El primer postulado

The Fifth Postulate

The Fifth Postulate
How Unraveling a Two-Thousand-Year-Old Mystery Unraveled the Universe

Jason Socrates Bardi

John Wiley & Sons, Inc.

Copyright # 2009 by Jason Socrates Bardi. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers,MA 01923, (978) 750–8400, fax (978) 646–8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748–6011, fax (201) 748–6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and the authorhave used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategiescontained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor the author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information about our other products and services, please contact our Customer CareDepartment within the United States at (800) 762–2974, outside the United States at (317) 572–3993 or fax (317) 572–4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Bardi,Jason Socrates. The fifth postulate: how unraveling a two-thousand-year-old mystery unraveled the universe/Jason Socrates Bardi. p. cm. Includes bibliographical references and index. ISBN 978-0-470-14909-6 (cloth) 1. Parallels (Geometry) 2. Geometry, Plane. 3. Pythagorean theorem. I. Title. II. Title: 5th postulate. QA481.B237 2008 516.2–dc22 2008012187 Printed in the United States of America 109 8 7 6 5 4 3 2 1

For Isaac B.

Contents

Acknowledgments Prologue 1 A Mathematician’s Waterloo 2 The Strange Vegetarian Cult and Mathematics 3 The Mystery Maker 4 Those False and Would-Be Proofs 5 A Codebreaker’s Fix 6 Searching for Ceres 7 The Dim Light of Exhaustion 8 Gauss’s Little Secret 9 Lessons of Curvature 10 To Stir the Nests of Wasps 11 A Strange New World 12 A Message forYou, Ambassador 13 ‘‘To Praise It Would Be to Praise Myself ’’ 14 The Birth of Electronic Communication 15 The Imaginary Man from Kazan

ix 1 3 25 45 57 71 83 95 105 111 123 137 147 157 167 177

vii

viii

CONTENTS

16 The Soul of the Universe 17 The Curvature of Space Notes Bibliography Index

193 207 211 235 245

Acknowledgments

‘‘How do you do it?’’ a casual acquaintance askedme the other day. I had been telling her about my book—this book—and how I was finishing it while at the same time working full-time at the American Institute of Physics. This was my second book, and the job was my first job in a management position. Both have been tough but rewarding, coming on top of the fact that my wife and I are raising two kids, both under the age of four (Isaac is not yet...