, or around four liters. If you eat or drink more than that, you re approaching the point at which the cookies would break through the lesser curvature of your stomach, and then you d better call an ambulance to Sesame Street."

    Davis has amused and edified us with fascinating facts about history, mythology, the Bible, the universe, geography, and the Civil War.Now, the sky's the limit in his latest irresistible installment—a grand tour of knowledge that carries us from the Great Smoky Mountains to the Berlin Wall, from the Salem Witch Trials to Watergate, from Michelangelo to Houdini. Brimming with busted myths, gripping true stories, and peculiar particulars about a plethora of people, places, and events, this captivating compendium is guaranteed to delight information lovers everywhere as it feeds our insatiable appetite to know everything!

    His explanation of the role of natural selection in driving the evolution of life on earth depended on steady variation of living things over time – but he was unable to explain how this variation occurred. In the 150 years since publication of the Origin of Species, we have discovered three main sources for this variation – mutation, hybridisation and epigenetics. Then on Sunday, 12th February, 2001 the evidence for perhaps the most extraordinary cause of variation was simultaneously released by two organisations – the code for the entire human genome. Not only was the human genome unbelievably simple (it is only ten times more complicated than a bacteria), but embedded in the code were large fragments that were derived from viruses – fragments that were vital to evolution of all organisms and the evidence for a fourth and vital source of variation – viruses.Virolution was the subject of a feature article in New Scientist. Translated into Russian, French, German and Japanese, this book has become a hot topic for discussion among scientists and thinkers in recent years. It offers a very new interpretation of our human evolution - and extrapolates to new avenues of approach to fight important diseases, such as cancer and MS.In early 2014 Dr Ryan has co-authored a relevant new paper with Swedish and Chinese scientists working on the Human Proteome project. More details about this paper and other developments will follow in his articles and blogs. So popular is the topic he has been commissioned to give a plenary lecture followed by planning and research advice to PhD students in biology and evolutionary biology at the annual European Society for Evolutionary Biology annual meeting for PhD students in Belgium in September 2014.More anon...

    . . . Baker examines a wide range of the achievements that have made, and still make, America great again—and again.” —The Wall Street Journal All made in America: The skyscraper and subway car. The telephone and telegraph. The safety elevator and safety pin. Plus the microprocessor, amusement park, MRI, supermarket, Pennsylvania rifle, and Tennessee Valley Authority. Not to mention the city of Chicago or jazz or that magnificent Golden Gate Bridge.   What is it about America that makes it a nation of inventors, tinkerers, researchers, and adventurers—obsessive pursuers of the never-before-created? And, equally, what is it that makes America such a fertile place to explore, discover, and launch the next big thing?   In America the Ingenious, bestselling author Kevin Baker brings his gift of storytelling and eye for historical detail to the grand, and grandly entertaining, tale of American innovation. Here are the Edisons and Bells and Carnegies, and the stories of how they followed their passions and changed our world. And also the less celebrated, like Jacob Youphes and Loeb Strauss, two Jewish immigrants from Germany who transformed the way at least half the world now dresses (hint: Levi Strauss). And Leo Fender, who couldn’t play a note of music, midwifing rock ’n’ roll through his solid-body electric guitar and amplifier. And the many women who weren’t legally recognized as inventors, but who created things to make their lives easier that we use every day—like Josephine Cochran, inventor of the dishwasher, or Marion O’Brien Donovan, who invented a waterproof diaper cover. Or a guy with the improbable name of Philo Farnsworth, who, with his invention of television, upended communication as significantly as Gutenberg did.   At a time when America struggles with different visions of what it wants to be, America the Ingenious shows the extraordinary power of what works: how immigration leads to innovation, what a strong government and strong public education mean to a climate of positive practical change, and why taking the long view instead of looking for short-term gain pays off many times over, not only for investors and inventors, but for the rest of us whose lives are made better by the new.   America and its nation of immigrants have excelled at taking ideas from anywhere and transforming them into the startling, often unexpectedly beautiful creations that have shaped our world. This is that story.

    Much as Brainiac offered a behind-the-scenes look at the little-known demimonde of competitive trivia buffs, Maphead finally gives equal time to that other downtrodden underclass: America's map nerds.In a world where geography only makes the headlines when college students are (endlessly) discovered to be bad at it, these hardy souls somehow thrive. Some crisscross the map working an endless geographic checklist: visiting all 3,143 U.S. counties, for example, or all 936 UNESCO World Heritage Sites. Some pore over million-dollar collections of the rarest maps of the past; others embrace the future by hunting real-world cartographic treasures like "geocaches" or "degree confluences" with GPS device in hand. Some even draw thousands of their own imaginary maps, lovingly detailing worlds that never were.Ken Jennings was a map nerd from a young age himself, you will not be surprised to learn, even sleeping with a bulky Hammond atlas at the side of his pillow, in lieu of the traditional Teddy bear. As he travels the nation meeting others of his tribe--map librarians, publishers, "roadgeeks," pint-sized National Geographic Bee prodigies, the computer geniuses behind Google Maps and other geo-technologies--he comes to admire these geographic obsessives. Now that technology and geographic illiteracy are increasingly insulating us from the lay of the land around us, we are going to be needing these people more than ever. Mapheads are the ones who always know exactly where they are--and where everything else is as well.