In fact, no relationship of the Maya linguistic group to any other has been discovered. It contains a number of words borrowed from the Aztec (Nahuatl); and the latter in turn presents many undoubtedly borrowed from the Maya dialects. But this only goes to show that these two great families had long and close relations; and that we already know, from their history, traditions and geographical positions.
-- 6. _The Numeral System._
The Mayas had a mathematical turn, and possessed a developed system of numeration. It counted by units and scores; in other words, it was a vigesimal system. The cardinal numbers were:--
Hun, one.
Ca, two.
Ox, three.
Can, four.
Ho, five.
Uac, six.
Uuc, seven.
Uaxac, eight.
Bolon, nine.
Lahun, ten.
Buluc, eleven.
Lahca, twelve.
Oxlahun, thirteen.
Canlahun, fourteen.
Holhun, fifteen.
Uaclahun, sixteen.
Uuclahun, seventeen.
Uaxaclahun, eighteen.
Bolonlahun, nineteen.
Hunkal, twenty.
The composition of these numerals from twelve to nineteen inclusive is easily seen. _Lahun_ is apparently a compound of _lah hun_ (sc.
_uinic_), "it finishes one (man);" that is, in counting on the fingers.
_Lah_ means the end, to end, and also the whole of anything. _Kal_, a score, is literally a fastening together, a shutting up, from the verb _kal_, to shut, to lock, to b.u.t.ton up, etc.
From twenty upward, the scores are used:--
Hun tu kal, one to the score, 21.
Ca tu kal, two to the score, 22.
Ox tu kal, three to the score, 23,
and so on up to
Ca kal, two score, 40.
Above forty, three different methods can be used to continue the numeration.
1. We may continue the same employed between 20 and 40, thus:--
Hun tu cakal, one to two score, 41.
Ca tu cakal, two to two score, 42.
Ox tu cakal, three to two score, 43,
and so on.
2. The numeral copulative _catac_ can be used, with the numeral particle _tul_; as:--
Cakal catac catul, two score and two, 42.
Cakal catac oxtul, two score and three, 43.
3. We may count upon the next score above, as:
Hun tu yoxkal, one on the third score, 41.
Ca tu yoxkal, two on the third score, 42.
Ox tu yoxkal, three on the third score, 43.
The last mentioned system is that advanced by Father Beltran, and is the only one formally mentioned by him. It has recently been carefully a.n.a.lyzed by Prof. Leon de Rosny, who has shown that it is a consistent vigesimal method.[40-1]
It might be asked, and the question is pertinent, and is left unanswered by Prof. Leon de Rosny, why _hun tu kal_ means "one to the score," and _hun tu can kal_ is translated, "one on the fourth score." This important shade of meaning may be given, I think, by the possessive _u_ which originally belonged in the phrase, but suffered elision. Properly it should be,
Hun tu u can kal.
This seems apparent from other numbers where it has not suffered elision, but merely incorporation, as:--
Hun tu yox kal=hun tu u ox kal, 41.
Hu tu yokal=hun tu u ho kal, 81.
This system of numeration, advanced by Beltran, appears to have been adopted by all of the later writers, who may have learned the Maya largely from his Grammar. Thus, in the translation of the Gospel of St.
John, published by the Baptist Bible Translation Society, chap. II, v.
20; _Xupan uactuyoxkal hab utial u mental letile kulnaa_, "forty and six years was this temple in building;"[41-1] and in that of the Gospel of St. Luke, said to have been the work of Father Joaquin Ruz, the same system is followed.[41-2]
Nevertheless, Beltran"s method has been severely criticised by Don Juan Pio Perez, who ranks among the ablest Yucatecan linguists of this century. He has p.r.o.nounced it artificial, not in accordance with either the past or present use of the natives themselves, and built up out of an effort to a.s.similate the Maya to the Latin numeral system.
I give his words in the original, from his unpublished essay on Maya grammar.[42-1]
"Los Indios de Yucatan cuentan por veintenas, que llaman _kal_ y en cierto modo tienen diez y nueve unidades hasta completar la primera veintena que es _hunkal_ aunque en el curso de esta solo se encuentran once numeros simples, pues los nombres de los restantes se forman de los de la primera decena.
"Para contar de una a otra veintena los numeros fraccionarios las diez y nueve unidades, terminadas por la particula _tul_ su sincopa _tu_,[42-2] se juntan antepuestas a la veintena espresada; por exemplo, _hunkal_, 20; _huntukal_, 21; _catukal_, 22; y _huntucakal_, 41; _catucakal_, 42; _oxtucankal_, 83; _cantuhokal_, 140, etc.
"El Padre Fr. Beltran de Santa Rosa, como puede verse en su _Arte de Lengua Maya_, formo un sistema distinto a este desde la 2 veintena hasta la ultima, pues para espresar las unidades entre este y la 3 veintena pone a esta terminandolas y por consiguiente rebajandole su valor por solo su anteposicion a dichas unidades fraccionarias, y asi para espresar el numero 45 por ejemplo dice _ho tu yoxkal_, cuando _oxkal_ _yoxkal_ significa 60.
"No se de donde tomo los fundamentos en que se apoya este sistema, quiza en el uso de su tiempo, que no ha llegado hasta este; aunque he visto en varios ma.n.u.scritos antiguos, que los Indios de entonces como los de ahora, usaban el sistema que indico, y espresaban las unidades integras que numeraban, y para espresar el numero 65 dicen; _Oxkal catac hotul_ u _hotu oxkal_, que usa el Padre Beltran por 45.[43-1]
"Mas el metodo que explico esta apoyado en el uso y aun en el curso que se advierte en la 1 y 2 veintena e indican que asi deben continuar las decenas hasta la 20 y no formar sistemas confusos que por ser mas o menos a.n.a.logos a la numeracion romana lo juzgaban mas o menos perfectos, porque la consideraban como un tipo a que debia arregla.r.s.e cualquiera otra lengua, cuando en ellas todo lo que no este conforme con el uso recibido y corriente, es construir castillos en el aire y hacer reformas que por mas ingeniosas que sean, no pasan de inoficiosas."
In the face of this severe criticism of Father Beltran"s system, I cannot explain how it is that in Pio Perez"s own Dictionary of the Maya, the numerals above 40 are given according to Beltran"s system; and that this was not the work of the editors of that volume (which was published after his death), is shown by an autographic ma.n.u.script of his dictionary in my possession, written about 1846,[44-1] in which also the numerals appear in Beltran"s form.
Three other ma.n.u.script dictionaries in my collection, all composed previous to 1690, affirm the system of Beltran, and I am therefore obliged to believe that it was authentic and current among the natives long before white scholars began to dress up their language in the ill-fitting garments of Aryan grammar.
Proceeding to higher numbers, it is interesting to note that they also proceed on the vigesimal system, although this has not heretofore been distinctly shown. The ancient computation was:
20 units = one _kal_ = 20 20 kal = one _bak_ = 400 20 bak = one _pic_ = 8,000 20 pic = one _calab_ = 160,000 20 calab = one _kinchil_ or _tzotzceh_ = 3,200,000 20 kinchil = one _alau_ = 64,000,000