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Euclid's Window : The Story of Geometry from Parallel Lines to Hyperspace Paperback – April 9, 2002

4.0 out of 5 stars 76 customer reviews

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Editorial Reviews

Amazon.com Review

"How do you know where you are?" asks Leonard Mlodinow in his charming mathematical history, Euclid's Window. This question and others about space and time grew out of simple observations of the environment by a select group of thinkers whose lives and brains Mlodinow dissects. Starting with Euclid, geometry has flowed out over the centuries, describing the universe, and, Mlodinow argues, making modern civilization possible.

This is not just a history of geometry--it's a timeline of reason and abstraction, with all the major players present: Euclid, Descartes, Gauss, Einstein, and Witten, each represented by a minibiography.

Lots of examples pepper the narrative to help readers achieve their own "eureka!" And it's impossible not to be staggered at the mathematical feats of these geniuses, accomplished as many of them were in the absence of anything but observation and intense thought. Each story builds satisfactorily on the last, until at the end of this delightful book, one has a sense of having climbed a peak of understanding.

A working knowledge of basic geometry is helpful but not essential for enjoying Euclid's Window, and Mlodinow's chatty style lends itself remarkably well to explaining these deep and revolutionary concepts. --Adam Fisher --This text refers to an out of print or unavailable edition of this title.

From Publishers 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, Inc.

--This text refers to an out of print or unavailable edition of this title.
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Product Details

  • Paperback: 320 pages
  • Publisher: Free Press (April 9, 2002)
  • Language: English
  • ISBN-10: 0684865246
  • ISBN-13: 978-0684865249
  • Product Dimensions: 5.2 x 0.9 x 9.2 inches
  • Shipping Weight: 11.2 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (76 customer reviews)
  • Amazon Best Sellers Rank: #273,432 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Marvin J. Greenberg on July 30, 2002
Format: Hardcover
Mlodinow ('M' below) writes entertainingly, as most of the other reviews here testify. It's good that the general public get a taste of the excitement of discovery/invention in these fields. He should just correct, in a subsequent edition, the serious distortions that IAS Professor Langlands (Notices of the American Mathematical Society, vol. 49, number 5, p. 554 - referred to as 'L' below) has pointed out; then the book could be a useful, reliable introduction to whet the appetite of people who might want to study the subjects in more depth. Here are a few of Langlands' criticisms:
1. M's portrayals of Proclus, Kant, Kronecker and Gauss' father are unfair caricatures. L provides evidence in their defense.
2. M strives for sensationalism, not fact. E.g., M speculates that Thales traded in leather dildos. Veracity is sacrificed to effect.
3. M missed the main point of Riemann's great 1854 habilitation lecture. L wrote: "I could hardly believe my eyes, but it seems [M] is persuaded that the introduction of elliptic geometry was the principal achievement of the lecture."
Since M acknowledges on p.205 that Einstein's general theory of relativity was based on Riemann's work, M owes the reader much more explanation of Riemann's new ideas, expanding on his p. 207 discussion, not dismissing Riemann by saying his work "wasn't pretty."
4. L criticizes M's account of Einstein's early years, saying: "...to represent Einstein as an academically narrow, misunderstood or mistreated high-school dropout is a cruel disservice to any young reader or to any educator who swallows such falsehoods."
5. L concludes that M's book is "thoroughly dishonest ... simply because the author shrinks from nothing in his desperation to be readable and entertaining.
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Format: Hardcover
As a teacher of geometry, I always keep an eye out for books that offer coherent explanations of the importance of this most intriguing and ancient branch of mathematics. This books offers that in spades. In fact, it is one of the best basic overviews of the field I have ever come across.
Mlodinow divides the history of the development of geometry into five major "revolutions." Starting first with Euclid and his Greek contemporaries, Mlodinow traces the field through Descartes and the development of analytic geometry, Gauss and the development of "non-Euclidean" geometries, Einstein and the physical application of these geometries, to Witten and the development of string theory--the attempt to understand the universe as a consequence of geometry. In high school we teach the basics of plane and analytic geometry but few people are aware of how the field has matured since then. This book takes us on that journey.
And it is a wonderful one. Along the way he gives insight not only into the mathematics but also into the personalities that created it. We too often forget that it is people who created this magnificent structure and that it was not just handed down to us perfectly formed. Even more, we need to be reminded that the development continues and people are still contributing to it.
The real achievement of this book, however, is its acessiblity. Despite the fact that most people will only have experience with the material from the first two sections of the book (Euclid and Descartes), Mlodinow's writing is understandable by anyone who has successfully navigated a course in high school geometry. In my view, he offers one of the most lucid explanations of Einstein's work and string theory that I have ever read. His style is engaging and very readable.
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Format: Paperback
This is by and large the worst popular science book I've ever come across (and being an astronomer and translator of popular science, I've read quite a number of them). Mlodinow violates almost all rules of scientific method and conduct, and even some of rules governing the plain civility in writing. There are literally hundreds of examples of such violations, so let me mention just a few of them. Mlodinow engages in hero-worship to an unprecedented degree: he does not shy away from pronouncing Witten "the most influential physicist and mathematician in the world" (p.253), as if such a grandeloquent statement can ever be proven or even properly supported. He enjoys judging long-dead people without proper history knowledge: he finds Cantor genius and Kronecker "a crab", he outrageously states that medieval Arabs didn't contribute anything original to mathematics (perhaps he should have taken some *history* courses from Witten, who knows better for certain!) and then, a dozen or so pages later, contradicts himself by citing some important results of two Arab mathematicians; he finds geometry and calculus more cognitively important than algebra (a dubious statement and quite improper for a popular work); he censores ancient Romans for their decadent ways (while simultaneously celebrating Athenian often quite promiscuous "symposia"); he does not know that Sirius is the brightest star which can be seen from Greece; he calls Aristotle just a meteorologist (p. 56). In addition, Mlodinow heavily indulges in what serious historians call "Whiggish interpretation of history", i.e. judging of the past by its present utility.Read more ›
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