The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley
It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades--all before his suicide at age forty-one. This New York Times–bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing's royal pardon in 2013, is the definitive account of an extraordinary mind and life.
Capturing both the inner and outer drama of Turing’s life, Andrew Hodges tells how Turing’s revolutionary idea of 1936--the concept of a universal machine--laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design. The book also tells how this work was directly related to Turing’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. At the same time, this is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program--all for trying to live honestly in a society that defined homosexuality as a crime.
The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley, Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.
With rigor and wit, Dawkins examines God in all his forms, from the sex-obsessed tyrant of the Old Testament to the more benign (but still illogical) Celestial Watchmaker favored by some Enlightenment thinkers. He eviscerates the major arguments for religion and demonstrates the supreme improbability of a supreme being. He shows how religion fuels war, foments bigotry, and abuses children, buttressing his points with historical and contemporary evidence. The God Delusion makes a compelling case that belief in God is not just wrong but potentially deadly. It also offers exhilarating insight into the advantages of atheism to the individual and society, not the least of which is a clearer, truer appreciation of the universe's wonders than any faith could ever muster.
The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.
Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?
How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.
Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
A New York Times Notable Book.
The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything.
In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.
“Where did the universe come from? What was there before it? What will the future bring? And finally, why is there something rather than nothing?”
One of the few prominent scientists today to have crossed the chasm between science and popular culture, Krauss describes the staggeringly beautiful experimental observations and mind-bending new theories that demonstrate not only can something arise from nothing, something will always arise from nothing. With a new preface about the significance of the discovery of the Higgs particle, A Universe from Nothing uses Krauss’s characteristic wry humor and wonderfully clear explanations to take us back to the beginning of the beginning, presenting the most recent evidence for how our universe evolved—and the implications for how it’s going to end.
Provocative, challenging, and delightfully readable, this is a game-changing look at the most basic underpinning of existence and a powerful antidote to outmoded philosophical, religious, and scientific thinking.
Space and time form the very fabric of the cosmos. Yet they remain among the most mysterious of concepts. Is space an entity? Why does time have a direction? Could the universe exist without space and time? Can we travel to the past? Greene has set himself a daunting task: to explain non-intuitive, mathematical concepts like String Theory, the Heisenberg Uncertainty Principle, and Inflationary Cosmology with analogies drawn from common experience. From Newton’s unchanging realm in which space and time are absolute, to Einstein’s fluid conception of spacetime, to quantum mechanics’ entangled arena where vastly distant objects can instantaneously coordinate their behavior, Greene takes us all, regardless of our scientific backgrounds, on an irresistible and revelatory journey to the new layers of reality that modern physics has discovered lying just beneath the surface of our everyday world.
—Bill Gates (May, 2017)
Selected by The New York Times Book Review as a Notable Book of the Year
The author of the forthcoming Enlightenment Now (February 2018) and The New York Times bestseller The Stuff of Thought offers a controversial history of violence.
Faced with the ceaseless stream of news about war, crime, and terrorism, one could easily think we live in the most violent age ever seen. Yet as New York Times bestselling author Steven Pinker shows in this startling and engaging new work, just the opposite is true: violence has been diminishing for millenia and we may be living in the most peaceful time in our species's existence. For most of history, war, slavery, infanticide, child abuse, assassinations, programs, gruesom punishments, deadly quarrels, and genocide were ordinary features of life. But today, Pinker shows (with the help of more than a hundred graphs and maps) all these forms of violence have dwindled and are widely condemned. How has this happened?
This groundbreaking book continues Pinker's exploration of the esesnce of human nature, mixing psychology and history to provide a remarkable picture of an increasingly nonviolent world. The key, he explains, is to understand our intrinsic motives--the inner demons that incline us toward violence and the better angels that steer us away--and how changing circumstances have allowed our better angels to prevail. Exploding fatalist myths about humankind's inherent violence and the curse of modernity, this ambitious and provocative book is sure to be hotly debated in living rooms and the Pentagon alike, and will challenge and change the way we think about our society.
