But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. 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.

    Brian Greene, one of the world's leading string theorists, peels away the layers of mystery surrounding string theory to reveal a universe that consists of eleven dimensions, where the fabric of space tears and repairs itself, and all matter—from the smallest quarks to the most gargantuan supernovas—is generated by the vibrations of microscopically tiny loops of energy.Today physicists and mathematicians throughout the world are feverishly working on one of the most ambitious theories ever proposed: superstring theory. String theory, as it is often called, is the key to the Unified Field Theory that eluded Einstein for more than thirty years. Finally, the century-old antagonism between the large and the small-General Relativity and Quantum Theory-is resolved. String theory proclaims that all of the wondrous happenings in the universe, from the frantic dancing of subatomic quarks to the majestic swirling of heavenly galaxies, are reflections of one grand physical principle and manifestations of one single entity: microscopically tiny vibrating loops of energy, a billionth of a billionth the size of an atom. In this brilliantly articulated and refreshingly clear book, Greene relates the scientific story and the human struggle behind twentieth-century physics' search for a theory of everything.Through the masterful use of metaphor and analogy, The Elegant Universe makes some of the most sophisticated concepts ever contemplated viscerally accessible and thoroughly entertaining, bringing us closer than ever to understanding how the universe works.

    Season 1, comprising 20 essays totaling approximately 30,000 words, is written by Venkatesh Rao and illustrated by Grace Witherell. This inaugural season is an in-depth exploration of Marc Andreessen’s observation that “software is eating the world.”

    The work is powerful and has established a passionate following as well as harsh critics.

    Our senses are not equipped to see the universe as it is, and routinely let us down in that quest—the world appears flat, the stars seem fixed in the heavens. That is why we invented math and science—the ultimate toolkit to explain how the world really works.In this book, mathematician Hannah Fry and geneticist Adam Rutherford investigate everyday mysteries (does your dog love you?) alongside the burning questions of time, space, and the origin of the universe. What will the end of the world look like, and when will it happen? What is time, and where does it come from? Approaching these questions and more with science and math rigorous and playful, Rutherford and Fry celebrate the weirdness of the cosmos, and reveal its secrets along the way.

    think of the artist or inventor all-consumedby his work, the boxer who lays his body and mind on the line in every fight, or the gardener whose mind is perfectly still among his creation.Have you found your Ikigai yet? This book is for you.In a series of essays on philosophy, history, strategy, planning, and achieving, this book is about living purposefully and with meaning.

    The freedom to explore and exchange - whether it's goods, ideas or people - has led to stunning achievements in science, technology and culture. As a result, we live at a time of unprecedented wealth and opportunity. So why are we so intent on ruining it? From Stone Age hunter-gatherers to contemporary Chinese-American relations, Open explores how across time and cultures, we have struggled with a constant tension between our yearning for co-operation and our profound need for belonging. Providing a bold new framework for understanding human history, bestselling author and thinker Johan Norberg examines why we're often uncomfortable with openness - but also why it is essential for progress. Part sweeping history and part polemic, this urgent book makes a compelling case for why an open world with an open economy is worth fighting for more than ever.

    Feed Your Brain   Tastier than a twizzler yet more protein-packed than a spinach smoothie, Brain Candy is guaranteed to entertain your brain—even as it reveals hundreds of secrets behind what’s driving that electric noodle inside your skull.    These delicious and nutritious pages are packed with bits of bite-sized goodness swiped from the bleeding edge of brain science (including the reason why reading these words is changing your hippocampus at this very moment!) Shelved alongside these succulent neurological nuggets are challenging puzzles and paradoxes, eye-opening perception tests and hacks, fiendish personality quizzes and genius testers, and a grab bag of recurring treats including Eye Hacks, Algebraic Eight Ball, iDread, Wild Kingdom, and Logic of Illogic.     Should you look between these covers and inhale the deliciously cherry-flavored scents of knowledge within, you will grow your grey matter while discovering:  • Why you should be writing bad poetry• The simple keys to brain training• What trust smells like  • The origins of human morality• Why expensive wine always tastes better• The truth about brain sweat • How your diet might be making you dumb• The secrets of game theory• Why economists hate psychology • The mental benefits of coffee and cigarettes • How to really spot a liar• Why you can’t make me eat pie• The benefits of daydreaming • Four simple secrets to persuasion• Why your barin’s fzzuy ligoc alowls you to raed this• How to brainwash friends and family• The science of body language• What pigeons know about art   …And much, much more.

    Drawing on their hugely popular BBC Radio 4 show More or Less,, journalist Michael Blastland and internationally known economist Andrew Dilnot delight, amuse, and convert American mathphobes by showing how our everyday experiences make sense of numbers. The radical premise of The Numbers Game is to show how much we already know, and give practical ways to use our knowledge to become cannier consumers of the media. In each concise chapter, the authors take on a different theme—such as size, chance, averages, targets, risk, measurement, and data—and present it as a memorable and entertaining story. If you’ve ever wondered what “average” really means, whether the scare stories about cancer risk should convince you to change your behavior, or whether a story you read in the paper is biased (and how), you need this book. Blastland and Dilnot show how to survive and thrive on the torrent of numbers that pours through everyday life. It’s the essential guide to every cause you love or hate, and every issue you follow, in the language everyone uses.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    Gonick’s The Cartoon Guide to Calculus is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier Cartoon Guide to Physics and Cartoon History of the Modern World, will prove a boon to students, educators, and eager learners everywhere.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    Do you have to be born musical to become musical? Do you have to start at the age of six? Using the tools of his day job as a cognitive psychologist, Gary Marcus becomes his own guinea pig as he takes up the guitar. In a powerful and incisive look at how both children and adults become musical, Guitar Zero traces Marcus’s journey, what he learned, and how anyone else can learn, too. A groundbreaking peek into the origins of music in the human brain, this musical journey is also an empowering tale of the mind’s enduring plasticity. Marcus investigates the most effective ways to train body and brain to learn to play an instrument, in a quest that takes him from Suzuki classes to guitar gods. From deliberate and efficient practicing techniques to finding the right music teacher, Marcus translates his own experience—as well as reflections from world-renowned musicians—into practical advice for anyone hoping to become musical, or to learn a new skill.Guitar Zero debunks the popular theory of an innate musical instinct while simultaneously challenging the idea that talent is only a myth. While standing the science of music on its head, Marcus brings new insight into humankind’s most basic question: what counts as a life well lived? Does one have to become the next Jimi Hendrix to make a passionate pursuit worthwhile, or can the journey itself bring the brain lasting satisfaction?For all those who have ever set out to play an instrument—or wish that they could—Guitar Zero is an inspiring and fascinating look at the pursuit of music, the mechanics of the mind, and the surprising rewards that come from following one’s dreams.

    In our ever-more-polarized society, there’s at least one thing we still agree on: The world is overrun with misinformation, faulty logic, and the gullible followers who buy into it all. Of course, we’re not among them—are we? Scientist David Robert Grimes is on a mission to expose the logical fallacies and cognitive biases that drive our discourse on a dizzying array of topics–from vaccination to abortion, 9/11 conspiracy theories to dictatorial doublespeak, astrology to alternative medicine, and wrongful convictions to racism. But his purpose in Good Thinking isn’t to shame or place blame. Rather, it’s to interrogate our own assumptions–to develop our eye for the glimmer of truth in a vast sea of dubious sources–in short, to think critically. Grimes’s expert takedown of irrationality is required reading for anyone wondering why bad thinking persists and how we can defeat it. Ultimately, no one changes anyone else’s mind; we can only change our own–and give others the tools to do the same.