Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

by Leonard Mlodinow
     
 

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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 inSee more details below

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.

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Editorial Reviews

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.

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.

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Product Details

ISBN-13:
9780684865249
Publisher:
Free Press
Publication date:
04/02/2002
Edition description:
Reprint
Pages:
320
Sales rank:
577,004
Product dimensions:
5.30(w) x 9.10(h) x 0.70(d)

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

What People are saying about this

Edward Witten
Edward Witten, California Institute of Technology
Mlodinow leads the reader on a fascinating tour through the history of geometry, from ancient times to our modern-day fumblings in trying to understand string theory. The book is written with grace and charm.
Amir Aczel
Euclid's Window is a very good introduction to geometry, from Euclid to Einstein. Readable and entertaining.
—(Amir Aczel, author of Fermat's Last Theorem)
Amy Brunvand
Amy Brunvand, University of Utah Lib, Salt Lake City
This surprisingly exciting history of how mathematicians and physicists discovered geometric space beyond Euclid's three dimensions ... 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.
Michael Guillen
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 whodunnit, as funny as the Sunday comics, Mlodinow's book is story-telling at its best.
—(Michael Guillen, Ph.D., author of Five Equations That Changed the World)
David Berlinsky
This is an exhilarating book, one that celebrates geometry as one of mathematics' shining suns. And it is an important book, if only because that sun has for too long been covered by a numver of scudding clouds. And it is, finally, a lovely book, one that reflects the radiance of its subject and so warms even as it instructs.
—(David Berlinski, author of A Tour of the Calculus)
Brian Greene
If there is one thing that progress in physics confirms again and again, it is that geometry is a powerful conceptual framework for describing and understanding the universe. In Euclid's Window, Leonard Mlodinow tells the intriguing story of geometry, from antiquity through the exciting and mind-bending developments of superstring theory. There is perhaps no better way to prepare for the scientific breakthroughts of tomorrow than to learn the language of geometry, and Euclid's Window makes this task lively and enjoyable.
—(Brian Greene, author of The Elegant Universe)

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