Numbers in Ch’ol
Lak ty’añ
Numbers in Ch’ol follow a vigesimal (base-20) system, unique among many Mesoamerican languages. Spoken mainly in the highlands of northeastern Chiapas, Mexico, by approximately 140,000 speakers, Ch’ol’s counting system is characterized by its use of the -c’al classifier for tens and the p’ej classifier for units. Its structure combines additive and subtractive patterns, especially in forming intermediate tens like 30 and 40. The language’s counting system reflects its rich cultural history and mathematical complexity, making it a fascinating subject for linguists and language enthusiasts alike. Understanding the numbers in Ch’ol reveals much about their worldview and cultural practices.
Number system
Ch’ol uses a vigesimal (base-20) counting system, where numbers 1-9 are formed with the root plus the classifier p’ej, such as jump’ej for 1 and cha’p’ej for 2. Tens are formed using the -c’al classifier, with 10 as lujump’ej, 20 as junk’al, and intermediate tens like 30 as lujump’ej i cha’c’al, which means 10 plus 20, but constructed as a subtractive pattern. For example, 30 is formed by combining 10 (lujump’ej) with 20 (junk’al), resulting in lujump’ej i cha’c’al. Similarly, 40 is cha’c’al, and 50 is lujump’ej i yuxc’al, where yuxc’al (60) is 3*20. Numbers from eleven to nineteen are formed by prefixing the word for ten (lujump’ej) with the unit root, such as junlujump’ej for 11, lajchämp’ej for 12, and uxlujump’ej for 13. Compound numbers above twenty combine units and multiples of twenty, for example, 35 is jo’lujump’ej i cha’c’al, and 67 is wucp’ej i chänc’al. Hundreds are formed with multipliers of 20, such as jo’c’al for 100 (5*20), and larger numbers like 200 (lujunc’al) and 400 (jumbasc’).
Number list (28)
Counting rules
Formation of units (1-9)
Numbers 1 to 9 are formed by adding the p’ej classifier to the root: jump’ej (1), cha’p’ej (2), uxp’ej (3), chänp’ej (4), jo’p’ej (5), wäcp’ej (6), wucp’ej (7), waxäcp’ej (8), bolomp’ej (9).
Formation of numbers 11-19
Numbers from eleven to nineteen are formed by prefixing 'lujump’ej' (10) with the unit root, such as junlujump’ej (11), lajchämp’ej (12), uxlujump’ej (13), chänlujump’ej (14), jo’lujump’ej (15), wäclujump’ej (16), wuclujump’ej (17), waxäclujump’ej (18), bolonlujump’ej (19).
Formation of tens
Tens are formed using the -c’al classifier: 10 is lujump’ej, 20 is junk’al, 30 is lujump’ej i cha’c’al, 40 is cha’c’al, 50 is lujump’ej i yuxc’al, 60 is uxc’al, 70 is lujump’ej i chänc’al, 80 is chänc’al, 90 is lujump’ej i jo’c’al, and 100 is jo’c’al. The pattern for intermediate tens involves combining the base ten with the next multiple of twenty, often in a subtractive manner, such as 30 (lujump’ej i cha’c’al) which is 10 plus 20, and 70 (lujump’ej i chänc’al) which is 10 plus 60.
Formation of compound numbers above twenty
Numbers above twenty are formed by combining the units (1-19) with the word 'i' and the multiple of twenty. For example, 35 is jo’lujump’ej i cha’c’al (15 plus 20), and 67 is wucp’ej i chänc’al (7 plus 60).
Formation of hundreds
Hundreds are formed with multipliers of 20, such as jo’c’al for 100 (5*20), wäcc’al for 120 (6*20), and larger multiples like 200 (lujunc’al). Larger numbers are formed by combining these with the units and tens, such as 240 (lajchänc’al, 12*20) or 380 (bolonlujunc’al, 19*20).
