Reconstruction of an Ancient Central American Numeric System
Data from modern and recently extinct languages in the Chibchan language family is analyzed in an attempt to unravel the counting system used by the Proto-Chibchan people living in Costa Rica and Panama around the year 3000 BC.
Background
Proto-Chibchan is a hypothetical language, believed to have been spoken by Native Americans near present-day Costa Rica and Panama around the year 3000 BC. The Proto-Chibchan speakers were primarily agriculturists, who also engaged in pottery and boat-making.[1] Today, the Chibchan languages make up a language family indigenous to the Isthmo-Columbian area, which extends from eastern Honduras to northern Columbia and includes populations of these countries as well as Nicaragua, Costa Rica and Panama.[2]
Methods
Based on available data on the numerals used by contemporary Native American peoples speaking descendant languages of Proto-Chibchan,[3][4][5] I have used comparative techniques to deduce a rough approximation of the original Proto-Chibchan numeral system that can be traced down to modern Native American languages (many of which have expanded or modified the system significantly).
The following tree represents the normally assumed structure of the Chibchan language family,[1][2] with the specific languages compared in this article in bold:
Chibchan A
+Talamancan branch
++Teribe
++Viceitic branch
+++Bribri
+++Cabécar
+Borũca
+Waimí branch
++Ngäbere
++Bocotá
++Buglere
Chibchan B
+Pech
+Votic Branch
++Rama
++Maléku
+Dorasque branch
++Dorasque
++Chánguena
+Eastern Chibchan
++Kuna
++Colombian subgroup
+++Northern Colombian group
++++Chimila
++++Arwako group
+++++Kogui
+++++Southern and Eastern Arhuacan
++++++Ijca
++++++Guamaca-Atanque
+++++++Guamaca
+++++++Kankuamo
+++Southern Colombian group
++++Barí
++++Cundicocuyese
+++++Tunebo
++++++Central Tunebo
++++++Tunebo de Margua
++++++Tunebo de Manare
++++++Sínsiga
+++++Muisca-Duit
++++++Chibcha
++++++Duit
Aside from Chánguena, for which I was unable to obtain data other than the expression for the numeral 1, all known nodes of the Chibchan language tree are represented.
The First Five Numerals
Significant evidence from the daughter languages remains to reconstruct the Proto-Chibchan expressions for the numerals 2, 3, and 4, as well as two possibly related expressions for the numeral 5 in Proto-Chibchan A and Proto-Chibchan B. Diversity among the expressions for the numeral representing 1 among modern languages likely reflect subsequent innovations replacing the expression used at the time of Chibchan unity, thereby making it rather difficult (if not impossible) to reconstruct a Proto-Chibchan expression for 1 based on the data reviewed. A discussion of the various expressions used to represent numerals 6 through 10 is undertaken separately from the results demonstrated in this section, as the etymologies are somewhat more complex, and since the higher numerals raise some interesting issues better discussed separately.
The following table demonstrates my reconstructions for the Proto-Chibchan numerals:
1. undetermined
2. *búk(ə)
3. *maya
4. *paká(i)
5. undetermined (PCA: *chiká, PCB: *əchí)
Due to the limited data reviewed, and the inconsistencies of sources relied upon, many of which employ different orthographic systems to display their data, this reconstruction is admittedly a very rough approximation with a rather large margin of error. As more accurate input data become available, I hope to have opportunity re-evaluate my reconstructions.
The following sections demonstrate the intermediate results upon which I arrived at these reconstructions, i.e. intermediate reconstructions at each node of the Chibchan language tree.
Chibchan A
Linguists classify genetically classify the present-day (and recently extinct) Chibchan languages into two categories, A and B respectively, representing a linguistic split early in the Chibchan time line. Variants of these proto-numerals have persisted throughout both branches. The modern descendant languages of Chibchan A include those of the Waimí and Talamancan branches, as well as the Borũca language. Each is discussed separately below.
Waimí
The three Waimí languages investigated have very similar numerals for the numbers 1 through 5, enabling the following Proto-Wiamí reconstructions:
1. *ité (Ngäbere: di, Bocotá: de, Buglere: ite)
2. *búke (Ngäbere: bu, Bocotá: boke, Buglere: boke)
3. *mai (Ngäbere: mɔ, Bocotá: bai, Buglere: mai)
4. *bagá (Ngäbere: bɡɔ, Bocotá: baga, Buglere: baga)
5. *tiga (Ngäbere: riɡɛ, Bocotá: tiga, Buglere: tiga)
Talamancan
The Talamancan branch consists of the Viceitic languages and Teribe. I have reconstructed Proto-Viceitic as follows:
1. *ekra (Bribri: ek, Cabécar: ecra)
2. *buk (Bribri: bök, Cabécar: bur)
3. *mañá (Bribri: mañá, Cabécar: mañór)
4. *tkal (Bribri: tkël, Cabécar: tkil)
5. *skel (Bribri: skel, Cabécar: skel)
The forms in the Teribe language are as follows:
1. kra-rá
2. púg-da
3. myá-re
4. pkégn-de
5. shkégn-de
Combining Proto-Viceitic and Teribe results in the following Proto-Talamancan expressions:
1. *ekra
2. *buk
3. *mayá
4. *p'ka
5. *s'ke
Borũca
The following are the forms of the numerals in Borũca:
1. e'tsé
2. bú'k
3. mang
4. ba'kang
5. xi'kang
Chibchan A Results
Without using data from Chibchan B languages, the following reconstructions seem likely:
1. undetermined (Proto-Waimí: *ité, Proto-Talamancan: *ekra, Borũca: e'tsé)
2. *buk (Proto-Waimí: *búke, Proto-Talamancan: *buk, Borũca: bú'k)
3. *mayá (Proto-Waimí: *mai, Proto-Talamancan: *mayá, Borũca: mang)
4. *paká (Proto-Waimí: *bagá, Proto-Talamancan: *p'ka, Borũca: ba'kang)
5. *chiká (Proto-Waimí: *tiga, Proto-Talamancan: *s'ke, Borũca: xi'kang)
Chibchan B
The modern descendant languages of Chibchan B include those of the Votic, Dorasque and Eastern Chibchan branches, as well as the Pech language. Each is discussed separately below.
