by MARJORIE HECHT
Language plays an important role in understanding the concept of numbers.
Numeracy or numerosity, the ability to think about and use numbers, varies among human cultures and within populations, much like intelligence does.
Many known languages, for example, have no words for numerals above 2 or 3. A linguist who curated a database of the world’s languages in 2015 estimated that of the 6,880 languages for which there are published data on numerals, 1,093 had a counting system that ends at 2 or 3.
Compare that lack of a developed counting system to today’s technologically complex societies, where the average person encounters about 1,000 numbers an hour in daily life, as estimated by cognitive neuroscientist Brian Butterworth, professor emeritus at University College London.
At a simple level, we keep time, keep a calendar, memorize addresses and phone numbers, and at a more complex level, we calculate interest rates and stock valuations, election vote percentages, temperatures and rain accumulations, missile trajectories, and astronomical relationships.
Cultures With Restricted Numeracy
What does a culture with a restricted number system look like? Early reports of this came from 16th-century explorers, who described the hunter-gatherer tribes they found, for example, the Taino and Tupinambá in the Americas. Anthropologists later documented hundreds of other societies that only used numbers up to 2 or 3.
Today, the Pirahã in Brazil are “the only known tribe/people whose language and culture appear not to have progressed beyond an analog notion of magnitude, similar to that of higher animals,” an applied mathematician wrote in 2023 in his review of prehistoric mathematics origins. The cultural reason suggested for this is that the Pirahã “reject the value of future planning and are completely non-materialistic.”
Anthropologist Caleb Everett, the son of missionaries who lived with the Pirahã in his youth, describes the tribe as “cognitively normal and well-adapted” to their environment, with a “superior understanding” of their river ecology.
The Pirahã number about 700 people and live in very small villages along the Maici River, a small tributary of the Amazon. They are semi-nomadic and thus have regular contact with outsiders. A comprehensive 2011 review of Pirahã numeracy described experiments in two Pirahã villages to test whether tribal individuals could match quantities larger than 3, which is where their number system ends. Matching consisted of selecting how many empty rubber balloons would match three spools of thread in various arrangements.
Everett and co-author Keren Madora reviewed previous research on the Pirahã and numeracy that had contradictory results about the Pirahã ability to make one-to-one number correspondence for quantities greater than 3. The reason, Everett and Madora suggested, is that the Pirahã have no number words for integers more than 3. They based their conclusion on fieldwork that Madora did with the Pirahã.
Madora, who has 30 years of experience speaking the Pirahã language, spent months in one village, and at the request of the Pirahã, taught them basic arithmetic. To do this, she invented words for numbers 4 through 10, based on their existing word for hand. After becoming familiar with the new number words, the research review stated that the Pirahã demonstrated “heightened performance on the one-to-one matching task.”
The researchers concluded that exact recognition of quantities greater than 3 “relies on a culturally constructed conceptual tool, namely precise number terminology, which is not universal to all human societies.”
The Brain and Numbers
The fact that members of a society with a restricted number system could accurately work with numbers larger than three when adult individuals were taught new words for larger numbers indicates both the importance of a language for numbers and the inherent ability of the human brain to develop.
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