Carved into our past, woven into our present, numbers shape our perceptions of the world and of ourselves much more than we commonly think. Numbers and the Making of Us is a sweeping account of how numbers radically enhanced our species' cognitive capabilities and sparked a revolution in human culture. Caleb Everett brings new insights in psychology, anthropology, primatology, linguistics, and other disciplines to bear in explaining the myriad human behaviors and modes of thought numbers have made possible, from enabling us to conceptualize time in new ways to facilitating the development of writing, agriculture, and other advances of civilization.
Number concepts are a human invention – a tool, much like the wheel, developed and refined over millennia. Numbers allow us to grasp quantities precisely, but they are not innate. Recent research confirms that most specific quantities are not perceived in the absence of a number system. In fact, without the use of numbers, we cannot precisely grasp quantities greater than three; our minds can only estimate beyond this surprisingly minuscule limit.
Everett examines the various types of numbers that have developed in different societies, showing how most number systems derived from anatomical factors such as the number of fingers on each hand. He details fascinating work with indigenous Amazonians who demonstrate that, unlike language, numbers are not a universal human endowment. Yet without numbers, the world as we know it would not exist.
"Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists. He does not avoid controversy, making this a key contribution to a developing debate."
– Bernard Comrie, University of California, Santa Barbara
"In his journey through the millennia of human evolution, from the forests of Amazonia to the deserts of Australia, ever in search of a better understanding of human diversity, Caleb Everett presents a breathtaking narrative of how the human species developed one of its most distinct cognitive and linguistic achievements: to count and to use concepts of quantity to expand and enrich a wide range of cultural activities."
– Bernd Heine, University of Cologne
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
What makes us human? Various authors have dished out various reasons in recently published books. From culture to cooking to creativity (see Fuentes’s I reviewed previously). Caleb Everett, a professor of linguistic anthropology, here makes the point that the invention of numbers, which could be considered another instance of human creativity at work, has been an instrumental tool in allowing humans to transform the world. Without them, quantities exist, but we have only a vague awareness of them.
Numbers and the Making of Us brings together strands from the fields of anthropology, linguistics and psychology into a tidy package structured in three parts. The first part looks at the pervasiveness of numbers, starting with our perception of time (why 24 hours and 60 minutes? Ask the Ancient Egyptians, Babylonians and Sumerians). Everett then looks at the archaeological and written record which shows a long history of symbolic representation of quantities (including a very interesting look at how the Mayas counted – apparently to 20, using a duodecimal rather than decimal system). A short survey of counting in a variety of indigenous languages reveals a bias for using words for hands (in English we, for example, have a phrase such as "a handful") and grouping in quantities of fives and tens, reflecting the number of fingers on each hand. Finally, Everett looks at other kinds of numeric language and shows there is more to some languages than a simplistic dichotomy in singular and plural, with some languages having several plural forms for specific quantities.
The second part looks at the cognitive side of things and surveys research on anumeric people (i.e. people who have no counting systems, such as the Pirahã, people indigenous to the Amazon rainforest on whom Caleb Everett and his parents have done anthropological research), prelinguistic children, and animals. This reveals a phylogenetically surprisingly conserved tendency: without numbers, all of these groups can only count to three. It seems the human brain has two number systems, one an exact number sense that can tell apart 1, 2, and 3; the other an approximate sense that can do fuzzy math and estimate quantities, as long as they differ sufficiently (roughly in a 1:2 ratio). Finally, the third part looks at how numbers and basic arithmetic were likely invented, how numbers transformed human subsistence (enabling progress in agriculture, architecture, and science), and the social and spiritual effects that numbers have had.
Everett delivers a neatly structured book, with each chapter having a summarising conclusion that leads to the next chapter. The first two parts, where he discusses linguistic, anthropological and cognitive findings, are in my opinion the best. But I was waiting for a payoff in the third part that never came and finished the book wanting more. I was left with all sorts of questions, such as “when did our Westen numerals first appear in the archaeological record?”, “when did larger numbers first make their appearance?”, “what about other numbers such as negative numbers, fractions or the number zero?”. Everett touches on these topics, but only ever so briefly. Perhaps it’s not fair to fault this book for not providing a comprehensive history of numbers. As witnessed by Stephen Chrisomalis’s book Numerical Notation: A Comparative History, which describes more than 100 such systems, this is a vast topic. So it’s an understandable decision to limit the scope of this book. Plus, Everett refers to other books that cover these questions – it looks like I should read Amir Aczel’s Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers.
However, based on the book’s title, I was expecting a brief "big history" of how numbers transformed agriculture and would have liked a bit more “show, don’t tell”. Though it is reasonable to assume that numbers were instrumental in the development of agriculture, trade, and nation-states, Everett provides what feels like a brief summary only. I would have liked to see more details here. What were the key stages of progress enabled by numbers? What evidence do we have from the archaeological record? Chapter 2 mentions clay tokens used in record-keeping but doesn’t provide much detail, nor illustrations. Similarly, a gypsum tablet housed in the British Museum is mentioned as the oldest artefact we currently have showing true numerals, but again, it is not illustrated. This feels like a missed opportunity, especially as the book contains other nice photos of old artefacts, such as a reindeer antler with carved markings, which was possibly used as a calendar.
Even though I was left wanting more detail where the effect of numbers on the evolution of human societies was concerned, the other two parts provide a very satisfying read, with especially the linguistic and cognitive sections being Everett’s strong suit. His writing is accessible, mixing in personal reflections on anthropological fieldwork with a neatly structured narrative, and the book is compellingly readable.
Caleb Everett is an Andrew Carnegie Fellow and Associate Professor of Anthropology at the University of Miami.