From One to Zero. The Universal History of Computing [1 ed.] 0670373958

Table of contents :
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