From Sam Harris, neuroscientist and author of numerous New York Times bestselling books, Waking Up is for the twenty percent of Americans who follow no religion but who suspect that important truths can be found in the experiences of such figures as Jesus, the Buddha, Lao Tzu, Rumi, and the other saints and sages of history. Throughout this book, Harris argues that there is more to understanding reality than science and secular culture generally allow, and that how we pay attention to the present moment largely determines the quality of our lives.
Waking Up is part memoir and part exploration of the scientific underpinnings of spirituality. No other book marries contemplative wisdom and modern science in this way, and no author other than Sam Harris—a scientist, philosopher, and famous skeptic—could write it.
In this illustrated history, Steven Johnson explores the history of innovation over centuries, tracing facets of modern life (refrigeration, clocks, and eyeglass lenses, to name a few) from their creation by hobbyists, amateurs, and entrepreneurs to their unintended historical consequences. Filled with surprising stories of accidental genius and brilliant mistakes—from the French publisher who invented the phonograph before Edison but forgot to include playback, to the Hollywood movie star who helped invent the technology behind Wi-Fi and Bluetooth—How We Got to Now investigates the secret history behind the everyday objects of contemporary life.
In his trademark style, Johnson examines unexpected connections between seemingly unrelated fields: how the invention of air-conditioning enabled the largest migration of human beings in the history of the species—to cities such as Dubai or Phoenix, which would otherwise be virtually uninhabitable; how pendulum clocks helped trigger the industrial revolution; and how clean water made it possible to manufacture computer chips. Accompanied by a major six-part television series on PBS, How We Got to Now is the story of collaborative networks building the modern world, written in the provocative, informative, and engaging style that has earned Johnson fans around the globe.
In this enlightening book, Sam Harris argues that this truth about the human mind does not undermine morality or diminish the importance of social and political freedom, but it can and should change the way we think about some of the most important questions in life.
“A glorious book . . . A spirited defense of science . . . From the first page to the last, this book is a manifesto for clear thought.”—Los Angeles Times
How can we make intelligent decisions about our increasingly technology-driven lives if we don’t understand the difference between the myths of pseudoscience and the testable hypotheses of science? Pulitzer Prize-winning author and distinguished astronomer Carl Sagan argues that scientific thinking is critical not only to the pursuit of truth but to the very well-being of our democratic institutions.
Casting a wide net through history and culture, Sagan examines and authoritatively debunks such celebrated fallacies of the past as witchcraft, faith healing, demons, and UFOs. And yet, disturbingly, in today's so-called information age, pseudoscience is burgeoning with stories of alien abduction, channeling past lives, and communal hallucinations commanding growing attention and respect. As Sagan demonstrates with lucid eloquence, the siren song of unreason is not just a cultural wrong turn but a dangerous plunge into darkness that threatens our most basic freedoms.
Praise for The Demon-Haunted World
“Powerful . . . A stirring defense of informed rationality. . . Rich in surprising information and beautiful writing.”—The Washington Post Book World
“A clear vision of what good science means and why it makes a difference. . . . A testimonial to the power of science and a warning of the dangers of unrestrained credulity.”—The Sciences
“Passionate.”—San Francisco Examiner-Chronicle
Sam Harris’s first book, The End of Faith, ignited a worldwide debate about the validity of religion. In the aftermath, Harris discovered that most people—from religious fundamentalists to nonbelieving scientists—agree on one point: science has nothing to say on the subject of human values. Indeed, our failure to address questions of meaning and morality through science has now become the most common justification for religious faith. It is also the primary reason why so many secularists and religious moderates feel obligated to "respect" the hardened superstitions of their more devout neighbors.
In this explosive new book, Sam Harris tears down the wall between scientific facts and human values, arguing that most people are simply mistaken about the relationship between morality and the rest of human knowledge. Harris urges us to think about morality in terms of human and animal well-being, viewing the experiences of conscious creatures as peaks and valleys on a "moral landscape." Because there are definite facts to be known about where we fall on this landscape, Harris foresees a time when science will no longer limit itself to merely describing what people do in the name of "morality"; in principle, science should be able to tell us what we ought to do to live the best lives possible.
