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This book is a cross-cultural reference volume of all attested numerical notation systems (graphic, non-phonetic systems for representing numbers), encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defies progressive, unilinear evolutionary models of change, Stephen Chrisomalis identifies five basic types of numerical notation systems, using a cultural phylogenetic framework to show relationships between systems and to create a general theory of change in numerical systems. Numerical notation systems are primarily representational systems, not computational technologies. Cognitive factors that help explain how numerical systems change relate to general principles, such as conciseness or avoidance of ambiguity, which apply also to writing systems. The transformation and replacement of numerical notation systems relates to specific social, economic, and technological changes, such as the development of the printing press or the expansion of the global world-system.
- Sales Rank: #752061 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2010-01-18
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x 1.38" w x 5.98" l, 1.73 pounds
- Binding: Hardcover
- 496 pages
- Used Book in Good Condition
Review
"Stephen Chrisomalis's Numerical Notation is an extraordinary book, comprehensively assembling information about a central human mode of notation, which is more widespread than writing systems and yet has never been fully explored. The author, who writes in an exceptionally lucid style, also offers cogent interpretations of the patterns that he identifies."
John Baines, University of Oxford
"Numbers are necessary to reasoned human existence yet largely unconsidered by those who use them. This important book brings together, in a polished and erudite presentation, the latest thoughts on the origins, development, meanings, and theories of numbers. Few people could have pulled off such a study. That Chrisomalis has done so speaks to the magisterial authority of the volume and its fresh views on the cultural basis and historical contours of quantification."
Stephen Houston, Brown University, Rhode Island
"In this extraordinary and unprecedented book, Stephen Chrisomalis succeeds in doing for numerical notations what the great theorists of the last generation - Gelb, Diringer, and Cohen - did for written language, providing an account that is encyclopedic in scope, conceptually rich, and explanatorily adequate to account for the origins, the transformations, the social uses, and the psychological implications of the world's remarkable systems for the notation of number."
David Olson, University Professor Emeritus, University of Toronto, and author of The World on Paper
"What this study has done is to remove the history of numerical notation from an outdated unilinear evolutionary scheme and place it in a new framework that puts no stock in progressivism as an inexorable consequence of history. It seems to me that no future work of numeral notation will be able to ignore this study. The detailed analysis and typology offered here, as well as the theoretical and interpretational exposition, sets a standard for future discussion of numerical notation as a social, technological, and cognitive phenomenon."
Francesca Rochberg, University of California, Berkeley
"Stephen Chrisomalis's Numerical Notation is a work of extraordinary scholarship and erudition. The author guides the reader on an informed and highly engaging survey of number naming systems around the world, from the cuneiform sexagesimal numeration of ancient Mesopotamia to the Indian-derived decimal numeration of much of the modern world. Along the way, Chrisomalis explores a host of intriguing intellectual historical questions relating to not just how different societies have met the challenges of classifying and naming quantities, but other matters of broad linguistic, philosophical, and anthropological interest. This book is destined to become a standard reference work in the field for many years to come."
Gary Urton, Harvard University, Massachusetts
"Prodigious in its theoretical scope, sweeping in the depth in which it probes and brings together a large number of seemingly diverse systems, Numerical Notation constitutes a well-informed quest for cultural universals in a subject usually left ... to narrowly focused specialists."
Anthony F. Aveni, Journal of Anthropological Research
"Chrisomalis's historical accounts are always impeccably clear ... he provides all kinds of fascinating historical and cultural tidbits."
Ernest Davis, SIAM News
"Numerical Notation is a masterly work - comprehensive, authoritative, and methodologically rigorous. It will be a cornerstone in the study of number systems for years to come."
Amir Alexander, Comparative Studies in Society and History
"Chrisomalis writes clearly and concisely. He has an excellent sense of balance and great methodological awareness - unlike some of the extant literature on the subject. He has produced, in my view, the definitive account of numerical notation for some time to come."
Serafina Cuomo, Antiquity
"... a substantial achievement in the intersection of the history of mathematics with anthropology."
Grattan Guinness, Annals of Science
"Numerical Notation: A Comparative History will remain a key reference text for years to come."
G. E. R. Lloyd, Isis
"By any standards, Stephen Chrisomalis's book is an illuminating work of extraordinary and unseen scholarship and it will certainly become the reference in the field for many years to come."
Jean-Claude Martzloff, Zentralblatt MATH
"This extraordinary book sheds new light on an often-simplified area. Linguists, anthropologists, historians, philosophers, and mathematicians would be well advised to read this delightful book ... Highly recommended."
