The
subject of the Mesoamerican calendars is one of the most important in the
field of the Precolumbian cultures. It translates the ancient Americans'
way of conceiving time, in relation to space, the deities, the course of
the planets and stars, the states of matter, the colors, and the other
symbols and associated elements that constitute the universe, and give
shape to cosmogony, in the native vision. Time is a "measure" (which always
presupposes a space), a module and a proportion linking the different parts
if the cosmos, and thus is an element of union among them. But above all,
it is the law, which, in its indefectible observance, makes all of this
possible. For we notice that its presencemanifested by movementobeys
the standards and periodic rhythms that bind together beings, phenomena,
and things, establishing parameters, analogies, and prototypes that lead
immediately to the idea of one single universal model, whose manifestation
is the totality of the possible, and its most evident expression universal
life, along with nature as a symbol thereof.^{1}
Time, then, is always present time. It is not something
generated in the beginning and subsisting as an abstract component of psychophysical
reality. Rather, it expresses that very reality now. It is one of the conditions
of realitythat is, an everpresent element without which life would be
impossible. Its quality, then, is that of a constitutive part of the cosmos,
and its manner of manifestationwhich can be measured quantitatively in
spacethe way in which time expresses itself, and therefore a key to an
understanding of its essence, is a valid module for creation as a whole.
In this perspective, the revolutions of the planets and stars in the firmament
will obviously be of particular importance. Being stable, in comparison
with the rapidity of the movement of the earth, they will of course serve
as guides, and points of reference, for the establishment of the general
standards of the wholethe harmony of what Pythagoras called the "music
of the spheres"which is achieved by the interaction of all individual
motions, including that of the earth, and involves what is produced on
the earth, beginning with the human being.^{2}
The latter, in the Precolumbian cultures, did not live in isolation, as
if divorced from the cosmogony, as we have said. After all, for traditional
cultures, all life is one, despite its multiple manifestations of various
orders. In that flux, in that navigation, whose protagonist is the human
being, objects change their form, and phenomena constantly succeed one
another, as do the moods of the gods, especially those linked with atmospheric
phenomena and with the earth, which are speedier and more changeable in
comparison with the nearimpassibility of the loftiest deities, who are
much slower, and far more ancient, and ply the sky with such imposing majesty.
If all of this occurs in time, and if time constitutes
a part of life, then this will all be expressed in the human person, whose
being is not without time. That is, the standards that fix the stars and
planets in the firmament are equivalent to those of the earth and human
beings. Nor are the periods and cycles that characterize these latter by
any means arbitrary. They correspond to a universal plan, which each part
reflects in its own fashion, with the sum total being the archetypal wholethe
model which repeats itself without variation and is expressed by "measures,"
symbolic modules, and numbers in their limitless mutual interrelationships,
creating this astounding universe. It is of this world of analogies, which
shape the cosmos, time, and life, that the Mesoamerican calendars treat,
be the chiseled in stone or the painted in codices, be they those of the
great eras (likewise registered in myth, rite, and symbol), or the lunar
and solar calendarsor the extremely complex tonalámatl (or
the Mayan tzolkin), a veritable synthesis of relationships, a full
expression of the cosmovision of the Mesoamericans, and their knowledge
of the universal laws.^{3}
The Aztec calendar

The "solar," civil calendar, called xihuitl by the
Aztecs and haab by the Mayas, consists of eighteen months of twenty
days, for a total of 360 days, to which, periodically, were joined five
additional days, considered ominous and left unmentioned, and called, in
Nahuatl, nemontemi.^{4}
Three hundred sixty is the number of the circumference and cycle (360 =
3 + 6 + 0 = 9), andin terms of what we have seen of the qualities of the
various numbersconnects heaven with earth, or the circle with the square
(9 x 4 = 36), in a module of quaternary division characterized by a regression
to its initial point, at which the new year begins.^{5}
This cycle is traversed in accordance with the angular velocity of the
starone day for each degree of the circumference. It was used for organizing
civil life and religious festivals. The Mayan computation is even more
perfect than the Gregorian. In the latter, the year lasts 365.2425 days,
while in the Mayan the figure is 365.242308, and in the tropical year lasts
an average of 365.242199 mean days.^{6}
The names of the twenty days in the Aztec calendar are
the following, and each is identified with a symbol, sign, or glyph:^{7}
The twenty days of the Aztec calendar

1. cipactli ("crocodile")
2. ehécatl ("wind")
3. calli ("house")
4. cuetzpalin ("lizard")
5. cóatl ("serpent")
6. miquiztli ("death")
7. mazatl ("deer," "stag")
8. tochtli ("rabbit")
9. atl ("water")
10. itzcuintli ("dog")
11. ozomatli ("monkey")
12. malinalli ("grass")
13. acátl ("cane")
14. ocelotl ("jaguar")
15. quauhtli ("eagle")
16. cozcaquauhtli ("carrion crow")
17. ollin ("motion")
18. tecpatl ("flint")
19. quiahuitl ("rain")
20. xóchitl ("flower")

These twenty days are divided into four groups of five days
(and correlated with the four directions in space: south, east, north,
and west), which rotate in reverse (from right to left), beginning invariably
with 1 cipactli.
