Finding Zero (23 page)

Varanasi (holy city),
42
,
114
,
127
,
134
,
168
–72,
200
–1

Vedas (Sanskrit texts),
48
,
62
–3,
214

very large numbers,
6
,
37
,
78
,
104
,
144
–5,
148

vigesimal (base 20),
31
–2.
See also
number systems: base–20

Vishnu (also Narayana),
35
–6,
78
,
91
,
100
–2,
115
,
129
,
139
,
214

void, Buddhist
(
Shunyata
),
40
–1,
78
,
104
,
105
–6,
127
,
135
,
137
–8,
142
,
148
,
152
–3,
154
–5,
161
–2,
223

Wats
(temples)

Angkor Wat,
91
–3,
123
,
129
,
139
,
165
,
169
,
174
,
176
,
205

Wat Langka (Bangkok),
122
–4

Wat Pho (Bangkok),
123
,
164

Wat Xieng Thong (Luang Phrabang),
135

Weierstrass, Karl (mathematician),
146

Western Ghats (mountain range),
64

Yama (ruler of the departed),
102

Yasovarman I (Angkorian king),
101

Zegarelli, Mark,
54
–5

zephirum
(zero),
26

zero

Gwalior zero,
78
–81,
83
–4,
90
,
93
,
95
,
107
, 210

Khmer,
150
,
156
,
175
,
218
,
219

Mayan,
31
,
79
–80,
203

as number,
212
–17

place-holding,
27
,
34
,
75
,
78
,
97
,
152
–3,
208
–9,
212

Shunya
(Sanskrit),
40
–1,
69

sifr
(Arabic),
26

See also
K-127 (inscription artifact)

Zhou Daguan (also Chou Ta-kuan),
101
–2

Zim Lines,
7
,
18
,
110
,
223

Acknowledgments

I am extremely grateful to the Alfred P. Sloan Foundation in New York and to Doron Weber, the Foundation's director of the Program for the Public Understanding of Science and Technology, as well as to members of the Foundation's staff, for supporting me in writing this book. I can easily say that without the Sloan Foundation's faith in me, and the research grant it generously provided, this book would not have been written, and the precious stone artifact known as K-127, which bears the earliest zero in our number system, would not have been rediscovered and brought to the attention of the world of science.

Others have helped me on this quest as well. I thank His Excellency Hab Touch, director general of the Cambodian Ministry of Culture and Fine Arts, for his invaluable assistance to me in rediscovering the stele he has since dubbed “Khmer Zero.” I thank Chamroeun Chhan, Rotanak Yang, Ty Sokheng, Sathal Khun, Darryl Collins, Takao Hayashi, C. K. Raju, Fred Linton, Jacob Meskin, Marina Ville, W. A. Casselman, Eric Dieu, and especially Andy Brouwer in Phnom Penh for their help.

I am grateful to my agent, Albert Zuckerman of Writers House in New York, for his enthusiasm for this project and his support of this book's publication. Many thanks to my editor at Palgrave Macmillan, Karen Wolny, for believing in this book and for her thoughtful editing, comments, and suggestions, which greatly improved the manuscript. Warm thanks also to Lauren LoPinto for her editing of the book, to Carol McGillivray for her superb editing and insightful comments, to production manager Alan Bradshaw for handling the subtle complexities of producing it, and to copy editor Bill Warhop for his superb editing. Thanks also to designer Rachel Ake, to art director David Baldeosingh Rotstein, and to typesetter Letra Libre for their work in turning the manuscript into a complete book.

Finally, I am extremely grateful to my wife, Debra, for all her suggestions and help, for joining me on parts of the big adventure of searching for the first zero, and for taking some of the photographs in this book.

About the Author

Amir D. Aczel
is the author of twenty books, including
The Riddle of the Compass, The Mystery of the Aleph,
and the international bestseller
Fermat's Last Theorem
. An internationally known writer of mathematics and science, he is a Fellow of the John Simon Guggenheim Memorial Foundation, and his research for this book was supported by a grant from the Alfred P. Sloan Foundation.

FINDING ZERO.
Copyright © Amir D. Aczel, 2015. All rights reserved. For information, address Palgrave Macmillan Trade, 175 Fifth Avenue, New York, N.Y. 10010.

us.macmillan.com

The Library of Congress has cataloged the print edition as follows:

Aczel, Amir D., author.

Finding zero : a mathematician's odyssey to uncover the origins of numbers / Amir D. Aczel.

pages cm

Includes bibliographical references (pages ).

ISBN 978-1-137-27984-2 (hardback)

1. Numerals—History. 2. Zero (The number)—History. I. Title.

QA141.2.A29 2015

513.5—dc23

2014024462

e-ISBN 978-1-4668-7910-2

First Edition: January 2015

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