Anthropology / Everything Human

How Do You Count Without Numbers?

Stranger Lands

How Do You Count Without Numbers?

This article was originally published at The Conversation and has been republished under Creative Commons.

Numbers do not exist in all cultures. There are numberless hunter-gatherers embedded deep in Amazonia, living along branches of the world’s largest river tree. Instead of using words for precise quantities, these people rely exclusively on terms analogous to “a few” or “some.” The Conversation

In contrast, our own lives are governed by numbers. As you read this, you are likely aware of what time it is, how old you are, your checking account balance, your weight, and so on. The exact (and exacting) numbers we think with impact everything from our schedules to our self-esteem.

But, in a historical sense, numerically fixated people like us are the unusual ones. For the bulk of our species’ approximately 200,000-year lifespan, we had no means of precisely representing quantities. What’s more, the 7,000 or so languages that exist today vary dramatically in how they utilize numbers.

Speakers of anumeric, or numberless, languages offer a window into how the invention of numbers reshaped the human experience. In a new book, I explore the ways in which humans invented numbers, and how numbers subsequently played a critical role in other milestones, from the advent of agriculture to the genesis of writing.

Numberless cultures

Cultures without numbers, or with only one or two precise numbers, include the Munduruku and Pirahã in Amazonia. Researchers have also studied some adults in Nicaragua who were never taught number words.

Without numbers, healthy human adults struggle to precisely differentiate and recall quantities as low as four. In an experiment, a researcher will place nuts into a can one at a time, then remove them one by one. The person watching is asked to signal when all the nuts have been removed. Responses suggest that anumeric people have some trouble keeping track of how many nuts remain in the can, even if there are only four or five in total.

anumeric

This Pirahã family lives in Amazonia and comes from a culture that has no words for numbers. Caleb Everett

This and many other experiments have converged upon a simple conclusion: When people do not have number words, they struggle to make quantitative distinctions that probably seem natural to someone like you or me. While only a small portion of the world’s languages are anumeric or nearly anumeric, they demonstrate that number words are not a human universal.

It is worth stressing that these anumeric people are cognitively normal, well-adapted to the environs they have dominated for centuries. As the child of missionaries, I spent some of my youth living with anumeric Indigenous people, the aforementioned Pirahã, who live along the sinuous banks of the black Maici River. Like other outsiders, I was continually impressed by their superior understanding of the riverine ecology we shared.

Yet numberless people struggle with tasks that require precise discrimination between quantities. Perhaps this should be unsurprising. After all, without counting, how can someone tell whether there are, say, seven or eight coconuts in a tree? Such seemingly straightforward distinctions become blurry through numberless eyes.

Children and animals

This conclusion is echoed by work with anumeric children in industrialized societies.

Prior to being spoon-fed number words, children can only approximately discriminate quantities beyond three. We must be handed the cognitive tools of numbers before we can consistently and easily recognize higher quantities.

anumeric

Other animals, such as an African grey parrot, show an improved capacity for quantitative thought after being introduced to numbers. Eli Duke/Flickr

In fact, acquiring the exact meaning of number words is a painstaking process that takes children years. Initially, kids learn numbers much like they learn letters. They recognize that numbers are organized sequentially but have little awareness of what each individual number means. With time, they start to understand that a given number represents a quantity greater by one than the preceding number. This “successor principle” is part of the foundation of our numerical cognition but requires extensive practice to understand.

None of us, then, is really a “numbers person.” We are not predisposed to handle quantitative distinctions adroitly. In the absence of the cultural traditions that infuse our lives with numbers from infancy, we would all struggle with even basic quantitative distinctions.

Number words and written numerals transform our quantitative reasoning as they are coaxed into our cognitive experience by our parents, peers, and school teachers. The process seems so normal that we sometimes think of it as a natural part of growing up, but it is not. Human brains come equipped with certain quantitative instincts that are refined with age, but these instincts are very limited. For instance, even at birth we are capable of distinguishing between two markedly different quantities—for instance, eight from 16 things.

But we are not the only species capable of such abstractions. Compared to chimps and other primates, our numerical instincts are not as remarkable as many presume. We even share some basic instinctual quantitative reasoning with distant nonmammalian relatives like birds. Indeed, work with some other species, including parrots, suggests they too can refine their quantitative thought if they are introduced to the cognitive power tools we call numbers.

THE BIRTH OF NUMBERS

So, how did we ever invent “unnatural” numbers in the first place?

The answer is, literally, at your fingertips. The bulk of the world’s languages use base-10, base-20, or base-5 number systems. That is, these smaller numbers are the basis of larger numbers. English is a base-10 or decimal language, as evidenced by words like 14 (“four” + “10”) and 31 (“three” x “10” + “one”).

We speak a decimal language because an ancestral tongue, proto-Indo-European, was decimally based. Proto-Indo-European was decimally oriented because, as in so many cultures, our linguistic ancestors’ hands served as the gateway to realizations like “five fingers on this hand is the same as five fingers on that hand.” Such transient thoughts were manifested into words and passed down across generations. This is why the word “five” in many languages is derived from the word for “hand.”

Most number systems, then, are the byproduct of two key factors: the human capacity for language and our propensity for focusing on our hands and fingers. This manual fixation—an indirect byproduct of walking upright on two legs—has helped yield numbers in most cultures, but not all.

