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.
Review
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.
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.
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.
"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
From 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 Reed Business Information, Inc.
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.
Product Description
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.
Review
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.
Excerpt. © Reprinted by permission. All rights reserved.
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
About 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.
From Booklist
Mlodinow's spry account of geometry stresses the stature of the greatest math book of all time, Euclid's Elements. Although the three-dimensional space he described in it doesn't truly represent the shape of nature, Euclid compensated by codifying an attitude essential to rational thinking--to wit, distrust intuition and therefore don't accept unjustified assumptions. Unfortunately, Euclid himself made one unjustified assumption, the parallel postulate, which worked fine in the flat-Earth mathematical world that existed until Carl Friedrich Gauss dismantled it in the nineteenth century. Gauss invented a new geometry of curved or hyperbolic space, a feat that Mlodinow honors in such amusing asides as his remark on Kant's defense of Euclid: "Gauss did not dismiss Kant's work out of hand. He read it, then dismissed it." Such japes lighten and popularize Mlodinow's approach to the further demolition of Euclid by Gauss' student Georg Riemann, whose work critically contributed to the theory of general relativity. Mlodinow's lively exposition concludes with string theorists' claim that geometry possesses no fewer than 11 dimensions. Gilbert Taylor
Copyright © American Library Association. All rights reserved
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
From 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 Reed Business Information, Inc.
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.