Digitization of Kaktovik numbers | Polarjournal
Kaktovik is located on the northern edge of Alaska, on the North Slope. The population of the village is about 280 inhabitants. This is where the figures for the Inupiaq were developed. Image: Google Maps

Invented nearly 30 years ago by a group of Iñupiak students who found Arabic numerals unsuitable for their language, the Kaktovik number system is now undergoing a digital rebirth. After being included in the latest version of Unicode, it should soon be found in its digital application.

In 1994, a group of students and their teacher in a classroom in Kaktovik, a community in Alaska’s North Slope Borough, are dealing with a problem because Arabic numerals, a numbering system that has become nearly universal, do not work for their language, Inupiaq.

The Arabic system is a decimal system, while the languages of the Eskimo-Aleutians, including Inupiak, use a vigesimal system, i.e., a base of 20 equal to the number of fingers and toes on a human. Like the ancient Egyptians, the Inuit use their fingers, hands, or body to count and measure. Since it is difficult to change from the vigesimal to the decimal system, the students in Kaktovik had problems.

Together with their teacher William Clark Bartley, they came up with the idea of developing their own number system that corresponded to the Inupiak way of counting.

Having recently received Silicon Valley support for its development on digital media such as phones and computers, the Kaktovik system has been included in Unicode’s update since last September. This computer standard enables both the exchange of texts in different languages and the digitization of the world’s written languages.

A new system for calculating

For North Slope Borough School District students, their system had to meet a number of criteria. They should be different from Arabic numerals, easy to remember, and quick and easy to write without having to lift the pen. In addition, the relationship between the numbers and their meaning had to be clear, and the lines had to be pleasing to the eye.

In Inupiak there is no word for the number zero. As the students thought about how to represent this number in their system, one classmate raised and crossed her arms forming a sign of the cross. The symbol for zero was invented.

The Kaktovik numbers, consisting of twenty digits. They are based on the Vigesimal system. Image: Wikicommons.

From one to four, each digit is represented by a dash corresponding to its value. Then, in the left column, the digits 5, 10 and 15 are represented by a number of dashes corresponding to their respective value in multiples of 5. The next digits between 6 and 19 are then formed by combining the strokes.

The system, which is much more visual than Arabic numerals, makes addition and subtraction operations simple. You just need to add or remove strokes to get the right result:

Calculation example from YouTube, The Ferret.

The same applies to divisions. You don’t have to do any math, just count the strokes, as in the following example, which is about dividing 30’561 by 61 to get 501 ( Remember that the system is not decimal, but vigesimal).

The divisor (in black) goes once through the first two digits of the dividend (in purple). So you put 1 (in purple) in the quotient. The divisor goes once through the next two digits (in red). But since they are rotated, the quotient is also rotated. Finally, the divisor goes through the last two digits once, so you put one in the quotient (in blue). Thus, 501 in a vigesimal system. Image: Wikicommons

An animated explanation of the Kaktovik system can be found in the following video:

Source: Youtube The Artifexian

A counting method that almost died out

The system developed by Kaktovik’s students is of remarkable simplicity and efficiency. However, besides the mathematical aspect, it was possible to preserve, above all, part of the Inupiak language, since the Kaktovik system revived the Inuit Vigesimal system.

With the colonization of the Inuit, which began in the 19th century, the Inuit were often forbidden to speak their own language, but they were also forced to learn the language of the colonizers and how to count using numbers and the decimal system. This was the case with the Inupiaq, whose counting method based on 20 was almost forgotten.

The Kaktovik system, which celebrates its 30th birthday next year, has been successful among the Inupiat, especially in programs where it was taught alongside the mathematical system using Arabic numerals. Two years after its establishment, the Commission on Inuit History Language and Culture adopted the Kaktovik figures. These have even been tested at the national Canadian level.

It has since been somewhat forgotten, but its application to digital media could mean a revival of this number system among the Inupiak population.

Featured image: Wikicommons

Mirjana Binggeli, PolarJournal

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