Keith Hunt - Technical Study in Maya Calendars Restitution of All

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Technical Study in the Maya Calendars

Here's the nitty-gritty of it all!

From the block-buster book "1491" by Charles C. Mann (2005) 


     Writing begins with counting. When a culture grows big
enough, it acquires an elite, which needs to monitor things it
considers important: money, stored goods, births and deaths, the
progression of time. In the Fertile Crescent, village accountants
began keeping records with clay tokens around 8000 B.C. As the
need for precision grew, they scratched marks on the tokens as
mnemonic devices. For example, they might have distinguished a
count of sheep from one of wheat by drawing a sheep on one and a
wheat stalk on the other. Gradually the information on each
record increased. The bureaucrats were not intending to create
writing. Instead they were simply adding useful features as they
became necessary. By 3200 B.C. Sumerian scribes had progressed to
inscribing on clay tablets with sharpened reeds. A tablet might
contain, say, two hash marks, a box, a circle with a cross in the
middle, an asterisk-like shape, and an arrangement of three
triangles. Scribes would know that the hash marks meant "two,"
the box was a "temple," the circle stood for "cattle," an
asterisk meant "goddess," and the triangles were "Inanna"-two
cattle owned by the goddess Inanna's temple. (Here I am lifting
an example from Gary Urton, a Harvard anthropologist.) They had
no way to indicate verbs or adjectives, no way to distinguish
subject from object, and only a limited vocabulary. Nonetheless,
Sumerians were moving toward something like writing.

     In Mesoamerica, timekeeping provided the stimulus that
accounting gave to the Middle East. Like contemporary
astrologers, the Olmec, Maya, and Zapotec believed that celestial
phenomena like the phases of the moon and Venus affect daily
life. To measure and predict these portents requires careful sky
watching and a calendar. Strikingly, Mesoamerican societies
developed three calendars: a 365-day secular calendar like the
contemporary calendar; a 260-day sacred calendar that was like no
other calendar on earth; and the equally unique Long Count, a
one-by-one tally of the days since a fixed starting point
thousands of years ago. Establishing these three calendars
required advances in astronomy; synchronizing them required
ventures into mathematics.
     The 260-day ritual calendar may have been linked to the
orbit of Venus; the 365-day calendar, of course, tracked the
earth's orbit around the sun. Dates were typically given in both
notations. For example, October I2, 2004, is 2 Lamat II Yax,
where 2 Lamat is the date in the ritual calendar and II Yax the
date in the secular calendar. Because the two calendars do not
have the same number of days, they are not synchronized; the next
time 2 Lamat occurs in the sacred calendar, it will be paired
with a different day in the secular calendar. After October 12,
2004, in fact, 2 Lamat and II Yax will not coincide again for
another 18,980 days, about fifty-two years.
     Mesoamerican cultures understood all this, and realized that
by citing dates with both calendars they were able to identify
every day in this fifty-two-year period uniquely. What they
couldn't do was distin guish one fifty-two-year period from
another. It was as if the Christian calendar referred to the year
only as, say, '04-one would then be unable to distinguish between
1904, 2004, and 2104. To prevent confusion, Mesoamerican
societies created the third calendar, the Long Count. The Long
Count tracks time from a starting point, much as the Christian
calendar begins with the purported birth date of Christ. The
starting point is generally calculated to have been August II,
3114, B.C., though some archaeologists put the proper date at
August 10 or 13, or even September 6. Either way, Long Count
dates consisted of the number of days, 20-day "months," 360-day
"years," 7,200-day "decades," and 144,000-day "millennia" since
the starting point. Archaeologists generally render these as a
series of five numbers separated by dots, in the manner of
Internet Protocol addresses. Using the August 1i starting date,
October 12, 2011, would be written in the Long Count as (For a more complete explanation, see Appendix D.)
Because it runs directly from I B.C. to I A.D., the Christian
calendar was long a headache for astronomers. Scientists tracking
supernovae, cometary orbits, and other celestial phenomena would
still have to add or subtract a year manually when they crossed
the A.D. - B.C. barrier if a sixteenth-century astronomer named
Joseph Scaliger hadn't got sick of the whole business and devised
a calendar for astronomers that doesn't skip a year. The Julian
calendar, which Scaliger named after his father, counts the days
since Day o. Scaliger chose Day 0 as January 1, 4713, B.C.; Day 1
was January 2. In this system, October 12, 2011, is Julian Day
     The Long Count calendar began with the date*
Mathematically, what is most striking about this date is that the
zeroes are true zeroes. Zero has two functions. It is a number,
manipulated like other numbers, which means that it is
differentiated from nothing. And it is a placeholder in a
positional notation system, such as our

