Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace [NOOK Book]

Overview

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in ...
See more details below
Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK
  • NOOK HD/HD+ Tablet
  • NOOK
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook)
$10.93
BN.com price

Overview

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology.

Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.
Read More Show Less

Editorial Reviews

From Barnes & Noble
A former faculty member at the California Institute of Technology and writer for Star Trek: The Next Generation, Leonard Mlodinow has written an entertaining and completely accessible history of geometry, from its beginnings as a method of calculating landholdings for ancient Egyptian tax collectors to the modern geometry of string theory.
Kirkus Review
Halfway through this articulate and droll history of math and physics, you wonder: Who is this guy ... you want to recommend to all your friends? .... Splendid exposition, accessible to the mathematically challenged as well as the mathematically inclined.
Publishers Weekly - Publisher's Weekly
Mlodinow's background in physics and educational CD-ROMs fails to gel in this episodic history of five "revolutions in geometry," each presented around a central figure. The first four Euclid, Descartes, Gauss and Einstein are landmarks, while the fifth, Edward Witten, should join their ranks if and when his M-theory produces its promised grand unification of all fundamental forces and particles. Mlodinow conveys a sense of excitement about geometry's importance in human thought, but sloppiness and distracting patter combine with slipshod presentation to bestow a feel for, rather than a grasp of, the subject. Certain misses are peripheral but annoying nonetheless confusing Keats with Blake, repeating a discredited account of Georg Cantor's depression, etc. Some of them, however, undermine the heart of the book's argument. Strictly speaking, Descartes, Einstein and Witten didn't produce revolutions in geometry but rather in how it's related to other subjects, while Gauss arguably produced two revolutions, one of which non-Euclidean geometry is featured, while the other differential geometry though equally necessary for Einstein's subsequent breakthrough, is barely developed. Mlodinow completely ignores another revolution in geometry, the development of topology, despite its crucial role in Witten's work. Occasionally Mlodinow delivers succinct explanations that convey key insights in easily graspable form, but far more often he tells jokes and avoids the issue, giving the false, probably unintentional impression that the subject itself is dull or inaccessible. More substance and less speculation about the Greeks could have laid the foundations for an equally spirited but far more informative book. 11 figures, two not seen by PW. (Apr.) Forecast: The Free Press may be looking for a math popularizer in the mold of Amir Aczel, but Mlodinow falls short. Don't look for big sales here. Copyright 2001 Cahners Business Information.
Library Journal
"Euclid's work [is] a work of beauty whose impact rivaled that of the Bible, whose ideas were as radical as those of Marx and Engels. For with his book Elements Euclid opened a window through which the nature of our universe has been revealed." Strong words, but Mlodinow backs them up with this surprisingly exciting history of how mathematicians and physicists discovered geometric space beyond Euclid's three dimensions. Each advance in mathematical geometry has been followed by unexpected discoveries proving that the strange mathematics actually describe measurable physical properties. Mlodinow, a physicist and a former faculty member at the California Institute of Technology, has also written TV screenplays for Star Trek: The Next Generation and other shows. He has a good sense of popular science writing, and he personalizes geometric abstractions by endowing them with the personalities of his adolescent sons, Alexei and Nicholai. Euclid, Descartes, Gauss, Einstein, and Witten are among the mathematicians profiled, and each of them also emerges with a distinct personality based on the style of their writing and historical anecdotes. This engaging history does an excellent job of explaining the importance of the study of geometry without making the reader learn any geometry. For all math and science collections. Amy Brunvand, Univ. of Utah Lib., Salt Lake City Copyright 2001 Cahners Business Information.
From the Publisher
Curt Suplee The Washington Post High-spirited, splendidly lucid and often hilarious.

Michael Guillen author of Five Equations That Changed the World How often can you say that a book on math — on math! — is a real page-turner? Well, this one is. As engaging as a soap opera, as fascinating as a whodunit, as funny as the Sunday comics, Mlodinow's book is storytelling at its best.

Brian Greene author of The Elegant Universe There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry, and Euclid's Window makes this task lively and enjoyable.