Votic
From the languages of Rama and Maléku, a unified set of Proto-Votic numerals can not be easily determined. However, the two languages appear to have some possible cognages with other branches of Chibchan B, upon which I made a few very weak reconstructions:
1. undetermined (Rama: saiming, Maléku: dooka)
2. *puk (Rama: púksak, Maléku: pángi)
3. *pan (Rama: pansak, Maléku: poóse)
4. *pakái (Rama: kungkungbi,Maléku: pakái)
5. undetermined (Rama: kʷikistar, Maléku: otini)
I also suggest the possibility that somehow the numbers two and three could have been reversed at some point.
Dorasque
With regard to the extinct language of Chánguena, I was only able to locate an expression for the numeral 1, i.e. "umai."
The numerals of the Dorasque language are as follows:
1. kue
2. mo
3. mas
4. paka
5. male
Pech
The Pech expressions for the numerals are as follows:
1. as
2. pok
3. mai
4. caa
5. aúnqui
Eastern Chibchan
The best documented Chibchan A data comes from the Eastern Chibchan or "Kuna-Colombian" language family. Due to the large number of languages compared, a series of trees demonstrating the numeral reconstructions at each node is perhaps the easiest way to demonstrate the results.
1. Proto-Eastern Chibchan: undetermined
Kuna: kwena
Proto-Colombian: undetermined
Proto-Northern Colombian: undetermined
Chimila: ti-tásu (ti is a prefix)
Proto-Arwako: undetermined
Kogui: éizua
Proto-Southern and Eastern Arhuacan: undetermined
Ijca: in'gwi
Proto-Guamaca-Atanque: *ishgua
Guamaca: ishgua
Kankuamo: ijkua
Proto-Southern Colombian group: undetermined
Barí: intok
Proto-Cundicocuyese: undetermined
Proto-Tunebo: undetermined
Central Tunebo: xesté
Tunebo de Margua: istan
Tunebo de Manare: ikti
Sínsiga: ikti
Proto-Muisca-Duit: *ata
Chibcha: ata
Duit: atia
2. Proto-Eastern Chibchan: *bókə
Kuna: po
Proto-Colombian: *bók(gw)a
Proto-Northern Colombian: *mógwa
Chimila: ti-múxuna (ti is a prefix)
Proto-Arwako: *mógwa
Kogui: mozhua
Proto-Southern and Eastern Arhuacan: *móga
Ijca: móuga
Proto-Guamaca-Atanque: *móga
Guamaca: móa
Kankuamo: moga
Proto-Southern Colombian group: *boka
Barí: insami (not a cognate)
Proto-Cundicocuyese: *bóka
Proto-Tunebo: *bukai
Central Tunebo: bukai
Tunebo de Margua: bukoï
Tunebo de Manare: bukai
Sínsiga: bukkai
Proto-Muisca-Duit: *bocha
Chibcha: boza
Duit: bocha
3. Proto-Eastern Chibchan: *máiə
Kuna: pa
Proto-Colombian: *mái(gw)a
Proto-Northern Colombian: *máigwa
Chimila: ti-máxana (ti is a prefix)
Proto-Arwako: *máigwa
Kogui: maigua
Proto-Southern and Eastern Arhuacan: *mái(gw)a
Ijca: máikeni
Proto-Guamaca-Atanque: *mái(gw)a
Guamaca: máigua
Kankuamo: ména
Proto-Southern Colombian group: *mái'a
Barí: tẽtahko (not a cognate)
Proto-Cundicocuyese: *mái'a
Proto-Tunebo: *mai
Central Tunebo: bay
Tunebo de Margua: maï
Tunebo de Manare: bai
Sínsiga: bai
Proto-Muisca-Duit: *mái'a
Chibcha: mica
Duit: meia
4. Proto-Eastern Chibchan: *məkaí
Kuna: pakke
Proto-Colombian: *makaí(gwa)
Proto-Northern Colombian: *makaígwa
Chimila: mbrí nyé (compound form, not a cognate)
Proto-Arwako: *makaígwa
Kogui: mukaiwa
Proto-Southern and Eastern Arhuacan: *makégwa
Ijca: ma'kéiwa
Proto-Guamaca-Atanque: *makégwa
Guamaca: makégua
Kankuamo: makéua
Proto-Southern Colombian group: *makái
Barí: ahduĩshkidã intok wa (not a cognate)
Proto-Cundicocuyese: *makái
Proto-Tunebo: *makái
Central Tunebo: bakaí
Tunebo de Margua: makaï
Tunebo de Manare: bagkai
Sínsiga: bakkai
Proto-Muisca-Duit: *muyhy'a
Chibcha: muyhyca
Duit: undetermined
5. Proto-Eastern Chibchan: *əchí
Kuna: attale
Proto-Colombian: *əchí(gwa)
Proto-Northern Colombian: *achígwa
Chimila: ti-ta (ti is a prefix)
Proto-Arwako: *achígwa
Kogui: juchiwu
Proto-Southern and Eastern Arhuacan: *achígwa
Ijca: aséwa
Proto-Guamaca-Atanque: *achígwa
Guamaca: achígua
Kankuamo: achíua
Proto-Southern Colombian group: *edzí
Barí: kobá (not a cognate)
Proto-Cundicocuyese: *edzí
Proto-Tunebo: *edzí
Central Tunebo: ezei
Tunebo de Margua: etsi
Tunebo de Manare: etsi
Sínsiga: edzí
Proto-Muisca-Duit: *hyz'a
Chibcha: hyzca
Duit: undetermined
Chibchan B Results
Without using data from Chibchan A languages, the following reconstructions seem likely:
1. undetermined (numerous forms in daughter languages, none bearing striking resemblance to any of the forms in other high-level branches)
2. *búkə (Proto-Votic: *puk, Dorasque: mo, Pech: pok, Proto-Eastern Chibchan: *bókə)
3. *máiə (Proto-Votic: *pan, Dorasque: mas, Pech: mai, Proto-Eastern Chibchan: *máiə)