*Actually, it didn't. Inexplicably, the biggest unit, the
144,000-day "millennium," began with 13, rather than o. The first
day in the calendar was thus When I remarked on the
peculiarity of this exception to a mathematician, he pointed out
societies whose timekeeping systems are so irregular that
children have to learn rhymes to remember the number of days in
the months ("Thirty days hath September . . .") are in no
position to scoff at the calendrical eccentricities of other
cultures. At least all the "months" in the Mesoamerican calendar
had the same number of days, he said.

base-10 system, in which a number like i can signify a single
unit if it is in the digits column or ten units if it is in the
adjacent column.
     That zero is not the same as nothing is a concept that
baffled Europeans as late as the Renaissance. How can you
calculate with nothing? they asked. Fearing that Hindu-Arabic
numerals-the 0 through 9 used today-would promote confusion and
fraud, some European authorities banned them until the fourteenth
century. A classic demonstration of zero's status as a number,
according to science historian Dick Teresi, is grade point

     In a four-point system, an A equals 4, B equals 3, and so
     on, down to E, which equals 0. If a student takes four
     courses and gets As in two but fails the other two, he
     receives a GPA of 2.0, or a C average. The two zeroes drag
     down the two A's. If zero were nothing, the student could
     claim that the grades for the courses he failed did not
     exist, and demand a 4.0 average. His dean would laugh at
     such logic.

     Without a positional notation system, arithmetic is tedious
and hard, as schoolchildren learn when teachers force them to
multiply or subtract with Roman numerals. In Roman numerals, CLIV
is 154, whereas XLII is 42. Maddeningly, both numbers have L (50)
as the second symbol, but the two L's aren't equivalent, because
the second is modified by the preceding X, which subtracts ten
from it to make forty. Even though both CLIV and XLII are
four-digit numbers, the left-hand symbol in the first number (C)
cannot be directly compared with the left-hand symbol in the
second (X). Positional notation symbols take the aggravation out
of arithmetic.
     Stirling's stela in Tres Zapotes bore a Long Count date of The implication is that by 32 B.C. the Olmec
already had all three calendars and zero to boot. One can't be
sure, because the date does not include a zero or a reference to
the other calendars. But it is hard to imagine how one could have
a Long Count without them. Tentatively, therefore, archaeologists
assign the invention of zero to sometime before 32 B.C.,
centuries ahead of its invention in India.
     How long before 32 B.C.? The carved cadaver in San Jose
Mogote may give a hint. In Mesoamerican cultures, the date of
one's birth was such an important augury of the future that
people often acquired

Discovered in 1975, this prone, disemboweled man was carved onto
the stone threshold of a temple in San Jose Mogote, near the city
of Oaxaca. Between the corpse's feet is the oldest certainly
dated writing in the Americas: two glyphs (shaded in drawing)
that probably represent his name, l-Earthquake. The ornate scroll
issuing from his side is blood. According to Joyce Marcus, the
first archaeologist to examine this hasrelief, the Zapotec words
for "flower" and "sacrificial object" are similar enough that the
flowery blood may be a visual pun.

that day as their name. It was as if coming into the world on New
Year's Day were such a sign of good fortune that children born on
that day would be named "January 1." This seems to have been the
case for the man whose death was celebrated in the San Jose
Mogote temple. Between his feet are two glyphs, one resembling a
stovepipe hat with a U painted across the front, the other
looking vaguely like a smiling pet monster from a Japanese
cartoon. According to Marcus, the Michigan anthropologist, the
glyphs correspond to I-Earthquake, the Zapotec name for the
seventeenth day of the 260-day sacred calendar. Because the
carving depicts a man instead of an event, the date is generally
thought to be the dead man's name. If so, 1-Earthquake is the
first named person in the history of the Americas. Even if the
date is not a name, the two glyphs indicate that by 750 B.C.,
when the slab was carved, the Zapotec were not only on the way to
some form of writing, but had also assembled some of the
astronomical and mathematical knowledge necessary for a calendar.

