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: 6934

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 Art of the Infinite

The Pleasures of Mathematics

Author: Robert Kaplan,Ellen Kaplan

Publisher: Bloomsbury Publishing USA

ISBN: 160819888X

Category: Mathematics

Page: 416

View: 5107

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?

Hidden Harmonies

The Lives and Times of the Pythagorean Theorem

Author: Ellen Kaplan,Robert Kaplan

Publisher: Bloomsbury Publishing USA

ISBN: 1608192911

Category: Mathematics

Page: 304

View: 4722

A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons-not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name. How can a theorem have more than one proof? Why does this one have more than two hundred-or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples. Like the authors' bestselling The Nothing That Is and Chances Are . . .-hailed as "erudite and witty," "magnificent," and "exhilarating"-Hidden Harmonies makes the excitement of mathematics palpable.

Eine kurze Geschichte der Menschheit

Author: Yuval Noah Harari

Publisher: DVA

ISBN: 364110498X

Category: History

Page: 528

View: 3710

Krone der Schöpfung? Vor 100 000 Jahren war der Homo sapiens noch ein unbedeutendes Tier, das unauffällig in einem abgelegenen Winkel des afrikanischen Kontinents lebte. Unsere Vorfahren teilten sich den Planeten mit mindestens fünf weiteren menschlichen Spezies, und die Rolle, die sie im Ökosystem spielten, war nicht größer als die von Gorillas, Libellen oder Quallen. Vor 70 000 Jahren dann vollzog sich ein mysteriöser und rascher Wandel mit dem Homo sapiens, und es war vor allem die Beschaffenheit seines Gehirns, die ihn zum Herren des Planeten und zum Schrecken des Ökosystems werden ließ. Bis heute hat sich diese Vorherrschaft stetig zugespitzt: Der Mensch hat die Fähigkeit zu schöpferischem und zu zerstörerischem Handeln wie kein anderes Lebewesen. Anschaulich, unterhaltsam und stellenweise hochkomisch zeichnet Yuval Harari die Geschichte des Menschen nach und zeigt alle großen, aber auch alle ambivalenten Momente unserer Menschwerdung.

Out of the Labyrinth

Setting Mathematics Free

Author: Robert Kaplan,Ellen Kaplan

Publisher: Bloomsbury Publishing USA

ISBN: 1608198898

Category: Mathematics

Page: 256

View: 6000

"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.

Ein Universum aus Nichts

... und warum da trotzdem etwas ist

Author: Lawrence M. Krauss

Publisher: Albrecht Knaus Verlag

ISBN: 3641091144

Category: Science

Page: 256

View: 1821

Eine Reise zu den Ursprüngen unseres Universums Warum gibt es alles und nicht nichts? Worüber sich Philosophen seit Jahrhunderten den Kopf zerbrechen, darauf weiß die Physik Antwort: Nach den neuesten Erkenntnissen kann durchaus alles aus dem Nichts entstanden sein. Und mit Lawrence Krauss ist das gar nicht so schwer zu verstehen. Ironisch, böse und zugleich mit einem Augenzwinkern weiß Krauss selbst die Erkenntnis, dass wir aller Wahrscheinlichkeit nach auch im Nichts verschwinden werden, höchst amüsant zu präsentieren, und schont dabei niemanden: weder Philosophen noch Theologen noch sich selbst. Die Frage nach der Entstehung unseres Universums ist eine der bemerkenswertesten Erkundungsreisen, die die Menschheit je unternommen hat. Einstein, Hubble, Relativitätstheorie, Inflation und Quantenmechanik – kein Bereich der Kosmologie, über den Lawrence Krauss nicht verständlich und vor allem spannend zu erzählen weiß. Dabei fragt er immer auch nach den Quellen unseres Wissens: Wie hat sich unsere Vorstellung vom Ursprung aller Dinge entwickelt? Weshalb wissen wir, was wir heute wissen? Und warum können wir davon ausgehen, dass das auch stimmt? Mit Ein Universum aus Nichts hat er ein Buch geschrieben, das schlau macht – voller Seitenhiebe gegen die theologische Zunft und alle anderen esoterischen Welterklärungen. Ganz ohne Berechnungen.

Homo Deus

Eine Geschichte von Morgen

Author: Yuval Noah Harari

Publisher: C.H.Beck

ISBN: 3406704026

Category: Social Science

Page: 576

View: 6304

In seinem Kultbuch „Eine kurze Geschichte der Menschheit“ erklärte Yuval Noah Harari, wie unsere Spezies die Erde erobern konnte. In „Homo Deus“ stößt er vor in eine noch verborgene Welt: die Zukunft. Was wird mit uns und unserem Planeten passieren, wenn die neuen Technologien dem Menschen gottgleiche Fähigkeiten verleihen – schöpferische wie zerstörerische – und das Leben selbst auf eine völlig neue Stufe der Evolution heben? Wie wird es dem Homo Sapiens ergehen, wenn er einen technikverstärkten Homo Deus erschafft, der sich vom heutigen Menschen deutlicher unterscheidet als dieser vom Neandertaler? Was bleibt von uns und der modernen Religion des Humanismus, wenn wir Maschinen konstruieren, die alles besser können als wir? In unserer Gier nach Gesundheit, Glück und Macht könnten wir uns ganz allmählich so weit verändern, bis wir schließlich keine Menschen mehr sind.