Bringing a fresh perspective to age-old questions of right and wrong and good and evil, Harris demonstrates that we already know enough about the human brain and its relationship to events in the world to say that there are right and wrong answers to the most pressing questions of human life. Because such answers exist, moral relativism is simply false—and comes at increasing cost to humanity. And the intrusions of religion into the sphere of human values can be finally repelled: for just as there is no such thing as Christian physics or Muslim algebra, there can be no Christian or Muslim morality.
Using his expertise in philosophy and neuroscience, along with his experience on the front lines of our "culture wars," Harris delivers a game-changing book about the future of science and about the real basis of human cooperation.
"Vivid . . . impressive. . . . Splendidly informative."—The New York Times
"A tour de force."—Salon
Already internationally acclaimed for his elegant, lucid writing on the most challenging notions in modern physics, Sean Carroll is emerging as one of the greatest humanist thinkers of his generation as he brings his extraordinary intellect to bear not only on Higgs bosons and extra dimensions but now also on our deepest personal questions: Where are we? Who are we? Are our emotions, our beliefs, and our hopes and dreams ultimately meaningless out there in the void? Do human purpose and meaning fit into a scientific worldview?
In short chapters filled with intriguing historical anecdotes, personal asides, and rigorous exposition, readers learn the difference between how the world works at the quantum level, the cosmic level, and the human level—and then how each connects to the other. Carroll's presentation of the principles that have guided the scientific revolution from Darwin and Einstein to the origins of life, consciousness, and the universe is dazzlingly unique.
Carroll shows how an avalanche of discoveries in the past few hundred years has changed our world and what really matters to us. Our lives are dwarfed like never before by the immensity of space and time, but they are redeemed by our capacity to comprehend it and give it meaning.
The Big Picture is an unprecedented scientific worldview, a tour de force that will sit on shelves alongside the works of Stephen Hawking, Carl Sagan, Daniel Dennett, and E. O. Wilson for years to come.
Sparked by a controversial debate in February 2014, Bill Nye has set off on an energetic campaign to spread awareness of evolution and the powerful way it shapes our lives. In Undeniable: Evolution and the Science of Creation, he explains why race does not really exist; evaluates the true promise and peril of genetically modified food; reveals how new species are born, in a dog kennel and in a London subway; takes a stroll through 4.5 billion years of time; and explores the new search for alien life, including aliens right here on Earth.
With infectious enthusiasm, Bill Nye shows that evolution is much more than a rebuttal to creationism; it is an essential way to understand how nature works—and to change the world. It might also help you get a date on a Saturday night.
Men of Mathematics provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension. Bell breaks down this majestic history of ideas into a series of engrossing biographies of the great mathematicians who made progress possible—and who also led intriguing, complicated, and often surprisingly entertaining lives.
Never pedantic or dense, Bell writes with clarity and simplicity to distill great mathematical concepts into their most understandable forms for the curious everyday reader. Anyone with an interest in math may learn from these rich lessons, an advanced degree or extensive research is never necessary.
The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples—from ice cream scoops and poker hands to measuring mountains and making magic squares—this book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You'll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus, but you'll also have fun fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks that will make you look like a math genius!
A mathematician who is known throughout the world as the “mathemagician,” Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand. In The Magic of Math, Benjamin does more than just teach skills: with a tip of his magic hat, he takes you on as his apprentice to teach you how to appreciate math the way he does. He motivates you to learn something new about how to solve for x, because there is real pleasure to be found in the solution to a challenging problem or in using numbers to do something useful. But what he really wants you to do is be able to figure out why, for that's where you'll find the real beauty, power, and magic of math.
If you are already someone who likes math, this book will dazzle and amuse you. If you never particularly liked or understood math, Benjamin will enlighten you and—with a wave of his magic wand—turn you into a math lover.
With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age.
This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context. Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.
Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others. For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others.
"The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.
Benoit Mandelbrot, the creator of fractal geometry, has significantly improved our understanding of, among other things, financial variability and erratic physical phenomena. In The Fractalist, Mandelbrot recounts the high points of his life with exuberance and an eloquent fluency, deepening our understanding of the evolution of his extraordinary mind. We begin with his early years: born in Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family to Paris in the 1930s, where he was mentored by an eminent mathematician uncle. During World War II, as he stayed barely one step ahead of the Nazis until France was liberated, he studied geometry on his own and dreamed of using it to solve fresh, real-world problems. We observe his unusually broad education in Europe, and later at Caltech, Princeton, and MIT. We learn about his thirty-five-year affiliation with IBM’s Thomas J. Watson Research Center and his association with Harvard and Yale. An outsider to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden laws governing utter roughness, turbulence, and chaos.
