Numbers in Kaqchikel
Numbers in Kaqchikel follow a vigesimal (base-20) system, making it uniquely complex among Mesoamerican languages. Spoken by approximately 450,000 people in the midwestern highlands of Guatemala, this language belongs to the Mayan family. Its counting system combines additive and substractive elements, but primarily relies on a vigesimal structure where multiples of twenty are fundamental. For example, 20 is 'jukʼal', 40 is 'kakʼal', and 100 is 'okʼal'. The language's counting system is distinctive because it constructs numbers above twenty by combining multiples of twenty with units, such as 'jukʼal oxlajuj' for 33. This makes the numbers in Kaqchikel both fascinating and complex to learn.
Number system
Kaqchikel uses a vigesimal system where the number 20 ('jukʼal') is fundamental. Numbers from 1 to 9 have unique words, for example, 1 is 'jun', 2 is 'kaʼiʼ', and 9 is 'bʼelejeʼ'. Numbers from 11 to 19 are formed by combining the unit with 'lajuj', such as 11 'julajuj' (10+1), 12 'kabʼlajuj' (10+2), and 19 'bʼelejlajuj' (10+9). Tens are formed by prefixing the root of the multiplier with 'kʼal', e.g., 40 is 'kakʼal' (2×20), 50 is 'kakʼal lajuj' (2×20+10), and 80 is 'kajkʼal' (4×20). For numbers above 20, the pattern involves starting with the multiple of twenty, then adding the units, such as 'jukʼal oxlajuj' for 33 (20+13). Hundreds are formed by multiplying twenty by another number, e.g., 100 is 'okʼal' (5×20), 120 is 'waqkʼal' (6×20), and 220 is 'julajujkʼal' (11×20). Compound numbers are built by combining these elements, for example, 142 is 'wuqkʼal kaʼiʼ' (7×20 + 2).
Number list (28)
Counting rules
Counting units from 0 to 9
Digits from zero to nine have specific names: wa’ix [0], jun [1], kaʼiʼ [2], oxiʼ [3], kajiʼ [4], woʼoʼ [5], waqiʼ [6], wuquʼ [7], waqxaqiʼ [8], and bʼelejeʼ [9]. For example, 1 is 'jun', 4 is 'kajiʼ', and 9 is 'bʼelejeʼ'.
Forming tens and multiples of twenty
Tens are formed by prefixing the root of the multiplier with 'kʼal'. For example, 20 is 'jukʼal', 40 is 'kakʼal' (2×20), 60 is 'oxkʼal' (3×20), 80 is 'kajkʼal' (4×20), and 100 is 'okʼal' (5×20). For 30, it's 'jukʼal lajuj' (20+10), and for 50, 'kakʼal lajuj' (40+10).
Forming numbers from eleven to nineteen
Numbers 11 to 19 are formed by combining the unit with 'lajuj'. For example, 11 is 'julajuj' (10+1), 12 is 'kabʼlajuj' (10+2), and 19 is 'bʼelejlajuj' (10+9).
Constructing compound numbers above twenty
Numbers like 33 are formed by starting with the previous multiple of twenty ('jukʼal'), then adding the units: 'jukʼal oxlajuj' (20+13). Similarly, 65 is 'oxkʼal woʼoʼ' (3×20+5).
Forming hundreds
Hundreds are formed by multiplying twenty by another number: 100 is 'okʼal' (5×20), 120 is 'waqkʼal' (6×20), 220 is 'julajujkʼal' (11×20), and 380 is 'bʼelelajujkʼal' (19×20).
Building larger numbers
Numbers above 100 are constructed by combining the multiple of twenty with the units. For example, 142 is 'wuqkʼal kaʼiʼ' (7×20 + 2), and 360 is 'waqxaqlajuj' (18×20).
Unique features
The number 20 ('jukʼal') is a fundamental building block, used to form all larger numbers, such as 40 ('kakʼal') and 100 ('okʼal').
Unlike many languages that use a decimal system, Kaqchikel relies on vigesimal (base-20) structure, similar to other Mayan languages.
Numbers from 11 to 19 are formed by adding 'lajuj' (10) to the units, e.g., 15 is 'woʼlajuj' (5+10).
Large numbers like 420 are formed by combining multiples of twenty, such as 'jukʼal juqʼoʼ' (21×20).
The language incorporates borrowed terms for large numbers, such as 'juqʼoʼ' for 400, which is a compound of 'juqʼ' (20) and 'oʼ' (a suffix).
Cultural context
Kaqchikel is spoken primarily in the midwestern highlands of Guatemala, where the community maintains rich cultural traditions, including vibrant festivals, traditional weaving, and Mayan spiritual practices. Numbers play a vital role in rituals, agriculture, and trade, often used in calendar calculations and ceremonial offerings. Certain numbers, like 13 or 20, hold cultural significance, while others may be avoided in specific contexts. The language's vigesimal system reflects a deep connection to the Mayan cosmology and worldview, emphasizing the importance of multiples of twenty in daily life and spiritual beliefs.
Fun facts
The number 19 is 'bʼelejlajuj', literally 'nine plus ten', illustrating the additive aspect of numbers 11-19.
Compared to English, which is decimal, Kaqchikel's vigesimal system is similar to the ancient Mayan number system, making it unique among modern languages.
Mathematically, the system demonstrates a pure base-20 structure, with no reliance on a decimal fallback for large numbers.
Historically, the Mayan civilization used vigesimal counting, which influenced Kaqchikel's system, preserved through oral tradition.
For very large numbers, Kaqchikel constructs them by multiplying twenty, such as 160,000 being 'jukalaʼ' (800×20), showing an elegant way to express large quantities.
Frequently asked questions
How do you count to 10 in Kaqchikel?
1 - 'jun', 2 - 'kaʼiʼ', 3 - 'oxiʼ', 4 - 'kajiʼ', 5 - 'woʼoʼ', 6 - 'waqiʼ', 7 - 'wuquʼ', 8 - 'waqxaqiʼ', 9 - 'bʼelejeʼ', 10 - 'lajuj'.
What number base does Kaqchikel use?
Kaqchikel uses a vigesimal (base-20) system, evidenced by words like 'jukʼal' for 20, 'kakʼal' for 40, and 'okʼal' for 100, all multiples of twenty.
How do you say 42 in Kaqchikel?
42 is 'kakʼal lajuj' (2×20 + 10). First, 'kakʼal' means 40, and 'lajuj' means 10, so combining them gives 42.
How do you say 100 in Kaqchikel?
100 is 'okʼal', which is a direct term for five times twenty, following the vigesimal pattern.
How many people speak Kaqchikel?
Approximately 450,000 speakers of Kaqchikel live mainly in Guatemala's highlands.
Is Kaqchikel related to other languages?
Yes, it belongs to the Mayan language family, specifically the Quichean-Mamean branch, related to other Mayan languages like K'icheʼ and Mam.
What makes Kaqchikel counting unique?
Its reliance on a vigesimal system, where numbers are built from multiples of twenty, and the way it combines units and tens, such as 'jukʼal oxlajuj' for 33, makes it distinctive.
Sources
- Escribiendo Kaqchikel, Martín Chacach Cutzal, Universidad Rafael Landívar (2004)