Euclid in the Rainforest

Discovering Universal Truth in Logic and Math

Author: Joseph Mazur

Publisher: Penguin

ISBN: 1101664878

Category: Mathematics

Page: 352

View: 9374

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Like Douglas Hofstadter’s Gödel, Escher, Bach, and David Berlinski’s A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore logic—the one indispensable tool in man’s quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

Fluke

Author: Joseph Mazur

Publisher: Oneworld Publications

ISBN: 1780749015

Category: Mathematics

Page: 256

View: 9767

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What are the chances?! This exclamation greets the scarcely believable coincidence – you’re picked up by the same taxi driver several years and thousands of miles apart or, in a second-hand bookshop far from home, you find your own childhood copy of Winnie-the-Pooh on the shelf. But the unlikely is more probable than you think. Against every fibre of common sense, the fact is that it’s quite likely that some squirrel, somewhere, will be struck by lightning as it crosses the road. The chaos and unpredictability of our lives is an illusion. There is a rational order to the universe, and it’s called mathematics. Fluke is a fascinating investigation into the true nature of chance, a must-read for maths enthusiasts and avid storytellers alike, it tears down the veil of improbability to reveal the wonderfully possible.

Mathematics in Ancient Greece

Author: Tobias Dantzig

Publisher: Courier Corporation

ISBN: 0486149986

Category: Mathematics

Page: 192

View: 946

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Written by a specialist in interpreting science for lay readers, this lively book recounts the human story behind mathematics, including the insights of such thinkers as Euclid and Hippocrates. 1955 edition.

What's Luck Got to Do with It?

The History, Mathematics, and Psychology of the Gambler's Illusion

Author: Joseph Mazur

Publisher: Princeton University Press

ISBN: 9781400834457

Category: Mathematics

Page: 296

View: 2829

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Why do so many gamblers risk it all when they know the odds of winning are against them? Why do they believe dice are "hot" in a winning streak? Why do we expect heads on a coin toss after several flips have turned up tails? What's Luck Got to Do with It? takes a lively and eye-opening look at the mathematics, history, and psychology of gambling to reveal the most widely held misconceptions about luck. It exposes the hazards of feeling lucky, and uses the mathematics of predictable outcomes to show when our chances of winning are actually good. Mathematician Joseph Mazur traces the history of gambling from the earliest known archaeological evidence of dice playing among Neolithic peoples to the first systematic mathematical studies of games of chance during the Renaissance, from government-administered lotteries to the glittering seductions of grand casinos, and on to the global economic crisis brought on by financiers' trillion-dollar bets. Using plenty of engaging anecdotes, Mazur explains the mathematics behind gambling--including the laws of probability, statistics, betting against expectations, and the law of large numbers--and describes the psychological and emotional factors that entice people to put their faith in winning that ever-elusive jackpot despite its mathematical improbability. As entertaining as it is informative, What's Luck Got to Do with It? demonstrates the pervasive nature of our belief in luck and the deceptive psychology of winning and losing. Some images inside the book are unavailable due to digital copyright restrictions.

The Motion Paradox

The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space

Author: Joseph Mazur

Publisher: Penguin

ISBN: 1440649650

Category: Science

Page: 272

View: 6017

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The epic tale of an ancient, unsolved puzzle and how it relates to all scientific attempts to explain the basic structure of the universe At the dawn of science the ancient Greek philosopher Zeno formulated his paradox of motion, and amazingly, it is still on the cutting edge of all investigations into the fabric of reality. Zeno used logic to argue that motion is impossible, and at the heart of his maddening puzzle is the nature of space and time. Is space-time continuous or broken up like a string of beads? Over the past two millennia, many of our greatest minds—including Aristotle, Galileo, Newton, Einstein, Stephen Hawking, and other current theoreticians—have been gripped by the mystery this puzzle represents. Joseph Mazur, acclaimed author of Euclid in the Rainforest, shows how historic breakthroughs in our understanding of motion shed light on Zeno’s paradox. The orbits of the planets were explained, the laws of motion were revealed, the theory of relativity was discovered—but the basic structure of time and space remained elusive. In the tradition of Fermat’s Enigma and Zero, The Motion Paradox is a lively history of this apparently simple puzzle whose solution—if indeed it can be solved—will reveal nothing less than the fundamental nature of reality.

