Number Words and Number Symbols: A Cultural History of Numbers

by Karl Menninger, Paul Broneer (Translator)

Overview

Classic study discusses number sequence and number language, then explores written numerals and computations in a wide range of cultures. 282 illustrations. "Superior narrative ability." - Library Journal.

Product Details

ISBN-13:	9780486270968
Publisher:	Dover Publications
Publication date:	11/24/2011
Edition description:	REPRINT
Pages:	512
Product dimensions:	6.53(w) x 9.24(h) x 1.06(d)

Table of Contents

Preface
List of Phonetic Symbols
NUMBER SEQUENCE AND NUMBER LANGUAGE
Introduction
The Number Sequence
  The Abstract Number Sequence
  The Number Sequence Use Concretely
    NUMBERS WITHOUT WORDS
    NUMBERS AS ATTRIBUTES
    NUMBERS AS ADJECTIVES
  Expansion of the Number Sequence by Means of Supplementary Quantities
    NUMBERING BY FINGERS AND TOES
  Principles of the Number Sequence
    SUCCESSION AND GROUP
    GROUPINGS OF HIGHER RANK
    GRADATION BY STEPS
    GROUPINGS IN THE GRADUATED NUMBER SEQUENCE
    "20-GROUP "MAN"
    NUMBER LANGUAGE AND NUMBER SYMBOLS
  Historical Gradations
    REPRESENTING THE GRADATION
    NUMBER SYSTEMS BASED ON GRADATIONS OF 20
    VIGESIMAL GRADATIONS IN EUROPEAN NUMBER SEQUENCES
    THE AINU NUMBER SEQUENCE
  Laws Governing the Formation of Number Words
    SUCCESSION OF MAGNITUDES
    BACK-COUNTING
    OVERCOUNTING
    ADDITIONAL WAYS OF FORMING NUMBER WORDS
    THE FIRST STEPS BEYOND TEN
Our Number Words
  Indo-European Family Languages
    SURVEY OF LANGUAGES AND NUMBER WORDS
    THE ORIGINAL INDO-EUROPEAN LANGUAGE
    THE INDIVIDUAL INDO-EUROPEAN LANGUAGES
  The Non-Indo-European Languages
  The Meaning of Our Number Words
    IMAGES BEHIND THE CONCEPTS OF SIZE AND NUMBER
    SEMANTIC FADING
    OUR INDO-EUROPEAN NUMBER WORDS
  Was There a Babylonian Influence on Our Number Sequence?
    THE BREAK AFTER SIXTY
    THE ROLE PLAYED BY THE NUMBER SIXTY IN CULTURAL HISTORY
    GREAT HUNDRED
    THE NUMBER TWELVE AS THE BASIC UNIT OF THE GREAT HUNDRED
    THE ROMAN DUODECIMAL FRACTIONS
    THE BABYLONIAN SEXAGESIMAL SYSTEM
    THE BREAK AFTER SIXTY IN THE GERMANIC NUMBER SEQUENCE
  Hidden Number Words
    ONE
    TWO
    THREE
    FOUR
    FIVE
    SIX
    SEVEN
    NINE
    TEN
    TWENTY
    FORTY
    FIFTY
    SEVENTY
    HUNDRED
    THOUSAND
    NUMBER
  The Evolution of the Number Sequence
    FOREIGN LOAN WORDS
WRITTEN NUMERALS AND COMPUTATIONS
Preface
Introduction
Finger Counting
  Finger Counting
    THE VENERABLE BEDE AND HIS FINGER COUNTING
    FINGER COUNTING IN ANTIQUITY
    FINGER COUNTING IN ARABIC AND EAST AFRICAN COMMERCE TRADE
    ROMAN FINGER COUNTING IN THE WEST
    COMPUTATIONS ON THE FINGERS
    SOME FORMS OF FINGER COUNTING USE BY PEOPLES OF OTHER CULTURES
Folk Symbols for Numbers
  Tally Sticks
    EARLY WRITING AND READING
    TALLY STICKS WERE UNIVERSAL
    VARIETIES OF TALLY STICKS
    THE BRITISH EXCHEQUER TALLIES
    THE NUMBERS ON THE TALLY STICKS
    ROMAN NUMERALS
    CHINESE HAN STICKS
  Peasant Numerals
  Knots Used as Numerals
Alphabetical Numerals
  The Gothic Numerals
  Letters and Numbers
    HISTORY OF THE ALPHABET
  The Two Greek Sets of Numerals
  Some Other Connections Between Letters and Numbers
"The "German" Roman Numerals"
  Roman Numerals in Cursive Form
    MEDIEVAL NUMBERS
    THE GRADUAL PENETRATION OF THE NEW INDIAN NUMERALS
    THE ACCOUNT BOOKS OF THE IMPERIAL FREE CITY OF AUGSBURG
    WRITTEN NUMERALS AND COMPUTATIONS
The Abacus
  The Nature of the Counting Board
  The Counting Board in Ancient Civilizations
    THE SALAMIS TABLET
    DARIUS VASE
    THE ETRUSCAN CAMEO
    THE ROMAN HAND ABACUS
    THE HAND ABACUS IN ASIA
    THE ROMAN COUNTING BOARD WITH LOOSE COUNTERS
  The Counting Board in the Early Middle Ages
    THE WEST
    THE MONASTIC ABACUS
  The Counting Board in the Later Middle Ages
    THE EVIDENCE FOR ITS USE
    THE NEW RECKONING BOARD
    THE NAMES OF THE COUNTING BOARDS
    "RECKONING "ON THE LINES"
    THE COUNTING BOARD IN EVERYDAY LIFE
    THE COUNTING BOARD AND WRITTEN NUMERALS
  The Counters
Our Own Numerals
  Place-Value Notation
  The Antecedents of Our Numerals
    THE KHAROSTHI NUMERALS
    THE BRAHMI NUMERALS
    PLACE-VALUE NOTATION
  The Westward Migration of the Indian Numerals
    THE ZERO
    ALEXANDRIA
    THE INDIAN NUMERALS IN ARAB HANDS
    THE FAMILY TREE OF INDIAN NUMERALS
  The Indian Numerals in Western Europe
    ITALY
    LEONARDO OF PISA
    THE GERMAN ARITHMETICIANS
    "THE "NEW" NUMERALS"
    RETROSPECT
Spoken Numbers and Number Symbols in China and Japan
  Far Eastern Number Systems
  Spoken Numbers
    THE CHINESE NUMBER WORDS
    JAPANESE NUMBER WORDS
    KOREAN NUMBER WORDS
    SUMMARY
    WRITTEN NUMERALS
    RETROSPECT: SPOKEN LANGUAGE?WRITING?WRITTEN NUMERALS
Index

Editorial Reviews

A reprint of the 1969 English translation (MIT Press) of the revised German edition of 1957-58 (Vandenhoeck & Ruprecht, Gottingen). A classic study documenting the origin and meaning of numbers in various cultures. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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