As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematicsas we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figurelarge sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treatingzero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools likedouble-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speakonly in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking notonly into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. Thebeauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

    Along the way he provides an engaging and witty commentary while introducing the lay reader to both classic and cutting-edge concepts in physics, including:What Superman's strength can tell us about the Newtonian physics of force, mass, and accelerationHow Iceman's and Storm's powers illustrate the principles of thermal dynamicsThe physics behind the death of Spider-Man's girlfriend Gwen StacyWhy physics professors gone bad are the most dangerous evil geniuses!

    Lacking the ability to measure their longitude, sailors throughout the great ages of exploration had been literally lost at sea as soon as they lost sight of land. Thousands of lives, and the increasing fortunes of nations, hung on a resolution.The scientific establishment of Europe—from Galileo to Sir Issac Newton—had mapped the heavens in both hemispheres in its certain pursuit of a celestial answer. In stark contrast, one man, John Harrison, dared to imagine a mechanical solution—a clock that would keep precise time at sea, something no clock had ever been able to do on land. Longitude is a dramatic human story of an epic scientific quest and Harrison's forty-year obsession with building his perfect timekeeper, known today as the chronometer. Full of heroism and chicanery, it is also a fascinating brief history of astronomy, navigation, and clock-making, and opens a new window on our world.On its 10th anniversary, a gift edition of this classic book, with a forward by one of history's greatest explorers, and eight pages of color illustrations.

    In captivity, octopuses have been known to identify individual human keepers, raid neighboring tanks for food, turn off lightbulbs by spouting jets of water, plug drains, and make daring escapes. How is it that a creature with such gifts evolved through an evolutionary lineage so radically distant from our own? What does it mean that evolution built minds not once but at least twice? The octopus is the closest we will come to meeting an intelligent alien. What can we learn from the encounter?In Other Minds, Peter Godfrey-Smith, a distinguished philosopher of science and a skilled scuba diver, tells a bold new story of how subjective experience crept into being—how nature became aware of itself. As Godfrey-Smith stresses, it is a story that largely occurs in the ocean, where animals first appeared. Tracking the mind’s fitful development, Godfrey-Smith shows how unruly clumps of seaborne cells began living together and became capable of sensing, acting, and signaling. As these primitive organisms became more entangled with others, they grew more complicated. The first nervous systems evolved, probably in ancient relatives of jellyfish; later on, the cephalopods, which began as inconspicuous mollusks, abandoned their shells and rose above the ocean floor, searching for prey and acquiring the greater intelligence needed to do so. Taking an independent route, mammals and birds later began their own evolutionary journeys.But what kind of intelligence do cephalopods possess? Drawing on the latest scientific research and his own scuba-diving adventures, Godfrey-Smith probes the many mysteries that surround the lineage. How did the octopus, a solitary creature with little social life, become so smart? What is it like to have eight tentacles that are so packed with neurons that they virtually “think for themselves”? What happens when some octopuses abandon their hermit-like ways and congregate, as they do in a unique location off the coast of Australia?By tracing the question of inner life back to its roots and comparing human beings with our most remarkable animal relatives, Godfrey-Smith casts crucial new light on the octopus mind—and on our own.

    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.

    Wolke, professor emeritus of chemistry at the University of Pittsburgh and acclaimed author of What Einstein Didn't Know, understands the need to...well, understand. Now he provides more amusing explanations of such everyday phenomena as gravity (If you're in a falling elevator, will jumping at the last instant save your life?) and acoustics (Why does a whip make such a loud cracking noise?), along with amazing facts, belly-up-to-the-bar bets, and mind-blowing reality bites all with his trademark wit and wisdom.If you shoot a bullet into the air, can it kill somebody when it comes down? You can find out about all this and more in an astonishing compendium of the proverbial mind-boggling mysteries of the physical world we inhabit.Arranged in a question-and-answer format and grouped by subject for browsing ease, WHAT EINSTEIN TOLD HIS BARBER is for anyone who ever pondered such things as why colors fade in sunlight, what happens to the rubber from worn-out tires, what makes red-hot objects glow red, and other scientific curiosities. Perfect for fans of Newton's Apple, Jeopardy!, and The Discovery Channel, WHAT EINSTEIN TOLD HIS BARBER also includes a glossary of important scientific buzz words and a comprehensive index. -->

    In this book, he expands the points he has made, and claims that this debate is not so much about religion versus science, as about the nature of science itself. With infectious enthusiasm, he reveals the mechanics of evolutionary theory, explains how it is rooted in the testable and verifiable scientific method, and why it is therefore a sound explanation of our beginning. He argues passionately that to continue to assert otherwise, to continue to insist that creationism has a place in the science classroom is harmful not only to our children, but to the future of the greater world as well.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life—patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within.Taking the reader on a wondrous journey through the invisible universe that surrounds us—a universe made visible by mathematics—Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers—all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture. An exploration of an often woefully misunderstood subject, The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics.

