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Book of Numbers: The Secret Numbers and How They Changed the World

Overview

Unraveling the secrets of numbers, from the discovery of zero to infinity.

In clear language, The Book of Numbers cuts through the mystery and fear surrounding numbers to reveal their fascinating nature and roles in architecture, quantum mechanics, computer technology, biology, commerce, philosophy, art, music, religion and more. Indeed, numbers are part of every discipline in the sciences and the arts.

With 350 illustrations, including ...

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Overview

Unraveling the secrets of numbers, from the discovery of zero to infinity.

In clear language, The Book of Numbers cuts through the mystery and fear surrounding numbers to reveal their fascinating nature and roles in architecture, quantum mechanics, computer technology, biology, commerce, philosophy, art, music, religion and more. Indeed, numbers are part of every discipline in the sciences and the arts.

With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:

  • The earliest ideas of numbers and counting
  • Patterns, logic, calculating
  • Natural, perfect, amicable and prime numbers
  • Numerology, the power of numbers, superstition
  • The computer, the Enigma Code
  • Infinity, the speed of light, relativity
  • Complex numbers
  • The Big Bang and Chaos theories
  • The Philosopher's Stone.

The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

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Editorial Reviews

Mathematics Teacher, Vol. 102, No. 7 - Cathleen M. Zucco-Teveloff
Beautifully illustrated with art reproductions, photographs and other images, this book is a fascinating read.... A thorough understanding of all kinds of number concepts—zero, rational numbers, irrational numbers, binary numbers, and imaginary numbers—should be part of every mathematics and student's and educator's general knowledge. This book, intended for a general audience, would serve as a good reference for mathematics students as well as preservice and in-service educators.
Waterloo Region Record - Bill Bean
BBC contributor and professor of pop science Peter J. Bentley brings the kind of enthusiasm and excitement to numbers that would well serve any high school math teacher This whimsically organized book (with chapters -1, 0 and 12a, for those afraid of 13) is a quirky and refereshing review of the science of numbers.... You might emerg from this book still baffled by sines, cosines and tangents, but [Bentley's] affection for understanding numbers is infectious.
The Globe and Maill - Evan Wexler
Mathematics, perhaps surprisingly, can be far more entertaining than the average high-school textbook lets on.... Bentley's account doubtless does not lay bare all of the mathematical secrets of the universe. But with illustrations, graphics and sidebar digressions, the presentation is a colourful and variegated companion to the most ubiquitous and deceptive components of knowledge.
Scientific American
No. 5, New and Notable Books about Numbers, Scientific American. "Numbers rule our lives," says Bentley, who then tells how and why this is so.
The Lethbridge Herald - Heather Steacy
[starred review] Peter J. Bentley's The Book of Numbers is quite an interesting read.... While this is a fairly out of the ordinary and informative book, it is written somewhat like a textbook which makes it a bit of a difficult read for longer periods of time. Though this may be the case, the layout is quite entertaining for the reader, with all kinds of unusual computer imagery, historical paintings and drawings, along with portraits of mathematicians scattered throughout.... I would, however, recommend it to anyone with even a remote interest in how numbers have completely changed the course of the world and how they are a giant part of how everything works.
Calliope
Book of Numbers proves that numbers are neither dull nor boring. The text is accompanied by great photos, illustrations, and explanatory sidebars. Worth the read.
Book of Numbers proves that numbers are neither dull nor boring. The text is accompanied by great photos, illustrations, and explanatory sidebars. Worth the read.
Annotopia - David Stahnke
This is a beautifully put together book that should be brought into every math classroom... It could bring to students that necessary curiosity that enables them to enjoy mathematics.
Calliope
Book of Numbers proves that numbers are neither dull nor boring. The text is accompanied by great photos, illustrations, and explanatory sidebars. Worth the read.
Book of Numbers proves that numbers are neither dull nor boring. The text is accompanied by great photos, illustrations, and explanatory sidebars. Worth the read.
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Product Details

  • ISBN-13: 9781554073610
  • Publisher: Firefly Books, Limited
  • Publication date: 2/15/2008
  • Pages: 272
  • Sales rank: 1,383,441
  • Product dimensions: 7.50 (w) x 9.75 (h) x 0.87 (d)

Meet the Author

Peter J. Bentley is a senior research fellow and professor at the Department of Computer Science, University College London, and is well known for his prolific research covering all aspects of evolutionary computation and digital biology. He is the author of the popular science book Digital Biology and a regular contributor to BBC Radio 4.

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Read an Excerpt

Chapter -1:
Before the Beginning

Numbers flow past us like a blizzard, wherever we are on the planet. We drive in rivers of numbers. We listen to numbers on headphones. We wear changing numbers on our wrists. We live in numbers, talk in numbers and watch numbers for entertainment. Numbers rule our lives, they wake us up, tell us where to go, how to get there and when to leave. Numbers are judges of all, they assess and compare with complete authority and impartiality. But numbers also lie; they may mean anything except the truth. Numbers can save our lives, and a love of the wrong kind of numbers can ruin us. Numbers can be our friends, our lifelines and our lucky charms. Numbers can also kill us. You are made of numbers. So am I.