Here is a remarkable story of both the man’s life and his unparalleled contributions to science, mathematics, and the arts.
The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
Collins's faith in God has been confirmed and enhanced by the revolutionary discoveries in biology that he has helped to oversee. He has absorbed the arguments for atheism of many scientists and pundits, and he can refute them. Darwinian evolution occurs, yet, as he explains, it cannot fully explain human nature -- evolution can and must be directed by God. He offers an inspiring tour of the human genome to show the miraculous nature of God's instruction book. Sure to be compared with C.S. Lewis's Mere Christianity, this is a stunning document, whether you are a believer, a seeker, or an atheist.
Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives.
Using seventeen of our most crucial equations--including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time--Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries.
An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.
Dr. Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations.
As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics.
Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself.
Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery.
For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs.Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.
Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.
On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.
In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.
The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.
From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.
Now, Carr expands his argument into the most compelling exploration of the Internet’s intellectual and cultural consequences yet published. As he describes how human thought has been shaped through the centuries by “tools of the mind”—from the alphabet to maps, to the printing press, the clock, and the computer—Carr interweaves a fascinating account of recent discoveries in neuroscience by such pioneers as Michael Merzenich and Eric Kandel. Our brains, the historical and scientific evidence reveals, change in response to our experiences. The technologies we use to find, store, and share information can literally reroute our neural pathways.
Building on the insights of thinkers from Plato to McLuhan, Carr makes a convincing case that every information technology carries an intellectual ethic—a set of assumptions about the nature of knowledge and intelligence. He explains how the printed book served to focus our attention, promoting deep and creative thought. In stark contrast, the Internet encourages the rapid, distracted sampling of small bits of information from many sources. Its ethic is that of the industrialist, an ethic of speed and efficiency, of optimized production and consumption—and now the Net is remaking us in its own image. We are becoming ever more adept at scanning and skimming, but what we are losing is our capacity for concentration, contemplation, and reflection.
Part intellectual history, part popular science, and part cultural criticism, The Shallows sparkles with memorable vignettes—Friedrich Nietzsche wrestling with a typewriter, Sigmund Freud dissecting the brains of sea creatures, Nathaniel Hawthorne contemplating the thunderous approach of a steam locomotive—even as it plumbs profound questions about the state of our modern psyche. This is a book that will forever alter the way we think about media and our minds.
Arguing that we must take seriously the possibility that the Nazis were in some measure correct, Gimbel examines Einstein and his work to explore how beliefs, background, and environment may—or may not—have influenced the work of the scientist. You cannot understand Einstein’s science, Gimbel declares, without knowing the history, religion, and philosophy that influenced it.
No one, especially Einstein himself, denies Einstein's Jewish heritage, but many are uncomfortable saying that he was being a Jew while he was at his desk working. To understand what "Jewish" means for Einstein’s work, Gimbel first explores the many definitions of "Jewish" and asks whether there are elements of Talmudic thinking apparent in Einstein’s theory of relativity. He applies this line of inquiry to other scientists, including Isaac Newton, René Descartes, Sigmund Freud, and Émile Durkheim, to consider whether their specific religious beliefs or backgrounds manifested in their scientific endeavors.
Einstein's Jewish Science intertwines science, history, philosophy, theology, and politics in fresh and fascinating ways to solve the multifaceted riddle of what religion means—and what it means to science. There are some senses, Gimbel claims, in which Jews can find a special connection to E = mc2, and this claim leads to the engaging, spirited debate at the heart of this book.
"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."
With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.
As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex.
Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.
From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.
Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.
Do long division as the ancient Egyptians did! Solve quadratic equations like the Babylonians! Study geometry just as students did in Euclid's day! This unique text offers students of mathematics an exciting and enjoyable approach to geometry and number systems. Written in a fresh and thoroughly diverting style, the text — while designed chiefly for classroom use — will appeal to anyone curious about mathematical inscriptions on Egyptian papyri, Babylonian cuneiform tablets, and other ancient records.
