From One to Zero: The Universal History of Computing

Introduction
I. AWARENESS OF NUMBERS
	1 The Origin and Discovery of Numbers
		Are animals able to count?
		Natural faculties of number perception
		Can one define a quantity without knowing how to count?
		Rudimentary "accounting" techniques
		Expressing number orally and by gestures
		Counting: a human faculty
		Symbolization of number
		Ten fingers for counting
	2 The Principle of the Base
		Decimal systems
		Traces of the base 5
		Twenty fingers and toes for counting
		The sexagesimal system
		The origin of the sexagesimal system
II. CONCRETE COUNTING
	3 The First Calculating Machine: The Hand
		A curious way of bargaining
		Counting on the bones and joints of the fingers
		Morra, a finger game
		Elements of finger computation
		An elaborate system of finger counting
		History recounted on the fingers
	4 Notching
	5 From Pebbles to Calculation
	6 Numbers on Strings
		The archives of the Incas
		Use of knotted strings in other parts of the world
	7 Number, Value, Money
	8 The Abacus
		Greek and Roman abacuses
		The first pocket calculator
		Abacists versus algorists: the Renaissance
		Rods on the Chinese counting board
		The bead abacus
III. THE INVENTION OF NUMERALS
	9 Roman Numerals: A Vestige of Primitive Origins?
		The numerals of Roman civilization
		Questionable ancestors
		The origin of Roman numerals
		Anthropological and historical evidence
	10 Was Writing Invented by Accountants?
		Five thousand years ago, the Sumerians and Elamites learned to write
		Precursors of written accounting
		From clay envelopes to account tablets
		The mnemonic function of Sumerian writing
	11 Sumerian Numerals
		The development of cuneiform numerals
		Difficulties of the cuneiform numeration system
		Continuance of the Sumerian system
		How modern scholars deciphered Sumerian numerals
	12 Deciphering a Forgotten Notation
	13 Egyptian Numerals
		The origin of hieroglyphs: Sumerian or Egyptian?
		From drawings to numerals
		Fractions and the dismembered eod
	14 Kindred Numeration Systems
		Cretan numerals
		The Hittite hieroglyphic system
		The Aztec system
		Greek acrophonic systems
		Numerals of the Kingdom of Saba
		A significant improvement
	15 The Egyptian Scribes9 Rapid Notation
		Hieratic script
		A remarkable simplification
		Numerals in the time of the Hebrew kings
IV. NUMERALS AND LETTERS
	16 Numerical Use of the Hebrew Alphabet
	17 Greek Alphabetic Numerals
	13 The Phoenician Origin of Numeral Letters: A Legend
	19 Syriac Numerals
	20 Arabic Numeral Letters
	21 Numerals, Letters, Magic, Mysticism, and Divination
		The art and composition of chronograms
		Interpretations and speculations of Gnostics, Cabalists, magicians, and soothsayers
V. HYBRID NUMERATION SYSTEMS
	22 The Drawbacks of the Additive Principle
		Roman notations for large numbers
		Appearance and extension of the multiplicative principle
	23 The Common Mesopotamian Numeration System
	24 Semitic Numerical Traditions
	25 The Traditional Chinese Numeration System
		The modern system
		Different forms of Chinese numerals
		Origin of the Chinese system
		Diffusion of the Chinese system in the Far East
		Systems similar to the common Chinese system
		A natural extension
		Chinese notations of large numbers in scientific works
VI. THE ULTIMATE STAGE OF NUMERICAL NOTATION
	26 The First Place-Value Numeration System
		The Babylonian place-value system
		Difficulties of this system
		The oldest zero in history
		Survival of the Babylonian system
	27 The Chinese Place-Value System
	28 Amazing Achievements of a Vanished Civilization
		Greatness and decline of Mayan civilization
		Sources of our knowledge
		Six centuries of intellectual and artistic achievement
		Writing, arithmetic, and astronomy
		The Mayan calendar
		Chronology and numeration
		Discovery of the place-value principle and the zero in the New World
		Conclusion
	29 The Origin of Hindu-Arabic Numerals
		The keystone of our modem numeration system
		A significant anecdote
		The cradle of our modern system
		The symbolic number words of Indian astronomers
		Origin of the Indian place-value system
		Worldwide propagation of the Indian system
		Adoption of the Indian system by the Eastern Arabs
		Numerals used by the Western Arabs
		Hindu-Arabic numerals in Europe
Chronology
Bibliography of Works Quoted or Mentioned in This Book
Acknowledgments