Cultures without numbers also offer insight into the cognitive influence of particular numeric traditions. Consider what time it is. Your day is ruled by minutes and seconds, but these entities are not real in any physical sense and are nonexistent to numberless people. Minutes and seconds are the verbal and written vestiges of an uncommon base-60 number system used in Mesopotamia millennia ago. They reside in our minds, numerical artifacts that not all humans inherit conceptually.

Research on the language of numbers shows, more and more, that one of our species’ key characteristics is tremendous linguistic and cognitive diversity. While there are undoubtedly cognitive commonalities across all human populations, our radically varied cultures foster profoundly different cognitive experiences. If we are to truly understand how much our cognitive lives differ cross-culturally, we must continually sound the depths of our species’ linguistic diversity.

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  • Pankaj Anand

    Although it is a good read, I am failing to grasp what the author is intending here. The article is loose and does not conclude or summarize the findings well. It is just some statements of facts and interpretations.

  • thyfere

    Interesting! So, it goes back to the fact that we are story-telling creatures. Most of the things around us are the stories that we have created over the time, numbers, time, hour, days, weeks are few of them 🙂

  • ray

    Thank you for the fascinating article . If the author has the time or inclination it would be evenmore fascinating to hear in more detail about his experiences in being exposed to his own culture and such a different one at such a young age and how he managed to reconcile the differences.

  • Eric Mankin

    The author is the son of Daniel Everett, who has used the same Piraha language to argue that Chomsky’s theory of Language is wrong, a theory Tom Wolfe turned into a book. What worries me about the whole situation is it seems to divide all language into two categories, Piraha and all others. Which raises questions for me. I mean, how? Why?

  • John Murphy

    The English currency used 12 pennies 20 shillings with 240 pennies to the £ . While both the English and most other weights , volumes and measurement systems 12 inches per foot 3 feet per yard 1760 yards miles and 2240 lbs ton 60 seconds minute 60 minutes hour and 24 hours day even 365 approx years 360degrees circles everywhere big numbers which many different numbers can divide exactly into. Supposedly going back many thousands of years. The entire metric system was gifted? To us by the emperor napoleon . The scientific community took to it very quickly the rest of us took another century or two.

    • tomtype

      The French even decreed a 10 day week with 3weeks to a month. The months were renamed from ancient gods to things associated with that season. They then added 5 or 6 extra calendar days that just didn’t count except as holidays. The Julian calendar usually started on April 1st. But when we changed to the Gregorian calendar because a pure 365 day year eventually gets out of whack with the seasons. So every four years a day is added to February, except on the century, except it is added every 4 centuries. England being Protestant didn’t adopt it until 1752, and Russia didn’t adopt it until 1917. Hence the October Revolution actually happening in November.

  • Jason Gottfried

    Great piece!
    Thinking about the impact numbers have on our experience is vital and not discussed often enough I think. The idea of numbers (or possibly number words in conjunction with “the successor principle” as being a cognitive power tool is a very powerful image for early number development.

  • Chaiwallah

    A few years ago, as I was sitting on my deck in Austin, TX before sunrise, drinking coffee, a bird landed on the roof behind and above my head. She, I believe it was a female cardinal who had studied me in the past, then proceeded to demonstrate to me that she could count to five. She sang a short refrain of four or five notes than uttered a sharp, short call. She repeated the refrain and the call. Then she repeated the refrain and followed it with two sharp, short calls, and repeated. Then the refrain and three calls and repeated. Then the same with four calls. She finished with the refrain and five calls, once, and then flew off.
    I am amazed by the intelligence she displayed. How else could she vocally communicate with me? And she wanted to . . . And so I am also touched and humbled by the encounter.
    Sometime later, I was wondering at the significance of five and on investigation found that songbirds typically have up to five offspring at a time. Counting to five probably helps mama keep track of how many have been fed and how many still need feeding.

  • tomtype

    The concept of written numbers may have lead to the idea of written sounds (written language). The current theory is that shepherds in the Middle East lacking numbers to report to the chief of the tribe on their flock. So they would place one white pebble for each white sheep and one black pebble for each black sheep. And perhaps a different kind of rock like perhaps a grey one or one with a sharp edge for goats. Or maybe two different sizes to represent differences. Much of the desert is actually gravel rather than sand as usually portrayed.
    Thus Abraham could know without numbers the state of his many scattered flocks.
    I remember learning numbers and many languages have some sort of quirk. Many people may remember that French does not say “eighty” but more like “four score.” We put the word ten (teen) after as seven teen but numbers above 20 the tens come first like twenty seven.
    Lastly, English also seems to have counted base 12 at one time. We have dozen, gross, and great gross. There is an old saying: he went eleventy-seven. So what is that number base 10?

  • The article above explores what happens when a society develops without words for numbers. Is perception itself filtered, such that all quantities regress to “a lot” or “a little”?

    For a broader take– what happens when a society’s entire vocabulary is maliciously and deliberately stolen from them– see this short story, “The Vote.” https://medium.com/the-junction/the-vote-ac2bf822ceb6

    Stephen D. Forman, CLTC

  • cougar2013

    This exposes the fact that some groups of people just aren’t as smart as others. It’s not that they consciously decided to stop counting at the number 5. It’s that they have difficulty keeping count of things greater than 5, are aware of that, and have not taken any action to remedy it. This signifies a lack of intelligence when compared with the rest of the world.

    If it is certainly not an indication of intelligence, then it must certainly be an indication of the opposite, since there are only 2 choices. Yay quantitative logic!

    • Jason Gottfried

      Have you consciously decided to stop at 2 choices (being aware that there are more but not taking any action to remedy it) or is it that you are not aware? 😛