Codex Vaticano B

The eighteen months are called: 1 Acahualco, 2 Tlacaxipehualiztli,
3 Tozoztontli, 4 Hueytozoztli, 5 Toxcatl, 6 Etzacualiztli, 7 Tecuilhuitontli,
8 Hueytecuilhuitontli, 9 Tlaxochimaco, 10 Xocohuetzi, 11 Ochpaniztli, 12
Teoteclo, 13 Tepeilhuitl, 14 Quecholli, 15 Panquetzaliztli, 16 Atemoztli,
17 Tititl, 18 Itzcalli. The exact translation of some of these names
is uncertain. For our purposes, we must take special account of the signs
of the twenty days, as they are identical with those of the tonalámatl,
the backbone of the high Precolumbian civilizations, a genuine divining
calendarin the etymological sense of the word. First, however, let us
note that these twenty days of the solar calendar meshed with the eighteen
months in rotating fashion. Nevertheless, this calendar is not strictly
solar. It does not follow the apparent movement of the sun, which proceeds
from north to south. Its course is retrograde (counterclockwise), as we
have already indicated, so that it moves from noon to dawn, from this to
midnight, and from it to the west, to return to the south. (The same occurs
with the seasons of the solar year: summer, spring, winter, autumn.) This
contradicts, or, better, is the reverse of, the apparent modalities of
the movement of the sun. We believe that it refers to a module related
to the great eras, since the equinoctial precession maintains this same
retrograde movement. Thus, this calendar, like the tonalámatl,
is symbolical. Nor is it strictly chronological in a scientific fashion,
as modern science, and our conditioning, might claim it to be. True, it
is this as well, but basically it is a numericalmagical calendar. This
is why it has a social and civil function, and why it marks religious commemorations
and ritual feasts: it is a system that finds its most finished expression
in the tonalámatl (or Mayan tzolkin), which we have
cited above.
The Tonalámatl
On the other hand, this tonalámatl had been
adjusted to the cycles of Venus and the Sun, as we shall presently see.
Of course, it was also adjusted to the other planets and stars, as is obvious
in the case of the Pleiades, the Pole Star, and the Milky Way (called Cloud
Serpent, or Saint James' Road). But its principal relationship was with
the precession of the equinoxes, which is the third motion of the earth
(the first, as we know, being the daily, or rotational, while the second
is the annual, or that of revolution), like the wobbling of a topa retrograde
movement (as well as one of revolution) inverse to the daily revolutions
of the planets, such that the signs of the zodiac appear to have shifted
backwards an arc of thirty degrees every 2,160 years, and to complete this
entire cycle in 25,920. After all, in our current astronomy, heir to the
conceptions of the Chaldeans and the Persians, the sky is divided into
twelve zodiacal signs.^{8}
There can be no doubt that the Mesoamericans were familiar with this grand
cycle, and that they would not have neglected to make observations and
calculations in accordance with the knowledge they had of the other celestial
bodies and their revolutions. Again, all traditional astronomies have known
it, and have regarded it as one of the supreme cycles: the great year of
the earth. We think it to be the inner key of the tonalámatl.
It has been calculated at 26,000 years (in "round numbers") as well as
by other peoples who have adopted it as the basis of their astronomical
speculationsor, to put it another way, who have made use of it in order
to understand the cosmic rhythms and laws reflected in these numbers and
this cycle. The "great year," however, has customarily been conceptualized
as consisting of onehalf of this cycle: 13,000 years. This is the case
with the Persians and the Greeks.
The tonalámatl, or ritual calendar, combines
the twenty signs or symbols of the days with the first thirteen numbers.
