Beyond Infinity

An expedition to the outer limits of the mathematical universe

Author: Eugenia Cheng

Publisher: Profile Books

ISBN: 1782830812

Category: Mathematics

Page: 204

View: 4919


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

An Expedition to the Outer Limits of Mathematics

Author: Eugenia Cheng

Publisher: Basic Books

ISBN: 0465094821

Category: Mathematics

Page: 304

View: 8862


"[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

An Expedition to the Outer-Limits of the Mathematical Universe

Author: Eugenia Cheng

Publisher: N.A

ISBN: 9781781252857


Page: 316

View: 4463


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

An Edible Exploration of the Mathematics of Mathematics

Author: Eugenia Cheng

Publisher: Basic Books

ISBN: 0465051693

Category: Mathematics

Page: 304

View: 7794


"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

How to Make Sense in a World that Doesn't

Author: Eugenia Cheng

Publisher: Profile Books

ISBN: 1782834427

Category: Mathematics

Page: N.A

View: 8674


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.


Beyond the Beyond the Beyond

Author: Lillian R. Lieber

Publisher: Paul Dry Books

ISBN: 1589880366

Category: Mathematics

Page: 262

View: 8128


This book offers an entertaining, yet thorough, explanation of the concept of, yes, infinity. Accessible to non-mathematicians, this book also cleverly connects mathematical reasoning to larger issues in society.

The Outer Limits of Reason

What Science, Mathematics, and Logic Cannot Tell Us

Author: Noson S. Yanofsky

Publisher: MIT Press

ISBN: 0262316781

Category: Science

Page: 424

View: 9069


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.

The Infinite Book

A Short Guide to the Boundless, Timeless and Endless

Author: John D. Barrow

Publisher: Vintage

ISBN: 0307428761

Category: Philosophy

Page: 352

View: 4575


For a thousand years, infinity has proven to be a difficult and illuminating challenge for mathematicians and theologians. It certainly is the strangest idea that humans have ever thought. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Is matter infinitely divisible into ever-smaller pieces? But infinity is also the place where things happen that don't. All manner of strange paradoxes and fantasies characterize an infinite universe. If our Universe is infinite then an infinite number of exact copies of you are, at this very moment, reading an identical sentence on an identical planet somewhere else in the Universe. Now Infinity is the darling of cutting edge research, the measuring stick used by physicists, cosmologists, and mathematicians to determine the accuracy of their theories. From the paradox of Zeno’s arrow to string theory, Cambridge professor John Barrow takes us on a grand tour of this most elusive of ideas and describes with clarifying subtlety how this subject has shaped, and continues to shape, our very sense of the world in which we live. The Infinite Book is a thoroughly entertaining and completely accessible account of the biggest subject of them all–infinity. From the Trade Paperback edition.

Wonders Beyond Numbers

A Brief History of All Things Mathematical

Author: Johnny Ball

Publisher: Bloomsbury Publishing

ISBN: 1472939964

Category: Mathematics

Page: 336

View: 5816


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.

The Mystery of the Aleph

Mathematics, the Kabbalah, and the Search for Infinity

Author: Amir D. Aczel

Publisher: Simon and Schuster

ISBN: 0743422996

Category: Biography & Autobiography

Page: 272

View: 2040


Journeys into the work of Georg Cantor, a Russian-born German mathematician, who developed set theory and the concept of infinite numbers, but was condemned by his peers and spent many years in an asylum.

Algebra & Geometry

An Introduction to University Mathematics

Author: Mark V. Lawson

Publisher: CRC Press

ISBN: 1482246481

Category: Mathematics

Page: 384

View: 682


Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra

How Not to be Wrong

The Power of Mathematical Thinking

Author: Jordan Ellenberg

Publisher: Penguin

ISBN: 0143127535

Category: Business & Economics

Page: 480

View: 9059


"Using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman, minus the jargon ... Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need"--

The Mathematics Lover's Companion

Masterpieces for Everyone

Author: Edward R. Scheinerman

Publisher: Yale University Press

ISBN: 0300223005

Category: Mathematics

Page: 296

View: 1483


Twenty-three mathematical masterpieces for exploration and enlightenment

A Brief History of Infinity

The Quest to Think the Unthinkable

Author: Brian Clegg

Publisher: Robinson

ISBN: 1472107640

Category: Mathematics

Page: 160

View: 6204


'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.

To Be a Machine

Adventures Among Cyborgs, Utopians, Hackers, and the Futurists Solving the Modest Problem of Death

Author: Mark O'Connell

Publisher: Anchor

ISBN: 110191159X

Category: Computers

Page: 256

View: 4846


"A globe-spanning investigation into the Transhumanist movement, considering the tech billionaires, scientific luminaries, and DIY body-hackers attempting to prolong, improve, and ultimately transcend the limits of human life"--

The Great Unknown Deluxe

Seven Journeys to the Frontiers of Science

Author: Marcus du Sautoy

Publisher: Penguin

ISBN: 0735224927

Category: Science

Page: 464

View: 4684


“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.

Does God Play Dice

The New Mathematics of Chaos

Author: Ian Stewart

Publisher: Wiley-Blackwell

ISBN: 9780631232513

Category: Science

Page: 416

View: 7441


The revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account of complexity theory. This witty, lucid and engaging book makes the complex mathematics of chaos accessible and entertaining. Presents complex mathematics in an accessible style. Includes three new chapters on prediction in chaotic systems, control of chaotic systems, and on the concept of chaos. Provides a discussion of complexity theory.

A Most Elegant Equation

Euler's Formula and the Beauty of Mathematics

Author: David Stipp

Publisher: Basic Books

ISBN: 0465093787

Category: Mathematics

Page: 240

View: 4311


An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

The Quantum Labyrinth

How Richard Feynman and John Wheeler Revolutionized Time and Reality

Author: Paul Halpern

Publisher: Basic Books

ISBN: 0465097596

Category: Science

Page: 336

View: 520


The story of the unlikely friendship between the two physicists who fundamentally recast the notion of time and history In 1939, Richard Feynman, a brilliant graduate of MIT, arrived in John Wheeler's Princeton office to report for duty as his teaching assistant. A lifelong friendship and enormously productive collaboration was born, despite sharp differences in personality. The soft-spoken Wheeler, though conservative in appearance, was a raging nonconformist full of wild ideas about the universe. The boisterous Feynman was a cautious physicist who believed only what could be tested. Yet they were complementary spirits. Their collaboration led to a complete rethinking of the nature of time and reality. It enabled Feynman to show how quantum reality is a combination of alternative, contradictory possibilities, and inspired Wheeler to develop his landmark concept of wormholes, portals to the future and past. Together, Feynman and Wheeler made sure that quantum physics would never be the same again.