This ancient system was obscured by the Spaniards using the word _pic_ to mean 1000 and _kinchil_ to mean 1,000,000, instead of their original significations.
The meaning of _kal_, I have already explained to be a fastening together, a package, a bundle. _Bak_, as a verb, is to tie around and around with a network of cords; _pic_ is the old word for the short petticoat worn by the women, which was occasionally used as a sac. If we remember that grains of corn or of cacao were what were generally employed as counters, then we may suppose these were measures of quant.i.ty. The word _kal_ (_qal_), in Kiche means a score and also specifically 20 grains of cacao; _bak_ in Cakchiquel means a corn-cob, and as a verb to sh.e.l.l an ear of corn, but I am not clear of any connection between this and the numeral. Other meanings of _bak_ in Maya are "meat" and the _partes pudendas_ of either s.e.x.
_Calab_, seems to be an instrumental form from _cal_, to stuff, to fill full.[45-1] The word _calam_ is used in the sense of excessive, overmuch. In Cakchiquel the phrase _mani hu cala_, not (merely) one _cala_, is synonymous with _mani hu chuvi_, not (merely) one bag or sack, both meaning a countless number.[46-1] In that dialect the specific meaning of _cala_ is 20 loads of cacao beans.[46-2]
The term _tzotzceh_ means deerskin, but for _kinchil_ and _alau_, I have found no satisfactory derivation that does not strain the forms of the word too much. I would, however, suggest one possible connection of meaning.
In _kinchil_, we have the word _kin_, day; in _alau_, the word _u_ month, and in the term for mathematical infinity, _hunhablat_, we find _hun haab_, one year, just as in the related expression, _hunhablazic_, which signifies that which lasts a whole year. If this suggestion is well grounded, then in these highest expressions of quant.i.ty (and I am inclined to think that originally _hun hablat_, one _hablat_=20 _alau_) we have applications of the three time periods, the day, the month, and the year, with the figurative sense that the increase of one over the other was as the relative lengths of these different periods.
I think it worth while to go into these etymologies, as they may throw some light on the graphic representation of the numerals in the Maya hieroglyphics. It is quite likely that the figures chosen to represent the different higher units would resemble the objects which their names literally signify. The first nineteen numerals were written by a combination of dots and lines, examples of which we find in abundance in the Codex Troano and other ma.n.u.scripts. The following explanation of it is from the pen of a native writer in the last century:--
[Ill.u.s.tration]
"Yantac thun yetel paiche tu pachob, he hunppel thune hunppel bin haabe, uaix cappele cappel bin haabe, uaix oxppel thuun, ua canppel thuune, canppel binbe, uaix oxppel thuun baixan; he paichee yan yokol xane, ua hunppel paichee, hoppel haab bin; ua cappel paichee lahunppiz bin; uaix hunppel paichee yan yokol xane, ua yan hunppel thuune uacppel bin be; uaix cappel thuune yan yokol paichee uucppel bin be; ua oxppel thuun yan yokole, uaxppel binbe; uaixcanppel thun yan yokole paichee (bolonppel binbe); yanix thun yokol (cappel) paichee buluc piz; uaix cappel thune lahcapiz; ua oxppel thuun, oxlahunpiz."
"They (our ancestors) used (for numerals in their calendars) dots and lines back of them; one dot for one year, two dots for two years, three dots for three, four dots for four, and so on; in addition to these they used a line; one line meant five years, two lines ten years; if one line and above it one dot, six years; if two dots above the line, seven years; if three dots above, eight; if four dots above the line, nine; a dot above two lines, eleven; if two dots, twelve; if three dots, thirteen."[48-1]
The plan of using the numerals in Maya differs somewhat from that in English.
In the first place, they are rarely named without the addition of a _numeral particle_, which is suffixed. These particles indicate the character or cla.s.s of the objects which are, or are about to be, enumerated. When they are uttered, the hearer at once knows what kind of objects are to be spoken of. Many of them can be traced to a meaning which has a definite application to a cla.s.s, and they have a.n.a.logues in European tongues. Thus I may say "seven head of"--and the hearer knows that I am going to speak of cattle, or sheep, or cabbages, or similar objects usually counted by heads. So in Maya _ac_ means a turtle or a turtle sh.e.l.l; hence it is used as a particle in counting canoes, houses, stools, vases, pits, caves, altars, and troughs, and some general appropriateness can be seen; but when it is applied also to cornfields, the a.n.a.logy seems remote.
