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Number Words and Number Symbols: A Cultural History of Numbers
'The historian of mathematics will find much to interest him here . . . while the casual reader is likely to be intrigued by the author's superior narrative ability." — Library Journal
This book is not only a fascinating introduction to the concept of number and to numbers themselves, hut a multifaceted linguistic and historical analysis of how numbers have developed and evolved in many different cultures. Drawing on evidence from history, literature, philosophy and ethnology, noted German scholar Karl Menninger. recounts the development of numbers both as they are spoken (and written as words) and as symbolic abstract numerals that can he readily manipulated and combined.
Despite the immense erudition the author brings to the topic, he maintains a light tone throughout, presenting much of the information in anecdotal form. Moreover, almost 300 illustrations (photographs and drawings) and many comparative language tables serve to enhance the text. The author begins with a lucid treatment of number sequence and number language, including the formation of number words in both Indo-European and non-IndoEuropean languages, hidden number words and the evolution of the number sequence. He then turns to written numerals and finger counting, folk symbols for numbers, alphabetical numerals, the "German" Roman numerals, the abacus and more. The final section concerns the development of our modem decimal system, with its place notation and zero, based on the Indian number system, and its introduction to the West through the work of the Italian mathematician Fibonacci. The author concludes with a review of spoken numbers and number symbols in China and Japan.
"The book is especially good on early counting and calculating primitive tally sticks, the knotted cords of ancient Peru, the elaborate finger symbols once used for numbers, counting boards with movable counters, and of course the abacus." — Martin Gardner, Book World
This book is not only a fascinating introduction to the concept of number and to numbers themselves, hut a multifaceted linguistic and historical analysis of how numbers have developed and evolved in many different cultures. Drawing on evidence from history, literature, philosophy and ethnology, noted German scholar Karl Menninger. recounts the development of numbers both as they are spoken (and written as words) and as symbolic abstract numerals that can he readily manipulated and combined.
Despite the immense erudition the author brings to the topic, he maintains a light tone throughout, presenting much of the information in anecdotal form. Moreover, almost 300 illustrations (photographs and drawings) and many comparative language tables serve to enhance the text. The author begins with a lucid treatment of number sequence and number language, including the formation of number words in both Indo-European and non-IndoEuropean languages, hidden number words and the evolution of the number sequence. He then turns to written numerals and finger counting, folk symbols for numbers, alphabetical numerals, the "German" Roman numerals, the abacus and more. The final section concerns the development of our modem decimal system, with its place notation and zero, based on the Indian number system, and its introduction to the West through the work of the Italian mathematician Fibonacci. The author concludes with a review of spoken numbers and number symbols in China and Japan.
"The book is especially good on early counting and calculating primitive tally sticks, the knotted cords of ancient Peru, the elaborate finger symbols once used for numbers, counting boards with movable counters, and of course the abacus." — Martin Gardner, Book World
510 pages, Paperback
First published September 15, 1958
16 people are currently reading
215 people want to read
About the author
Karl A. Menninger
81 books50 followersKarl Augustus Menninger (July 22, 1893 – July 18, 1990) was an American psychiatrist and a member of the Menninger family of psychiatrists who founded the Menninger Foundation and the Menninger Clinic in Topeka, Kansas.
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Displaying 1 - 5 of 5 reviews
April 14, 2017
If you're one of those people suffering from apophenia, who delight in finding patterns in things, especially numbers, than this volume, latter-day (and wackily sympathetic) kabbalists and numerologists, you'd probably love this book.
Conversely, lovers of more precise--I hesitate to use the word 'real', but, fuck it--'real' sciences, like math and linguistics, will also love this book.
For me, a layman, or, ahem, layperson it was tangentially interesting in both the latter senses. Math-wise, you get an immense and obsessive, almost fanatical, exploration of the inherent logic of numbers, where numbers came from, how we think of numbers, ways of counting--all sorts of weird stuff you'd never considered about a basic fundament of our lives. Language-wise, you get even more fanatical delvings-into of cognates, word origin, word sense, 'hidden' numbers, and all that.
A little too detailed for my tastes to the point of drudgery, but in an overall sense, satisfying in the way that the Cliff Notes to 'Finnegan's Wake' might be, with the same, muted sense of achievement.
Conversely, lovers of more precise--I hesitate to use the word 'real', but, fuck it--'real' sciences, like math and linguistics, will also love this book.
For me, a layman, or, ahem, layperson it was tangentially interesting in both the latter senses. Math-wise, you get an immense and obsessive, almost fanatical, exploration of the inherent logic of numbers, where numbers came from, how we think of numbers, ways of counting--all sorts of weird stuff you'd never considered about a basic fundament of our lives. Language-wise, you get even more fanatical delvings-into of cognates, word origin, word sense, 'hidden' numbers, and all that.
A little too detailed for my tastes to the point of drudgery, but in an overall sense, satisfying in the way that the Cliff Notes to 'Finnegan's Wake' might be, with the same, muted sense of achievement.
December 11, 2019
Karl Menninger seemed like a very interesting person to me, based on him being mentioned in Joan Didion's Blue Nights, except it wasn't for this book, it was for Man Against Himself. Nonetheless, what interested me was the big difference in topic since this book is about Numbers/Counting and the latter about Self-Mutilation/Suicide.