     To judge by the archaeological record, this development took
place in an astonishingly compressed period; what took the
Sumerians six thousand years apparently occurred in Mesoamerica
in fewer than a thousand. Indeed, Mesoamerican societies during
that time created more than a dozen systems of writing, some of
which are known only from a single brief text. The exact
chronology of their evolution remains unknown, but could be
resolved by the next object that a farmer discovers in a field.
The earliest known Olmec writing, for example, is on a potsherd
from Chiapas that dates from about 300 B.C. For a long time
nobody could read it. In 1986 a workcrew building a dock on the
Acula River in Veracruz pulled out a seven-foot stela covered
with Olmec symbols. Thought to have been written in 159 A.D., the
twenty-one columns of glyphs were the first Olmec text long
enough to permit linguists to decipher the language. Two
linguists did just that in 1993. The stela recounted the rise of
a warrior-king named Harvest Mountain Lord who celebrated his
ascension to the throne by decapitating his main rival during the
coronation. This information in hand, the linguists went back to
the writing on the potsherd. Disappointingly, it turned out to be
some banal utterances about dying and cutting cloth.


Calendar Math

     Dictionaries define the calendar almost as if it were a
machine: "a system for fixing the beginning, length, and
divisions of the civil year." But in every society calendars are
much more than that. People experience time as both linear and
circular. On the one hand, it marches remorselessly from birth to
death, a vector with fixed endpoints and a constant velocity. On
the other hand, time is cyclical, with the wheel of the seasons
endlessly spinning, and no clear end or beginning. Calendars are
records of a culture's attempt to weight and reconcile these
different visions.
     In early European societies, the end of the year was
regarded as dangerous: a period when the calendar literally runs
out of days, the landscape is blanketed by night and cold, and
nobody can be truly certain that the heavens would usher in a new
year. Embodying that mysterious time when the end of the calendar
somehow looped round and rejoined itself at the beginning, Romans
celebrated Saturnalia, an upside-down week when masters served
their servants and slaves held the great offices of state. The
Christian calendar bracketed the strange, perilous final days of
the year on one end with the birth of Christ, symbol of renewal,
on December 25, and on the other with Epiphany, the day when the
three kings recognized the infant Jesus as the Savior, another
symbol of renewal, on January 6. Christmas and Epiphany bridge
the dangerous gap between the end of one year and the beginning
of the next.
     The Mesoamerican calendar also tied together linear and
cyclical time, but more elaborately. In its most fully developed
form, at the height of Maya power, it consisted of three separate
but interrelated calendars: a sacred tally known as the tzolk'in;
the haab, a secular calendar based, like the Western calendar, on
the rotation of the sun; and the Long Count, a system that, among
other things, linked the other two.
     The sacred calendar is both the calendar most dissimilar to
Western calendars and the most important culturally. Each day in
the tzolk'in had a name and a number, in somewhat the same way
that one might refer to, say, "Wednesday the 15th." In the
Western calendar, the day names (e.g., Wednesday) run through
cycles of seven, making weeks, and the day numbers (e.g., the
15th) run through cycles of 28, 30, or 31, making months. The
tzolk'in used the same principle, but with less variation in the
lengths of the cycles; it had a twenty-day "week" of named days
and a thirteen-day "month" of numbered days. The analogy I am
drawing is imprecise; what I am describing as the tzolk'in "week"
was longer than the "month." But just as Thursday the 16th
follows Wednesday the 15th in the Christian calendar, to Akbal
would follow 9 Ik in the tzolk'in. (The Maya had a twenty-day
"week" in part because their number system was base-2o, instead
of the base-io in European societies.)
     Because the tzolk'in was not intended to track the earth's
orbit around the sun, its inventors didn't have to worry about
fitting their "weeks" and "months" into the 365 days of the solar
year. Instead they simply set the first day of the year to be the
first day of the twenty-day "week" and the thirteen-day "month,"
and let the cycle spin. In the language of elementary school
mathematics, the least common multiple (the smallest number that
two numbers will divide into evenly) of 13 and 20 is 260. Hence,
the tzolk'in had a length of 260 days.
     In the Western calendar, a given combination of named and
numbered days, such as Wednesday the 15th, will occur a few times
in a calendar year. For instance, in 2006 the 15th of the month
falls on Wednesday three times, in February, March, and November;
in 2007 Wednesday the 15th occurs just once, in August. The
irregular intervals are due to the differing lengths of the
months, which throw off the cycle. In the tzolk'in, every "month"
and every "week" are the same length. As a result, "Wednesday the
15th" - or 1 Imix, to give a real example-in the tzolk'in recurs
at precise intervals; each is exactly 13 x 20 or 260 days apart.
Many researchers believe the movements of Venus, which
Mesoamerican astronomers tracked carefully, originally inspired
the tzolk'in. Venus is visible for about 263 consecutive days as
the morning star, then goes behind the sun for 50 days, then
reappears for another 263 days as the evening star. It was a
powerful presence in the heavens, as I noted in Chapter 8, and a
calendar based on its celestial trajectory would have shared some
of that power. Within the sacred year, every day was thought to
have particular characteristics, so much so that people were
often named after their birth dates: 12 Eb, 2 Ik, and so on. In
some places men and women apparently could not marry if they had
the same name day. Days in the tzolk'in had import

