Inuit Schoolchildren Will Make Its Silicon Valley Debut
Math is called the “universal language,” but a unique dialect is being reborn
In the remote Arctic almost 30 years ago, a group of Inuit middle school students and their teacher invented the Western Hemisphere’s first new number system in more than a century. The “Kaktovik numerals,” named after the Alaskan village where they were created, looked utterly different from decimal system numerals and functioned differently, too. But they were uniquely suited for quick, visual arithmetic using the traditional Inuit oral counting system, and they swiftly spread throughout the region. Now, with support from Silicon Valley, they will soon be available on smartphones and computers—creating a bridge for the Kaktovik numerals to cross into the digital realm.
Today’s numerical world is dominated by the Hindu-Arabic decimal system. This system, adopted by almost every society, is what many people think of as “numbers”—values expressed in a written form using the digits 0 through 9. But meaningful alternatives exist, and they are as varied as the cultures they belong to.
The Alaskan Inuit language, known as Iñupiaq, uses an oral counting system built around the human body. Quantities are first described in groups of five, 10, and 15 and then in sets of 20. The system “is really the count of your hands and the count of your toes,” says Nuluqutaaq Maggie Pollock, who taught with the Kaktovik numerals in Utqiagvik, a city 300 miles northwest of where the numerals were invented. For example, she says, tallimat—the Iñupiaq word for 5—comes from the word for arm: taliq. “In your one arm, you have tallimat fingers,” Pollock explains. Iñuiññaq, the word for 20, represents a whole person. In traditional practices, the body also serves as a mathematical multitool. “When my mother made me a parka, she used her thumb and her middle finger to measure how many times she would be able to cut the material,” Pollock says. “Before yardsticks or rulers, [Iñupiat people] used their hands and fingers to calculate or measure.”
During the 19th and 20th centuries, American schools suppressed the Iñupiaq language—first violently and then quietly. “We had a tutor from the village who would help us blend into the white man’s world,” Pollock says of her own education. “But when my father went to school, if he spoke the language, they would slap his hands. It was torture for them.” By the 1990s the Iñupiaq counting system was dangerously close to being forgotten.
The Kaktovik numerals started as a class project to adapt the counting system to a written form. The numerals, based on tally marks, “look like” the Iñupiaq words they represent. For example, the Iñupiaq word for 18, “akimiaq piŋasut,” meaning “15-3,” is depicted with three horizontal strokes, representing three groups of 5 (15) above three vertical strokes representing 3.
“In the Iñupiaq language, there wasn’t
a word for 0,” says William Clark Bartley, the teacher who helped develop the numerals. “The girl who gave us the symbol for 0, she just crossed her arms above her head like there was nothing.” The class added her suggestion—an X-like mark—to their set of unique numerals for 1 through 19 and invented what mathematicians would call a base 20 positional value system. (Technically, it is a two-dimensional positional value system with a primary base of 20 and a sub-base of 5.)
Because of the tally-inspired design, arithmetic using the Kaktovik numerals is strikingly visual. Addition, subtraction and even long division become almost geometric. The Hindu-Arabic digits are an awkward system, Bartley says, but “the students found, with their numerals, they could solve problems a better way, a faster way.”