Revelation of the Bible

The Book of Genesis

Author: Moshe Mazin

Publisher: iUniverse

ISBN: 9781450285605

Category: Religion

Page: 284

View: 7738

Revelation of the Bible: The Book of Genesis is the first volume in a series on biblical revelations offering timely insights into the world and revealing the prophecies of Jacob. Author Moshe Mazin identifies the Messiah out of the house of Judah. This volume explores creation from both scientific and biblical perspectives. The secrets of creation are examined along with the meaning of life, the location of the Garden of Eden, and the story of Adam and Eve. What is the meaning of the tree of knowledge and who are the children of God? HaLevi provides a detailed analysis of the seven names of God and their meanings as well as the selection of Abraham as God’s chosen person. He follows the Hebrew text of Genesis and in some cases paraphrases the specific content for clarity. He has not included any English translations of the Hebrew text because he believes that there are many such translations that vary too widely in their interpretations. Revelation of the Bible offers rare insights into the book of Genesis based upon the Kabbalah and scientific scrutiny.

Algorithmic Composition

Paradigms of Automated Music Generation

Author: Gerhard Nierhaus

Publisher: Springer Science & Business Media

ISBN: 3211755403

Category: Mathematics

Page: 287

View: 488

Algorithmic composition – composing by means of formalizable methods – has a century old tradition not only in occidental music history. This is the first book to provide a detailed overview of prominent procedures of algorithmic composition in a pragmatic way rather than by treating formalizable aspects in single works. In addition to an historic overview, each chapter presents a specific class of algorithm in a compositional context by providing a general introduction to its development and theoretical basis and describes different musical applications. Each chapter outlines the strengths, weaknesses and possible aesthetical implications resulting from the application of the treated approaches. Topics covered are: markov models, generative grammars, transition networks, chaos and self-similarity, genetic algorithms, cellular automata, neural networks and artificial intelligence are covered. The comprehensive bibliography makes this work ideal for the musician and the researcher alike.

Kurze Antworten auf große Fragen

Author: Stephen Hawking

Publisher: Klett-Cotta

ISBN: 3608115102

Category: Political Science

Page: 160

View: 2205

Stephen Hawkings Vermächtnis In seinem letzten Buch gibt Stephen Hawking Antworten auf die drängendsten Fragen unserer Zeit und nimmt uns mit auf eine persönliche Reise durch das Universum seiner Weltanschauung. Seine Gedanken zu Ursprung und Zukunft der Menschheit sind zugleich eine Mahnung, unseren Heimatplaneten besser vor den Gefahren unserer Gegenwart zu schützen. Zugänglich und klar finden Sie in diesem Buch Hawkings Antworten auf die drängendsten Fragen unserer Zeit. - Warum gibt es uns Menschen überhaupt? - Und woher kommen wir? - Gibt es im Weltall andere intelligente Lebewesen? - Existiert Gott? - In welchem Zustand befindet sich unser Heimatplanet? - Werden wir auf der Erde überleben? - Retten oder zerstören uns Naturwissenschaften und Technik? - Hilft uns die künstliche Intelligenz, die Erde zu bewahren? - Können wir den Weltraum bevölkern? - Wie werden wir die Schwächsten – Kinder, Kranke, alte Menschen – schützen? - Wie werden wir unsere Kinder erziehen? Brillanter Physiker, revolutionärer Kosmologe, unerschütterlicher Optimist. Für Stephen Hawking bergen die Weiten des Universums nicht nur naturwissenschaftliche Geheimnisse. In seinem persönlichsten Buch beantwortet der Autor die großen Fragen des menschlichen Lebens und spricht die wichtigsten Themen unserer Zeit an. Zugänglich und klar erläutert er die Folgen des menschlichen Fortschritts – vom Klimawandel bis hin zu künstlicher Intelligenz – und diskutiert seine Gefahren. Hier finden Sie Hawkings Antworten auf die Urfragen der Menschheit. Ein großer Appell an politische Machthaber und jeden Einzelnen von uns, unseren bedrohten Heimatplaneten besser zu schützen.

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: 5038

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.

Anatomy of a Short Story

Nabokov's Puzzles, Codes, "Signs and Symbols"

Author: Yuri Leving

Publisher: Bloomsbury Publishing USA

ISBN: 1441107681

Category: Literary Criticism

Page: 432

View: 3504

Since its first publication in 1948, one of Vladimir Nabokov's shortest short stories, "Signs and Symbols," has generated perhaps more interpretations and critical appraisal than any other that he wrote. It has been called "one of the greatest short stories ever written" and "a triumph of economy and force, minute realism and shimmering mystery" (Brian Boyd, Vladimir Nabokov: The American Years). Anatomy of a Short Story contains: Â? the full text of "Signs and Symbols," line numbered and referenced throughout Â? correspondence about the story, most of it never before published, between Nabokov and the editor of The New Yorker, where the story was first published Â? 33 essays of literary criticism, bringing together classic essays and new interpretations Â? a round-table discussion in which a screenwriter, a theater scholar, a mathematician, a psychiatrist, and a literary scholar bring their perspectives to bear on "Signs and Symbols" Anatomy of a Short Story illuminates the ways in which we interpret fiction, and the short story in particular.

