We’re only able to mentally represent an exact number if we have a word for it

By Emma Young

Babies, monkeys and even bees have a basic “sense of number”. They can instantly perceive that there are one, two, three or four objects in a pile, without having to count them. They can also tell at a glance that a pile of 50 objects contains more than a pile of 20, say. But what explains the unique ability of older kids and adults to go far beyond this, and mentally represent quantities much bigger than four exactly? Some researchers argue that language must be key — that learning to count “one”, “two”, “three”, and on and on, enables this cognitive feat. Others argue that language can’t be fundamental to this “numerical” ability.

Now a striking new study in Psychological Science by Benjamin Pitt at the University of California, Berkeley, and colleagues comes down firmly on the side of language as being key. And this has a broader significance. It supports the hotly contested idea that language itself influences or even enables abilities that have been viewed as being completely independent — such as colour perception, or, in this case, understanding of number.

Earlier studies have suggested that a knowledge of number words is important for understanding exact numbers above four. But these studies have suffered from various drawbacks. Take work on the Pirahã, an indigenous group living in the Brazilian Amazon who have no words for any exact quantity, not even “one”. Pirahã adults seem to be able to mentally represent only up to about four objects. But as Pitt and his colleagues note, they differ from WEIRD comparison groups in all sorts of ways, beyond differences in number language. Some researchers have suggested that their performance might reflect simply their society’s “indifference” to exact large numbers, rather than an inability to form concepts of them, for example. 

Pitt and his team turned to the Tsimane’, a society of farmer-foragers who live in the remote Bolivian Amazon (but who, it has to be said, have featured in all manner of studies looking at cross-cultural differences in perception, including music perception; they may not be familiar with Western culture but they must be getting very familiar with Western researchers).

Ideally for the team’s research purposes, the Tsimane’ language features a full number system, but while some adults have an excellent knowledge of it and can count indefinitely, others have a very limited knowledge of number words. This allowed the team to compare the performance of “high” vs “low” counters within the same culture.

To do this, they gave adult participants pebble-matching tasks. The strongest test of exact number understanding was an “orthogonal-matching task”. A line of white pebbles was placed vertically, stretching away from the participant. Their task was to use glass pebbles to create a matching horizontal line beneath. To succeed at this task, a participant had to understand the exact number of white pebbles, and place the same number of glass pebbles in their line.

The team first ascertained the participant’s highest verbal word count. Then high counters (who could count above 40) started with a line of 10 white pebbles, while low counters started with two fewer pebbles than their highest verbal word count (which ranged from 6 to 20). From this point on, if they placed the correct number of glass pebbles to match the white ones,  the team increased the number of pebbles in the next array by two. If they were wrong, they were given one fewer pebble in their next array. This continued until a participant did one of three things: they did not make a perfect match for the same number of pebbles three times; they correctly matched three arrays of 20 pebbles or more; they completed 20 trials.

The team were then able to compare each participant’s verbal word count with the number of pebbles at which they started to make mistakes — the point at which they switched from exactly reproducing the target array to approximating it.

The results were clear: the switch point for high counters was far higher — averaging 28, compared with just 7 (and never exceeding 11) for the low counters. Importantly, with one exception, the participants’ switch points were at or below their highest verbal word count — even for pebble sets smaller than ten. When the number of target pebbles approached or reached the number that they had a word for, they started approximating. And this led to the team to an important conclusion: within this group “the ability to represent exact numbers was limited to the part of the verbal count list they had mastered”. This, they argue, “represents the strongest evidence to date that number words play a functional role in representing large exact numbers”.

Given the debate over the extent to which language might underpin or enable very different abilities, this is a really significant finding. It doesn’t mean that language is the only tool that can enable understanding of large exact numbers, however. Patterns of counters on an abacus, for example, work as wordless symbols of even extremely large numbers. But as the team writes, their new findings suggest that “whatever set of symbols people use, their ability to represent large exact numbers extends only as far as their mastery of those symbols”.

Exact Number Concepts Are Limited to the Verbal Count Range

Emma Young (@EmmaELYoung) is a staff writer at BPS Research Digest