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Numbers and the Making of Us

Caleb Everett
Harvard University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Frank Swetz
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Ask the average person “What is mathematics?” and likely you will get the answer that it is “Something to do with numbers.” More knowledgeable respondents would certainly supply a variety of comprehensive and possibly complex answers, but numbers and their use do lie at the historical base of mathematics.

As a matter of survival, early humans had to recognize quantity, and at a later stage, communicate this information to their colleagues — thus the birth of numbers and numerals. Much research, spanning a multitude of disciplines, has focused on understanding and explaining the conceptualization, utilization and communication of number. Numbers and the Making of Us: Counting and the Course of Human Cultures is a recent contribution to this effort.

The book’s title promises much. It is divided into three parts: “Numbers Pervade the Human Experience”, “Worlds without Numbers”, and “Numbers and the Shaping of Our Lives”. Each part contains three or four chapters.

Numbers and the Making of Us supplies a narrative of facts. Ample “Notes” support each chapter, but there is no separate final bibliography. Caleb Everett is an anthropologist, so many of the examinations he supplies seem to stress the concerns and issues of linguistic anthropology. He has lived among and researched peoples of the Brazilian Amazonian forests, principally the indigenous Munduruku and Jarawara peoples.

Much of Everett’s narrative is based on these observations of how these people conceptualize quantity and use numeration. His findings are informative but limited as a basis for broader generalizations. For example, while the human hand and its fingers are singled out as a basic counting device, no mention is made of a “one-to-one correspondence” although this term does appear much later in the text. Also overlooked are various finger counting strategies and systems, or are the words: digitus, digit or digital, recognized for their finger origins. The fascinating hypothesis of cave hand images having some numerical significance is offered (pp. 40–41), an intriguing hypothesis I investigated several years ago and dismissed, accepting such hand images as the human statement “I was here!”, a Paleolithic equivalent to modern initials scratched on a wall.

The third section of the book, “Numbers and the Shaping of Our Lives,” offers the greatest promise for a renewed understanding and appreciation of number as a human invention, one that is adaptable and evolving. However, the promise falls short. Several topics are presented, such as: “Unnatural Numbers”, “Numbers in the Brain”, “Numbers at the Heart of Symbolic Innovation: Back to Writing” and “Numbers and Deities,” all of which could have provided a satisfying read and enriched appreciation of number but lacked a convincing emphasis such as provided in Alfred Crosby’s The Measure of Reality: Quantification and Western Society, 1250–1600 (Cambridge University Press, 1997). A much repeated phrase throughout Numbers and the Making of Us is “More research must be done”. Yes, I agree.

Still, the author does provide some valuable information on current research and theories. Students of ethnomathematics will appreciate Caleb Everett’s observations and opinions on the quantitative/mathematical abilities of traditional people. What is sorely missing or overlooked is the fact that a society develops the mathematics it needs. Extensive numeration is only required in large depersonalized societies where information is transmitted remotely over a distance. In most traditional societies an individual knows the objects of concern beyond the act of counting them. For example, when I was living in Borneo (1965), I tested a local Iban woman’s numerical skills by asking her how many pigs she had. Despite my number prompting in our common shared language, Malay, she could not enumerate them. Instead, the old woman took me outside the longhouse and introduced me to her pigs, all seven of them. She knew them as individuals among the larger group of pigs wallowing in the mud. Yes, more research must be done and its story told.

Frank Swetz is Professor of Mathematics and Education Emeritus at The Pennsylvania State University. While tending his garden, he still ponders the issue of “humanizing” mathematics teaching and learning.

  • Prologue: On the Success of Our Species
  • I. Numbers Pervade the Human Experience
    • 1. Numbers Woven into Our Present
    • 2. Numbers Carved into Our Past
    • 3. A Numerical Journey around the World Today
    • 4. Beyond Number Words: Other Kinds of Numeric Language
  • II. Worlds without Numbers
    • 5. Anumeric People Today
    • 6. Quantities in the Minds of Young Children
    • 7. Quantities in the Minds of Animals
  • III. Numbers and the Shaping of Our Lives
    • 8. Inventing Numbers and Arithmetic
    • 9. Numbers and Culture: Subsistence and Symbolism
    • 10. Transformative Tools
  • Notes
  • Acknowledgments
  • Index