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) COUNTING and CALEDARS of the MAYA 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 12.19.18.14.4. (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 2,455,847. The Long Count calendar began with the date 0.0.0.0.0.* 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 13.0.0.0.0. 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 average: 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 7.16.6.16.18. 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. ...... APPENDIX D 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 end. ...... 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 seconds. 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 11.13.12.4.3, 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 13.0.0.0.0, 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 13.0.0.0.0 only occurs every 5,126 years in the Maya calendar. But the claim that 13.0.0.0.0 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 13.0.0.0.0. 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. .......... NOTE: 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 But people will jump at everything that for them this or that, or the other, meant this age of man sooooooon be over??? Many left with their tail between their legs. God has one calendar and set of end-time events---- ya and it's all In the holy Bible.
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