In some traditional cultures, counting is as easy as one, two, three—because it stops there: Their languages have no words for higher numerals, and instead simply use varieties of words like “many.” But over time some societies acquired higher numbers, as the major languages spoken on the planet today must have done long ago. Now, a new study of an Australian language family reveals how languages add, and sometimes lose, higher numbers—and how some languages lasted for thousands of years without them.
For some cultures, big numbers just don’t make sense. Take the shepherd who knows that he has the right number of sheep not by counting them one by one but by grasping the gestalt of his flock. That may sound strange to people from other cultures, says Patience Epps, a linguist at the University of Texas, Austin. Indeed, she says she’s often asked by incredulous Americans how people with few numerals know, for instance, how many children they have. When she asks this of the Amazonian tribe she works with, “they look at me like it’s a weird question. They list the names, they count on their fingers, but they don’t go around with a quantity in their heads,” she says.
But once a society becomes complex enough to require more abstract counting, higher numerals are needed. Amazonian languages add numerals when groups that don’t know or trust each other begin trading goods and need to track exchanges more closely, Epps says. Something like this must have happened in familiar languages many millennia ago. Looking at how languages with only a few numerals add or lose them could provide insight into how humans build numeral systems. But uncovering these patterns of cultural evolution required data from many related languages with small numeral systems over a long period of time.
Enter the Pama-Nyungan language family, which once extended across most of Australia. It contains about 300 languages that are currently spoken by about 25,000 people, though in the past they may have numbered as many as 2 million. Most of these languages have numeral systems that stop at five. Yale University historical linguist Claire Bowern collected current and historical data about these languages, many of which are no longer spoken. Together with undergraduate researcher Kevin Zhou, she reconstructed how numerals in the language family evolved over about 6500 years, borrowing a method from evolutionary biology to explore how the Pama-Nyungan languages were related to each other and also how they changed over time.
The researchers plugged their data into a computer model, which then generated the most likely family tree for all the languages’ numeral systems. Then they tracked how those systems added or lost numerals within the tree.
The upper limits of these Australian numeral systems most often varied between three, four, and five, the team reports this month in the Proceedings of the Royal Society B. Over time, even small numeral systems sometimes lost a numeral or two, but they mainly gained numerals—yet not by plodding up the number line, one numeral after another. Surprisingly, they tended to acquire numerals in bunches, leaping from five numerals to 10 or 20, for example. The numeral five was often the tipping point—once a system reached five, it was likely to add more numerals, up to 20. As a result, numeral systems with five as an upper limit are rare in Pama-Nyungan languages.
“This is surprising, given the predominance of fingers and toes as things to count,” Bowern notes. Adding or losing the numeral four was the most frequent change. (The words for “four” were most often composed out of words for “two,” not by creating or borrowing a new word that means “four,” showing how the numeral systems evolved.)
Bowern thinks that numerals were added in clusters for practical reasons: If you need to count above five, you probably need to go higher than seven or eight as well. And she speculates that perhaps a cognitive shift occurs at about five. “Once you generalize beyond five or so, it becomes easier to generalize to an infinite system.”
“This is the kind of historical linguistics using computational methods that gives me a lot of confidence,” said Brian Joseph, a historical linguist at Ohio State University, Columbus, adding that “there are a lot of nonlinguists who apply this methodology to data that they don’t seem to control or understand.”
“These conclusions seem sound to me,” agrees Russell Gray of the University of Auckland in New Zealand and director of the Max Planck Institute for the Science of Human History in Jena, Germany, “and remind us that cultural evolution doesn't always proceed incrementally.”