Well, being someone who deals with numbers at home and at work, I sort of was drawn to this textbook for that reason too. You learn a lot about how as a species we developed numbers from having the need to count and record things, all the way to how we symbolized those recordings for easy interpretations and how we derived words and meaning for those numbers/symbols.
He goes through the history of both the west and the east, but its mostly focused on the west and middle east- with Romans, Vikings, Greek, etc... to Arabs, before he gives a glimpse into China and Asia in general. The dive into language formation was super informative, and you learn A LOT about language and how language came to form alongside how numbers came to form. Without being able to properly count or symbolize numbers, we wouldn't be where we are today - as a species, we wouldn't even be able to think the way we now do by default. We owe so much for all the transfer learning set upon us by our ancestors when it came to this.
I think one thing I really wanted to learn was more about the myths behind certain numbers, like the number 13 or 7. There were some unexplored topics there I would have loved for more information on.
Read this if you really love numbers, language, are naturally curious about how we developed those things, and want to better understand how we came to the state we are in today in terms of the culture of numbers, counting numbers and symbolizing numbers.
Well, being someone who deals with numbers at home and at work, I sort of was drawn to this textbook for that reason too. You learn a lot about how as a species we developed numbers from having the need to count and record things, all the way to how we symbolized those recordings for easy interpretations and how we derived words and meaning for those numbers/symbols.
He goes through the history of both the west and the east, but its mostly focused on the west and middle east- with Romans, Vikings, Greek, etc... to Arabs, before he gives a glimpse into China and Asia in general. The dive into language formation was super informative, and you learn A LOT about language and how language came to form alongside how numbers came to form. Without being able to properly count or symbolize numbers, we wouldn't be where we are today - as a species, we wouldn't even be able to think the way we now do by default. We owe so much for all the transfer learning set upon us by our ancestors when it came to this.
I think one thing I really wanted to learn was more about the myths behind certain numbers, like the number 13 or 7. There were some unexplored topics there I would have loved for more information on.
Read this if you really love numbers, language, are naturally curious about how we developed those things, and want to better understand how we came to the state we are in today in terms of the culture of numbers, counting numbers and symbolizing numbers.
December 3, 2022
Karl Menninger's book Number Words and Number Symbols from 1969 (the first German edition Zahlwort und Ziffer in 1934) was mentioned in Howard Eves's book and I was happy to find a recent Dover paperback edition of it. It has nearly 500 pages of the history of human counting and use of words and symbols to quantify entities around us, why, for example, modern Germans say fünfundzwanzig (5'2') for twentyfive (2'5), how the number 20 has a very special role in many languages, e.g., quatre-vingt (4'20) for 80 in French. It also claims that the Finns form words for 8 and 9 by counting back from 10, i.e., kahdeksan being 2 before 10, and yhdeksän being 1 before 10, respectively. Although, not sure why he believes that -deksa/än refers to 10 (kymmenen). Reading a book from 1958 leaves a thought that may there has been some developments in the field of the etymology of number words in the last 60 years which is not covered here.
I mostly skipped the chapters about counting boards and abacuses but it is good to understand how important those have been for thousands of years. For example, roman numerals are very hard to use for any calculations on paper and those were basically never used that way. Romans numbers are only used to write numbers in text but all computations were done using counting boards and abacuses.
In retrospective it is amazing how difficult it was for the Europeans to adopt the Indian place-value system and especially the concept of zero! It was understood by best mathematicians of the time, such as Fibonacci, who was a supporter of the Indian system in the 13th century, but it still took hundreds of years before it became standard in Europe. I guess we can blame the awkward (greco-)roman number system for the stagnation in the development of mathematics and science in Europe for hundreds of years.
It is a rare pleasure to read a book where one can learn so much about something as familiar as numbers and elementary arithmetic operations. This Karl Menninger is by the way not the same person a the famous psychiatrist with the same name.
I mostly skipped the chapters about counting boards and abacuses but it is good to understand how important those have been for thousands of years. For example, roman numerals are very hard to use for any calculations on paper and those were basically never used that way. Romans numbers are only used to write numbers in text but all computations were done using counting boards and abacuses.
In retrospective it is amazing how difficult it was for the Europeans to adopt the Indian place-value system and especially the concept of zero! It was understood by best mathematicians of the time, such as Fibonacci, who was a supporter of the Indian system in the 13th century, but it still took hundreds of years before it became standard in Europe. I guess we can blame the awkward (greco-)roman number system for the stagnation in the development of mathematics and science in Europe for hundreds of years.
It is a rare pleasure to read a book where one can learn so much about something as familiar as numbers and elementary arithmetic operations. This Karl Menninger is by the way not the same person a the famous psychiatrist with the same name.
August 31, 2018
An excellent book if your interested in numbers or etymology.
August 29, 2016
By having read this book, I know, for instance, how some Chinese words are written, where some of common Dutch proverbs come from, how to bugger my friends with riddles they will most likely never be able to solve. Not to mention it can teach you to count in every significant language, both dead and alive. Number Words and Number Symbols can be a dense read at times, but it is a veritable treasure box of knowledge.
Displaying 1 - 5 of 5 reviews