Read More Show Less

Product Details

  • ISBN-13: 9781439135372
  • Publisher: Free Press
  • Publication date: 9/28/2010
  • Sold by: SIMON & SCHUSTER
  • Format: eBook
  • Pages: 320
  • Sales rank: 273,699
  • File size: 4 MB

Meet the Author

Leonard Mlodinow, Ph.D., was a member of the faculty of the California Institute of Technology before moving to Hollywood to become a writer for numerous television shows ranging from Star Trek: The Next Generation to Night Court. He has also developed many bestselling and award-winning educational CD-ROMs, and delivered technical and general lectures in ten countries. He is currently Vice President, Emerging Technologies and R&D, at Scholastic Inc. He lives in New York City.
Read More Show Less

Read an Excerpt

Chapter One: The First Revolution

Euclid was a man who possibly did not discover even one significant law of geometry. Yet he is the most famous geometer ever known and for good reason: for millennia it has been his window that people first look through when they view geometry. Here and now, he is our poster boy for the first great revolution in the concept of space -- the birth of abstraction, and the idea of proof.

The concept of space began, naturally enough, as a concept of place, our place, earth. It began with a development the Egyptians and Babylonians called "earth measurement." The Greek word for that is geometry, but the subjects are not at all alike. The Greeks were the first to realize that nature could be understood employing mathematics -- that geometry could be applied to reveal, not merely to describe. Evolving geometry from simple descriptions of stone and sand, the Greeks extracted the ideals of point, line, and plane. Stripping away the window-dressing of matter, they uncovered a structure possessing a beauty civilization had never before seen. At the climax of this struggle to invent mathematics stands Euclid. The story of Euclid is a story of revolution. It is the story of the axiom, the theorem, the proof, the story of the birth of reason itself.

Copyright © 2001 by Leonard Mlodinow
Read More Show Less

Table of Contents

Contents

Introduction

I THE STORY OF EUCLID

1. The First Revolution

2. The Geometry of Taxation

3. Among the Seven Sages

4. The Secret Society

5. Euclid's Manifesto

6. A Beautiful Woman, a Library, and the End of Civilization

II THE STORY OF DESCARTES

7. The Revolution in Place

8. The Origin of Latitude and Longitude

9. The Legacy of the Rotten Romans

10. The Discreet Charm of the Graph

11. A Soldier's Story

12. Iced by the Snow Queen

III THE STORY OF GAUSS

13. The Curved Space Revolution

14. The Trouble with Ptolemy

15. A Napoleonic Hero

16. The Fall of the Fifth Postulate

17. Lost in Hyperbolic Space

18. Some Insects Called the Human Race

19. A Tale of Two Aliens

20. After 2,000 Years, a Face-lift

IV THE STORY OF EINSTEIN

21. Revolution at the Speed of Light

22. Relativity's Other Albert

23. The Stuff of Space

24. Probationary Technical Expert, Third Class

25. A Relatively Euclidean Approach

26. Einstein's Apple

27. From Inspiration to Perspiration

28. Blue Hair Triumphs

V THE STORY OF WITTEN

29. The Weird Revolution

30. Ten Things I Hate About Your Theory

31. The Necessary Uncertainty of Being

32. Clash of the Titans

33. A Message in a Kaluza-Klein Bottle

34. The Birth of Strings

35. Particles, Schmarticles!

36. The Trouble with Strings

37. The Theory Formerly Known As Strings

Epilogue

Notes

Acknowledgments

Index
Read More Show Less

First Chapter

Chapter One: The First Revolution

Euclid was a man who possibly did not discover even one significant law of geometry. Yet he is the most famous geometer ever known and for good reason: for millennia it has been his window that people first look through when they view geometry. Here and now, he is our poster boy for the first great revolution in the concept of space — the birth of abstraction, and the idea of proof.

The concept of space began, naturally enough, as a concept of place, our place, earth. It began with a development the Egyptians and Babylonians called "earth measurement." The Greek word for that is geometry, but the subjects are not at all alike. The Greeks were the first to realize that nature could be understood employing mathematics — that geometry could be applied to reveal, not merely to describe. Evolving geometry from simple descriptions of stone and sand, the Greeks extracted the ideals of point, line, and plane. Stripping away the window-dressing of matter, they uncovered a structure possessing a beauty civilization had never before seen. At the climax of this struggle to invent mathematics stands Euclid. The story of Euclid is a story of revolution. It is the story of the axiom, the theorem, the proof, the story of the birth of reason itself.

Copyright © 2001 by Leonard Mlodinow

Read More Show Less

Introduction

Introduction

Twenty-four centuries ago, a Greek man stood at the sea's edge watching ships disappear in the distance. Aristotle must have passed much time there, quietly observing many vessels, for eventually he was struck by a peculiar thought. All ships seemed to vanish hull first, then masts and sails. He wondered, how could that be? On a flat earth, ships should dwindle evenly until they disappear as a tiny featureless dot. That the masts and sails vanish first, Aristotle saw in a flash of genius, is a sign that the earth is curved. To observe the large-scale structure of our planet, Aristotle had looked through the window of geometry.