Thousands of years ago, when there was no difference between science and religion, numbers seemed to hold the key to understanding the universe. They might not have trickled down in front of our eyes like a scene from The Matrix, but lurking inside many forms were important numbers that seemed too common to be coincidental. The same ratios kept reappearing in nature, perhaps between the diameter of a circle and its circumference, or in the curvature of seashells. The same geometric shapes and the numbers embedded within them kept being discovered in unlikely places, such as the spacing of the planets of our solar system. Even something as unlikely as a speed—for example the speed of light—seemed to be at the heart of the construction of our universe. In those days it was widely believed that such numbers pointed to the mysterious underlying design of God. An understanding of those numbers would be like reading divinemessages written into the fabric of existence. Those pioneers and adventurers who dared to explore the uncharted territories of numbers were exploring the very substance of their world. They were unpicking the details of life, the universe and everything. Their solutions were not a single number, but a whole collection of important numbers, as well as tools to manipulate those numbers.

Today, science has taken over from religion. We still believe that our universe has hugely important numbers associated with it. We now know that they are the patterns visible in the woven tapestry from which everything is made. Some patterns in the tapestry are made from such thick threads that they catch the eye immediately: numbers such as π, e and θ. Some form the bulk of the material: numbers like 0, 1, 2, 3 and √2. Some stand out like accidental spills on the fabric, such as 10 and 13. Other numbers and concepts, like c and ∞, point to the size and shape of the tapestry. Some, such as i, are only visible as tenuous ripples of complexity that flow through the cloth.

Those who explore the fundamental truths of nature are now known by names such as mathematicians, astronomers and physicists. But however we label them, these people were (and still are) explorers. They did not weave the tapestry they examined. They did not invent their numbers or mathematical ideas as a novelist might invent a story. They searched for the truth, and tried to explain it, inventing new languages of numbers simply to be able to write down their discoveries. Some pursued this goal for science, some for religion and some for fame

The explorers we will follow in this book were very clever and many have been called geniuses—but they were people too. They had complicated lives, had arguments, failings and successes. Galileo was a medical school dropout, Newton threatened to burn down his parents' house, Bernoulli stole his son's work, Pascal was a bully and Einstein had a child out of wedlock. Some were murdered because of numbers. Others lost their sanity. Put them all. in a room together and you'd probably be deafened by the shouting. But they all had an appreciation of numbers that made them exceptional. They came from all over the world, yet their language was universal. As their explanations improved, so did the language of numbers.

Through our quirky pioneers we learned how numbers make shapes, angles and connections, enabling us to measure our land, to design and build complicated machines. We discovered the numbers of interacting waves, allowing us to understand music, the swing of pendulums and the bizarre properties of light We learned how numbers describe position, speed and accelerations, enabling us to understand the motion of the planets and comprehend the planet we live on. We learned how numbers define time, space and the different sizes of infinity, enabling us to understand how the flow of time changes and how our universe began. Today we continue to learn the numbers that affect subatomic particles, and those behind complex systems such as economies, societies and consciousness. These remarkable achievements have created our modern world of telephones, cars, music, computers and airplanes. They have enabled almost every modern device you use, the food you eat and the lob you do. Your entire lifestyle is shaped by our understanding of numbers

This book is about the explorers of numbers and the inventors of mathematics. The motivations and beliefs of these eccentric characters are often surprising However, more surprising than their discoverers, are the numbers themselves.

Albert Einstein once said, "There are two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle." Numbers don't remove your ability to marvel at the world, they increase it.

Numbers are miraculous, as you're about to find out.

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Table of Contents

Chapter -1: Before the Beginning Chapter 0: Much Ado About Nothing

  • Writing Numbers
  • Speaking Numbers
  • The Invention of Nothing
  • The Year Zero?
Chapter 0.000000001: Small is Beautiful
  • Rational Numbers
  • An Important Period
  • Thinking Small
Chapter 1: All is One
  • Natural Numbers
  • Perfect Numbers
  • Amicable Numbers
  • Prime Numbers
  • Secure Primes
  • Fractionally One
Chapter √2: Murdering Irrationals
  • Being Irrational
  • Measuring the World
  • Moving the World with Numbers
  • When Is a Number not a Number
  • An Equation Paints a Thousand Words
  • Lost in the Margins
Chapter Φ: Golden Phi
  • Seriously, Rabbits?
  • Out of this World
  • Don't Be Absurd
Chapter 2: Good and Even
  • There Are 10 Types of People in the World: Those Who Understand Binary and Those Who Don't
  • Weaving Patterns of Numbers
  • Thinking Logically
  • Knocking Down the Foundations of Mathematics
  • It Does Not Compute
  • Designing Computer Architectures
  • Creating the Information Revolution
Chapter e: The Greatest
Invention
  • Calculating Without Calculators
  • Natural Curves
  • Pebbles and Fluxions
Chapter 3: The Eternal Triangle
  • Placing Rubber Bands
  • Crossing Bridges
  • Wormholes of Paper
  • Colorful Maps
Chapter π: A Slice of Pi
  • Making a Circle
  • How to Make a Pi
  • Measuring Angles
  • Surfing Sine Waves
  • Pendulums and Heresy
Chapter 10: Decimalization
  • Weird Counting
  • At the Third Stroke, the Time Will Be 86 Past 5 Precisely
  • Sacred Tetractys and Triangles
Chapter
12a: Triskaidekaphobia
  • Be Careful What You Believe
  • Mathematics of Luck
  • Finding Meaning with Numbers
Chapter c: As Fast As You Can Go
  • Seeing c
  • Seeing Is Not the Same as Hearing
  • Special Relativity
  • General Relativity
Chapter ∞: The Neverending Story
  • The Beginning of Forever
  • Wheels Within Wheels
  • Meeting the Infinite
Chapter i: Unimaginable Complexity
  • Using Your Imagination
  • Drawing on Imagination
  • Turning Dreams into Reality (or Reality into Dreams?)
  • Complex Visions
  • All is
    Numbers

