Numbers in Yup’ik
Numbers in Yup’ik follow a vigesimal (base-20) system, which is common among many indigenous Arctic languages. Spoken by around 20,000 people in western and southwestern Alaska, Yup’ik's counting system is notably complex and incorporates unique markers for dual and plural forms. Its structure reflects cultural and practical aspects of daily life, such as hunting and trading. The language's counting system is distinct because it combines base-20 with additive and multiplicative patterns, making it both fascinating and challenging to learn. Understanding the numbers in Yup’ik offers insight into their worldview, emphasizing the importance of community and the natural environment.
Number system
Yup’ik uses a vigesimal system, with 20 as a key multiplier. Numbers 1-5 are basic words: atauciq (1), malruk (2), pingayun (3), cetaman (4), talliman (5). Numbers 6-9 are formed by adding to 5: arvinglegen (6) is 'two-cross over' meaning 5+1, and malrunglegen (7) is 'two-cross over' meaning 5+2. Tens are formed by combining 20 with the number: 30 is yuinaq qula (20 + 10), 40 is yuinaak malruk (20 * 2), and 50 is yuinaak malruk qula (20 * 2 + 10). Larger numbers are built by multiplying 20 with the number: 60 is yuinaat pingayun (20 * 3), 80 is yuinaat cetaman (20 * 4), and 100 is yuinaat talliman (20 * 5). Compound numbers like 42 are constructed as yuinaak malruk pingayun (20 * 2 + 3). For 78, it’s yuinaat cetaman pingayun (20 * 4 + 3). The system combines additive, multiplicative, and dual/plural markers, making it highly systematic yet complex.
Number list (29)
Counting rules
Dual marker (-k)
The suffix -k indicates the dual form, used for counting two entities. For example, yuinaak malruk [40] is 'twenty-dual two', meaning 20 * 2. Similarly, yuinaat cetaman [80] is 'twenty-dual four', or 20 * 4. This marker shows the count of exactly two units, emphasizing the duality concept in Yup’ik.
Plural marker (-t)
The suffix -t indicates the plural form, used for more than two entities. For example, yuinaat pingayun [60] translates as 'twenty-plural three', or 20 * 3, and qulen tiissitsaat [10,000] is 'hundred-plural five thousand', showing how larger quantities are expressed with this marker.
Cross-over (legen)
The term legen means crossing over, adding to the base number. For example, malrunglegen [7] is 'two-cross over', meaning 2 + 5, and pingayunlegen [8] is 'three-cross over', meaning 3 + 5. This pattern is used to form numbers just above the base units, combining the core numbers with the five or ten markers.
Adhesion (ata) and attachment (-usiq)
The prefix ata means to cling or adhere, indicating numbers that are attached or combined. For example, atauciq [1] means 'attached' or 'indivisible'. The suffix -usiq refers to the manner or habit of doing something, but in number formation, it emphasizes the indivisibility of the units.
Following unit (malik- and -ruq)
Malik- means to follow or accompany, and -ruq indicates a section or part. For example, malruk [2] is 'the following unit', emphasizing the sequential aspect of counting. This pattern helps form compound numbers like 12 (qula malruk) or 13 (qula pingayun).
Unique features
Yup’ik uses a vigesimal (base-20) system, with specific dual (-k) and plural (-t) markers, as seen in yuinaak malruk [40] and qulen tiissitsaat [10,000].
Unlike many languages that use a decimal system, Yup’ik’s counting reflects cultural emphasis on groups of twenty, common in Arctic hunting and gathering practices.
Numbers like malrunglegen [7] and pingayunlegen [8] demonstrate how the language combines base numbers with the concept of crossing over, adding complexity.
Large numbers such as one million (miilicaaq) and one billion (tiissitsaaq miilicaaq) are formed by combining the basic words for thousand (tiissitsaaq) and million, showing an additive system for very large quantities.
The word miilicaaq (one million) is borrowed from a linguistic pattern that emphasizes the importance of large-scale counting in trade and resource management.
Cultural context
Yup’ik is spoken by indigenous communities in western and southwestern Alaska, where subsistence hunting, fishing, and gathering are vital. Numbers are essential in daily life, from counting game and fish to trading goods. The vigesimal system reflects their environment, where groups of twenty are culturally significant. Certain numbers may hold symbolic value, and large numbers like miilicaaq (one million) are used in storytelling and ceremonial contexts. The language’s counting system underscores community cooperation and respect for natural cycles, with dual and plural forms emphasizing collective effort. There are no specific taboos on numbers, but understanding the system reveals the deep connection between language, environment, and social structure.
Fun facts
The number yuinaq qula [30] literally means 'twenty ten', illustrating how Yup’ik combines base-20 with the number ten.
