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Number Words and Number Symbols: A Cultural History of Numbers

Karl Menninger
Publisher: 
Dover Publications
Publication Date: 
2015
Number of Pages: 
480
Format: 
Paperback
Price: 
29.95
ISBN: 
9780486270968
Category: 
Monograph
BLL Rating: 

The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Underwood Dudley
, on
10/5/2015
]

This is a translation by Paul Broneer of the 1957 edition of Zahlwort und Ziffer, which originally appeared in 1934. It was published by the MIT Press in 1969 and taken over, unaltered, by Dover Publications in 1992.

Karl Menninger (1898–1963) spent his career, 1923–1963, as a teacher of mathematics in Heppenheim in southwestern Germany; the population in Menninger’s time was around 15,000. Number Words and Number Symbols is his monument. Other than that, he wrote a book translated into English (1965) as Calculator’s Cunning that had had ten German editions, and a work that appeared in English (1962) as Mathematics in Your World. They are trifles in comparison.

He should not to be confused with the American psychiatrist Karl Menninger (1893–1990). He was, of course. A copy of Number Words and Number Symbols was sent, because of the confusion, for review to the Journal of Analytical Psychology. The reviewer was sufficiently impressed to review it anyway, finding in it material useful for, or of interest to, analytical psychologists.

As might be expected, the book is about number words and number symbols. The table of contents shows what the author includes. He doesn’t leave much out! For example, there nine pages of tables of number words in Indo-European languages, from Sanskrit to Gothic, Tocharian, Old Church Slavonic, Breton, and even including French, German, and English.

The book is well illustrated with 282 figures. The writing is clear and lively. There are anecdotes. With good reason has it lasted eighty years. (There is no book like it because, if anyone ever had the idea of writing one, he or she would look at Menninger’s, see that it would be of no use and decide to write something else.)

The book is a marvel of scholarship. In his acknowledgments, Menninger gives special thanks to twenty-five separate libraries. All the others that he went to, the ones that deserve only ordinary thanks, don’t get mentioned.

It’s not a book to curl up with for leisure reading. It contains so much material that it’s difficult to digest big hunks of it all at once. Dipping into it at random is rewarding, and if you want to know about tally sticks, or quipu, or the abacus, this is the place to start.

The 1957 German edition was in two volumes. To fit the English edition into one volume, the references and bibliographies were left out. That’s too bad, but I suppose reasonable — most of the references would be in German, date to before 1934, and hence would not be very useful for monoglot English speakers in 2015.

One misprint (“Diphantus”, p. 272) has survived for eighty-one years, or from whenever it was introduced.

That aside, a wonderful book!


Woody Dudley stopped teaching in 2004, but he hasn’t stopped being fascinated with numbers.

 
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
 
 
 

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