The Mesoamerican calendar was both more complex and more accurate
than the European calendars of the same period. It consisted of a
365-day secular calendar, the haab (right), much like
contemporary European calendars. The haab was tied to the second,
sacred calendar, the tzolk'in (left), which was unlike any
Western calendar. With a "week" of twenty named days and a
"month" of thirteen numbered days, the tzolk'in produced a
260-day "year." Mesoamerican societies used both simultaneously,
so that every date was labeled with two names (1 Ix 0 Xul in the
drawing). I have not rendered the haab as a wheel-within-wheel
like the tzolk'in, even though it, too, had perfectly regular
"weeks" and "months." This is because the haab had to fit the
365-day solar year, which forced Maya calendar designers to spoil
their system by tacking on an irregular, extra-short month at the

for larger occasions, too. Events from ceremonies to declarations
of war were thought to be more likely to succeed if they occurred
on a propitious day.
     Because people also needed a civil calendar for mundane
purposes like knowing when to sow and harvest, Mesoamerican
societies had a second, secular calendar, the haab: eighteen
"months," each of twenty days. (Unlike the tzolk'in, which
counted off the days from 1, the haab months began with 0; nobody
knows why the system was different.) Simple arithmetic shows that
eighteen twentyday months generates a 360-day year, five days
short of the requisite 365 days. Indians knew it, too. Rather
than sprinkling the extra five days throughout the year as we do,
though, they tacked them onto the end in a special "month" of
their own. These days were thought to be unlucky-it was as if the
year ended with five straight days of Friday the 13th. Although
the ancient Maya knew (unlike their contemporaries in Europe)
that the solar year is actually 365 and 1/4 days, they did not
bother to account for the extra quarter day; there were no leap
years in Mesoamerica. The failure to do so seems surprising,
given that their astronomers' mania for precision had led them to
measure the length of the lunar month to within about ten
     With two calendars, every day thus had two names, a sacred
tzolk'in name and a civil haab name. Usually the Maya referred to
them by both at once: 1 Ix 0 Xul. The two different calendars,
each perfectly regular (but one more regular than the other),
marched in lockstep, forming what is now called the Calendar
Round. After one i Ix o Xul, there would not be another 1 Ix 0
Xul for 18,980 days, about fifty-two years.
     By describing dates with both calendars Mesoamerican
societies were able to give every day in this fifty-two-year
period a unique name. But they couldn't distinguish one
fifty-two-year period from its predecessors and successors-as if
the Christian calendar couldn't distinguish 1810, 1910, and 2010.
To avoid confusion and acknowledge time's linear dimension,
Mesoamerican societies invented the Long Count, which counts off
the days from a starting point that is believed to have been in
mid-August, 3114 B.C. Long Count dates consisted of the number of
days, 20-day "months," 360-day "years," 7,200-day "decades," and
144,000-day "centuries" since the beginning. Archaeologists
generally render these as a set of five numbers separated by
dots. When Columbus landed, on Tuesday, October 11, 1492, the
Maya would have marked the day as, with the
"centuries" first and the days last. In the tzolk'in and haab,
the day was 2 Akbal 6 Zotz.

