The Nothing that is

A Natural History of Zero

Author: Robert Kaplan

Publisher: Oxford University Press on Demand

ISBN: 0195128427

Category: Mathematics

Page: 225

View: 4934

The value of nothing is explored in rich detail as the author reaches back as far as the ancient Sumerians to find evidence that humans have long struggled with the concept of zero, from the Greeks who may or may not have known of it, to the East where it was first used, to the modern-day desktop PC, which uses it as an essential letter in its computational alphabet.

The Nothing that Is

A Natural History of Zero

Author: Robert Kaplan

Publisher: Oxford University Press

ISBN: 9780198029458

Category: Science

Page: 240

View: 9622

A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. 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 mathematics as 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 figure large 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 treating zero 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 like double-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 speak only 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 not only 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. The beauty 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.

The Nothing that Is

A Natural History of Zero

Author: Robert Kaplan

Publisher: Oxford University Press

ISBN: 0199880891

Category: Science

Page: 240

View: 5596

A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. 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 mathematics as 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 figure large 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 treating zero 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 like double-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 speak only 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 not only 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. The beauty 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.

The Art of the Infinite

The Pleasures of Mathematics

Author: Robert Kaplan,Ellen Kaplan

Publisher: Bloomsbury Publishing USA

ISBN: 160819888X

Category: Mathematics

Page: 416

View: 6509

A classic now available in a new, expanded edition-a witty, literate, and accessible tour of the world of mathematics. The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Robert and Ellen Kaplan guide us through the "Republic of Numbers,†? where we meet both its upstanding citizens and its more shadowy dwellers; and transport us across the plane of geometry into the unlikely realm where parallel lines meet. The journey is enriched by deft character studies of great mathematicians (and equally colorful lesser ones). And as we go deeper into infinity, we explore the most profound mystery of mathematics: Are its principles eternal truths that we discover? Or ones that we invent?

The Book of Nothing

Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

Author: John D. Barrow

Publisher: Vintage

ISBN: 0307554813

Category: Science

Page: 384

View: 9784

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

Finding Zero

A Mathematician's Odyssey to Uncover the Origins of Numbers

Author: Amir D. Aczel

Publisher: St. Martin's Press

ISBN: 1466879106

Category: Mathematics

Page: 256

View: 1012

The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is an adventure filled saga of Amir Aczel's lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride. The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from.

Zero

The Biography of a Dangerous Idea

Author: Charles Seife

Publisher: Penguin

ISBN: 9780140296471

Category: Biography & Autobiography

Page: 248

View: 6722

The history of a controversial but important number begins with its inventors, the Babylonians, and follows its tumultuous and fascinating story to the present era of supercomputers and quantum physics. Reprint.

Out of the Labyrinth

Setting Mathematics Free

Author: Robert Kaplan,Ellen Kaplan

Publisher: Bloomsbury Publishing USA

ISBN: 1608198898

Category: Mathematics

Page: 256

View: 9207

"In this sparkling narrative, mathematics is indeed set free.†? -Michael Shermer Who hasn't feared the math Minotaur in its labyrinth of abstractions? The subject can seem convoluted and forbidding. Yet to do mathematics is to wrestle with "accessible mysteries†?-and Out of the Labyrinth shows how exhilarating the challenge can be. Robert and Ellen Kaplan are founders of the Math Circle, a pioneering learning program begun at Harvard in 1994 and now spreading around the world. In their classrooms students ages six to sixty have discovered mathematics as the highest form of intellectual play, while exploring topics that range from Roman numerals to quantum mechanics. The Kaplans reveal the secrets of their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics. Stocked with puzzles, colorful anecdotes, and insights from the authors' own teaching experience, Out of the Labyrinth is both an engaging and practical guide for parents and educators, and a treasure chest of mathematical discoveries. For any reader who has felt the excitement of mathematical discovery-or tried to convey it to someone else-this volume will be a delightful and valued companion.

Wonder of Wonders

A Cultural History of Fiddler on the Roof

Author: Alisa Solomon

Publisher: Metropolitan Books

ISBN: 0805095292

Category: Performing Arts

Page: 448

View: 517

A sparkling and eye-opening history of the Broadway musical that changed the world In the half-century since its premiere, Fiddler on the Roof has had an astonishing global impact. Beloved by audiences the world over, performed from rural high schools to grand state theaters, Fiddler is a supremely potent cultural landmark. In a history as captivating as its subject, award-winning drama critic Alisa Solomon traces how and why the story of Tevye the milkman, the creation of the great Yiddish writer Sholem-Aleichem, was reborn as blockbuster entertainment and a cultural touchstone, not only for Jews and not only in America. It is a story of the theater, following Tevye from his humble appearance on the New York Yiddish stage, through his adoption by leftist dramatists as a symbol of oppression, to his Broadway debut in one of the last big book musicals, and his ultimate destination—a major Hollywood picture. Solomon reveals how the show spoke to the deepest conflicts and desires of its time: the fraying of tradition, generational tension, the loss of roots. Audiences everywhere found in Fiddler immediate resonance and a usable past, whether in Warsaw, where it unlocked the taboo subject of Jewish history, or in Tokyo, where the producer asked how Americans could understand a story that is "so Japanese." Rich, entertaining, and original, Wonder of Wonders reveals the surprising and enduring legacy of a show about tradition that itself became a tradition. Wonder of wonders, miracle of miracles.

