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Ideas | Kelly Kasulis

Is there life without math?

H. Hopp-Bruce/Globe staff

Inside of an open hut overlooking Amazon basin’s Maici River, the 5-year-old son of two Christian missionaries watched as his parents tallied numbers on a board, trying to teach a group of adults how to count. “I remember being puzzled — these people were smarter than me, and yet they were just totally flummoxed by counting,” said Caleb Everett, now 40 years old and an anthropological linguist. “I coincidentally happened to be spending my time as a kid with one of the few anumeric groups in the world.”

The Pirahã language has no words for exact integer numbers, an exceedingly rare linguistic evolution. Furthermore, research has found, the Pirahã people simply don’t count things.

Everett’s time with the tribe has led him to conclude that, though some cultures don’t find use in numbers, they’re still one of the greatest inventions in history, right next to cooking, stone tools, and the wheel. He makes the case in his new book, “Numbers and the Making of Us: Counting and the Course of Human Cultures.”

There’s a long list of things that numbers enable, their ubiquity as a “human invention” hints at a darker tale of colonization — and a fear that a life without digits may soon be impossible. “As cultures are forced to have contact, they learn these things,” Everett said. “There’s not that many cultures like this anymore, and there won’t be so many much longer.”


There are about 700 Pirahã, all hunter-gatherers, who use words that translate to a vague “few” or “many,” participating in a “tit for tat” bargaining system, according to Peter Gordon, an associate professor of neuroscience and education at Columbia University. “They live a very simple life,” he said. “There’s nothing they really have to count.”

Contact between numbered and numberless societies has always come with an imbalance of power. Records from the 1800s show European traders scamming the nearly numberless Munduruku people, and, in recent years, some tribes have become beneficiaries (and possible victims) of a Brazilian government welfare system that pulls tribal populations into the cash economy by giving them money. “You get these old ladies who go into towns they haven’t set foot in before, who don’t speak Portuguese, who get ripped off right and left,” said Patience Epps, a professor of linguistics at the University of Texas at Austin who studies the Hup people, another population with a limited number system.


But numbers are contagious. Social interaction and the allure of a market economy can spread counting systems like “cognitive fire,” Everett writes.

In early human history, farmers would watch astronomical cycles in the sky to track the seasons, working off of a calendar built from a basic understanding of patterns and math. In Mesopotamia, where writing was developed about 5,200 years ago, the first hieroglyphic symbols seem to represent quantities of items like stored beer or crops. Instead of cooking tokens in clay and physically using them to represent objects, Mesopotamians eventually started etching symbols that could do the same thing. In Central America and China — where writing systems were also independently developed — numbers also appear to be the first written symbols.

Other evidence suggests that numbers first started with people along the coast of southern Africa about 60,000 years ago. Archaeologists discovered necklaces made with beads from materials more than a day’s walk away, which implies an economy in which certain goods were assigned a numerical (or monetary) value. As humans evolved in Africa and started to migrate across the world in various groups, they ultimately fostered the spread of number words across thousands of languages and vast expanses of land.

But no matter the date or the location, numbers likely began with humans looking at their hands. In many world languages, five often translates to “hand,” or 10 translates to “two hands.” Some languages are based on a five or 20 system, resetting after one hand or after all 20 fingers and toes. Even our perception of time, based on 60 seconds or minutes, probably comes from the notches in our knuckles — we have three prominent folds on each finger (excluding the thumb), meaning 12 on a hand. Multiply that by the five fingers on your opposite hand and you get 60 — a system used by Babylonians and Sumerians in Mesopotamia.


“Patterns exist in nature, but we would never have access to [them] if we didn’t have numbers,” Everett said. “It doesn’t trivialize math — it makes it all the cooler.”

The image of a mathematician first sketching the digits of pi is a romantic tale of mankind’s genius. But that’s not to say that the Pirahã and other anumeric indigenous groups are less intelligent. They simply get by using their fingers to indicate quantities, and memory tests show that they’re usually in the right ball park when they estimate numbers larger than three. “In early human history, very low number systems were pretty much the norm,” Epps said.

Those cultures with numbers can never abandon them. And as indigenous, numberless societies dwindle or adopt outside ways, the possibility of living a number-free human existence dwindles with it.

“I don’t think the whole [Pirahã] tribe is going to change, and I think it’s a shame if they do,” Gordon said. “It’s going to be trouble once they start using money and wanting things. It never turns out well.”


Kelly Kasulis is a journalist living in Boston and the deputy digital editor of The GroundTruth Project. Follow her on Twitter @KasulisK.