Of these numeral particles, not less than _seventy-six_ are given by Beltran, in his Grammar, and he does not exhaust the list. Of these _piz_ and _pel_, both of which mean, single, singly, are used in counting years, and will frequently recur in the annals I present in this volume.
By their aid another method of numeration was in vogue for counting time. For "eighty-one years," they did not say _hutuyokal haab_, but _can kal haab catac hunpel haab_, literally, "four score years and one year." The copulative _catac_ is also used in adding a smaller number to a _bak_, or 400, as for 450, _hun bak catac lahuyoxkal_, "one _bak_ and ten toward the third score." _Catac_ is a compound of _ca tac_, _ca_ meaning "then" or "and," and _tac_, which Dr. Berendt considered to be an irregular future of _talel_, to come, "then will come fifty," but which may be the imperative of _tac_ (_tacah_, _tace_, third conjugation), which means to put something under another, as in the phrase _tac ex che yalan c.u.m_, put you wood under the pot.
It will be seen that the latter method is by addition, the former by subtraction. Another variety of the latter is found in the annals. For instance, "ninety-nine years" is not expressed by _bolonlahutuyokal haab_, nor yet by _cankal haab catac bolonlahunpel haab_, but by _hunpel haab minan ti hokal haab_, "one single year lacking from five score years."
-- 7. _The Calendar._
The system of computing time adopted by the Mayas is a subject too extensive to be treated here in detail, but it is indispensable, for the proper understanding of their annals, that the outlines of their chronological scheme be explained.
The year, _haab_, was intended to begin on the day of the transit of the sun by the zenith, and was counted from July 16th. It was divided into eighteen months, _u_ (_u_, month, moon), of twenty days, _kin_ (sun, day, time), each. The days were divided into groups of five, as follows:--
1. _Kan._ 6. _Muluc._ 11. _Ix._ 16. _Cauac._ 2. Chicchan. 7. Oc. 12. Men. 17. Ahau.
3. Cimi. 8. Chuen. 13. Cib. 18. Imix.
4. Manik. 9. Eb. 14. Caban. 19. Ik.
5. Lamat. 10. Ben. 15. E?nab. 20. Akbal.
The months, in their order, were:--
1. Pop.
2. Uo.
3. Zip.
4. Zo?.
5. Zeec.
6. Xul.
7. ?e-yaxkin.
8. Mol.
9. Chen.
10. Yaax.
11. Zac.
12. Ceh.
13. Mac.
14. Kankin.
15. Moan.
16. Pax.
17. Kayab.
18. c.u.mku.
As the Maya year was of 365 days, and as 18 months of 20 days each counted only 360 days, there were five days intervening between the last of the month c.u.mku and the first day of the following year. These were called "days without names," _xma kaba kin_ (_xma_, without, _kaba_, names, _kin_, days), an expression not quite correct, as they were named in regular order, only they were not counted in any month.
It will be seen, by glancing at the list of days, that this arrangement brought at the beginning of each year, the days Kan, Muluc, Ix and Cauac in turn, and that no other days could begin the year. These days were therefore called _cuch haab_, "the bearers of the years" (_cuch_, to bear, carry, _haab_, year), and years were distinguished as "a year Kan," "a year Muluc," etc., as they began with one or another of these "year bearers."
But the calendar was not so simple as this. The days were not counted from one to twenty, and then beginning at one again, and so on, but by periods of 13 days each. Thus, in the first month, beginning with 1 Kan, the 14th day of that month begins a new "week," as it has been called, and is named 1 Caban. Twenty-eight of these weeks make 364 days, thus leaving one day to complete the year. When the number of these odd days amounted to 13, in other words when thirteen years had elapsed, this formed a period which was called "the _katun_ of days," _kin katun_, and by Spanish writers an "indiction."