R. L. Pour, Choice
"Numerical Notation: A Comparative History is an important contribution to the study of the history and structure of numerical systems. It is well-written, well-edited, and packed with information. This book is an essential component of any college library and will be a well-thumbed reference for historians of mathematics."
James V. Rauff, Mathematics and Computer Education
About the Author
Stephen Chrisomalis is currently an assistant professor of anthropology at Wayne State University in Detroit, Michigan. He completed his PhD at McGill University in Montreal, Quebec, where he studied under the late Bruce Trigger. His doctoral dissertation (on which this book is founded) was awarded the Prix de l'ADESAQ for the top 2003 dissertation in any arts, social sciences, or fine arts discipline in the province of Quebec. His work has appeared in journals including Antiquity, Cambridge Archaeological Journal, and Cross-Cultural Research. He is the editor of the Stop: Toutes Directions project and the author of the academic weblog Glossographia.
Most helpful customer reviews
5 of 6 people found the following review helpful.
An Amazingly Worthy Successor to Menninger...
By Let's Compare Options Preptorial
Those of us who grew up astonished at Karl Menningers 1958 Number Words and Number Symbols: A Cultural History of Numbers, now available itself in an inexpensive 2011 reprint, will DELIGHT in this, the FIRST AND ONLY recent, thorough and scholarly COMPARATIVE history of numeric notation. In fact, most other "previous" -- and dated-- authors in this field actually explore math notation more as an adjunct to their study of linguistic notation in general. It is not an exaggeration to say that this is probably the ONLY book dedicated just to the evolution of comparative math symbology. The fact that it was done in so breathtakingly elegant, deep and scholarly a fashion is even more delightful. The "predecessor" authors include Denise Schmandt-Besserat, perhaps Volk's work on Sumerian, and Daniels on written symbology, but none (only journals) in this exact (comparative notation) field. See below for a bib of a few notable related titles available on Amazon.
When studying any science, we begin by learning the language. Unfortunately for mathematics, there are thousands of math books, but only a few that explore the symbols and notation! If math is the language of science, then mathematical notation is the language UNDER that language-- the language of math itself, yet there are only four or five books written JUST on math notation, many dated or only historic. Remember, many math symbols are also "borrowed" from Physics, and notations (Dirac vs. Einstein vs. Feynman and many others, like the lower case omega for angular velocity) present the same logic with different notation systems to confuse the novice! No wonder there is angst about math.
This book is not cheap, and even though it is the only thorough and scholarly history of comparative notation just for math, if you're studying math notation, it will be disappointing if you're trying to acquire practical skill, but thrilling if you're into the details of the thinking, cognitive and practical comparative evolution behind the logic of symbols chosen. Remember the difference between math objects as studied here (symbols - notation), and their USE in math processes (called algorithms today).
The evolutionary history here also includes interesting multifaceted insights that don't make sense logically (like stars, fingers and toes!), but did "mechanically" in terms of instruments available to create or reproduce symbols of any kind. If you're into pattern recognition and data mining as I am (I'm the CTO of payroy dot com for reference of my limited and specialized machine learning skill set), you'll find this fascinating simply from the pattern aspect even if you're not, or never plan to be a symbolic history scholar!
Should be on the shelf of every math historian, which is shocking since it's been out for a while and this is the first review. An undiscovered gem. PLEASE NOTE that this book is filled with original research and ideas of broad value and applicability, because the author takes a multivariate, nonlinear approach to notation evolution. He doesn't make the naive assumption like others of us that evolution is clean, compartmentalized and linear, but fractal, dynamic and multi-sourced. Amazing point of view for any field, more such needed. You WON'T find axioms like the Greeks did this, India this, Islam this, China this, Persia that... etc. as the approach includes an unprecedented blending of confluences.
Notable Predecessor Bib:
Florian Cajori, 1929, A History of Mathematical Notations, 2 volumes
A History of Mathematical Notations (Two Volume in One)
Howard Eves, 1990, An Introduction to the History of Mathematics
An Introduction to the History of Mathematics (Saunders Series)
Georges Ifrah, 2000, The Universal History of Numbers, From prehistory to the invention of the computer
The Universal History of Numbers: From Prehistory to the Invention of the Computer
A few others in this genre, not nearly as scholarly, broad or deep, but also not as expensive, include:
The Story of Numbers: How Mathematics Has Shaped Civilization, The Anthropology of Numbers (Cambridge Studies in Social and Cultural Anthropology), Mathematics Elsewhere: An Exploration of Ideas Across Cultures, The Historical Roots of Elementary Mathematics (Dover books explaining science), Native American Mathematics and Greek Mathematical Thought and the Origin of Algebra (Dover Books on Mathematics).
