The Maya Chronicles | Page 8

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
button 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
analyzed 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 pronounced it artificial, not in accordance with either
the past or present use of the natives themselves, and built up out of an
effort to assimilate 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 à otra veintena los numeros fraccionarios ò las diez
y nueve unidades, terminadas por la particula tul ò su sincopa tu,[42-2]
se juntan antepuestas à 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, formó un sistema distinto à este desde la 2ª veintena
hasta la ultima, pues para espresar las unidades entre este y la 3ª

veintena pone à esta terminandolas y por consiguiente rebajandole su
valor por solo su anteposicion à dichas unidades fraccionarias, y asi
para espresar el