# Muisca numerals

Muisca numerals were the numeric notation system used by the Muisca, one of the civilizations of the Americas before the Spanish conquest of the Muisca. Just like the Mayas, the Muisca had a vigesimal numerical system, based on multiples of twenty (Chibcha: gueta). The Muisca numerals were based on counting with fingers and toes. They had specific numbers from one to ten, yet for the numbers between eleven and nineteen they used "foot one" (11) to "foot nine" (19). The number 20 was the 'perfect' number for the Muisca which is visible in their calendar. To calculate higher numbers than 20 they used multiples of their 'perfect' number; gue-muyhica would be "20 times 4", so 80. To describe "50" they used "20 times 2 plus 10"; gue-bosa asaqui ubchihica, transcribed from guêboʒhas aſaqɣ hubchìhicâ.[1] In their calendar, which was lunisolar, they only counted from one to ten and twenty. Each number had a special meaning, related to their deities and certain animals, especially the abundant toads.[2]

For the representation of their numbers they used digits inspired by their natural surroundings, especially toads; ata ("one") and aca ("nine") were both derived from the animals so abundant on the Bogotá savanna and other parts of the Altiplano Cundiboyacense where the Muisca lived in their confederation.

The most important scholars who provided knowledge about the Muisca numerals were Bernardo de Lugo (1619),[1] Pedro Simón (17th century), Alexander von Humboldt and José Domingo Duquesne (late 18th and 19th century) and Liborio Zerda.[3][4][5][6][7]

## Numerals

The Muisca used a vigesimal counting system and counted primarily with their fingers and secondarily with their toes. Their system went from 1 to 10 and for higher numerations they used the prefix quihicha or qhicha, which means "foot" in their Chibcha language Muysccubun. Eleven became thus "foot one", twelve: "foot two", etc. As in the other pre-Columbian civilizations, the number 20 was special. It was the total number of all body extremities; fingers and toes. The Muisca used two forms to express twenty: "foot ten"; quihícha ubchihica or their exclusive word gueta, derived from gue, which means "house". Numbers between 20 and 30 were counted gueta asaqui ata ("twenty plus one"; 21), gueta asaqui ubchihica ("twenty plus ten"; 30). Larger numbers were counted as multiples of twenty; gue-bosa ("20 times 2"; 40), gue-hisca ("20 times 5"; 100).[3]

The numeral symbols below were first provided by Duquesne and reproduced by Humboldt,[3] Acosta, and Zerda. These glyphs have been criticized and their authenticity questioned, as they are “practically nonexistent” in the surviving archaeological record, including the calendar stone from Choachí. Potentially, they might represent asterisms or months instead of numerals.[8]

### Numbers 1 to 10 and 20

Number Humboldt, 1878[3] De Lugo, 1619[1] Muisca digits[9][10]
1 ata
2 bozha / bosa boʒha
3 mica
4 mhuyca / muyhica mhuɣcâ
5 hicsca / hisca hɣcſcâ
6 taa[11]
7 qhupqa / cuhupqua qhûpqâ
8 shuzha / suhuza shûʒhâ
9 aca
10 hubchibica / ubchihica hubchìhicâ
20 quihicha ubchihica
gueta
qhicħâ hubchìhicâ
guêata

### Higher numbers

Number Humboldt, 1878[3] De Lugo, 1619[1]
11 quihicha ata qhicħâ ata
12 quihicha bosa qhicħâ boʒha
13 quihicha mica qhicħâ mica
14 quihicha mhuyca qhicħâ mhuɣcâ
15 quihicha hisca qhicħâ hɣcſcâ
16 quihicha ta qhicħâ ta
17 quihicha cuhupqua qhicħâ qhûpqâ
18 quihicha suhuza qhicħâ shûʒhâ
19 quihicha aca qhicħâ aca
20 gueta guêata
21 guetas asaqui ata guêatas aſaqɣ ata
30 guetas asaqui ubchihica guêatas aſaqɣ hubchìhicâ
40 gue-bosa guêboʒha
50 gue-bosa asaqui ubchihica guêboʒhas aſaqɣ hubchìhicâ
60 gue-mica guêmica
70 gue-mica asaqui ubchihica guêmicas aſaqɣ hubchìhicâ
80 gue-muyhica guêmhuɣcâ
90 gue-muyhica asaqui ubchihica guêmhuɣcâs aſaqɣ hubchìhicâ
99 gue-muyhica asaqui quihicha aca guêmhuɣcâs aſaqɣ qhicħâ aca
100 gue-hisca guêhɣcſcâ
101 gue-hisca asaqui ata guêhɣcſcâs aſaqɣ ata
110 gue-hisca asaqui hubchihica guêhɣcſcâs aſaqɣ hubchìhicâ
120 gue-ta guêta
150 gue-muyhica asaqui hubchihica guêqhûpqâs aſaqɣ hubchìhicâ
199 gue-aca asaqui quihicha aca guêacas aſaqɣ qhicħâ aca
200 gue-ubchihica guêhubchìhicâ
250 gue-quihicha bozha asaqui hubchihica guêqhicħâ boʒhas aſaqɣ hubchìhicâ
300 gue-chihica hisca guêqhicħâ hɣcſcâ
365 gue-chihica suhuza asaqui hisca guêqhicħâ shûʒhâs aſaqɣ hɣcſcâ
399 gue-chihica aca asaqui quihicha aca guêqhicħâ acas aſaqɣ qhicħâ aca

## References

1. ^ a b c d (in Spanish) 1619 - Muisca numbers according to Bernardo de Lugo - accessed 29-04-2016
2. ^ Izquierdo, 2009, p.30
3. Humboldt, 1878, Part 1
4. ^ Humboldt, 1878, Part 2
5. ^ Humboldt, 1878, Part 3
6. ^ Duquesne, 1795
7. ^ Zerda, 1883
8. ^ Izquierdo Peña, 2009, pp.42-44, 118-120
9. ^ Humboldt, 1878, Part 1, p.389
10. ^ Izquierdo Peña, 2009, p.43
11. ^ (in Spanish) Taa on Muysccubun Dictionary