Indispensable Numerals

How old are you? From an early age, the answer to that question is literally at your fingertips. And it probably took only a fraction of a second for you to come up with an answer. Could there be an easier question, really? Many facets of your life are filtered by the number of your years. Can you drive a car by yourself? Well, it depends on how many years you have lived. Are you pleased with what you see in the mirror? That likely is influenced at least somewhat by your age, and what you expect to see in the mirror. Should you have a more fulfilling occupation? Hard to answer without knowing your age. The response to these and many other questions, which strike at the core of your identity and your day-to-day experience, can really only be stated if you know the answer to that first simple question. That question is undeniably meaningful to people in our own cultural matrix.

Yet, remarkably to those of us who attribute so much significance to our age, that same question is meaningless to members of some other cultures. This is not simply because members of such cultures fail to keep track of the earth’s revolutions around the sun, but because they do not have the means of precisely quantifying such revolutions. In other words, they do not have numbers. Among the Amazonian indigenes known as the Munduruku, for instance, there are no precise words for numbers beyond ‘two.’ In the case of their Amazonian counterparts the Pirahã, no number words of any sort are used, not even for ‘one.’ How then could the “how old are you” question be answered by speakers of these languages? Or what of other number-based questions that, to most of the world’s people, also get at basic aspects of life? Consider a few more examples: What is your salary? How tall are you? How much do you weigh? In a world without numbers, such questions are useless— unaskable and unanswerable.

These questions and their potential responses cannot be formulated, at least not with any precision, in anumeric cultures. And for much of the history of our species, all human cultures were anumeric. Numbers, the verbal and symbolic representations of quantities, radically transformed the human condition. In this book I explore the extent of that transformation, which has been remarkably recent. I focus on the transformative power of verbal numbers but also examine the role of written num- bers. For terminological clarity, I usually refer to verbal numbers simply as numbers, and reserve the term numerals for written num- bers. When referring to the abstract quantities described by num- bers, I use symbols like 1, 2, 3, 4, and so forth.

During the past decade, a flurry of research has been done on numbers and numerals by archaeologists, linguists, psychologists, and others. From that research, a new story of numbers is beginning to take shape, a story that is told in this book. In short, it goes something like this: Despite what we once thought, numbers are not concepts that come to people naturally and natively. While quantities and sets of items may exist independently, apart from our mental experience, numbers are a creation of the human mind, a cognitive invention that has altered forever how we see and distinguish quantities. This notion is perhaps unintuitive to many of us who have lived our entire lives with numbers, having them coaxed into our mental experience from infancy. Yet, like another key interrelated symbolic innovation of our species—language— numbers are in fact a culturally variable creation. Unlike language, however, numbers are absent in some of the world’s populations. They are an innovation that indelibly impacts how most, but not all, people construe much of their daily experience.