The authors have produced an illuminated volume that traces the history of mathematics — beginning with the Egyptians and ending with abstract foundations laid at the end of the nineteenth century. By focusing on the actual operations and processes outlined in the text, students become involved in the same problems and situations that once confronted the ancient pioneers of mathematics. The text encourages readers to carry out fundamental algebraic and geometric operations used by the Egyptians and Babylonians, to examine the roots of Greek mathematics and philosophy, and to tackle still-famous problems such as squaring the circle and various trisectorizations.
Unique in its detailed discussion of these topics, this book is sure to be welcomed by a broad range of interested readers. The subject matter is suitable for prospective elementary and secondary school teachers, as enrichment material for high school students, and for enlightening the general reader. No specialized or advanced background beyond high school mathematics is required.
This classroom-tested book covers the main subjects of a standard undergraduate probability course, including basic probability rules, standard models for describing collections of data, and the laws of large numbers. It also discusses several more advanced topics, such as the ballot theorem, the arcsine law, and random walks, as well as some specialized poker issues, such as the quantification of luck and skill in Texas Hold’em. Homework problems are provided at the end of each chapter.
The author includes examples of actual hands of Texas Hold’em from the World Series of Poker and other major tournaments and televised games. He also explains how to use R to simulate Texas Hold’em tournaments for student projects. R functions for running the tournaments are freely available from CRAN (in a package called holdem).
See Professor Schoenberg discuss the book.
With coverage spanning the foundations of origami construction and advanced methods using both paper and pencil and custom-built free software, Origami Design Secrets helps readers cultivate the intuition and skills necessary to develop their own designs. It takes them beyond merely following a recipe to crafting a work of art.
For every problem mathematicians solve, another awaits to perplex and galvanize them. Such challenges offer a tantalizing glimpse of the field's unlimited potential and keep mathematicians looking toward the horizons of intellectual possibility.
In Visions of Infinity, Ian Stewart explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. Stewart describes solved problems as well as those like the P/NP problem, which could easily remain unproved for another hundred years.
An approachable and illuminating history of mathematics as told through fourteen of its greatest problems, Visions of Infinity reveals how mathematics the world over have risen to meet the challenges set by their predecessors-and how the enigmas of the past inevitably surrender to the powerful techniques of the present.
Julian Havil explores Napier’s original development of logarithms, the motivations for his approach, and the reasons behind certain adjustments to them. Napier’s inventive mathematical ideas also include formulas for solving spherical triangles, "Napier’s Bones" (a more basic but extremely popular alternative device for calculation), and the use of decimal notation for fractions and binary arithmetic. Havil also considers Napier’s study of the Book of Revelation, which led to his prediction of the Apocalypse in his first book, A Plaine Discovery of the Whole Revelation of St. John—the work for which Napier believed he would be most remembered.
John Napier assesses one man’s life and the lasting influence of his advancements on the mathematical sciences and beyond.
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.
"Sweeping, erudite, sharply argued, and fun to read..also highly persuasive." -Time
Now updated with a new afterword
One of the world's leading experts on language and the mind explores the idea of human nature and its moral, emotional, and political colorings. With characteristic wit, lucidity, and insight, Pinker argues that the dogma that the mind has no innate traits-a doctrine held by many intellectuals during the past century-denies our common humanity and our individual preferences, replaces objective analyses of social problems with feel-good slogans, and distorts our understanding of politics, violence, parenting, and the arts. Injecting calm and rationality into debates that are notorious for ax-grinding and mud-slinging, Pinker shows the importance of an honest acknowledgment of human nature based on science and common sense.
Awake Mathemagician Inside You !
- Can you multiply 44465 by 8888 in single line ?
- Can you figure out day on 24/5/2014 in 10 seconds ?
- Can you divide 123456 by 44444 instantaneously ?
- Can you raise number to any integral power ?
- Can you determine divisibility of 124356 by 37 just in 5 seconds ?
- Can you find square root, cube root or any root of any number without using calculator ?
- Can you convert (2134)6 = ( ? )12 in 20 seconds ?
SILENT FEATURES OF BOOK
Introduce VJ's universal divisibility test for all number !