Formation of larger numbers and thousands
Numbers like 400 are formed with the classifier bajc’: jumbasc’ (400, 1*400). Larger numbers like 500 are formed as jumbasc’ yic’ot jo’c’al (400 + 100). Thousands are formed with the classifier pic: 1,000 is junpic (3*400-200), and 2,000 is jo’bajc’ (5*400).
Unique features
The use of the -c’al classifier for tens and the subtractive pattern in forming intermediate tens like 30 and 70, e.g., lujump’ej i cha’c’al (30).
Compound numbers above twenty are formed by combining units with the multiple of twenty using 'i', such as jo’lujump’ej i cha’c’al (35).
Large numbers like 1,200 are formed with the pattern jo’bajc’ (5*400), showing a full vigesimal system with multipliers of 20 and 400.
The number for 100, jo’c’al, is a core unit, and larger numbers are built by multiplying and adding these core units, reflecting a highly systematic vigesimal structure.
The language incorporates borrowed terms for large units, such as bajc’ for 400 and pic for 1,000, integrating cultural elements into the counting system.
Cultural context
The Ch’ol people primarily inhabit the highlands of northeastern Chiapas, Mexico, where their language and traditions are deeply intertwined. Counting plays a vital role in their daily life, especially in trade, agriculture, and rituals. Numbers like 13 (uxlujump’ej) and 20 (junk’al) are common in traditional markets and ceremonies. The system’s complexity reflects their rich cosmology and worldview, where numbers often symbolize spiritual and social concepts. Certain numbers, such as 13 or 20, may hold cultural significance, although specific taboos or lucky numbers are not documented here. Their counting system demonstrates a sophisticated understanding of mathematics rooted in their cultural identity.
Fun facts
The number 13 in Ch’ol is uxlujump’ej, which combines the prefix for 10 with 3, illustrating the additive pattern used in compound numbers.
Unlike many languages that use a decimal system, Ch’ol’s vigesimal system is similar to that of the Mayan numerals, emphasizing the importance of 20 as a base.
The formation of 30 as lujump’ej i cha’c’al is a subtractive pattern, where 10 plus 20 is expressed as a combination rather than simple addition.
The word for 400, jumbasc’, is derived from a classifier bajc’, showing how large numbers incorporate specific classifiers unique to the language.
Ch’ol’s system allows for expressing very large numbers like 1,200 and 2,000 systematically, reflecting a highly developed mathematical structure.
Frequently asked questions
How do you count to 10 in Ch’ol?
1 – jump’ej, 2 – cha’p’ej, 3 – uxp’ej, 4 – chänp’ej, 5 – jo’p’ej, 6 – wäcp’ej, 7 – wucp’ej, 8 – waxäcp’ej, 9 – bolomp’ej, 10 – lujump’ej.
What number base does Ch’ol use?
Ch’ol uses a vigesimal (base-20) system, evidenced by the formation of 20 as junk’al, 40 as cha’c’al, and intermediate tens like 30 as lujump’ej i cha’c’al, which combines 10 and 20 in a subtractive pattern.
How do you say 42 in Ch’ol?
42 is formed as lajchäm’ej i cha’c’al, meaning 12 (lajchäm’ej) plus 20 (junk’al).
How do you say 100 in Ch’ol?
100 is jo’c’al, which is 5 times 20, reflecting the core unit of the vigesimal system.
How many people speak Ch’ol?
Approximately 140,000 speakers, mainly in the highlands of northeastern Chiapas, Mexico.
Is Ch’ol related to other languages?
Yes, it belongs to the Mayan language family, specifically the Ch’ol branch, which shares features with other Mayan languages.
What makes Ch’ol counting unique?
Its use of the subtractive pattern for intermediate tens like 30 and 70, such as lujump’ej i cha’c’al and lujump’ej i chänc’al, distinguishes it from other vigesimal systems that typically use additive patterns.
Sources
- Gramatica Ch’ol, Viola Warkentin & Ruby Scott, Summer Institute of Linguistics (1980)