It will be readily observed by an inspection of the following table, that four of these indictions, in other words 52 years, will elapse before a "year bearer" of the same name and number recommences a year.
___________________________________________________________ _1st year.__14th year.__27th year.__40th year_[TN-5]
----------------------------------------------------------- 1KanMulucIxCauac 2MulucIxCauacKan 3IxCauacKanMuluc 4CauacKanMulucIx 5KanMulucIxCauac 6MulucIxCauacKan 7IxCauacKanMuluc 8CauacKanMulucIx 9KanMulucIxCauac 10MulucIxCauacKan 11IxCauacKanMuluc 12CauacKanMulucIx 13KanMulucIxCauac.
A cycle of 52 years was thus obtained in a manner almost identical with that of the Aztecs, Tarascos and other nations.
But the Mayas took an important step in advance of all their contemporaries in arranging a much longer cycle.
This long cycle was an application of the vigesimal system to their reckoning of time. Twenty days were a month, _u_ or _uinal_; twenty years was a cycle, _katun_. To ask one"s age the question was put _haypel u katunil_? How many katuns have you? And the answer was, _hunpel katun_, one katun (twenty years), or, _hopel in katunil_, I am five katuns, or a hundred years old, as the case might be.
The division of the katuns was on the principle of the Beltran system of numeration (see page 40), as,
_xel u ca katun_, thirty years.
_xel u yox katun_, fifty years.
Literally these expressions are, "dividing the second katun," "dividing the third katun," _xel_ meaning to cut in pieces, to divide as with a knife. They may be compared to the German _dritthalb_, two and a half, or "the third a half."[54-1]
The Katun of 20 years was divided into five lesser divisions of 4 years each, called _tzuc_, a word with a signification something like the English "bunch," and which came to be used as a numeral particle in counting parts, divisions, paragraphs, reasons, groups of towns, etc.[54-2]
These _tzuc_ were called by the Spaniards _l.u.s.tros_, from the Latin _l.u.s.trum_, although that was a period _five_ years. Cogolludo says: "They counted their eras and ages, which they entered in their books, by periods of 20 years each, and by _l.u.s.tros_ of four years each. The first year they placed in the East [that is, on the Katun-wheel, and in the figures in their books], calling it _cuch haab_; the second in the West, called _Hijx_; the third in the South, _Cavac_; and the fourth, Muluc, in the North, and this served them for the Dominical letter. When five of the _l.u.s.tros_ had pa.s.sed, that is 20 years, they called it a _Katun_, and they placed one carved stone upon another, cemented with lime and sand, in the walls of their temples, or in the houses of their priests."[55-1]
The historian is wrong in saying that the first year was called _cuchhaab_; that was the name applied to all the Dominical days, and as I have said, means "year bearer." The first year was called _Kan_, from the first day of its first month.
This is but one of many ill.u.s.trations of how cautious we must be in accepting any statement of the early Spanish writers about the usages of the natives.
There is, however, some obscurity about the length of the _Katun_. All the older Spanish writers, without exception, and most of the native ma.n.u.scripts, speak of it distinctly as a period of twenty years. Yet there are three ma.n.u.scripts of high authority in the Maya which state that it embraced twenty-four years, although the last four were not reckoned. This theory was adopted and warmly advocated by Pio Perez, in his essay on the ancient chronology of Yucatan, and is also borne out by calculations which have been made on the hieroglyphic Codex Troano, by M. Delaporte, in France, and Professor Cyrus Thomas, in the United States.[56-1]
This discrepancy may arise from the custom of counting the katuns by two different systems, ground for which supposition is furnished by various ma.n.u.scripts; but for purposes of chronology and ordinary life, it will be evident that the writers of the annals in the present volume adopted the Katun of twenty years" length; while on the other hand the native Pech, in his History of the Conquest, which is the last piece in the volume, gives for the beginning and the end of the Katun the years 1517-1541, and therefore must have had in mind one of twenty-four years"
duration. The solution of these contradictions is not yet at hand.