4. *pəkái (Proto-Votic: *pakái, Dorasque: paka, Pech: caa, Proto-Eastern Chibchan: *makái)
5. *əchí (Maléku: otini, Proto-Eastern Chibchan: *əchí)
Comparison of Chibchan A and Chibchan B Results
The resemblance between the reconstructed numerals in the two branches is striking, and suggest the following reconstructions of the first five Proto-Chibchan numerals:
1. undetermined
2. *búk(ə) (from Proto-Chibchan A *buk and Proto-Chibchan B *búkə)
3. *maya (from Proto-Chibchan A *mayá and Proto-Chibchan B *máiə)
4. *paká(i) (from Proto-Chibchan A *paká and Proto-Chibchan B *pəkái)
5. undetermined (although there is likely some relation between the two expressions, I feel that there is too little data to determine whether the roots of Proto-Chibchan A *chiká and Proto-Chibchan B *əchí are cognate)
The only Chibchan language that does not use cognate forms of the reconstructions above is Barí, which appears to have adopted a different numeric system entirely. Perhaps worthy of note is the fact that Barí is one of only two Chibchan languages that is reportedly tonal.[6]
Six Through Ten
Most of the living and recently extinct Chibchan languages have forms for the numerals 6 through 10 that appear distinct from the numerals 1 through 5. Of the languages for which I was able to obtain data beyond the numeral 5, only Cabécar and Rama have numeric systems where the expression for the numeral 6 is merely a compound word with components indicating 5+1. In both languages, 7 is indicated by 5+2, 8 by 5+3, etc. Cabécar has a distinct expression for the numeral 10, whereas Rama expresses 10 as 5+5.
The fact that Cabécar and Rama stop at 5 and repeat tend to show that Proto-Chibchan probably only had distinct expressions for the numerals 1 through 5, whereas higher quantities were expressed using compound forms, if at all. Furthermore, since Cabécar is a Chibchan A language and Rama is a Chibchan B language, it is likely that the innovation of using distinct expressions for higher numerals occurred after the two sub-famlies became divergent.
That being said, a number of languages in both Chibchan A and Chibchan B appear to have distinct expressions for numerals 6 through 10, some of which have cognates on both the A and B side of the family. One possible scenerio explaining this seemingly paradoxical situation is that one or more extended numeric systems innovated in the daughter Chibchan languages was borrowed by other Chibchan languages, perhaps as a result of trade. Another possible scenario is that some of the daughter languages on both the A and B sides of the family borrowed expressions for numerals 6 through 10 from a common source. A third but in my opinion more remote possibility is a scenario where Proto-Chibchan had a numeric system with distinct expressions for the numbers 6 through 10, but for some reason or another, Cabécar and Rama lost these expressions perhaps after a long period where they were not often used.
Tunebo de Margua is an interesting language, and perhaps provides some clues. It uses expressions for the numerals 6, 7 and 8 that are cognate to those of other Chibchan languages, while 9 and 10 are represented by expressions meaning 8+1 and 8+2 respectively. All of the other modern Tunebo languages I have reviewed use a system that continues to 10 without the use of compounds.
Relationships Among Non-Compound Expressions for Six Through Ten
Excluding compound forms, all of the examined Chibchan expressions for the numeral 6 appear to have cognate roots with one-another:
6.
Ngäbere: ti
Buglere: dereke
Borũca: texén
Bribri: terl
Teribe: tér-de
Pech: séra
Kuna: nerkwd
Chibcha: taá
all Tunebo languages: terai
Guamaca: tainnúa
Ijca: chíngua
Kogui: taij-uña
Nicholas Ostler has proposed a Proto-Chibchan *ted-ua based on these forms.[7] For reasons stated above, I question whether such a reconstruction could be properly labeled Proto-Chibchan, considering the possibility that Proto-Chibchan did not have a non-compound expression for 6.
Moving on to expressions for 7, there is similar widespread simiilarity in expressions, spanning Chibchan A and B:
7.
Ngäbere: kɯɡɯ
Buglere: ɡuke
Borũca: kugtán
Bribri: cugl
Teribe: kógu-de
Kuna: kukle
Chibcha: cuhupqua
Central Tunebo: kukué
Tunebo de Margua: kuki
Tunebo de Manare: kukuni
Sinsiga: kukuí
Guamaca: kúgua
Kogui: kúgua
Exceptions which are clearly not cognate are Pech "tavuá" which may be a derivative related to "óva" (8), and Icja "shkába," also potentially a derivative related to "abéba" (8).