The signs of the days begin with cipactli, crocodile, and to each
of the following days corresponds one of the signs, in the order that we
have indicated, until xóchitl, flower, is reached. On the
following (twentyfirst) day, it falls to the sign of the cipactli
to head the list once more, the complete cycle now being repeated in identical
fashion, indefinitely. In turn, to the first glyph, or sign of the day,
there corresponds the number one, and the subsequent numbers are accompanied
by the signs of the corresponding days (1 crocodile; 2 wind; 3 house, and
so on), up to the number thirteen. Day fourteen will bear the sign of the
fourteenth day (ocelotl), but the number one will return at this
point, as the first thirteen numbers are the only ones that come into play
(1 ocelotl; 2 quauhtli; 3 cozcaquauhtli, and so forth).
Thus, the numbers recommence every thirteen days, and the signs every twenty.
Owing to the combination of numbers and signs (thirteen being a "prime
number"), no number occurs twice with the same sign before the lapse of
the complete cycle of 260 days (13 x 20 = 260). The 261st day will once
more bear the character, ce cipactli (one crocodile), and the wheel
of the tonalámatl starts all over again, repeating the same
number with the same sign every 260 days, identically and indefinitely.^{9}
According to Alfonso Caso, this tonalámatl
in turn strikes a relationship with the 365day calendar, and it is precisely
this numerical combination that determines the "fastening," or fiftytwoyear
periodwhich corresponds as well to the cycle of the Pleiadesat the end
of which the festival of the New Fire, or toxiuh molpilia, is always
celebrated. This cycle of fiftytwo years, called the xiuhmolpilli,
consists of 18,980 days (365 x 52 = 18,980), which is also the least common
multiple of 365 and 260. Every fiftytwo years, then, the wheel of the
solar calendar will have rotated fiftytwo times, while that of the tonalámatl
will have executed seventythree revolutions (18,980 = 73 x 260), both
calendars being found at the same point after this span of time. This will
not occur again until after the lapse of the 18,980 days of the xiuhmolpilli,
a period that the ancient Mexicans subdivided into four parts of thirteen
years each, called a tlalpilli. The concurrence acquires its whole
significance when we know, as has been shown, that the culmination of the
Pleiades by the zenith at midnight, a phenomenon occurring every fiftytwo
years, was known.
Furthermore, these civilizations took account, in their
calculations, of the cycles of the synodical, or apparent, revolution of
Venus, which takes (in "round numbers") 584 days. Thus, they observed that,
every eight solar years (2,920 days: 365 x 8 = 2,920), five cycles of Venus
elapsed (584 x 5 = 2,920); and that, as fiftytwo is not a perfect multiple
of eight, while its double (104) is, it happens that, every 104 years,
a major cycle is completeddetermined by the fact that, on the first day
of that cycle, all three cycles (of the tonalámatl, the Sun,
and Venus) are at their starting points, a circumstance that will recur
only after 104 years or 37,960 days, since this last number (37,960) is
the least common multiple of 260, 365, and 584. This double "fastening
of years," or major cycle, was regarded as a fundamental unit of time,
called a huehuetiliztli, or an "old age," in which Venus completes
sixtyfive synodical revolutions (37,960 = 584 x 65).
On the other handto continue, now, with the "concurrences"
and relationships (or points of conjuncture in the spatiotemporal, "magic"
among the proportions expressed by numbers)we observe that 260 x 18 is
equal to 360 x 13, which connects the tonalámatl with the
perimeter of the circumference and its division into degrees. After all,
every eighteen^{10}
periods of the tonalámatl correspond to thirteen of the xihuitlwithout,
in this case, adding, to the civil calendar of 360 days (in order to facilitate
certain calculations), the nemontemi, the five days needed in order
to strike a coincidence with the solar year. The nemontemi total,
in round numbers, sixtyfive days in thirteen years, which is equivalent
to 260 daysthe duration of a complete tonalámatlin fiftytwo
years, or 130,000 days (500 complete tonalámatles) in 26,000
years. This last is the supreme cyclical period (the Great Year of the
Earth, or two Great Years of 13,000 years), that of the equinoctial precession.
(In this same cycle, let us recall, the Pleiades have also completed 500
times their culmination.) We reach this figure without computing the thirteen
leapyear days, which correspond to the correction of the tropical year
throughout each "fastening of the years," and which, in the period of the
equinoctial precession, would amount to 6,500 (13 x 500) days.^{11}
We think that leapyear days were computed only for certain calculations,
and not for others. At the same time, there appear to have been differences
here between the Aztecs and the Mayassince they made different correctionsas
well as in the case of the nemontemi, and the way in which those
ominous days were added and computed.