Bibliography
Index

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Preface

Chapter -1:
Before the Beginning

Numbers flow past us like a blizzard, wherever we are on the planet. We drive in rivers of numbers. We listen to numbers on headphones. We wear changing numbers on our wrists. We live in numbers, talk in numbers and watch numbers for entertainment. Numbers rule our lives, they wake us up, tell us where to go, how to get there and when to leave. Numbers are judges of all, they assess and compare with complete authority and impartiality. But numbers also lie; they may mean anything except the truth. Numbers can save our lives, and a love of the wrong kind of numbers can ruin us. Numbers can be our friends, our lifelines and our lucky charms. Numbers can also kill us. You are made of numbers. So am I.

Thousands of years ago, when there was no difference between science and religion, numbers seemed to hold the key to understanding the universe. They might not have trickled down in front of our eyes like a scene from The Matrix, but lurking inside many forms were important numbers that seemed too common to be coincidental. The same ratios kept reappearing in nature, perhaps between the diameter of a circle and its circumference, or in the curvature of seashells. The same geometric shapes and the numbers embedded within them kept being discovered in unlikely places, such as the spacing of the planets of our solar system. Even something as unlikely as a speed — for example the speed of light — seemed to be at the heart of the construction of our universe. In those days it was widely believed that such numbers pointed to the mysterious underlying design of God. An understanding of those numbers would be like reading divine messages written into the fabric of existence. Those pioneers and adventurers who dared to explore the uncharted territories of numbers were exploring the very substance of their world. They were unpicking the details of life, the universe and everything. Their solutions were not a single number, but a whole collection of important numbers, as well as tools to manipulate those numbers.

Today, science has taken over from religion. We still believe that our universe has hugely important numbers associated with it. We now know that they are the patterns visible in the woven tapestry from which everything is made. Some patterns in the tapestry are made from such thick threads that they catch the eye immediately: numbers such as π, e and θ. Some form the bulk of the material: numbers like 0, 1, 2, 3 and √2. Some stand out like accidental spills on the fabric, such as 10 and 13. Other numbers and concepts, like c and ∞, point to the size and shape of the tapestry. Some, such as i, are only visible as tenuous ripples of complexity that flow through the cloth.

Those who explore the fundamental truths of nature are now known by names such as mathematicians,
astronomers and physicists. But however we label them, these people were (and still are) explorers. They did not weave the tapestry they examined. They did not invent their numbers or mathematical ideas as a novelist might invent a story. They searched for the truth, and tried to explain it, inventing new languages of numbers simply to be able to write down their discoveries. Some pursued this goal for science, some for religion and some for fame

The explorers we will follow in this book were very clever and many have been called geniuses — but they were people too. They had complicated lives, had arguments, failings and successes. Galileo was a medical school dropout, Newton threatened to burn down his parents' house, Bernoulli stole his son's work, Pascal was a bully and Einstein had a child out of wedlock. Some were murdered because of numbers. Others lost their sanity. Put them all. in a room together and you'd probably be deafened by the shouting. But they all had an appreciation of numbers that made them exceptional. They came from all over the world, yet their language was universal. As their explanations improved, so did the language of numbers.

Through our quirky pioneers we learned how numbers make shapes, angles and connections, enabling us to measure our land, to design and build complicated machines. We discovered the numbers of interacting waves, allowing us to understand music, the swing of pendulums and the bizarre properties of light We learned how numbers describe position, speed and accelerations, enabling us to understand the motion of the planets and comprehend the planet we live on. We learned how numbers define time, space and the different sizes of infinity, enabling us to understand how the flow of time changes and how our universe began. Today we continue to learn the numbers that affect subatomic particles, and those behind complex systems such as economies, societies and consciousness. These remarkable achievements have created our modern world of telephones, cars, music, computers and airplanes. They have enabled almost every modern device you use, the food you eat and the lob you do. Your entire lifestyle is shaped by our understanding of numbers

This book is about the explorers of numbers and the inventors of mathematics. The motivations and beliefs of these eccentric characters are often surprising However, more surprising than their discoverers, are the numbers themselves.

Albert Einstein once said, "There are two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle." Numbers don't remove your ability to marvel at the world, they increase it.

Numbers are miraculous, as you're about to find out.

Read More Show Less

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