Today we explore space as millennia ago we explored the earth. A few people have traveled to the moon. Unmanned ships have ventured to the outer reaches of the solar system. It is feasible that within this millennium we will reach the nearest star — a journey of about fifty years at the probably-some-day-attainable speed of one-tenth the speed of light. But measured even in multiples of the distance to Alpha Centauri, the outer reaches of the universe are several billion measuring sticks away. It is unlikely that we will ever be able to watch a vessel approach the horizon of space as Aristotle did on earth. Yet we have discerned much about the nature and structure of the universe as Aristotle did, by observing, employing logic, and staring blankly into space an awful lot. Over the centuries, genius and geometry have helped us gaze beyond our horizons. What can you prove about space? How do you know where you are? Can space be curved? How many dimensions are there? How does geometry explain the natural order and unity of the cosmos? These are the questions behind the five geometric revolutions of world history.

It started with a little scheme hatched by Pythagoras: to employ mathematics as the abstract system of rules that can model the physical universe. Then came a concept of space removed from the ground we trod upon, or the water we swam through. It was the birth of abstraction and proof. Soon the Greeks seemed to be able to find geometric answers to every scientific question, from the theory of the lever to the orbits of the heavenly bodies. But Greek civilization declined and the Romans conquered the Western world. One day just before Easter in A.D. 415, a woman was pulled from a chariot and killed by an ignorant mob. This scholar, devoted to geometry, to Pythagoras, and to rational thought, was the last famous scholar to work in the library at Alexandria before the descent of civilization into the thousand years of the Dark Ages.

Soon after civilization reemerged, so did geometry, but it was a new kind of geometry. It came from a man most civilized — he liked to gamble, sleep until the afternoon, and criticize the Greeks because he considered their method of geometric proof too taxing. To save mental labor, René Descartes married geometry and number. With his idea of coordinates, place and shape could be manipulated as never before, and number could be visualized geometrically. These techniques enabled calculus and the development of modern technology. Thanks to Descartes, geometric concepts such as coordinates and graphs, sines and cosines, vectors and tensors, angles and curvature, appear in every context of physics from solid state electronics to the large-scale structure of space-time, from the technology of transistors and computers to lasers and space travel. But Descartes's work also enabled a more abstract — and revolutionary — idea, the idea of curved space. Do all triangles really have angle sums of 180 degrees, or is that only true if the triangle is on a flat piece of paper? It is not just a question of origami. The mathematics of curved space caused a revolution in the logical foundations, not only of geometry but of all of mathematics. And it made possible Einstein's theory of relativity. Einstein's geometric theory of space and that extra dimension, time, and of the relation of space-time to matter and energy, represented a paradigm change of a magnitude not seen in physics since Newton. It sure seemed radical. But that was nothing, compared to the latest revolution.

One day in June 1984, a scientist announced that he had made a breakthrough in the theory that would explain everything from why subatomic particles exist, and how they interact, to the large-scale structure of space-time and the nature of black holes. This man believed that the key to understanding the unity and order of the universe lies in geometry — geometry of a new and rather bizarre nature. He was carried off the stage by a group of men in white uniforms.

It turned out the event was staged. But the sentiment and genius were real. John Schwarz had been working for a decade and a half on a theory, called string theory, that most physicists reacted to in much the same way they would react to a stranger with a crazed expression asking for money on the street. Today, most physicists believe that string theory is correct: the geometry of space is responsible for the physical laws governing that which exists within it.

The manifesto of the seminal revolution in geometry was written by a mystery man named Euclid. If you don't recall much of that deadly subject called Euclidean Geometry, it is probably because you slept through it. To gaze upon geometry the way it is usually presented is a good way to turn a young mind to stone. But Euclidean geometry is actually an exciting subject, and Euclid's work a work of beauty whose impact rivaled that of the Bible, whose ideas were as radical as those of Marx and Engels. For with his book, Elements, Euclid opened a window through which the nature of our universe has been revealed. And as his geometry has passed through four more revolutions, scientists and mathematicians have shattered theologians' beliefs, destroyed philosophers' treasured worldviews, and forced us to reexamine and reimagine our place in the cosmos. These revolutions, and the prophets and stories behind them, are the subject of this book.