    How does Jane Goodall’s relationship with her dog Rusty inform her thinking about our relationship to other species? Which time and place would Jared Diamond most prefer to live in, in light of his work on the role of chance in history? What does driving a sports car have to do with Steven Weinberg’s quest for the “theory of everything”? Physicist and journalist Stefan Klein’s intimate conversations with nineteen of the world’s best-known scientists (including three Nobel Laureates) let us listen in as they talk about their paradigm-changing work—and how it is deeply rooted in their daily lives. • Cosmologist Martin Rees on the beginning and end of the world • Evolutionary biologist Richard Dawkins on egoism and selflessness • Neuroscientist V. S. Ramachandran on consciousness • Molecular biologist Elizabeth Blackburn on aging • Philosopher Peter Singer on morality • Physician and social scientist Nicholas Christakis on human relationships • Biochemist Craig Venter on the human genome • Chemist and poet Roald Hoffmann on beauty

    Can you believe that physical reality is created by our observation of it? Physicists were forced to this conclusion, the quantum enigma, by what they observed in their laboratories.Trying to understand the atom, physicists built quantum mechanics and found, to their embarrassment, that their theory intimately connects consciousness with the physical world. Quantum Enigma explores what that implies and why some founders of the theory became the foremost objectors to it. Schr�dinger showed that it absurdly allowed a cat to be in a superposition simultaneously dead and alive. Einstein derided the theory's spooky interactions. With Bell's Theorem, we now know Schr�dinger's superpositions and Einstein's spooky interactions indeed exist.Authors Bruce Rosenblum and Fred Kuttner explain all of this in non-technical terms with help from some fanciful stories and bits about the theory's developers. They present the quantum mystery honestly, with an emphasis on what is and what is not speculation.Physics' encounter with consciousness is its skeleton in the closet. Because the authors open the closet and examine the skeleton, theirs is a controversial book. Quantum Enigma's description of the experimental quantum facts, and the quantum theory explaining them, is undisputed. Interpreting what it all means, however, is controversial.Every interpretation of quantum physics encounters consciousness. Rosenblum and Kuttner therefore turn to exploring consciousness itself--and encounter quantum physics. Free will and anthropic principles become crucial issues, and the connection of consciousness with the cosmos suggested by some leading quantum cosmologists is mind-blowing.Readers are brought to a boundary where the particular expertise of physicists is no longer a sure guide. They will find, instead, the facts and hints provided by quantum mechanics and the ability to speculate for themselves.

    Scientists are confident that there is alien life across the universe yet we have not moved beyond our perception of 'aliens' as Hollywood stereotypes. The time has come to abandon our fixation on alien monsters and place our expectations on solid scientific footing.Using his own expert understanding of life on Earth and Darwin's theory of evolution - which applies throughout the universe - Cambridge zoologist Dr Arik Kershenbaum explains what alien life must be like: how these creatures will move, socialise and communicate.For example, by observing fishes whose electrical pulses indicate social status, we can see that other planets might allow for communication by electricity. As there was evolutionary pressure to wriggle along a sea floor, Earthling animals tend to have left/right symmetry; on planets where creatures evolved mid-air or in soupy tar they might be lacking any symmetry at all.Might there be an alien planet with supersonic animals? Will they scream with fear, act honestly, or have technology? Is the universe swarming with robots? Dr Kershenbaum uses cutting-edge science to paint an entertaining and compelling picture of extra-terrestrial life.The Zoologist's Guide to the Galaxy is the story of how life really works, on Earth and in space.***'If you don't want to be surprised by extraterrestrial life, look no further than this lively overview of the laws of evolution that have produced life on earth' - Frans de Waal, author of Mama's Last Hug - Animal Emotions and What They Tell Us about Ourselves'A fun, and thoroughly biological, exploration of possible and impossible alien beings. If you'd love to know what real aliens from other planets might really be like, this is the book for you' - Susan Blackmore, author of Seeing Myself'Surveying the deep-time of evolution on Earth and his own cutting-edge research into animal communication, Kershenbaum provides a fascinating insight into the deepest of questions: what might an alien actually look like'- Lewis Dartnell, author of Origins'Arik Kershenbaum takes us on a joyous voyage of animal diversity and illustrates the singular importance of natural selection in explaining life - here on Earth - and what will likely be discovered throughout the galaxy. A stimulating read!' - Daniel T. Blumstein, Professor of Ecology and Evolutionary Biology, University of California Los Angeles

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    Though the answers may seem simple, their profound implications make the prisoner's dilemma one of the great unifying concepts of science. Watching players bluff in a poker game inspired John von Neumann--father of the modern computer and one of the sharpest minds of the century--to construct game theory, a mathematical study of conflict and deception. Game theory was readily embraced at the RAND Corporation, the archetypical think tank charged with formulating military strategy for the atomic age, and in 1950 two RAND scientists made a momentous discovery.Called the prisoner's dilemma, it is a disturbing and mind-bending game where two or more people may betray the common good for individual gain. Introduced shortly after the Soviet Union acquired the atomic bomb, the prisoner's dilemma quickly became a popular allegory of the nuclear arms race. Intellectuals such as von Neumann and Bertrand Russell joined military and political leaders in rallying to the preventive war movement, which advocated a nuclear first strike against the Soviet Union. Though the Truman administration rejected preventive war the United States entered into an arms race with the Soviets and game theory developed into a controversial tool of public policy--alternately accused of justifying arms races and touted as the only hope of preventing them.A masterful work of science writing, Prisoner's Dilemma weaves together a biography of the brilliant and tragic von Neumann, a history of pivotal phases of the cold war, and an investigation of game theory's far-reaching influence on public policy today. Most important, Prisoner's Dilemma is the incisive story of a revolutionary idea that has been hailed as a landmark of twentieth-century thought.

    Bronowski's exciting, illustrated investigation offers a perspective not just on science, but on civilization itself. Lower than the angelsForewordThe harvest of the seasons The grain in the stoneThe hidden structure The music of the spheresThe starry messanger The majestic clockworkThe drive for power The ladder of creation World within world Knowledge or certainty Generation upon generationThe long childhoodBibliographyIndex