On the web: Stephen Wolfram, Mathematical Notation, Past and Future (Google this to see Steve's talk on computers learning to read math symbols, interesting take, from 2013. He jokes that he was chosen to speak second because the first choice author-- noted above-- was found out to be dead for 70 years!).
Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors or publishers of the books we review. We always buy the books we review for the sake of objectivity, and although we search for gems, are not shy about trashing a title if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself or her field, it is only for the sake of a point of reference for the skill set viewpoint to help you gauge the bias.
1 of 5 people found the following review helpful.
Pioneering work, lacks in the Linguistics department.
By Larry Rogers Logographic
This is a very welcome work for the "study of all writing systems", covering ground just touched on Bright and Daniels' The World's Writing Systems. Dr. Stephen Chrisomalis seeks to present a study of all numerals in writing systems. And so for that reason, and because he did a very good job, I recommend this book for both the general public as well as professors.
And what's more, it's very well written and well-organized.
However, the area where this book is deficient, and hopefully will be remedied by future scholarship, is this : The author does not discuss the origins of the signs, especially those in the logographic writing systems, in sufficient detail.
In writing systems, signs are chosen by their inventors or inherited from a past choice. The earliest writing systems are called pictographic because most of their signs are pictures of things. Even our alphabet signs are all pictures of things, or rather, once were (cf. Wadi El-Hol script and the work of Johns Hopkins University). Now, when these pictures were used for writing, most often they were used for the sound of the name of that which was depicted. If it was done today, "belief" (cf. J. Allen 2000) would be written with a picture of a "bee" and a picture of a "leaf", like a rebus game or charades. Then sometimes glyphs would be used for meaning value, perhaps the word "beef" would be written with a "sound-sign" "bee" and a "meaning-sign" "meat sign", with the intended reading of the "sound sign" being here "beef".
The author hardly at all discusses these origins of the numeral signs, and it is quite a flaw in the work. He should have looked up each sign in resources (such as Labat's Manuel for cuneiform) and discussed potential puns between how the name of the number sounded (its "reconstructed phonetic realization"), similar-sounding words also written with the same sign, and what the sign looks like.
An easy example and a hard example, both not touched upon in the book at all :: Easy first : Chinese "1,000" sounded like *s.nhi^n in the earliest language of Chinese writing (Old Chinese) (Schuessler 2006, modern Mandarin reading qian_ ) and in the Oracle Bone and Bronze Scripts (the earliest) looked like the picture for "man" (Old Chinese *nin, modern Mandarin reading ren/ (Sch 06) with a line through it which is used with "10" "100", and "10,000" and meant either "number" or "sign variant". And so specialist professors when writing about this glyph guess, probably correctly, that this sign for "1,000" was chosen because it merely sounded like "man", as in the "belief" : "bee" "leaf" example.
Now the hard example : The earliest Cuneiform sign for "10" does resemble a "hole" and the word for "hole" sounds like the word for "10" in the language of the earliest Cuneiform, Sumerian : 10 , u : hole , buru ; and both words were written with that sign. And so perhaps this sign was chosen because it was a picture of a hole and sounded like "ten" in Sumerian.
And there are also cases where we know so little about an ancient writing system's language that we cannot guess what the puns might have been, if any. But all this ought to be addressed.
And these things are very important when studying writing systems because it helps us to really understand and use well our own writing system and to more quickly learn others. To give an example, it is much easier to learn Chinese writing, for everyone, if the learner realizes the 150 frequent signs of which the Chinese characters are composed. If the learner does not know about this, they must memorize every character as if it was arbitarary scribble. And learning Arabic or Hindi script is also like that, though less so because they are more similar to our alpabet. These things also help us see the overall picture of the interaction between sound and meaning which is present in writing systems at all times.
The author missed this because it seems his training in linguistics, at least the linguistics of writing systems, is lacking. His training is BA and PhD in Anthropology, not linguistics, and it shows in all of his writing. Even his treatment of writing systems is mostly mathematical, with little anthropological commentary. But despite its serious flaws, I recommend it and hope to see better treatments of the same subject in the future.
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