As we reach 8, the uniformity begins to erode. To represent the data, I grouped the expressions that are seemingly related, and indicated either and A or B to denote which side of the Chibchan family each expression falls on:
8.
Pech (B): óva
Central Tunebo (B): abé
Tunebo de Margua (B): avi
Tunebo de Manare (B): abi
Sinsiga (B): aví
Guamaca (B): ámbigua
Icja (B): abéba
Kogui (B): abi-kua
Ngäbere (A): kwɔ
Teribe (A): kwógu-de
Buglere (A): pa
Bribri (A): pagle
Chibcha (B): suhuza
Chimila (B): komá-na
Note that none of the groups span both Chibchan A and B, unless one or more of the groups can be combined. Such opportunity for combination is not apparent to me given the data.
The expressions for 9 are equally fragmented, although there is at least one group that spans Chibchan A and B:
9.
Ngäbere (A): ɤɡɔ
Buglere (A): inka
Guamaca (B): ihkágua
Icja (B): ihkágua
Kogui (B): kóga
Pech (B): tax (difficult to discern whether this expression belongs to the group)
Central Tunebo (B): estare
Tunebo de Manare (B): ettari
Sinsiga (B): stari
Teribe (A): shkówu-de
Bribri (A): sunito
Chibcha (B): aca
As expected, the expressions for 10 are across the board, as were those for 1 and 5. These numeric positions are particularly succeptable to replacement and innovation, as in addition to representing numerals, they may also express the ideas (such as the body parts upon which they were counted, for example). Forms that are not obvious compounds are listed only:
10.
Buglere (A): taboko
Bribri (A): d'bob
Cabécar (A): dobob
Teribe (A): dwówu-de
Pech (B): úca
Central Tunebo (B): ukafe
Tunebo de Manare (B): uteasi
Sinsiga (B): ukkasi
Guamaca (B): ugua
Kogui (B): uúga
Ngäbere (A): ni hɔdɔ
Maléku (B): paunka
Kuna (B): ampeki
Chibcha (B): ubchihica (probably a compound form of "hyzca" (5))
Chimila (B): che
Apparent cognate expressions for the numeral 10 do not span Chibchan A and B.
Irregularity in Kuna Compound Expressions for Eight and Nine
The numerals of the Kuna language deserve special attention, because the Kuna expressions for the numerals 8 and 9 have inexplicable compound forms:
1. kwena (unknown origin)
2. po (descendant of Proto-Chibchan *búk(ə))
3. pa (descendant of Proto-Chibchan *maya)
4. pakke (descendant of Proto-Chibchan *paká(i))
5. attale (unknown origin)
6. nerkwd (root is cognate to most common Chibchan form)
7. kukle (cognate to most common Chibchan form)
8. paapakka (lit. 3+4)
9. pakkepakka (lit. 4+4)
10. ampeki (unknown origin)
Paapakka for 8 appears to be a combination of pa + pakke (indicating 3 plus 4). Likewise, pakkepakka for 9 appears to be a combination of pakke + pakke (indicating 4 plus 4). As we all know, 3 plus 4 is 7 rather than 8, and 4 plus 4 is 8 rather than 9. I can not explain this apparent inconsistency.
Irregulary in Chimila Compound Forms
Chimila numerals also deserve attention, because they seem to belong to two classes, one of the classes consisting largely of unusual compound forms:
1. ti-tásu
2. ti-múxuna
3. ti-máxana
4. mbrí nyé
5. ti-ta
6. ráta mbrí nyé
7. ráta nyé
8. komá-na
9. ráta nyé
10. che
With the exception of the expression for 1, those numerals beginning with the prefix ti all appear to be cognate to Proto-Chibchan B. (Remember that the Proto-Chibchan B expression for 1 could not be determined.) However, the non-prefixed numerals for 4, 6, 7 and 9 appear to be compounds not based upon any of the Chibchan B forms. Furthermore, the expressions for 7 and 9 appear to be the same, unless the orthography used in the source from which these expressions were obtained did not catch a perhaps minute distinction. Of note, Chimila is a tonal language.[6]
Peer Review
As a general disclaimer to this article, I do not claim to have any formal linguistic training. I've read a few books on comparative linguistics, and seen a number of examples in practice. Furthermore, my methods and resources are assuredly not up to the standard of other linguists who have the luxury of a more complete lexicon of these languages and proper training. However, I have not found a thorough analysis of the Proto-Chibchan numerals anywhere else thusfar, so I set out to make this preliminary attempt to undertake the analysis.
Accordingly, I would love to have some review of my results by those in the field. Any and all comments, corrections, suggestions, additions, and even outright disagreements are absolutely welcome and encouraged by anyone with knowledge on this subject.
On a related note, I would like to give special thanks to Lloyd Anderson of Ecological Linguistics, who provided an extremely detailed critique of this article's first draft, based upon which I made numerous major edits, many of which resulted in what I feel are more accurate reconstructions. Mr. Anderson also provided a list of potential resources containing more data and insight (as well as a considerable amount of his own insight), which I intend to pursue prior to a planned second overhaul of this article.
References
1. American Indian Languages: The Historical Linguistics of Native America. Campbell, Lyle. 1997.
2. Wikipedia: Chibchan Languages
3. Numeral Systems of the World's Languages. Comrie, Bernard. 2008.
4. Native Languages of the Americas: Preserving and promoting American Indian languages
5. Numbers from 1 to 10 in Over 5000 Languages. Rosenfelder, Mark.
6. Evidence and Counter-Evidence. Lubotsky, Alexander.
7. U'wa, a dialect of Muisca. Ostler, Nicholas.
Data from modern and recently extinct languages in the Chibchan language family is analyzed in an attempt to unravel the counting system used by the Proto-Chibchan people living in Costa Rica and Panama around the year 3000 BC.