Reveal unique secret behind speed mathematics !
Explain concept behind each method !
Unifies Vedic math, Trachtenberg system and modern math .
Presents faster method for n'th root of any number !
Give quicker methods for converting number from one base to other!
Introduce one-line method to compute root of any number or polynomial equation (VJ's matrix method)
Introduce novel pattern called golden pattern
Golden Lemma and Golden pattern
- Simplify everything right from polynomial multiplication, division , power , root , inverse etc.
- Help to build generic module in high level language to carry out basic operation on polynomial
- Parallel multiplication architecture for multiprocessor environment
- Golden pattern(process) is applicable in many area of algebra.
- Golden pattern is superior over vertically crosswise pattern mentioned in Vedic math.
Now–a -days speed math system ( like Vedic Mathematics , Trachtenberg System) are gaining widespread popularity among students as well as teachers. Speed math refers to faster methods and techniques to solve arithmetic calculation mentally. It saves considerable amount of time in competitive exam. So it is worthy to study speed math.
In order to compute given calculation mentally, one need to recall right kind of specific method (shortcut) out of 1000's. Instead of doing so,
i) Is it possible to compute any arithmetic operation (like addition, multiplication) quickly by using scientific approach ?
ii) Is it possible to derive all methods in speed math by using unique principle ?
iii) Is there any unique secret (principle) behind speed mathematics ?
After researching speed math about 2-3 years, I realized that there is unique secret (principle) behind speed mathematics !! This book explains entire speed mathematics by using single principle and gives introduction to new number system called as global number system. It extends VM framework in some of the area like divisibility, n'th root.
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" Essence of mathematics lies in its freedom" - Georg Cantor
" Pure mathematics is, in its way, the poetry of logical ideas." - Albert Einstein
" As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. " - Albert Einstein
“ In my opinion, all things in nature occur mathematically.”
― René Descartes
" Mathematical Knowledge adds vigour to the mind, free it from prejudices & superstition " - John Arbuthnot
Some mathematician, I believe, has said that true pleasure lies not in the discovery of truth, but in the search for it." -Tolstoy
"Mathematics is the queen of science, and arithmetic the queen of mathematics."
- Carl Friedrich Gauss
"Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things." - Isaac Newton
"Quantification is ultimate goal of mathematics.." - V. B. Jadhav
"Truth is ultimate goal of supreme knowledge.." - V.B. Jadhav
Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism.
Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design explains the process of designing an origami pattern. It answers the questions "how is a tessellation folded" and "what are the further possibilities."
The author introduces an innovative pleat pattern technique of origami design that is easily accessible to anyone who enjoys the geometry of paper. The book begins with basic forms and systematically builds upon them to teach a limitless number of patterns. It then describes a process of design for the building blocks themselves. At the end, what emerges is a fascinating art form that will enrich folders for many years.
Unlike standard, project-based origami books, Six Simple Twists focuses on how to design rather than construct. This leads to a better understanding of more complicated tessellations at the advanced level.
"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."
(David Parrott, Australian Mathematical Society)
"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community."
(European Mathematical Society)
"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."
(Denis Bonheure, Bulletin of the Belgian Society)
This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.
The quest for the circle in the square, the trisected angle, duplicated cube and other straight-edge-compass constructions may be conveniently divided into three periods: from the Greeks, to seventeenth-century calculus and analytic geometry, to nineteenth-century sophistication in irrational and transcendental numbers. Mathematics teacher Benjamin Bold devotes a chapter to each problem, with additional chapters on complex numbers and analytic criteria for constructability. The author guides amateur straight-edge puzzlists into these fascinating complexities with commentary and sets of problems after each chapter. Some knowledge of calculus will enable readers to follow the problems; full solutions are given at the end of the book.
Students of mathematics and geometry, anyone who would like to challenge the Greeks at their own game and simultaneously delve into the development of modern mathematics, will appreciate this book. Find out how Gauss decided to make mathematics his life work upon waking one morning with a vision of a 17-sided polygon in his head; discover the crucial significance of eπi = -1, "one of the most amazing formulas in all of mathematics." These famous problems, clearly explicated and diagrammed, will amaze and edify curious students and math connoisseurs.