The Grand Design

Author: Stephen Hawking,Leonard Mlodinow

Publisher: Bantam

ISBN: 0553907077

Category: Science

Page: 208

View: 954

#1 NEW YORK TIMES BESTSELLER When and how did the universe begin? Why are we here? What is the nature of reality? Is the apparent “grand design” of our universe evidence of a benevolent creator who set things in motion—or does science offer another explanation? In this startling and lavishly illustrated book, Stephen Hawking and Leonard Mlodinow present the most recent scientific thinking about these and other abiding mysteries of the universe, in nontechnical language marked by brilliance and simplicity. According to quantum theory, the cosmos does not have just a single existence or history. The authors explain that we ourselves are the product of quantum fluctuations in the early universe, and show how quantum theory predicts the “multiverse”—the idea that ours is just one of many universes that appeared spontaneously out of nothing, each with different laws of nature. They conclude with a riveting assessment of M-theory, an explanation of the laws governing our universe that is currently the only viable candidate for a “theory of everything”: the unified theory that Einstein was looking for, which, if confirmed, would represent the ultimate triumph of human reason.

The Value of Nothing

How to Reshape Market Society and Redefine Democracy

Author: Raj Patel

Publisher: Picador

ISBN: 9781429982627

Category: Political Science

Page: 256

View: 3202

"A deeply though-provoking book about the dramatic changes we must make to save the planet from financial madness."--Naomi Klein, author of The Shock Doctrine Opening with Oscar Wilde's observation that "nowadays people know the price of everything and the value of nothing," Patel shows how our faith in prices as a way of valuing the world is misplaced. He reveals the hidden ecological and social costs of a hamburger (as much as $200), and asks how we came to have markets in the first place. Both the corporate capture of government and our current financial crisis, Patel argues, are a result of our democratically bankrupt political system. If part one asks how we can rebalance society and limit markets, part two answers by showing how social organizations, in America and around the globe, are finding new ways to describe the world's worth. If we don't want the market to price every aspect of our lives, we need to learn how such organizations have discovered democratic ways in which people, and not simply governments, can play a crucial role in deciding how we might share our world and its resources in common. This short, timely and inspiring book reveals that our current crisis is not simply the result of too much of the wrong kind of economics. While we need to rethink our economic model, Patel argues that the larger failure beneath the food, climate and economic crises is a political one. If economics is about choices, Patel writes, it isn't often said who gets to make them. The Value of Nothing offers a fresh and accessible way to think about economics and the choices we will all need to make in order to create a sustainable economy and society.

Trespassing on Einstein's Lawn

A Father, a Daughter, the Meaning of Nothing, and the Beginning of Everything

Author: Amanda Gefter

Publisher: Bantam

ISBN: 034553963X

Category: Science

Page: 432

View: 8267

NAMED ONE OF THE BEST BOOKS OF THE YEAR BY KIRKUS REVIEWS In a memoir of family bonding and cutting-edge physics for readers of Brian Greene’s The Hidden Reality and Jim Holt’s Why Does the World Exist?, Amanda Gefter tells the story of how she conned her way into a career as a science journalist—and wound up hanging out, talking shop, and butting heads with the world’s most brilliant minds. At a Chinese restaurant outside of Philadelphia, a father asks his fifteen-year-old daughter a deceptively simple question: “How would you define nothing?” With that, the girl who once tried to fail geometry as a conscientious objector starts reading up on general relativity and quantum mechanics, as she and her dad embark on a life-altering quest for the answers to the universe’s greatest mysteries. Before Amanda Gefter became an accomplished science writer, she was a twenty-one-year-old magazine assistant willing to sneak her and her father, Warren, into a conference devoted to their physics hero, John Wheeler. Posing as journalists, Amanda and Warren met Wheeler, who offered them cryptic clues to the nature of reality: The universe is a self-excited circuit, he said. And, The boundary of a boundary is zero. Baffled, Amanda and Warren vowed to decode the phrases—and with them, the enigmas of existence. When we solve all that, they agreed, we’ll write a book. Trespassing on Einstein’s Lawn is that book, a memoir of the impassioned hunt that takes Amanda and her father from New York to London to Los Alamos. Along the way, they bump up against quirky science and even quirkier personalities, including Leonard Susskind, the former Bronx plumber who invented string theory; Ed Witten, the soft-spoken genius who coined the enigmatic M-theory; even Stephen Hawking. What they discover is extraordinary: the beginnings of a monumental paradigm shift in cosmology, from a single universe we all share to a splintered reality in which each observer has her own. Reality, the Gefters learn, is radically observer-dependent, far beyond anything of which Einstein or the founders of quantum mechanics ever dreamed—with shattering consequences for our understanding of the universe’s origin. And somehow it all ties back to that conversation, to that Chinese restaurant, and to the true meaning of nothing. Throughout their journey, Amanda struggles to make sense of her own life—as her journalism career transforms from illusion to reality, as she searches for her voice as a writer, as she steps from a universe shared with her father to at last carve out one of her own. It’s a paradigm shift you might call growing up. By turns hilarious, moving, irreverent, and profound, Trespassing on Einstein’s Lawn weaves together story and science in remarkable ways. By the end, you will never look at the universe the same way again. Praise for Trespassing on Einstein’s Lawn “Nothing quite prepared me for this book. Wow. Reading it, I alternated between depression—how could the rest of us science writers ever match this?—and exhilaration.”—Scientific American “To Do: Read Trespassing on Einstein’s Lawn. Reality doesn’t have to bite.”—New York “A zany superposition of genres . . . It’s at once a coming-of-age chronicle and a father-daughter road trip to the far reaches of this universe and 10,500 others.”—The Philadelphia Inquirer From the Hardcover edition.