Copyright © 2001 by Leonard Mlodinow

Read More Show Less

Interviews & Essays

Exclusive Author Essay
No matter who is credited with a scientific discovery, in the end, each of us involved in science has to rediscover it anew. Playing baseball when I was 8 years old, I began to think that, while there was obviously a geometry to the diamond, there must also be a geometry to the arc of the ball in the air. Maybe understanding it would make me a better hitter... I learned about spin and air resistance. Soon, geometry had opened the door to a love of physics. I discovered non-Euclidean geometry a couple of years later while picking through stacks of battered old books in a rummage sale. I knew what Euclidean geometry was by then, and something about trajectories, but somehow the term "non-Euclidean" seemed enchanting. It was as if I had been eating hamburgers all my life and suddenly stumbled upon a bacon cheeseburger. I paid a quarter for the book and flipped through it. I marveled at the part about how "parallel" lines could intersect. An 11-year-old doesn't forget things like that. What was "curved space"? How would a baseball fly in that?

I went on to get an advanced degree and conduct research in mathematical physics. I pretty much gave up baseball and started writing stories when I wasn't doing mathematical physics (or doing my laundry). To me, telling stories and doing science never seemed that different. One is phrased in language, the other in mathematics; but the thrill of each resides in creating or exploring new worlds. Eventually, I got to merge writing and science when I was offered a job writing for Star Trek: the Next Generation. I ended up writing for numerous shows, even sitcoms such as Night Court, in which I was prone to building plots around mad scientists and baseball.

Then kids came, and a responsible job as a vice president with an office in downtown New York. A couple of years ago I decided to write Euclid's Window for the child I hoped still lurked somewhere inside me. Could I recapture that excitement about the way geometry underlies everything? From standing on that baseball diamond to arguing physics with Richard Feynman at Cal Tech to dreaming up a Star Trek story to discussing math with my two boisterous boys, it has always seemed to me that geometry -- just understanding the space around us near and far -- is at the heart of much of human civilization. The best way to convey my vision of this wonderful art was to tell the stories of the five people I see as the poster boys of the great revolutions that occurred over the last 3,000 years or so: Euclid, Descartes, Gauss, Einstein, and Witten -- the last of whom is still very much alive, wasn't happy about being set up alongside these hall of famers, and will probably never really forgive me for doing it anyway.

My plan was ambitious: to take the reader on a voyage of 3,000 years, through all the revolutions in thought that brought us from Euclid to today's twisted 11-dimensional world of string theory, and to do it without letting the mathematics interfere with the story, which really is a page-turner. It was a far bigger project than I imagined. But I'm still alive and look forward to the time when, in a few years, my eldest will be able to understand my book. While I hope that it will inspire him as I was inspired, I know one thing is certain: To find it he won't have to go searching through any bins at the rummage sale. (Leonard Mlodinow)

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously
Sort by: Showing all of 8 Customer Reviews
  • Anonymous

    Posted April 26, 2006

    An Interesting Twist

    Mlodinow has given an interesting twist to ordinary history. I am not partial to history books, however, the information presented in this novel has some humor to it. It describes the geniuses who formed our current mathematical ideas and explains why some mathematical elements are called what they are. Unlike the critics who responded with their utmost praise, I did not enjoy this book because it dragged along. I love math but do not consider this book to be a pleasurable read.

    1 out of 2 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted April 29, 2013

    Very Good Book about the history of mathematics and its basic id

    Very Good Book about the history of mathematics and its basic ideas. Presented in a way that even a non-math savvy reader can understand. Very practical, without complex formulas of theorems. Awesome examples for laymen. Presents the story like a sort of drama! Very funny at times. Def must read!

    Was this review helpful? Yes  No   Report this review
  • Posted July 4, 2011

    more from this reviewer

    Marred by ebook rendering errors

    Buy this one in paper unless you enjoy looking at weird character errors. Every umlauted O has been changed to an umlauted A, for example. Doesn't anyone proofread these?

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted December 28, 2011

    No text was provided for this review.

  • Anonymous

    Posted May 23, 2011

    No text was provided for this review.

  • Anonymous

    Posted March 29, 2010

    No text was provided for this review.

  • Anonymous

    Posted January 7, 2011

    No text was provided for this review.

  • Anonymous

    Posted December 7, 2008

    No text was provided for this review.

Sort by: Showing all of 8 Customer Reviews

If you find inappropriate content, please report it to Barnes & Noble
Why is this product inappropriate?
Comments (optional)