Background
Proto-Chibchan is a hypothetical language, believed to have been spoken by Native Americans near present-day Costa Rica and Panama around the year 3000 BC. The Proto-Chibchan speakers were primarily agriculturists, who also engaged in pottery and boat-making.[1] Today, the Chibchan languages make up a language family indigenous to the Isthmo-Columbian area, which extends from eastern Honduras to northern Columbia and includes populations of these countries as well as Nicaragua, Costa Rica and Panama.[2]
Methods
Based on available data on the numerals used by contemporary Native American peoples speaking descendant languages of Proto-Chibchan,[3][4][5] I have used comparative techniques to deduce a rough approximation of the original Proto-Chibchan numeral system that can be traced down to modern Native American languages (many of which have expanded or modified the system significantly).
The following tree represents the normally assumed structure of the Chibchan language family,[1][2] with the specific languages compared in this article in bold:
Chibchan A
+Talamancan branch
++Teribe
++Viceitic branch
+++Bribri
+++Cabécar
+Borũca
+Waimí branch
++Ngäbere
++Bocotá
++Buglere
Chibchan B
+Pech
+Votic Branch
++Rama
++Maléku
+Dorasque branch
++Dorasque
++Chánguena
+Eastern Chibchan
++Kuna
++Colombian subgroup
+++Northern Colombian group
++++Chimila
++++Arwako group
+++++Kogui
+++++Southern and Eastern Arhuacan
++++++Ijca
++++++Guamaca-Atanque
+++++++Guamaca
+++++++Kankuamo
+++Southern Colombian group
++++Barí
++++Cundicocuyese
+++++Tunebo
++++++Central Tunebo
++++++Tunebo de Margua
++++++Tunebo de Manare
++++++Sínsiga
+++++Muisca-Duit
++++++Chibcha
++++++Duit
Aside from Chánguena, for which I was unable to obtain data other than the expression for the numeral 1, all known nodes of the Chibchan language tree are represented.
The First Five Numerals
Significant evidence from the daughter languages remains to reconstruct the Proto-Chibchan expressions for the numerals 2, 3, and 4, as well as two possibly related expressions for the numeral 5 in Proto-Chibchan A and Proto-Chibchan B. Diversity among the expressions for the numeral representing 1 among modern languages likely reflect subsequent innovations replacing the expression used at the time of Chibchan unity, thereby making it rather difficult (if not impossible) to reconstruct a Proto-Chibchan expression for 1 based on the data reviewed. A discussion of the various expressions used to represent numerals 6 through 10 is undertaken separately from the results demonstrated in this section, as the etymologies are somewhat more complex, and since the higher numerals raise some interesting issues better discussed separately.
The following table demonstrates my reconstructions for the Proto-Chibchan numerals:
1. undetermined
2. *búk(ə)
3. *maya
4. *paká(i)
5. undetermined (PCA: *chiká, PCB: *əchí)
Due to the limited data reviewed, and the inconsistencies of sources relied upon, many of which employ different orthographic systems to display their data, this reconstruction is admittedly a very rough approximation with a rather large margin of error. As more accurate input data become available, I hope to have opportunity re-evaluate my reconstructions.
The following sections demonstrate the intermediate results upon which I arrived at these reconstructions, i.e. intermediate reconstructions at each node of the Chibchan language tree.
Chibchan A
Linguists classify genetically classify the present-day (and recently extinct) Chibchan languages into two categories, A and B respectively, representing a linguistic split early in the Chibchan time line. Variants of these proto-numerals have persisted throughout both branches. The modern descendant languages of Chibchan A include those of the Waimí and Talamancan branches, as well as the Borũca language. Each is discussed separately below.
Waimí
The three Waimí languages investigated have very similar numerals for the numbers 1 through 5, enabling the following Proto-Wiamí reconstructions:
1. *ité (Ngäbere: di, Bocotá: de, Buglere: ite)
2. *búke (Ngäbere: bu, Bocotá: boke, Buglere: boke)
3. *mai (Ngäbere: mɔ, Bocotá: bai, Buglere: mai)
4. *bagá (Ngäbere: bɡɔ, Bocotá: baga, Buglere: baga)
5. *tiga (Ngäbere: riɡɛ, Bocotá: tiga, Buglere: tiga)
Talamancan
The Talamancan branch consists of the Viceitic languages and Teribe. I have reconstructed Proto-Viceitic as follows:
1. *ekra (Bribri: ek, Cabécar: ecra)
2. *buk (Bribri: bök, Cabécar: bur)
3. *mañá (Bribri: mañá, Cabécar: mañór)
4. *tkal (Bribri: tkël, Cabécar: tkil)
5. *skel (Bribri: skel, Cabécar: skel)
The forms in the Teribe language are as follows:
1. kra-rá
2. púg-da
3. myá-re
4. pkégn-de
5. shkégn-de
Combining Proto-Viceitic and Teribe results in the following Proto-Talamancan expressions:
1. *ekra
2. *buk
3. *mayá
4. *p'ka
5. *s'ke
Borũca
The following are the forms of the numerals in Borũca:
1. e'tsé
2. bú'k
3. mang
4. ba'kang
5. xi'kang
Chibchan A Results
Without using data from Chibchan B languages, the following reconstructions seem likely:
1. undetermined (Proto-Waimí: *ité, Proto-Talamancan: *ekra, Borũca: e'tsé)
2. *buk (Proto-Waimí: *búke, Proto-Talamancan: *buk, Borũca: bú'k)
3. *mayá (Proto-Waimí: *mai, Proto-Talamancan: *mayá, Borũca: mang)
4. *paká (Proto-Waimí: *bagá, Proto-Talamancan: *p'ka, Borũca: ba'kang)
5. *chiká (Proto-Waimí: *tiga, Proto-Talamancan: *s'ke, Borũca: xi'kang)
Chibchan B
The modern descendant languages of Chibchan B include those of the Votic, Dorasque and Eastern Chibchan branches, as well as the Pech language. Each is discussed separately below.
