Bartley reports that after a year of the students working fluently in both systems, scores on standardized math exams jumped from below the 20th percentile to “significantly above” the national average. Visualizing arithmetic makes the concepts a lot easier to understand, she says.Īt first, students would convert their assigned math problems into Kaktovik numerals to do calculations, but middle school math classes in Kaktovik began teaching the numerals in equal measure with their Hindu-Arabic counterparts in 1997. “The Iñupiaq way of knowing is often done by showing,” adds Qaġġuna Tenna Judkins, director of Iñupiaq education in northern Alaska's North Slope Borough. Submitted to Unicode Technical Committee Document Registry Ma( reference) 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.”Ĭredit: Amanda Montañez Source: “Unicode Request for Kaktovik Numerals, by Eduardo Marín Silva and Catherine Strand. Addition, subtraction and even long division become almost geometric. (More technically, it is a two-dimensional positional value system with a primary base of 20 and a subbase of 5.)īecause of the tally-inspired design, arithmetic using the Kaktovik numerals is strikingly visual. “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. “In the Iñupiaq language, there wasn't a word for 0,” says William Clark Bartley, the teacher who helped develop the numerals. For example, the Iñupiaq word for 18, “ akimiaq pinasut,” meaning “15-3,” is depicted with three horizontal strokes, representing three groups of 5 (15), above three vertical strokes representing 3.Ĭredit: Amanda Montañez Source: “Unicode Request for Kaktovik Numerals,” by Eduardo Marín Silva and Catherine Strand. The numerals, based on tally marks, “look like” the Iñupiaq words they represent. The Kaktovik numerals started as a class project to adapt the counting system to a written form. It was torture for them.” By the 1990s the Iñupiaq oral counting system was dangerously close to being forgotten. “But when my father went to school, if he spoke the language, they would slap his hands.

“We had a tutor from the village who would help us blend into the white man's world,” Pollock says of her own education. “Before yardsticks or rulers, used their hands and fingers to calculate or measure.”ĭuring the 19th and 20th centuries American schools suppressed the Iñupiaq language-first violently and then quietly. “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. In traditional practices, the body also serves as a mathematical multitool. Iñuiññaq, the word for 20, represents a whole person. “In your one arm, you have tallimat fingers,” Pollock explains. For example, she says, tallimat-the Iñupiaq word for 5-comes from the word for arm: taliq. 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 they were invented. Quantities are first described in groups of five, 10 and 15, and then in sets of 20. The Alaskan Inuit language, known as Iñupiaq, uses an oral counting system built around the human body. But other number systems exist, and they are as varied as the cultures they belong to. 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.

Today's numerical world is dominated by the Hindu-Arabic decimal system. 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. But they were uniquely suited for quick, visual arithmetic using the traditional Inuit oral counting system, and they swiftly spread throughout the region. The “Kaktovik numerals,” named after the Alaskan village where they were created, looked utterly different from decimal system numerals and functioned differently, too. 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 numeral system in more than a century.