Multiplying by five is the same as dividing by two, if
the zeros that are added or subtracted in these operations be discounted
and looked upon as merely secondary elements when it comes to the central
numerical symbolism and the properties of the numbers under consideration.
This particularity of the numbers two and five, as indicated above, can
be observed, for example, in the relationship between the fiftytwoyear
cycle and its double, 104 (an "old age"): 52 x 5 = 260; 52 : 2 = 26; 104
x 5 = 520; 104 2 = 52. The result is that the two cycles can be taken as
analogous and equivalent, just as happens in the case of the symbols of
the circumference (360^{o}) and the semicircumference (180^{o}).
Let us indicate another example, namely for the case of
the number thirteen and its double, twentysix (13 x 5 = 65; 13 : 2 = 6.5;
26 x 5 = 130; 26 : 2 = 13). This example acquires a particular importance
in view of the fact that 26,000 years (half of which is 13,000) is the
period of the equinoctial precession, and that, for the Hindu tradition,
a manvantara lasts 65,000 years.^{12}
It is scarcely necessary to add that the Precolumbian traditions worked
with proportional numbers, where terminal zeros in no way alter the numerical
root, the key of all computations.
It is evident that the number five is the core and basis
of all of these calculations flowing from it, and is also the module that
will intervene in the constitution of the vigesimal (and decimal) system
and in the Precolumbian cosmogony. Here let us indicate that the numerical
structure of the divining calendar, or the various elements that act upon
it in various numbers or proportions, are the following. In the first place,
we have the signs of the twenty days. Second, we have the number corresponding
to each of these signs or daysand we have seen that, upon arriving at
thirteen, the numbers recommence from one, although the signs (or days)
number twenty. Third, besides the determination with which they are characterized
by their respective numbers, each of the twenty signs of the days has a
ruling numen, a governor or sovereign. Again, the number nine comes into
play, since there are nine "companions" of the night (perfectly identified,
and painted in the codices) who escort the signs as wellas do the deities
just citedalthough their cycle recommences every nine days. The tonalámatl
is divided into four groups of five thirteens each, yielding a total of
twenty series of thirteen. Each of these series begins with one of the
successive signs, and is presided over by the deity corresponding to it.
To this division into groups of thirteen there also corresponds an orientation
in terms of the four directions of the universe, or quadrants of space,
which is also applied to the twenty signs of the days. Certain birds are
matched with the days, as welland with their respective numina or rulersconstituting
elements surely as meaningful as they are mysterious.
As will be seen, these calendars are the kind of thing
whose structure is so complex in itself that it is impossible to simplify
it, by virtue of the interrelations it promotes. The science of astronomy
is that of the "measurement" of the heavenly bodies (which, in antiquity,
always constituted one and the same discipline with astrology). Accordingly,
it deals with the laws of the heavens and their correspondences, which
express themselves in an unlimited mode, but in a constant procession or
order: on modular structures, it articulates ever changing, mutually related
and coinciding, rhythms that are contained within one another. We shall
make no attempt, in this brief space, to handle this topic exhaustively,
although we have sought to offer an example of a calendrical schema structured
in conformity with numerical guidelines, analogicosymbolical correspondences,
and astronomical (and astrological) concepts that we find packaged in these
constructions as an expression of the cosmogonic and magicotheurgical
thought of the Mesoamericans.
At all events, may we be permitted to insist, by way of
conclusion, on the fact that the rotary play of the symbolsglyphs, numbers,
colors, directions, and so forthas well as of the deities, configure a
situation, a framework, a single reality that exists for every day, every
being, and every spatiotemporal event, signing (and conditioning) it with
the specific nahual that stamps its destiny and its identity. Persons
and historical events alike, and even mythical personages, bear the name
of a day, each one's calendrical position being the determining seal of
its proper being and the mark of the type of energies that constitute that
person or event. This denomination, and the characteristics deriving from
the conjunction or interaction of these astronomical cycles with other
constant, precise, although movable and alternating, spatiotemporal rhythms,
configure the Mesoamerican rotary calendrical system, in which beings,
things, and phenomena find their metaphysical identity in their perpetual
cyclical return. In other words, they attain their Destiny.^{13} 