beyond infinity an expedition to the outer limits of the mathematical universe

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Beyond Infinity

Author : Eugenia Cheng
ISBN : 9780465094820
Genre : Mathematics
File Size : 63. 50 MB
Format : PDF, ePub
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"[Cheng] does a great service by showing us non-mathematician schlubs how real mathematical creativity works." --Wall Street Journal How big is the universe? How many numbers are there? And is infinity + 1 is the same as 1 + infinity? Such questions occur to young children and our greatest minds. And they are all the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way, she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how one little symbol holds the biggest idea of all.

Beyond Infinity

Author : Eugenia Cheng
ISBN : 9781782830818
Genre : Mathematics
File Size : 34. 23 MB
Format : PDF
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SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

Beyond Infinity

Author : Eugenia Cheng
ISBN : 1781252858
Genre :
File Size : 62. 59 MB
Format : PDF, ePub, Mobi
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Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity.What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough?Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

How To Bake Pi

Author : Eugenia Cheng
ISBN : 9780465051694
Genre : Mathematics
File Size : 56. 1 MB
Format : PDF
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"Whimsical...rigorous and insightful." -- New York Times Book Review What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the béchamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cutting-edge "mathematics of mathematics," that is about figuring out how math works. Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.

The Art Of Logic

Author : Eugenia Cheng
ISBN : 9781782834427
Genre : Mathematics
File Size : 31. 86 MB
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Emotions are powerful. In newspaper headlines and on social media, they have become the primary way of understanding the world. But strong feelings make it more difficult to see the reality behind the rhetoric. In The Art of Logic, Eugenia Cheng shows how mathematical logic can help us see things more clearly - and know when politicians and companies are trying to mislead us. First Cheng explains how to use black-and-white logic to illuminate the world around us, giving us new insight into thorny political questions like public healthcare, Black Lives Matter and Brexit. Then she explains how logic and emotions, used side-by-side, can help us not only to be more rational individuals, but also to live more thoughtfully. Clear-sighted, revelatory and filled with useful real-life examples of logic and illogic at work, The Art of Logic is an essential guide to decoding modern life.

The Outer Limits Of Reason

Author : Noson S. Yanofsky
ISBN : 9780262316781
Genre : Science
File Size : 84. 49 MB
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Many books explain what is known about the universe. 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.

A Brief History Of Infinity

Author : Brian Clegg
ISBN : 9781472107640
Genre : Mathematics
File Size : 82. 79 MB
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'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

Wonders Beyond Numbers

Author : Johnny Ball
ISBN : 9781472939968
Genre : Mathematics
File Size : 62. 73 MB
Format : PDF
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In this book, Johnny Ball tells one of the most important stories in world history – the story of mathematics. By introducing us to the major characters and leading us through many historical twists and turns, Johnny slowly unravels the tale of how humanity built up a knowledge and understanding of shapes, numbers and patterns from ancient times, a story that leads directly to the technological wonderland we live in today. As Galileo said, 'Everything in the universe is written in the language of mathematics', and Wonders Beyond Numbers is your guide to this language. Mathematics is only one part of this rich and varied tale; we meet many fascinating personalities along the way, such as a mathematician who everyone has heard of but who may not have existed; a Greek philosopher who made so many mistakes that many wanted his books destroyed; a mathematical artist who built the largest masonry dome on earth, which builders had previously declared impossible; a world-renowned painter who discovered mathematics and decided he could no longer stand the sight of a brush; and a philosopher who lost his head, but only after he had died. Enriched with tales of colourful personalities and remarkable discoveries, there is also plenty of mathematics for keen readers to get stuck into. Written in Johnny Ball's characteristically light-hearted and engaging style, this book is packed with historical insight and mathematical marvels; join Johnny and uncover the wonders found beyond the numbers.

Worlds Beyond The Poles

Author : Amadeo F. Giannini
ISBN : 078730347X
Genre : Science
File Size : 43. 83 MB
Format : PDF, Kindle
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1959 Physical continuity of the universe. Contents: the Changing Scene; Extrasensory Perception; Connected Universe; Modern Columbus Seeks Queen Isabella; Disclosing Southern Land Corridor into the Heavens Above; Stratosphere Revelations; Journey.

The Great Unknown Deluxe

Author : Marcus du Sautoy
ISBN : 9780735224926
Genre : Science
File Size : 90. 55 MB
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“Brilliant and fascinating. No one is better at making the recondite accessible and exciting.” —Bill Bryson This enhanced eBook edition takes readers even deeper into The Great Unknown with exclusive video and audio clips. Watch du Sautoy demonstrate chaos theory with his wooden pendulum, stumble to find logic in a paradoxical notecard, search his own iPhone for signs of consciousness, and show off the portable pot of uranium he purchased, curiously enough, off the Internet. Ever since the dawn of civilization we have been driven by a desire to know—to understand the physical world and the laws of nature. But are there limits to human knowledge? Are some things simply beyond the predictive powers of science? Or are those challenges the next big discovery waiting to happen? In The Great Unknown, one of the world’s most beloved mathematicians takes us into the minds of science’s greatest innovators as he probes the many deep mysteries we have yet to solve. He reminds us that major breakthroughs were often ridiculed at the time of their discovery and takes us on a whirlwind tour of seven frontiers of knowledge, where scientists are grappling with the unknown. Can you locate consciousness in the brain? Is our universe infinite? What is dark energy made of? What happens to time in space? Is it possible to beat ageing? At once exhilarating and mind-bending, The Great Unknown will challenge you to think in new ways about every aspect of the known world. It invites us to consider big questions—about who we are and the nature of God—that even the most creative scientists have yet to answer definitively.

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