Votic
From the languages of Rama and Maléku, a unified set of Proto-Votic numerals can not be easily determined. However, the two languages appear to have some possible cognages with other branches of Chibchan B, upon which I made a few very weak reconstructions:
1. undetermined (Rama: saiming, Maléku: dooka)
2. *puk (Rama: púksak, Maléku: pángi)
3. *pan (Rama: pansak, Maléku: poóse)
4. *pakái (Rama: kungkungbi,Maléku: pakái)
5. undetermined (Rama: kʷikistar, Maléku: otini)
I also suggest the possibility that somehow the numbers two and three could have been reversed at some point.
Dorasque
With regard to the extinct language of Chánguena, I was only able to locate an expression for the numeral 1, i.e. "umai."
The numerals of the Dorasque language are as follows:
1. kue
2. mo
3. mas
4. paka
5. male
Pech
The Pech expressions for the numerals are as follows:
1. as
2. pok
3. mai
4. caa
5. aúnqui
Eastern Chibchan
The best documented Chibchan A data comes from the Eastern Chibchan or "Kuna-Colombian" language family. Due to the large number of languages compared, a series of trees demonstrating the numeral reconstructions at each node is perhaps the easiest way to demonstrate the results.
1. Proto-Eastern Chibchan: undetermined
Kuna: kwena
Proto-Colombian: undetermined
Proto-Northern Colombian: undetermined
Chimila: ti-tásu (ti is a prefix)
Proto-Arwako: undetermined
Kogui: éizua
Proto-Southern and Eastern Arhuacan: undetermined
Ijca: in'gwi
Proto-Guamaca-Atanque: *ishgua
Guamaca: ishgua
Kankuamo: ijkua
Proto-Southern Colombian group: undetermined
Barí: intok
Proto-Cundicocuyese: undetermined
Proto-Tunebo: undetermined
Central Tunebo: xesté
Tunebo de Margua: istan
Tunebo de Manare: ikti
Sínsiga: ikti
Proto-Muisca-Duit: *ata
Chibcha: ata
Duit: atia
2. Proto-Eastern Chibchan: *bókə
Kuna: po
Proto-Colombian: *bók(gw)a
Proto-Northern Colombian: *mógwa
Chimila: ti-múxuna (ti is a prefix)
Proto-Arwako: *mógwa
Kogui: mozhua
Proto-Southern and Eastern Arhuacan: *móga
Ijca: móuga
Proto-Guamaca-Atanque: *móga
Guamaca: móa
Kankuamo: moga
Proto-Southern Colombian group: *boka
Barí: insami (not a cognate)
Proto-Cundicocuyese: *bóka
Proto-Tunebo: *bukai
Central Tunebo: bukai
Tunebo de Margua: bukoï
Tunebo de Manare: bukai
Sínsiga: bukkai
Proto-Muisca-Duit: *bocha
Chibcha: boza
Duit: bocha
3. Proto-Eastern Chibchan: *máiə
Kuna: pa
Proto-Colombian: *mái(gw)a
Proto-Northern Colombian: *máigwa
Chimila: ti-máxana (ti is a prefix)
Proto-Arwako: *máigwa
Kogui: maigua
Proto-Southern and Eastern Arhuacan: *mái(gw)a
Ijca: máikeni
Proto-Guamaca-Atanque: *mái(gw)a
Guamaca: máigua
Kankuamo: ména
Proto-Southern Colombian group: *mái'a
Barí: tẽtahko (not a cognate)
Proto-Cundicocuyese: *mái'a
Proto-Tunebo: *mai
Central Tunebo: bay
Tunebo de Margua: maï
Tunebo de Manare: bai
Sínsiga: bai
Proto-Muisca-Duit: *mái'a
Chibcha: mica
Duit: meia
4. Proto-Eastern Chibchan: *məkaí
Kuna: pakke
Proto-Colombian: *makaí(gwa)
Proto-Northern Colombian: *makaígwa
Chimila: mbrí nyé (compound form, not a cognate)
Proto-Arwako: *makaígwa
Kogui: mukaiwa
Proto-Southern and Eastern Arhuacan: *makégwa
Ijca: ma'kéiwa
Proto-Guamaca-Atanque: *makégwa
Guamaca: makégua
Kankuamo: makéua
Proto-Southern Colombian group: *makái
Barí: ahduĩshkidã intok wa (not a cognate)
Proto-Cundicocuyese: *makái
Proto-Tunebo: *makái
Central Tunebo: bakaí
Tunebo de Margua: makaï
Tunebo de Manare: bagkai
Sínsiga: bakkai
Proto-Muisca-Duit: *muyhy'a
Chibcha: muyhyca
Duit: undetermined
5. Proto-Eastern Chibchan: *əchí
Kuna: attale
Proto-Colombian: *əchí(gwa)
Proto-Northern Colombian: *achígwa
Chimila: ti-ta (ti is a prefix)
Proto-Arwako: *achígwa
Kogui: juchiwu
Proto-Southern and Eastern Arhuacan: *achígwa
Ijca: aséwa
Proto-Guamaca-Atanque: *achígwa
Guamaca: achígua
Kankuamo: achíua
Proto-Southern Colombian group: *edzí
Barí: kobá (not a cognate)
Proto-Cundicocuyese: *edzí
Proto-Tunebo: *edzí
Central Tunebo: ezei
Tunebo de Margua: etsi
Tunebo de Manare: etsi
Sínsiga: edzí
Proto-Muisca-Duit: *hyz'a
Chibcha: hyzca
Duit: undetermined
Chibchan B Results
Without using data from Chibchan A languages, the following reconstructions seem likely:
1. undetermined (numerous forms in daughter languages, none bearing striking resemblance to any of the forms in other high-level branches)
2. *búkə (Proto-Votic: *puk, Dorasque: mo, Pech: pok, Proto-Eastern Chibchan: *bókə)
3. *máiə (Proto-Votic: *pan, Dorasque: mas, Pech: mai, Proto-Eastern Chibchan: *máiə)