Compared to English, which is decimal, Yup’ik’s vigesimal system is similar to the traditional French counting system used in some regions, like 'quatre-vingt-dix' for 90.
The formation of 78 as yuinaat cetaman pingayun [20 * 4 + 3] showcases a systematic use of multiplication and addition, unlike many Indo-European languages.
Historically, the Yup’ik counting system reflects their adaptation to Arctic life, where counting large groups of animals or resources was crucial for survival.
Large numbers like one billion are constructed by combining the words for thousand and million, demonstrating the language’s capacity for expressing vast quantities without borrowing from other languages.
Frequently asked questions
How do you count to 10 in Yup’ik?
1 - atauciq, 2 - malruk, 3 - pingayun, 4 - cetaman, 5 - talliman, 6 - arvinglegen, 7 - malrunglegen, 8 - pingayunlegen, 9 - qulngunritaraan, 10 - qula.
What number base does Yup’ik use?
Yup’ik uses a vigesimal (base-20) system, as evidenced by words like yuinaq [20], yuinaq qula [30], and yuinaat pingayun [60], which show multiplication of 20 with other numbers.
How do you say 42 in Yup’ik?
42 is yuinaak malruk pingayun, meaning 20 * 2 + 3, combining the word for twenty, the dual marker for two, and the number three.
How do you say 100 in Yup’ik?
100 is yuinaat talliman, which is 20 * 5, showing the multiplicative pattern for hundreds.
How many people speak Yup’ik?
Approximately 20,000 people speak Yup’ik, primarily in western and southwestern Alaska.
Is Yup’ik related to other languages?
Yes, it belongs to the Eskimo-Aleut language family, closely related to Alutiiq and Siberian Yupik languages.
What makes Yup’ik counting unique?
Its vigesimal system combined with dual and plural markers, as well as the use of crossing over (legen), makes Yup’ik counting highly distinctive and culturally significant.
Sources
- As Yup’ik is using a vigesimal system, i.e. a numeral system of base 20, numbers from one to nineteen are specific words, namely atauciq [1], malruk [2], pingayun [3], cetaman [4], talliman [5], arvinglegen [6], malrunglegen [7], pingayunlegen [8], qulngunritaraan [9], qula [10], qula atauciq [11], qula malruk [12], qula pingayun [13], akimiarunrita’ar [14], akimiaq [15], akimiaq atauciq [16], akimiaq malruk [17], akimiaq pingayun [18], and yuinaunrita’ar [19]. As we can see, from eleven to thirteen, we add the digit after the ten, then we nearly arrive to fifteen, and from sixteen to eighteen, we add the unit to fifteen, making the base a mix between a vigesimal system (of base 20) and a quinary system (of base 5): to count up to twenty, we need four steps of five units.
- The tens are built by multiplying twenty and adding ten: qula [10], yuinaq [20], yuinaq quala [30] (20 + 10), yuinaak malruk [40] (20 * 2), yuinaak malruk qula [50] (20 * 2 + 10), yuinaat pingayun [60] (20 * 3), yuinaat pingayun qula [70] (20 * 3 + 10), yuinaat cetaman [80] (20 * 4) and yuinaat cetaman qula [90] (20 * 4 + 10). Numbers from twenty-one to ninety-nine are built by saying the ten, then the digit separated with a space (e.g.: yuinaq talliman [25]).
- The forming of hundreds follows the tens, adding the fifteen word in the calculation. In a base 20 system, the role of 100, the base multiplied by itself (10 * 10), is played by 400 (which is twenty times twenty). Thus we have: yuinaat talliman [100] (20 * 5), yuinaat qulen [200] (20 * 10), yuinaat akimiaq [300] (20 * 15), yuinaat yuinaq [400] (20 * 20), yuinaat yuinaq talliman [500] (20 * (20 + 5)), yuinaat yuinaq qula [600] (20 * (20 + 10)), yuinaat yuinaq akimiaq [700] (20 * (20 + 15)), yuinaat yuinaak malruk [800] (20 * 20 * 2), and yuinaat yuinaak malruk talliman [900] (20 * 20 * 2 + (5 * 20)).
- One thousand is rendered by tiissitsaaq, and the other thousands are made by setting the multiplier before them (e.g.: malruk tiissitsaak [2,000], qulen tiissitsaat [10,000], yuinaat talliman tiissitsaaq [100,000]).
- The word for one million is miilicaaq, and one billion (109) is tiissitsaaq miilicaaq, namely one thousand million, hence putting de facto the Yup’ik language in the group of the long scale users (where every new word greater than a million is one million times bigger than the previous term).
- Culturally negociated schooling: toward a Yup’ik mathematics, by Jerry Lipka, in Journal of American Indian Education, Volume 33 Number 3, May 1994