Enlightening Symbols

A Short History of Mathematical Notation and Its Hidden Powers

Author: Joseph Mazur

Publisher: Princeton University Press

ISBN: 1400850118

Category: Mathematics

Page: 312

View: 2454

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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

The Parrot's Theorem

A Novel

Author: Denis Guedj

Publisher: Macmillan

ISBN: 1466851678

Category: Fiction

Page: 352

View: 8557

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Mr. Ruche, a Parisian bookseller, receives a bequest from a long lost friend in the Amazon of a vast library of math books, which propels him into a great exploration of the story of mathematics. Meanwhile Max, whose family lives with Mr. Ruche, takes in a voluble parrot who will discuss math with anyone. When Mr. Ruche learns of his friend's mysterious death in a Brazilian rainforest, he decides that with the parrot's help he will use these books to teach Max and his brother and sister the mysteries of Euclid's Elements, Pythagoras's Theorem and the countless other mathematical wonders. But soon it becomes clear that Mr. Ruche has inherited the library for reasons other than enlightenment, and before he knows it the household is racing to prevent the parrot and vital, new theorems from falling into the wrong hands. An immediate bestseller when first published in France, The Parrot's Theorem charmingly combines a straightforward history of mathematics and a first-rate murder mystery.

Here's Looking at Euclid

A Surprising Excursion Through the Astonishing World of Math

Author: Alex Bellos

Publisher: Simon and Schuster

ISBN: 1416596348

Category: Mathematics

Page: 336

View: 520

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Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place." Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games. Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.

Darwin in Atlantic Cultures

Evolutionary Visions of Race, Gender, and Sexuality

Author: Jeannette Eileen Jones,Patrick B. Sharp

Publisher: Routledge

ISBN: 1135178720

Category: Literary Criticism

Page: 318

View: 8435

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This collection is an interdisciplinary edited volume that examines the circulation of Darwinian ideas in the Atlantic space as they impacted systems of Western thought and culture. Specifically, the book explores the influence of the principle tenets of Darwinism -- such as the theory of evolution, the ape-man theory of human origins, and the principle of sexual selection -- on established transatlantic intellectual traditions and cultural practices. In doing so, it pays particular attention to how Darwinism reconfigured discourses on race, gender, and sexuality in a transnational context. Covering the period from the publication of The Origin of Species (1859) to 1933, when the Nazis (National Socialist Party) took power in Germany, the essays demonstrate the dissemination of Darwinian thought in the Western world in an unprecedented commerce of ideas not seen since the Protestant Reformation. Learned societies, literary groups, lyceums, and churches among other sites for public discourse sponsored lectures on the implications of Darwin’s theory of evolution for understanding the very ontological codes by which individuals ordered and made sense of their lives. Collectively, these gatherings reflected and constituted what the contributing scholars to this volume view as the discursive power of the cultural politics of Darwinism.

Pollination Ecology and the Rain Forest

Sarawak Studies

Author: David Roubik,Shoko Sakai,Abang A. Hamid Karim

Publisher: Springer Science & Business Media

ISBN: 9780387213095

Category: Nature

Page: 307

View: 4902

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Rain Forest Biology and the Canopy System, Sarawak, 1992–2002 The rain forest takes an immense breath and then exhales, once every four or ?ve years, as a major global weather pattern plays out, usually heralded by El Nin ̃o–Southern Oscillation. While this powerful natural cycle has occurred for many millennia, it is during the past decade that both the climate of Earth and the people living on it have had an increasing in?uence on the weather pattern itself, with many biological consequences. In Southeast Asia, as also in most of the Neotropics, El Nin ̃o accompanies one of the most exuberant o- pourings of nature’s diversity. After several years of little activity, the incredibly diverse rain forests suddenly burst into ?ower—a phenomenon referred to as General Flowering in Asia. Plant populations are rejuvenated and animals are fed, but the process involves a delicate and complex balance. When the canopy access system was under construction at Lambir Hills - tional Park in the early 1990s, it made use of an underlying technology that was already in place: bridges. For centuries, bridges have spanned the natural chasms over rivers. This existing network of bridges and the people who built and use them produced the technology we needed to gain access to the canopy. Bridge builders were our natural allies in the quest for biological knowledge of the high canopy.