4. *pəkái (Proto-Votic: *pakái, Dorasque: paka, Pech: caa, Proto-Eastern Chibchan: *makái)
5. *əchí (Maléku: otini, Proto-Eastern Chibchan: *əchí)
Comparison of Chibchan A and Chibchan B Results
The resemblance between the reconstructed numerals in the two branches is striking, and suggest the following reconstructions of the first five Proto-Chibchan numerals:
1. undetermined
2. *búk(ə) (from Proto-Chibchan A *buk and Proto-Chibchan B *búkə)
3. *maya (from Proto-Chibchan A *mayá and Proto-Chibchan B *máiə)
4. *paká(i) (from Proto-Chibchan A *paká and Proto-Chibchan B *pəkái)
5. undetermined (although there is likely some relation between the two expressions, I feel that there is too little data to determine whether the roots of Proto-Chibchan A *chiká and Proto-Chibchan B *əchí are cognate)
The only Chibchan language that does not use cognate forms of the reconstructions above is Barí, which appears to have adopted a different numeric system entirely. Perhaps worthy of note is the fact that Barí is one of only two Chibchan languages that is reportedly tonal.[6]
Six Through Ten
Most of the living and recently extinct Chibchan languages have forms for the numerals 6 through 10 that appear distinct from the numerals 1 through 5. Of the languages for which I was able to obtain data beyond the numeral 5, only Cabécar and Rama have numeric systems where the expression for the numeral 6 is merely a compound word with components indicating 5+1. In both languages, 7 is indicated by 5+2, 8 by 5+3, etc. Cabécar has a distinct expression for the numeral 10, whereas Rama expresses 10 as 5+5.
The fact that Cabécar and Rama stop at 5 and repeat tend to show that Proto-Chibchan probably only had distinct expressions for the numerals 1 through 5, whereas higher quantities were expressed using compound forms, if at all. Furthermore, since Cabécar is a Chibchan A language and Rama is a Chibchan B language, it is likely that the innovation of using distinct expressions for higher numerals occurred after the two sub-famlies became divergent.
That being said, a number of languages in both Chibchan A and Chibchan B appear to have distinct expressions for numerals 6 through 10, some of which have cognates on both the A and B side of the family. One possible scenerio explaining this seemingly paradoxical situation is that one or more extended numeric systems innovated in the daughter Chibchan languages was borrowed by other Chibchan languages, perhaps as a result of trade. Another possible scenario is that some of the daughter languages on both the A and B sides of the family borrowed expressions for numerals 6 through 10 from a common source. A third but in my opinion more remote possibility is a scenario where Proto-Chibchan had a numeric system with distinct expressions for the numbers 6 through 10, but for some reason or another, Cabécar and Rama lost these expressions perhaps after a long period where they were not often used.
Tunebo de Margua is an interesting language, and perhaps provides some clues. It uses expressions for the numerals 6, 7 and 8 that are cognate to those of other Chibchan languages, while 9 and 10 are represented by expressions meaning 8+1 and 8+2 respectively. All of the other modern Tunebo languages I have reviewed use a system that continues to 10 without the use of compounds.
Relationships Among Non-Compound Expressions for Six Through Ten
Excluding compound forms, all of the examined Chibchan expressions for the numeral 6 appear to have cognate roots with one-another:
6.
Ngäbere: ti
Buglere: dereke
Borũca: texén
Bribri: terl
Teribe: tér-de
Pech: séra
Kuna: nerkwd
Chibcha: taá
all Tunebo languages: terai
Guamaca: tainnúa
Ijca: chíngua
Kogui: taij-uña
Nicholas Ostler has proposed a Proto-Chibchan *ted-ua based on these forms.[7] For reasons stated above, I question whether such a reconstruction could be properly labeled Proto-Chibchan, considering the possibility that Proto-Chibchan did not have a non-compound expression for 6.
Moving on to expressions for 7, there is similar widespread simiilarity in expressions, spanning Chibchan A and B:
7.
Ngäbere: kɯɡɯ
Buglere: ɡuke
Borũca: kugtán
Bribri: cugl
Teribe: kógu-de
Kuna: kukle
Chibcha: cuhupqua
Central Tunebo: kukué
Tunebo de Margua: kuki
Tunebo de Manare: kukuni
Sinsiga: kukuí
Guamaca: kúgua
Kogui: kúgua
Exceptions which are clearly not cognate are Pech "tavuá" which may be a derivative related to "óva" (8), and Icja "shkába," also potentially a derivative related to "abéba" (8).