     Although extant Long Count dates have only five positions
for numbers, the Maya knew that eventually that time would pass
and they would have to add more positions. Indeed, their priestly
mathematicians had calculated nineteen further positions,
culminating in what is now called the alautun, a period of
23,040,000,000 days, which is about 63 million years. Probably
the longest named interval of time in any calendar, the alautun
is a testament to the grandiosity of Mesoamerican calendries.
Just as the tzolk'in is one of the most impeccably circular time
cycles ever invented, the Long Count is among the most purely
linear, an arrow pointing straight ahead for millions of years
into the future.
     But wait - isn't the Internet full of claims that the Maya
calendar doesn't go into the future? That it ends, suddenly and
dramatically, on the date, which in today's terms is
December 21, 2012? And when the calendar ends, didn't the Maya
predict a global calamity?
     To be sure, a four-zero date like only occurs
every 5,126 years in the Maya calendar. But the claim that date will lead to disaster dates back not to ancient
times but mainly to 1996, when two modern epigraphers released a
partial description of a Maya text on a broken monument found in
the Mexican state of Tobasco. The monument, the epigraphers
explained, "recorded a calendrical event in the early 21st
century A.D., at which time, apparently, the god [Bolon Yokte'
K'uh] may 'descend' ye-ma, y-emal [there are some technical
problems with this translation]." The "event," the two scholars
said, was apparently related to the fact that "the 13 baktuns
will be finished at in the Maya Long Count." To some
readers, this sounded like an ancient prophecy: on the day the
calendar runs out of numbers, a celestial being will touch down
on the planet-the end of life as we know it.
     Despite being printed as an aside - in a footnote, no less -
in an archaeological journal, the "prophecy" was picked up by the
surprisingly large number of people with a passionate interest in
the implications of pre-Columbian timekeeping and active Internet
connections. Noting the interest, archaeologists paid more
attention to the text. A more formal rendering appeared in 2010:

     Eight Katun and three Baktun (forward), 
     it will be completed the thirteenth Baktun; 
     It will be 4 Ajau 3 Kankin.
     It will happen; the witnessing of 
     The adornments of Bolon Yokte 
     In the great investiture.

     Matthew Restall and Amara Solari, Maya specialists at,
respectively, Pennsylvania State University and Oregon State
University, have suggested that the translation might be more
colloquially put as:

     The thirteenth calendrical cycle will end on the day of 4
     Ahau 3 Kankin, when there will occur a spectacle and Bolon
     Yokte will come down to a great investiture.

Put this way, the text sounds less like a prophecy and more like
a promise, in a far-distant time, of an excellent party. But when
Stephen Houston and David Stuart, the two original translators,
retracted their initial paraphrase and said the monument made no
prophecy, they were attacked by what might be called
"2012ologists," who accused them of covering up the truth.

     Archaeologists of the Maya tend to be annoyed by 2012
speculation. Not only is it mistaken, they believe, but it
fundamentally misrepresents the Maya. Rather than being an
example of native wisdom, scholars say, the apocalyptic
"prophecy" is a projection of European values and ideas onto
non-European people. The society with a long history of
anticipating the Apocalypse is not the Maya, but Christian
Europe. Europeans, not Maya, went into panic when the calendar
turned up zeroes in 1000 A.D. The 2012 commotion, Restall and
Solari argue, is testament to our continuing inability to stop
viewing other societies as extensions of ourselves. Four
centuries after Columbus, his descendants still have trouble
seeing the people he encountered.


We have always had people (secular and religious) that have
pounced upon DATES from here and from there - they are date
setters. They all have NO CLUE about real Bible Prophecy - it is
the Bible that tells you the future. I have expounded for you ALL
the prophet books of the Bible on this website. Therein lies the
truth of the matter. So it is written and so it will come to

Keith Hunt 

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