Book Lust

Recommended Reading for Every Mood, Moment, and Reason

Author: Nancy Pearl

Publisher: Sasquatch Books

ISBN: 1570616590

Category: Literary Criticism

Page: 304

View: 6409

What to read next is every book lover's greatest dilemma. Nancy Pearl comes to the rescue with this wide-ranging and fun guide to the best reading new and old. Pearl, who inspired legions of litterateurs with "What If All (name the city) Read the Same Book," has devised reading lists that cater to every mood, occasion, and personality. These annotated lists cover such topics as mother-daughter relationships, science for nonscientists, mysteries of all stripes, African-American fiction from a female point of view, must-reads for kids, books on bicycling, "chick-lit," and many more. Pearl's enthusiasm and taste shine throughout.

The Why of Things

Causality in Science, Medicine, and Life

Author: Peter V. Rabins

Publisher: Columbia University Press

ISBN: 0231535457

Category: Science

Page: 304

View: 353

Why was there a meltdown at the Fukushima power plant? Why do some people get cancer and not others? Why is global warming happening? Why does one person get depressed in the face of life's vicissitudes while another finds resilience? Questions like these—questions of causality—form the basis of modern scientific inquiry, posing profound intellectual and methodological challenges for researchers in the physical, natural, biomedical, and social sciences. In this groundbreaking book, noted psychiatrist and author Peter Rabins offers a conceptual framework for analyzing daunting questions of causality. Navigating a lively intellectual voyage between the shoals of strict reductionism and relativism, Rabins maps a three-facet model of causality and applies it to a variety of questions in science, medicine, economics, and more. Throughout this book, Rabins situates his argument within relevant scientific contexts, such as quantum mechanics, cybernetics, chaos theory, and epigenetics. A renowned communicator of complex concepts and scientific ideas, Rabins helps readers stretch their minds beyond the realm of popular literary tipping points, blinks, and freakonomic explanations of the world.

Eine kurze Geschichte der Zeit

Author: Stephen Hawking

Publisher: Rowohlt Verlag GmbH

ISBN: 3644008612

Category: Science

Page: 272

View: 1686

Ist das Universum unendlich oder begrenzt? Hat die Raumzeit einen Anfang, den Urknall? Dehnt sie sich aus? Wird sie wieder in sich zusammenstürzen? Liefe die Zeit dann rückwärts? Welchen Platz im Universum nehmen wir ein? Und ist in den atemberaubenden Modellen der Kosmologen noch Platz für einen Gott? – Es sind existenzielle Fragen, mit denen sich Stephen Hawking befasst, Fragen, die Forschung und Lehre in den Zentren der modernen Physik ebenso bestimmen wie die Diskussion von Geisteswissenschaftlern. Dieses Meisterwerk eines Jahrhundert-Genies hat unsere Weltsicht verändert. Zugleich hat Stephen Hawking damit neue Maßstäbe für die Erklärung komplexer physikalischer Zusammenhänge gesetzt. In diesem Buch, weltweit inzwischen über zehn Millionen Mal verkauft, ist das Credo des großen Physikers enthalten und lebendig. «Der Physiker Stephen Hawking ist im Begriff, die Formel zu finden, die das Universum erklärt.» ZEIT-Magazin

The Zeronauts

Breaking the Sustainability Barrier

Author: John Elkington

Publisher: Routledge

ISBN: 1849713979

Category: Business & Economics

Page: 276

View: 9403

A world of 9 billion people by mid-century will demand fundamental changes in our mindsets, behaviors, cultures, and overarching paradigm. Just as our species broke the Sound Barrier during the 1940s and 1950s, a new breed of innovator, entrepreneur, and investor is lining up to break the Sustainability Barrier. In this book, John Elkington introduces the Zeronauts – a new breed of innovator, determined to drive problems such as carbon, waste, toxics, and poverty to zero – as well as creating the first Zeronaut Roll of Honor, spotlighting 50 pioneers in the field of zero. Zeronauts are innovating in an astonishing range of areas, tackling hugely diverse economic, social, environmental, and governance challenges. To give a sense of progress to date, we zero in on five key challenges (the 5Ps): population growth, pandemics, poverty, pollution, and proliferation. The power of zero has been trumpeted, notably in relation to zero defects. This book spotlights key lessons learned in the field of total quality management – and introduces a five-stage "Pathways to Zero" model, running through from the Eureka! discovery moment to the point where a new way of doing things becomes endemic in the economy. In order to move from incremental to transformative change, we must embrace wider framings, deeper insights, higher targets, and longer time scales. This book investigates some ways in which leading Zeronauts are pushing change in relevant directions, with cases drawn from a spectrum of human activity – from water profligacy to human genital mutilation. If we learn from these pioneers, the twenty-first century could be our best yet.