The Brain

Die Geschichte von dir

Author: David Eagleman

Publisher: Pantheon Verlag

ISBN: 3641183154

Category: Science

Page: 224

View: 1586

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Unterhaltend und fundiert: Ein Pageturner über die Hirnforschung Die Hirnforschung macht rasante Fortschritte, aber nur selten treten wir einen Schritt zurück und fragen uns, was es heißt, ein Lebewesen und Mensch zu sein. Der renommierte Neurowissenschaftler David Eagleman nimmt uns mit auf die Reise durch das Gewirr aus Milliarden von Hirnzellen und Billionen von Synapsen – und zu uns selbst. Das sonderbare Rechengewebe in unserem Schädel ist der Apparat, mit dem wir uns in der Welt orientieren, Entscheidungen treffen und Vorstellungen entwickeln. Seine unendlich vielen Zellen bringen unser Bewusstsein und unsere Träume hervor. In diesem Buch baut Bestsellerautor David Eagleman eine Brücke zwischen der Hirnforschung und uns, den Besitzern eines Gehirns. Er hilft uns, uns selbst zu verstehen. Denn ein besseres Verständnis unseres inneren Kosmos wirft auch ein neues Licht auf unsere persönlichen Beziehungen und unser gesellschaftliches Zusammenleben: wie wir unser Leben lenken, warum wir lieben, was wir für wahr halten, wie wir unsere Kinder erziehen, wie wir unsere Gesellschaftspolitik verbessern und wie wir den menschlichen Körper auf die kommenden Jahrhunderte vorbereiten können.

The Amazon

Land without History

Author: Euclides da Cunha

Publisher: Oxford University Press

ISBN: 0199938954

Category: History

Page: 128

View: 4430

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In the eight pieces that make up Land Without History, first published in Portuguese in 1909, Euclides da Cunha offers a rare look into twentieth century Amazonia, and the consolidation of South American nation states. Mixing scientific jargon and poetic language, the essays in Land Without History provide breathtaking descriptions of the Amazonian rivers and the ever-changing nature that surrounds them. Brilliantly translated by Ronald Sousa, Land Without History offers a view of the ever changing ecology of the Amazon, and a compelling testimony to the Brazilian colonial enterprise, and its imperialist tendencies with regard to neighboring nation-states.

Meilensteine der Mathematik

Author: Ian Stewart

Publisher: Spektrum Akademischer Verlag

ISBN: 9783827423009

Category: Science

Page: 288

View: 1885

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Wer hat die Null erfunden? Wie können imaginäre Zahlen helfen, dass reale Wolkenkratzer nicht umfallen? Wo treffen sich parallele Linien? Und wann haben Sie heute zuletzt abstrakte Algebra genutzt? (Doch, Sie haben.) Wie die Mathematik die moderne Welt erschaffen hat – eine illustrierte Geschichte der Mathematik für ein breites Publikum, von den Ursprüngen im Zweistromland bis zur Gegenwart Ian Stewarts spannende Geschichte der Mathematik führt uns von der frühen Hochkultur der Babylonier bis zu den letzten ungelösten Rätseln dieser Disziplin. In typisch Stewart'scher Manier, also unterhaltsam und zugleich fundiert, schildert und erklärt er die großen Meilensteine der Mathematik – von den ersten Zahlensystemen bis zur Chaostheorie – und geht der Frage nach, welche Auswirkungen sie auf die Gesellschaft hatten und wie sie den Alltag auf alle Zeit veränderten. Er bringt uns dabei auch die Geistesgrößen der Mathematik näher, von den Naturforschern und Denkern Babyloniens, Griechenlands und Ägyptens über Newton und Descartes bis zu Fermat, Babbage und Gödel. Ohne den Leser mit komplizierten Formeln zu erschrecken, macht er die Schlüsselkonzepte der Mathematik verständlich. Als anregender historischer Streifzug für den interessierten Laien steckt Meilensteine der Mathematik voller faszinierender Details und kurioser Anekdoten. Hundert Abbildungen und Diagramme beleuchten und erhellen ein Gebiet, das von vielen Menschen gefürchtet wird, das aber unsere heutige Welt entscheidend geprägt hat.

Untersuchungen über höhere Arithmetik

Author: Carl Friedrich Gauss

Publisher: American Mathematical Soc.

ISBN: 0821842137

Category: Mathematics

Page: 695

View: 5617

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In this volume are included all of Gauss's number-theoretic works: his masterpiece, Disquisitiones Arithmeticae, published when Gauss was only 25 years old; several papers published during the ensuing 31 years; and papers taken from material found in Gauss's handwriting after his death. These papers include a fourth, fifth, and sixth proof of the Quadratic Reciprocity Law, researches on biquadratic residues, quadratic forms, and other topics. This reprint of the German translation from Latin of the second edition published in 1889 includes an extensive appendix and concludes with a commentary on the papers (with references, where appropriate, to the relevant pages of the Disquisitiones).