As we reach 8, the uniformity begins to erode. To represent the data, I grouped the expressions that are seemingly related, and indicated either and A or B to denote which side of the Chibchan family each expression falls on:
8.
Pech (B): óva
Central Tunebo (B): abé
Tunebo de Margua (B): avi
Tunebo de Manare (B): abi
Sinsiga (B): aví
Guamaca (B): ámbigua
Icja (B): abéba
Kogui (B): abi-kua
Ngäbere (A): kwɔ
Teribe (A): kwógu-de
Buglere (A): pa
Bribri (A): pagle
Chibcha (B): suhuza
Chimila (B): komá-na
Note that none of the groups span both Chibchan A and B, unless one or more of the groups can be combined. Such opportunity for combination is not apparent to me given the data.
The expressions for 9 are equally fragmented, although there is at least one group that spans Chibchan A and B:
9.
Ngäbere (A): ɤɡɔ
Buglere (A): inka
Guamaca (B): ihkágua
Icja (B): ihkágua
Kogui (B): kóga
Pech (B): tax (difficult to discern whether this expression belongs to the group)
Central Tunebo (B): estare
Tunebo de Manare (B): ettari
Sinsiga (B): stari
Teribe (A): shkówu-de
Bribri (A): sunito
Chibcha (B): aca
As expected, the expressions for 10 are across the board, as were those for 1 and 5. These numeric positions are particularly succeptable to replacement and innovation, as in addition to representing numerals, they may also express the ideas (such as the body parts upon which they were counted, for example). Forms that are not obvious compounds are listed only:
10.
Buglere (A): taboko
Bribri (A): d'bob
Cabécar (A): dobob
Teribe (A): dwówu-de
Pech (B): úca
Central Tunebo (B): ukafe
Tunebo de Manare (B): uteasi
Sinsiga (B): ukkasi
Guamaca (B): ugua
Kogui (B): uúga
Ngäbere (A): ni hɔdɔ
Maléku (B): paunka
Kuna (B): ampeki
Chibcha (B): ubchihica (probably a compound form of "hyzca" (5))
Chimila (B): che
Apparent cognate expressions for the numeral 10 do not span Chibchan A and B.
Irregularity in Kuna Compound Expressions for Eight and Nine
The numerals of the Kuna language deserve special attention, because the Kuna expressions for the numerals 8 and 9 have inexplicable compound forms:
1. kwena (unknown origin)
2. po (descendant of Proto-Chibchan *búk(ə))
3. pa (descendant of Proto-Chibchan *maya)
4. pakke (descendant of Proto-Chibchan *paká(i))
5. attale (unknown origin)
6. nerkwd (root is cognate to most common Chibchan form)
7. kukle (cognate to most common Chibchan form)
8. paapakka (lit. 3+4)
9. pakkepakka (lit. 4+4)
10. ampeki (unknown origin)
Paapakka for 8 appears to be a combination of pa + pakke (indicating 3 plus 4). Likewise, pakkepakka for 9 appears to be a combination of pakke + pakke (indicating 4 plus 4). As we all know, 3 plus 4 is 7 rather than 8, and 4 plus 4 is 8 rather than 9. I can not explain this apparent inconsistency.
Irregulary in Chimila Compound Forms
Chimila numerals also deserve attention, because they seem to belong to two classes, one of the classes consisting largely of unusual compound forms:
1. ti-tásu
2. ti-múxuna
3. ti-máxana
4. mbrí nyé
5. ti-ta
6. ráta mbrí nyé
7. ráta nyé
8. komá-na
9. ráta nyé
10. che
With the exception of the expression for 1, those numerals beginning with the prefix ti all appear to be cognate to Proto-Chibchan B. (Remember that the Proto-Chibchan B expression for 1 could not be determined.) However, the non-prefixed numerals for 4, 6, 7 and 9 appear to be compounds not based upon any of the Chibchan B forms. Furthermore, the expressions for 7 and 9 appear to be the same, unless the orthography used in the source from which these expressions were obtained did not catch a perhaps minute distinction. Of note, Chimila is a tonal language.[6]
Peer Review
As a general disclaimer to this article, I do not claim to have any formal linguistic training. I've read a few books on comparative linguistics, and seen a number of examples in practice. Furthermore, my methods and resources are assuredly not up to the standard of other linguists who have the luxury of a more complete lexicon of these languages and proper training. However, I have not found a thorough analysis of the Proto-Chibchan numerals anywhere else thusfar, so I set out to make this preliminary attempt to undertake the analysis.
Accordingly, I would love to have some review of my results by those in the field. Any and all comments, corrections, suggestions, additions, and even outright disagreements are absolutely welcome and encouraged by anyone with knowledge on this subject.
On a related note, I would like to give special thanks to Lloyd Anderson of Ecological Linguistics, who provided an extremely detailed critique of this article's first draft, based upon which I made numerous major edits, many of which resulted in what I feel are more accurate reconstructions. Mr. Anderson also provided a list of potential resources containing more data and insight (as well as a considerable amount of his own insight), which I intend to pursue prior to a planned second overhaul of this article.
References
1. American Indian Languages: The Historical Linguistics of Native America. Campbell, Lyle. 1997.
2. Wikipedia: Chibchan Languages
3. Numeral Systems of the World's Languages. Comrie, Bernard. 2008.
4. Native Languages of the Americas: Preserving and promoting American Indian languages
5. Numbers from 1 to 10 in Over 5000 Languages. Rosenfelder, Mark.
6. Evidence and Counter-Evidence. Lubotsky, Alexander.
7. U'wa, a dialect of Muisca. Ostler, Nicholas.
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