A Farewell to Alms

A Brief Economic History of the World

Author: Gregory Clark

Publisher: Princeton University Press

ISBN: 9781400827817

Category: Business & Economics

Page: 432

View: 5356

Why are some parts of the world so rich and others so poor? Why did the Industrial Revolution--and the unprecedented economic growth that came with it--occur in eighteenth-century England, and not at some other time, or in some other place? Why didn't industrialization make the whole world rich--and why did it make large parts of the world even poorer? In A Farewell to Alms, Gregory Clark tackles these profound questions and suggests a new and provocative way in which culture--not exploitation, geography, or resources--explains the wealth, and the poverty, of nations. Countering the prevailing theory that the Industrial Revolution was sparked by the sudden development of stable political, legal, and economic institutions in seventeenth-century Europe, Clark shows that such institutions existed long before industrialization. He argues instead that these institutions gradually led to deep cultural changes by encouraging people to abandon hunter-gatherer instincts-violence, impatience, and economy of effort-and adopt economic habits-hard work, rationality, and education. The problem, Clark says, is that only societies that have long histories of settlement and security seem to develop the cultural characteristics and effective workforces that enable economic growth. For the many societies that have not enjoyed long periods of stability, industrialization has not been a blessing. Clark also dissects the notion, championed by Jared Diamond in Guns, Germs, and Steel, that natural endowments such as geography account for differences in the wealth of nations. A brilliant and sobering challenge to the idea that poor societies can be economically developed through outside intervention, A Farewell to Alms may change the way global economic history is understood.

Proofiness

How You're Being Fooled by the Numbers

Author: Charles Seife

Publisher: Penguin Paperbacks

ISBN: 9780143120070

Category: Mathematics

Page: 295

View: 1740

Demonstrates how mathematical misinformation pervades--and shapes--people's daily lives and is used to bring down government officials, convict the innocent, and ruin the U.S. economy.

Nothing

From absolute zero to cosmic oblivion -- amazing insights into nothingness

Author: New Scientist,

Publisher: John Murray

ISBN: 1473642698

Category: Social Science

Page: 256

View: 4024

Zero, zip, nada, zilch. It's all too easy to ignore the fascinating possibilities of emptiness and non-existence, and we may well wonder what there is to say about nothing. But scientists have known for centuries that nothing is the key to understanding absolutely everything, from why particles have mass to the expansion of the universe; without nothing we'd be precisely nowhere. With chapters by 22 science writers, including top names such as Ian Stewart, Marcus Chown, Helen Pilcher, Nigel Henbest, Michael Brooks, Linda Geddes, Paul Davies, Jo Marchant and David Fisher, this fascinating and intriguing book revels in a subject that has tantalised the finest minds for centuries, and shows there's more to nothing than meets the eye.

A Universe from Nothing

Why There Is Something Rather than Nothing

Author: Lawrence M. Krauss

Publisher: Simon and Schuster

ISBN: 1451624476

Category: Science

Page: 224

View: 8380

Bestselling author and acclaimed physicist Lawrence Krauss offers a paradigm-shifting view of how everything that exists came to be in the first place. “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.

The Meaning of Trump

Author: Brian Francis Culkin

Publisher: John Hunt Publishing

ISBN: 1789040477

Category: Political Science

Page: 96

View: 5489

The election of Donald Trump was a shattering moment to the political sensibilities of America; immediately sending the country into a frenzy of commentary, critique, and a never-ending media coverage that has bordered on the absurd. But the question still remains: what does it all mean? The Meaning of Trump is an ideological critique that sees the election of Donald Trump as a completely natural progression to the general trajectory of digitized technologies, neoliberalism, and a new breed of financialized capitalism; destructive global forces that know no party affiliation or national boundary. Although Donald Trump is undoubtedly the symptom that has exploded to the surface after nearly four decades of failed policies and broken promises by both Republicans and Democrats alike, his election can also be seen as an existential fork in the road for both the United States and even humanity itself. What path is taken still remains to be seen.

Relativity Simply Explained

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 0486315614

Category: Science

Page: 192

View: 7254

One of the subject's clearest, most entertaining introductions offers lucid explanations of special and general theories of relativity, gravity, and spacetime, models of the universe, and more. 100 illustrations.