Last week, I reported on a set of studies that suggest that 12-to-14-month-old infants have difficulty representing the number four. They’re cool with one, fine with two and three, but should you place four objects in a box, the babies seem to have no clue how many objects they’ll find in that box. Adults, as I mentioned, can successfully track four or five. But for all numbers, high and low, we have another trick up our sleeve—counting. It’s worth asking then (as some commenters did) just how adults might represent exact numbers if we couldn’t count.
Take Pirahã, the language of a tribe of hunter-gatherers living in small Amazonian villages. Pirahã is a quirky tongue all around, but here we’ll focus only on its treatment of number. For starters, number is not marked morphologically as it is in many other languages (e.g., there is no distinction between pot and pots depending on the number of objects in question). But more strikingly, according to research published in 2008 by Michael Frank, now at Stanford, and his collaborators—including linguist Daniel Everett, the subject of a fascinating New Yorker profile that focuses on his work with the tribe—the language has no exact number terms. None.
In one study, six members of the Pirahã tribe watched as 10 spools of thread were displayed, one at a time. After each spool was laid down, participants were instructed (by Everett, who speaks the language) to label the number of spools currently displayed. In doing so, participants used three terms: one was used for a “single” spool, one roughly corresponded to “two-or-three” spools, and the last was used to indicate the rest of the spools, or “many.”
But then researchers asked participants to label the spools in descending order, beginning with 10 spools and going down to one. Here, the labeling looked considerably different: nine and 10 were still labeled as “many,” now but eight, seven, and six were given the label that had previously corresponded to “two-or-three.” And all numbers under six were fair game for the label that had earlier indicated “one.” Thus, it seems that all number terms in Pirahã are relative. Rather than meaning “one”, “two” and “many,” they, like “small,” “medium,” and “large,” can have very different meanings depending on whether they’re used to describe growing piles of objects or shrinking ones.
But are exact number terms necessary for understanding fundamental concepts related to counting, such as one-to-one mapping? In a second experiment, 14 members of the Pirahã tribe (the better part of an entire village) participated in a series of tasks designed to test just this. In some tasks, one-to-one mappings could be made visually, as when an experimenter lined up between four and 10 spools of thread on a table, and participants were asked to line up an equivalent number of objects in parallel. But other tasks—like the “nuts-in-a-can” task, which went down exactly as its name suggests—forced participants to make one-to-one mappings between objects in front of them and objects they could only represent in memory. The participants largely succeeded when mappings could be made visually, but failed when they could not be, suggesting that Pirahã speakers do possess the concept of one-to-one exactness, just not—for larger quantities at least—the linguistic resources required for purely mental mappings.
And neither do Americans, once we’ve been stripped of our ability to count. In further work, a group of Bostonians was led through the same cluster of one-to-one mapping tasks while simultaneously “verbally shadowing,” or repeating aloud words from a speech stream. With their linguistic system otherwise occupied, these English speakers couldn’t access exact number terms, and like the speakers of Pirahã, they were left guessing at nuts in a can.
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